Advances in Water Resources 32 (2009) 1066–1076

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Advances in Water Resources

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Towards flash-flood prediction in the dry Dead Sea region utilizingradar rainfall information

Efrat Morin *, Yael Jacoby, Shilo Navon, Erez Bet-HalachmiDepartment of Geography, Hebrew University of Jerusalem, Mount Scopus, 91905 Jerusalem, Israel

a r t i c l e i n f o a b s t r a c t

Article history:Received 26 January 2008Received in revised form 21 November 2008Accepted 22 November 2008Available online 7 December 2008

Keywords:Flash floodsWeather radarHydrological modelDry climateDead Sea

0309-1708/$ - see front matter � 2008 Elsevier Ltd. Adoi:10.1016/j.advwatres.2008.11.011

* Corresponding author. Tel.: +972 2 5883020; fax:E-mail address: msmorin@mscc.huji.ac.il (E. Morin

Flash-flood warning models can save lives and protect various kinds of infrastructure. In dry climateregions, rainfall is highly variable and can be of high-intensity. Since rain gauge networks in such areasare sparse, rainfall information derived from weather radar systems can provide useful input for flash-flood models. This paper presents a flash-flood warning model which utilizes radar rainfall data andapplies it to two catchments that drain into the dry Dead Sea region. Radar-based quantitative precipita-tion estimates (QPEs) were derived using a rain gauge adjustment approach, either on a daily basis(allowing the adjustment factor to change over time, assuming available real-time gauge data) or usinga constant factor value (derived from rain gauge data) over the entire period of the analysis. The QPEsserved as input for a continuous hydrological model that represents the main hydrological processesin the region, namely infiltration, flow routing and transmission losses. The infiltration function is appliedin a distributed mode while the routing and transmission loss functions are applied in a lumped mode.Model parameters were found by calibration based on the 5 years of data for one of the catchments. Val-idation was performed for a subsequent 5-year period for the same catchment and then for an entire 10-year record for the second catchment. The probability of detection and false alarm rates for the validationcases were reasonable. Probabilistic flash-flood prediction is presented applying Monte Carlo simulationswith an uncertainty range for the QPEs and model parameters. With low probability thresholds, one canmaintain more than 70% detection with no more than 30% false alarms. The study demonstrates that aflash-flood warning model is feasible for catchments in the area studied.

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1. Introduction

A flash flood can be generated during or shortly following arainfall event, especially when the rain is of high-intensity. As flashfloods are among the most destructive natural disasters that strikepeople and infrastructures, it is not surprising that forecasting suchevents has increasingly become a high priority in many countries.Georgakakos [17] presented the physical characteristics of flashfloods and the requirements for a warning system. Collier [11] re-viewed flash-flood forecasting, considering the limitations anduncertainty involved.

Flash-flood prediction using numerical models has become fea-sible only in the last two decades with the advance of remotelysensed quantitative precipitation estimation (QPE) from weatherradar systems and satellites. Until then, QPEs from sparse raingauge networks were unable to represent the spatial variabilityof rainfall, which is typically large during storms that generateflash floods (e.g., [13,32]).

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+972 2 5820549.).

In the recent years, several research groups have studied vari-ous hydrometeorological aspects of flash floods. These includethe use of radar information for flash-flood prediction [3,4,14,41,44,49,50], development of flash-flood guidance for warning sys-tems [7,18], and uncertainty analysis of flash-flood warnings [6].The focus, however, of these and many other investigations hasbeen mainly on humid regions; few have dealt with dry climaticregions (e.g., [28,36]). Dry climate, according to the Köppen classi-fication, is characterized by potential evapotranspiration thatexceeds precipitation and may further be divided into semi-aridand arid climate types (e.g., [1]). Dry regions occupy more than aquarter of the world’s land area (more than any other major cli-matic type).

Accurate QPE is clearly an essential element in flash-flood pre-diction. The emergence of high-resolution (spatial and temporal)remotely sensed QPE technology has improved flash-flood predic-tion in many regions (e.g., [11]). A typical ground-based weatherradar system, the most common source of QPE, has an areal coverof more than 30,000 km2 with typical space–time resolutions of1 km2 and 5 min. Radar systems measure the reflectivity (Z inm3/mm6) of the electromagnetic energy backscattered from rain-drops in the atmosphere. The reflectivity values have been found

E. Morin et al. / Advances in Water Resources 32 (2009) 1066–1076 1067

to correspond with rain intensity (R in mm/h), leading to thewidely used Z–R relationships (e.g., [27]). Radar-based QPE is sub-ject to several sources of error (e.g., [23]), but some of these can bereduced by applying correction procedures prior to, or as part of,the Z–R transformation. Radar data are often combined with raingauge data to obtain quantitatively accurate and spatially continu-ous radar-derived precipitation fields.

Morin and Gabella [35] have recently shown that in dry cli-mates, radar-based QPEs are significantly better than QPEs basedonly on gauge data. Flash-flood prediction is obtained by usingthe QPE as input to a hydrological model to compute the catch-ment flow. Examples of hydrological models that utilize radar datafor flood prediction include Vieux and Bedient [48], Giannoni et al.[20], Bedient et al. [2], Borga et al. [4], and Smith et al. [44]. A fewhydrological models have been developed for catchments in dry(semi-arid and arid) climate regimes. One example is the Kinerosmodel [45], which was developed for semi-arid conditions insouthern Arizona and subsequently incorporated into many hydro-logical studies of that region (e.g., [33,36]). Shamir et al. [42] pre-sented a model for the Santa Cruz River in Arizona. In Israel, theZin model was applied to two flooding events in the arid Zin catch-ment [28]. The present paper focuses on flash-flood prediction un-der dry climate conditions of the Dead Sea region.

