9th International Conference on Hydroinformatics HIC 2010, Tianjin, CHINA

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ACCURACY OF X-BAND LOCAL AREA WEATHER RADAR (LAWR) OF LEUVEN AND ITS FIRST HYDROLOGICAL APPLICATION FOR RIVER CATCHMENT MODELLING

N. K. SHRESTHA, P. WILLEMS

Hydraulics Laboratory, Department of Civil Engineering, Katholieke Universiteit Leuven, 3000 Leuven, Belgium

& Department of Hydrology & Hydraulic Engineering, Vrije Universiteit Brussel

Pleinlaan 2, 1050 Brussels, Belgium

T. GOORMANS Hydraulics Laboratory, Department of Civil Engineering, Katholieke Universiteit Leuven,

3000 Leuven, Belgium

This paper discusses the hydro-meteorological potential of the X-band Local Area Weather Radar installed in the densely populated city centre of Leuven, Belgium. Different merging techniques are applied to raw radar data using gauge readings from a network of 12 rain gauges. The hydrological response is investigated in the 48.17 km2 Molenbeek/Parkbeek catchment in Belgium. For this, two lumped conceptual models, VHM and the NAM are used. Range dependent adjustment followed by Mean Field Bias Adjustment and Brandes Spatial Adjustment improved the radar estimates to a great extent. After adjustments, the mean absolute error is found to decrease by 47% and the root mean square error by 45% compared to the original radar estimates. No large differences in streamflow simulation capability of the two models can be distinguished. More uniform winter storms are simulated with greater accuracy than summer storms. INTRODUCTION For most of the simulation models used in water engineering, rainfall is primary input and often considered spatially uniform over the catchment, or over subregions defined by the density of the rain gauge network, which is usually not the case. Rather, it is highly variable in both space and time. Even in a single storm, rainfall can vary from tens of mm/hr from minute to minute within distances of few centimeters (Austin et al., (2002) [1]). Hence the assumption of uniform rainfall leads to a major uncertainty in simulated events (Willems, (2001) [8]). Accurate high-resolution – in both space and time – rainfall input to the hydrological modelling is required to acquire more robust and accurate hydrological simulations. Accurate and short duration rainfall input can be provided by rain gauges; high spatial resolution data by a dense rain gauge network (Wilson and Brandes, (1979) [10]) or weather radars. Radar measurements however, have the disadvantage that they have high uncertainty in rainfall intensity

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measurements (Einfalt et al., (2004) [4]). These uncertainties should be minimized before using radar measurements as input to simulation models by using adjustment techniques (Wilson and Brandes, (1979) [10]). This could be done by merging radar and rain gauge information.

The hydro-meteorological potential of weather radars has already been explored by many researchers. An X-band weather radar is relatively new and it has rarely been used in hydrological modelling. Owing to its finer resolution, better results are expected than those obtained by conventional S and C-band radars if optimal adjustment procedures are applied. This study focuses on accuracy of LAWR estimates, based on a case in Belgium where an X-band weather radar has been installed. METHODOLOGY The X-band Local Area Weather Radar (LAWR) of Leuven As outcome of a project aiming at the “development of a system for short-time prediction of rainfall”, the Danish Hydrological Institute (DHI) together with the Danish Meteorological Institute (DMI) developed cost effective X-band radar called LAWR. From this, DHI also developed a smaller version of the LAWR, the so-called City LAWR. A City LAWR is installed on the roof of the Provinciehuis Building at the city of Leuven, Belgium as this location produced acceptable amounts of clutter, mainly due to a pit wall which cuts off the lower part of the beam (Goormans et al., (2008) [5]). The LAWR records reflectivity values (representation of back scattered energy) which are converted to rainfall rates by a linear relationship. The slope of this relationship represents a Calibration Factor (CF), which is a conversion factor that converts radar reflectivity records to rainfall rates. Study area The study area is within 15 km radius of the LAWR. The rain gauge network comprises of 12 rain gauges. A catchment named Molenbeek/Parkbeek, having area of 48.17 km2, has been selected which is situated south/south-east direction of the LAWR. The elevation of the catchment ranges from 22 m to 117 m above mean sea level. Agricultural land and sandy soil is the dominant land-use and soil type of the catchment. Radar-gauge merging techniques Owing to the rainfall pattern in Belgium, the study is distinguished into two periods namely summer storm and winter storm periods. The summer period considered spans from July 2, 2008 to September 30, 2008 and the winter period from December 1, 2008 to March 31, 2009. Different CFs are obtained for each rain gauge as the result of a regression analysis, based on the storm average rain gauge intensities and the measured counts in the corresponding radar pixels. The average value of these CFs is used to obtain rainfall rates. After using a constant CF value for all radar pixels, following merging techniques are applied sequentially:

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1. Range Dependent Adjustment: this adjustment on CFs is essential to some extent because of ever increasing height of measurement, beam broadening and attenuation effect. It assumes the CF as a ratio as a function of the distance from the radar site.

