Research ArticleUncertainty of Flood Forecasting Based onRadar Rainfall Data Assimilation

Xinchi Chen12 Liping Zhang13 Christopher James Gippel4

Lijie Shan12 Shaodan Chen12 and Wei Yang12

1State Key Laboratory of Water Resources and Hydropower Engineering Science Wuhan University Wuhan 430072 China2Hubei Collaborative Innovation Center for Water Resources Security Wuhan University Wuhan 430072 China3College of Tourism Culture and Geographical Science Huanggang Normal University Huanggang 438000 China4Australian Rivers Institute Griffith University Nathan QLD 4111 Australia

Correspondence should be addressed to Liping Zhang zhanglpwhueducn

Received 21 April 2016 Revised 26 July 2016 Accepted 30 August 2016

Academic Editor Fateh Chebana

Copyright copy 2016 Xinchi Chen et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Precipitation is the core data input to hydrological forecasting The uncertainty in precipitation forecast data can lead to poorperformance of predictive hydrological models Radar-based precipitation measurement offers advantages over ground-basedmeasurement in the quantitative estimation of temporal and spatial aspects of precipitation but errors inherent in this methodwill still act to reduce the performance Using data from White Lotus River of Hubei Province China five methods were used toassimilate radar rainfall data transformed from the classified 119885-119877 relationship and the postassimilation data were compared withprecipitation measured by rain gauges The five sets of assimilated rainfall data were then used as input to the Xinanjiang modelThe effect of precipitation data input error on runoff simulation was analyzed quantitatively by disturbing the input data usingthe Breeding of Growing Modes method The results of practical application demonstrated that the statistical weight integrationand variational assimilationmethodswere superiorThe corresponding performance in flood hydrograph predictionwas also betterusing the statistical weight integration and variational methods compared to the others It was found that the errors of radar rainfalldata disturbed by the Breeding of Growing Modes had a tendency to accumulate through the hydrological model

1 Introduction

Flooding is a hazard with potentially serious consequencesof loss of life displacement of communities and economiccosts The risks can be reduced by issuing warnings andimplementing planned responses to avoid the threat Thisrelies on access to accurate real-time forecasts of flood peakmagnitude and timing and duration at the time-scales ofnowcasting (sim2 hours) and short-range forecasting (sim1-2days) The time required for rainfall to be converted intorunoff and be conveyed downstream through channels issufficient that forecasting of flash floods can use recentlyobserved rainfall data rather than less accurate forecastrainfall Thus accurate rainfall data is the key input to floodforecasting [1] Such data is usually obtained from an auto-matic network of rain gauges set up according to establishedstandards to continuously measure rainfall volume at short

intervals with an acceptable accuracy For practical reasonsthe density of gauges in the network will often be too low toproperly characterize the spatial and temporal distributionof rainfall throughout a catchment Failure to capture dataconcerning the intensity of the main storm cell can leadto underestimation of flood peak magnitude and timingWeather radar offers an alternative method of capturingrainfall data that has the potential to overcome this limitationof a rain gauge network or to enhance the informationfrom the network Radar echoes provide real-time highspatial resolution information on cloud extent and thick-ness evolution and direction of travel of storm cells andprecipitation distribution but with a degree of uncertaintythat could be considered less than desirable for reliable floodforecasting The accuracy of radar-derived rainfall data canbe improved by calibration with observed data using dataassimilation techniques [2ndash4] Data assimilation refers to

Hindawi Publishing CorporationAdvances in MeteorologyVolume 2016 Article ID 2710457 12 pageshttpdxdoiorg10115520162710457

2 Advances in Meteorology

the process of incorporating observed data into the modelstate of a numerical model of a system and is employed insituations when the number of available observations of thesystem is much smaller than the number required to specifythe model state Postassimilation rainfall data can be inputto distributed hydrological models tomore accurately predictflood hydrograph characteristics [5ndash9]

There has been considerable progress in practical appli-cation of weather radar for estimation of surface rainfall Forexample the UK Met Office uses a network of 13 weatherradars that provides 2 km times 2 km gridded radar echo data at5-minute intervals as well as an extrapolation based on radardata every 30 minutes produced and accumulated in realtime Precipitation forecasts are provided every 6 hours [10]The US Weather Bureau has operated a national river fore-casting system since the early 1990s that combines weatherforecasts with flood prediction models to disseminate floodwarnings [11] The precipitation input data are derivedfrom satellite ground radar and rainfall gauges Chinahas established a network of 172 new generation Dopplerweather radars achieved a real-time data transmission every6 minutes and provides composite weather radar data Thishas helped to enhance the monitoring of sudden potentiallycalamitous weather and improved the warning services forrainstorm disasters [12]

The performance of conceptual hydrological modelsdepends to a large extent on the quality of the rainfall databut also on the selection of parameter values and modelstructure Ideally parameters are optimized using historicalflood events but model performance also relies to someextent on expert judgment and could be limited by thestructure of the model which is a simplification of a complexhydrological process [13ndash15] Uncertainty associated withmodel structure and parameters has received attention [16ndash20] as has uncertainty associated with the quality of therainfall data input [21 22] Error in remotely sensed precipita-tion data will be transmitted and possibly amplified throughthe hydrological simulation processThis paper examines thenature of uncertainty in flood forecasting due to transmissionof errors associated with assimilated radar-based rainfalldata

In this paper the data assimilation methods of averagecalibration (AVG) optimum interpolation (OPT) Kalmanfilter (KLM) statistical weight integration (SWI) and vari-ational calibration (VAR) were applied to radar rainfalldata transformed from the classified 119885-119877 (radar reflectivity-rainfall rates) relationship and then the result was com-pared with precipitation data observed from a rain gaugenetwork The rainfall data were then used as input to theXinanjiang hydrological model to predict flood hydrographsusing the five sets of assimilated radar-based rainfall dataand uncalibrated (UC) classified 119885-119877 relationship rainfalldata This paper provides critical descriptive analysis of themain assimilation methods and the effect of the errors onuncertainty of flood forecasting using new data sets from theWhite Lotus River catchment China A novel aspect of thispaper is quantification of the influence of the propagationof rainfall input error on simulated flood event peak flowmagnitude flood event volume and flood peak timing This

Table 1 Timing of the eight rainstorms chosen for the study

Event Starting time Ending time Duration(hours)

050408 2005-04-08 2200 2005-04-09 1400 16050429 2005-04-29 0700 2005-05-01 2100 62050609 2005-06-09 2200 2005-06-10 1400 16060411 2006-04-11 2000 2006-04-13 0000 28060508 2006-05-08 0800 2006-05-09 2300 39060627 2006-06-27 0200 2006-06-27 1900 17060705 2006-07-05 1000 2006-07-06 0800 22060726 2006-07-26 1500 2006-07-27 1300 22

was done by perturbing radar rainfall data using the Breedingof Growing Modes (BGM) method

2 Study Area

The White Lotus River located in Hubei Province Chinahas a catchment area of 1797 km2 Its headwaters are in theDabie Mountains and it forms a midcatchment tributary ofthe Xishui River which flows into the lower Yangtze River(Figure 1) The catchment lies within the subtropical mon-soon climate zone with cold dry winters hot wet summersand distinct climatic seasonality Mean annual temperatureis 167∘C and annual average precipitation is 1366mm withthe majority falling from June to August In the wet seasonrainstorms occur with a high frequency and intensity and theshort convergence time typically results in flood hydrographswith rapid rates of rise and fall

3 Data and Method

31 Data Sets TheWhite Lotus catchment has 19 rain gaugesand one river hydrological station at the outlet (Figure 1)This study used hourly recorded rainfall data from the years2005 and 2006 The radar data were sourced from theCINRADSA Doppler weather radar located in Wuhan forthe flood seasons of 2005 and 2006 The study area is locatedwithin the radar radius of 150 to 250 km Generally the 05∘elevation [23] reflectivity factor plan position indicator (PPI)was used to develop the transformation of 119885-119877 relationshipRadar estimated rainfall was quantified on a 1 km times 1 kmgrid at a 1-hour time step Eight rainstorms were chosen foranalysis (Table 1) The total sampled period for these eventswas 222 hours

32 Radar-Based Rainfall Data Assimilation

321 Average Calibration (AVG) AVG is a simple and pre-cise method for calculating regional rainfall volume [2425] whereby119873 rain gauges are used to calculate themean cal-ibration factor

119865 =1

119873

119873

sum

119894=1

119866119894

119868119894

(1)

where 119866119894is the observed rainfall of station 119894 and 119868

119894is

the radar reflection rate of the station AVG is applied by

Advances in Meteorology 3

N

0 16 24 324Kilometers

White lotus catchment

Hydrologic stationMeteorological stationMain stem

Elevation (m)High 1701

Low 53

830∘30998400 N

30∘40998400 N

30∘50998400 N

31∘0998400 N

31∘10998400 N

30∘30998400 N

30∘40998400 N

30∘50998400 N

31∘0998400 N

31∘10998400 N

115∘20998400E 115∘30998400E 115∘40998400E 115∘50998400E 116∘0998400E

115∘20998400E 115∘30998400E 115∘40998400E 115∘50998400E 116∘0998400E

Figure 1 Location of White Lotus River catchment and the meteorological and river gauging stations within the catchment

multiplying 119868 by 119865 to give regional rainfall distribution Inthe situation of an inconsistent spatial pattern of rainfall overan area of interest a number of regional AVG factors couldbe calculated

322 Kalman Filter (KLM) In radar-based precipitationmeasurement there exists not only system errors producedby unstable radar capability but also the random errors dueto the unstable relation between119885 and 119877 and the influence ofwind field These random errors are called noise KLM aimsto find the optimum estimation of calibration factor 119891 fromnoisy data

The basic theory of KLM [26 27] is that if 1198911and 119891

2 two

independent estimations of the variable119891 can be obtained bydifferent equations the relation between 119891 119891

1 and 119891

2is

119891 = (1 minus 120596) 1198911+ 1205961198912 (2)

where 120596 is a weighting factor The criterion for determining120596 is minimizing the variance of the calibrated 119891 KLM isused to determine the weight with the input being observeddata and the output being the optimum estimation of 119891 TheKLM algorithm is a real-time recursive filter using presentinput data and the previously calculated state It is a real-timerecursive filter with the accuracy of estimation improvingcontinuously as the number of observations increases

323 Optimum Interpolation (OPT) The OPT method usesradar rainfall data derived from echoes as the first-guess

background meteorological field and then corrects this usinga linear combination of the differences between this firstguess and observed data from the rain gauges The weightingfunction is determined by minimizing the expected squareerror of the data [28 29] An OPT is generally expressed asfollows

119860119892= 119861119892+

119873

sum

119894=1

(119874119894minus 119861119894) 119875119894 (3)

where 119860119892(119861119892) is an analysis (first guess) value at a grid cell

119892 to be interpolated119874119894(119861119894) is an observed (first guess) value

given at observation point 119894 and 119875119894denotes a weight function

at observation point 119894 The optimum weight is computed bysupposing that the errors are unbiased and uncorrelated andcan be expressed as

119873

sum

119895=1

119875119894120583119894119895= 120583119892119894

(119894 = 1 2 119873) (4)

where 120583 represents the first-guess error correlation coefficientbetween two arbitrary grid points

324 Variational Calibration (VAR) The VAR method [3031] uses radar-based and gauge-measured precipitation foreach observation point to achieve a calibration factor 119862(119896)(119896 = 1 2 119899) and then obtain 119862(119894 119895) in every grid cell(119894 119895) by interpolation Next an optimum calibration factor

4 Advances in Meteorology

field 119862119877(119894 119895) which minimizes the sum of squared errorsbetween 119862119877(119894 119895) and 119862(119894 119895) is sought Finally the analyzedprecipitation in the grid (119894 119895) is

119875 (119894 119895) = 119875119877(119894 119895) + 119862119877 (119894 119895) (5)

where 119875 (119875119877) is analysis (radar-based) value at grid (119894 119895)

325 Statistical Weight Integration (SWI) The SWI methodaverages 119872 results of precipitation intensity distributionderived by 119872 methods according to weighting that dependson the reciprocal of error statistics

Error 119890119894119896

= 119909119894119896minus 119910119896 where 119909

119894119896is the output value of 119894th

method in grid 119896 and 119910119896is the measured value of automatic

rain gauge in the same grid Error variance 1205902

119894= (1

119873)sum119873

119896=1(119890119894119896minus 119890119894)2 where 119890

119894is themean error of eachmethod

The reciprocal of the error variance of various methods isusually used as the weight of the integration analysis Theresult after integrating is

119896=

sum119872

119894=11199091198941198961205902

119894

sum119872

119894=111205902

119894

(6)

where 119896is estimated results of the 119896th grid after integration

326 Evaluation Criteria The absolute error (AE) and rel-ative error (RE) were used as criteria to evaluate the fiveassimilation methods The Nash-Sutcliffe (NS) peak relativeerror (PRE) and peak time difference (PTD) were used toevaluate the results of hydrological modelling

NS = 1 minus

sum119873

119894=1(119894minus 119876119894)2

sum119873

119894=1(119876119894minus 119876)2

PRE = (sum119873

119894=1119894minus sum119873

119894=1119902119894

sum119873

119894=1119902119894

) times 100

PTD = sum(1003816100381610038161003816119879119904 minus 119879

119900

1003816100381610038161003816 le 3)

119873

(7)

where 119894is the predicted streamflow at time step 119894 119876

119894is the

observation at time step 119894 while 119876 is the mean of observa-tions119873 represents the total number of observations

119894is the

predicted peak flow at time step 119894 119902119894is themeasured peak flow

at the same time 119879119904is the predicted peak time and 119879

119900is the

observed peak time

33 Precipitation-Runoff Model The Xinanjiang model de-veloped by Zhao [32] has been applied extensively andsuccessfully to predict runoff from precipitation in humidand semihumid regions [33] This model conceptualizes thatrunoff is not produced until the soil moisture content of theaeration zone reaches field capacity and thereafter runoffequals the rainfall excess without further loss It consistsof three submodels a three-layer evapotranspiration sub-model a runoff generation submodel and a runoff routingsubmodel Many studies have described the structure of the

model in detail [32ndash35] The inputs to the model are dailyareal precipitation and pan evaporation with observed dailydischarge used for calibration The outputs are the modelleddaily discharge at the catchment outlet and the estimatedactual evapotranspiration of the catchment [36] The waterbalance equation of the model can be expressed as follows

If 119875119864+ 119860 lt 119882

1015840

mm

119877 = 119875119864+119882 minus119882

119872+119882119872(1 minus

119875119864+ 119860

1198821015840mm)

1+119861

(8)

If 119875119864+ 119860 ge 119882

1015840

mm

119877 = 119875119864+119882 minus119882

119872 (9)

where 119877 is the runoff 119875119864is the effective precipitation

which equals the precipitation minus evaporation119882is the initial water storage within the catchment and119860 is the ordinate value corresponding to 119882 1198821015840mmis the maximum storage capacity of the catchment119882119872

is the areal mean tension water capacity whichis composed of the capacity of each soil layer andrepresents drought conditions and 119861 is a parameterthat represents the heterogeneity of the water storagecapacity of the catchment

To reasonably describe the evapotranspiration processthe soil profile is divided into three layers the upper soillayer the lower soil layer and the deepest layer If the watercontent in the upper layer is sufficient evaporation equalsthe evaporation capacity of the upper layer If not all upperwater is evaporated and the residual evaporation is sourcedfrom the lower layer If the water content in the lower layeris insufficient to meet the residual evaporation capacity thewater in the deepest layer will be evaporated

The generated runoff is divided into the surface flowinterflow and groundwater using steady infiltration Thetotal runoff can be routed by a linear system before arrivingat the outlet of the catchment [37] Flow routing uses theMuskingum or piecewise continuous algorithm Taking intoconsideration the uneven distribution of rainfall and thenature of the underlying surface the catchment is dividedinto a set of subcatchments using an appropriate methodsuch asThiessen polygons Finally the total catchment runoffis obtained after the hydrographs at the outlets of eachsubcatchment are simulated and flood routing is applied [35]

34 Uncertainty Methods Most research into uncertainty ofhydrograph forecasting has focused onmodel parameters andstructure rather than quality of input data Toth and Kalnay[38] recommended perturbation of the initial condition withperturbation fields that are representative of errors present inthe analysis and then using these perturbations as the inputto the model in the analysis of input uncertainty The mainmethods used to generate perturbations that reflect the initialuncertainty are Monte Carlo Singular Vector and Breedingof Growing Modes (BGM) Monte Carlo is a statisticalmethod whereby the smaller the sample number the less

Advances in Meteorology 5

Table 2 Comparison of calibration results among different methods UC is uncalibrated KLM is Kalman filter AVG is average calibrationOPT is optimum interpolation VAR is variational calibration and SWI is statistical weight integration

Method Statistic Storm event start date (yymmdd) Average050408 050429 050609 060411 060508 060627 060705 060726

UCAE (mm) 2735 2138 579 397 573 752 358 672 1026RE () 7002 4489 2306 1349 1413 2693 1178 3702 3017

Results (mm) 1171 2625 1932 3339 348 2042 2679 2488 2470

KLMAE (mm) 481 461 145 138 158 19 129 106 226RE () 1232 968 576 469 389 679 426 584 665

Results (mm) 3425 5224 2367 2804 3895 2605 2908 171 3117

AVGAE (mm) 422 522 12 2 314 52 117 203 302RE () 1081 1096 48 68 775 1859 386 1117 934

Results (mm) 3483 5285 2391 3142 3738 2275 292 1613 3106

OPTAE (mm) 411 427 132 036 079 147 116 01 170RE () 1052 896 525 124 194 527 381 057 470

Results (mm) 3495 519 2379 2906 3974 2647 2921 1805 3165

VARAE (mm) 411 426 132 005 032 147 105 016 159RE () 1053 894 527 018 078 527 347 088 442

Results (mm) 3495 5189 2379 2937 4021 2647 2931 18 3175

SWIAE (mm) 411 295 132 005 026 147 105 005 141RE () 1053 618 527 018 065 526 347 029 398

Results (mm) 3495 5058 2379 2937 4026 2647 2932 181 3161Measured (mm) 3906 4763 2511 2942 4053 2794 3037 1816 3228

powerful the statistics However the sample number is oftenvery limited and randomly chosen initial values do notperfectly match with the dynamical mode Although closeto actual weather at initial time the predicted results oftendeviate rapidly from the actual atmospheric condition due tothe adjustment of the mode itself [39] The Singular Vectormethod is better able to deal with many nonquantitativehypotheses in the data assimilation increase the numberof ensemble members and more easily capture the errorsgenerated by analysis It can also determine the direction ofthe fastest disturbance and have a better dispersion Disad-vantages of this method are that the components of errorsthat do not grow are ignored and the calculations are tedious[40 41]

The BGM proposed by Toth and Kalnay [38 42] wasdesigned to model how growing errors are bred and main-tained in a conventional analysis cycle through successiveuse of short-range forecasts with the bred modes offering anestimate of possible growing error fields in the analysis Thegrowth rate obtained by this method is better than that of theMonte Carlo method and even higher than the growth rateof the lagged average forecasting A formula for the specificperturbation is generated

119875 = 119878 times Rmse times Rand (10)

where 119875 is random perturbation field and 119878 is perturbationamplitude coefficient In order to make the disturbanceamplitude not too large 119878 is set equal to 1 Rmse is themean square error between themeasured rainfall and rainfallestimation from radar data assimilation Rand is a randomdistribution function which is evenly distributed between

minus1 and 1 where the equation [43] for producing a randomnumber that is uniformly distributed in [119886 119887] is

119909119894= 119886 + (119887 minus 119886) 119903

119894 (11)

where 119903119894is a uniformly distributed random number that

belongs to [0 1]Using the measured data of eight storm events from 19

rain gauge stations and radar estimations calibrated by theKLM method 100 sets of random perturbation field wereproduced for each event by the BGM of initial disturbanceThen 200 sets of disturbance for each event formed afterthe superposition and deduction of the perturbation fieldwere used as the input to the Xinanjiang hydrological modelFor the eight storm events this resulted in 1600 predictedhydrographs The influence of the propagation of rainfallinput error on runoff simulation was quantified using thethree previously described goodness-of-fit statistics

4 Results and Discussion

41 Evaluation of Methods of Assimilation of Radar RainfallData A comparison of uncalibrated and calibrated resultsof five kinds of assimilation methods for eight storm events(Table 2) revealed that among the methods the SWImethodproduced results closest to the observed data followed bythe VAR method with a mean absolute error smaller thanthat of the SWI method The next best method was the OPTmethod followed by the KLM method and finally the AVGmethod The average of the results across the eight stormevents (Table 2) allows a rapid comparison of the relativeperformances of the five assimilation methods

6 Advances in Meteorology

0

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0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

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(mm

h)

(a)

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(b)

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(c)

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(mm

h)

(f)

Figure 2 Hourly gauged rainfall observations compared to radar-based estimations (a) uncalibrated classified Z-R data (b) Kalman filter(c) average calibration (d) optimum interpolation (e) variational calibration and (f) statistical weight integration

For AVG the accuracy of regional total precipitation esti-mation improved after calibration and the accuracy wouldimprove further with more rain gauges One problem withthe AVG method is that it does not account for the shiftinglocation of the focus of intense rainfall during storm eventsAVG cannot assign greater weight to points independentlyidentified to be of particular interest and it does not considerthe representativeness of the data derived by the automaticrain gauges and radar echoes These problems explain therelatively low performance of the AVG method

Variable terrain synoptic conditions and precipitationintensity impart a high degree of spatial and temporal

variability to radar rainfall data that presents a challengefor data assimilation The results indicated that the KLMmethod of data assimilation with its strong theoretical basisand consideration of the distribution of error in determiningthe calibration factor produced a better result than the AVGmethodTheKLMmethod can improve accuracy by reducingthe relative deviation and degree of dispersion betweenthe hyetometer and radar rainfall data and eliminating theintrusion of nonrainfall echoes from rainfall estimationThismethod calibrates the radar estimated rainfall distributionfield in the time domain rather than the spatial structureerror of precipitation which means it is more suitable for

Advances in Meteorology 7

the calibration of stable stratiform cloud precipitation andin places with low density of rain gauges These may be thekey factors that limit the calibration accuracy of the KLMmethod The spatial structure and distribution of rain cloudsare complicated and changeable with mixed convectiveprecipitation being a common phenomenon Under theseconditions the OPT and VAR methods which have similarresults (Table 2) outperform the KLM method This relativeperformance differencewould also apply in places with a highdensity of rain gauges While each precipitation calibrationmodel has its advantages depending on the conditions SWIcombines the advantages of the other four methods and givesan appropriate weighting after the calculation On this basisthe SWI method would be expected to be superior to theother data assimilationmethods tested here [44] and this wassupported by the results (Table 2)

Scatterplots of hourly gauged rainfall and uncalibratedand calibrated radar-based rainfall (Figure 2) illustrated thegood agreement between the rainfall distribution obtainedby the SWI method and gauged rainfall The VAR and OPTassimilation methods also performed well The KLM andAVG method produced noticeably poorer results (Figure 2)

42 HydrologicalModel for FloodHydrograph Prediction TheXinanjiang hydrological model was applied in the WhiteLotus River catchment taking into consideration temporaland spatial variation of rainfall and the nonlinear effects ofwatershed topography and river channel characteristics onthe runoff concentration and dispersed inflow and nonlin-ear convergence Model parameters were calibrated by themethod of Rosenbrock [45] The three indexes certaintyfactor peak relative error and peak time difference wereused to evaluate the flood forecasting results Goodness-of-fit statistics (Table 3) and simulated hydrographs (Figure 3)indicated that themethods of SWI OPT andVARwere supe-rior in producing rainfall input data for storm hydrographmodelling In particular the SWI simulated hydrographswere in almost perfect agreement with the observed dataTherainfall data generated by themethods of KLMAVG andUCled to unsatisfactory hydrograph prediction

43 Uncertainty Analysis of Hydrological Forecasting Therelative error of predicted results increased after assimilatedrainfall data were randomly disturbed compared with theundisturbed peak flow flood volume and peak time differ-ence The peak flow and flood volume were increased by 5and 8 respectively (Figures 4 and 5) which means thatthe model input errors increased when they were processedthrough the hydrological model Also most of the predictedpeak times lagged the observed times (Figure 6)

The error of precipitation input data in hydrologicalmodelling is a significant source of error in predicted peakflow flood volume and peak time Therefore the spreadof precipitation uncertainty has a great influence on runoffprediction In China practical applications usually adoptqualitative rainfall prediction and assumed rainfall inputand this would have implications for the forecast period andaccuracy of flood forecasting At present both the accuracyand resolution of rainfall forecasts provided by numerical

weather prediction (NWP) cannot meet the requirements ofquantitative flood forecasting and this situation may con-tinue to exist into the foreseeable future Weather radar andsatellite remote sensing (SRS) can perform an important rolein quantitative precipitation forecasting Use of precipitationforecasts obtained by SRS as the input of hydrological modelsto simulate and predict runoff warrants further researchattention This could be a key step towards improving theaccuracy of flood forecasting It will be necessary to developmethods for combining and assimilating the SRS data andobserved data from rain gauges for producing better precipi-tation forecasts SRS has sufficiently high spatial and temporalresolution to effectively characterize the instantaneous distri-bution of precipitation throughout a catchment while raingauges can provide high-precision single-point observations

The generation of floods is a complex and dynamicprocess Modelling this process can be improved through theuse of rainfall input data with high spatial and temporal reso-lution How to best make use of rainfall information availablefrom multiple sources including gauge networks radar andsatellite monitoring is one of the key problems to be solvedin hydrological modelling and forecasting

5 Conclusions

Because of the high level of risk posed by floods especiallyflash floods it is critical that warning procedures make useof accurate nowcasting and short-range runoff forecastingcapability Precipitation data is the most important input tohydrological models used for forecasting hydrographsWhilerainfall data is usually sourced from a network of gauges analternative is weather radar detector which offers superiorspatial and temporal resolution but at the cost of lowprecisionand accuracy This paper investigated methods of precip-itation data assimilation with the objective of improvingthe quality of radar-based rainfall estimates as a means ofachieving more reliable flood forecasts Using data from anetwork of rain gauges in the White Lotus River in HubeiProvince China and data from the weather radar detectorbased in nearby Wuhan five established methods of assimi-lating radar data estimated by the classified 119885-119877 relationshipwere applied The assimilated data was compared with theobserved rainfall data and then used in a hydrological modelto predict historical flood hydrographs Finally BGM wasused for the perturbation of radar data to evaluate the effectof the rainfall data input error on runoff simulationThemainconclusions arising from this work were as follows

(1) Statistical weight integration variational calibrationand optimum interpolation were superior methodsof data assimilation while Kalman filter and averagecalibration methods gave a less satisfactory result

(2) For modelling storm event hydrographs rainfall datagenerated by the statistical weight integration varia-tional calibration and optimum interpolation meth-ods resulted in hydrographs that were the closest fitto the gauged data Rainfall data generated by theaverage calibration and Kalman filter methods of dataassimilation resulted in unsatisfactory hydrographprediction

8 Advances in Meteorology

Table 3 Comparison of flood hydrograph prediction using different rainfall data assimilation methods MPF is measured peak flow and FPFis forecast peak flow

Method Flood event MPF (m3s) FPF (m3s) NS PRE () PTD (h)

UC

050408 3133 584 minus073 8136 1050429 6182 1676 minus105 7289 32050609 1879 968 minus047 4848 2060411 2327 157 minus087 3253 15060508 2409 1081 minus059 5513 10060627 1896 766 minus295 596 4060705 3109 1348 minus3 5664 1060726 1473 1134 02 2301 8

KLM

050408 3133 2756 083 1203 2050429 6182 5622 087 906 1050609 1879 1667 09 1128 1060411 2327 2147 09 774 1060508 2409 2241 09 697 1060627 1896 1685 084 1113 2060705 3109 2627 082 155 2060726 1473 1361 086 76 1

AVG

050408 3133 2833 079 958 1050429 6182 6515 086 539 5050609 1879 1551 088 1746 2060411 2327 1962 083 1569 0060508 2409 2122 085 1191 1060627 1896 1552 044 1814 4060705 3109 2505 065 1943 1060726 1473 1082 022 2654 0

OPT

050408 3133 3117 089 051 2050429 6182 6154 09 045 1050609 1879 1876 09 016 3060411 2327 2317 089 043 2060508 2409 2403 09 025 2060627 1896 1886 089 053 1060705 3109 3071 089 122 2060726 1473 1446 09 183 3

VAR

050408 3133 3133 09 054 0050429 6182 6182 091 036 0050609 1879 1879 089 085 1060411 2327 2327 09 116 2060508 2409 2409 09 023 1060627 1896 1896 089 063 1060705 3109 3109 089 121 2060726 1473 1473 074 047 0

SWI

050408 3133 3125 089 026 1050429 6182 6166 089 026 0050609 1879 1879 09 034 2060411 2327 2072 087 1096 1060508 2409 2406 089 012 0060627 1896 1886 089 053 1060705 3109 3072 089 119 1060726 1473 1468 09 034 2

Advances in Meteorology 9

P

M

UCKLM

AVGOPTVARSWI

16

12

8

4

0

P (m

m)

11 21 31 41 51 61 711t (h)

0

50

100

150

200

250

Q(m

3s

)

12

10

8

6

4

2

0

P (m

m)

40

30

20

10

0

P (m

m)

0

200

400

600

800

Q(m

3s

)

21 41 61 81 1011t (h)

20

15

10

5

0

P (m

m)

0

90

180

270

360

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

250

300

Q(m

3s

)

11 21 31 41 51 61 71 811t (h)

12

8

4

0

P (m

m)

0

50

100

150

200

Q(m

3s

)

18

15

12

9

6

3

0

P (m

m)

11 21 31 41 51 611t (h)

0

40

80

120

160

Q(m

3s

)

11 21 31 41 51 61 711t (h)

10

8

6

4

2

0

P (m

m)

0

70

140

210

280

350

Q(m

3s

)

11 21 31 41 51 61 711t (h)

28

21

14

7

0

P (m

m)

P

M

UCKLM

AVGOPTVARSWI

Figure 3 Comparison of simulated hydrographs for eight storm events using rainfall input data derived from five assimilation methods anduncalibrated radar data119872 is measured hydrograph

10 Advances in Meteorology

00

05

10

15

20

25

00 05 10 15 20Rainfall relative error

Relat

ive e

rror

of p

eak

flow

y = 10581x + 00146

R2 = 09126

Figure 4 Relationship between relative error in predicted floodpeak magnitude and rainfall relative error

00 05 10 15 20Rainfall relative error

00

05

10

15

20

25

Relat

ive e

rror

of fl

ood

volu

me

R2 = 09392

y = 10807x + 00201

Figure 5 Relationship between relative error in predicted flood vol-ume and rainfall relative error

(3) The random errors generated by model input had atendency to increase during the process of runningthe hydrological model Also most of predicted floodpeak times were lagged

(4) As hydrometeorology ensemble forecasts becomemore widely available and the data acquisition meth-ods develop there will be an ongoing need for evalu-ation of uncertainty in input data

(5) This paper provides critical descriptive analysis ofthe main assimilation methods and the effect of theerrors on uncertainty of flood forecasting It demon-strates that weather radar has potential to improvethe precision of hydrological forecasting which hasimplications for improved flood control and disas-ter mitigation The influence of the propagation ofrainfall input error on three simulated factors ofhydrological forecast is quantified

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

minus4

minus2

0

2

4

6

8

Peak

tim

e diff

eren

ce (h

)

05 10 15 2000Rainfall relative error

Figure 6 Relationship between error in predicted flood peak timeand rainfall relative error

Acknowledgments

This study was supported by the State Key Program ofNational Natural Science of China (no 51339004) andthe National Natural Science Foundation of China (no51279139)

References

[1] I Yucel A Onen K K Yilmaz and D J Gochis ldquoCalibrationand evaluation of a flood forecasting system utility of numericalweather prediction model data assimilation and satellite-basedrainfallrdquo Journal of Hydrology vol 523 pp 49ndash66 2015

[2] L P Zhang L Li A Z Ye et al ldquoContrast research on precisionof estimating regional precipitation with weather radar and raingaugerdquo Engineering Journal of Wuhan University EngineeringEdition vol 40 no 1 pp 1ndash5 2007 (Chinese)

[3] J Liu M Bray and D Han ldquoA study on WRF radar dataassimilation for hydrological rainfall predictionrdquoHydrology andEarth System Sciences vol 17 no 8 pp 3095ndash3110 2013