The objectives of the study were to

1. Develop a radar-based QPE for flash-flood warnings over theDead Sea and assess its accuracy.

2. Construct a continuous hydrological model that utilizes the QPEand computes flow at the catchment outlet. The model wouldissue a flash-flood warning according to the pre-definedcriteria.

3. Validate the model using deterministic and probabilistic modes.

Fig. 1. Location map showing the Dead Sea and other areas of interest. The triangleindicates the location of the radar system.

Table 1Rainfall statistics for Jerusalem, Jericho and Sedom rain stations.

Jerusalem Jericho Sedom

Station elevation 815 m �290 m �390 mRecord length 59 yr 39 yr 45 yrAnnual rain depth 532 mm 156 mm 45 mmMean number of rainy days 60 40 17Mean percent rainfall in September–November 13.1 17.1 15.6Mean percent rainfall in December–February 64.9 61.7 57.2Mean percent rainfall in March–June 22.0 21.2 27.2

2. Study area and data

The Dead Sea (Fig. 1) is a terminal saline lake located at the low-est point on the Earth’s surface at about �400 m [15]. The study fo-cuses on catchments that drain directly into the Dead Sea from thewest where the water divide is at 600–1000 m, on the eastern flankof the Judea Mountains. These catchments are prone to flash floodsthat often cause heavy casualties and severe damage. Therefore, aflash-flood warning system for this region is essential for protect-ing lives and infrastructure.

Dayan and Morin [13] reviewed the main synoptic systems thataccount for most of the major flash floods in the region, includingextra-tropical cyclones from the Mediterranean Sea and the ActiveRed Sea Trough, an extension of the African Monsoon [24]. Theauthors also describe the sub-synoptic processes leading to deepconvection and the resulting spatial-temporal rainfall characteris-tics. The climate in the region varies from Mediterranean (mild wetwinter followed by hot and rainless summer) on the western, up-stream parts of the catchments to semi-arid and arid to the east,near the lake. The sharp climatic gradient is demonstrated by therainfall statistics presented in Table 1, based on the daily rainfallfor three stations: Jerusalem, Jericho and Sedom (Fig. 1). Differentcharacteristics of rain intensities are presented through the Inten-sity–Duration–Frequency (IDF) curves of the Jerusalem and Jerichorain stations (Fig. 2). As can be inferred from Table 1 and Fig. 2, an-nual rainfall decreases from west to east and from north to south,and a smaller proportion of the rainfall occurs in the autumn andspring. In addition, extreme rain intensities for short durationsand long recurrence intervals are higher as the climate becomesdrier.

Late Cretaceous carbonates of the Judea Group, up to a thicknessof 600 m, underlie the study area, declining eastward, covered by

Senonian marine sediments of the Mt. Scopus Group. Soil coverchanges as a reflection of the rainfall gradient from reddish carbon-ate soil (Terra Rosa) in the west to desert soil on the plateau [29].The desert plateau is bounded by the Dead Sea Fault Escarpment,with a relief of up to 650 m above the Dead Sea level. The catch-ments in the study region are characterized by a relatively fasthydrological response controlled by the large areas of bare rock,shallow soils, absence of vegetation, presence of debris cover anddesert pavement, formation of physical crusts during rainstormscaused by raindrop impact on the top soil, and rapid decay of theinfiltration curve ([22] and references therein).

Two gauged catchments were selected as case studies (Fig. 3):the Arugot catchment (235 km2) and the Darga catchment(70 km2). Table 2 lists some of the catchment and flow character-istics of the two areas studied.

Fig. 2. Intensity–Duration–Frequency (IDF) curves of the (a) Jerusalem and (b) Jericho rain stations. Jerusalem station record: 1950–1998; Jericho station record: 1967–1994.Charts were generated by Rainplot software developed as part of the Regional Rainfall-Intensity Project.

Fig. 3. Location of the studied catchments, Arugot and Darga. Catchment bound-aries, channel network, and hydrometric station (red points) are presented. Blackcircles indicate manual daily rain gauges in the area. Annual rainfall contours arepresented. Grid represents the pixels of the radar over the region. (For interpre-tation of the references to colour in this figure legend, the reader is referred to theweb version of this article.)

1068 E. Morin et al. / Advances in Water Resources 32 (2009) 1066–1076

Radar data were obtained from the system operated by the Sha-cham Mekorot Company located at Ben-Gurion airport (triangle inFig. 1). Daily rain depth data were obtained from the Israel Meteo-rological Service and included 30 gauges located in the study re-

gion. Flow data were obtained from the Israel HydrologicalService for the hydrometric stations at the two catchment outlets.The data were derived from the digitized charts of flow stage con-verted into flow discharge by the rating curves of each hydrometricstation. Because of the manual digitizing process and the mechan-ical clocks in the stations, the timing of the flow might be inaccu-rate. Cross-section data were obtained by field measurements forthe two catchments.

The study period was the water years 1992–2001, when bothradar and flow data were available. Recall a water year that is de-fined as the 12-month period from October through Septemberand is designated by the calendar year in which it ends. Data forthe first 5 years of the Arugot catchment were used for calibration,and the following 5 years of data were used for model validation.The 10-year data record of the neighboring Darga catchment wasused for model validation to test the model transferability to anungauged catchment.

