Streamflow simulation using radar-based precipitation applied to the Illinois River basin in...

Streamflow simulation using radar-based precipitation data

applied to the Illinois River basin, USA

Alireza Safari and F. De SmedtDepartment of Hydrology and Hydraulic Engineering,Vrije Universiteit Brussel

Pleinlaan 2, 1050 Brussels, Belgium

February 19, 2008

Abstract

This paper describes the application of a spatially distributed hydrological model WetSpa (Water

and Energy Transfer between Soil, Plants and Atmosphere) using radar-based rainfall data provide by

the United States Hydrology Laboratory of NOAA’s National Weather Service for a distributed model

intercomparison project. The model is applied to the Illinois river basin above Tahlequah hydrometry

station with 30-m spatial resolution and one hour time–step for a total simulation period of 6 years.

Rainfall inputs are derived from radar. The distributed model parameters are based on an extensive

database of watershed characteristics available for the region, including digital maps of DEM, soil type,

and land use. The model is calibrated and validated on part of the river flow records. The simulated

hydrograph shows a good correspondence with observation, indicating that the model is able to simulate

the relevant hydrologic processes in the basin accurately.

Keywords: WetSpa, Physically-based Distributed Hydrologic Model, DMIP, NEXRAD Stage III rainfall data, Stream-

flow Simulation, PEST, Illinois River basin.

1 Introduction

Rainfall–runoff models are used and developed by hydrologists to model rainfall–runoff processes. TheNOAA–sponsored Distributed Model Intercomparison Project (DMIP) provides a forum to explore theapplicability of distributed models using operational quality data in order to improve flow modeling andprediction along the entire river system [Smith, 2002, Smith, 2004, Smith et al., 2004].The US National Weather Service’s (NWS) Next Generation Weather Radar WSR-88D (NEXRAD) precip-itation products are widely used in hydrometeorology and climatology for rainfall estimation [Ciach et al.,1997, Seo et al., 1999, Krajewsk and Smith, 2002, Uijlenhoet et al., 2003], precipitation and weather fore-casting [Johnson et al., 1998,Grecu and Krajewski, 2000] and flood forecasting [Johnson et al., 1999,Younget al., 2000, Smith et al., 2005, Reed et al., 2007]. The most commonly NEXRAD product in hydrometeo-rological applications is the NEXRAD Stage III data, since it involves the correction of radar rainfall rateswith multiple surface rain gauges and has a significant degree of meteorological quality control [R.A.Fulton

1

BALWOIS 2008-Ohrid, Republic of Macedonia- 27, 31 May 2008 2

et al., 1998]. However, because the Stage III products consist of high-resolution spatial-temporal precipi-tation data over large regions, it is difficult to use in conjunction with other geospatial products [Reed andMaidment, 1995,Reed and Maidment, 1999]. The nominal size of an HRAP grid cell is 4 km by 4 km andthe temporal resolution of these grids is 1-hour. The grid data is provided in binary XMRG format [Officeof Hydrologic Development, 2006].Distributed hydrological models are usually parameterized by deriving estimates of parameters from topog-raphy and physical properties of the soils, aquifers and land use in the basin. In recent years, a number ofmethods have been developed for the estimation of hydrologic model parameters. One frequently used andrelatively simple algorithm is the parameter estimation PEST method. This automatic calibration procedureuses a nonlinear estimation technique known as the Gauss-Marquardt-Levenberg method. The strength ofthis method lies in the fact that it can generally estimate parameter values using fewer model runs thanany other method. The program is able to run a model as many times as needed while adjusting parametervalues until the discrepancies between selected model outputs and a complementary set of field or labora-tory measurements is reduced to a minimum in a weighted least-squares sense. Numerous examples of theapplication of the PEST algorithm for the calibration of hydrologic models can be found in the literatureand PEST proves to be a time-saving tool compared to other model calibration techniques [Al-Abed andWhiteley, 2002, Baginska et al., 2003, Zyvoloski et al., 2003, Doherty and Johnston, 2003, Wang and Me-lesse, 2005, Liu et al., 2005, Bahremand and De Smedt, 2006, Bahremand and De Smedt, 2007, Goegebeurand Pauwels, 2007, Nossent and Bauwens, 2007].A few years ago, the United States Hydrology Laboratory (HL) (then the Hydrologic Research Laboratory)of NWS began a major research effort called Distributed Model Intercomparison Project (DMIP) to addressthe question: how can the NWS best utilize the NEXRAD data to improve its river forecasts? The resultsuggested that spatial rainfall averages derived from the NEXRAD data can improve flood prediction inmid/large basins as compared to gage-only averages [Bandaragoda et al., 2004, Reed et al., 2004, Smithet al., 2004,Reed et al., 2007]. Previous studies on some of the DMIP basins have shown that calibration ofdistributed hydrological models significantly improves simulation results [Ajami et al., 2004,Bandaragodaet al., 2004, Carpenter and Georgakakos, 2004, Ivanov et al., 2004, Butts et al., 2005].In this paper, a spatially distributed physically based hydrologic model, WetSpa, is applied to a subwater-shed of the Illinois River basin which forms part of the DMIP basins [Smith, 2002]. The paper is organizedas follows. First, a brief description of the hydrologic model used in this study is given. Next, model per-formance indicators are discussed. In section 3, the site and data used are described. Details of the modelcalibrations and a comparison of the results are given in section 4. Finally, conclusions that can be drawnfrom this work are presented.