[4] I Maiello R Ferretti S Gentile et al ldquoImpact of radar dataassimilation for the simulation of a heavy rainfall case incentral Italy using WRF-3DVARrdquo Atmospheric MeasurementTechniques vol 7 no 9 pp 2919ndash2935 2014

[5] M Borga ldquoAccuracy of radar rainfall estimates for streamflowsimulationrdquo Journal of Hydrology vol 267 no 1-2 pp 26ndash392002

[6] Q Dai and D Han ldquoExploration of discrepancy between radarand gauge rainfall estimates driven by wind fieldsrdquo WaterResources Research vol 50 no 11 pp 8571ndash8588 2014

[7] F Giannoni J A Smith Y Zhang and G Roth ldquoHydrologicmodeling of extreme floods using radar rainfall estimatesrdquoAdvances in Water Resources vol 26 no 2 pp 195ndash203 2003

[8] Z Sokol ldquoUtilization of regression models for rainfall estimatesusing radar-derived rainfall data and rain gauge datardquo Journalof Hydrology vol 278 no 1ndash4 pp 144ndash152 2003

[9] C A Velasco-Forero D Sempere-Torres E F Cassiraga and JJaime Gomez-Hernandez ldquoA non-parametric automatic blend-ing methodology to estimate rainfall fields from rain gauge andradar datardquo Advances inWater Resources vol 32 no 7 pp 986ndash1002 2009

Advances in Meteorology 11

[10] X Sun R G Mein T D Keenan and J F Elliott ldquoFlood esti-mation using radar and raingauge datardquo Journal of Hydrologyvol 239 no 1ndash4 pp 4ndash18 2000

[11] J Z Sun ldquoConvective-scale assimilation of radar data progressand challengesrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 131 no 613 pp 3439ndash3463 2006

[12] X D Yu X P Yao T N Xiong et al The Principle and Appli-cation of Doppler Weather Radar China Meteorological PressBeijing China 2007

[13] M Borga E N Anagnostou and E Frank ldquoOn the use of real-time radar rainfall estimates for flood prediction in mountain-ous basinsrdquo Journal of Geophysical Research Atmospheres vol105 no 2 pp 2269ndash2280 2000

[14] H G Zhang S L Guo and X L He ldquoRecent advancement andprospect of hydrological forecasting uncertainty studyrdquo Journalof Shihezi University (Natural Science) vol 24 no 1 pp 15ndash212006 (Chinese)

[15] GVillarini andW F Krajewski ldquoReview of the different sourcesof uncertainty in single polarization radar-based estimates ofrainfallrdquo Surveys in Geophysics vol 31 no 1 pp 107ndash129 2010

[16] K Beven and A Binley ldquoThe future of distributed modelsmodel calibration and uncertainty predictionrdquo HydrologicalProcesses vol 6 no 3 pp 279ndash298 1992

[17] F Quintero D Sempere-Torres M Berenguer and E BaltasldquoA scenario-incorporating analysis of the propagation of uncer-tainty to flash flood simulationsrdquo Journal of Hydrology vol 460-461 pp 90ndash102 2012

[18] L Xiong andKMOrsquoConnor ldquoAn empiricalmethod to improvethe prediction limits of the GLUE methodology in rainfall-runoffmodelingrdquo Journal of Hydrology vol 349 no 1-2 pp 115ndash124 2008

[19] X R Yin J Xia and X Zhang ldquoRecent progress and prospectof the study on uncertainties in hydrologicalmodeling and fore-castingrdquoWater Power vol 32 no 10 pp 27ndash31 2006 (Chinese)

[20] D Zhu Y Xuan and I Cluckie ldquoHydrological appraisal ofoperational weather radar rainfall estimates in the context ofdifferent modelling structuresrdquo Hydrology and Earth SystemSciences vol 18 no 1 pp 257ndash272 2014

[21] A S Falck V Maggioni J Tomasella D A Vila and F LR Diniz ldquoPropagation of satellite precipitation uncertaintiesthrough a distributed hydrologic model a case study in theTocantins-Araguaia basin in Brazilrdquo Journal of Hydrology vol527 pp 943ndash957 2015

[22] P A Mendoza J McPhee and X Vargas ldquoUncertainty in floodforecasting a distributed modeling approach in a sparse datacatchmentrdquoWater Resources Research vol 48 no 9 Article IDW09532 2012

[23] V TWood R A Brown and S V Vasiloff ldquoImproved detectionusing negative elevation angles for mountaintop WSR-88DsPart II simulations of the three radars covering UtahrdquoWeatherand Forecasting vol 18 no 3 pp 393ndash403 2003

[24] T P Dai and D S Fu ldquoPrecision of precipitation amount in thejoint detection areas by weather radar and the auto-rain Gaugenetworkrdquo Journal of Nanjing Institute of Meteorology vol 13 no4 pp 592ndash597 1990 (Chinese)

[25] J W Wilson and E A Brandes ldquoRadar measurement ofrainfallmdasha summaryrdquo Bulletin of the American MeteorologicalSociety vol 60 no 9 pp 1048ndash1058 1979

[26] S Chumchean A Seed and A Sharma ldquoCorrecting of real-time radar rainfall bias using a Kalman filtering approachrdquoJournal of Hydrology vol 317 no 1-2 pp 123ndash137 2006

[27] M Costa and M Monteiro ldquoBias-correction of Kalman filterestimators associated to a linear state space model with esti-mated parametersrdquo Journal of Statistical Planning and Inferencevol 176 pp 22ndash32 2016

[28] S I Kako A Isobe and M Kubota ldquoHigh-resolution ASCATwind vector data set gridded by applying an optimum inter-polation method to the global oceanrdquo Journal of GeophysicalResearch Atmospheres vol 116 no 23 Article ID D23107 2011

[29] S Kako andMKubota ldquoRelationship between an ElNino eventand the interannual variability of significant wave heights in theNorth Pacificrdquo Atmosphere-Ocean vol 44 no 4 pp 377ndash3952006

[30] W Castaings D Dartus F-X Le Dimet and G-M SaulnierldquoSensitivity analysis and parameter estimation for distributedhydrological modeling potential of variational methodsrdquoHydrology and Earth System Sciences vol 13 no 4 pp 503ndash5172009

[31] P C Zhang T P Dai D S Fu et al ldquoPrinciple and accuracyof adjusting the area precipitation from digital weather radarthrough variational methodrdquo Atmospheric Science vol 16 no2 pp 248ndash256 1992 (Chinese)

[32] R-J Zhao ldquoThe Xinanjiang model applied in Chinardquo Journal ofHydrology vol 135 no 1ndash4 pp 371ndash381 1992

[33] A A Alazzy H S Lu and Y H Zhu ldquoAssessing the uncertaintyof the Xinanjiang rainfall-runoff model effect of the likelihoodfunction choice on the GLUE methodrdquo Journal of HydrologicEngineering vol 20 no 10 Article ID 04015016 2015

[34] J Liu X Chen J Zhang and M Flury ldquoCoupling the Xinan-jiangmodel to a kinematic flowmodel based on digital drainagenetworks for flood forecastingrdquo Hydrological Processes vol 23no 9 pp 1337ndash1348 2009

[35] C Zhang R-BWang andQ-XMeng ldquoCalibration of concep-tual rainfall-runoffmodels using global optimizationrdquoAdvancesin Meteorology vol 2015 Article ID 545376 12 pages 2015

[36] H Xu C-Y Xu N R Saeliglthun B Zhou and Y Xu ldquoEvaluationof reanalysis and satellite-based precipitation datasets in drivinghydrological models in a humid region of Southern ChinardquoStochastic Environmental Research and Risk Assessment vol 29no 8 pp 2003ndash2020 2015

[37] S S Meng X H Xie and X Yu ldquoTracing temporal changesof model parameters in rainfall-runoffmodeling via a real-timedata assimilationrdquoWater vol 8 no 1 article 19 2016

[38] Z Toth and E Kalnay ldquoEnsemble Forecasting at NMC thegeneration of perturbationsrdquo Bulletin of the American Meteoro-logical Society vol 74 no 12 pp 2317ndash2330 1993

[39] S LMullen andD P Baumhefner ldquoMonte Carlo simulations ofexplosive cyclogenesisrdquoMonthlyWeather Review vol 122 no 7pp 1548ndash1567 1994

[40] R Buizza and T N Palmer ldquoImpact of ensemble size onensemble predictionrdquo Monthly Weather Review vol 126 no 9pp 2503ndash2518 1998

[41] F Molteni R Buizza T N Palmer and T Petroliagis ldquoTheECMWF ensemble prediction system methodology and vali-dationrdquo Quarterly Journal of the Royal Meteorological Societyvol 122 no 529 pp 73ndash119 1996

[42] Z Toth and E Kalnay ldquoEnsemble forecasting at NCEP and thebreeding methodrdquoMonthlyWeather Review vol 125 no 12 pp3297ndash3319 1997

[43] F Wu ldquoSeveral methods of creating stochastic numbers andapplicationsrdquo Journal on Numerical Methods and ComputerApplications vol 27 no 1 pp 48ndash51 2006 (Chinese)

12 Advances in Meteorology

[44] Y-H Shao and W-C Zhang ldquoApplication of statistical weightmatrix method in estimation of regional rainfallrdquo Advances inWater Science vol 20 no 6 pp 755ndash762 2009 (Chinese)

[45] X Y Song Y J Li H Y Yu et al ldquoApplication of quantitativeprecipitation estimation by radar to flood forecastrdquo EngineeringJournal of Wuhan University Engineering Edition vol 40 no 2pp 51ndash54 2007 (Chinese)

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

2 Advances in Meteorology

the process of incorporating observed data into the modelstate of a numerical model of a system and is employed insituations when the number of available observations of thesystem is much smaller than the number required to specifythe model state Postassimilation rainfall data can be inputto distributed hydrological models tomore accurately predictflood hydrograph characteristics [5ndash9]

There has been considerable progress in practical appli-cation of weather radar for estimation of surface rainfall Forexample the UK Met Office uses a network of 13 weatherradars that provides 2 km times 2 km gridded radar echo data at5-minute intervals as well as an extrapolation based on radardata every 30 minutes produced and accumulated in realtime Precipitation forecasts are provided every 6 hours [10]The US Weather Bureau has operated a national river fore-casting system since the early 1990s that combines weatherforecasts with flood prediction models to disseminate floodwarnings [11] The precipitation input data are derivedfrom satellite ground radar and rainfall gauges Chinahas established a network of 172 new generation Dopplerweather radars achieved a real-time data transmission every6 minutes and provides composite weather radar data Thishas helped to enhance the monitoring of sudden potentiallycalamitous weather and improved the warning services forrainstorm disasters [12]

The performance of conceptual hydrological modelsdepends to a large extent on the quality of the rainfall databut also on the selection of parameter values and modelstructure Ideally parameters are optimized using historicalflood events but model performance also relies to someextent on expert judgment and could be limited by thestructure of the model which is a simplification of a complexhydrological process [13ndash15] Uncertainty associated withmodel structure and parameters has received attention [16ndash20] as has uncertainty associated with the quality of therainfall data input [21 22] Error in remotely sensed precipita-tion data will be transmitted and possibly amplified throughthe hydrological simulation processThis paper examines thenature of uncertainty in flood forecasting due to transmissionof errors associated with assimilated radar-based rainfalldata

In this paper the data assimilation methods of averagecalibration (AVG) optimum interpolation (OPT) Kalmanfilter (KLM) statistical weight integration (SWI) and vari-ational calibration (VAR) were applied to radar rainfalldata transformed from the classified 119885-119877 (radar reflectivity-rainfall rates) relationship and then the result was com-pared with precipitation data observed from a rain gaugenetwork The rainfall data were then used as input to theXinanjiang hydrological model to predict flood hydrographsusing the five sets of assimilated radar-based rainfall dataand uncalibrated (UC) classified 119885-119877 relationship rainfalldata This paper provides critical descriptive analysis of themain assimilation methods and the effect of the errors onuncertainty of flood forecasting using new data sets from theWhite Lotus River catchment China A novel aspect of thispaper is quantification of the influence of the propagationof rainfall input error on simulated flood event peak flowmagnitude flood event volume and flood peak timing This

Table 1 Timing of the eight rainstorms chosen for the study

Event Starting time Ending time Duration(hours)

050408 2005-04-08 2200 2005-04-09 1400 16050429 2005-04-29 0700 2005-05-01 2100 62050609 2005-06-09 2200 2005-06-10 1400 16060411 2006-04-11 2000 2006-04-13 0000 28060508 2006-05-08 0800 2006-05-09 2300 39060627 2006-06-27 0200 2006-06-27 1900 17060705 2006-07-05 1000 2006-07-06 0800 22060726 2006-07-26 1500 2006-07-27 1300 22

was done by perturbing radar rainfall data using the Breedingof Growing Modes (BGM) method

2 Study Area

The White Lotus River located in Hubei Province Chinahas a catchment area of 1797 km2 Its headwaters are in theDabie Mountains and it forms a midcatchment tributary ofthe Xishui River which flows into the lower Yangtze River(Figure 1) The catchment lies within the subtropical mon-soon climate zone with cold dry winters hot wet summersand distinct climatic seasonality Mean annual temperatureis 167∘C and annual average precipitation is 1366mm withthe majority falling from June to August In the wet seasonrainstorms occur with a high frequency and intensity and theshort convergence time typically results in flood hydrographswith rapid rates of rise and fall

3 Data and Method

31 Data Sets TheWhite Lotus catchment has 19 rain gaugesand one river hydrological station at the outlet (Figure 1)This study used hourly recorded rainfall data from the years2005 and 2006 The radar data were sourced from theCINRADSA Doppler weather radar located in Wuhan forthe flood seasons of 2005 and 2006 The study area is locatedwithin the radar radius of 150 to 250 km Generally the 05∘elevation [23] reflectivity factor plan position indicator (PPI)was used to develop the transformation of 119885-119877 relationshipRadar estimated rainfall was quantified on a 1 km times 1 kmgrid at a 1-hour time step Eight rainstorms were chosen foranalysis (Table 1) The total sampled period for these eventswas 222 hours

32 Radar-Based Rainfall Data Assimilation

321 Average Calibration (AVG) AVG is a simple and pre-cise method for calculating regional rainfall volume [2425] whereby119873 rain gauges are used to calculate themean cal-ibration factor

119865 =1

119873

119873

sum

119894=1

119866119894

119868119894

(1)

where 119866119894is the observed rainfall of station 119894 and 119868

119894is

the radar reflection rate of the station AVG is applied by

Advances in Meteorology 3

N

0 16 24 324Kilometers

White lotus catchment

Hydrologic stationMeteorological stationMain stem

Elevation (m)High 1701

Low 53

830∘30998400 N

30∘40998400 N

30∘50998400 N

31∘0998400 N

31∘10998400 N

30∘30998400 N

30∘40998400 N

30∘50998400 N

31∘0998400 N

31∘10998400 N

115∘20998400E 115∘30998400E 115∘40998400E 115∘50998400E 116∘0998400E

115∘20998400E 115∘30998400E 115∘40998400E 115∘50998400E 116∘0998400E

Figure 1 Location of White Lotus River catchment and the meteorological and river gauging stations within the catchment

multiplying 119868 by 119865 to give regional rainfall distribution Inthe situation of an inconsistent spatial pattern of rainfall overan area of interest a number of regional AVG factors couldbe calculated

322 Kalman Filter (KLM) In radar-based precipitationmeasurement there exists not only system errors producedby unstable radar capability but also the random errors dueto the unstable relation between119885 and 119877 and the influence ofwind field These random errors are called noise KLM aimsto find the optimum estimation of calibration factor 119891 fromnoisy data

The basic theory of KLM [26 27] is that if 1198911and 119891

2 two

independent estimations of the variable119891 can be obtained bydifferent equations the relation between 119891 119891

1 and 119891

2is

119891 = (1 minus 120596) 1198911+ 1205961198912 (2)

where 120596 is a weighting factor The criterion for determining120596 is minimizing the variance of the calibrated 119891 KLM isused to determine the weight with the input being observeddata and the output being the optimum estimation of 119891 TheKLM algorithm is a real-time recursive filter using presentinput data and the previously calculated state It is a real-timerecursive filter with the accuracy of estimation improvingcontinuously as the number of observations increases

323 Optimum Interpolation (OPT) The OPT method usesradar rainfall data derived from echoes as the first-guess

background meteorological field and then corrects this usinga linear combination of the differences between this firstguess and observed data from the rain gauges The weightingfunction is determined by minimizing the expected squareerror of the data [28 29] An OPT is generally expressed asfollows

119860119892= 119861119892+

119873

sum

119894=1

(119874119894minus 119861119894) 119875119894 (3)

where 119860119892(119861119892) is an analysis (first guess) value at a grid cell

119892 to be interpolated119874119894(119861119894) is an observed (first guess) value

given at observation point 119894 and 119875119894denotes a weight function

at observation point 119894 The optimum weight is computed bysupposing that the errors are unbiased and uncorrelated andcan be expressed as

119873

sum

119895=1

119875119894120583119894119895= 120583119892119894

(119894 = 1 2 119873) (4)

where 120583 represents the first-guess error correlation coefficientbetween two arbitrary grid points

324 Variational Calibration (VAR) The VAR method [3031] uses radar-based and gauge-measured precipitation foreach observation point to achieve a calibration factor 119862(119896)(119896 = 1 2 119899) and then obtain 119862(119894 119895) in every grid cell(119894 119895) by interpolation Next an optimum calibration factor

4 Advances in Meteorology

field 119862119877(119894 119895) which minimizes the sum of squared errorsbetween 119862119877(119894 119895) and 119862(119894 119895) is sought Finally the analyzedprecipitation in the grid (119894 119895) is

119875 (119894 119895) = 119875119877(119894 119895) + 119862119877 (119894 119895) (5)

where 119875 (119875119877) is analysis (radar-based) value at grid (119894 119895)

325 Statistical Weight Integration (SWI) The SWI methodaverages 119872 results of precipitation intensity distributionderived by 119872 methods according to weighting that dependson the reciprocal of error statistics

Error 119890119894119896

= 119909119894119896minus 119910119896 where 119909

119894119896is the output value of 119894th

method in grid 119896 and 119910119896is the measured value of automatic

rain gauge in the same grid Error variance 1205902

119894= (1

119873)sum119873

119896=1(119890119894119896minus 119890119894)2 where 119890

119894is themean error of eachmethod

The reciprocal of the error variance of various methods isusually used as the weight of the integration analysis Theresult after integrating is

119896=

sum119872

119894=11199091198941198961205902

119894

sum119872

119894=111205902

119894

(6)

where 119896is estimated results of the 119896th grid after integration

326 Evaluation Criteria The absolute error (AE) and rel-ative error (RE) were used as criteria to evaluate the fiveassimilation methods The Nash-Sutcliffe (NS) peak relativeerror (PRE) and peak time difference (PTD) were used toevaluate the results of hydrological modelling

NS = 1 minus

sum119873

119894=1(119894minus 119876119894)2

sum119873

119894=1(119876119894minus 119876)2

PRE = (sum119873

119894=1119894minus sum119873

119894=1119902119894

sum119873

119894=1119902119894

) times 100

PTD = sum(1003816100381610038161003816119879119904 minus 119879

119900

1003816100381610038161003816 le 3)

119873

(7)

where 119894is the predicted streamflow at time step 119894 119876

119894is the

observation at time step 119894 while 119876 is the mean of observa-tions119873 represents the total number of observations

119894is the

predicted peak flow at time step 119894 119902119894is themeasured peak flow

at the same time 119879119904is the predicted peak time and 119879

119900is the

observed peak time

33 Precipitation-Runoff Model The Xinanjiang model de-veloped by Zhao [32] has been applied extensively andsuccessfully to predict runoff from precipitation in humidand semihumid regions [33] This model conceptualizes thatrunoff is not produced until the soil moisture content of theaeration zone reaches field capacity and thereafter runoffequals the rainfall excess without further loss It consistsof three submodels a three-layer evapotranspiration sub-model a runoff generation submodel and a runoff routingsubmodel Many studies have described the structure of the

model in detail [32ndash35] The inputs to the model are dailyareal precipitation and pan evaporation with observed dailydischarge used for calibration The outputs are the modelleddaily discharge at the catchment outlet and the estimatedactual evapotranspiration of the catchment [36] The waterbalance equation of the model can be expressed as follows

If 119875119864+ 119860 lt 119882

1015840

mm

119877 = 119875119864+119882 minus119882

119872+119882119872(1 minus

119875119864+ 119860

1198821015840mm)

1+119861

(8)

If 119875119864+ 119860 ge 119882

1015840

mm

119877 = 119875119864+119882 minus119882

119872 (9)

where 119877 is the runoff 119875119864is the effective precipitation

which equals the precipitation minus evaporation119882is the initial water storage within the catchment and119860 is the ordinate value corresponding to 119882 1198821015840mmis the maximum storage capacity of the catchment119882119872

is the areal mean tension water capacity whichis composed of the capacity of each soil layer andrepresents drought conditions and 119861 is a parameterthat represents the heterogeneity of the water storagecapacity of the catchment

To reasonably describe the evapotranspiration processthe soil profile is divided into three layers the upper soillayer the lower soil layer and the deepest layer If the watercontent in the upper layer is sufficient evaporation equalsthe evaporation capacity of the upper layer If not all upperwater is evaporated and the residual evaporation is sourcedfrom the lower layer If the water content in the lower layeris insufficient to meet the residual evaporation capacity thewater in the deepest layer will be evaporated

The generated runoff is divided into the surface flowinterflow and groundwater using steady infiltration Thetotal runoff can be routed by a linear system before arrivingat the outlet of the catchment [37] Flow routing uses theMuskingum or piecewise continuous algorithm Taking intoconsideration the uneven distribution of rainfall and thenature of the underlying surface the catchment is dividedinto a set of subcatchments using an appropriate methodsuch asThiessen polygons Finally the total catchment runoffis obtained after the hydrographs at the outlets of eachsubcatchment are simulated and flood routing is applied [35]

34 Uncertainty Methods Most research into uncertainty ofhydrograph forecasting has focused onmodel parameters andstructure rather than quality of input data Toth and Kalnay[38] recommended perturbation of the initial condition withperturbation fields that are representative of errors present inthe analysis and then using these perturbations as the inputto the model in the analysis of input uncertainty The mainmethods used to generate perturbations that reflect the initialuncertainty are Monte Carlo Singular Vector and Breedingof Growing Modes (BGM) Monte Carlo is a statisticalmethod whereby the smaller the sample number the less

Advances in Meteorology 5

Table 2 Comparison of calibration results among different methods UC is uncalibrated KLM is Kalman filter AVG is average calibrationOPT is optimum interpolation VAR is variational calibration and SWI is statistical weight integration

Method Statistic Storm event start date (yymmdd) Average050408 050429 050609 060411 060508 060627 060705 060726

UCAE (mm) 2735 2138 579 397 573 752 358 672 1026RE () 7002 4489 2306 1349 1413 2693 1178 3702 3017

Results (mm) 1171 2625 1932 3339 348 2042 2679 2488 2470

KLMAE (mm) 481 461 145 138 158 19 129 106 226RE () 1232 968 576 469 389 679 426 584 665

Results (mm) 3425 5224 2367 2804 3895 2605 2908 171 3117

AVGAE (mm) 422 522 12 2 314 52 117 203 302RE () 1081 1096 48 68 775 1859 386 1117 934

Results (mm) 3483 5285 2391 3142 3738 2275 292 1613 3106

OPTAE (mm) 411 427 132 036 079 147 116 01 170RE () 1052 896 525 124 194 527 381 057 470

Results (mm) 3495 519 2379 2906 3974 2647 2921 1805 3165

VARAE (mm) 411 426 132 005 032 147 105 016 159RE () 1053 894 527 018 078 527 347 088 442

Results (mm) 3495 5189 2379 2937 4021 2647 2931 18 3175

SWIAE (mm) 411 295 132 005 026 147 105 005 141RE () 1053 618 527 018 065 526 347 029 398

Results (mm) 3495 5058 2379 2937 4026 2647 2932 181 3161Measured (mm) 3906 4763 2511 2942 4053 2794 3037 1816 3228

powerful the statistics However the sample number is oftenvery limited and randomly chosen initial values do notperfectly match with the dynamical mode Although closeto actual weather at initial time the predicted results oftendeviate rapidly from the actual atmospheric condition due tothe adjustment of the mode itself [39] The Singular Vectormethod is better able to deal with many nonquantitativehypotheses in the data assimilation increase the numberof ensemble members and more easily capture the errorsgenerated by analysis It can also determine the direction ofthe fastest disturbance and have a better dispersion Disad-vantages of this method are that the components of errorsthat do not grow are ignored and the calculations are tedious[40 41]

The BGM proposed by Toth and Kalnay [38 42] wasdesigned to model how growing errors are bred and main-tained in a conventional analysis cycle through successiveuse of short-range forecasts with the bred modes offering anestimate of possible growing error fields in the analysis Thegrowth rate obtained by this method is better than that of theMonte Carlo method and even higher than the growth rateof the lagged average forecasting A formula for the specificperturbation is generated

119875 = 119878 times Rmse times Rand (10)

where 119875 is random perturbation field and 119878 is perturbationamplitude coefficient In order to make the disturbanceamplitude not too large 119878 is set equal to 1 Rmse is themean square error between themeasured rainfall and rainfallestimation from radar data assimilation Rand is a randomdistribution function which is evenly distributed between

minus1 and 1 where the equation [43] for producing a randomnumber that is uniformly distributed in [119886 119887] is

119909119894= 119886 + (119887 minus 119886) 119903

119894 (11)

where 119903119894is a uniformly distributed random number that

belongs to [0 1]Using the measured data of eight storm events from 19

rain gauge stations and radar estimations calibrated by theKLM method 100 sets of random perturbation field wereproduced for each event by the BGM of initial disturbanceThen 200 sets of disturbance for each event formed afterthe superposition and deduction of the perturbation fieldwere used as the input to the Xinanjiang hydrological modelFor the eight storm events this resulted in 1600 predictedhydrographs The influence of the propagation of rainfallinput error on runoff simulation was quantified using thethree previously described goodness-of-fit statistics

4 Results and Discussion

41 Evaluation of Methods of Assimilation of Radar RainfallData A comparison of uncalibrated and calibrated resultsof five kinds of assimilation methods for eight storm events(Table 2) revealed that among the methods the SWImethodproduced results closest to the observed data followed bythe VAR method with a mean absolute error smaller thanthat of the SWI method The next best method was the OPTmethod followed by the KLM method and finally the AVGmethod The average of the results across the eight stormevents (Table 2) allows a rapid comparison of the relativeperformances of the five assimilation methods

6 Advances in Meteorology

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(a)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(b)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(c)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(d)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(e)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(f)

Figure 2 Hourly gauged rainfall observations compared to radar-based estimations (a) uncalibrated classified Z-R data (b) Kalman filter(c) average calibration (d) optimum interpolation (e) variational calibration and (f) statistical weight integration

For AVG the accuracy of regional total precipitation esti-mation improved after calibration and the accuracy wouldimprove further with more rain gauges One problem withthe AVG method is that it does not account for the shiftinglocation of the focus of intense rainfall during storm eventsAVG cannot assign greater weight to points independentlyidentified to be of particular interest and it does not considerthe representativeness of the data derived by the automaticrain gauges and radar echoes These problems explain therelatively low performance of the AVG method

Variable terrain synoptic conditions and precipitationintensity impart a high degree of spatial and temporal

variability to radar rainfall data that presents a challengefor data assimilation The results indicated that the KLMmethod of data assimilation with its strong theoretical basisand consideration of the distribution of error in determiningthe calibration factor produced a better result than the AVGmethodTheKLMmethod can improve accuracy by reducingthe relative deviation and degree of dispersion betweenthe hyetometer and radar rainfall data and eliminating theintrusion of nonrainfall echoes from rainfall estimationThismethod calibrates the radar estimated rainfall distributionfield in the time domain rather than the spatial structureerror of precipitation which means it is more suitable for

Advances in Meteorology 7

the calibration of stable stratiform cloud precipitation andin places with low density of rain gauges These may be thekey factors that limit the calibration accuracy of the KLMmethod The spatial structure and distribution of rain cloudsare complicated and changeable with mixed convectiveprecipitation being a common phenomenon Under theseconditions the OPT and VAR methods which have similarresults (Table 2) outperform the KLM method This relativeperformance differencewould also apply in places with a highdensity of rain gauges While each precipitation calibrationmodel has its advantages depending on the conditions SWIcombines the advantages of the other four methods and givesan appropriate weighting after the calculation On this basisthe SWI method would be expected to be superior to theother data assimilationmethods tested here [44] and this wassupported by the results (Table 2)

Scatterplots of hourly gauged rainfall and uncalibratedand calibrated radar-based rainfall (Figure 2) illustrated thegood agreement between the rainfall distribution obtainedby the SWI method and gauged rainfall The VAR and OPTassimilation methods also performed well The KLM andAVG method produced noticeably poorer results (Figure 2)

42 HydrologicalModel for FloodHydrograph Prediction TheXinanjiang hydrological model was applied in the WhiteLotus River catchment taking into consideration temporaland spatial variation of rainfall and the nonlinear effects ofwatershed topography and river channel characteristics onthe runoff concentration and dispersed inflow and nonlin-ear convergence Model parameters were calibrated by themethod of Rosenbrock [45] The three indexes certaintyfactor peak relative error and peak time difference wereused to evaluate the flood forecasting results Goodness-of-fit statistics (Table 3) and simulated hydrographs (Figure 3)indicated that themethods of SWI OPT andVARwere supe-rior in producing rainfall input data for storm hydrographmodelling In particular the SWI simulated hydrographswere in almost perfect agreement with the observed dataTherainfall data generated by themethods of KLMAVG andUCled to unsatisfactory hydrograph prediction

43 Uncertainty Analysis of Hydrological Forecasting Therelative error of predicted results increased after assimilatedrainfall data were randomly disturbed compared with theundisturbed peak flow flood volume and peak time differ-ence The peak flow and flood volume were increased by 5and 8 respectively (Figures 4 and 5) which means thatthe model input errors increased when they were processedthrough the hydrological model Also most of the predictedpeak times lagged the observed times (Figure 6)

The error of precipitation input data in hydrologicalmodelling is a significant source of error in predicted peakflow flood volume and peak time Therefore the spreadof precipitation uncertainty has a great influence on runoffprediction In China practical applications usually adoptqualitative rainfall prediction and assumed rainfall inputand this would have implications for the forecast period andaccuracy of flood forecasting At present both the accuracyand resolution of rainfall forecasts provided by numerical

weather prediction (NWP) cannot meet the requirements ofquantitative flood forecasting and this situation may con-tinue to exist into the foreseeable future Weather radar andsatellite remote sensing (SRS) can perform an important rolein quantitative precipitation forecasting Use of precipitationforecasts obtained by SRS as the input of hydrological modelsto simulate and predict runoff warrants further researchattention This could be a key step towards improving theaccuracy of flood forecasting It will be necessary to developmethods for combining and assimilating the SRS data andobserved data from rain gauges for producing better precipi-tation forecasts SRS has sufficiently high spatial and temporalresolution to effectively characterize the instantaneous distri-bution of precipitation throughout a catchment while raingauges can provide high-precision single-point observations

The generation of floods is a complex and dynamicprocess Modelling this process can be improved through theuse of rainfall input data with high spatial and temporal reso-lution How to best make use of rainfall information availablefrom multiple sources including gauge networks radar andsatellite monitoring is one of the key problems to be solvedin hydrological modelling and forecasting

5 Conclusions

Because of the high level of risk posed by floods especiallyflash floods it is critical that warning procedures make useof accurate nowcasting and short-range runoff forecastingcapability Precipitation data is the most important input tohydrological models used for forecasting hydrographsWhilerainfall data is usually sourced from a network of gauges analternative is weather radar detector which offers superiorspatial and temporal resolution but at the cost of lowprecisionand accuracy This paper investigated methods of precip-itation data assimilation with the objective of improvingthe quality of radar-based rainfall estimates as a means ofachieving more reliable flood forecasts Using data from anetwork of rain gauges in the White Lotus River in HubeiProvince China and data from the weather radar detectorbased in nearby Wuhan five established methods of assimi-lating radar data estimated by the classified 119885-119877 relationshipwere applied The assimilated data was compared with theobserved rainfall data and then used in a hydrological modelto predict historical flood hydrographs Finally BGM wasused for the perturbation of radar data to evaluate the effectof the rainfall data input error on runoff simulationThemainconclusions arising from this work were as follows