3. Radar rainfall

The study area is located about 40–70 km southeast of the radarsystem. The radar is a C-band, non-Doppler system. The spatial res-olution of the radar data is 1.4� � 1 km (an average of 0.8 km2 overthe study area) and the temporal resolution is 5 min (see radar gridin Fig. 3 over the study catchments). The radar-scanning pattern isnot constant due to an unstable antennae and changes of elevationangle over time. Typically, the radar scans at about 13 elevation an-gles where the beam center of the first, second and the third eleva-tion angle is in the range of 0.5–1o, 1.1–1.9o, and 2.0–2.7o,respectively. Unfortunately, the mountainous ridge west of thestudy area blocks the radar’s lowest beams. Fig. 4 displays thetopography and the beam centers toward and over the Arugotcatchment at the typical first three elevation angles. As can beseen, the first elevation angle is completely blocked by topography.The second elevation may be partly blocked, depending on its spe-cific angle, and the third elevation angle is potentially available foranalysis. At the latter elevation angle, however, overshooting mayoccur and cause severe underestimation of surface rainfall. In thepresent analysis, the maximal radar value from the second andthird elevation angles was used for the analysis. Forty-five daysin which the radar data refer to the elevation of more than 1 kmabove the freezing level (as obtained from sounding data) wereeliminated from the analysis. Floods occurring on these days are

Table 2Catchment flow characteristics (1991/2–2000/1).

Arugot Darga

Area 235 km2 70 km2

Height range �390–1011 m

�12–822 m

Percent of desert soils 37% 45%Main channel lengtha 46 (20) km 24 (12) kmMean channel gradient 0.027 0.025Time of concentrationb 370 min 231 minMean annual runoff volume 2.00 106 m3 0.12 106 m3

Maximal observed peak discharge 418 m3/s 61 m3/sAverage number of flow events per year 3.8 1.6Threshold discharge value (1.5 year recurrence

interval)2.1 m3/s 3 m3/s

a Number in parentheses is the main channel length located in desert soils (fortransmission loss computation).

b According to the formula Tc ¼ 5:4ðL=ffiffispÞ0:75, L is the main channel length in km,

s is the channel gradient and Tc is the time of concentration in minutes.

Fig. 4. Profile from the radar location eastwards over the Arugot catchment. Thethick solid line represents topography; the thin solid lines represent the central lineof the radar beam for the typical three lowest elevation angles. The dashed verticallines mark the location of the Arugot catchment in the profile.

Fig. 5. The lower part of the graph shows a comparison of freezing levels (blue line)as obtained from sounding data and elevation (green line) of radar beam center(median height value for the different gauges in the region). Horizontal lines at thebottom mark days eliminated from the analysis because the radar data are morethan 1 km above the freezing level. The upper part of the graph shows a comparisonof the daily rain gauge adjustment factor (computed for each day) and the constantrain gauge adjustment factor computed from data over the 5-year calibrationperiod. The graphs represent all the rainy days in the 10-year record. (Forinterpretation of the references to colour in this figure legend, the reader is referredto the web version of this article.)

Table 3Cross-validation of radar rainfall estimates by rain gauges.

RMSD (relativea) AD (relativeb)

Daily adjustment 10.0 mm (67%) 6.0 mm (41%)Constant adjustment (1.93) 10.0 mm (67%) 6.2 mm (42%)

a Root Mean Square Difference (RMSD) is compared to the root of sum of thesquares of gauge daily data.

b Absolute Difference (AD) is compared to mean daily data.

E. Morin et al. / Advances in Water Resources 32 (2009) 1066–1076 1069

considered undetectable and are not included in the score com-puted for the model (Section 4.4, below). The lower part of Fig. 5presents the freezing level and the height of the radar beam center(median height value for the different gauges in the region) foreach rainy day in the record. Marks indicate days eliminated fromthe analysis because of suspected overshooting.

Ground clutters contaminate almost 30 km2 of the western partof the Arugot area. Data for this area were obtained from the near-by radar pixels.

The rain gauge adjustment method was used to compute rain-fall intensity, R (mm/h), from radar reflectivity data, Z (mm6 m�3).The power law, Z = 316R1.5, was applied as the first step, and theestimates were then adjusted by applying an adjustment factorcomputed as the ratio of total rainfall in gauges to total rainfallin radar pixels above the gauges. Two bulk adjustment approacheswere used:

1. Daily adjustment: the adjustment factor is allowed to changefrom day to day. The gauge to radar ratio is computed betweenthe accumulations of rain from the storm’s beginning to theanalyzed day. Storms are separated by at least one day withno rain in the region. It should be emphasized that the calcula-tion of the daily adjustment factor is currently not feasible inreal time in the Dead Sea region because an automatic gaugenetwork has not been installed in the region. However, we hopethat the findings of this study will encourage the installation ofsuch a network that will allow a real-time update of the adjust-

ment factor every time a new data set of rain gauge accumula-tion is obtained.

2. Constant adjustment: the adjustment factor is computed overthe calibration period (water years 1992–1996) and is not chan-ged during the analysis. The value found was 1.93. Estimatesbased on the constant gauge adjustment are currently availableand do not require an automatic rain gauge network for real-time calibration. These estimates, however, are expected to beless accurate.

The upper part of Fig. 5 presents the daily gauge-adjustmentfactors compared to the constant adjustment factor.

Other rainfall estimation methods were examined but did notprovide a significant improvement relative to the rain gaugeadjustment method. Morin and Gabella [35] found that for dryareas in Israel, the bulk adjustment method performed well com-pared to other, more sophisticated methods that relate the adjust-ment factor to spatial characteristics such as distance from theradar and altitude.

Evaluation of the radar rainfall estimates over the study areawas performed by applying a cross-validation technique. For eachiteration, one gauge were removed from the computation of theadjustment factor and the daily rainfall for the gauge locationwas estimated from the adjusted radar data. The estimated dailyrain was then compared to the observed gauge data that was re-moved. The average errors for all gauges (presented in Table 3)indicate an error range of 40–70% for daily rainfall estimates,which lies in the reported error range of other studies (e.g.,[16,35]).

1070 E. Morin et al. / Advances in Water Resources 32 (2009) 1066–1076

4. Flash-flood warning model

The flash-flood warning model presented in this study is de-signed to work in an operational framework. This implies real-timerainfall data, a continuous hydrological model that accounts forwetting and drying of the soil, and short computation time. Themodel is described below.