2 Methodology

The WetSpa model is capable of predicting runoff and river flow at any gauged and ungauged location in awatershed on hourly time scale [Wang et al., 1997,De Smedt et al., 2000,Liu et al., 2003,Bahremand et al.,2006, Zeinivand et al., 2007]. Availability of spatially distributed data sets (digital elevation model, lan-duse, soil and radar-based precipitation data) coupled with GIS technology enables the WetSpa to performspatially distributed calculations. The hydrological processes considered in the model are precipitation,interception, depression storage, surface runoff, infiltration, evapotranspiration, percolation, interflow and


ground water drainage. The total water balance for each raster cell is composed of a separate water balancefor the vegetated, bare-soil, open water, and impervious part of each cell. A mixture of physical and em-pirical relationships is used to describe the hydrological processes. The model predicts discharges in anylocation of the channel network and the spatial distribution of hydrological characteristics. Hydrologicalprocesses are set in a cascading way. Starting from precipitation, incident rainfall first encounters the plantcanopy, which intercepts all or part of the rainfall until the interception storage capacity is reached. Excesswater reaches the soil surface and can infiltrate the soil zone, enter depression storage, or is diverted assurface runoff. The sum of interception and depression storage forms the initial loss at the beginning ofa storm, and does not contribute to the storm flow. A fraction of the infiltrated water percolates to thegroundwater storage and some is diverted as interflow. Soil water is also subjected to evapotranspirationdepending on the potential evapotranspiration rate and the available soil moisture. Groundwater dischargesto the nearest channel proportional to the groundwater storage and a recession coefficient. Possible evapo-transpiration from groundwater storage is also accounted for. For each grid cell, the root zone water balanceis modeled continuously by equating inputs and outputs:

Ddθdt

= P − I − S − E − R − F (1)

where D [L] is root depth, θ [L3L−3] soil moisture, t [T] time, I [LT−1] interception loss, S [LT−1] surfacerunoff, E [LT−1] evapotranspiration from the soil, R [LT−1] percolation out of the root zone, and F [LT−1]interflow. The surface runoff is calculated using a moisture–related modified rational method with a runoff

coefficient depending on land cover, soil type, slope, magnitude of rainfall, and antecedent soil moisture:

S = C(P − I)(θ

θs

)α(2)

where θs [L3L−3] is water content at saturation, C[−] potential runoff coefficient, and α[−] a parameterreflecting the effect of rainfall intensity. The values of C are derived from a lookup table, linking values toslope, soil type and landuse classes [Liu and De Smedt, 2004]. The value of α reflects the influence of thesoil wetness on runoff and needs to be set by the user or optimized by model calibration, within the interval0 to 1.Evapotranspiration from the soil and vegetation is calculated based on the relationship developed by Thorn-thwaite and Mather [Thornthwaite and Mather, 1955], as a function of potential evapotranspiration, vege-tation type, stage of growth and soil moisture content.