(1) Statistical weight integration variational calibrationand optimum interpolation were superior methodsof data assimilation while Kalman filter and averagecalibration methods gave a less satisfactory result

(2) For modelling storm event hydrographs rainfall datagenerated by the statistical weight integration varia-tional calibration and optimum interpolation meth-ods resulted in hydrographs that were the closest fitto the gauged data Rainfall data generated by theaverage calibration and Kalman filter methods of dataassimilation resulted in unsatisfactory hydrographprediction

8 Advances in Meteorology

Table 3 Comparison of flood hydrograph prediction using different rainfall data assimilation methods MPF is measured peak flow and FPFis forecast peak flow

Method Flood event MPF (m3s) FPF (m3s) NS PRE () PTD (h)

UC

050408 3133 584 minus073 8136 1050429 6182 1676 minus105 7289 32050609 1879 968 minus047 4848 2060411 2327 157 minus087 3253 15060508 2409 1081 minus059 5513 10060627 1896 766 minus295 596 4060705 3109 1348 minus3 5664 1060726 1473 1134 02 2301 8

KLM

050408 3133 2756 083 1203 2050429 6182 5622 087 906 1050609 1879 1667 09 1128 1060411 2327 2147 09 774 1060508 2409 2241 09 697 1060627 1896 1685 084 1113 2060705 3109 2627 082 155 2060726 1473 1361 086 76 1

AVG

050408 3133 2833 079 958 1050429 6182 6515 086 539 5050609 1879 1551 088 1746 2060411 2327 1962 083 1569 0060508 2409 2122 085 1191 1060627 1896 1552 044 1814 4060705 3109 2505 065 1943 1060726 1473 1082 022 2654 0

OPT

050408 3133 3117 089 051 2050429 6182 6154 09 045 1050609 1879 1876 09 016 3060411 2327 2317 089 043 2060508 2409 2403 09 025 2060627 1896 1886 089 053 1060705 3109 3071 089 122 2060726 1473 1446 09 183 3

VAR

050408 3133 3133 09 054 0050429 6182 6182 091 036 0050609 1879 1879 089 085 1060411 2327 2327 09 116 2060508 2409 2409 09 023 1060627 1896 1896 089 063 1060705 3109 3109 089 121 2060726 1473 1473 074 047 0

SWI

050408 3133 3125 089 026 1050429 6182 6166 089 026 0050609 1879 1879 09 034 2060411 2327 2072 087 1096 1060508 2409 2406 089 012 0060627 1896 1886 089 053 1060705 3109 3072 089 119 1060726 1473 1468 09 034 2

Advances in Meteorology 9

P

M

UCKLM

AVGOPTVARSWI

16

12

8

4

0

P (m

m)

11 21 31 41 51 61 711t (h)

0

50

100

150

200

250

Q(m

3s

)

12

10

8

6

4

2

0

P (m

m)

40

30

20

10

0

P (m

m)

0

200

400

600

800

Q(m

3s

)

21 41 61 81 1011t (h)

20

15

10

5

0

P (m

m)

0

90

180

270

360

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

250

300

Q(m

3s

)

11 21 31 41 51 61 71 811t (h)

12

8

4

0

P (m

m)

0

50

100

150

200

Q(m

3s

)

18

15

12

9

6

3

0

P (m

m)

11 21 31 41 51 611t (h)

0

40

80

120

160

Q(m

3s

)

11 21 31 41 51 61 711t (h)

10

8

6

4

2

0

P (m

m)

0

70

140

210

280

350

Q(m

3s

)

11 21 31 41 51 61 711t (h)

28

21

14

7

0

P (m

m)

P

M

UCKLM

AVGOPTVARSWI

Figure 3 Comparison of simulated hydrographs for eight storm events using rainfall input data derived from five assimilation methods anduncalibrated radar data119872 is measured hydrograph

10 Advances in Meteorology

00

05

10

15

20

25

00 05 10 15 20Rainfall relative error

Relat

ive e

rror

of p

eak

flow

y = 10581x + 00146

R2 = 09126

Figure 4 Relationship between relative error in predicted floodpeak magnitude and rainfall relative error

00 05 10 15 20Rainfall relative error

00

05

10

15

20

25

Relat

ive e

rror

of fl

ood

volu

me

R2 = 09392

y = 10807x + 00201

Figure 5 Relationship between relative error in predicted flood vol-ume and rainfall relative error

(3) The random errors generated by model input had atendency to increase during the process of runningthe hydrological model Also most of predicted floodpeak times were lagged

(4) As hydrometeorology ensemble forecasts becomemore widely available and the data acquisition meth-ods develop there will be an ongoing need for evalu-ation of uncertainty in input data

(5) This paper provides critical descriptive analysis ofthe main assimilation methods and the effect of theerrors on uncertainty of flood forecasting It demon-strates that weather radar has potential to improvethe precision of hydrological forecasting which hasimplications for improved flood control and disas-ter mitigation The influence of the propagation ofrainfall input error on three simulated factors ofhydrological forecast is quantified

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

minus4

minus2

0

2

4

6

8

Peak

tim

e diff

eren

ce (h

)

05 10 15 2000Rainfall relative error

Figure 6 Relationship between error in predicted flood peak timeand rainfall relative error

Acknowledgments

This study was supported by the State Key Program ofNational Natural Science of China (no 51339004) andthe National Natural Science Foundation of China (no51279139)

References

[1] I Yucel A Onen K K Yilmaz and D J Gochis ldquoCalibrationand evaluation of a flood forecasting system utility of numericalweather prediction model data assimilation and satellite-basedrainfallrdquo Journal of Hydrology vol 523 pp 49ndash66 2015

[2] L P Zhang L Li A Z Ye et al ldquoContrast research on precisionof estimating regional precipitation with weather radar and raingaugerdquo Engineering Journal of Wuhan University EngineeringEdition vol 40 no 1 pp 1ndash5 2007 (Chinese)

[3] J Liu M Bray and D Han ldquoA study on WRF radar dataassimilation for hydrological rainfall predictionrdquoHydrology andEarth System Sciences vol 17 no 8 pp 3095ndash3110 2013

[4] I Maiello R Ferretti S Gentile et al ldquoImpact of radar dataassimilation for the simulation of a heavy rainfall case incentral Italy using WRF-3DVARrdquo Atmospheric MeasurementTechniques vol 7 no 9 pp 2919ndash2935 2014

[5] M Borga ldquoAccuracy of radar rainfall estimates for streamflowsimulationrdquo Journal of Hydrology vol 267 no 1-2 pp 26ndash392002

[6] Q Dai and D Han ldquoExploration of discrepancy between radarand gauge rainfall estimates driven by wind fieldsrdquo WaterResources Research vol 50 no 11 pp 8571ndash8588 2014

[7] F Giannoni J A Smith Y Zhang and G Roth ldquoHydrologicmodeling of extreme floods using radar rainfall estimatesrdquoAdvances in Water Resources vol 26 no 2 pp 195ndash203 2003

[8] Z Sokol ldquoUtilization of regression models for rainfall estimatesusing radar-derived rainfall data and rain gauge datardquo Journalof Hydrology vol 278 no 1ndash4 pp 144ndash152 2003

[9] C A Velasco-Forero D Sempere-Torres E F Cassiraga and JJaime Gomez-Hernandez ldquoA non-parametric automatic blend-ing methodology to estimate rainfall fields from rain gauge andradar datardquo Advances inWater Resources vol 32 no 7 pp 986ndash1002 2009

Advances in Meteorology 11

[10] X Sun R G Mein T D Keenan and J F Elliott ldquoFlood esti-mation using radar and raingauge datardquo Journal of Hydrologyvol 239 no 1ndash4 pp 4ndash18 2000

[11] J Z Sun ldquoConvective-scale assimilation of radar data progressand challengesrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 131 no 613 pp 3439ndash3463 2006

[12] X D Yu X P Yao T N Xiong et al The Principle and Appli-cation of Doppler Weather Radar China Meteorological PressBeijing China 2007

[13] M Borga E N Anagnostou and E Frank ldquoOn the use of real-time radar rainfall estimates for flood prediction in mountain-ous basinsrdquo Journal of Geophysical Research Atmospheres vol105 no 2 pp 2269ndash2280 2000

[14] H G Zhang S L Guo and X L He ldquoRecent advancement andprospect of hydrological forecasting uncertainty studyrdquo Journalof Shihezi University (Natural Science) vol 24 no 1 pp 15ndash212006 (Chinese)

[15] GVillarini andW F Krajewski ldquoReview of the different sourcesof uncertainty in single polarization radar-based estimates ofrainfallrdquo Surveys in Geophysics vol 31 no 1 pp 107ndash129 2010

[16] K Beven and A Binley ldquoThe future of distributed modelsmodel calibration and uncertainty predictionrdquo HydrologicalProcesses vol 6 no 3 pp 279ndash298 1992

[17] F Quintero D Sempere-Torres M Berenguer and E BaltasldquoA scenario-incorporating analysis of the propagation of uncer-tainty to flash flood simulationsrdquo Journal of Hydrology vol 460-461 pp 90ndash102 2012

[18] L Xiong andKMOrsquoConnor ldquoAn empiricalmethod to improvethe prediction limits of the GLUE methodology in rainfall-runoffmodelingrdquo Journal of Hydrology vol 349 no 1-2 pp 115ndash124 2008

[19] X R Yin J Xia and X Zhang ldquoRecent progress and prospectof the study on uncertainties in hydrologicalmodeling and fore-castingrdquoWater Power vol 32 no 10 pp 27ndash31 2006 (Chinese)

[20] D Zhu Y Xuan and I Cluckie ldquoHydrological appraisal ofoperational weather radar rainfall estimates in the context ofdifferent modelling structuresrdquo Hydrology and Earth SystemSciences vol 18 no 1 pp 257ndash272 2014

[21] A S Falck V Maggioni J Tomasella D A Vila and F LR Diniz ldquoPropagation of satellite precipitation uncertaintiesthrough a distributed hydrologic model a case study in theTocantins-Araguaia basin in Brazilrdquo Journal of Hydrology vol527 pp 943ndash957 2015

[22] P A Mendoza J McPhee and X Vargas ldquoUncertainty in floodforecasting a distributed modeling approach in a sparse datacatchmentrdquoWater Resources Research vol 48 no 9 Article IDW09532 2012

[23] V TWood R A Brown and S V Vasiloff ldquoImproved detectionusing negative elevation angles for mountaintop WSR-88DsPart II simulations of the three radars covering UtahrdquoWeatherand Forecasting vol 18 no 3 pp 393ndash403 2003

[24] T P Dai and D S Fu ldquoPrecision of precipitation amount in thejoint detection areas by weather radar and the auto-rain Gaugenetworkrdquo Journal of Nanjing Institute of Meteorology vol 13 no4 pp 592ndash597 1990 (Chinese)

[25] J W Wilson and E A Brandes ldquoRadar measurement ofrainfallmdasha summaryrdquo Bulletin of the American MeteorologicalSociety vol 60 no 9 pp 1048ndash1058 1979

[26] S Chumchean A Seed and A Sharma ldquoCorrecting of real-time radar rainfall bias using a Kalman filtering approachrdquoJournal of Hydrology vol 317 no 1-2 pp 123ndash137 2006

[27] M Costa and M Monteiro ldquoBias-correction of Kalman filterestimators associated to a linear state space model with esti-mated parametersrdquo Journal of Statistical Planning and Inferencevol 176 pp 22ndash32 2016

[28] S I Kako A Isobe and M Kubota ldquoHigh-resolution ASCATwind vector data set gridded by applying an optimum inter-polation method to the global oceanrdquo Journal of GeophysicalResearch Atmospheres vol 116 no 23 Article ID D23107 2011

[29] S Kako andMKubota ldquoRelationship between an ElNino eventand the interannual variability of significant wave heights in theNorth Pacificrdquo Atmosphere-Ocean vol 44 no 4 pp 377ndash3952006

[30] W Castaings D Dartus F-X Le Dimet and G-M SaulnierldquoSensitivity analysis and parameter estimation for distributedhydrological modeling potential of variational methodsrdquoHydrology and Earth System Sciences vol 13 no 4 pp 503ndash5172009

[31] P C Zhang T P Dai D S Fu et al ldquoPrinciple and accuracyof adjusting the area precipitation from digital weather radarthrough variational methodrdquo Atmospheric Science vol 16 no2 pp 248ndash256 1992 (Chinese)

[32] R-J Zhao ldquoThe Xinanjiang model applied in Chinardquo Journal ofHydrology vol 135 no 1ndash4 pp 371ndash381 1992

[33] A A Alazzy H S Lu and Y H Zhu ldquoAssessing the uncertaintyof the Xinanjiang rainfall-runoff model effect of the likelihoodfunction choice on the GLUE methodrdquo Journal of HydrologicEngineering vol 20 no 10 Article ID 04015016 2015

[34] J Liu X Chen J Zhang and M Flury ldquoCoupling the Xinan-jiangmodel to a kinematic flowmodel based on digital drainagenetworks for flood forecastingrdquo Hydrological Processes vol 23no 9 pp 1337ndash1348 2009

[35] C Zhang R-BWang andQ-XMeng ldquoCalibration of concep-tual rainfall-runoffmodels using global optimizationrdquoAdvancesin Meteorology vol 2015 Article ID 545376 12 pages 2015

[36] H Xu C-Y Xu N R Saeliglthun B Zhou and Y Xu ldquoEvaluationof reanalysis and satellite-based precipitation datasets in drivinghydrological models in a humid region of Southern ChinardquoStochastic Environmental Research and Risk Assessment vol 29no 8 pp 2003ndash2020 2015

[37] S S Meng X H Xie and X Yu ldquoTracing temporal changesof model parameters in rainfall-runoffmodeling via a real-timedata assimilationrdquoWater vol 8 no 1 article 19 2016

[38] Z Toth and E Kalnay ldquoEnsemble Forecasting at NMC thegeneration of perturbationsrdquo Bulletin of the American Meteoro-logical Society vol 74 no 12 pp 2317ndash2330 1993

[39] S LMullen andD P Baumhefner ldquoMonte Carlo simulations ofexplosive cyclogenesisrdquoMonthlyWeather Review vol 122 no 7pp 1548ndash1567 1994

[40] R Buizza and T N Palmer ldquoImpact of ensemble size onensemble predictionrdquo Monthly Weather Review vol 126 no 9pp 2503ndash2518 1998

[41] F Molteni R Buizza T N Palmer and T Petroliagis ldquoTheECMWF ensemble prediction system methodology and vali-dationrdquo Quarterly Journal of the Royal Meteorological Societyvol 122 no 529 pp 73ndash119 1996

[42] Z Toth and E Kalnay ldquoEnsemble forecasting at NCEP and thebreeding methodrdquoMonthlyWeather Review vol 125 no 12 pp3297ndash3319 1997

[43] F Wu ldquoSeveral methods of creating stochastic numbers andapplicationsrdquo Journal on Numerical Methods and ComputerApplications vol 27 no 1 pp 48ndash51 2006 (Chinese)

12 Advances in Meteorology

[44] Y-H Shao and W-C Zhang ldquoApplication of statistical weightmatrix method in estimation of regional rainfallrdquo Advances inWater Science vol 20 no 6 pp 755ndash762 2009 (Chinese)

[45] X Y Song Y J Li H Y Yu et al ldquoApplication of quantitativeprecipitation estimation by radar to flood forecastrdquo EngineeringJournal of Wuhan University Engineering Edition vol 40 no 2pp 51ndash54 2007 (Chinese)

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

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Applied ampEnvironmentalSoil Science

Volume 2014

Mining

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Journal of

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International Journal of

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OceanographyInternational Journal of

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Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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MineralogyInternational Journal of

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Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Geological ResearchJournal of

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Geology Advances in

Advances in Meteorology 3

N

0 16 24 324Kilometers

White lotus catchment

Hydrologic stationMeteorological stationMain stem

Elevation (m)High 1701

Low 53

830∘30998400 N

30∘40998400 N

30∘50998400 N

31∘0998400 N

31∘10998400 N

30∘30998400 N

30∘40998400 N

30∘50998400 N

31∘0998400 N

31∘10998400 N

115∘20998400E 115∘30998400E 115∘40998400E 115∘50998400E 116∘0998400E

115∘20998400E 115∘30998400E 115∘40998400E 115∘50998400E 116∘0998400E

Figure 1 Location of White Lotus River catchment and the meteorological and river gauging stations within the catchment

multiplying 119868 by 119865 to give regional rainfall distribution Inthe situation of an inconsistent spatial pattern of rainfall overan area of interest a number of regional AVG factors couldbe calculated

322 Kalman Filter (KLM) In radar-based precipitationmeasurement there exists not only system errors producedby unstable radar capability but also the random errors dueto the unstable relation between119885 and 119877 and the influence ofwind field These random errors are called noise KLM aimsto find the optimum estimation of calibration factor 119891 fromnoisy data

The basic theory of KLM [26 27] is that if 1198911and 119891

2 two

independent estimations of the variable119891 can be obtained bydifferent equations the relation between 119891 119891

1 and 119891

2is

119891 = (1 minus 120596) 1198911+ 1205961198912 (2)

where 120596 is a weighting factor The criterion for determining120596 is minimizing the variance of the calibrated 119891 KLM isused to determine the weight with the input being observeddata and the output being the optimum estimation of 119891 TheKLM algorithm is a real-time recursive filter using presentinput data and the previously calculated state It is a real-timerecursive filter with the accuracy of estimation improvingcontinuously as the number of observations increases

323 Optimum Interpolation (OPT) The OPT method usesradar rainfall data derived from echoes as the first-guess

background meteorological field and then corrects this usinga linear combination of the differences between this firstguess and observed data from the rain gauges The weightingfunction is determined by minimizing the expected squareerror of the data [28 29] An OPT is generally expressed asfollows

119860119892= 119861119892+

119873

sum

119894=1

(119874119894minus 119861119894) 119875119894 (3)

where 119860119892(119861119892) is an analysis (first guess) value at a grid cell

119892 to be interpolated119874119894(119861119894) is an observed (first guess) value

given at observation point 119894 and 119875119894denotes a weight function

at observation point 119894 The optimum weight is computed bysupposing that the errors are unbiased and uncorrelated andcan be expressed as

119873

sum

119895=1

119875119894120583119894119895= 120583119892119894

(119894 = 1 2 119873) (4)

where 120583 represents the first-guess error correlation coefficientbetween two arbitrary grid points

324 Variational Calibration (VAR) The VAR method [3031] uses radar-based and gauge-measured precipitation foreach observation point to achieve a calibration factor 119862(119896)(119896 = 1 2 119899) and then obtain 119862(119894 119895) in every grid cell(119894 119895) by interpolation Next an optimum calibration factor

4 Advances in Meteorology

field 119862119877(119894 119895) which minimizes the sum of squared errorsbetween 119862119877(119894 119895) and 119862(119894 119895) is sought Finally the analyzedprecipitation in the grid (119894 119895) is

119875 (119894 119895) = 119875119877(119894 119895) + 119862119877 (119894 119895) (5)

where 119875 (119875119877) is analysis (radar-based) value at grid (119894 119895)

325 Statistical Weight Integration (SWI) The SWI methodaverages 119872 results of precipitation intensity distributionderived by 119872 methods according to weighting that dependson the reciprocal of error statistics

Error 119890119894119896

= 119909119894119896minus 119910119896 where 119909

119894119896is the output value of 119894th

method in grid 119896 and 119910119896is the measured value of automatic

rain gauge in the same grid Error variance 1205902

119894= (1

119873)sum119873

119896=1(119890119894119896minus 119890119894)2 where 119890

119894is themean error of eachmethod

The reciprocal of the error variance of various methods isusually used as the weight of the integration analysis Theresult after integrating is

119896=

sum119872

119894=11199091198941198961205902

119894

sum119872

119894=111205902

119894

(6)

where 119896is estimated results of the 119896th grid after integration

326 Evaluation Criteria The absolute error (AE) and rel-ative error (RE) were used as criteria to evaluate the fiveassimilation methods The Nash-Sutcliffe (NS) peak relativeerror (PRE) and peak time difference (PTD) were used toevaluate the results of hydrological modelling

NS = 1 minus

sum119873

119894=1(119894minus 119876119894)2

sum119873

119894=1(119876119894minus 119876)2

PRE = (sum119873

119894=1119894minus sum119873

119894=1119902119894

sum119873

119894=1119902119894

) times 100

PTD = sum(1003816100381610038161003816119879119904 minus 119879

119900

1003816100381610038161003816 le 3)

119873

(7)

where 119894is the predicted streamflow at time step 119894 119876

119894is the

observation at time step 119894 while 119876 is the mean of observa-tions119873 represents the total number of observations

119894is the

predicted peak flow at time step 119894 119902119894is themeasured peak flow

at the same time 119879119904is the predicted peak time and 119879

119900is the

observed peak time

33 Precipitation-Runoff Model The Xinanjiang model de-veloped by Zhao [32] has been applied extensively andsuccessfully to predict runoff from precipitation in humidand semihumid regions [33] This model conceptualizes thatrunoff is not produced until the soil moisture content of theaeration zone reaches field capacity and thereafter runoffequals the rainfall excess without further loss It consistsof three submodels a three-layer evapotranspiration sub-model a runoff generation submodel and a runoff routingsubmodel Many studies have described the structure of the

model in detail [32ndash35] The inputs to the model are dailyareal precipitation and pan evaporation with observed dailydischarge used for calibration The outputs are the modelleddaily discharge at the catchment outlet and the estimatedactual evapotranspiration of the catchment [36] The waterbalance equation of the model can be expressed as follows

If 119875119864+ 119860 lt 119882

1015840

mm

119877 = 119875119864+119882 minus119882

119872+119882119872(1 minus

119875119864+ 119860

1198821015840mm)

1+119861

(8)

If 119875119864+ 119860 ge 119882

1015840

mm

119877 = 119875119864+119882 minus119882

119872 (9)

where 119877 is the runoff 119875119864is the effective precipitation

which equals the precipitation minus evaporation119882is the initial water storage within the catchment and119860 is the ordinate value corresponding to 119882 1198821015840mmis the maximum storage capacity of the catchment119882119872

is the areal mean tension water capacity whichis composed of the capacity of each soil layer andrepresents drought conditions and 119861 is a parameterthat represents the heterogeneity of the water storagecapacity of the catchment

To reasonably describe the evapotranspiration processthe soil profile is divided into three layers the upper soillayer the lower soil layer and the deepest layer If the watercontent in the upper layer is sufficient evaporation equalsthe evaporation capacity of the upper layer If not all upperwater is evaporated and the residual evaporation is sourcedfrom the lower layer If the water content in the lower layeris insufficient to meet the residual evaporation capacity thewater in the deepest layer will be evaporated

The generated runoff is divided into the surface flowinterflow and groundwater using steady infiltration Thetotal runoff can be routed by a linear system before arrivingat the outlet of the catchment [37] Flow routing uses theMuskingum or piecewise continuous algorithm Taking intoconsideration the uneven distribution of rainfall and thenature of the underlying surface the catchment is dividedinto a set of subcatchments using an appropriate methodsuch asThiessen polygons Finally the total catchment runoffis obtained after the hydrographs at the outlets of eachsubcatchment are simulated and flood routing is applied [35]

34 Uncertainty Methods Most research into uncertainty ofhydrograph forecasting has focused onmodel parameters andstructure rather than quality of input data Toth and Kalnay[38] recommended perturbation of the initial condition withperturbation fields that are representative of errors present inthe analysis and then using these perturbations as the inputto the model in the analysis of input uncertainty The mainmethods used to generate perturbations that reflect the initialuncertainty are Monte Carlo Singular Vector and Breedingof Growing Modes (BGM) Monte Carlo is a statisticalmethod whereby the smaller the sample number the less

Advances in Meteorology 5

Table 2 Comparison of calibration results among different methods UC is uncalibrated KLM is Kalman filter AVG is average calibrationOPT is optimum interpolation VAR is variational calibration and SWI is statistical weight integration

Method Statistic Storm event start date (yymmdd) Average050408 050429 050609 060411 060508 060627 060705 060726

UCAE (mm) 2735 2138 579 397 573 752 358 672 1026RE () 7002 4489 2306 1349 1413 2693 1178 3702 3017

Results (mm) 1171 2625 1932 3339 348 2042 2679 2488 2470

KLMAE (mm) 481 461 145 138 158 19 129 106 226RE () 1232 968 576 469 389 679 426 584 665

Results (mm) 3425 5224 2367 2804 3895 2605 2908 171 3117

AVGAE (mm) 422 522 12 2 314 52 117 203 302RE () 1081 1096 48 68 775 1859 386 1117 934

Results (mm) 3483 5285 2391 3142 3738 2275 292 1613 3106

OPTAE (mm) 411 427 132 036 079 147 116 01 170RE () 1052 896 525 124 194 527 381 057 470

Results (mm) 3495 519 2379 2906 3974 2647 2921 1805 3165

VARAE (mm) 411 426 132 005 032 147 105 016 159RE () 1053 894 527 018 078 527 347 088 442

Results (mm) 3495 5189 2379 2937 4021 2647 2931 18 3175

SWIAE (mm) 411 295 132 005 026 147 105 005 141RE () 1053 618 527 018 065 526 347 029 398

Results (mm) 3495 5058 2379 2937 4026 2647 2932 181 3161Measured (mm) 3906 4763 2511 2942 4053 2794 3037 1816 3228

powerful the statistics However the sample number is oftenvery limited and randomly chosen initial values do notperfectly match with the dynamical mode Although closeto actual weather at initial time the predicted results oftendeviate rapidly from the actual atmospheric condition due tothe adjustment of the mode itself [39] The Singular Vectormethod is better able to deal with many nonquantitativehypotheses in the data assimilation increase the numberof ensemble members and more easily capture the errorsgenerated by analysis It can also determine the direction ofthe fastest disturbance and have a better dispersion Disad-vantages of this method are that the components of errorsthat do not grow are ignored and the calculations are tedious[40 41]

The BGM proposed by Toth and Kalnay [38 42] wasdesigned to model how growing errors are bred and main-tained in a conventional analysis cycle through successiveuse of short-range forecasts with the bred modes offering anestimate of possible growing error fields in the analysis Thegrowth rate obtained by this method is better than that of theMonte Carlo method and even higher than the growth rateof the lagged average forecasting A formula for the specificperturbation is generated

119875 = 119878 times Rmse times Rand (10)

where 119875 is random perturbation field and 119878 is perturbationamplitude coefficient In order to make the disturbanceamplitude not too large 119878 is set equal to 1 Rmse is themean square error between themeasured rainfall and rainfallestimation from radar data assimilation Rand is a randomdistribution function which is evenly distributed between

minus1 and 1 where the equation [43] for producing a randomnumber that is uniformly distributed in [119886 119887] is

119909119894= 119886 + (119887 minus 119886) 119903

119894 (11)

where 119903119894is a uniformly distributed random number that

belongs to [0 1]Using the measured data of eight storm events from 19

rain gauge stations and radar estimations calibrated by theKLM method 100 sets of random perturbation field wereproduced for each event by the BGM of initial disturbanceThen 200 sets of disturbance for each event formed afterthe superposition and deduction of the perturbation fieldwere used as the input to the Xinanjiang hydrological modelFor the eight storm events this resulted in 1600 predictedhydrographs The influence of the propagation of rainfallinput error on runoff simulation was quantified using thethree previously described goodness-of-fit statistics

4 Results and Discussion

41 Evaluation of Methods of Assimilation of Radar RainfallData A comparison of uncalibrated and calibrated resultsof five kinds of assimilation methods for eight storm events(Table 2) revealed that among the methods the SWImethodproduced results closest to the observed data followed bythe VAR method with a mean absolute error smaller thanthat of the SWI method The next best method was the OPTmethod followed by the KLM method and finally the AVGmethod The average of the results across the eight stormevents (Table 2) allows a rapid comparison of the relativeperformances of the five assimilation methods

6 Advances in Meteorology

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(a)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(b)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(c)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(d)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(e)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(f)

Figure 2 Hourly gauged rainfall observations compared to radar-based estimations (a) uncalibrated classified Z-R data (b) Kalman filter(c) average calibration (d) optimum interpolation (e) variational calibration and (f) statistical weight integration

For AVG the accuracy of regional total precipitation esti-mation improved after calibration and the accuracy wouldimprove further with more rain gauges One problem withthe AVG method is that it does not account for the shiftinglocation of the focus of intense rainfall during storm eventsAVG cannot assign greater weight to points independentlyidentified to be of particular interest and it does not considerthe representativeness of the data derived by the automaticrain gauges and radar echoes These problems explain therelatively low performance of the AVG method

Variable terrain synoptic conditions and precipitationintensity impart a high degree of spatial and temporal

variability to radar rainfall data that presents a challengefor data assimilation The results indicated that the KLMmethod of data assimilation with its strong theoretical basisand consideration of the distribution of error in determiningthe calibration factor produced a better result than the AVGmethodTheKLMmethod can improve accuracy by reducingthe relative deviation and degree of dispersion betweenthe hyetometer and radar rainfall data and eliminating theintrusion of nonrainfall echoes from rainfall estimationThismethod calibrates the radar estimated rainfall distributionfield in the time domain rather than the spatial structureerror of precipitation which means it is more suitable for

Advances in Meteorology 7

the calibration of stable stratiform cloud precipitation andin places with low density of rain gauges These may be thekey factors that limit the calibration accuracy of the KLMmethod The spatial structure and distribution of rain cloudsare complicated and changeable with mixed convectiveprecipitation being a common phenomenon Under theseconditions the OPT and VAR methods which have similarresults (Table 2) outperform the KLM method This relativeperformance differencewould also apply in places with a highdensity of rain gauges While each precipitation calibrationmodel has its advantages depending on the conditions SWIcombines the advantages of the other four methods and givesan appropriate weighting after the calculation On this basisthe SWI method would be expected to be superior to theother data assimilationmethods tested here [44] and this wassupported by the results (Table 2)

Scatterplots of hourly gauged rainfall and uncalibratedand calibrated radar-based rainfall (Figure 2) illustrated thegood agreement between the rainfall distribution obtainedby the SWI method and gauged rainfall The VAR and OPTassimilation methods also performed well The KLM andAVG method produced noticeably poorer results (Figure 2)

42 HydrologicalModel for FloodHydrograph Prediction TheXinanjiang hydrological model was applied in the WhiteLotus River catchment taking into consideration temporaland spatial variation of rainfall and the nonlinear effects ofwatershed topography and river channel characteristics onthe runoff concentration and dispersed inflow and nonlin-ear convergence Model parameters were calibrated by themethod of Rosenbrock [45] The three indexes certaintyfactor peak relative error and peak time difference wereused to evaluate the flood forecasting results Goodness-of-fit statistics (Table 3) and simulated hydrographs (Figure 3)indicated that themethods of SWI OPT andVARwere supe-rior in producing rainfall input data for storm hydrographmodelling In particular the SWI simulated hydrographswere in almost perfect agreement with the observed dataTherainfall data generated by themethods of KLMAVG andUCled to unsatisfactory hydrograph prediction

43 Uncertainty Analysis of Hydrological Forecasting Therelative error of predicted results increased after assimilatedrainfall data were randomly disturbed compared with theundisturbed peak flow flood volume and peak time differ-ence The peak flow and flood volume were increased by 5and 8 respectively (Figures 4 and 5) which means thatthe model input errors increased when they were processedthrough the hydrological model Also most of the predictedpeak times lagged the observed times (Figure 6)

The error of precipitation input data in hydrologicalmodelling is a significant source of error in predicted peakflow flood volume and peak time Therefore the spreadof precipitation uncertainty has a great influence on runoffprediction In China practical applications usually adoptqualitative rainfall prediction and assumed rainfall inputand this would have implications for the forecast period andaccuracy of flood forecasting At present both the accuracyand resolution of rainfall forecasts provided by numerical

weather prediction (NWP) cannot meet the requirements ofquantitative flood forecasting and this situation may con-tinue to exist into the foreseeable future Weather radar andsatellite remote sensing (SRS) can perform an important rolein quantitative precipitation forecasting Use of precipitationforecasts obtained by SRS as the input of hydrological modelsto simulate and predict runoff warrants further researchattention This could be a key step towards improving theaccuracy of flood forecasting It will be necessary to developmethods for combining and assimilating the SRS data andobserved data from rain gauges for producing better precipi-tation forecasts SRS has sufficiently high spatial and temporalresolution to effectively characterize the instantaneous distri-bution of precipitation throughout a catchment while raingauges can provide high-precision single-point observations