4.1. Flash-flood warning criteria

Flash-flood warning models require pre-defined criteria forissuing a flood warning. Often, a bankfull flow is used to indicatethe possibility of a flood occurring (e.g., [7]). Regional field studies

Fig. 6. Photo of a typical channel cross-section in the area. First terrace and flowdirection is marked. The photo was taken near the hydrometric station in the Dargacatchment.

Fig. 7. Empirical flood frequency curve for stream flow in the Arugot and Dargacatchments derived from the catchment annual maxima flow data. Interpolation forthe exceedence probability associated with a 1.5 year recurrence interval (0.67) wasperformed to derive a discharge threshold for flash-flood warnings (see Section 4.1).

Table 4Hydraulic parameters for the threshold discharge values based on four the sections.

Catchment Threshold discharge (m3/s) Manning roughness Energy slope

Arugot 2.1 0.03 0.009Darga 3.0 0.03 0.012

have concluded that bankfull flow is associated with a recurrencestream flow interval of about 1.5 years [30]. Although recent stud-ies have examined bankfull flow characteristics in non-humidenvironments (e.g., [8,40]), a comprehensive study has yet to becarried out in dry climates, which examines the bankfull flow con-cept, its related recurrence interval and its relations to upstreamcatchment characteristics. Such questions, however, are beyondthe scope of the present paper.

The assumption made in the present study is that the flow thatreaches the first terrace of the channel is the bankfull flow. Fig. 6shows a photo of a typical cross-section in the region with terracelevels marked. Field measurements were conducted for four cross-sections near the hydrometric station of the two studied catch-ments. For the Arugot catchment, the station is located down-stream of the Dead Sea Fault Escarpment, which may alter flowcharacteristics, and thus the cross-sections were taken at a closerpoint, upstream of the escarpment.

The discharge values related to the lowest level of the first ter-race were computed using HEC-RAS hydraulic software [46]. Thewater surface profiles were produced based on the four cross-sec-tions in subcritical flow regime with a Manning roughness param-eter value of 0.03 as evaluated in the field. The computed dischargevalues are only approximations and should be treated with cau-tion. The derived values ranged from 0.75 to 2.4 m3/s for the Aru-got catchment and from 2.5 to 9 m3/s for the Darga catchment.

In addition, discharge values associated with 1.5 year recur-rence intervals were computed for both catchments based on theempirical frequencies of annual maxima series (Fig. 7), with thevalues of 2.1 and 3 m3/s for the Arugot and the Darga catchments,respectively. Since the 1.5 year discharge values are in the range ofthe values derived from cross-section data, it was decided to usethem as the criteria for flash-flood occurrence in both catchments(see Table 4 for hydraulic parameters of the selected threshold dis-charge values). It should be emphasized that these are relativelyconservative values and do not necessarily imply destructive ordangerous flow. However, flow up to the first terrace is a signifi-cant event requiring an alert, especially in desert areas where flowis rare and unexpected.

4.2. Model description

The hydrological model was developed to accommodate real-time operation and is optimized in terms of peak discharge, whichis the target threshold in flash-flood prediction. Peak timing is notconsidered here because the observed flow timing is not suffi-ciently accurate. The model runs continuously at 5 min time steps,gets rainfall updates, computes outlet peak discharge, and gener-ates warnings if the pre-defined criteria are met.

The main hydrological processes typical of dry catchments,namely infiltration excess runoff, flow routing and channel loss,are represented in the hydrological model according to the existingknowledge about these processes, while also considering the com-putation time. A distributed infiltration module and a lumped rout-ing module are utilized.

4.2.1. Rainfall inputRain intensity data are obtained from the calibrated radar data at

the resolution of the radar system, i.e., 5 min in time and �0.8 km2

Wetted area (m2) Flow velocity (m/s) Top width (m) Froude number

1.9 1.1 8.8 0.82.5 1.2 9.7 0.8

E. Morin et al. / Advances in Water Resources 32 (2009) 1066–1076 1071

in space. Missing scans resulting from radar system malfunction arehandled by interpolation, providing the time gap is that less than15 min; for larger time gaps, zero rainfall is assumed. This assump-tion fits the typical short duration of showers in the region.

4.2.2. InfiltrationIn dry (semi-arid and arid) catchments, the dominating runoff

generation mechanism is infiltration excess. In this process, rainintensities higher than the soil infiltration capacity generate infil-tration excess runoff. Infiltration decay is typically quick and in arelatively short time, the final infiltration rates are attained [22].Accordingly, we used the constant initial losses and constant infil-tration capacity model to represent the infiltration process:

DiðtÞ ¼0 siðt � 1Þ þ RiðtÞ � Dt=3600 6 li

RiðtÞ � fi siðt � 1Þ þ RiðtÞ � Dt=3600 > li; RiðtÞ > fi

� �ð1Þ

where i represents a specific pixel, RiðtÞ (mm/h) is the rain intensityover pixel i at time step t, Dt (s) is the time interval, li (mm) is theinitial loss parameter of pixel i, fi (mm/h) is the infiltration capacityparameter of pixel i, siðt � 1Þ (mm) is the state variable representingrainfall storage at pixel i at the end of the previous time step (t � 1),and DiðtÞ (mm/h) is the infiltration excess runoff rate at pixel i andtime step t.

