PLEASE SCROLL DOWN FOR ARTICLE

This article was downloaded by:On: 7 March 2011Access details: Access Details: Free AccessPublisher Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Hydrological Sciences JournalPublication details, including instructions for authors and subscription information:http://www.informaworld.com/smpp/title~content=t911751996

The coupled routing and excess storage (CREST) distributed hydrologicalmodelJiahu Wangab; Hong Yanga; Li Liab; Jonathan J. Gourleyc; Khan Sadiq I.a; Koray K. Yilmazde; Robert F.Adlerde; Frederick S. Policellid; Shahid Habibd; Daniel Irwnf; Ashutosh S. Limayef; Tesfaye Kormeg;Lawrence Okellog

a School of Civil Engineering and Environmental Sciences, University of Oklahoma, Norman,Oklahoma, USA b State Key Laboratory of Hydrology - Water Resources and Hydraulic Engineering,Hohai University, Nanjing, China c NOAA/National Severe Storm Laboratory, Norman, Oklahoma,USA d NASA Goddard Space Flight Center, Greenbelt, Maryland, USA e Earth System ScienceInterdisciplinary Center, University of Maryland, College Park, Maryland, USA f NASA MarshallSpace Flight Center, Huntsville, Alabama, USA g African Regional Centre for Mapping of Resources forDevelopment (RCMRD), Nairobi, Kenya

Online publication date: 13 February 2011

To cite this Article Wang, Jiahu , Yang, Hong , Li, Li , Gourley, Jonathan J. , Sadiq I., Khan , Yilmaz, Koray K. , Adler,Robert F. , Policelli, Frederick S. , Habib, Shahid , Irwn, Daniel , Limaye, Ashutosh S. , Korme, Tesfaye and Okello,Lawrence(2011) 'The coupled routing and excess storage (CREST) distributed hydrological model', Hydrological SciencesJournal, 56: 1, 84 — 98To link to this Article: DOI: 10.1080/02626667.2010.543087URL: http://dx.doi.org/10.1080/02626667.2010.543087

Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf

This article may be used for research, teaching and private study purposes. Any substantial orsystematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply ordistribution in any form to anyone is expressly forbidden.

The publisher does not give any warranty express or implied or make any representation that the contentswill be complete or accurate or up to date. The accuracy of any instructions, formulae and drug dosesshould be independently verified with primary sources. The publisher shall not be liable for any loss,actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directlyor indirectly in connection with or arising out of the use of this material.

84Hydrological Sciences Journal – Journal des Sciences Hydrologiques, 56(1) 2011

The coupled routing and excess storage (CREST) distributedhydrological model

Jiahu Wang1,2, Hong Yang1, Li Li1,2, Jonathan J. Gourley3, Khan Sadiq I.1, Koray K. Yilmaz4,5,Robert F. Adler4,5, Frederick S. Policelli4, Shahid Habib4, Daniel Irwn6, Ashutosh S. Limaye6,Tesfaye Korme7 & Lawrence Okello7

1School of Civil Engineering and Environmental Sciences, University of Oklahoma, Norman, Oklahoma 73019, USAyanghong@ou.edu

2State Key Laboratory of Hydrology – Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China3NOAA/National Severe Storm Laboratory, Norman, Oklahoma 73072, USA4NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA5Earth System Science Interdisciplinary Center, University of Maryland, College Park, Maryland 20740, USA6NASA Marshall Space Flight Center, Huntsville, Alabama 35812, USA7African Regional Centre for Mapping of Resources for Development (RCMRD), Nairobi, Kenya

Received 6 April 2010; accepted 5 October 2010; open for discussion until 1 August 2011

Citation Wang, J., Yang, H., Li, L., Gourley, J. J., Sadiq, I. K., Yilmaz, K. K., Adler, R. F., Policelli, F. S., Habib, S., Irwn, D., Limaye,A. S., Korme, T. & Okello, L. (2011) The coupled routing and excess storage (CREST) distributed hydrological model. Hydrol. Sci. J.56(1), 84–98.