The generation of floods is a complex and dynamicprocess Modelling this process can be improved through theuse of rainfall input data with high spatial and temporal reso-lution How to best make use of rainfall information availablefrom multiple sources including gauge networks radar andsatellite monitoring is one of the key problems to be solvedin hydrological modelling and forecasting

5 Conclusions

Because of the high level of risk posed by floods especiallyflash floods it is critical that warning procedures make useof accurate nowcasting and short-range runoff forecastingcapability Precipitation data is the most important input tohydrological models used for forecasting hydrographsWhilerainfall data is usually sourced from a network of gauges analternative is weather radar detector which offers superiorspatial and temporal resolution but at the cost of lowprecisionand accuracy This paper investigated methods of precip-itation data assimilation with the objective of improvingthe quality of radar-based rainfall estimates as a means ofachieving more reliable flood forecasts Using data from anetwork of rain gauges in the White Lotus River in HubeiProvince China and data from the weather radar detectorbased in nearby Wuhan five established methods of assimi-lating radar data estimated by the classified 119885-119877 relationshipwere applied The assimilated data was compared with theobserved rainfall data and then used in a hydrological modelto predict historical flood hydrographs Finally BGM wasused for the perturbation of radar data to evaluate the effectof the rainfall data input error on runoff simulationThemainconclusions arising from this work were as follows

(1) Statistical weight integration variational calibrationand optimum interpolation were superior methodsof data assimilation while Kalman filter and averagecalibration methods gave a less satisfactory result

(2) For modelling storm event hydrographs rainfall datagenerated by the statistical weight integration varia-tional calibration and optimum interpolation meth-ods resulted in hydrographs that were the closest fitto the gauged data Rainfall data generated by theaverage calibration and Kalman filter methods of dataassimilation resulted in unsatisfactory hydrographprediction

8 Advances in Meteorology

Table 3 Comparison of flood hydrograph prediction using different rainfall data assimilation methods MPF is measured peak flow and FPFis forecast peak flow

Method Flood event MPF (m3s) FPF (m3s) NS PRE () PTD (h)

UC

050408 3133 584 minus073 8136 1050429 6182 1676 minus105 7289 32050609 1879 968 minus047 4848 2060411 2327 157 minus087 3253 15060508 2409 1081 minus059 5513 10060627 1896 766 minus295 596 4060705 3109 1348 minus3 5664 1060726 1473 1134 02 2301 8

KLM

050408 3133 2756 083 1203 2050429 6182 5622 087 906 1050609 1879 1667 09 1128 1060411 2327 2147 09 774 1060508 2409 2241 09 697 1060627 1896 1685 084 1113 2060705 3109 2627 082 155 2060726 1473 1361 086 76 1

AVG

050408 3133 2833 079 958 1050429 6182 6515 086 539 5050609 1879 1551 088 1746 2060411 2327 1962 083 1569 0060508 2409 2122 085 1191 1060627 1896 1552 044 1814 4060705 3109 2505 065 1943 1060726 1473 1082 022 2654 0

OPT

050408 3133 3117 089 051 2050429 6182 6154 09 045 1050609 1879 1876 09 016 3060411 2327 2317 089 043 2060508 2409 2403 09 025 2060627 1896 1886 089 053 1060705 3109 3071 089 122 2060726 1473 1446 09 183 3

VAR

050408 3133 3133 09 054 0050429 6182 6182 091 036 0050609 1879 1879 089 085 1060411 2327 2327 09 116 2060508 2409 2409 09 023 1060627 1896 1896 089 063 1060705 3109 3109 089 121 2060726 1473 1473 074 047 0

SWI

050408 3133 3125 089 026 1050429 6182 6166 089 026 0050609 1879 1879 09 034 2060411 2327 2072 087 1096 1060508 2409 2406 089 012 0060627 1896 1886 089 053 1060705 3109 3072 089 119 1060726 1473 1468 09 034 2

Advances in Meteorology 9

P

M

UCKLM

AVGOPTVARSWI

16

12

8

4

0

P (m

m)

11 21 31 41 51 61 711t (h)

0

50

100

150

200

250

Q(m

3s

)

12

10

8

6

4

2

0

P (m

m)

40

30

20

10

0

P (m

m)

0

200

400

600

800

Q(m

3s

)

21 41 61 81 1011t (h)

20

15

10

5

0

P (m

m)

0

90

180

270

360

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

250

300

Q(m

3s

)

11 21 31 41 51 61 71 811t (h)

12

8

4

0

P (m

m)

0

50

100

150

200

Q(m

3s

)

18

15

12

9

6

3

0

P (m

m)

11 21 31 41 51 611t (h)

0

40

80

120

160

Q(m

3s

)

11 21 31 41 51 61 711t (h)

10

8

6

4

2

0

P (m

m)

0

70

140

210

280

350

Q(m

3s

)

11 21 31 41 51 61 711t (h)

28

21

14

7

0

P (m

m)

P

M

UCKLM

AVGOPTVARSWI

Figure 3 Comparison of simulated hydrographs for eight storm events using rainfall input data derived from five assimilation methods anduncalibrated radar data119872 is measured hydrograph

10 Advances in Meteorology

00

05

10

15

20

25

00 05 10 15 20Rainfall relative error

Relat

ive e

rror

of p

eak

flow

y = 10581x + 00146

R2 = 09126

Figure 4 Relationship between relative error in predicted floodpeak magnitude and rainfall relative error

00 05 10 15 20Rainfall relative error

00

05

10

15

20

25

Relat

ive e

rror

of fl

ood

volu

me

R2 = 09392

y = 10807x + 00201

Figure 5 Relationship between relative error in predicted flood vol-ume and rainfall relative error

(3) The random errors generated by model input had atendency to increase during the process of runningthe hydrological model Also most of predicted floodpeak times were lagged

(4) As hydrometeorology ensemble forecasts becomemore widely available and the data acquisition meth-ods develop there will be an ongoing need for evalu-ation of uncertainty in input data

(5) This paper provides critical descriptive analysis ofthe main assimilation methods and the effect of theerrors on uncertainty of flood forecasting It demon-strates that weather radar has potential to improvethe precision of hydrological forecasting which hasimplications for improved flood control and disas-ter mitigation The influence of the propagation ofrainfall input error on three simulated factors ofhydrological forecast is quantified

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

minus4

minus2

0

2

4

6

8

Peak

tim

e diff

eren

ce (h

)

05 10 15 2000Rainfall relative error

Figure 6 Relationship between error in predicted flood peak timeand rainfall relative error

Acknowledgments

This study was supported by the State Key Program ofNational Natural Science of China (no 51339004) andthe National Natural Science Foundation of China (no51279139)

References

[1] I Yucel A Onen K K Yilmaz and D J Gochis ldquoCalibrationand evaluation of a flood forecasting system utility of numericalweather prediction model data assimilation and satellite-basedrainfallrdquo Journal of Hydrology vol 523 pp 49ndash66 2015

[2] L P Zhang L Li A Z Ye et al ldquoContrast research on precisionof estimating regional precipitation with weather radar and raingaugerdquo Engineering Journal of Wuhan University EngineeringEdition vol 40 no 1 pp 1ndash5 2007 (Chinese)

[3] J Liu M Bray and D Han ldquoA study on WRF radar dataassimilation for hydrological rainfall predictionrdquoHydrology andEarth System Sciences vol 17 no 8 pp 3095ndash3110 2013

[4] I Maiello R Ferretti S Gentile et al ldquoImpact of radar dataassimilation for the simulation of a heavy rainfall case incentral Italy using WRF-3DVARrdquo Atmospheric MeasurementTechniques vol 7 no 9 pp 2919ndash2935 2014

[5] M Borga ldquoAccuracy of radar rainfall estimates for streamflowsimulationrdquo Journal of Hydrology vol 267 no 1-2 pp 26ndash392002

[6] Q Dai and D Han ldquoExploration of discrepancy between radarand gauge rainfall estimates driven by wind fieldsrdquo WaterResources Research vol 50 no 11 pp 8571ndash8588 2014

[7] F Giannoni J A Smith Y Zhang and G Roth ldquoHydrologicmodeling of extreme floods using radar rainfall estimatesrdquoAdvances in Water Resources vol 26 no 2 pp 195ndash203 2003

[8] Z Sokol ldquoUtilization of regression models for rainfall estimatesusing radar-derived rainfall data and rain gauge datardquo Journalof Hydrology vol 278 no 1ndash4 pp 144ndash152 2003

[9] C A Velasco-Forero D Sempere-Torres E F Cassiraga and JJaime Gomez-Hernandez ldquoA non-parametric automatic blend-ing methodology to estimate rainfall fields from rain gauge andradar datardquo Advances inWater Resources vol 32 no 7 pp 986ndash1002 2009

Advances in Meteorology 11

[10] X Sun R G Mein T D Keenan and J F Elliott ldquoFlood esti-mation using radar and raingauge datardquo Journal of Hydrologyvol 239 no 1ndash4 pp 4ndash18 2000

[11] J Z Sun ldquoConvective-scale assimilation of radar data progressand challengesrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 131 no 613 pp 3439ndash3463 2006

[12] X D Yu X P Yao T N Xiong et al The Principle and Appli-cation of Doppler Weather Radar China Meteorological PressBeijing China 2007

[13] M Borga E N Anagnostou and E Frank ldquoOn the use of real-time radar rainfall estimates for flood prediction in mountain-ous basinsrdquo Journal of Geophysical Research Atmospheres vol105 no 2 pp 2269ndash2280 2000

[14] H G Zhang S L Guo and X L He ldquoRecent advancement andprospect of hydrological forecasting uncertainty studyrdquo Journalof Shihezi University (Natural Science) vol 24 no 1 pp 15ndash212006 (Chinese)

[15] GVillarini andW F Krajewski ldquoReview of the different sourcesof uncertainty in single polarization radar-based estimates ofrainfallrdquo Surveys in Geophysics vol 31 no 1 pp 107ndash129 2010

[16] K Beven and A Binley ldquoThe future of distributed modelsmodel calibration and uncertainty predictionrdquo HydrologicalProcesses vol 6 no 3 pp 279ndash298 1992

[17] F Quintero D Sempere-Torres M Berenguer and E BaltasldquoA scenario-incorporating analysis of the propagation of uncer-tainty to flash flood simulationsrdquo Journal of Hydrology vol 460-461 pp 90ndash102 2012

[18] L Xiong andKMOrsquoConnor ldquoAn empiricalmethod to improvethe prediction limits of the GLUE methodology in rainfall-runoffmodelingrdquo Journal of Hydrology vol 349 no 1-2 pp 115ndash124 2008

[19] X R Yin J Xia and X Zhang ldquoRecent progress and prospectof the study on uncertainties in hydrologicalmodeling and fore-castingrdquoWater Power vol 32 no 10 pp 27ndash31 2006 (Chinese)

[20] D Zhu Y Xuan and I Cluckie ldquoHydrological appraisal ofoperational weather radar rainfall estimates in the context ofdifferent modelling structuresrdquo Hydrology and Earth SystemSciences vol 18 no 1 pp 257ndash272 2014

[21] A S Falck V Maggioni J Tomasella D A Vila and F LR Diniz ldquoPropagation of satellite precipitation uncertaintiesthrough a distributed hydrologic model a case study in theTocantins-Araguaia basin in Brazilrdquo Journal of Hydrology vol527 pp 943ndash957 2015

[22] P A Mendoza J McPhee and X Vargas ldquoUncertainty in floodforecasting a distributed modeling approach in a sparse datacatchmentrdquoWater Resources Research vol 48 no 9 Article IDW09532 2012

[23] V TWood R A Brown and S V Vasiloff ldquoImproved detectionusing negative elevation angles for mountaintop WSR-88DsPart II simulations of the three radars covering UtahrdquoWeatherand Forecasting vol 18 no 3 pp 393ndash403 2003

[24] T P Dai and D S Fu ldquoPrecision of precipitation amount in thejoint detection areas by weather radar and the auto-rain Gaugenetworkrdquo Journal of Nanjing Institute of Meteorology vol 13 no4 pp 592ndash597 1990 (Chinese)

[25] J W Wilson and E A Brandes ldquoRadar measurement ofrainfallmdasha summaryrdquo Bulletin of the American MeteorologicalSociety vol 60 no 9 pp 1048ndash1058 1979

[26] S Chumchean A Seed and A Sharma ldquoCorrecting of real-time radar rainfall bias using a Kalman filtering approachrdquoJournal of Hydrology vol 317 no 1-2 pp 123ndash137 2006

[27] M Costa and M Monteiro ldquoBias-correction of Kalman filterestimators associated to a linear state space model with esti-mated parametersrdquo Journal of Statistical Planning and Inferencevol 176 pp 22ndash32 2016

[28] S I Kako A Isobe and M Kubota ldquoHigh-resolution ASCATwind vector data set gridded by applying an optimum inter-polation method to the global oceanrdquo Journal of GeophysicalResearch Atmospheres vol 116 no 23 Article ID D23107 2011

[29] S Kako andMKubota ldquoRelationship between an ElNino eventand the interannual variability of significant wave heights in theNorth Pacificrdquo Atmosphere-Ocean vol 44 no 4 pp 377ndash3952006

[30] W Castaings D Dartus F-X Le Dimet and G-M SaulnierldquoSensitivity analysis and parameter estimation for distributedhydrological modeling potential of variational methodsrdquoHydrology and Earth System Sciences vol 13 no 4 pp 503ndash5172009

[31] P C Zhang T P Dai D S Fu et al ldquoPrinciple and accuracyof adjusting the area precipitation from digital weather radarthrough variational methodrdquo Atmospheric Science vol 16 no2 pp 248ndash256 1992 (Chinese)

[32] R-J Zhao ldquoThe Xinanjiang model applied in Chinardquo Journal ofHydrology vol 135 no 1ndash4 pp 371ndash381 1992

[33] A A Alazzy H S Lu and Y H Zhu ldquoAssessing the uncertaintyof the Xinanjiang rainfall-runoff model effect of the likelihoodfunction choice on the GLUE methodrdquo Journal of HydrologicEngineering vol 20 no 10 Article ID 04015016 2015

[34] J Liu X Chen J Zhang and M Flury ldquoCoupling the Xinan-jiangmodel to a kinematic flowmodel based on digital drainagenetworks for flood forecastingrdquo Hydrological Processes vol 23no 9 pp 1337ndash1348 2009

[35] C Zhang R-BWang andQ-XMeng ldquoCalibration of concep-tual rainfall-runoffmodels using global optimizationrdquoAdvancesin Meteorology vol 2015 Article ID 545376 12 pages 2015

[36] H Xu C-Y Xu N R Saeliglthun B Zhou and Y Xu ldquoEvaluationof reanalysis and satellite-based precipitation datasets in drivinghydrological models in a humid region of Southern ChinardquoStochastic Environmental Research and Risk Assessment vol 29no 8 pp 2003ndash2020 2015

[37] S S Meng X H Xie and X Yu ldquoTracing temporal changesof model parameters in rainfall-runoffmodeling via a real-timedata assimilationrdquoWater vol 8 no 1 article 19 2016

[38] Z Toth and E Kalnay ldquoEnsemble Forecasting at NMC thegeneration of perturbationsrdquo Bulletin of the American Meteoro-logical Society vol 74 no 12 pp 2317ndash2330 1993

[39] S LMullen andD P Baumhefner ldquoMonte Carlo simulations ofexplosive cyclogenesisrdquoMonthlyWeather Review vol 122 no 7pp 1548ndash1567 1994

[40] R Buizza and T N Palmer ldquoImpact of ensemble size onensemble predictionrdquo Monthly Weather Review vol 126 no 9pp 2503ndash2518 1998

[41] F Molteni R Buizza T N Palmer and T Petroliagis ldquoTheECMWF ensemble prediction system methodology and vali-dationrdquo Quarterly Journal of the Royal Meteorological Societyvol 122 no 529 pp 73ndash119 1996

[42] Z Toth and E Kalnay ldquoEnsemble forecasting at NCEP and thebreeding methodrdquoMonthlyWeather Review vol 125 no 12 pp3297ndash3319 1997

[43] F Wu ldquoSeveral methods of creating stochastic numbers andapplicationsrdquo Journal on Numerical Methods and ComputerApplications vol 27 no 1 pp 48ndash51 2006 (Chinese)

12 Advances in Meteorology

[44] Y-H Shao and W-C Zhang ldquoApplication of statistical weightmatrix method in estimation of regional rainfallrdquo Advances inWater Science vol 20 no 6 pp 755ndash762 2009 (Chinese)

[45] X Y Song Y J Li H Y Yu et al ldquoApplication of quantitativeprecipitation estimation by radar to flood forecastrdquo EngineeringJournal of Wuhan University Engineering Edition vol 40 no 2pp 51ndash54 2007 (Chinese)

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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EarthquakesJournal of

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Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

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GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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MineralogyInternational Journal of

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Geological ResearchJournal of

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Geology Advances in

4 Advances in Meteorology

field 119862119877(119894 119895) which minimizes the sum of squared errorsbetween 119862119877(119894 119895) and 119862(119894 119895) is sought Finally the analyzedprecipitation in the grid (119894 119895) is

119875 (119894 119895) = 119875119877(119894 119895) + 119862119877 (119894 119895) (5)

where 119875 (119875119877) is analysis (radar-based) value at grid (119894 119895)

325 Statistical Weight Integration (SWI) The SWI methodaverages 119872 results of precipitation intensity distributionderived by 119872 methods according to weighting that dependson the reciprocal of error statistics

Error 119890119894119896

= 119909119894119896minus 119910119896 where 119909

119894119896is the output value of 119894th

method in grid 119896 and 119910119896is the measured value of automatic

rain gauge in the same grid Error variance 1205902

119894= (1

119873)sum119873

119896=1(119890119894119896minus 119890119894)2 where 119890

119894is themean error of eachmethod

The reciprocal of the error variance of various methods isusually used as the weight of the integration analysis Theresult after integrating is

119896=

sum119872

119894=11199091198941198961205902

119894

sum119872

119894=111205902

119894

(6)

where 119896is estimated results of the 119896th grid after integration

326 Evaluation Criteria The absolute error (AE) and rel-ative error (RE) were used as criteria to evaluate the fiveassimilation methods The Nash-Sutcliffe (NS) peak relativeerror (PRE) and peak time difference (PTD) were used toevaluate the results of hydrological modelling

NS = 1 minus

sum119873

119894=1(119894minus 119876119894)2

sum119873

119894=1(119876119894minus 119876)2

PRE = (sum119873

119894=1119894minus sum119873

119894=1119902119894

sum119873

119894=1119902119894

) times 100

PTD = sum(1003816100381610038161003816119879119904 minus 119879

119900

1003816100381610038161003816 le 3)

119873

(7)

where 119894is the predicted streamflow at time step 119894 119876

119894is the

observation at time step 119894 while 119876 is the mean of observa-tions119873 represents the total number of observations

119894is the

predicted peak flow at time step 119894 119902119894is themeasured peak flow

at the same time 119879119904is the predicted peak time and 119879

119900is the

observed peak time

33 Precipitation-Runoff Model The Xinanjiang model de-veloped by Zhao [32] has been applied extensively andsuccessfully to predict runoff from precipitation in humidand semihumid regions [33] This model conceptualizes thatrunoff is not produced until the soil moisture content of theaeration zone reaches field capacity and thereafter runoffequals the rainfall excess without further loss It consistsof three submodels a three-layer evapotranspiration sub-model a runoff generation submodel and a runoff routingsubmodel Many studies have described the structure of the

model in detail [32ndash35] The inputs to the model are dailyareal precipitation and pan evaporation with observed dailydischarge used for calibration The outputs are the modelleddaily discharge at the catchment outlet and the estimatedactual evapotranspiration of the catchment [36] The waterbalance equation of the model can be expressed as follows

If 119875119864+ 119860 lt 119882

1015840

mm

119877 = 119875119864+119882 minus119882

119872+119882119872(1 minus

119875119864+ 119860

1198821015840mm)

1+119861

(8)

If 119875119864+ 119860 ge 119882

1015840

mm

119877 = 119875119864+119882 minus119882

119872 (9)

where 119877 is the runoff 119875119864is the effective precipitation

which equals the precipitation minus evaporation119882is the initial water storage within the catchment and119860 is the ordinate value corresponding to 119882 1198821015840mmis the maximum storage capacity of the catchment119882119872

is the areal mean tension water capacity whichis composed of the capacity of each soil layer andrepresents drought conditions and 119861 is a parameterthat represents the heterogeneity of the water storagecapacity of the catchment

To reasonably describe the evapotranspiration processthe soil profile is divided into three layers the upper soillayer the lower soil layer and the deepest layer If the watercontent in the upper layer is sufficient evaporation equalsthe evaporation capacity of the upper layer If not all upperwater is evaporated and the residual evaporation is sourcedfrom the lower layer If the water content in the lower layeris insufficient to meet the residual evaporation capacity thewater in the deepest layer will be evaporated

The generated runoff is divided into the surface flowinterflow and groundwater using steady infiltration Thetotal runoff can be routed by a linear system before arrivingat the outlet of the catchment [37] Flow routing uses theMuskingum or piecewise continuous algorithm Taking intoconsideration the uneven distribution of rainfall and thenature of the underlying surface the catchment is dividedinto a set of subcatchments using an appropriate methodsuch asThiessen polygons Finally the total catchment runoffis obtained after the hydrographs at the outlets of eachsubcatchment are simulated and flood routing is applied [35]

34 Uncertainty Methods Most research into uncertainty ofhydrograph forecasting has focused onmodel parameters andstructure rather than quality of input data Toth and Kalnay[38] recommended perturbation of the initial condition withperturbation fields that are representative of errors present inthe analysis and then using these perturbations as the inputto the model in the analysis of input uncertainty The mainmethods used to generate perturbations that reflect the initialuncertainty are Monte Carlo Singular Vector and Breedingof Growing Modes (BGM) Monte Carlo is a statisticalmethod whereby the smaller the sample number the less

Advances in Meteorology 5

Table 2 Comparison of calibration results among different methods UC is uncalibrated KLM is Kalman filter AVG is average calibrationOPT is optimum interpolation VAR is variational calibration and SWI is statistical weight integration

Method Statistic Storm event start date (yymmdd) Average050408 050429 050609 060411 060508 060627 060705 060726

UCAE (mm) 2735 2138 579 397 573 752 358 672 1026RE () 7002 4489 2306 1349 1413 2693 1178 3702 3017

Results (mm) 1171 2625 1932 3339 348 2042 2679 2488 2470

KLMAE (mm) 481 461 145 138 158 19 129 106 226RE () 1232 968 576 469 389 679 426 584 665

Results (mm) 3425 5224 2367 2804 3895 2605 2908 171 3117

AVGAE (mm) 422 522 12 2 314 52 117 203 302RE () 1081 1096 48 68 775 1859 386 1117 934

Results (mm) 3483 5285 2391 3142 3738 2275 292 1613 3106

OPTAE (mm) 411 427 132 036 079 147 116 01 170RE () 1052 896 525 124 194 527 381 057 470

Results (mm) 3495 519 2379 2906 3974 2647 2921 1805 3165

VARAE (mm) 411 426 132 005 032 147 105 016 159RE () 1053 894 527 018 078 527 347 088 442

Results (mm) 3495 5189 2379 2937 4021 2647 2931 18 3175

SWIAE (mm) 411 295 132 005 026 147 105 005 141RE () 1053 618 527 018 065 526 347 029 398

Results (mm) 3495 5058 2379 2937 4026 2647 2932 181 3161Measured (mm) 3906 4763 2511 2942 4053 2794 3037 1816 3228

powerful the statistics However the sample number is oftenvery limited and randomly chosen initial values do notperfectly match with the dynamical mode Although closeto actual weather at initial time the predicted results oftendeviate rapidly from the actual atmospheric condition due tothe adjustment of the mode itself [39] The Singular Vectormethod is better able to deal with many nonquantitativehypotheses in the data assimilation increase the numberof ensemble members and more easily capture the errorsgenerated by analysis It can also determine the direction ofthe fastest disturbance and have a better dispersion Disad-vantages of this method are that the components of errorsthat do not grow are ignored and the calculations are tedious[40 41]

The BGM proposed by Toth and Kalnay [38 42] wasdesigned to model how growing errors are bred and main-tained in a conventional analysis cycle through successiveuse of short-range forecasts with the bred modes offering anestimate of possible growing error fields in the analysis Thegrowth rate obtained by this method is better than that of theMonte Carlo method and even higher than the growth rateof the lagged average forecasting A formula for the specificperturbation is generated

119875 = 119878 times Rmse times Rand (10)

where 119875 is random perturbation field and 119878 is perturbationamplitude coefficient In order to make the disturbanceamplitude not too large 119878 is set equal to 1 Rmse is themean square error between themeasured rainfall and rainfallestimation from radar data assimilation Rand is a randomdistribution function which is evenly distributed between

minus1 and 1 where the equation [43] for producing a randomnumber that is uniformly distributed in [119886 119887] is

119909119894= 119886 + (119887 minus 119886) 119903

119894 (11)

where 119903119894is a uniformly distributed random number that

belongs to [0 1]Using the measured data of eight storm events from 19

rain gauge stations and radar estimations calibrated by theKLM method 100 sets of random perturbation field wereproduced for each event by the BGM of initial disturbanceThen 200 sets of disturbance for each event formed afterthe superposition and deduction of the perturbation fieldwere used as the input to the Xinanjiang hydrological modelFor the eight storm events this resulted in 1600 predictedhydrographs The influence of the propagation of rainfallinput error on runoff simulation was quantified using thethree previously described goodness-of-fit statistics

4 Results and Discussion

41 Evaluation of Methods of Assimilation of Radar RainfallData A comparison of uncalibrated and calibrated resultsof five kinds of assimilation methods for eight storm events(Table 2) revealed that among the methods the SWImethodproduced results closest to the observed data followed bythe VAR method with a mean absolute error smaller thanthat of the SWI method The next best method was the OPTmethod followed by the KLM method and finally the AVGmethod The average of the results across the eight stormevents (Table 2) allows a rapid comparison of the relativeperformances of the five assimilation methods

6 Advances in Meteorology

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(a)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(b)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(c)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(d)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(e)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(f)

Figure 2 Hourly gauged rainfall observations compared to radar-based estimations (a) uncalibrated classified Z-R data (b) Kalman filter(c) average calibration (d) optimum interpolation (e) variational calibration and (f) statistical weight integration

For AVG the accuracy of regional total precipitation esti-mation improved after calibration and the accuracy wouldimprove further with more rain gauges One problem withthe AVG method is that it does not account for the shiftinglocation of the focus of intense rainfall during storm eventsAVG cannot assign greater weight to points independentlyidentified to be of particular interest and it does not considerthe representativeness of the data derived by the automaticrain gauges and radar echoes These problems explain therelatively low performance of the AVG method

Variable terrain synoptic conditions and precipitationintensity impart a high degree of spatial and temporal

variability to radar rainfall data that presents a challengefor data assimilation The results indicated that the KLMmethod of data assimilation with its strong theoretical basisand consideration of the distribution of error in determiningthe calibration factor produced a better result than the AVGmethodTheKLMmethod can improve accuracy by reducingthe relative deviation and degree of dispersion betweenthe hyetometer and radar rainfall data and eliminating theintrusion of nonrainfall echoes from rainfall estimationThismethod calibrates the radar estimated rainfall distributionfield in the time domain rather than the spatial structureerror of precipitation which means it is more suitable for

Advances in Meteorology 7

the calibration of stable stratiform cloud precipitation andin places with low density of rain gauges These may be thekey factors that limit the calibration accuracy of the KLMmethod The spatial structure and distribution of rain cloudsare complicated and changeable with mixed convectiveprecipitation being a common phenomenon Under theseconditions the OPT and VAR methods which have similarresults (Table 2) outperform the KLM method This relativeperformance differencewould also apply in places with a highdensity of rain gauges While each precipitation calibrationmodel has its advantages depending on the conditions SWIcombines the advantages of the other four methods and givesan appropriate weighting after the calculation On this basisthe SWI method would be expected to be superior to theother data assimilationmethods tested here [44] and this wassupported by the results (Table 2)

Scatterplots of hourly gauged rainfall and uncalibratedand calibrated radar-based rainfall (Figure 2) illustrated thegood agreement between the rainfall distribution obtainedby the SWI method and gauged rainfall The VAR and OPTassimilation methods also performed well The KLM andAVG method produced noticeably poorer results (Figure 2)

42 HydrologicalModel for FloodHydrograph Prediction TheXinanjiang hydrological model was applied in the WhiteLotus River catchment taking into consideration temporaland spatial variation of rainfall and the nonlinear effects ofwatershed topography and river channel characteristics onthe runoff concentration and dispersed inflow and nonlin-ear convergence Model parameters were calibrated by themethod of Rosenbrock [45] The three indexes certaintyfactor peak relative error and peak time difference wereused to evaluate the flood forecasting results Goodness-of-fit statistics (Table 3) and simulated hydrographs (Figure 3)indicated that themethods of SWI OPT andVARwere supe-rior in producing rainfall input data for storm hydrographmodelling In particular the SWI simulated hydrographswere in almost perfect agreement with the observed dataTherainfall data generated by themethods of KLMAVG andUCled to unsatisfactory hydrograph prediction

43 Uncertainty Analysis of Hydrological Forecasting Therelative error of predicted results increased after assimilatedrainfall data were randomly disturbed compared with theundisturbed peak flow flood volume and peak time differ-ence The peak flow and flood volume were increased by 5and 8 respectively (Figures 4 and 5) which means thatthe model input errors increased when they were processedthrough the hydrological model Also most of the predictedpeak times lagged the observed times (Figure 6)

The error of precipitation input data in hydrologicalmodelling is a significant source of error in predicted peakflow flood volume and peak time Therefore the spreadof precipitation uncertainty has a great influence on runoffprediction In China practical applications usually adoptqualitative rainfall prediction and assumed rainfall inputand this would have implications for the forecast period andaccuracy of flood forecasting At present both the accuracyand resolution of rainfall forecasts provided by numerical

weather prediction (NWP) cannot meet the requirements ofquantitative flood forecasting and this situation may con-tinue to exist into the foreseeable future Weather radar andsatellite remote sensing (SRS) can perform an important rolein quantitative precipitation forecasting Use of precipitationforecasts obtained by SRS as the input of hydrological modelsto simulate and predict runoff warrants further researchattention This could be a key step towards improving theaccuracy of flood forecasting It will be necessary to developmethods for combining and assimilating the SRS data andobserved data from rain gauges for producing better precipi-tation forecasts SRS has sufficiently high spatial and temporalresolution to effectively characterize the instantaneous distri-bution of precipitation throughout a catchment while raingauges can provide high-precision single-point observations

The generation of floods is a complex and dynamicprocess Modelling this process can be improved through theuse of rainfall input data with high spatial and temporal reso-lution How to best make use of rainfall information availablefrom multiple sources including gauge networks radar andsatellite monitoring is one of the key problems to be solvedin hydrological modelling and forecasting

5 Conclusions

Because of the high level of risk posed by floods especiallyflash floods it is critical that warning procedures make useof accurate nowcasting and short-range runoff forecastingcapability Precipitation data is the most important input tohydrological models used for forecasting hydrographsWhilerainfall data is usually sourced from a network of gauges analternative is weather radar detector which offers superiorspatial and temporal resolution but at the cost of lowprecisionand accuracy This paper investigated methods of precip-itation data assimilation with the objective of improvingthe quality of radar-based rainfall estimates as a means ofachieving more reliable flood forecasts Using data from anetwork of rain gauges in the White Lotus River in HubeiProvince China and data from the weather radar detectorbased in nearby Wuhan five established methods of assimi-lating radar data estimated by the classified 119885-119877 relationshipwere applied The assimilated data was compared with theobserved rainfall data and then used in a hydrological modelto predict historical flood hydrographs Finally BGM wasused for the perturbation of radar data to evaluate the effectof the rainfall data input error on runoff simulationThemainconclusions arising from this work were as follows

(1) Statistical weight integration variational calibrationand optimum interpolation were superior methodsof data assimilation while Kalman filter and averagecalibration methods gave a less satisfactory result

(2) For modelling storm event hydrographs rainfall datagenerated by the statistical weight integration varia-tional calibration and optimum interpolation meth-ods resulted in hydrographs that were the closest fitto the gauged data Rainfall data generated by theaverage calibration and Kalman filter methods of dataassimilation resulted in unsatisfactory hydrographprediction