The storage state variable, si, ranges from 0 to li, increases inrainy time steps and decreases by evaporation in time steps withno rain. The drying of the storage takes into account the currentstorage state at the pixel. The following equation describes thechange of the variable over time:

siðtÞ ¼maxfsiðt � 1Þ � EðmðtÞÞ � siðt�1Þ

li� Dt=3600; 0g RiðtÞ ¼ 0

minfsiðt � 1Þ þ RiðtÞ � Dt=3600; lig RiðtÞ > 0

( )

ð2Þ

where EðmðtÞÞ is the climatological potential evaporation (mm/h) inthe month of time step t. Setting the li parameter to zero impliesthat there is no significant storage in the pixel and, the above equa-tion is not applied.

The infiltration computation is done in a distributed mode (i.e.,for each radar pixel separately). The two infiltration parameters,namely initial loss, l (mm) and infiltration capacity, f (mm/h), de-pend on soil type. Two general types were considered: (1) moun-tainous soil located in the western part of the catchment with aMediterranean climate and (2) desert soil located in dry (semi-aridand arid) areas on the eastern part of the catchment.

4.2.3. Flow routingThe infiltration excess runoff generated over the catchment

flows toward its outlet. This study uses the relatively simplelumped flow routing procedure based on a unit hydrograph model,rather than on the more complicated numerical models represent-ing hillslope and channel flow, to allow for the rapid computation

Table 5Calibrated parameter values (Arugot 1991/2–1995/6).

Parameter Value

Initial loss – mountainous soils 70 mmInfiltration capacity – mountainous soils 25 mm/hInitial loss – desert soils 0 mmInfiltration capacity – desert soils 2 mm/hChannel loss 0.0 m3/s/kmStorage time constant parameter of linear reservoir 9000 sNumber of linear reservoirs in a series 1

a Change in RMSE per +5% change in parameter value. For the zero value parameters,parameter values in +1 mm and +0.1 m3/s/km, respectively.

b Percent change in RMSE per +5% change in parameter value. This computation can

time required for real-time operation. The unit hydrograph is com-puted as a series of linear reservoirs having the same storage con-stant according to the following equation [39]:

uðtÞ ¼ 1kðn� 1Þ!

t � Dtk

� �n�1

e�t�Dt=k ð3Þ

where n is the number of linear reservoirs, k (s) is the storage timeconstant parameter of the reservoirs, and uðtÞ (m3/s/(mm/h)) is theunit hydrograph value at time step t. At each time step, the averageinfiltration excess runoff is multiplied by the unit hydrograph vec-tor and the result is added to the real-time computed outlet runoffhydrograph.

The two routing parameters, number of reservoirs, n, and theirstorage time constant, k, are found by the visual comparison of ob-served and computed hydrographs over the calibration periods.

4.2.4. Transmission lossesThe process of infiltration into the channel alluvium during

flow events is known to be important in some arid and semi-aridcatchments [43]. This process is represented in the model as a con-stant loss of discharge per unit length of the main channel. Theconstant loss rate multiplied by half the channel length (shownin Table 2), representing the average flow length, is subtractedfrom the outlet runoff hydrograph. This is performed only oncefor each time step and the constant loss parameter value is foundby calibration.

Note that the above model enables a rapid computation in acontinuous mode to predict flow discharge at the catchment outletand its update at each time step (5-min) when new rain data areobtained.

4.3. Model calibration

Table 5 shows the seven model parameters calibrated, based onthe observed flow for the calibration period (water years 1992–1996). To ensure relatively high quality calibration data, days onwhich more than half of the radar scans are missing were removedfrom the analysis. For the same reason, radar rainfall data esti-mated with daily adjustments were used in the calibration process.The two routing parameters that mainly affect the hydrographshape were found by trial and error by visually comparing ob-served and computed hydrographs. The five other parameters werederived by an automatic search over the parameter space consider-ing two objective functions: the Root Mean Square Error (RMSE)and the multiplicative Bias:

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n

Xn

i¼1

ðQ Ci � Q OiÞ2vuut ; Bias ¼

Pni¼1Q CiPni¼1Q Oi

ð4Þ

where QOi and QCi are the observed and computed daily peak dis-charge over the calibration period, respectively, and n is the numberof days compared.

Range Absolute sensitivitya Relative sensitivityb

42–91 mm 1.3E–5 m3/s/mm 1.4E–417.5–32.5 mm/h 0.02 m3/s/mm/h 0.080–2 mm 0.04 m3/s/mm1.4–2.6 mm/h 0.41 m3/s/mm/h 0.130.0–0.1 m3/s/km 0.10 m3/s/m3/s/km

initial loss in desert soils and channel loss, the calculation is done by changing the

be performed for non-zero parameters only.

Fig. 9. Observed and computed flood hydrographs for validation of the 2/5/2001event at the Darga catchment. The event was the largest one on the record. The timeat which the model provided the flash-flood warning is marked in the figure.

0

1

2

3

4

0 2 4 6 8 10 12 14

RMSE (m3/s)

Mul

tiplic

ativ

e B

ias

Fig. 8. The RMSE and multiplicative Bias objective function values of parameter sets(black circles) examined in the model calibration process. The objective functionsare computed based on the observed and computed daily peak discharge. Optimalsets are located as near as possible to RMSE = 0 and multiplicative Bias = 1. Redcircles mark the trade-off solution group composed of all sets of parameters suchthat none of them is better than the others in terms of the two objective functions.The empty yellow circle marks the parameter set selected for the model; itsparameter values are given in Table 5. (For interpretation of the references to colourin this figure legend, the reader is referred to the web version of this article.)

1072 E. Morin et al. / Advances in Water Resources 32 (2009) 1066–1076

Fig. 8 presents the RMSE and multiplicative Bias values obtainedin the calibration process for the parameter sets examined. Ideally,we search for an optimal set of parameters that provide a minimalRMSE value and closest to one multiplicative Bias value; however,there is no single data set that provides a model optimum basedon the two objective functions; rather, there are several trade-offsolutions (e.g., [5,12]) represented by the red circles in the figure.The trade-off solution group is composed of all sets of parameterssuch that none is better than the others in terms of the two objectivefunctions. From this group, a parameter set was subjectively se-lected (marked in Fig. 8), which seems reasonable in terms of itsparameter values and objective function values (RMSE = 6.3 m3/s,Multiplicative Bias = 0.99).