E = 0

E = (cvEp − Ei − Ed)

E = cvEp − Ei − Ed

(θ − θw

θ f − θw

) f or

f or

f or

θ < θw

θw ≤ θ < θ f

θ ≥ θ f

(3)

where cv[−] is a vegetation coefficient, which varies throughout the year depending on growing stage andvegetation type, Ep [LT−1] is the potential evapotranspiration, Ei [LT−1] and Ed [LT−1] are evaporationfrom interception storage and depression storage respectively, θw [L3L−3] is the moisture content at per-


manent wilting point, and θ f [L3L−3] is the moisture content at field capacity. The rate of percolation R orgroundwater recharge is determined by Darcy’s law [Hillel, 1980] in function of the hydraulic conductivityand the gradient of hydraulic potential. When the assumption is made that the pressure potential only variesslightly in the soil, the percolation is controlled by gravity alone [Famiglietti and Wood, 1994]. Therefore,the percolation out of root zone is simply the hydraulic conductivity corresponding to the moisture contentin the soil layer, which can be derived by the Brooks and Corey relationship [Eagleson, 1978]:

R = K (θ) = Ks

(θ − θr

θs − θr

)3+2/B

(4)

where K(θ) [LT−1] is the unsaturated hydraulic conductivity, Ks [LT−1] is the saturated hydraulic conduc-tivity, θr [L3L−3] is the residual soil moisture content, and B[−] is the soil pore size distribution index. Thevertical transport of water through the unsaturated soil matrix is slow. It generally takes days or monthsbefore the percolating water reaches the saturated zone. Nevertheless, precipitation is followed by an al-most immediate rise of the groundwater table in consequence of a rapid transfer of increased soil-waterpressure through the unsaturated zone [Myrobo, 1997]. In addition, macro pores in the subsurface layersresulting from root and fauna activity may allow rapid bypassing of the unsaturated zone when the rate ofprecipitation is high [Beven and Germann, 1982].Interflow is assumed to become significant only when the soil moisture is higher than field capacity. Darcy’slaw and a kinematic wave approximation are used to determine the amount of interflow, in function of hy-draulic conductivity, moisture content, slope angle, and root depth:

F = c f DS 0K (θ)/W (5)

where S 0 [LL−1] is the surface slope, W [L] is the cell width, and c f [-] is a scaling parameter dependingon land use, used to consider river density and the effects of organic matter on the horizontal hydraulicconductivity in the top soil layer. Apparently, interflow will be generated in areas with high moisture andsteep slope.The routing of overland flow and channel flow is implemented by the method of the diffusive wave approx-imation of the St. Venant equation:

∂Q∂t

+ c∂Q∂x− d

∂2Q∂t2 = 0 (6)

where Q [L3T−1] is the discharge, t [T] is the time, x [L] is the distance along the flow direction, c [LT−1]is the kinematic wave celerity, interpreted as the velocity by which a disturbance travels along the flowpath, and d [L2T−1] is the location dependent dispersion coefficient, which measures the tendency of thedisturbance to disperse longitudinally as it travels downstream. Assuming that the water level gradientequals the bottom slope and the hydraulic radius approaches the average flow depth for overland flow, c andd can be estimated by c = (5/3) v, and d = (vH) / (2S 0) [18], where v [LT−1] is the flow velocity calculatedby the Manning equation, and H[L] is the hydraulic radius or average flow depth. An approximate solutionto the diffusive wave equation in the form of a first passage time distribution is applied [Liu et al., 2003],relating the discharge at the end of a flow path to the available runoff at the beginning:

U (t) =1

σ√

2πt3/t30

exp[−

(t − t0)2

2σ2t/t0

](7)


where U (t)[T−1] is the flow path unit response function, serving as an instantaneous unit hydrograph (IUH)of the flow path, which makes it possible to route water surplus from any grid cell to the basin outlet orany downstream convergent point, t0 [T] is the average flow time, and σ [T] is the standard deviation of theflow time. The parameters t0 and σ are spatially distributed, and can be obtained by integration along thetopographic determined flow paths as a function of flow celerity and dispersion coefficient:

t0 =

∫c−1dx (8)

andσ2 =

∫2dc−3dx (9)

Hence, flow hydrographs at the basin outlet or any downstream convergent point are obtained by a convo-lution integral of the flow response from all contributing cells:

Q (t) =

∫A

∫ t

0S (τ) U (t − τ) dτdA (10)

where Q (t) [L3T−1] is the direct flow hydrograph, S (τ) [LT−1] is the surface runoff generated in a grid cell,τ [T] is the time delay, and A [L2] is the drainage area of the watershed.Because, groundwater movement is much slower than the movement of water in the surface and nearsurface water system, groundwater flow is simplified as a lumped linear reservoir on small GIS derivedsubwatershed scale. Direct flow and groundwater flow are joined at the subwatershed outlet, and the totalflow is routed to the basin outlet by the channel response function derived from equation (7).One advantage of WetSpa is that it allows spatially distributed hydrological parameters of the basin tobe used as inputs to the model simulated within a GIS framework. Inputs to the model include digitalelevation data, soil type, land use data, and climatological data. Stream discharge data is optional formodel calibration.Efficiency criteria are defined as mathematical measures of how well a model simulation fits the availableobservations [Beven, 2001]. The efficiency criteria used in this study are listed in Table 1. Criterion C1