8 Advances in Meteorology

Table 3 Comparison of flood hydrograph prediction using different rainfall data assimilation methods MPF is measured peak flow and FPFis forecast peak flow

Method Flood event MPF (m3s) FPF (m3s) NS PRE () PTD (h)

UC

050408 3133 584 minus073 8136 1050429 6182 1676 minus105 7289 32050609 1879 968 minus047 4848 2060411 2327 157 minus087 3253 15060508 2409 1081 minus059 5513 10060627 1896 766 minus295 596 4060705 3109 1348 minus3 5664 1060726 1473 1134 02 2301 8

KLM

050408 3133 2756 083 1203 2050429 6182 5622 087 906 1050609 1879 1667 09 1128 1060411 2327 2147 09 774 1060508 2409 2241 09 697 1060627 1896 1685 084 1113 2060705 3109 2627 082 155 2060726 1473 1361 086 76 1

AVG

050408 3133 2833 079 958 1050429 6182 6515 086 539 5050609 1879 1551 088 1746 2060411 2327 1962 083 1569 0060508 2409 2122 085 1191 1060627 1896 1552 044 1814 4060705 3109 2505 065 1943 1060726 1473 1082 022 2654 0

OPT

050408 3133 3117 089 051 2050429 6182 6154 09 045 1050609 1879 1876 09 016 3060411 2327 2317 089 043 2060508 2409 2403 09 025 2060627 1896 1886 089 053 1060705 3109 3071 089 122 2060726 1473 1446 09 183 3

VAR

050408 3133 3133 09 054 0050429 6182 6182 091 036 0050609 1879 1879 089 085 1060411 2327 2327 09 116 2060508 2409 2409 09 023 1060627 1896 1896 089 063 1060705 3109 3109 089 121 2060726 1473 1473 074 047 0

SWI

050408 3133 3125 089 026 1050429 6182 6166 089 026 0050609 1879 1879 09 034 2060411 2327 2072 087 1096 1060508 2409 2406 089 012 0060627 1896 1886 089 053 1060705 3109 3072 089 119 1060726 1473 1468 09 034 2

Advances in Meteorology 9

P

M

UCKLM

AVGOPTVARSWI

16

12

8

4

0

P (m

m)

11 21 31 41 51 61 711t (h)

0

50

100

150

200

250

Q(m

3s

)

12

10

8

6

4

2

0

P (m

m)

40

30

20

10

0

P (m

m)

0

200

400

600

800

Q(m

3s

)

21 41 61 81 1011t (h)

20

15

10

5

0

P (m

m)

0

90

180

270

360

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

250

300

Q(m

3s

)

11 21 31 41 51 61 71 811t (h)

12

8

4

0

P (m

m)

0

50

100

150

200

Q(m

3s

)

18

15

12

9

6

3

0

P (m

m)

11 21 31 41 51 611t (h)

0

40

80

120

160

Q(m

3s

)

11 21 31 41 51 61 711t (h)

10

8

6

4

2

0

P (m

m)

0

70

140

210

280

350

Q(m

3s

)

11 21 31 41 51 61 711t (h)

28

21

14

7

0

P (m

m)

P

M

UCKLM

AVGOPTVARSWI

Figure 3 Comparison of simulated hydrographs for eight storm events using rainfall input data derived from five assimilation methods anduncalibrated radar data119872 is measured hydrograph

10 Advances in Meteorology

00

05

10

15

20

25

00 05 10 15 20Rainfall relative error

Relat

ive e

rror

of p

eak

flow

y = 10581x + 00146

R2 = 09126

Figure 4 Relationship between relative error in predicted floodpeak magnitude and rainfall relative error

00 05 10 15 20Rainfall relative error

00

05

10

15

20

25

Relat

ive e

rror

of fl

ood

volu

me

R2 = 09392

y = 10807x + 00201

Figure 5 Relationship between relative error in predicted flood vol-ume and rainfall relative error

(3) The random errors generated by model input had atendency to increase during the process of runningthe hydrological model Also most of predicted floodpeak times were lagged

(4) As hydrometeorology ensemble forecasts becomemore widely available and the data acquisition meth-ods develop there will be an ongoing need for evalu-ation of uncertainty in input data

(5) This paper provides critical descriptive analysis ofthe main assimilation methods and the effect of theerrors on uncertainty of flood forecasting It demon-strates that weather radar has potential to improvethe precision of hydrological forecasting which hasimplications for improved flood control and disas-ter mitigation The influence of the propagation ofrainfall input error on three simulated factors ofhydrological forecast is quantified

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

minus4

minus2

0

2

4

6

8

Peak

tim

e diff

eren

ce (h

)

05 10 15 2000Rainfall relative error

Figure 6 Relationship between error in predicted flood peak timeand rainfall relative error

Acknowledgments

This study was supported by the State Key Program ofNational Natural Science of China (no 51339004) andthe National Natural Science Foundation of China (no51279139)

References

[1] I Yucel A Onen K K Yilmaz and D J Gochis ldquoCalibrationand evaluation of a flood forecasting system utility of numericalweather prediction model data assimilation and satellite-basedrainfallrdquo Journal of Hydrology vol 523 pp 49ndash66 2015

[2] L P Zhang L Li A Z Ye et al ldquoContrast research on precisionof estimating regional precipitation with weather radar and raingaugerdquo Engineering Journal of Wuhan University EngineeringEdition vol 40 no 1 pp 1ndash5 2007 (Chinese)

[3] J Liu M Bray and D Han ldquoA study on WRF radar dataassimilation for hydrological rainfall predictionrdquoHydrology andEarth System Sciences vol 17 no 8 pp 3095ndash3110 2013

[4] I Maiello R Ferretti S Gentile et al ldquoImpact of radar dataassimilation for the simulation of a heavy rainfall case incentral Italy using WRF-3DVARrdquo Atmospheric MeasurementTechniques vol 7 no 9 pp 2919ndash2935 2014

[5] M Borga ldquoAccuracy of radar rainfall estimates for streamflowsimulationrdquo Journal of Hydrology vol 267 no 1-2 pp 26ndash392002

[6] Q Dai and D Han ldquoExploration of discrepancy between radarand gauge rainfall estimates driven by wind fieldsrdquo WaterResources Research vol 50 no 11 pp 8571ndash8588 2014

[7] F Giannoni J A Smith Y Zhang and G Roth ldquoHydrologicmodeling of extreme floods using radar rainfall estimatesrdquoAdvances in Water Resources vol 26 no 2 pp 195ndash203 2003

[8] Z Sokol ldquoUtilization of regression models for rainfall estimatesusing radar-derived rainfall data and rain gauge datardquo Journalof Hydrology vol 278 no 1ndash4 pp 144ndash152 2003

[9] C A Velasco-Forero D Sempere-Torres E F Cassiraga and JJaime Gomez-Hernandez ldquoA non-parametric automatic blend-ing methodology to estimate rainfall fields from rain gauge andradar datardquo Advances inWater Resources vol 32 no 7 pp 986ndash1002 2009

Advances in Meteorology 11

[10] X Sun R G Mein T D Keenan and J F Elliott ldquoFlood esti-mation using radar and raingauge datardquo Journal of Hydrologyvol 239 no 1ndash4 pp 4ndash18 2000

[11] J Z Sun ldquoConvective-scale assimilation of radar data progressand challengesrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 131 no 613 pp 3439ndash3463 2006

[12] X D Yu X P Yao T N Xiong et al The Principle and Appli-cation of Doppler Weather Radar China Meteorological PressBeijing China 2007

[13] M Borga E N Anagnostou and E Frank ldquoOn the use of real-time radar rainfall estimates for flood prediction in mountain-ous basinsrdquo Journal of Geophysical Research Atmospheres vol105 no 2 pp 2269ndash2280 2000

[14] H G Zhang S L Guo and X L He ldquoRecent advancement andprospect of hydrological forecasting uncertainty studyrdquo Journalof Shihezi University (Natural Science) vol 24 no 1 pp 15ndash212006 (Chinese)

[15] GVillarini andW F Krajewski ldquoReview of the different sourcesof uncertainty in single polarization radar-based estimates ofrainfallrdquo Surveys in Geophysics vol 31 no 1 pp 107ndash129 2010

[16] K Beven and A Binley ldquoThe future of distributed modelsmodel calibration and uncertainty predictionrdquo HydrologicalProcesses vol 6 no 3 pp 279ndash298 1992

[17] F Quintero D Sempere-Torres M Berenguer and E BaltasldquoA scenario-incorporating analysis of the propagation of uncer-tainty to flash flood simulationsrdquo Journal of Hydrology vol 460-461 pp 90ndash102 2012

[18] L Xiong andKMOrsquoConnor ldquoAn empiricalmethod to improvethe prediction limits of the GLUE methodology in rainfall-runoffmodelingrdquo Journal of Hydrology vol 349 no 1-2 pp 115ndash124 2008

[19] X R Yin J Xia and X Zhang ldquoRecent progress and prospectof the study on uncertainties in hydrologicalmodeling and fore-castingrdquoWater Power vol 32 no 10 pp 27ndash31 2006 (Chinese)

[20] D Zhu Y Xuan and I Cluckie ldquoHydrological appraisal ofoperational weather radar rainfall estimates in the context ofdifferent modelling structuresrdquo Hydrology and Earth SystemSciences vol 18 no 1 pp 257ndash272 2014

[21] A S Falck V Maggioni J Tomasella D A Vila and F LR Diniz ldquoPropagation of satellite precipitation uncertaintiesthrough a distributed hydrologic model a case study in theTocantins-Araguaia basin in Brazilrdquo Journal of Hydrology vol527 pp 943ndash957 2015

[22] P A Mendoza J McPhee and X Vargas ldquoUncertainty in floodforecasting a distributed modeling approach in a sparse datacatchmentrdquoWater Resources Research vol 48 no 9 Article IDW09532 2012

[23] V TWood R A Brown and S V Vasiloff ldquoImproved detectionusing negative elevation angles for mountaintop WSR-88DsPart II simulations of the three radars covering UtahrdquoWeatherand Forecasting vol 18 no 3 pp 393ndash403 2003

[24] T P Dai and D S Fu ldquoPrecision of precipitation amount in thejoint detection areas by weather radar and the auto-rain Gaugenetworkrdquo Journal of Nanjing Institute of Meteorology vol 13 no4 pp 592ndash597 1990 (Chinese)

[25] J W Wilson and E A Brandes ldquoRadar measurement ofrainfallmdasha summaryrdquo Bulletin of the American MeteorologicalSociety vol 60 no 9 pp 1048ndash1058 1979

[26] S Chumchean A Seed and A Sharma ldquoCorrecting of real-time radar rainfall bias using a Kalman filtering approachrdquoJournal of Hydrology vol 317 no 1-2 pp 123ndash137 2006

[27] M Costa and M Monteiro ldquoBias-correction of Kalman filterestimators associated to a linear state space model with esti-mated parametersrdquo Journal of Statistical Planning and Inferencevol 176 pp 22ndash32 2016

[28] S I Kako A Isobe and M Kubota ldquoHigh-resolution ASCATwind vector data set gridded by applying an optimum inter-polation method to the global oceanrdquo Journal of GeophysicalResearch Atmospheres vol 116 no 23 Article ID D23107 2011

[29] S Kako andMKubota ldquoRelationship between an ElNino eventand the interannual variability of significant wave heights in theNorth Pacificrdquo Atmosphere-Ocean vol 44 no 4 pp 377ndash3952006

[30] W Castaings D Dartus F-X Le Dimet and G-M SaulnierldquoSensitivity analysis and parameter estimation for distributedhydrological modeling potential of variational methodsrdquoHydrology and Earth System Sciences vol 13 no 4 pp 503ndash5172009

[31] P C Zhang T P Dai D S Fu et al ldquoPrinciple and accuracyof adjusting the area precipitation from digital weather radarthrough variational methodrdquo Atmospheric Science vol 16 no2 pp 248ndash256 1992 (Chinese)

[32] R-J Zhao ldquoThe Xinanjiang model applied in Chinardquo Journal ofHydrology vol 135 no 1ndash4 pp 371ndash381 1992

[33] A A Alazzy H S Lu and Y H Zhu ldquoAssessing the uncertaintyof the Xinanjiang rainfall-runoff model effect of the likelihoodfunction choice on the GLUE methodrdquo Journal of HydrologicEngineering vol 20 no 10 Article ID 04015016 2015

[34] J Liu X Chen J Zhang and M Flury ldquoCoupling the Xinan-jiangmodel to a kinematic flowmodel based on digital drainagenetworks for flood forecastingrdquo Hydrological Processes vol 23no 9 pp 1337ndash1348 2009

[35] C Zhang R-BWang andQ-XMeng ldquoCalibration of concep-tual rainfall-runoffmodels using global optimizationrdquoAdvancesin Meteorology vol 2015 Article ID 545376 12 pages 2015

[36] H Xu C-Y Xu N R Saeliglthun B Zhou and Y Xu ldquoEvaluationof reanalysis and satellite-based precipitation datasets in drivinghydrological models in a humid region of Southern ChinardquoStochastic Environmental Research and Risk Assessment vol 29no 8 pp 2003ndash2020 2015

[37] S S Meng X H Xie and X Yu ldquoTracing temporal changesof model parameters in rainfall-runoffmodeling via a real-timedata assimilationrdquoWater vol 8 no 1 article 19 2016

[38] Z Toth and E Kalnay ldquoEnsemble Forecasting at NMC thegeneration of perturbationsrdquo Bulletin of the American Meteoro-logical Society vol 74 no 12 pp 2317ndash2330 1993

[39] S LMullen andD P Baumhefner ldquoMonte Carlo simulations ofexplosive cyclogenesisrdquoMonthlyWeather Review vol 122 no 7pp 1548ndash1567 1994

[40] R Buizza and T N Palmer ldquoImpact of ensemble size onensemble predictionrdquo Monthly Weather Review vol 126 no 9pp 2503ndash2518 1998

[41] F Molteni R Buizza T N Palmer and T Petroliagis ldquoTheECMWF ensemble prediction system methodology and vali-dationrdquo Quarterly Journal of the Royal Meteorological Societyvol 122 no 529 pp 73ndash119 1996

[42] Z Toth and E Kalnay ldquoEnsemble forecasting at NCEP and thebreeding methodrdquoMonthlyWeather Review vol 125 no 12 pp3297ndash3319 1997

[43] F Wu ldquoSeveral methods of creating stochastic numbers andapplicationsrdquo Journal on Numerical Methods and ComputerApplications vol 27 no 1 pp 48ndash51 2006 (Chinese)

12 Advances in Meteorology

[44] Y-H Shao and W-C Zhang ldquoApplication of statistical weightmatrix method in estimation of regional rainfallrdquo Advances inWater Science vol 20 no 6 pp 755ndash762 2009 (Chinese)

[45] X Y Song Y J Li H Y Yu et al ldquoApplication of quantitativeprecipitation estimation by radar to flood forecastrdquo EngineeringJournal of Wuhan University Engineering Edition vol 40 no 2pp 51ndash54 2007 (Chinese)

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Advances in Meteorology 5

Table 2 Comparison of calibration results among different methods UC is uncalibrated KLM is Kalman filter AVG is average calibrationOPT is optimum interpolation VAR is variational calibration and SWI is statistical weight integration

Method Statistic Storm event start date (yymmdd) Average050408 050429 050609 060411 060508 060627 060705 060726

UCAE (mm) 2735 2138 579 397 573 752 358 672 1026RE () 7002 4489 2306 1349 1413 2693 1178 3702 3017

Results (mm) 1171 2625 1932 3339 348 2042 2679 2488 2470

KLMAE (mm) 481 461 145 138 158 19 129 106 226RE () 1232 968 576 469 389 679 426 584 665

Results (mm) 3425 5224 2367 2804 3895 2605 2908 171 3117

AVGAE (mm) 422 522 12 2 314 52 117 203 302RE () 1081 1096 48 68 775 1859 386 1117 934

Results (mm) 3483 5285 2391 3142 3738 2275 292 1613 3106

OPTAE (mm) 411 427 132 036 079 147 116 01 170RE () 1052 896 525 124 194 527 381 057 470

Results (mm) 3495 519 2379 2906 3974 2647 2921 1805 3165

VARAE (mm) 411 426 132 005 032 147 105 016 159RE () 1053 894 527 018 078 527 347 088 442

Results (mm) 3495 5189 2379 2937 4021 2647 2931 18 3175

SWIAE (mm) 411 295 132 005 026 147 105 005 141RE () 1053 618 527 018 065 526 347 029 398

Results (mm) 3495 5058 2379 2937 4026 2647 2932 181 3161Measured (mm) 3906 4763 2511 2942 4053 2794 3037 1816 3228

powerful the statistics However the sample number is oftenvery limited and randomly chosen initial values do notperfectly match with the dynamical mode Although closeto actual weather at initial time the predicted results oftendeviate rapidly from the actual atmospheric condition due tothe adjustment of the mode itself [39] The Singular Vectormethod is better able to deal with many nonquantitativehypotheses in the data assimilation increase the numberof ensemble members and more easily capture the errorsgenerated by analysis It can also determine the direction ofthe fastest disturbance and have a better dispersion Disad-vantages of this method are that the components of errorsthat do not grow are ignored and the calculations are tedious[40 41]

The BGM proposed by Toth and Kalnay [38 42] wasdesigned to model how growing errors are bred and main-tained in a conventional analysis cycle through successiveuse of short-range forecasts with the bred modes offering anestimate of possible growing error fields in the analysis Thegrowth rate obtained by this method is better than that of theMonte Carlo method and even higher than the growth rateof the lagged average forecasting A formula for the specificperturbation is generated

119875 = 119878 times Rmse times Rand (10)

where 119875 is random perturbation field and 119878 is perturbationamplitude coefficient In order to make the disturbanceamplitude not too large 119878 is set equal to 1 Rmse is themean square error between themeasured rainfall and rainfallestimation from radar data assimilation Rand is a randomdistribution function which is evenly distributed between

minus1 and 1 where the equation [43] for producing a randomnumber that is uniformly distributed in [119886 119887] is

119909119894= 119886 + (119887 minus 119886) 119903

119894 (11)

where 119903119894is a uniformly distributed random number that

belongs to [0 1]Using the measured data of eight storm events from 19

rain gauge stations and radar estimations calibrated by theKLM method 100 sets of random perturbation field wereproduced for each event by the BGM of initial disturbanceThen 200 sets of disturbance for each event formed afterthe superposition and deduction of the perturbation fieldwere used as the input to the Xinanjiang hydrological modelFor the eight storm events this resulted in 1600 predictedhydrographs The influence of the propagation of rainfallinput error on runoff simulation was quantified using thethree previously described goodness-of-fit statistics

4 Results and Discussion

41 Evaluation of Methods of Assimilation of Radar RainfallData A comparison of uncalibrated and calibrated resultsof five kinds of assimilation methods for eight storm events(Table 2) revealed that among the methods the SWImethodproduced results closest to the observed data followed bythe VAR method with a mean absolute error smaller thanthat of the SWI method The next best method was the OPTmethod followed by the KLM method and finally the AVGmethod The average of the results across the eight stormevents (Table 2) allows a rapid comparison of the relativeperformances of the five assimilation methods

6 Advances in Meteorology

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(a)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(b)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(c)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(d)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(e)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(f)

Figure 2 Hourly gauged rainfall observations compared to radar-based estimations (a) uncalibrated classified Z-R data (b) Kalman filter(c) average calibration (d) optimum interpolation (e) variational calibration and (f) statistical weight integration

For AVG the accuracy of regional total precipitation esti-mation improved after calibration and the accuracy wouldimprove further with more rain gauges One problem withthe AVG method is that it does not account for the shiftinglocation of the focus of intense rainfall during storm eventsAVG cannot assign greater weight to points independentlyidentified to be of particular interest and it does not considerthe representativeness of the data derived by the automaticrain gauges and radar echoes These problems explain therelatively low performance of the AVG method

Variable terrain synoptic conditions and precipitationintensity impart a high degree of spatial and temporal

variability to radar rainfall data that presents a challengefor data assimilation The results indicated that the KLMmethod of data assimilation with its strong theoretical basisand consideration of the distribution of error in determiningthe calibration factor produced a better result than the AVGmethodTheKLMmethod can improve accuracy by reducingthe relative deviation and degree of dispersion betweenthe hyetometer and radar rainfall data and eliminating theintrusion of nonrainfall echoes from rainfall estimationThismethod calibrates the radar estimated rainfall distributionfield in the time domain rather than the spatial structureerror of precipitation which means it is more suitable for

Advances in Meteorology 7

the calibration of stable stratiform cloud precipitation andin places with low density of rain gauges These may be thekey factors that limit the calibration accuracy of the KLMmethod The spatial structure and distribution of rain cloudsare complicated and changeable with mixed convectiveprecipitation being a common phenomenon Under theseconditions the OPT and VAR methods which have similarresults (Table 2) outperform the KLM method This relativeperformance differencewould also apply in places with a highdensity of rain gauges While each precipitation calibrationmodel has its advantages depending on the conditions SWIcombines the advantages of the other four methods and givesan appropriate weighting after the calculation On this basisthe SWI method would be expected to be superior to theother data assimilationmethods tested here [44] and this wassupported by the results (Table 2)

Scatterplots of hourly gauged rainfall and uncalibratedand calibrated radar-based rainfall (Figure 2) illustrated thegood agreement between the rainfall distribution obtainedby the SWI method and gauged rainfall The VAR and OPTassimilation methods also performed well The KLM andAVG method produced noticeably poorer results (Figure 2)

42 HydrologicalModel for FloodHydrograph Prediction TheXinanjiang hydrological model was applied in the WhiteLotus River catchment taking into consideration temporaland spatial variation of rainfall and the nonlinear effects ofwatershed topography and river channel characteristics onthe runoff concentration and dispersed inflow and nonlin-ear convergence Model parameters were calibrated by themethod of Rosenbrock [45] The three indexes certaintyfactor peak relative error and peak time difference wereused to evaluate the flood forecasting results Goodness-of-fit statistics (Table 3) and simulated hydrographs (Figure 3)indicated that themethods of SWI OPT andVARwere supe-rior in producing rainfall input data for storm hydrographmodelling In particular the SWI simulated hydrographswere in almost perfect agreement with the observed dataTherainfall data generated by themethods of KLMAVG andUCled to unsatisfactory hydrograph prediction

43 Uncertainty Analysis of Hydrological Forecasting Therelative error of predicted results increased after assimilatedrainfall data were randomly disturbed compared with theundisturbed peak flow flood volume and peak time differ-ence The peak flow and flood volume were increased by 5and 8 respectively (Figures 4 and 5) which means thatthe model input errors increased when they were processedthrough the hydrological model Also most of the predictedpeak times lagged the observed times (Figure 6)

The error of precipitation input data in hydrologicalmodelling is a significant source of error in predicted peakflow flood volume and peak time Therefore the spreadof precipitation uncertainty has a great influence on runoffprediction In China practical applications usually adoptqualitative rainfall prediction and assumed rainfall inputand this would have implications for the forecast period andaccuracy of flood forecasting At present both the accuracyand resolution of rainfall forecasts provided by numerical

weather prediction (NWP) cannot meet the requirements ofquantitative flood forecasting and this situation may con-tinue to exist into the foreseeable future Weather radar andsatellite remote sensing (SRS) can perform an important rolein quantitative precipitation forecasting Use of precipitationforecasts obtained by SRS as the input of hydrological modelsto simulate and predict runoff warrants further researchattention This could be a key step towards improving theaccuracy of flood forecasting It will be necessary to developmethods for combining and assimilating the SRS data andobserved data from rain gauges for producing better precipi-tation forecasts SRS has sufficiently high spatial and temporalresolution to effectively characterize the instantaneous distri-bution of precipitation throughout a catchment while raingauges can provide high-precision single-point observations

The generation of floods is a complex and dynamicprocess Modelling this process can be improved through theuse of rainfall input data with high spatial and temporal reso-lution How to best make use of rainfall information availablefrom multiple sources including gauge networks radar andsatellite monitoring is one of the key problems to be solvedin hydrological modelling and forecasting

5 Conclusions

Because of the high level of risk posed by floods especiallyflash floods it is critical that warning procedures make useof accurate nowcasting and short-range runoff forecastingcapability Precipitation data is the most important input tohydrological models used for forecasting hydrographsWhilerainfall data is usually sourced from a network of gauges analternative is weather radar detector which offers superiorspatial and temporal resolution but at the cost of lowprecisionand accuracy This paper investigated methods of precip-itation data assimilation with the objective of improvingthe quality of radar-based rainfall estimates as a means ofachieving more reliable flood forecasts Using data from anetwork of rain gauges in the White Lotus River in HubeiProvince China and data from the weather radar detectorbased in nearby Wuhan five established methods of assimi-lating radar data estimated by the classified 119885-119877 relationshipwere applied The assimilated data was compared with theobserved rainfall data and then used in a hydrological modelto predict historical flood hydrographs Finally BGM wasused for the perturbation of radar data to evaluate the effectof the rainfall data input error on runoff simulationThemainconclusions arising from this work were as follows

(1) Statistical weight integration variational calibrationand optimum interpolation were superior methodsof data assimilation while Kalman filter and averagecalibration methods gave a less satisfactory result

(2) For modelling storm event hydrographs rainfall datagenerated by the statistical weight integration varia-tional calibration and optimum interpolation meth-ods resulted in hydrographs that were the closest fitto the gauged data Rainfall data generated by theaverage calibration and Kalman filter methods of dataassimilation resulted in unsatisfactory hydrographprediction

8 Advances in Meteorology

Table 3 Comparison of flood hydrograph prediction using different rainfall data assimilation methods MPF is measured peak flow and FPFis forecast peak flow

Method Flood event MPF (m3s) FPF (m3s) NS PRE () PTD (h)

UC

050408 3133 584 minus073 8136 1050429 6182 1676 minus105 7289 32050609 1879 968 minus047 4848 2060411 2327 157 minus087 3253 15060508 2409 1081 minus059 5513 10060627 1896 766 minus295 596 4060705 3109 1348 minus3 5664 1060726 1473 1134 02 2301 8

KLM

050408 3133 2756 083 1203 2050429 6182 5622 087 906 1050609 1879 1667 09 1128 1060411 2327 2147 09 774 1060508 2409 2241 09 697 1060627 1896 1685 084 1113 2060705 3109 2627 082 155 2060726 1473 1361 086 76 1

AVG

050408 3133 2833 079 958 1050429 6182 6515 086 539 5050609 1879 1551 088 1746 2060411 2327 1962 083 1569 0060508 2409 2122 085 1191 1060627 1896 1552 044 1814 4060705 3109 2505 065 1943 1060726 1473 1082 022 2654 0

OPT

050408 3133 3117 089 051 2050429 6182 6154 09 045 1050609 1879 1876 09 016 3060411 2327 2317 089 043 2060508 2409 2403 09 025 2060627 1896 1886 089 053 1060705 3109 3071 089 122 2060726 1473 1446 09 183 3

VAR

050408 3133 3133 09 054 0050429 6182 6182 091 036 0050609 1879 1879 089 085 1060411 2327 2327 09 116 2060508 2409 2409 09 023 1060627 1896 1896 089 063 1060705 3109 3109 089 121 2060726 1473 1473 074 047 0

SWI

050408 3133 3125 089 026 1050429 6182 6166 089 026 0050609 1879 1879 09 034 2060411 2327 2072 087 1096 1060508 2409 2406 089 012 0060627 1896 1886 089 053 1060705 3109 3072 089 119 1060726 1473 1468 09 034 2

Advances in Meteorology 9

P

M

UCKLM

AVGOPTVARSWI

16

12

8

4

0

P (m

m)

11 21 31 41 51 61 711t (h)

0

50

100

150

200

250

Q(m

3s

)

12

10

8

6

4

2

0

P (m

m)

40

30

20

10

0

P (m

m)

0

200

400

600

800

Q(m

3s

)

21 41 61 81 1011t (h)

20

15

10

5

0

P (m

m)

0

90

180

270

360

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

250

300

Q(m

3s

)

11 21 31 41 51 61 71 811t (h)

12

8

4

0

P (m

m)

0

50

100

150

200

Q(m

3s

)

18

15

12

9

6

3

0

P (m

m)

11 21 31 41 51 611t (h)

0

40

80

120

160

Q(m

3s

)

11 21 31 41 51 61 711t (h)

10

8

6

4

2

0

P (m

m)

0

70

140

210

280

350

Q(m

3s

)

11 21 31 41 51 61 711t (h)

28

21

14

7

0

P (m

m)

P

M

UCKLM

AVGOPTVARSWI

Figure 3 Comparison of simulated hydrographs for eight storm events using rainfall input data derived from five assimilation methods anduncalibrated radar data119872 is measured hydrograph

10 Advances in Meteorology

00

05

10

15

20

25

00 05 10 15 20Rainfall relative error

Relat

ive e

rror

of p

eak

flow

y = 10581x + 00146

R2 = 09126

Figure 4 Relationship between relative error in predicted floodpeak magnitude and rainfall relative error

00 05 10 15 20Rainfall relative error

00

05

10

15

20

25

Relat

ive e

rror

of fl

ood

volu

me

R2 = 09392

y = 10807x + 00201

Figure 5 Relationship between relative error in predicted flood vol-ume and rainfall relative error

(3) The random errors generated by model input had atendency to increase during the process of runningthe hydrological model Also most of predicted floodpeak times were lagged

(4) As hydrometeorology ensemble forecasts becomemore widely available and the data acquisition meth-ods develop there will be an ongoing need for evalu-ation of uncertainty in input data

(5) This paper provides critical descriptive analysis ofthe main assimilation methods and the effect of theerrors on uncertainty of flood forecasting It demon-strates that weather radar has potential to improvethe precision of hydrological forecasting which hasimplications for improved flood control and disas-ter mitigation The influence of the propagation ofrainfall input error on three simulated factors ofhydrological forecast is quantified

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

minus4

minus2

0

2

4

6

8

Peak

tim

e diff

eren

ce (h

)

05 10 15 2000Rainfall relative error

Figure 6 Relationship between error in predicted flood peak timeand rainfall relative error

Acknowledgments

This study was supported by the State Key Program ofNational Natural Science of China (no 51339004) andthe National Natural Science Foundation of China (no51279139)

References

[1] I Yucel A Onen K K Yilmaz and D J Gochis ldquoCalibrationand evaluation of a flood forecasting system utility of numericalweather prediction model data assimilation and satellite-basedrainfallrdquo Journal of Hydrology vol 523 pp 49ndash66 2015

[2] L P Zhang L Li A Z Ye et al ldquoContrast research on precisionof estimating regional precipitation with weather radar and raingaugerdquo Engineering Journal of Wuhan University EngineeringEdition vol 40 no 1 pp 1ndash5 2007 (Chinese)

[3] J Liu M Bray and D Han ldquoA study on WRF radar dataassimilation for hydrological rainfall predictionrdquoHydrology andEarth System Sciences vol 17 no 8 pp 3095ndash3110 2013

[4] I Maiello R Ferretti S Gentile et al ldquoImpact of radar dataassimilation for the simulation of a heavy rainfall case incentral Italy using WRF-3DVARrdquo Atmospheric MeasurementTechniques vol 7 no 9 pp 2919ndash2935 2014

[5] M Borga ldquoAccuracy of radar rainfall estimates for streamflowsimulationrdquo Journal of Hydrology vol 267 no 1-2 pp 26ndash392002

[6] Q Dai and D Han ldquoExploration of discrepancy between radarand gauge rainfall estimates driven by wind fieldsrdquo WaterResources Research vol 50 no 11 pp 8571ndash8588 2014

[7] F Giannoni J A Smith Y Zhang and G Roth ldquoHydrologicmodeling of extreme floods using radar rainfall estimatesrdquoAdvances in Water Resources vol 26 no 2 pp 195ndash203 2003

[8] Z Sokol ldquoUtilization of regression models for rainfall estimatesusing radar-derived rainfall data and rain gauge datardquo Journalof Hydrology vol 278 no 1ndash4 pp 144ndash152 2003

[9] C A Velasco-Forero D Sempere-Torres E F Cassiraga and JJaime Gomez-Hernandez ldquoA non-parametric automatic blend-ing methodology to estimate rainfall fields from rain gauge andradar datardquo Advances inWater Resources vol 32 no 7 pp 986ndash1002 2009

Advances in Meteorology 11

[10] X Sun R G Mein T D Keenan and J F Elliott ldquoFlood esti-mation using radar and raingauge datardquo Journal of Hydrologyvol 239 no 1ndash4 pp 4ndash18 2000