The values found for the infiltration capacity parameters (Table5) are somewhat low relative to the values presented in Cerda [9]of 30–51 mm/h in the Mediterranean parts and 2–18 mm/h in thearid parts close to the Dead Sea. It should be noted, however, thatin many cases, including that of Cerda [9], infiltration rates arefound by a rainfall simulator experiment performed on a small area(less than 1 m2 in [9]), while the calibrated parameters found inthis study represent much larger areas, on the order of km2 (radarpixel). Differences in parameter values are expected as a result ofthe different scales (see, e.g., [25]). The initial loss parameter formountainous soils was found to be 70 mm, implying runoff contri-butions from the upper part of the catchment only after a consid-erable amount of storm rainfall (the daily rain depth of 70 mm inthe Jerusalem rain station has a return period of 2.7 years) orwet soil conditions from the previous storms. Indeed, low and rarerunoff flow is observed in hydrometric stations located in similarmountainous areas, west of the Dead Sea region. The channel lossparameter was found to be zero. This implies that, at least for thestudied catchments and data, the transmission loss process is notof major importance in the context of flash-flood peak dischargeprediction. It may be important in terms of flood volume or otherparameters not examined in this study [43].

Analysis of the sensitivity of the RMSE objective function to thedifferent model parameters (Table 5) indicates that the initial lossparameter for mountainous soils is the least sensitive. Anotherindication of this insensitivity is that the trade-off solutions foundin calibration included the whole range of values examined for thisparameter, as opposed to a much lower range of values for the fourother parameters. As a result, the assurance in the parameter cali-brated value is lower than for the other parameters. The sensitivity

to infiltration capacity for desert soils is higher than the sameparameter for mountainous soils, which probably results fromthe rare activation of the latter area in runoff generation.

4.4. Model validation

Model validation was performed by running the model for theArugot catchment for the water years 1997–2001 and for the Dargacatchment for the water years 1992–2001. All model parametervalues were the same for the two catchments; only the thresholddischarge for warning was different (see Section 4.1). The simula-tions utilize the radar-based QPE with daily rain gauge adjustmentand with constant rain gauge adjustment factor found for the cal-ibration period (see Section 3, above). Fig. 9 presents the observedand computed hydrographs as well as the time warning issued forthe largest flood in the Darga catchment (2/5/2001). Although thefit between the two hydrographs is only moderate, it is sufficient interms of a flash-flood warning model whose goal is to identify theoccurrence of a significant flow.

5. Modeling results and analysis

5.1. Model performances

In order to examine the performance of the flash-flood warningmodel, two scores were computed:

1. Probability of detection (POD): the number of floods detectedby the model, out of the total number of detectable floods.

2. False alarm rate (FAR): the number of rainfall events detected asfloods by the model for which observations did not indicatefloods, divided by the total rain event number.

The scores were computed on an event basis, where an event isdefined as a consecutive sequence of days with rainfall over thecatchment, with at least 2 days without rain separating events.Events with less than 1 mm mean areal rain depth were not includedin the FAR score computation. Because of the rainfall threshold,some small differences in the event sequence may be found for dif-ferent QPEs. The number of detectable floods is the number of floodevents observed (according to the pre-defined criteria), excludingevents where freezing level was more than 1 km below the heightof the radar beam over the catchment (see Section 3).

Table 6 shows the scores for both validation cases using differ-ent radar QPE data. Relatively good scores of probability of detec-

Table 6Validation scores of the flash-flood warning model for the Arugot and the Dargacatchments.

Catchment Period Rainfalldata

Numberof rainfalleventsa

Number ofdetectablefloods

Probabilityofdetection

Falsealarmrate

Arugot 1995/6–2000/1

Dailyadjustment

53 17 0.82 0.23

Darga 1991/2–2000/1

Dailyadjustment

93 11 0.73 0.25

Arugot 1995/6–2000/1

Constantadjustment

55 17 0.41 0.22

Darga 1991/2–2000/1

Constantadjustment

113 11 0.73 0.21

a A rainfall event with mean areal rainfall >1 mm.

E. Morin et al. / Advances in Water Resources 32 (2009) 1066–1076 1073

tion are presented with daily gauge-adjusted radar QPEs but thefalse alarm rate is somewhat high. For the Arugot catchment, thescores based on daily gauge-adjusted radar QPEs are better thanfor constant gauge-adjusted radar QPEs. For the Darga catchment,however, the two radar inputs result in similar scores.

The cases where model error occurred (a flash flood was eithermissed or wrongly detected) were closely examined. A key reasonfor the model failing to detect a flood is often the large gaps in ra-dar data. Since the radar system is not intended for precipitationmeasurement but for other purposes, it is shut down from timeto time, or scans with low temporal resolution. For example, forthe first validation case (first row in Table 6), 3 of the 17 floodswere missed (18%). In all three cases, the number of available scanswas less than half (27%, 40% and 37%) of the expected scans for thestorm. Two of the three missed floods in the second validation casehad only 0.17 and 6% available scans. For other flood events, how-ever, even with a relatively low proportion of radar scans, the floodis detected, although the peak discharge may be underestimated.Of the 14 correctly detected floods in the first validation case, 6had less than half of the expected number of scans. Althoughscreening out events with a low proportion of scans improvesmodel scores, it was decided not to apply this criterion in orderto maintain a larger number of flood events in the analysis.