2. Mean Field Bias (MFB) Adjustment: in MFB adjustment, it is assumed that the radar estimates can be corrected by a uniform multiplicative factor and is given by:

i

ii

R

G

NN

F 1MFB (1)

3. Brandes Spatial Adjustment (BRA): the main idea is to use a weighted average of the correction factors from the rain gauge sites to each radar grid cell, with weights wi depending on the distance from the radar grid cell to gauge i. For a network consisting of “N” raingauges, it can be given by (Brandes, (1975) [2]):

N

ii

N

iiii

BRA

w

RGw

C

1

1

)/( Where,

k

dwi

2

exp and, 12 k (2)

In equations (1) and (2), Gi and Ri = gauge and radar valid pair readings; N = total number of valid pairs; d = distance between the gauge and the grid point in km; k = a factor controlling the degree of smoothening, generally given as the inverse of two times the mean gauge density (number of gauges divided by total area, denoted by “δ”); CBRA = Brandes spatial adjustment factor.

If both the daily rain gauge depth and radar depth are greater than 1 mm then these were considered as “valid pairs”. For all purposes, the average number of counts over 9 radar pixels surrounding the gauge location is used. In order to evaluate the improvements achieved by each step in the adjustment procedure, comparison on some goodness-of-fit statistics is made before and after adjustment. The Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Nash Sutcliff Efficiency (NSE) are used for this study. Rainfall-Runoff models and modelling approach Two different conceptual rainfall-runoff modeling methods (VHM and NAM) have been used to simulate the effect of the various rainfall input estimations on the catchment runoff. VHM is a Dutch abbreviation for generalized lumped conceptual and parsimonious model structure identification and calibration. The VHM modeling approach aims to derive parameter values which are as much as possible unique, physically realistic and accurate (Willems, (2000) [7]). NAM (Nedbør-Afstrømnings-Model) is the Danish abbreviation for precipitation runoff model. NAM is a deterministic, lumped and conceptual rainfall-runoff model which simulates the rainfall-runoff processes occurring at the catchment scale (DHI, (2004) [3]).

The rainfall derived from the rain gauge network was perceived as more robust and hence considered as reference rainfall (Pref) to be used as input for the calibration process.

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The parameter set thus derived is used to simulate the catchment runoff by using adjusted radar estimates. The NSEobs (Equation 3) is Nash-Sutcliffe efficiency (Nash and Sutcliffe, (1970) [6]), considered as statistics to validate the goodness-of-fit of the simulated runoff results to observed discharges of the river gauging station downstream the catchment:

2

1

2

1

2

1

)(

)()(

1NSEoQ

n

i

oo

n

i

om

S

MSE

QiQ

iQiQ (3)

with, Qo(i) = the observed river discharge; Qm(i) = the modelled river discharge; n = the total number of observations; i = the ith number of observation; S2

Qo= the variance of observed discharge series;

oQ = the mean of observed discharge series. The simulated flow driven by the reference rainfall (Pref) is referred to as the

reference flow (Qref). The difference between the reference flow and the flow driven by adjusted radar estimates is the error induced due to the tested rainfall input keeping model parameter uncertainty the same. A modified definition of NSE is introduced to measure the performance of the simulated runoff in comparison to reference flow defined by equation (3) where Qo is replaced by Qref. Both the NSEobs and NSEref will be defined for the NAM as well as the VHM. To quantify the effects of using LAWR estimates, 4 storms were selected as shown in Table 1. Table 1. Selected storm events; LT means Local Time.

Start [LT] End [LT] Duration Pref Storm Events [mm/dd/yy

HH:MM] [mm/dd/yy HH:MM] [h] [mm]

3-Aug-08 8/3/08 19:00 8/4/08 2:00 8 30.7

5-Dec-08 12/5/08 14:00 12/5/08 20:00 7 7.80

22-Jan-09 1/22/09 12:00 1/23/09 19:00 32 30.4

9-Feb-09 2/9/09 16:00 2/10/09 23:00 32 27.2 RESULTS AND DISCUSSION Accuracy of radar estimates Using the average value of CF showed significant fluctuation on the radar and gauge values for cumulative rainfall volumes in the summer period. The Relative Field Bias (RFB; given by the difference in radar and gauge value normalized by gauge value) ranges from +1.25 (125% overestimation) to -0.57 (57% underestimation). The radar tends to overestimate rainfall in those pixels which are closely located to the LAWR and tends to underestimate rainfall in those pixels which are further away. Combining a second degree polynomial equation (CF = 0.0006 r2 + 0.015r + 0.0159, for r < 1.5 km) and a power function (CF = 0.0272 r 0.8226, for r ≥ 1.5; with, r = from the distance to the