[11] J Z Sun ldquoConvective-scale assimilation of radar data progressand challengesrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 131 no 613 pp 3439ndash3463 2006

[12] X D Yu X P Yao T N Xiong et al The Principle and Appli-cation of Doppler Weather Radar China Meteorological PressBeijing China 2007

[13] M Borga E N Anagnostou and E Frank ldquoOn the use of real-time radar rainfall estimates for flood prediction in mountain-ous basinsrdquo Journal of Geophysical Research Atmospheres vol105 no 2 pp 2269ndash2280 2000

[14] H G Zhang S L Guo and X L He ldquoRecent advancement andprospect of hydrological forecasting uncertainty studyrdquo Journalof Shihezi University (Natural Science) vol 24 no 1 pp 15ndash212006 (Chinese)

[15] GVillarini andW F Krajewski ldquoReview of the different sourcesof uncertainty in single polarization radar-based estimates ofrainfallrdquo Surveys in Geophysics vol 31 no 1 pp 107ndash129 2010

[16] K Beven and A Binley ldquoThe future of distributed modelsmodel calibration and uncertainty predictionrdquo HydrologicalProcesses vol 6 no 3 pp 279ndash298 1992

[17] F Quintero D Sempere-Torres M Berenguer and E BaltasldquoA scenario-incorporating analysis of the propagation of uncer-tainty to flash flood simulationsrdquo Journal of Hydrology vol 460-461 pp 90ndash102 2012

[18] L Xiong andKMOrsquoConnor ldquoAn empiricalmethod to improvethe prediction limits of the GLUE methodology in rainfall-runoffmodelingrdquo Journal of Hydrology vol 349 no 1-2 pp 115ndash124 2008

[19] X R Yin J Xia and X Zhang ldquoRecent progress and prospectof the study on uncertainties in hydrologicalmodeling and fore-castingrdquoWater Power vol 32 no 10 pp 27ndash31 2006 (Chinese)

[20] D Zhu Y Xuan and I Cluckie ldquoHydrological appraisal ofoperational weather radar rainfall estimates in the context ofdifferent modelling structuresrdquo Hydrology and Earth SystemSciences vol 18 no 1 pp 257ndash272 2014

[21] A S Falck V Maggioni J Tomasella D A Vila and F LR Diniz ldquoPropagation of satellite precipitation uncertaintiesthrough a distributed hydrologic model a case study in theTocantins-Araguaia basin in Brazilrdquo Journal of Hydrology vol527 pp 943ndash957 2015

[22] P A Mendoza J McPhee and X Vargas ldquoUncertainty in floodforecasting a distributed modeling approach in a sparse datacatchmentrdquoWater Resources Research vol 48 no 9 Article IDW09532 2012

[23] V TWood R A Brown and S V Vasiloff ldquoImproved detectionusing negative elevation angles for mountaintop WSR-88DsPart II simulations of the three radars covering UtahrdquoWeatherand Forecasting vol 18 no 3 pp 393ndash403 2003

[24] T P Dai and D S Fu ldquoPrecision of precipitation amount in thejoint detection areas by weather radar and the auto-rain Gaugenetworkrdquo Journal of Nanjing Institute of Meteorology vol 13 no4 pp 592ndash597 1990 (Chinese)

[25] J W Wilson and E A Brandes ldquoRadar measurement ofrainfallmdasha summaryrdquo Bulletin of the American MeteorologicalSociety vol 60 no 9 pp 1048ndash1058 1979

[26] S Chumchean A Seed and A Sharma ldquoCorrecting of real-time radar rainfall bias using a Kalman filtering approachrdquoJournal of Hydrology vol 317 no 1-2 pp 123ndash137 2006

[27] M Costa and M Monteiro ldquoBias-correction of Kalman filterestimators associated to a linear state space model with esti-mated parametersrdquo Journal of Statistical Planning and Inferencevol 176 pp 22ndash32 2016

[28] S I Kako A Isobe and M Kubota ldquoHigh-resolution ASCATwind vector data set gridded by applying an optimum inter-polation method to the global oceanrdquo Journal of GeophysicalResearch Atmospheres vol 116 no 23 Article ID D23107 2011

[29] S Kako andMKubota ldquoRelationship between an ElNino eventand the interannual variability of significant wave heights in theNorth Pacificrdquo Atmosphere-Ocean vol 44 no 4 pp 377ndash3952006

[30] W Castaings D Dartus F-X Le Dimet and G-M SaulnierldquoSensitivity analysis and parameter estimation for distributedhydrological modeling potential of variational methodsrdquoHydrology and Earth System Sciences vol 13 no 4 pp 503ndash5172009

[31] P C Zhang T P Dai D S Fu et al ldquoPrinciple and accuracyof adjusting the area precipitation from digital weather radarthrough variational methodrdquo Atmospheric Science vol 16 no2 pp 248ndash256 1992 (Chinese)

[32] R-J Zhao ldquoThe Xinanjiang model applied in Chinardquo Journal ofHydrology vol 135 no 1ndash4 pp 371ndash381 1992

[33] A A Alazzy H S Lu and Y H Zhu ldquoAssessing the uncertaintyof the Xinanjiang rainfall-runoff model effect of the likelihoodfunction choice on the GLUE methodrdquo Journal of HydrologicEngineering vol 20 no 10 Article ID 04015016 2015

[34] J Liu X Chen J Zhang and M Flury ldquoCoupling the Xinan-jiangmodel to a kinematic flowmodel based on digital drainagenetworks for flood forecastingrdquo Hydrological Processes vol 23no 9 pp 1337ndash1348 2009

[35] C Zhang R-BWang andQ-XMeng ldquoCalibration of concep-tual rainfall-runoffmodels using global optimizationrdquoAdvancesin Meteorology vol 2015 Article ID 545376 12 pages 2015

[36] H Xu C-Y Xu N R Saeliglthun B Zhou and Y Xu ldquoEvaluationof reanalysis and satellite-based precipitation datasets in drivinghydrological models in a humid region of Southern ChinardquoStochastic Environmental Research and Risk Assessment vol 29no 8 pp 2003ndash2020 2015

[37] S S Meng X H Xie and X Yu ldquoTracing temporal changesof model parameters in rainfall-runoffmodeling via a real-timedata assimilationrdquoWater vol 8 no 1 article 19 2016

[38] Z Toth and E Kalnay ldquoEnsemble Forecasting at NMC thegeneration of perturbationsrdquo Bulletin of the American Meteoro-logical Society vol 74 no 12 pp 2317ndash2330 1993

[39] S LMullen andD P Baumhefner ldquoMonte Carlo simulations ofexplosive cyclogenesisrdquoMonthlyWeather Review vol 122 no 7pp 1548ndash1567 1994

[40] R Buizza and T N Palmer ldquoImpact of ensemble size onensemble predictionrdquo Monthly Weather Review vol 126 no 9pp 2503ndash2518 1998

[41] F Molteni R Buizza T N Palmer and T Petroliagis ldquoTheECMWF ensemble prediction system methodology and vali-dationrdquo Quarterly Journal of the Royal Meteorological Societyvol 122 no 529 pp 73ndash119 1996

[42] Z Toth and E Kalnay ldquoEnsemble forecasting at NCEP and thebreeding methodrdquoMonthlyWeather Review vol 125 no 12 pp3297ndash3319 1997

[43] F Wu ldquoSeveral methods of creating stochastic numbers andapplicationsrdquo Journal on Numerical Methods and ComputerApplications vol 27 no 1 pp 48ndash51 2006 (Chinese)

12 Advances in Meteorology

[44] Y-H Shao and W-C Zhang ldquoApplication of statistical weightmatrix method in estimation of regional rainfallrdquo Advances inWater Science vol 20 no 6 pp 755ndash762 2009 (Chinese)

[45] X Y Song Y J Li H Y Yu et al ldquoApplication of quantitativeprecipitation estimation by radar to flood forecastrdquo EngineeringJournal of Wuhan University Engineering Edition vol 40 no 2pp 51ndash54 2007 (Chinese)

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

6 Advances in Meteorology

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(a)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(b)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(c)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(d)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(e)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80Rain gauge observations (mmh)

Rada

r esti

mat

ions

(mm

h)

(f)

Figure 2 Hourly gauged rainfall observations compared to radar-based estimations (a) uncalibrated classified Z-R data (b) Kalman filter(c) average calibration (d) optimum interpolation (e) variational calibration and (f) statistical weight integration

For AVG the accuracy of regional total precipitation esti-mation improved after calibration and the accuracy wouldimprove further with more rain gauges One problem withthe AVG method is that it does not account for the shiftinglocation of the focus of intense rainfall during storm eventsAVG cannot assign greater weight to points independentlyidentified to be of particular interest and it does not considerthe representativeness of the data derived by the automaticrain gauges and radar echoes These problems explain therelatively low performance of the AVG method

Variable terrain synoptic conditions and precipitationintensity impart a high degree of spatial and temporal

variability to radar rainfall data that presents a challengefor data assimilation The results indicated that the KLMmethod of data assimilation with its strong theoretical basisand consideration of the distribution of error in determiningthe calibration factor produced a better result than the AVGmethodTheKLMmethod can improve accuracy by reducingthe relative deviation and degree of dispersion betweenthe hyetometer and radar rainfall data and eliminating theintrusion of nonrainfall echoes from rainfall estimationThismethod calibrates the radar estimated rainfall distributionfield in the time domain rather than the spatial structureerror of precipitation which means it is more suitable for

Advances in Meteorology 7

the calibration of stable stratiform cloud precipitation andin places with low density of rain gauges These may be thekey factors that limit the calibration accuracy of the KLMmethod The spatial structure and distribution of rain cloudsare complicated and changeable with mixed convectiveprecipitation being a common phenomenon Under theseconditions the OPT and VAR methods which have similarresults (Table 2) outperform the KLM method This relativeperformance differencewould also apply in places with a highdensity of rain gauges While each precipitation calibrationmodel has its advantages depending on the conditions SWIcombines the advantages of the other four methods and givesan appropriate weighting after the calculation On this basisthe SWI method would be expected to be superior to theother data assimilationmethods tested here [44] and this wassupported by the results (Table 2)

Scatterplots of hourly gauged rainfall and uncalibratedand calibrated radar-based rainfall (Figure 2) illustrated thegood agreement between the rainfall distribution obtainedby the SWI method and gauged rainfall The VAR and OPTassimilation methods also performed well The KLM andAVG method produced noticeably poorer results (Figure 2)

42 HydrologicalModel for FloodHydrograph Prediction TheXinanjiang hydrological model was applied in the WhiteLotus River catchment taking into consideration temporaland spatial variation of rainfall and the nonlinear effects ofwatershed topography and river channel characteristics onthe runoff concentration and dispersed inflow and nonlin-ear convergence Model parameters were calibrated by themethod of Rosenbrock [45] The three indexes certaintyfactor peak relative error and peak time difference wereused to evaluate the flood forecasting results Goodness-of-fit statistics (Table 3) and simulated hydrographs (Figure 3)indicated that themethods of SWI OPT andVARwere supe-rior in producing rainfall input data for storm hydrographmodelling In particular the SWI simulated hydrographswere in almost perfect agreement with the observed dataTherainfall data generated by themethods of KLMAVG andUCled to unsatisfactory hydrograph prediction

43 Uncertainty Analysis of Hydrological Forecasting Therelative error of predicted results increased after assimilatedrainfall data were randomly disturbed compared with theundisturbed peak flow flood volume and peak time differ-ence The peak flow and flood volume were increased by 5and 8 respectively (Figures 4 and 5) which means thatthe model input errors increased when they were processedthrough the hydrological model Also most of the predictedpeak times lagged the observed times (Figure 6)

The error of precipitation input data in hydrologicalmodelling is a significant source of error in predicted peakflow flood volume and peak time Therefore the spreadof precipitation uncertainty has a great influence on runoffprediction In China practical applications usually adoptqualitative rainfall prediction and assumed rainfall inputand this would have implications for the forecast period andaccuracy of flood forecasting At present both the accuracyand resolution of rainfall forecasts provided by numerical

weather prediction (NWP) cannot meet the requirements ofquantitative flood forecasting and this situation may con-tinue to exist into the foreseeable future Weather radar andsatellite remote sensing (SRS) can perform an important rolein quantitative precipitation forecasting Use of precipitationforecasts obtained by SRS as the input of hydrological modelsto simulate and predict runoff warrants further researchattention This could be a key step towards improving theaccuracy of flood forecasting It will be necessary to developmethods for combining and assimilating the SRS data andobserved data from rain gauges for producing better precipi-tation forecasts SRS has sufficiently high spatial and temporalresolution to effectively characterize the instantaneous distri-bution of precipitation throughout a catchment while raingauges can provide high-precision single-point observations

The generation of floods is a complex and dynamicprocess Modelling this process can be improved through theuse of rainfall input data with high spatial and temporal reso-lution How to best make use of rainfall information availablefrom multiple sources including gauge networks radar andsatellite monitoring is one of the key problems to be solvedin hydrological modelling and forecasting

5 Conclusions

Because of the high level of risk posed by floods especiallyflash floods it is critical that warning procedures make useof accurate nowcasting and short-range runoff forecastingcapability Precipitation data is the most important input tohydrological models used for forecasting hydrographsWhilerainfall data is usually sourced from a network of gauges analternative is weather radar detector which offers superiorspatial and temporal resolution but at the cost of lowprecisionand accuracy This paper investigated methods of precip-itation data assimilation with the objective of improvingthe quality of radar-based rainfall estimates as a means ofachieving more reliable flood forecasts Using data from anetwork of rain gauges in the White Lotus River in HubeiProvince China and data from the weather radar detectorbased in nearby Wuhan five established methods of assimi-lating radar data estimated by the classified 119885-119877 relationshipwere applied The assimilated data was compared with theobserved rainfall data and then used in a hydrological modelto predict historical flood hydrographs Finally BGM wasused for the perturbation of radar data to evaluate the effectof the rainfall data input error on runoff simulationThemainconclusions arising from this work were as follows

(1) Statistical weight integration variational calibrationand optimum interpolation were superior methodsof data assimilation while Kalman filter and averagecalibration methods gave a less satisfactory result

(2) For modelling storm event hydrographs rainfall datagenerated by the statistical weight integration varia-tional calibration and optimum interpolation meth-ods resulted in hydrographs that were the closest fitto the gauged data Rainfall data generated by theaverage calibration and Kalman filter methods of dataassimilation resulted in unsatisfactory hydrographprediction

8 Advances in Meteorology

Table 3 Comparison of flood hydrograph prediction using different rainfall data assimilation methods MPF is measured peak flow and FPFis forecast peak flow

Method Flood event MPF (m3s) FPF (m3s) NS PRE () PTD (h)

UC

050408 3133 584 minus073 8136 1050429 6182 1676 minus105 7289 32050609 1879 968 minus047 4848 2060411 2327 157 minus087 3253 15060508 2409 1081 minus059 5513 10060627 1896 766 minus295 596 4060705 3109 1348 minus3 5664 1060726 1473 1134 02 2301 8

KLM

050408 3133 2756 083 1203 2050429 6182 5622 087 906 1050609 1879 1667 09 1128 1060411 2327 2147 09 774 1060508 2409 2241 09 697 1060627 1896 1685 084 1113 2060705 3109 2627 082 155 2060726 1473 1361 086 76 1

AVG

050408 3133 2833 079 958 1050429 6182 6515 086 539 5050609 1879 1551 088 1746 2060411 2327 1962 083 1569 0060508 2409 2122 085 1191 1060627 1896 1552 044 1814 4060705 3109 2505 065 1943 1060726 1473 1082 022 2654 0

OPT

050408 3133 3117 089 051 2050429 6182 6154 09 045 1050609 1879 1876 09 016 3060411 2327 2317 089 043 2060508 2409 2403 09 025 2060627 1896 1886 089 053 1060705 3109 3071 089 122 2060726 1473 1446 09 183 3

VAR

050408 3133 3133 09 054 0050429 6182 6182 091 036 0050609 1879 1879 089 085 1060411 2327 2327 09 116 2060508 2409 2409 09 023 1060627 1896 1896 089 063 1060705 3109 3109 089 121 2060726 1473 1473 074 047 0

SWI

050408 3133 3125 089 026 1050429 6182 6166 089 026 0050609 1879 1879 09 034 2060411 2327 2072 087 1096 1060508 2409 2406 089 012 0060627 1896 1886 089 053 1060705 3109 3072 089 119 1060726 1473 1468 09 034 2

Advances in Meteorology 9

P

M

UCKLM

AVGOPTVARSWI

16

12

8

4

0

P (m

m)

11 21 31 41 51 61 711t (h)

0

50

100

150

200

250

Q(m

3s

)

12

10

8

6

4

2

0

P (m

m)

40

30

20

10

0

P (m

m)

0

200

400

600

800

Q(m

3s

)

21 41 61 81 1011t (h)

20

15

10

5

0

P (m

m)

0

90

180

270

360

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

250

300

Q(m

3s

)

11 21 31 41 51 61 71 811t (h)

12

8

4

0

P (m

m)

0

50

100

150

200

Q(m

3s

)

18

15

12

9

6

3

0

P (m

m)

11 21 31 41 51 611t (h)

0

40

80

120

160

Q(m

3s

)

11 21 31 41 51 61 711t (h)

10

8

6

4

2

0

P (m

m)

0

70

140

210

280

350

Q(m

3s

)

11 21 31 41 51 61 711t (h)

28

21

14

7

0

P (m

m)

P

M

UCKLM

AVGOPTVARSWI

Figure 3 Comparison of simulated hydrographs for eight storm events using rainfall input data derived from five assimilation methods anduncalibrated radar data119872 is measured hydrograph

10 Advances in Meteorology

00

05

10

15

20

25

00 05 10 15 20Rainfall relative error

Relat

ive e

rror

of p

eak

flow

y = 10581x + 00146

R2 = 09126

Figure 4 Relationship between relative error in predicted floodpeak magnitude and rainfall relative error

00 05 10 15 20Rainfall relative error

00

05

10

15

20

25

Relat

ive e

rror

of fl

ood

volu

me

R2 = 09392

y = 10807x + 00201

Figure 5 Relationship between relative error in predicted flood vol-ume and rainfall relative error

(3) The random errors generated by model input had atendency to increase during the process of runningthe hydrological model Also most of predicted floodpeak times were lagged

(4) As hydrometeorology ensemble forecasts becomemore widely available and the data acquisition meth-ods develop there will be an ongoing need for evalu-ation of uncertainty in input data

(5) This paper provides critical descriptive analysis ofthe main assimilation methods and the effect of theerrors on uncertainty of flood forecasting It demon-strates that weather radar has potential to improvethe precision of hydrological forecasting which hasimplications for improved flood control and disas-ter mitigation The influence of the propagation ofrainfall input error on three simulated factors ofhydrological forecast is quantified

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

minus4

minus2

0

2

4

6

8

Peak

tim

e diff

eren

ce (h

)

05 10 15 2000Rainfall relative error

Figure 6 Relationship between error in predicted flood peak timeand rainfall relative error

Acknowledgments

This study was supported by the State Key Program ofNational Natural Science of China (no 51339004) andthe National Natural Science Foundation of China (no51279139)

References

[1] I Yucel A Onen K K Yilmaz and D J Gochis ldquoCalibrationand evaluation of a flood forecasting system utility of numericalweather prediction model data assimilation and satellite-basedrainfallrdquo Journal of Hydrology vol 523 pp 49ndash66 2015

[2] L P Zhang L Li A Z Ye et al ldquoContrast research on precisionof estimating regional precipitation with weather radar and raingaugerdquo Engineering Journal of Wuhan University EngineeringEdition vol 40 no 1 pp 1ndash5 2007 (Chinese)

[3] J Liu M Bray and D Han ldquoA study on WRF radar dataassimilation for hydrological rainfall predictionrdquoHydrology andEarth System Sciences vol 17 no 8 pp 3095ndash3110 2013

[4] I Maiello R Ferretti S Gentile et al ldquoImpact of radar dataassimilation for the simulation of a heavy rainfall case incentral Italy using WRF-3DVARrdquo Atmospheric MeasurementTechniques vol 7 no 9 pp 2919ndash2935 2014

[5] M Borga ldquoAccuracy of radar rainfall estimates for streamflowsimulationrdquo Journal of Hydrology vol 267 no 1-2 pp 26ndash392002

[6] Q Dai and D Han ldquoExploration of discrepancy between radarand gauge rainfall estimates driven by wind fieldsrdquo WaterResources Research vol 50 no 11 pp 8571ndash8588 2014

[7] F Giannoni J A Smith Y Zhang and G Roth ldquoHydrologicmodeling of extreme floods using radar rainfall estimatesrdquoAdvances in Water Resources vol 26 no 2 pp 195ndash203 2003

[8] Z Sokol ldquoUtilization of regression models for rainfall estimatesusing radar-derived rainfall data and rain gauge datardquo Journalof Hydrology vol 278 no 1ndash4 pp 144ndash152 2003

[9] C A Velasco-Forero D Sempere-Torres E F Cassiraga and JJaime Gomez-Hernandez ldquoA non-parametric automatic blend-ing methodology to estimate rainfall fields from rain gauge andradar datardquo Advances inWater Resources vol 32 no 7 pp 986ndash1002 2009

Advances in Meteorology 11

[10] X Sun R G Mein T D Keenan and J F Elliott ldquoFlood esti-mation using radar and raingauge datardquo Journal of Hydrologyvol 239 no 1ndash4 pp 4ndash18 2000

[11] J Z Sun ldquoConvective-scale assimilation of radar data progressand challengesrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 131 no 613 pp 3439ndash3463 2006

[12] X D Yu X P Yao T N Xiong et al The Principle and Appli-cation of Doppler Weather Radar China Meteorological PressBeijing China 2007

[13] M Borga E N Anagnostou and E Frank ldquoOn the use of real-time radar rainfall estimates for flood prediction in mountain-ous basinsrdquo Journal of Geophysical Research Atmospheres vol105 no 2 pp 2269ndash2280 2000

[14] H G Zhang S L Guo and X L He ldquoRecent advancement andprospect of hydrological forecasting uncertainty studyrdquo Journalof Shihezi University (Natural Science) vol 24 no 1 pp 15ndash212006 (Chinese)

[15] GVillarini andW F Krajewski ldquoReview of the different sourcesof uncertainty in single polarization radar-based estimates ofrainfallrdquo Surveys in Geophysics vol 31 no 1 pp 107ndash129 2010

[16] K Beven and A Binley ldquoThe future of distributed modelsmodel calibration and uncertainty predictionrdquo HydrologicalProcesses vol 6 no 3 pp 279ndash298 1992

[17] F Quintero D Sempere-Torres M Berenguer and E BaltasldquoA scenario-incorporating analysis of the propagation of uncer-tainty to flash flood simulationsrdquo Journal of Hydrology vol 460-461 pp 90ndash102 2012

[18] L Xiong andKMOrsquoConnor ldquoAn empiricalmethod to improvethe prediction limits of the GLUE methodology in rainfall-runoffmodelingrdquo Journal of Hydrology vol 349 no 1-2 pp 115ndash124 2008

[19] X R Yin J Xia and X Zhang ldquoRecent progress and prospectof the study on uncertainties in hydrologicalmodeling and fore-castingrdquoWater Power vol 32 no 10 pp 27ndash31 2006 (Chinese)

[20] D Zhu Y Xuan and I Cluckie ldquoHydrological appraisal ofoperational weather radar rainfall estimates in the context ofdifferent modelling structuresrdquo Hydrology and Earth SystemSciences vol 18 no 1 pp 257ndash272 2014

[21] A S Falck V Maggioni J Tomasella D A Vila and F LR Diniz ldquoPropagation of satellite precipitation uncertaintiesthrough a distributed hydrologic model a case study in theTocantins-Araguaia basin in Brazilrdquo Journal of Hydrology vol527 pp 943ndash957 2015

[22] P A Mendoza J McPhee and X Vargas ldquoUncertainty in floodforecasting a distributed modeling approach in a sparse datacatchmentrdquoWater Resources Research vol 48 no 9 Article IDW09532 2012

[23] V TWood R A Brown and S V Vasiloff ldquoImproved detectionusing negative elevation angles for mountaintop WSR-88DsPart II simulations of the three radars covering UtahrdquoWeatherand Forecasting vol 18 no 3 pp 393ndash403 2003

[24] T P Dai and D S Fu ldquoPrecision of precipitation amount in thejoint detection areas by weather radar and the auto-rain Gaugenetworkrdquo Journal of Nanjing Institute of Meteorology vol 13 no4 pp 592ndash597 1990 (Chinese)

[25] J W Wilson and E A Brandes ldquoRadar measurement ofrainfallmdasha summaryrdquo Bulletin of the American MeteorologicalSociety vol 60 no 9 pp 1048ndash1058 1979

[26] S Chumchean A Seed and A Sharma ldquoCorrecting of real-time radar rainfall bias using a Kalman filtering approachrdquoJournal of Hydrology vol 317 no 1-2 pp 123ndash137 2006

[27] M Costa and M Monteiro ldquoBias-correction of Kalman filterestimators associated to a linear state space model with esti-mated parametersrdquo Journal of Statistical Planning and Inferencevol 176 pp 22ndash32 2016

[28] S I Kako A Isobe and M Kubota ldquoHigh-resolution ASCATwind vector data set gridded by applying an optimum inter-polation method to the global oceanrdquo Journal of GeophysicalResearch Atmospheres vol 116 no 23 Article ID D23107 2011

[29] S Kako andMKubota ldquoRelationship between an ElNino eventand the interannual variability of significant wave heights in theNorth Pacificrdquo Atmosphere-Ocean vol 44 no 4 pp 377ndash3952006

[30] W Castaings D Dartus F-X Le Dimet and G-M SaulnierldquoSensitivity analysis and parameter estimation for distributedhydrological modeling potential of variational methodsrdquoHydrology and Earth System Sciences vol 13 no 4 pp 503ndash5172009

[31] P C Zhang T P Dai D S Fu et al ldquoPrinciple and accuracyof adjusting the area precipitation from digital weather radarthrough variational methodrdquo Atmospheric Science vol 16 no2 pp 248ndash256 1992 (Chinese)

[32] R-J Zhao ldquoThe Xinanjiang model applied in Chinardquo Journal ofHydrology vol 135 no 1ndash4 pp 371ndash381 1992

[33] A A Alazzy H S Lu and Y H Zhu ldquoAssessing the uncertaintyof the Xinanjiang rainfall-runoff model effect of the likelihoodfunction choice on the GLUE methodrdquo Journal of HydrologicEngineering vol 20 no 10 Article ID 04015016 2015

[34] J Liu X Chen J Zhang and M Flury ldquoCoupling the Xinan-jiangmodel to a kinematic flowmodel based on digital drainagenetworks for flood forecastingrdquo Hydrological Processes vol 23no 9 pp 1337ndash1348 2009

[35] C Zhang R-BWang andQ-XMeng ldquoCalibration of concep-tual rainfall-runoffmodels using global optimizationrdquoAdvancesin Meteorology vol 2015 Article ID 545376 12 pages 2015

[36] H Xu C-Y Xu N R Saeliglthun B Zhou and Y Xu ldquoEvaluationof reanalysis and satellite-based precipitation datasets in drivinghydrological models in a humid region of Southern ChinardquoStochastic Environmental Research and Risk Assessment vol 29no 8 pp 2003ndash2020 2015

[37] S S Meng X H Xie and X Yu ldquoTracing temporal changesof model parameters in rainfall-runoffmodeling via a real-timedata assimilationrdquoWater vol 8 no 1 article 19 2016

[38] Z Toth and E Kalnay ldquoEnsemble Forecasting at NMC thegeneration of perturbationsrdquo Bulletin of the American Meteoro-logical Society vol 74 no 12 pp 2317ndash2330 1993

[39] S LMullen andD P Baumhefner ldquoMonte Carlo simulations ofexplosive cyclogenesisrdquoMonthlyWeather Review vol 122 no 7pp 1548ndash1567 1994

[40] R Buizza and T N Palmer ldquoImpact of ensemble size onensemble predictionrdquo Monthly Weather Review vol 126 no 9pp 2503ndash2518 1998

[41] F Molteni R Buizza T N Palmer and T Petroliagis ldquoTheECMWF ensemble prediction system methodology and vali-dationrdquo Quarterly Journal of the Royal Meteorological Societyvol 122 no 529 pp 73ndash119 1996

[42] Z Toth and E Kalnay ldquoEnsemble forecasting at NCEP and thebreeding methodrdquoMonthlyWeather Review vol 125 no 12 pp3297ndash3319 1997

[43] F Wu ldquoSeveral methods of creating stochastic numbers andapplicationsrdquo Journal on Numerical Methods and ComputerApplications vol 27 no 1 pp 48ndash51 2006 (Chinese)

12 Advances in Meteorology

[44] Y-H Shao and W-C Zhang ldquoApplication of statistical weightmatrix method in estimation of regional rainfallrdquo Advances inWater Science vol 20 no 6 pp 755ndash762 2009 (Chinese)

[45] X Y Song Y J Li H Y Yu et al ldquoApplication of quantitativeprecipitation estimation by radar to flood forecastrdquo EngineeringJournal of Wuhan University Engineering Edition vol 40 no 2pp 51ndash54 2007 (Chinese)

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Advances in Meteorology 7

the calibration of stable stratiform cloud precipitation andin places with low density of rain gauges These may be thekey factors that limit the calibration accuracy of the KLMmethod The spatial structure and distribution of rain cloudsare complicated and changeable with mixed convectiveprecipitation being a common phenomenon Under theseconditions the OPT and VAR methods which have similarresults (Table 2) outperform the KLM method This relativeperformance differencewould also apply in places with a highdensity of rain gauges While each precipitation calibrationmodel has its advantages depending on the conditions SWIcombines the advantages of the other four methods and givesan appropriate weighting after the calculation On this basisthe SWI method would be expected to be superior to theother data assimilationmethods tested here [44] and this wassupported by the results (Table 2)

Scatterplots of hourly gauged rainfall and uncalibratedand calibrated radar-based rainfall (Figure 2) illustrated thegood agreement between the rainfall distribution obtainedby the SWI method and gauged rainfall The VAR and OPTassimilation methods also performed well The KLM andAVG method produced noticeably poorer results (Figure 2)

42 HydrologicalModel for FloodHydrograph Prediction TheXinanjiang hydrological model was applied in the WhiteLotus River catchment taking into consideration temporaland spatial variation of rainfall and the nonlinear effects ofwatershed topography and river channel characteristics onthe runoff concentration and dispersed inflow and nonlin-ear convergence Model parameters were calibrated by themethod of Rosenbrock [45] The three indexes certaintyfactor peak relative error and peak time difference wereused to evaluate the flood forecasting results Goodness-of-fit statistics (Table 3) and simulated hydrographs (Figure 3)indicated that themethods of SWI OPT andVARwere supe-rior in producing rainfall input data for storm hydrographmodelling In particular the SWI simulated hydrographswere in almost perfect agreement with the observed dataTherainfall data generated by themethods of KLMAVG andUCled to unsatisfactory hydrograph prediction

43 Uncertainty Analysis of Hydrological Forecasting Therelative error of predicted results increased after assimilatedrainfall data were randomly disturbed compared with theundisturbed peak flow flood volume and peak time differ-ence The peak flow and flood volume were increased by 5and 8 respectively (Figures 4 and 5) which means thatthe model input errors increased when they were processedthrough the hydrological model Also most of the predictedpeak times lagged the observed times (Figure 6)

The error of precipitation input data in hydrologicalmodelling is a significant source of error in predicted peakflow flood volume and peak time Therefore the spreadof precipitation uncertainty has a great influence on runoffprediction In China practical applications usually adoptqualitative rainfall prediction and assumed rainfall inputand this would have implications for the forecast period andaccuracy of flood forecasting At present both the accuracyand resolution of rainfall forecasts provided by numerical

weather prediction (NWP) cannot meet the requirements ofquantitative flood forecasting and this situation may con-tinue to exist into the foreseeable future Weather radar andsatellite remote sensing (SRS) can perform an important rolein quantitative precipitation forecasting Use of precipitationforecasts obtained by SRS as the input of hydrological modelsto simulate and predict runoff warrants further researchattention This could be a key step towards improving theaccuracy of flood forecasting It will be necessary to developmethods for combining and assimilating the SRS data andobserved data from rain gauges for producing better precipi-tation forecasts SRS has sufficiently high spatial and temporalresolution to effectively characterize the instantaneous distri-bution of precipitation throughout a catchment while raingauges can provide high-precision single-point observations