A clear cause for the second type of error, i.e., false alarms, couldnot be identified. It is postulated, however, that these are mainlythe result of uncertainties in model prediction resulting fromuncertainties in model parameters and structure as well as rainfallestimation. The following section presents model simulations, con-sidering the above uncertainties.

5.2. Probabilistic prediction

Probabilistic prediction allows to account for the uncertainty inthe model and to assign a probability of a flood occurring (e.g.,[19,47]). It is assumed that the error in the rainfall data is of themultiplicative form:

Rradar ¼ e � Rtrue ð5Þ

where Rradar is the rain rate derived from the radar data, Rtrue is thetrue rain rate over the location of interest, and the error term e is dis-tributed uniformly between 0.3 and 1.7. The ±70% level of error isaccording to the cross-validation analysis (Section 3). We assumethe value of e to be uniform over the entire study area and thevalidation period. We are aware that this assumption is not neces-sarily correct, but support for a different assumption is not currentlyavailable. The spatial–temporal structure of the QPE error requiresan in depth investigation utilizing a dense gauge network that wasnot available for the present study (see an example of such a networkin Ciach and Krajewski [10]). In addition, uncertainty is assumed forthe model parameters found by automatic calibration. The parame-

ter values are assumed to be uniformly distributed within a rangerepresenting 30% uncertainty for parameters with a calibrated valuelarger than zero and the subjective selection of an upper limit for thetwo zero value parameters (Table 5, third column).

A Monte Carlo simulation was performed, applying the aboveuncertainty range for QPE and parameters, and the probability ofa flood at a given time step was calculated as the fraction of simu-lations in which the discharge exceeded the threshold value.

With a probabilistic model output, the user can decide on differ-ent probability thresholds according to the risk associated with aflood. Fig. 10 presents the POD and FAR for the different validationcases and QPE data with probability threshold values between 0.1and 0.9. The model obviously performs better in terms of POD witha low threshold value but, at the same time, the FAR may be rela-tively high. For example, with a probability threshold of 0.1 inmore than 70% of the events the flood is correctly detected, butthe false alarm rate reaches a level of 40%. High threshold valuesreduce false alarm rates but the POD decreases (Fig. 10). With anintermediate probability threshold, for example 0.4, the model per-formance is about the same as the deterministic model (Table 6).The main advantage of the probabilistic mode of the model is inthe flexibility it provides to users to select different thresholds con-sidering the risk involved.

5.3. Analysis of rainfall-runoff characteristics

The flash-flood prediction model allows investigating the rela-tionships between rainfall characteristics as obtained from the ra-dar data and the runoff response as simulated by the model. Thecurrent section presents this analysis for the 10-year record inthe Darga catchment using the model in its deterministic formwith radar data applying daily rain gauge adjustments. Accordingto the model, while the mountainous part of the catchment sys-tematically received larger amounts of rain (80% more on average),most floods were generated from rainfall over its desert part. Thisdissimilar hydrological response is well understood and clearlymanifested in the model infiltration parameters (Table 5). For only6 of the 93 rain events analyzed, mountainous soils contributedmore than 10% to the flood peak discharge, with the largest contri-bution occurring for the largest flood in the record (2/5/2001).

The relationships between storm characteristics and computedflood peak discharge for the 93 events are assessed by the coeffi-cient of determination (r2) fitting the second-order polynomial(Table 7). The storm characteristics examined are maximal rainintensity for the durations of 5, 15, 30, 60, 120, 180, and240 min; storm rain depth; and coverage area of convective rainfall(rain intensity over 10 mm/h) at the time of maximal intensity.Each of the above characteristics was examined once for the entirecatchment and once for its desert part. The analysis again indicatesthat for the analyzed cases, rainfall over the desert areas is morerelevant to the catchment peak discharge. It also indicates thatthe shorter rain intensity durations (�30 min) are more importantthan the long duration intensities. The correlation found for therain intensity duration represented by the time of concentration(�4 h, see Table 2) is reduced to r2 = 0.60 suggesting that this timeparameter does not fit the typical rapid response of arid and semi-arid catchments, as already shown, for example, in [34]. Fig. 11shows the relationship found between 30 min maximal rain inten-sity over the desert area and the computed peak discharge ofr2 = 0.95. The convective rainfall coverage area was also found tobe an important factor, although with lower correlation coeffi-cients. In addition to the rainfall characteristics, other characteris-tics, such as storm velocity and direction, were examined, but hadno significant relation to the peak discharge.

Fig. 12 presents the change over time of the 30-min rain inten-sity (areal mean) and the convective rain coverage area over the

a b

c d

Fig. 10. Probability of detection (POD) and false alarm rate (FAR) for different probability thresholds: (a) the Arugot catchment with daily rain gauge-adjusted QPEs, (b) theDarga catchment with daily rain gauge-adjusted QPEs, (c) the Arugot catchment with constant rain gauge-adjusted QPEs, and (d) the Darga catchment with constant raingauge-adjusted QPEs.

Table 7Relationships between rainfall characteristics and peak discharge for the Dargacatchment.

rb,a

I15b 0.83I15Dc 0.92I30 0.83I30D 0.95I60 0.81I60D 0.95I120 0.81I120D 0.85I180 0.80I180D 0.72I240 0.79I240D 0.60Rain depth 0.29Rain depth desert 0.46Convective rain coverage aread 0.74Convective rain coverage aread – desert 0.67

a Coefficient of determination between rainfall characteristics and computedpeak discharge applying the second-order polynomial curve for the 93 rain events.

b In is the storm maximal rain intensity for the duration of n minutes.c InD is the storm maximal rain intensity for the duration of n minutes taken over

the desert part only.d Area of rainfall pixels with rain intensity larger than 10 mm/h at the time of

maximal rain intensity (at the observed resolution) over the catchment.