is reflecting the ability of reproducing the water balance; C2 is a proposed index [McCuen and Snyder,1975] which reflects differences both in hydrograph size and in hydrograph shape, C3 evaluates the abilityof reproducing the streamflow hydrograph [Nash and Sutcliffe, 1970], and finally C4 and C5 evaluate theability of reproducing low flows and high flows respectively. In all equations, Qs and Qo are the simulatedand observed streamflows at time step i, Q̄o is the mean observed streamflow over the simulation period, σo

and σs are the standard deviations of observed and simulated discharges respectively, r is the correlationcoefficient between observed and simulated hydrographs, and N is the number of observations. To evaluatethe goodness of the model performance during calibration and validation periods, the intervals listed inTable 2 have been adopted [Andersen et al., 2001, Andersen et al., 2002, Henriksen et al., 2003]. Thesecriteria are not of the fail/pass type, but evaluate the performance in five categories from excellent to verypoor. The perfect value for C1 is 0 and for the other four criteria it is 1.


Table 1: Performance criteria for model assessmentCriterion Equation

Model Bias C1 =

[∑Ni=1(Qsi−Qoi)∑N

i=1 Qoi

]Modified correlation index C2 =

[min{σo,σs}

max{σo,σs}× r

]Nash-Sutcliffe efficiency C3 = 1 −

[ ∑Ni=1(Qsi−Qoi)2∑Ni=1(Qoi−Q̄o)2

]Logarithmic version of Nash-Sutcliffe efficiency for lowflow evaluation

C4 = 1 −[ ∑N

i=1(ln Qsi−ln Qoi)2∑Ni=1(ln Qoi−ln Q̄o)2

]Adapted version of Nash-Sutcliffe efficiency for high flowevaluation

C5 = 1 −[ ∑N

i=1(Qoi+Q̄o)(Qsi−Qoi)2∑Ni=1(Qoi+Q̄o)(Qoi−Q̄o)2

]

Table 2: Model performance categories to indicate the goodness of fit levelCategory Model bias criterion: C1 Model efficiencies’ criteria: C2, C3, C4 and C5

Excellent <0.05 >0.85Very good 0.05-0.10 0.65-0.85

Good 0.10-0.20 0.50-0.65Poor 0.20-0.40 0.20-0.50

Very poor >0.40 <0.20

3 Study Area and Data

The Illinois river is located in eastern Oklahoma and western Arkansas. Streamflow data from Tahlequahgauging station are used in this study. Figure 1 shows the location of this station and the correspondingbasin boundaries. The basin area is 2454 km2. The average maximum and minimum air temperature inthe region are approximately 22 and 9◦C, respectively. Summer maximum temperatures can get as high as38◦C. The annual average precipitation is 1200 mm, and the annual average potential evaporation is 1050mm.The topographic data was obtained from the DMIP web site in raster form with a resolution of 30 m. Thetopography is gently rolling to hilly and the elevation ranges from 210 m to 600 m (Figure 1).Landuse and soil types information are important inputs to the WetSpa model, as these influence hydrolog-ical processes like evapotranspiration, interception, infiltration, runoff, etc. Soil types were derived fromPennsylvania State University STATSGO data [Soil Survey Staff, 1994a, Soil Survey Staff, 1994b] andlanduse from satellite images processed through the NASA Land Data Assimilation Systems (LDAS) pro-gram with an International Geosphere-Biosphere Program (IGBP) classification system [Eidenshink andFaundeen, 1994]. The spatial resolution of the soil types and landuse maps is 1 km. Figure 2 shows theland use and soil maps of the study area.Hourly radar-based rainfall data was acquired from the DMIP database. The data sets have to be untarred,

uncompressed, transformed into ASCII format, and projected into a common coordinate system. The se-lected mesh of NEXRAD (pseudo-station network) consisting of 150 radar points is shown in Figure 3together with associated Thiessen polygons covering the study area.