The generation of floods is a complex and dynamicprocess Modelling this process can be improved through theuse of rainfall input data with high spatial and temporal reso-lution How to best make use of rainfall information availablefrom multiple sources including gauge networks radar andsatellite monitoring is one of the key problems to be solvedin hydrological modelling and forecasting

5 Conclusions

Because of the high level of risk posed by floods especiallyflash floods it is critical that warning procedures make useof accurate nowcasting and short-range runoff forecastingcapability Precipitation data is the most important input tohydrological models used for forecasting hydrographsWhilerainfall data is usually sourced from a network of gauges analternative is weather radar detector which offers superiorspatial and temporal resolution but at the cost of lowprecisionand accuracy This paper investigated methods of precip-itation data assimilation with the objective of improvingthe quality of radar-based rainfall estimates as a means ofachieving more reliable flood forecasts Using data from anetwork of rain gauges in the White Lotus River in HubeiProvince China and data from the weather radar detectorbased in nearby Wuhan five established methods of assimi-lating radar data estimated by the classified 119885-119877 relationshipwere applied The assimilated data was compared with theobserved rainfall data and then used in a hydrological modelto predict historical flood hydrographs Finally BGM wasused for the perturbation of radar data to evaluate the effectof the rainfall data input error on runoff simulationThemainconclusions arising from this work were as follows

(1) Statistical weight integration variational calibrationand optimum interpolation were superior methodsof data assimilation while Kalman filter and averagecalibration methods gave a less satisfactory result

(2) For modelling storm event hydrographs rainfall datagenerated by the statistical weight integration varia-tional calibration and optimum interpolation meth-ods resulted in hydrographs that were the closest fitto the gauged data Rainfall data generated by theaverage calibration and Kalman filter methods of dataassimilation resulted in unsatisfactory hydrographprediction

8 Advances in Meteorology

Table 3 Comparison of flood hydrograph prediction using different rainfall data assimilation methods MPF is measured peak flow and FPFis forecast peak flow

Method Flood event MPF (m3s) FPF (m3s) NS PRE () PTD (h)

UC

050408 3133 584 minus073 8136 1050429 6182 1676 minus105 7289 32050609 1879 968 minus047 4848 2060411 2327 157 minus087 3253 15060508 2409 1081 minus059 5513 10060627 1896 766 minus295 596 4060705 3109 1348 minus3 5664 1060726 1473 1134 02 2301 8

KLM

050408 3133 2756 083 1203 2050429 6182 5622 087 906 1050609 1879 1667 09 1128 1060411 2327 2147 09 774 1060508 2409 2241 09 697 1060627 1896 1685 084 1113 2060705 3109 2627 082 155 2060726 1473 1361 086 76 1

AVG

050408 3133 2833 079 958 1050429 6182 6515 086 539 5050609 1879 1551 088 1746 2060411 2327 1962 083 1569 0060508 2409 2122 085 1191 1060627 1896 1552 044 1814 4060705 3109 2505 065 1943 1060726 1473 1082 022 2654 0

OPT

050408 3133 3117 089 051 2050429 6182 6154 09 045 1050609 1879 1876 09 016 3060411 2327 2317 089 043 2060508 2409 2403 09 025 2060627 1896 1886 089 053 1060705 3109 3071 089 122 2060726 1473 1446 09 183 3

VAR

050408 3133 3133 09 054 0050429 6182 6182 091 036 0050609 1879 1879 089 085 1060411 2327 2327 09 116 2060508 2409 2409 09 023 1060627 1896 1896 089 063 1060705 3109 3109 089 121 2060726 1473 1473 074 047 0

SWI

050408 3133 3125 089 026 1050429 6182 6166 089 026 0050609 1879 1879 09 034 2060411 2327 2072 087 1096 1060508 2409 2406 089 012 0060627 1896 1886 089 053 1060705 3109 3072 089 119 1060726 1473 1468 09 034 2

Advances in Meteorology 9

P

M

UCKLM

AVGOPTVARSWI

16

12

8

4

0

P (m

m)

11 21 31 41 51 61 711t (h)

0

50

100

150

200

250

Q(m

3s

)

12

10

8

6

4

2

0

P (m

m)

40

30

20

10

0

P (m

m)

0

200

400

600

800

Q(m

3s

)

21 41 61 81 1011t (h)

20

15

10

5

0

P (m

m)

0

90

180

270

360

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

250

300

Q(m

3s

)

11 21 31 41 51 61 71 811t (h)

12

8

4

0

P (m

m)

0

50

100

150

200

Q(m

3s

)

18

15

12

9

6

3

0

P (m

m)

11 21 31 41 51 611t (h)

0

40

80

120

160

Q(m

3s

)

11 21 31 41 51 61 711t (h)

10

8

6

4

2

0

P (m

m)

0

70

140

210

280

350

Q(m

3s

)

11 21 31 41 51 61 711t (h)

28

21

14

7

0

P (m

m)

P

M

UCKLM

AVGOPTVARSWI

Figure 3 Comparison of simulated hydrographs for eight storm events using rainfall input data derived from five assimilation methods anduncalibrated radar data119872 is measured hydrograph

10 Advances in Meteorology

00

05

10

15

20

25

00 05 10 15 20Rainfall relative error

Relat

ive e

rror

of p

eak

flow

y = 10581x + 00146

R2 = 09126

Figure 4 Relationship between relative error in predicted floodpeak magnitude and rainfall relative error

00 05 10 15 20Rainfall relative error

00

05

10

15

20

25

Relat

ive e

rror

of fl

ood

volu

me

R2 = 09392

y = 10807x + 00201

Figure 5 Relationship between relative error in predicted flood vol-ume and rainfall relative error

(3) The random errors generated by model input had atendency to increase during the process of runningthe hydrological model Also most of predicted floodpeak times were lagged

(4) As hydrometeorology ensemble forecasts becomemore widely available and the data acquisition meth-ods develop there will be an ongoing need for evalu-ation of uncertainty in input data

(5) This paper provides critical descriptive analysis ofthe main assimilation methods and the effect of theerrors on uncertainty of flood forecasting It demon-strates that weather radar has potential to improvethe precision of hydrological forecasting which hasimplications for improved flood control and disas-ter mitigation The influence of the propagation ofrainfall input error on three simulated factors ofhydrological forecast is quantified

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

minus4

minus2

0

2

4

6

8

Peak

tim

e diff

eren

ce (h

)

05 10 15 2000Rainfall relative error

Figure 6 Relationship between error in predicted flood peak timeand rainfall relative error

Acknowledgments

This study was supported by the State Key Program ofNational Natural Science of China (no 51339004) andthe National Natural Science Foundation of China (no51279139)

References

[1] I Yucel A Onen K K Yilmaz and D J Gochis ldquoCalibrationand evaluation of a flood forecasting system utility of numericalweather prediction model data assimilation and satellite-basedrainfallrdquo Journal of Hydrology vol 523 pp 49ndash66 2015

[2] L P Zhang L Li A Z Ye et al ldquoContrast research on precisionof estimating regional precipitation with weather radar and raingaugerdquo Engineering Journal of Wuhan University EngineeringEdition vol 40 no 1 pp 1ndash5 2007 (Chinese)

[3] J Liu M Bray and D Han ldquoA study on WRF radar dataassimilation for hydrological rainfall predictionrdquoHydrology andEarth System Sciences vol 17 no 8 pp 3095ndash3110 2013

[4] I Maiello R Ferretti S Gentile et al ldquoImpact of radar dataassimilation for the simulation of a heavy rainfall case incentral Italy using WRF-3DVARrdquo Atmospheric MeasurementTechniques vol 7 no 9 pp 2919ndash2935 2014

[5] M Borga ldquoAccuracy of radar rainfall estimates for streamflowsimulationrdquo Journal of Hydrology vol 267 no 1-2 pp 26ndash392002

[6] Q Dai and D Han ldquoExploration of discrepancy between radarand gauge rainfall estimates driven by wind fieldsrdquo WaterResources Research vol 50 no 11 pp 8571ndash8588 2014

[7] F Giannoni J A Smith Y Zhang and G Roth ldquoHydrologicmodeling of extreme floods using radar rainfall estimatesrdquoAdvances in Water Resources vol 26 no 2 pp 195ndash203 2003

[8] Z Sokol ldquoUtilization of regression models for rainfall estimatesusing radar-derived rainfall data and rain gauge datardquo Journalof Hydrology vol 278 no 1ndash4 pp 144ndash152 2003

[9] C A Velasco-Forero D Sempere-Torres E F Cassiraga and JJaime Gomez-Hernandez ldquoA non-parametric automatic blend-ing methodology to estimate rainfall fields from rain gauge andradar datardquo Advances inWater Resources vol 32 no 7 pp 986ndash1002 2009

Advances in Meteorology 11

[10] X Sun R G Mein T D Keenan and J F Elliott ldquoFlood esti-mation using radar and raingauge datardquo Journal of Hydrologyvol 239 no 1ndash4 pp 4ndash18 2000

[11] J Z Sun ldquoConvective-scale assimilation of radar data progressand challengesrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 131 no 613 pp 3439ndash3463 2006

[12] X D Yu X P Yao T N Xiong et al The Principle and Appli-cation of Doppler Weather Radar China Meteorological PressBeijing China 2007

[13] M Borga E N Anagnostou and E Frank ldquoOn the use of real-time radar rainfall estimates for flood prediction in mountain-ous basinsrdquo Journal of Geophysical Research Atmospheres vol105 no 2 pp 2269ndash2280 2000

[14] H G Zhang S L Guo and X L He ldquoRecent advancement andprospect of hydrological forecasting uncertainty studyrdquo Journalof Shihezi University (Natural Science) vol 24 no 1 pp 15ndash212006 (Chinese)

[15] GVillarini andW F Krajewski ldquoReview of the different sourcesof uncertainty in single polarization radar-based estimates ofrainfallrdquo Surveys in Geophysics vol 31 no 1 pp 107ndash129 2010

[16] K Beven and A Binley ldquoThe future of distributed modelsmodel calibration and uncertainty predictionrdquo HydrologicalProcesses vol 6 no 3 pp 279ndash298 1992

[17] F Quintero D Sempere-Torres M Berenguer and E BaltasldquoA scenario-incorporating analysis of the propagation of uncer-tainty to flash flood simulationsrdquo Journal of Hydrology vol 460-461 pp 90ndash102 2012

[18] L Xiong andKMOrsquoConnor ldquoAn empiricalmethod to improvethe prediction limits of the GLUE methodology in rainfall-runoffmodelingrdquo Journal of Hydrology vol 349 no 1-2 pp 115ndash124 2008

[19] X R Yin J Xia and X Zhang ldquoRecent progress and prospectof the study on uncertainties in hydrologicalmodeling and fore-castingrdquoWater Power vol 32 no 10 pp 27ndash31 2006 (Chinese)

[20] D Zhu Y Xuan and I Cluckie ldquoHydrological appraisal ofoperational weather radar rainfall estimates in the context ofdifferent modelling structuresrdquo Hydrology and Earth SystemSciences vol 18 no 1 pp 257ndash272 2014

[21] A S Falck V Maggioni J Tomasella D A Vila and F LR Diniz ldquoPropagation of satellite precipitation uncertaintiesthrough a distributed hydrologic model a case study in theTocantins-Araguaia basin in Brazilrdquo Journal of Hydrology vol527 pp 943ndash957 2015

[22] P A Mendoza J McPhee and X Vargas ldquoUncertainty in floodforecasting a distributed modeling approach in a sparse datacatchmentrdquoWater Resources Research vol 48 no 9 Article IDW09532 2012

[23] V TWood R A Brown and S V Vasiloff ldquoImproved detectionusing negative elevation angles for mountaintop WSR-88DsPart II simulations of the three radars covering UtahrdquoWeatherand Forecasting vol 18 no 3 pp 393ndash403 2003

[24] T P Dai and D S Fu ldquoPrecision of precipitation amount in thejoint detection areas by weather radar and the auto-rain Gaugenetworkrdquo Journal of Nanjing Institute of Meteorology vol 13 no4 pp 592ndash597 1990 (Chinese)

[25] J W Wilson and E A Brandes ldquoRadar measurement ofrainfallmdasha summaryrdquo Bulletin of the American MeteorologicalSociety vol 60 no 9 pp 1048ndash1058 1979

[26] S Chumchean A Seed and A Sharma ldquoCorrecting of real-time radar rainfall bias using a Kalman filtering approachrdquoJournal of Hydrology vol 317 no 1-2 pp 123ndash137 2006

[27] M Costa and M Monteiro ldquoBias-correction of Kalman filterestimators associated to a linear state space model with esti-mated parametersrdquo Journal of Statistical Planning and Inferencevol 176 pp 22ndash32 2016

[28] S I Kako A Isobe and M Kubota ldquoHigh-resolution ASCATwind vector data set gridded by applying an optimum inter-polation method to the global oceanrdquo Journal of GeophysicalResearch Atmospheres vol 116 no 23 Article ID D23107 2011

[29] S Kako andMKubota ldquoRelationship between an ElNino eventand the interannual variability of significant wave heights in theNorth Pacificrdquo Atmosphere-Ocean vol 44 no 4 pp 377ndash3952006

[30] W Castaings D Dartus F-X Le Dimet and G-M SaulnierldquoSensitivity analysis and parameter estimation for distributedhydrological modeling potential of variational methodsrdquoHydrology and Earth System Sciences vol 13 no 4 pp 503ndash5172009

[31] P C Zhang T P Dai D S Fu et al ldquoPrinciple and accuracyof adjusting the area precipitation from digital weather radarthrough variational methodrdquo Atmospheric Science vol 16 no2 pp 248ndash256 1992 (Chinese)

[32] R-J Zhao ldquoThe Xinanjiang model applied in Chinardquo Journal ofHydrology vol 135 no 1ndash4 pp 371ndash381 1992

[33] A A Alazzy H S Lu and Y H Zhu ldquoAssessing the uncertaintyof the Xinanjiang rainfall-runoff model effect of the likelihoodfunction choice on the GLUE methodrdquo Journal of HydrologicEngineering vol 20 no 10 Article ID 04015016 2015

[34] J Liu X Chen J Zhang and M Flury ldquoCoupling the Xinan-jiangmodel to a kinematic flowmodel based on digital drainagenetworks for flood forecastingrdquo Hydrological Processes vol 23no 9 pp 1337ndash1348 2009

[35] C Zhang R-BWang andQ-XMeng ldquoCalibration of concep-tual rainfall-runoffmodels using global optimizationrdquoAdvancesin Meteorology vol 2015 Article ID 545376 12 pages 2015

[36] H Xu C-Y Xu N R Saeliglthun B Zhou and Y Xu ldquoEvaluationof reanalysis and satellite-based precipitation datasets in drivinghydrological models in a humid region of Southern ChinardquoStochastic Environmental Research and Risk Assessment vol 29no 8 pp 2003ndash2020 2015

[37] S S Meng X H Xie and X Yu ldquoTracing temporal changesof model parameters in rainfall-runoffmodeling via a real-timedata assimilationrdquoWater vol 8 no 1 article 19 2016

[38] Z Toth and E Kalnay ldquoEnsemble Forecasting at NMC thegeneration of perturbationsrdquo Bulletin of the American Meteoro-logical Society vol 74 no 12 pp 2317ndash2330 1993

[39] S LMullen andD P Baumhefner ldquoMonte Carlo simulations ofexplosive cyclogenesisrdquoMonthlyWeather Review vol 122 no 7pp 1548ndash1567 1994

[40] R Buizza and T N Palmer ldquoImpact of ensemble size onensemble predictionrdquo Monthly Weather Review vol 126 no 9pp 2503ndash2518 1998

[41] F Molteni R Buizza T N Palmer and T Petroliagis ldquoTheECMWF ensemble prediction system methodology and vali-dationrdquo Quarterly Journal of the Royal Meteorological Societyvol 122 no 529 pp 73ndash119 1996

[42] Z Toth and E Kalnay ldquoEnsemble forecasting at NCEP and thebreeding methodrdquoMonthlyWeather Review vol 125 no 12 pp3297ndash3319 1997

[43] F Wu ldquoSeveral methods of creating stochastic numbers andapplicationsrdquo Journal on Numerical Methods and ComputerApplications vol 27 no 1 pp 48ndash51 2006 (Chinese)

12 Advances in Meteorology

[44] Y-H Shao and W-C Zhang ldquoApplication of statistical weightmatrix method in estimation of regional rainfallrdquo Advances inWater Science vol 20 no 6 pp 755ndash762 2009 (Chinese)

[45] X Y Song Y J Li H Y Yu et al ldquoApplication of quantitativeprecipitation estimation by radar to flood forecastrdquo EngineeringJournal of Wuhan University Engineering Edition vol 40 no 2pp 51ndash54 2007 (Chinese)

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

8 Advances in Meteorology

Table 3 Comparison of flood hydrograph prediction using different rainfall data assimilation methods MPF is measured peak flow and FPFis forecast peak flow

Method Flood event MPF (m3s) FPF (m3s) NS PRE () PTD (h)

UC

050408 3133 584 minus073 8136 1050429 6182 1676 minus105 7289 32050609 1879 968 minus047 4848 2060411 2327 157 minus087 3253 15060508 2409 1081 minus059 5513 10060627 1896 766 minus295 596 4060705 3109 1348 minus3 5664 1060726 1473 1134 02 2301 8

KLM

050408 3133 2756 083 1203 2050429 6182 5622 087 906 1050609 1879 1667 09 1128 1060411 2327 2147 09 774 1060508 2409 2241 09 697 1060627 1896 1685 084 1113 2060705 3109 2627 082 155 2060726 1473 1361 086 76 1

AVG

050408 3133 2833 079 958 1050429 6182 6515 086 539 5050609 1879 1551 088 1746 2060411 2327 1962 083 1569 0060508 2409 2122 085 1191 1060627 1896 1552 044 1814 4060705 3109 2505 065 1943 1060726 1473 1082 022 2654 0

OPT

050408 3133 3117 089 051 2050429 6182 6154 09 045 1050609 1879 1876 09 016 3060411 2327 2317 089 043 2060508 2409 2403 09 025 2060627 1896 1886 089 053 1060705 3109 3071 089 122 2060726 1473 1446 09 183 3

VAR

050408 3133 3133 09 054 0050429 6182 6182 091 036 0050609 1879 1879 089 085 1060411 2327 2327 09 116 2060508 2409 2409 09 023 1060627 1896 1896 089 063 1060705 3109 3109 089 121 2060726 1473 1473 074 047 0

SWI

050408 3133 3125 089 026 1050429 6182 6166 089 026 0050609 1879 1879 09 034 2060411 2327 2072 087 1096 1060508 2409 2406 089 012 0060627 1896 1886 089 053 1060705 3109 3072 089 119 1060726 1473 1468 09 034 2

Advances in Meteorology 9

P

M

UCKLM

AVGOPTVARSWI

16

12

8

4

0

P (m

m)

11 21 31 41 51 61 711t (h)

0

50

100

150

200

250

Q(m

3s

)

12

10

8

6

4

2

0

P (m

m)

40

30

20

10

0

P (m

m)

0

200

400

600

800

Q(m

3s

)

21 41 61 81 1011t (h)

20

15

10

5

0

P (m

m)

0

90

180

270

360

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

250

300

Q(m

3s

)

11 21 31 41 51 61 71 811t (h)

12

8

4

0

P (m

m)

0

50

100

150

200

Q(m

3s

)

18

15

12

9

6

3

0

P (m

m)

11 21 31 41 51 611t (h)

0

40

80

120

160

Q(m

3s

)

11 21 31 41 51 61 711t (h)

10

8

6

4

2

0

P (m

m)

0

70

140

210

280

350

Q(m

3s

)

11 21 31 41 51 61 711t (h)

28

21

14

7

0

P (m

m)

P

M

UCKLM

AVGOPTVARSWI

Figure 3 Comparison of simulated hydrographs for eight storm events using rainfall input data derived from five assimilation methods anduncalibrated radar data119872 is measured hydrograph

10 Advances in Meteorology

00

05

10

15

20

25

00 05 10 15 20Rainfall relative error

Relat

ive e

rror

of p

eak

flow

y = 10581x + 00146

R2 = 09126

Figure 4 Relationship between relative error in predicted floodpeak magnitude and rainfall relative error

00 05 10 15 20Rainfall relative error

00

05

10

15

20

25

Relat

ive e

rror

of fl

ood

volu

me

R2 = 09392

y = 10807x + 00201

Figure 5 Relationship between relative error in predicted flood vol-ume and rainfall relative error

(3) The random errors generated by model input had atendency to increase during the process of runningthe hydrological model Also most of predicted floodpeak times were lagged

(4) As hydrometeorology ensemble forecasts becomemore widely available and the data acquisition meth-ods develop there will be an ongoing need for evalu-ation of uncertainty in input data

(5) This paper provides critical descriptive analysis ofthe main assimilation methods and the effect of theerrors on uncertainty of flood forecasting It demon-strates that weather radar has potential to improvethe precision of hydrological forecasting which hasimplications for improved flood control and disas-ter mitigation The influence of the propagation ofrainfall input error on three simulated factors ofhydrological forecast is quantified

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

minus4

minus2

0

2

4

6

8

Peak

tim

e diff

eren

ce (h

)

05 10 15 2000Rainfall relative error

Figure 6 Relationship between error in predicted flood peak timeand rainfall relative error

Acknowledgments

This study was supported by the State Key Program ofNational Natural Science of China (no 51339004) andthe National Natural Science Foundation of China (no51279139)

References

[1] I Yucel A Onen K K Yilmaz and D J Gochis ldquoCalibrationand evaluation of a flood forecasting system utility of numericalweather prediction model data assimilation and satellite-basedrainfallrdquo Journal of Hydrology vol 523 pp 49ndash66 2015

[2] L P Zhang L Li A Z Ye et al ldquoContrast research on precisionof estimating regional precipitation with weather radar and raingaugerdquo Engineering Journal of Wuhan University EngineeringEdition vol 40 no 1 pp 1ndash5 2007 (Chinese)

[3] J Liu M Bray and D Han ldquoA study on WRF radar dataassimilation for hydrological rainfall predictionrdquoHydrology andEarth System Sciences vol 17 no 8 pp 3095ndash3110 2013

[4] I Maiello R Ferretti S Gentile et al ldquoImpact of radar dataassimilation for the simulation of a heavy rainfall case incentral Italy using WRF-3DVARrdquo Atmospheric MeasurementTechniques vol 7 no 9 pp 2919ndash2935 2014

[5] M Borga ldquoAccuracy of radar rainfall estimates for streamflowsimulationrdquo Journal of Hydrology vol 267 no 1-2 pp 26ndash392002

[6] Q Dai and D Han ldquoExploration of discrepancy between radarand gauge rainfall estimates driven by wind fieldsrdquo WaterResources Research vol 50 no 11 pp 8571ndash8588 2014

[7] F Giannoni J A Smith Y Zhang and G Roth ldquoHydrologicmodeling of extreme floods using radar rainfall estimatesrdquoAdvances in Water Resources vol 26 no 2 pp 195ndash203 2003

[8] Z Sokol ldquoUtilization of regression models for rainfall estimatesusing radar-derived rainfall data and rain gauge datardquo Journalof Hydrology vol 278 no 1ndash4 pp 144ndash152 2003

[9] C A Velasco-Forero D Sempere-Torres E F Cassiraga and JJaime Gomez-Hernandez ldquoA non-parametric automatic blend-ing methodology to estimate rainfall fields from rain gauge andradar datardquo Advances inWater Resources vol 32 no 7 pp 986ndash1002 2009

Advances in Meteorology 11

[10] X Sun R G Mein T D Keenan and J F Elliott ldquoFlood esti-mation using radar and raingauge datardquo Journal of Hydrologyvol 239 no 1ndash4 pp 4ndash18 2000

[11] J Z Sun ldquoConvective-scale assimilation of radar data progressand challengesrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 131 no 613 pp 3439ndash3463 2006

[12] X D Yu X P Yao T N Xiong et al The Principle and Appli-cation of Doppler Weather Radar China Meteorological PressBeijing China 2007

[13] M Borga E N Anagnostou and E Frank ldquoOn the use of real-time radar rainfall estimates for flood prediction in mountain-ous basinsrdquo Journal of Geophysical Research Atmospheres vol105 no 2 pp 2269ndash2280 2000

[14] H G Zhang S L Guo and X L He ldquoRecent advancement andprospect of hydrological forecasting uncertainty studyrdquo Journalof Shihezi University (Natural Science) vol 24 no 1 pp 15ndash212006 (Chinese)

[15] GVillarini andW F Krajewski ldquoReview of the different sourcesof uncertainty in single polarization radar-based estimates ofrainfallrdquo Surveys in Geophysics vol 31 no 1 pp 107ndash129 2010

[16] K Beven and A Binley ldquoThe future of distributed modelsmodel calibration and uncertainty predictionrdquo HydrologicalProcesses vol 6 no 3 pp 279ndash298 1992

[17] F Quintero D Sempere-Torres M Berenguer and E BaltasldquoA scenario-incorporating analysis of the propagation of uncer-tainty to flash flood simulationsrdquo Journal of Hydrology vol 460-461 pp 90ndash102 2012

[18] L Xiong andKMOrsquoConnor ldquoAn empiricalmethod to improvethe prediction limits of the GLUE methodology in rainfall-runoffmodelingrdquo Journal of Hydrology vol 349 no 1-2 pp 115ndash124 2008

[19] X R Yin J Xia and X Zhang ldquoRecent progress and prospectof the study on uncertainties in hydrologicalmodeling and fore-castingrdquoWater Power vol 32 no 10 pp 27ndash31 2006 (Chinese)

[20] D Zhu Y Xuan and I Cluckie ldquoHydrological appraisal ofoperational weather radar rainfall estimates in the context ofdifferent modelling structuresrdquo Hydrology and Earth SystemSciences vol 18 no 1 pp 257ndash272 2014

[21] A S Falck V Maggioni J Tomasella D A Vila and F LR Diniz ldquoPropagation of satellite precipitation uncertaintiesthrough a distributed hydrologic model a case study in theTocantins-Araguaia basin in Brazilrdquo Journal of Hydrology vol527 pp 943ndash957 2015

[22] P A Mendoza J McPhee and X Vargas ldquoUncertainty in floodforecasting a distributed modeling approach in a sparse datacatchmentrdquoWater Resources Research vol 48 no 9 Article IDW09532 2012

[23] V TWood R A Brown and S V Vasiloff ldquoImproved detectionusing negative elevation angles for mountaintop WSR-88DsPart II simulations of the three radars covering UtahrdquoWeatherand Forecasting vol 18 no 3 pp 393ndash403 2003

[24] T P Dai and D S Fu ldquoPrecision of precipitation amount in thejoint detection areas by weather radar and the auto-rain Gaugenetworkrdquo Journal of Nanjing Institute of Meteorology vol 13 no4 pp 592ndash597 1990 (Chinese)

[25] J W Wilson and E A Brandes ldquoRadar measurement ofrainfallmdasha summaryrdquo Bulletin of the American MeteorologicalSociety vol 60 no 9 pp 1048ndash1058 1979

[26] S Chumchean A Seed and A Sharma ldquoCorrecting of real-time radar rainfall bias using a Kalman filtering approachrdquoJournal of Hydrology vol 317 no 1-2 pp 123ndash137 2006

[27] M Costa and M Monteiro ldquoBias-correction of Kalman filterestimators associated to a linear state space model with esti-mated parametersrdquo Journal of Statistical Planning and Inferencevol 176 pp 22ndash32 2016

[28] S I Kako A Isobe and M Kubota ldquoHigh-resolution ASCATwind vector data set gridded by applying an optimum inter-polation method to the global oceanrdquo Journal of GeophysicalResearch Atmospheres vol 116 no 23 Article ID D23107 2011

[29] S Kako andMKubota ldquoRelationship between an ElNino eventand the interannual variability of significant wave heights in theNorth Pacificrdquo Atmosphere-Ocean vol 44 no 4 pp 377ndash3952006

[30] W Castaings D Dartus F-X Le Dimet and G-M SaulnierldquoSensitivity analysis and parameter estimation for distributedhydrological modeling potential of variational methodsrdquoHydrology and Earth System Sciences vol 13 no 4 pp 503ndash5172009

[31] P C Zhang T P Dai D S Fu et al ldquoPrinciple and accuracyof adjusting the area precipitation from digital weather radarthrough variational methodrdquo Atmospheric Science vol 16 no2 pp 248ndash256 1992 (Chinese)

[32] R-J Zhao ldquoThe Xinanjiang model applied in Chinardquo Journal ofHydrology vol 135 no 1ndash4 pp 371ndash381 1992

[33] A A Alazzy H S Lu and Y H Zhu ldquoAssessing the uncertaintyof the Xinanjiang rainfall-runoff model effect of the likelihoodfunction choice on the GLUE methodrdquo Journal of HydrologicEngineering vol 20 no 10 Article ID 04015016 2015

[34] J Liu X Chen J Zhang and M Flury ldquoCoupling the Xinan-jiangmodel to a kinematic flowmodel based on digital drainagenetworks for flood forecastingrdquo Hydrological Processes vol 23no 9 pp 1337ndash1348 2009

[35] C Zhang R-BWang andQ-XMeng ldquoCalibration of concep-tual rainfall-runoffmodels using global optimizationrdquoAdvancesin Meteorology vol 2015 Article ID 545376 12 pages 2015

[36] H Xu C-Y Xu N R Saeliglthun B Zhou and Y Xu ldquoEvaluationof reanalysis and satellite-based precipitation datasets in drivinghydrological models in a humid region of Southern ChinardquoStochastic Environmental Research and Risk Assessment vol 29no 8 pp 2003ndash2020 2015

[37] S S Meng X H Xie and X Yu ldquoTracing temporal changesof model parameters in rainfall-runoffmodeling via a real-timedata assimilationrdquoWater vol 8 no 1 article 19 2016

[38] Z Toth and E Kalnay ldquoEnsemble Forecasting at NMC thegeneration of perturbationsrdquo Bulletin of the American Meteoro-logical Society vol 74 no 12 pp 2317ndash2330 1993

[39] S LMullen andD P Baumhefner ldquoMonte Carlo simulations ofexplosive cyclogenesisrdquoMonthlyWeather Review vol 122 no 7pp 1548ndash1567 1994

[40] R Buizza and T N Palmer ldquoImpact of ensemble size onensemble predictionrdquo Monthly Weather Review vol 126 no 9pp 2503ndash2518 1998

[41] F Molteni R Buizza T N Palmer and T Petroliagis ldquoTheECMWF ensemble prediction system methodology and vali-dationrdquo Quarterly Journal of the Royal Meteorological Societyvol 122 no 529 pp 73ndash119 1996

[42] Z Toth and E Kalnay ldquoEnsemble forecasting at NCEP and thebreeding methodrdquoMonthlyWeather Review vol 125 no 12 pp3297ndash3319 1997

[43] F Wu ldquoSeveral methods of creating stochastic numbers andapplicationsrdquo Journal on Numerical Methods and ComputerApplications vol 27 no 1 pp 48ndash51 2006 (Chinese)

12 Advances in Meteorology

[44] Y-H Shao and W-C Zhang ldquoApplication of statistical weightmatrix method in estimation of regional rainfallrdquo Advances inWater Science vol 20 no 6 pp 755ndash762 2009 (Chinese)

[45] X Y Song Y J Li H Y Yu et al ldquoApplication of quantitativeprecipitation estimation by radar to flood forecastrdquo EngineeringJournal of Wuhan University Engineering Edition vol 40 no 2pp 51ndash54 2007 (Chinese)

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Advances in Meteorology 9

P

M

UCKLM

AVGOPTVARSWI

16

12

8

4

0

P (m

m)

11 21 31 41 51 61 711t (h)

0

50

100

150

200

250

Q(m

3s

)

12

10

8

6

4

2

0

P (m

m)

40

30

20

10

0

P (m

m)

0

200

400

600

800

Q(m

3s

)

21 41 61 81 1011t (h)

20

15

10

5

0

P (m

m)

0

90

180

270

360

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

Q(m

3s

)

11 21 31 41 51 611t (h)

0

50

100

150

200

250

300

Q(m

3s

)

11 21 31 41 51 61 71 811t (h)

12

8

4

0

P (m

m)

0

50

100

150

200

Q(m

3s

)

18

15

12

9

6

3

0

P (m

m)