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LAWR in km), the range dependency problem is addressed which also produced quite good results reducing overall the RFB to nearly 6%. The frequency distribution of individual Field Bias showed that the bias followed a near perfect lognormal distribution. Hence the mean of lognormal distribution was calculated to get the MFB. The MFB for the summer and winter period was found to be 1.015 and 0.974 respectively. The radar field is then subjected to the Brandes Spatial Adjustment.

The goodness-of-fit statistics for the subsequent adjustment procedures can be observed in Figure 1. It can be seen that the adjustment procedures have greatly improved the radar estimates for both periods. A decreasing trend of the RMSE as well as MAE values and an increasing trend of NSE value can be observed when the raw radar data are subjected to subsequent adjustment steps. It is calculated that the RMSE values improved by 25%, the MAE by about 34% for summer weeks. More significant improvements have been observed in the winter period than the summer period denoted by about 45% improvement on the RMSE and 47% on the MAE compared to the original LAWR estimates.

0

1

2

3

4

5

RMSE MAE NSE

[mm

] for

RM

SE &

MA

E, N

SE [-

]

Statistical Indicators

[a] Raw data

Range dependent adjustment

MFB adjustment

BRA adjustment

-1

0

1

2

3

4

5

6

7

RMSE MAE NSE

[mm

] for

RM

SE &

MA

E, N

SE [-

]

Statistical Indicators

[b] Raw data

Range dependent adjustment

MFB adjustment

BRA adjustment

Figure 1. Evolution of different rainfall goodness-of-fit statistical after adjustment step on the LAWR-Leuven estimates; [a]-summer period and [b]-winter period Hydrological application Tuning of the model parameters has been done with an heuristic approach. Optimization of model parameters has been based on good matching on total water balance, shape of the hydrograph, peak flows and low flows. Table 2 shows the results of hydrological model performance evaluation based on the Water Engineering Time Series PROcessing tool (WETSPRO). The model performance statistics shown in that table are the MSE and NSE for “nearly independent” peak and low runoff flows extracted from the hourly time series ranging from 9/10/2003 to 2/28/2009. Details about WETSPRO can be found on Willems, (2009) [9].

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Table 2. Some goodness-of-fit-statistics

MSE [m3/s] NSE [-] Flow Periods VHM NAM VHM NAM

Quick Flow 1.06 1.14 90% 75%

Slow Flow 1.01 1.02 92% 89%

Figure 2 shows results in terms of NSEobs.The result in terms of NSEref can be found in Figure 3 and expresses the errors in reproducing the reference flow introduced by the LAWR rainfall, keeping the parameter uncertainty the same.

0.0

0.2

0.4

0.6

0.8

1.0

3-Aug-08 4-Dec-08 22-Jan-09 9-Feb-09

NSE

obs

[-]

Storm events

[NAM] Pref LAWR

0.0

0.2

0.4

0.6

0.8

1.0

3-Aug-08 4-Dec-08 22-Jan-09 9-Feb-09

NSE

obs

[-]

Storm events

[VHM] Pref LAWR

Figure 2. NSEobs for different rainfall descriptors and for different storm events

Across all storm events, the NSEobs for Pref varies from 0.66 to 0.90 for the VHM and from 0.34 to 0.93 for the NAM simulated flows. The storm event of 9-Feb-09 results in the highest NSEobs value for both models. The storm event of 3-Aug-08 results in the lowest NSEobs value for the VHM and the storm of 5-Dec-08 for the NAM. Degradation of the NSEobs can be observed for the LAWR derived flows in most of the cases. Considerable improvement can be observed in NSEobs values when using LAWR estimates in winter periods rather than in summer periods. Results indicate that lower NSEobs values are expected for summer events than for winter events. This may be due to the rainfall spatial variability in summer events. Summer events are of highly convective nature and the raingauge may have missed this information. On the other hand, the winter events have less spatial gradients and the rain gauge network can represent them with considerable accuracy. Likewise, the average NSEref values for the LAWR driven flows are 0.83 and 0.86 and NSEobs values are 0.72 and 0.62 for VHM and NAM simulated runoff respectively. The average NSEobs for the Pref driven flow is 0.79 for the VHM and 0.70 for the NAM (the difference from 1 can be regarded as model error). Hence the deviation from NSEref and NSEobs can be considered as the additional error (in comparison with the use of the reference rainfall) introduced by using the LAWR estimates.