#

Tahlequah gauging station#

10 0 10 20 Kilometers

N

EW

S

Elevation (m)200 - 300300 - 400400 - 400400 - 500500 - 600

Figure 1: The Illinois river basin above Tahlequah on the border of Oklahoma and Arkansas, USA


N

EW

S

(a) Landuse categories:Evergreen Needleleaf ForestDeciduous Broadleaf ForestMixed ForestWoody Savannah

Urban and Built-UpCropland/Natural veg. Mosaic

Croplands

(b) Soil Texture Classes:Silt LoamSandy Clay LoamSilty Clay LoamSilty Clay


N

EW

S

Figure 2: The landuse and soil maps of the study area


#

# #

# #

# # #

#

# # #

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# # #

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N

EW

S

Thiessen polygons# Mesh of NEXRAD cells over the basin

Rivers

Figure 3: Thiessen polygons of the study area


Table 3: WetSpa global parameters and their calibrated valuesParameter Symbol Unit calibrated valueInterflow scaling factor Ki - 4.0Groundwater flow recession coefficient Kg d−1 0.00125Correction factor for potential evapotranspiration Kep - 0.875Maximum groundwater storage gmax mm 300Surface runoff exponent Krun - 10.0

Table 4: Simulation statistics for the calibration and validation periodsCriterion Calibration period Validation period

C1 0.145 0.043C2 0.875 0.765C3 0.785 0.854C4 0.745 0.738C5 0.886 0.906

4 Results and discussion

Theoretically the parameters of the physically based WetSpa model need not to be calibrated. However,due to uncertainty of the model input and structure, a calibration of global model parameters (Table 3)improves the model performance. Global model parameters are time invariant and are either adjustmentcoefficients or empirical constants. These parameters and their calibration with PEST have been describedin other studies [Liu and De Smedt, 2004, Liu et al., 2005, Bahremand et al., 2006, Bahremand and DeSmedt, 2007]. The historical discharge record was divided into two periods: one for calibration and onefor validation. The calibration period covers the period October 1996 to September 1999 and the validationperiod the remainder until September 2002.Figures 4 and 5 give a graphical comparison between observed and calculated hourly flows for the calibra-

tion and the validation periods, showing that the calibrated model simulates the timing and the magnitudeof the peak flows reasonably well. Table 4 presents summary statistics for the calibration and validationperiods. It is clear that the WetSpa model is performing well (Nash-Sutcliffe efficiency and modified cor-relation index > 0.75). The results show in particular that the model is able to simulate high flows witha very good accuracy (C5 > 0.85), while also performing well for the low base flows (C4 >0.7). Thelesser precision for low flows might be due to the simplified approach of modeling ground water storageand drainage in WetSpa. The use of distributed and physically based predicting models could improvebase flow predictions. There is also significant uncertainty in precipitation estimates derived from weatherradar [Smith et al., 1996, Stellman et al., 2001, Carpenter and Georgakakos, 2004], which influence modelsimulations significantly on all model output scales. Also, there is some uncertainty due to the inability ofthe model to represent the heterogeneous nature of hydrological processes on basin scale.

5 Conclusions and recommendations

This paper presents an application of the physically based distributed hydrologic WetSpa model, forcedwith radar-based precipitation data for a Distributed Model Intercomparison Project (DMIP) watershed.Coupling to GIS makes WetSpa a powerful tool to capture local complexities of a watershed and temporal


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Figure 5: Observed and simulated hydrographs for the validation period with hourly time scale


variation of river flows, especially peak discharges. The model can predict not only the streamflow hydro-graph at any controlling point of the basin, but also the spatially distributed hydrological processes, suchas surface runoff , infiltration, evapotranspiration and the like, at each time step during a simulation. Allmodel parameters can be obtained from DEM, land use and soil type data of the watershed or combinationsof these three fundamental maps.Evaluation of flow simulations from WetSpa is presented in terms of summary statistics covering calibra-tion and validation periods. The goodness of the model performance during calibration and validationperiods was evaluated and shows that the calibrated WetSpa reproduces water balance and especially highstreamflows accurately, while this is somewhat less for low flows, due to the simplified model descriptionof ground water flow processes. Hence, the model performance is satisfactory for both calibration andvalidation periods. The model’s ability to reproduce observed hydrographs for the validation period showsthat the model can be used for prediction purposes, in particular for storm events that lead to flooding.A potential future research is to validate the model in watersheds where snow accumulation and abla-tion is significant (e.g. DMIP California Sierra Nevada watersheds). For these cases and especially inmountainous terrain, uncertainty in estimated distributed precipitation is high as weather radar data can besignificantly biased (e.g. partial beam filling, ground clutter, etc.).

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