11 21 31 41 51 611t (h)

0

40

80

120

160

Q(m

3s

)

11 21 31 41 51 61 711t (h)

10

8

6

4

2

0

P (m

m)

0

70

140

210

280

350

Q(m

3s

)

11 21 31 41 51 61 711t (h)

28

21

14

7

0

P (m

m)

P

M

UCKLM

AVGOPTVARSWI

Figure 3 Comparison of simulated hydrographs for eight storm events using rainfall input data derived from five assimilation methods anduncalibrated radar data119872 is measured hydrograph

10 Advances in Meteorology

00

05

10

15

20

25

00 05 10 15 20Rainfall relative error

Relat

ive e

rror

of p

eak

flow

y = 10581x + 00146

R2 = 09126

Figure 4 Relationship between relative error in predicted floodpeak magnitude and rainfall relative error

00 05 10 15 20Rainfall relative error

00

05

10

15

20

25

Relat

ive e

rror

of fl

ood

volu

me

R2 = 09392

y = 10807x + 00201

Figure 5 Relationship between relative error in predicted flood vol-ume and rainfall relative error

(3) The random errors generated by model input had atendency to increase during the process of runningthe hydrological model Also most of predicted floodpeak times were lagged

(4) As hydrometeorology ensemble forecasts becomemore widely available and the data acquisition meth-ods develop there will be an ongoing need for evalu-ation of uncertainty in input data

(5) This paper provides critical descriptive analysis ofthe main assimilation methods and the effect of theerrors on uncertainty of flood forecasting It demon-strates that weather radar has potential to improvethe precision of hydrological forecasting which hasimplications for improved flood control and disas-ter mitigation The influence of the propagation ofrainfall input error on three simulated factors ofhydrological forecast is quantified

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

minus4

minus2

0

2

4

6

8

Peak

tim

e diff

eren

ce (h

)

05 10 15 2000Rainfall relative error

Figure 6 Relationship between error in predicted flood peak timeand rainfall relative error

Acknowledgments

This study was supported by the State Key Program ofNational Natural Science of China (no 51339004) andthe National Natural Science Foundation of China (no51279139)

References

[1] I Yucel A Onen K K Yilmaz and D J Gochis ldquoCalibrationand evaluation of a flood forecasting system utility of numericalweather prediction model data assimilation and satellite-basedrainfallrdquo Journal of Hydrology vol 523 pp 49ndash66 2015

[2] L P Zhang L Li A Z Ye et al ldquoContrast research on precisionof estimating regional precipitation with weather radar and raingaugerdquo Engineering Journal of Wuhan University EngineeringEdition vol 40 no 1 pp 1ndash5 2007 (Chinese)

[3] J Liu M Bray and D Han ldquoA study on WRF radar dataassimilation for hydrological rainfall predictionrdquoHydrology andEarth System Sciences vol 17 no 8 pp 3095ndash3110 2013

[4] I Maiello R Ferretti S Gentile et al ldquoImpact of radar dataassimilation for the simulation of a heavy rainfall case incentral Italy using WRF-3DVARrdquo Atmospheric MeasurementTechniques vol 7 no 9 pp 2919ndash2935 2014

[5] M Borga ldquoAccuracy of radar rainfall estimates for streamflowsimulationrdquo Journal of Hydrology vol 267 no 1-2 pp 26ndash392002

[6] Q Dai and D Han ldquoExploration of discrepancy between radarand gauge rainfall estimates driven by wind fieldsrdquo WaterResources Research vol 50 no 11 pp 8571ndash8588 2014

[7] F Giannoni J A Smith Y Zhang and G Roth ldquoHydrologicmodeling of extreme floods using radar rainfall estimatesrdquoAdvances in Water Resources vol 26 no 2 pp 195ndash203 2003

[8] Z Sokol ldquoUtilization of regression models for rainfall estimatesusing radar-derived rainfall data and rain gauge datardquo Journalof Hydrology vol 278 no 1ndash4 pp 144ndash152 2003

[9] C A Velasco-Forero D Sempere-Torres E F Cassiraga and JJaime Gomez-Hernandez ldquoA non-parametric automatic blend-ing methodology to estimate rainfall fields from rain gauge andradar datardquo Advances inWater Resources vol 32 no 7 pp 986ndash1002 2009

Advances in Meteorology 11

[10] X Sun R G Mein T D Keenan and J F Elliott ldquoFlood esti-mation using radar and raingauge datardquo Journal of Hydrologyvol 239 no 1ndash4 pp 4ndash18 2000

[11] J Z Sun ldquoConvective-scale assimilation of radar data progressand challengesrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 131 no 613 pp 3439ndash3463 2006

[12] X D Yu X P Yao T N Xiong et al The Principle and Appli-cation of Doppler Weather Radar China Meteorological PressBeijing China 2007

[13] M Borga E N Anagnostou and E Frank ldquoOn the use of real-time radar rainfall estimates for flood prediction in mountain-ous basinsrdquo Journal of Geophysical Research Atmospheres vol105 no 2 pp 2269ndash2280 2000

[14] H G Zhang S L Guo and X L He ldquoRecent advancement andprospect of hydrological forecasting uncertainty studyrdquo Journalof Shihezi University (Natural Science) vol 24 no 1 pp 15ndash212006 (Chinese)

[15] GVillarini andW F Krajewski ldquoReview of the different sourcesof uncertainty in single polarization radar-based estimates ofrainfallrdquo Surveys in Geophysics vol 31 no 1 pp 107ndash129 2010

[16] K Beven and A Binley ldquoThe future of distributed modelsmodel calibration and uncertainty predictionrdquo HydrologicalProcesses vol 6 no 3 pp 279ndash298 1992

[17] F Quintero D Sempere-Torres M Berenguer and E BaltasldquoA scenario-incorporating analysis of the propagation of uncer-tainty to flash flood simulationsrdquo Journal of Hydrology vol 460-461 pp 90ndash102 2012

[18] L Xiong andKMOrsquoConnor ldquoAn empiricalmethod to improvethe prediction limits of the GLUE methodology in rainfall-runoffmodelingrdquo Journal of Hydrology vol 349 no 1-2 pp 115ndash124 2008

[19] X R Yin J Xia and X Zhang ldquoRecent progress and prospectof the study on uncertainties in hydrologicalmodeling and fore-castingrdquoWater Power vol 32 no 10 pp 27ndash31 2006 (Chinese)

[20] D Zhu Y Xuan and I Cluckie ldquoHydrological appraisal ofoperational weather radar rainfall estimates in the context ofdifferent modelling structuresrdquo Hydrology and Earth SystemSciences vol 18 no 1 pp 257ndash272 2014

[21] A S Falck V Maggioni J Tomasella D A Vila and F LR Diniz ldquoPropagation of satellite precipitation uncertaintiesthrough a distributed hydrologic model a case study in theTocantins-Araguaia basin in Brazilrdquo Journal of Hydrology vol527 pp 943ndash957 2015

[22] P A Mendoza J McPhee and X Vargas ldquoUncertainty in floodforecasting a distributed modeling approach in a sparse datacatchmentrdquoWater Resources Research vol 48 no 9 Article IDW09532 2012

[23] V TWood R A Brown and S V Vasiloff ldquoImproved detectionusing negative elevation angles for mountaintop WSR-88DsPart II simulations of the three radars covering UtahrdquoWeatherand Forecasting vol 18 no 3 pp 393ndash403 2003

[24] T P Dai and D S Fu ldquoPrecision of precipitation amount in thejoint detection areas by weather radar and the auto-rain Gaugenetworkrdquo Journal of Nanjing Institute of Meteorology vol 13 no4 pp 592ndash597 1990 (Chinese)

[25] J W Wilson and E A Brandes ldquoRadar measurement ofrainfallmdasha summaryrdquo Bulletin of the American MeteorologicalSociety vol 60 no 9 pp 1048ndash1058 1979

[26] S Chumchean A Seed and A Sharma ldquoCorrecting of real-time radar rainfall bias using a Kalman filtering approachrdquoJournal of Hydrology vol 317 no 1-2 pp 123ndash137 2006

[27] M Costa and M Monteiro ldquoBias-correction of Kalman filterestimators associated to a linear state space model with esti-mated parametersrdquo Journal of Statistical Planning and Inferencevol 176 pp 22ndash32 2016

[28] S I Kako A Isobe and M Kubota ldquoHigh-resolution ASCATwind vector data set gridded by applying an optimum inter-polation method to the global oceanrdquo Journal of GeophysicalResearch Atmospheres vol 116 no 23 Article ID D23107 2011

[29] S Kako andMKubota ldquoRelationship between an ElNino eventand the interannual variability of significant wave heights in theNorth Pacificrdquo Atmosphere-Ocean vol 44 no 4 pp 377ndash3952006

[30] W Castaings D Dartus F-X Le Dimet and G-M SaulnierldquoSensitivity analysis and parameter estimation for distributedhydrological modeling potential of variational methodsrdquoHydrology and Earth System Sciences vol 13 no 4 pp 503ndash5172009

[31] P C Zhang T P Dai D S Fu et al ldquoPrinciple and accuracyof adjusting the area precipitation from digital weather radarthrough variational methodrdquo Atmospheric Science vol 16 no2 pp 248ndash256 1992 (Chinese)

[32] R-J Zhao ldquoThe Xinanjiang model applied in Chinardquo Journal ofHydrology vol 135 no 1ndash4 pp 371ndash381 1992

[33] A A Alazzy H S Lu and Y H Zhu ldquoAssessing the uncertaintyof the Xinanjiang rainfall-runoff model effect of the likelihoodfunction choice on the GLUE methodrdquo Journal of HydrologicEngineering vol 20 no 10 Article ID 04015016 2015

[34] J Liu X Chen J Zhang and M Flury ldquoCoupling the Xinan-jiangmodel to a kinematic flowmodel based on digital drainagenetworks for flood forecastingrdquo Hydrological Processes vol 23no 9 pp 1337ndash1348 2009

[35] C Zhang R-BWang andQ-XMeng ldquoCalibration of concep-tual rainfall-runoffmodels using global optimizationrdquoAdvancesin Meteorology vol 2015 Article ID 545376 12 pages 2015

[36] H Xu C-Y Xu N R Saeliglthun B Zhou and Y Xu ldquoEvaluationof reanalysis and satellite-based precipitation datasets in drivinghydrological models in a humid region of Southern ChinardquoStochastic Environmental Research and Risk Assessment vol 29no 8 pp 2003ndash2020 2015

[37] S S Meng X H Xie and X Yu ldquoTracing temporal changesof model parameters in rainfall-runoffmodeling via a real-timedata assimilationrdquoWater vol 8 no 1 article 19 2016

[38] Z Toth and E Kalnay ldquoEnsemble Forecasting at NMC thegeneration of perturbationsrdquo Bulletin of the American Meteoro-logical Society vol 74 no 12 pp 2317ndash2330 1993

[39] S LMullen andD P Baumhefner ldquoMonte Carlo simulations ofexplosive cyclogenesisrdquoMonthlyWeather Review vol 122 no 7pp 1548ndash1567 1994

[40] R Buizza and T N Palmer ldquoImpact of ensemble size onensemble predictionrdquo Monthly Weather Review vol 126 no 9pp 2503ndash2518 1998

[41] F Molteni R Buizza T N Palmer and T Petroliagis ldquoTheECMWF ensemble prediction system methodology and vali-dationrdquo Quarterly Journal of the Royal Meteorological Societyvol 122 no 529 pp 73ndash119 1996

[42] Z Toth and E Kalnay ldquoEnsemble forecasting at NCEP and thebreeding methodrdquoMonthlyWeather Review vol 125 no 12 pp3297ndash3319 1997

[43] F Wu ldquoSeveral methods of creating stochastic numbers andapplicationsrdquo Journal on Numerical Methods and ComputerApplications vol 27 no 1 pp 48ndash51 2006 (Chinese)

12 Advances in Meteorology

[44] Y-H Shao and W-C Zhang ldquoApplication of statistical weightmatrix method in estimation of regional rainfallrdquo Advances inWater Science vol 20 no 6 pp 755ndash762 2009 (Chinese)

[45] X Y Song Y J Li H Y Yu et al ldquoApplication of quantitativeprecipitation estimation by radar to flood forecastrdquo EngineeringJournal of Wuhan University Engineering Edition vol 40 no 2pp 51ndash54 2007 (Chinese)

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

10 Advances in Meteorology

00

05

10

15

20

25

00 05 10 15 20Rainfall relative error

Relat

ive e

rror

of p

eak

flow

y = 10581x + 00146

R2 = 09126

Figure 4 Relationship between relative error in predicted floodpeak magnitude and rainfall relative error

00 05 10 15 20Rainfall relative error

00

05

10

15

20

25

Relat

ive e

rror

of fl

ood

volu

me

R2 = 09392

y = 10807x + 00201

Figure 5 Relationship between relative error in predicted flood vol-ume and rainfall relative error

(3) The random errors generated by model input had atendency to increase during the process of runningthe hydrological model Also most of predicted floodpeak times were lagged

(4) As hydrometeorology ensemble forecasts becomemore widely available and the data acquisition meth-ods develop there will be an ongoing need for evalu-ation of uncertainty in input data

(5) This paper provides critical descriptive analysis ofthe main assimilation methods and the effect of theerrors on uncertainty of flood forecasting It demon-strates that weather radar has potential to improvethe precision of hydrological forecasting which hasimplications for improved flood control and disas-ter mitigation The influence of the propagation ofrainfall input error on three simulated factors ofhydrological forecast is quantified

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

minus4

minus2

0

2

4

6

8

Peak

tim

e diff

eren

ce (h

)

05 10 15 2000Rainfall relative error

Figure 6 Relationship between error in predicted flood peak timeand rainfall relative error

Acknowledgments

This study was supported by the State Key Program ofNational Natural Science of China (no 51339004) andthe National Natural Science Foundation of China (no51279139)

References

[1] I Yucel A Onen K K Yilmaz and D J Gochis ldquoCalibrationand evaluation of a flood forecasting system utility of numericalweather prediction model data assimilation and satellite-basedrainfallrdquo Journal of Hydrology vol 523 pp 49ndash66 2015

[2] L P Zhang L Li A Z Ye et al ldquoContrast research on precisionof estimating regional precipitation with weather radar and raingaugerdquo Engineering Journal of Wuhan University EngineeringEdition vol 40 no 1 pp 1ndash5 2007 (Chinese)

[3] J Liu M Bray and D Han ldquoA study on WRF radar dataassimilation for hydrological rainfall predictionrdquoHydrology andEarth System Sciences vol 17 no 8 pp 3095ndash3110 2013

[4] I Maiello R Ferretti S Gentile et al ldquoImpact of radar dataassimilation for the simulation of a heavy rainfall case incentral Italy using WRF-3DVARrdquo Atmospheric MeasurementTechniques vol 7 no 9 pp 2919ndash2935 2014

[5] M Borga ldquoAccuracy of radar rainfall estimates for streamflowsimulationrdquo Journal of Hydrology vol 267 no 1-2 pp 26ndash392002

[6] Q Dai and D Han ldquoExploration of discrepancy between radarand gauge rainfall estimates driven by wind fieldsrdquo WaterResources Research vol 50 no 11 pp 8571ndash8588 2014

[7] F Giannoni J A Smith Y Zhang and G Roth ldquoHydrologicmodeling of extreme floods using radar rainfall estimatesrdquoAdvances in Water Resources vol 26 no 2 pp 195ndash203 2003

[8] Z Sokol ldquoUtilization of regression models for rainfall estimatesusing radar-derived rainfall data and rain gauge datardquo Journalof Hydrology vol 278 no 1ndash4 pp 144ndash152 2003

[9] C A Velasco-Forero D Sempere-Torres E F Cassiraga and JJaime Gomez-Hernandez ldquoA non-parametric automatic blend-ing methodology to estimate rainfall fields from rain gauge andradar datardquo Advances inWater Resources vol 32 no 7 pp 986ndash1002 2009

Advances in Meteorology 11

[10] X Sun R G Mein T D Keenan and J F Elliott ldquoFlood esti-mation using radar and raingauge datardquo Journal of Hydrologyvol 239 no 1ndash4 pp 4ndash18 2000

[11] J Z Sun ldquoConvective-scale assimilation of radar data progressand challengesrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 131 no 613 pp 3439ndash3463 2006

[12] X D Yu X P Yao T N Xiong et al The Principle and Appli-cation of Doppler Weather Radar China Meteorological PressBeijing China 2007

[13] M Borga E N Anagnostou and E Frank ldquoOn the use of real-time radar rainfall estimates for flood prediction in mountain-ous basinsrdquo Journal of Geophysical Research Atmospheres vol105 no 2 pp 2269ndash2280 2000

[14] H G Zhang S L Guo and X L He ldquoRecent advancement andprospect of hydrological forecasting uncertainty studyrdquo Journalof Shihezi University (Natural Science) vol 24 no 1 pp 15ndash212006 (Chinese)

[15] GVillarini andW F Krajewski ldquoReview of the different sourcesof uncertainty in single polarization radar-based estimates ofrainfallrdquo Surveys in Geophysics vol 31 no 1 pp 107ndash129 2010

[16] K Beven and A Binley ldquoThe future of distributed modelsmodel calibration and uncertainty predictionrdquo HydrologicalProcesses vol 6 no 3 pp 279ndash298 1992

[17] F Quintero D Sempere-Torres M Berenguer and E BaltasldquoA scenario-incorporating analysis of the propagation of uncer-tainty to flash flood simulationsrdquo Journal of Hydrology vol 460-461 pp 90ndash102 2012

[18] L Xiong andKMOrsquoConnor ldquoAn empiricalmethod to improvethe prediction limits of the GLUE methodology in rainfall-runoffmodelingrdquo Journal of Hydrology vol 349 no 1-2 pp 115ndash124 2008

[19] X R Yin J Xia and X Zhang ldquoRecent progress and prospectof the study on uncertainties in hydrologicalmodeling and fore-castingrdquoWater Power vol 32 no 10 pp 27ndash31 2006 (Chinese)

[20] D Zhu Y Xuan and I Cluckie ldquoHydrological appraisal ofoperational weather radar rainfall estimates in the context ofdifferent modelling structuresrdquo Hydrology and Earth SystemSciences vol 18 no 1 pp 257ndash272 2014

[21] A S Falck V Maggioni J Tomasella D A Vila and F LR Diniz ldquoPropagation of satellite precipitation uncertaintiesthrough a distributed hydrologic model a case study in theTocantins-Araguaia basin in Brazilrdquo Journal of Hydrology vol527 pp 943ndash957 2015

[22] P A Mendoza J McPhee and X Vargas ldquoUncertainty in floodforecasting a distributed modeling approach in a sparse datacatchmentrdquoWater Resources Research vol 48 no 9 Article IDW09532 2012

[23] V TWood R A Brown and S V Vasiloff ldquoImproved detectionusing negative elevation angles for mountaintop WSR-88DsPart II simulations of the three radars covering UtahrdquoWeatherand Forecasting vol 18 no 3 pp 393ndash403 2003

[24] T P Dai and D S Fu ldquoPrecision of precipitation amount in thejoint detection areas by weather radar and the auto-rain Gaugenetworkrdquo Journal of Nanjing Institute of Meteorology vol 13 no4 pp 592ndash597 1990 (Chinese)

[25] J W Wilson and E A Brandes ldquoRadar measurement ofrainfallmdasha summaryrdquo Bulletin of the American MeteorologicalSociety vol 60 no 9 pp 1048ndash1058 1979

[26] S Chumchean A Seed and A Sharma ldquoCorrecting of real-time radar rainfall bias using a Kalman filtering approachrdquoJournal of Hydrology vol 317 no 1-2 pp 123ndash137 2006

[27] M Costa and M Monteiro ldquoBias-correction of Kalman filterestimators associated to a linear state space model with esti-mated parametersrdquo Journal of Statistical Planning and Inferencevol 176 pp 22ndash32 2016

[28] S I Kako A Isobe and M Kubota ldquoHigh-resolution ASCATwind vector data set gridded by applying an optimum inter-polation method to the global oceanrdquo Journal of GeophysicalResearch Atmospheres vol 116 no 23 Article ID D23107 2011

[29] S Kako andMKubota ldquoRelationship between an ElNino eventand the interannual variability of significant wave heights in theNorth Pacificrdquo Atmosphere-Ocean vol 44 no 4 pp 377ndash3952006

[30] W Castaings D Dartus F-X Le Dimet and G-M SaulnierldquoSensitivity analysis and parameter estimation for distributedhydrological modeling potential of variational methodsrdquoHydrology and Earth System Sciences vol 13 no 4 pp 503ndash5172009

[31] P C Zhang T P Dai D S Fu et al ldquoPrinciple and accuracyof adjusting the area precipitation from digital weather radarthrough variational methodrdquo Atmospheric Science vol 16 no2 pp 248ndash256 1992 (Chinese)

[32] R-J Zhao ldquoThe Xinanjiang model applied in Chinardquo Journal ofHydrology vol 135 no 1ndash4 pp 371ndash381 1992

[33] A A Alazzy H S Lu and Y H Zhu ldquoAssessing the uncertaintyof the Xinanjiang rainfall-runoff model effect of the likelihoodfunction choice on the GLUE methodrdquo Journal of HydrologicEngineering vol 20 no 10 Article ID 04015016 2015

[34] J Liu X Chen J Zhang and M Flury ldquoCoupling the Xinan-jiangmodel to a kinematic flowmodel based on digital drainagenetworks for flood forecastingrdquo Hydrological Processes vol 23no 9 pp 1337ndash1348 2009

[35] C Zhang R-BWang andQ-XMeng ldquoCalibration of concep-tual rainfall-runoffmodels using global optimizationrdquoAdvancesin Meteorology vol 2015 Article ID 545376 12 pages 2015

[36] H Xu C-Y Xu N R Saeliglthun B Zhou and Y Xu ldquoEvaluationof reanalysis and satellite-based precipitation datasets in drivinghydrological models in a humid region of Southern ChinardquoStochastic Environmental Research and Risk Assessment vol 29no 8 pp 2003ndash2020 2015

[37] S S Meng X H Xie and X Yu ldquoTracing temporal changesof model parameters in rainfall-runoffmodeling via a real-timedata assimilationrdquoWater vol 8 no 1 article 19 2016

[38] Z Toth and E Kalnay ldquoEnsemble Forecasting at NMC thegeneration of perturbationsrdquo Bulletin of the American Meteoro-logical Society vol 74 no 12 pp 2317ndash2330 1993

[39] S LMullen andD P Baumhefner ldquoMonte Carlo simulations ofexplosive cyclogenesisrdquoMonthlyWeather Review vol 122 no 7pp 1548ndash1567 1994

[40] R Buizza and T N Palmer ldquoImpact of ensemble size onensemble predictionrdquo Monthly Weather Review vol 126 no 9pp 2503ndash2518 1998

[41] F Molteni R Buizza T N Palmer and T Petroliagis ldquoTheECMWF ensemble prediction system methodology and vali-dationrdquo Quarterly Journal of the Royal Meteorological Societyvol 122 no 529 pp 73ndash119 1996

[42] Z Toth and E Kalnay ldquoEnsemble forecasting at NCEP and thebreeding methodrdquoMonthlyWeather Review vol 125 no 12 pp3297ndash3319 1997

[43] F Wu ldquoSeveral methods of creating stochastic numbers andapplicationsrdquo Journal on Numerical Methods and ComputerApplications vol 27 no 1 pp 48ndash51 2006 (Chinese)

12 Advances in Meteorology

[44] Y-H Shao and W-C Zhang ldquoApplication of statistical weightmatrix method in estimation of regional rainfallrdquo Advances inWater Science vol 20 no 6 pp 755ndash762 2009 (Chinese)

[45] X Y Song Y J Li H Y Yu et al ldquoApplication of quantitativeprecipitation estimation by radar to flood forecastrdquo EngineeringJournal of Wuhan University Engineering Edition vol 40 no 2pp 51ndash54 2007 (Chinese)

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Advances in Meteorology 11

[10] X Sun R G Mein T D Keenan and J F Elliott ldquoFlood esti-mation using radar and raingauge datardquo Journal of Hydrologyvol 239 no 1ndash4 pp 4ndash18 2000

[11] J Z Sun ldquoConvective-scale assimilation of radar data progressand challengesrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 131 no 613 pp 3439ndash3463 2006

[12] X D Yu X P Yao T N Xiong et al The Principle and Appli-cation of Doppler Weather Radar China Meteorological PressBeijing China 2007

[13] M Borga E N Anagnostou and E Frank ldquoOn the use of real-time radar rainfall estimates for flood prediction in mountain-ous basinsrdquo Journal of Geophysical Research Atmospheres vol105 no 2 pp 2269ndash2280 2000

[14] H G Zhang S L Guo and X L He ldquoRecent advancement andprospect of hydrological forecasting uncertainty studyrdquo Journalof Shihezi University (Natural Science) vol 24 no 1 pp 15ndash212006 (Chinese)

[15] GVillarini andW F Krajewski ldquoReview of the different sourcesof uncertainty in single polarization radar-based estimates ofrainfallrdquo Surveys in Geophysics vol 31 no 1 pp 107ndash129 2010

[16] K Beven and A Binley ldquoThe future of distributed modelsmodel calibration and uncertainty predictionrdquo HydrologicalProcesses vol 6 no 3 pp 279ndash298 1992

[17] F Quintero D Sempere-Torres M Berenguer and E BaltasldquoA scenario-incorporating analysis of the propagation of uncer-tainty to flash flood simulationsrdquo Journal of Hydrology vol 460-461 pp 90ndash102 2012

[18] L Xiong andKMOrsquoConnor ldquoAn empiricalmethod to improvethe prediction limits of the GLUE methodology in rainfall-runoffmodelingrdquo Journal of Hydrology vol 349 no 1-2 pp 115ndash124 2008

[19] X R Yin J Xia and X Zhang ldquoRecent progress and prospectof the study on uncertainties in hydrologicalmodeling and fore-castingrdquoWater Power vol 32 no 10 pp 27ndash31 2006 (Chinese)

[20] D Zhu Y Xuan and I Cluckie ldquoHydrological appraisal ofoperational weather radar rainfall estimates in the context ofdifferent modelling structuresrdquo Hydrology and Earth SystemSciences vol 18 no 1 pp 257ndash272 2014

[21] A S Falck V Maggioni J Tomasella D A Vila and F LR Diniz ldquoPropagation of satellite precipitation uncertaintiesthrough a distributed hydrologic model a case study in theTocantins-Araguaia basin in Brazilrdquo Journal of Hydrology vol527 pp 943ndash957 2015

[22] P A Mendoza J McPhee and X Vargas ldquoUncertainty in floodforecasting a distributed modeling approach in a sparse datacatchmentrdquoWater Resources Research vol 48 no 9 Article IDW09532 2012

[23] V TWood R A Brown and S V Vasiloff ldquoImproved detectionusing negative elevation angles for mountaintop WSR-88DsPart II simulations of the three radars covering UtahrdquoWeatherand Forecasting vol 18 no 3 pp 393ndash403 2003

[24] T P Dai and D S Fu ldquoPrecision of precipitation amount in thejoint detection areas by weather radar and the auto-rain Gaugenetworkrdquo Journal of Nanjing Institute of Meteorology vol 13 no4 pp 592ndash597 1990 (Chinese)

[25] J W Wilson and E A Brandes ldquoRadar measurement ofrainfallmdasha summaryrdquo Bulletin of the American MeteorologicalSociety vol 60 no 9 pp 1048ndash1058 1979

[26] S Chumchean A Seed and A Sharma ldquoCorrecting of real-time radar rainfall bias using a Kalman filtering approachrdquoJournal of Hydrology vol 317 no 1-2 pp 123ndash137 2006

[27] M Costa and M Monteiro ldquoBias-correction of Kalman filterestimators associated to a linear state space model with esti-mated parametersrdquo Journal of Statistical Planning and Inferencevol 176 pp 22ndash32 2016

[28] S I Kako A Isobe and M Kubota ldquoHigh-resolution ASCATwind vector data set gridded by applying an optimum inter-polation method to the global oceanrdquo Journal of GeophysicalResearch Atmospheres vol 116 no 23 Article ID D23107 2011

[29] S Kako andMKubota ldquoRelationship between an ElNino eventand the interannual variability of significant wave heights in theNorth Pacificrdquo Atmosphere-Ocean vol 44 no 4 pp 377ndash3952006

[30] W Castaings D Dartus F-X Le Dimet and G-M SaulnierldquoSensitivity analysis and parameter estimation for distributedhydrological modeling potential of variational methodsrdquoHydrology and Earth System Sciences vol 13 no 4 pp 503ndash5172009

[31] P C Zhang T P Dai D S Fu et al ldquoPrinciple and accuracyof adjusting the area precipitation from digital weather radarthrough variational methodrdquo Atmospheric Science vol 16 no2 pp 248ndash256 1992 (Chinese)

[32] R-J Zhao ldquoThe Xinanjiang model applied in Chinardquo Journal ofHydrology vol 135 no 1ndash4 pp 371ndash381 1992

[33] A A Alazzy H S Lu and Y H Zhu ldquoAssessing the uncertaintyof the Xinanjiang rainfall-runoff model effect of the likelihoodfunction choice on the GLUE methodrdquo Journal of HydrologicEngineering vol 20 no 10 Article ID 04015016 2015

[34] J Liu X Chen J Zhang and M Flury ldquoCoupling the Xinan-jiangmodel to a kinematic flowmodel based on digital drainagenetworks for flood forecastingrdquo Hydrological Processes vol 23no 9 pp 1337ndash1348 2009

[35] C Zhang R-BWang andQ-XMeng ldquoCalibration of concep-tual rainfall-runoffmodels using global optimizationrdquoAdvancesin Meteorology vol 2015 Article ID 545376 12 pages 2015

[36] H Xu C-Y Xu N R Saeliglthun B Zhou and Y Xu ldquoEvaluationof reanalysis and satellite-based precipitation datasets in drivinghydrological models in a humid region of Southern ChinardquoStochastic Environmental Research and Risk Assessment vol 29no 8 pp 2003ndash2020 2015

[37] S S Meng X H Xie and X Yu ldquoTracing temporal changesof model parameters in rainfall-runoffmodeling via a real-timedata assimilationrdquoWater vol 8 no 1 article 19 2016

[38] Z Toth and E Kalnay ldquoEnsemble Forecasting at NMC thegeneration of perturbationsrdquo Bulletin of the American Meteoro-logical Society vol 74 no 12 pp 2317ndash2330 1993

[39] S LMullen andD P Baumhefner ldquoMonte Carlo simulations ofexplosive cyclogenesisrdquoMonthlyWeather Review vol 122 no 7pp 1548ndash1567 1994

[40] R Buizza and T N Palmer ldquoImpact of ensemble size onensemble predictionrdquo Monthly Weather Review vol 126 no 9pp 2503ndash2518 1998

[41] F Molteni R Buizza T N Palmer and T Petroliagis ldquoTheECMWF ensemble prediction system methodology and vali-dationrdquo Quarterly Journal of the Royal Meteorological Societyvol 122 no 529 pp 73ndash119 1996

[42] Z Toth and E Kalnay ldquoEnsemble forecasting at NCEP and thebreeding methodrdquoMonthlyWeather Review vol 125 no 12 pp3297ndash3319 1997

[43] F Wu ldquoSeveral methods of creating stochastic numbers andapplicationsrdquo Journal on Numerical Methods and ComputerApplications vol 27 no 1 pp 48ndash51 2006 (Chinese)

12 Advances in Meteorology

[44] Y-H Shao and W-C Zhang ldquoApplication of statistical weightmatrix method in estimation of regional rainfallrdquo Advances inWater Science vol 20 no 6 pp 755ndash762 2009 (Chinese)

[45] X Y Song Y J Li H Y Yu et al ldquoApplication of quantitativeprecipitation estimation by radar to flood forecastrdquo EngineeringJournal of Wuhan University Engineering Edition vol 40 no 2pp 51ndash54 2007 (Chinese)

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

12 Advances in Meteorology

[44] Y-H Shao and W-C Zhang ldquoApplication of statistical weightmatrix method in estimation of regional rainfallrdquo Advances inWater Science vol 20 no 6 pp 755ndash762 2009 (Chinese)

[45] X Y Song Y J Li H Y Yu et al ldquoApplication of quantitativeprecipitation estimation by radar to flood forecastrdquo EngineeringJournal of Wuhan University Engineering Edition vol 40 no 2pp 51ndash54 2007 (Chinese)

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in