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0.0

0.2

0.4

0.6

0.8

1.0

3-Aug-08 4-Dec-08 22-Jan-09 9-Feb-09

NSE

ref [

-]

Storm events

VHM

NAM

Figure 3. Results in terms of NSEref for the different rainfall descriptors

Hence from the results, contrary to expectation, underperformance of the LAWR estimated rainfall can be observed. This underperformance can be attributed to the calibration strategy used, where both models were calibrated against Pref. It is also related to the nature of the models used. Both are lumped rainfall runoff models, using averaged areal rainfall rather than using spatially variable input. Hence, for extreme and summer events where the spatial variability of rainfall is high, the radar estimates are always tend to be dampened due to averaging effects of the large number of pixels covering the catchment. The underestimation may also be due to discrepancies in the sampling mode, an inappropriate conversion equation, a non-optimal adjustment methodology. Another, more important and perhaps more evident reason may be that the radar has limited accuracy in its rainfall intensities and that the adjustment based on the rain gauges may have failed to capture all the spatial variability. Moreover, it can be worthwhile to note that the importance of spatial rainfall such as the estimates of LAWR depends on how variable the rainfall is and whether there is enough variability to overcome the damping and filtering effect of the basins because fast responding catchments are more sensitive to spatial rainfall variability. As the studied catchment is flat and characterized by predominant sandy soils, a large portion of rainfall infiltrates and local variation of the rainfall input is smoothed and delayed within the soil. Hence, rainfall variations are dampened by integrating the response of the catchment. CONCLUSIONS AND RECOMMENDATIONS Range dependent adjustment followed by the MFB adjustment and Brandes Spatial Adjustment improved raw radar estimates quite significantly. In numerical terms, the Root Mean Square Error was improved by 45% whereby 47% improvement has been observed on the Mean Absolute Error. After adjustments, the radar-gauge comparison in the considered summer period improved more than that in the winter period. In terms of runoff simulations, the performance of both the VHM and NAM models could not be highly distinguished. Four storm events were investigated to test the prediction capability

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of the LAWR estimates. NSEref values less than 0.7 for summer storms indicate that local summer rain cells played a role to produce lower peaks. This can also be attributed to the high dampening effect of the catchment.

Separate analysis on different storm periods (summer and winter) based on longer series of data is recommended. Use of a model which can use full spatial information of rainfall is also recommended. Testing the rainfall spatial information on more urbanized catchments having a lower dampening effect is also recommended. REFERENCES [1] Austin G. L., Nicol J., Smith K., Peace A. and Stow D., “The Space Time

Variability of Rainfall Patterns: Implications for Measurement and Prediction”, Proc. Western Pacific Geophysics Meeting, AGU, Wellington, New Zealand, (2002).

[2] Brandes E. A., “Optimizing rainfall estimates with the aid of radar.”, J. Appl. Meteor., 14(4), (1975), pp 1339-1345.

[3] DHI, “MIKE 11 User & Reference Manual”, Danish Hydraulic Institute, Denmark, (2004).

[4] Einfalt T., Nielsen K.A., Golz C., Jensen N. E., Quirmbach M., Vaes G. and Vieux B, “Towards a roadmap for use of radar rainfall data in urban drainage” , J. Hydrol., 299(3-4), (2004), pp 186-202.

[5] Goormans T., Willems P. and Jensen N. E., “Empirical assessment of possible X-band radar installation sites, based on on-site clutter tests”, proc. 5th Eur. Conf. on Radar in Meteorology and Hydrology (ERAD 2008), Helsinki, Finland, 30 June – 4 July, (2008).

[6] Nash J. E. and Sutcliffe J. V., “River flow forecasting through conceptual models part I − A discussion of principles”, J. Hydrol., 10 (3), (1970), pp 282-290.

[7] Willems P., “Probabilistic immission modelling of receiving surface waters”, PhD Thesis, Katholieke Universiteit Leuven, Faculty of Engineering, Leuven, Belgium, (2000).

[8] Willems P., “Stochastic description of the rainfall input errors in lumped hydrological models”, Stoch. Env. Res. and Risk Assess., 15(2), (2001), pp 132-152.

[9] Willems P., “A time series tool to support the multi-criteria performance evaluation of rainfall-runoff models”, Env. Mod. Soft., 24(3), (2009), pp 311-321.

[10] Wilson J. W. and Brandes E. A., “Radar Measurement of Rainfall: A Summary”, Bull. Am. Meteor. Soc., 60(9), (1979), pp 1048-1058.