Fig. 11. Relationships between maximal rain intensities for a duration of 30 minaveraged over the desert area of the Darga catchment and the computed peakdischarge of the flow generated by the storm. A fitted second-order polynomial isshown with a coefficient of determination equal to 0.95.

1074 E. Morin et al. / Advances in Water Resources 32 (2009) 1066–1076

desert part of the catchment for two flash floods: the largest one onrecord (2/5/2001) and a medium flash flood (2/11/1995). Note thetypically small coverage area of the 2/11/1995 storm (mediumflash flood) where at the most intense stage of the storm only30% of the desert area (about 10 km2) is covered by convectiverainfall, as opposed to the almost full coverage for the storm that

generated the large flash flood (2/5/2001). At its peak, the latterstorm also covered almost the entire Mediterranean part of thecatchment (not shown). The synchronization of the time series ofthe two parameters, rain intensity and coverage area is, clearly evi-denced in the figure.

The lead time between flood detection by the model and the ac-tual occurrence of the flood at the catchment outlet is estimated inthis study as the time it takes for the water to flow from the centerof the mass of rainfall excess to the catchment outlet, assuming achannel flow velocity of 2 m/s. The lead time is computed for everyoccasion when the computed peak discharge reached the thresholddischarge of 3 m3/s. The computed lead times range from 21 to230 min, with a median value of 73 min and lower and upper quar-

a

b

Fig. 12. Time series of mean areal rain intensities for 30 min (moving averaged) andcoverage area of convective rainfall (intensity larger than 10 mm/h) computed forthe desert part of the Darga catchment (31 km2) for two flash flood events: (a) 2/11/1995 (a medium flash flood) and (b) 2/5/2001 (the largest flash flood on record).

E. Morin et al. / Advances in Water Resources 32 (2009) 1066–1076 1075

tiles of 60 and 90 min, respectively. It should be emphasized thatthe lead times cannot be estimated in relation to the observed flowbecause of the low timing accuracy of these data (see Section 2above).

6. Discussion

This study presents a flash-flood warning model based on thereal-time radar data for the dry Dead Sea region. To the best ofour knowledge, no radar-based flood-warning model exists fordry regions. In such environments, the meteorological, geomor-phological and hydrological conditions are substantially differentfrom those of humid areas. In dry regions, precipitation is typicallylow, irregular and highly variable [1,21]. Even relatively dense raingauge networks cannot accurately characterize the high variabilityof rainfall in such environments and, because of the low populationdensity, rain gauge networks tend to be sparse and insufficient foradequate QPEs (e.g., [32]). Accordingly, in dry climate regimes, theadvantage of radar-based QPEs is potentially great.

QPEs were obtained for this study from a radar system, adjustedby rain gauge data. Because of the blockage of low radar elevationangles, data from the relatively high altitudes were used. It may beclaimed that the high altitude of radar data for the Dead Sea region(about 1800 m on average) prevents them from being practical.Obviously, lower altitudes are recommended for radar data; how-ever, similar situations exist in other radar operating locations. Forexample, Maddox et al. [31] show that only a very limited portionof the US has radar data available within 2 km of the surface, and inthe western US, radar data are typically sampled near to and above3 km. Nevertheless, these data provide useful precipitation esti-

mates as well as adequate input for a runoff prediction model(e.g., [37]).

Two rain gauge adjustment methods were utilized in this study:(1) daily adjustment and (2) constant adjustment. The former re-quires an automatic rain gauge network that is currently not avail-able. The average error in daily rainfall estimation of 67% wasestimated by a cross-validation technique for the two methods.For the Arugot catchment, hydrological prediction based on thefirst method was superior, whereas for the Darga catchment, bothadjustment methods resulted in similar scores. These results sug-gest that the daily bias is not the major source of uncertainty inprecipitation estimates. Therefore, eliminating it does not signifi-cantly improve the accuracy of either the precipitation or the floodestimates. Further investigation is needed to identify the sources ofuncertainties in these estimates.

The study applied both deterministic and probabilistic flash-flood prediction. The latter accounted for uncertainties in QPEsand model parameters, and provided the probability of a floodoccurring. This information can be utilized in conjunction with acost-loss model to optimize decision making in terms of economicimpacts [38]. In the current analysis, with a low probability thresh-old, one can maintain more than 60% POD with no more than 30%FAR (Fig. 10). If the risk of a false alarm is great, then higher prob-ability thresholds can be introduced that reduce FAR (but alsoPOD), while on the other hand, if the risk of missing a flood is great,reduction of the threshold will improve model performance.

The probabilistic prediction conducted here is based on the sim-plified assumptions, as no information is available about space–time structures of QPE uncertainties. Characterization of thesestructures is still a challenge in the utilization of radar-based QPEsfor different hydrological applications [26] and requires data froma very dense rain gauge network to reflect sub-pixel variability[10].

7. Conclusions

The dry Dead Sea region is prone to flash floods. Rain storms inthis region are highly variable in space and time, and therefore theutilization of radar data is required.

A distributed flash-flood warning model utilizing radar rainfalldata was developed and applied to two catchments in the DeadSea region. The model was examined in deterministic and probabi-listic modes. The model performances are acceptable despite therelatively large uncertainties in the model input.

Further investigation is required to better characterize uncer-tainties in radar-based QPE to improve their representation inthe probabilistic model frame.

Acknowledgements

Radar data were provided by E.M.S. Mekorot, rain gauge data bythe Israel Meteorological Service and flow data by the Israel Hydro-logical Service. Funds for the project were provided by the IsraelMinistry of Science and Technology. Rainfall frequency analysiswas performed using a software developed as part of the RegionalRainfall-Intensity Project. The authors thank Simon Berkowicz andGila Haimovic for assistance in editing the manuscript. The thor-ough reviews of the three anonymous reviewers significantly con-tributed to the quality of the paper.

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