Abstract The Coupled Routing and Excess STorage model (CREST, jointly developed by the University ofOklahoma and NASA SERVIR) is a distributed hydrological model developed to simulate the spatial and temporalvariation of land surface, and subsurface water fluxes and storages by cell-to-cell simulation. CREST’s distin-guishing characteristics include: (1) distributed rainfall–runoff generation and cell-to-cell routing; (2) coupledrunoff generation and routing via three feedback mechanisms; and (3) representation of sub-grid cell variabilityof soil moisture storage capacity and sub-grid cell routing (via linear reservoirs). The coupling between the runoffgeneration and routing mechanisms allows detailed and realistic treatment of hydrological variables such as soilmoisture. Furthermore, the representation of soil moisture variability and routing processes at the sub-grid scaleenables the CREST model to be readily scalable to multi-scale modelling research. This paper presents the modeldevelopment and demonstrates its applicability for a case study in the Nzoia basin located in Lake Victoria, Africa.

Key words distributed hydrological model; cell-to-cell routing; excess storage; water balance; CREST; Lake Victoria

Le modèle hydrologique distribué couplé routage et stockage des excédents (CREST)Résumé Le modèle couplé routage et stockage des excédents (CREST, développé conjointement par l’Universitéde l’Oklahoma et NASA SERVIR) est un modèle hydrologique distribué développé pour simuler les variationsspatiales et temporelles des flux d’eau de surface et souterraine ainsi que les stockages, par simulation de celluleà cellule. Les caractéristiques distinctives de CREST sont les suivantes: (1) production pluie–débit distribuée etroutage de cellule à cellule; (2) couplage de la production et du routage du ruissellement via trois mécanismesde rétroaction; et (3) représentation de la variabilité sub-cellulaire de la capacité de stockage en eau du sol et duroutage infra-cellulaire (via des réservoirs linéaires). Le couplage entre la genèse du ruissellement et les mécan-ismes de routage permet un traitement détaillé et réaliste des variables hydrologiques telles que l’humidité dusol. En outre, la représentation de la variabilité de l’humidité du sol et des processus de routage à l’échelle sub-cellulaire permet au modèle CREST d’être facilement étendu à la recherche sur la modélisation multi-échelles.Cet article présente le développement du modèle et démontre son applicabilité pour une étude de cas dans le bassinde la Nzoia, Lac Victoria, Afrique.

Mots clefs modèle hydrologique distribué; routage de cellule à cellule; stockage des excédents; bilan hydrique; CREST; LacVictoria

ISSN 0262-6667 print/ISSN 2150-3435 online© 2011 IAHS Pressdoi: 10.1080/02626667.2010.543087http://www.informaworld.com

Downloaded At: 19:38 7 March 2011

The coupled routing and excess storage (CREST) distributed hydrological model 85

1 INTRODUCTION

Knowledge of the spatiotemporal distribution ofwater over the landscape is of paramount impor-tance for sustainable management of water resourcesand for mitigating water-related natural hazards suchas flooding. Hydrological models serve as importanttools for providing critical information in this regard.A variety of hydrological models have been devel-oped in the past (see Singh, 1995, for a comprehen-sive overview) with various degrees of hydrologicalprocesses represented according to the intended appli-cation or availability of data. Hydrological modelshave been classified as conceptual or physically-based(Beck, 1987; Refsgaard, 1996; Yilmaz et al., 2010).Conceptual models represent complex, spatially vari-able, hydrological processes in a watershed using sim-ple, parsimonious mathematical expressions withoutexplicit treatment of the underlying physics or intra-basin heterogeneity (e.g. Bergström, 1995; Burnash,1995). Spatially distributed, physically-based hydro-logical models mathematically represent each of theimportant components of the hydrological cycle basedon their physical governing equations (Woolhiseret al., 1990; Refsgaard & Storm, 1995). The poten-tial strengths of distributed hydrological models are:(a) the ability to account for the intra-basin variabilityof runoff-producing mechanisms; and (b) the abil-ity to infer model parameter values from geospatialdata (e.g. geology, topography, soils, and land cover).A hybrid modelling strategy that maintains a bal-ance between the degree of physical realism and datarequirements, so as to provide reliable simulationsunder a variety of settings, seems to be advantageous.

The Coupled Routing and Excess STorage(CREST) distributed hydrological model representsa hybrid modelling strategy and was recentlydeveloped by the University of Oklahoma, USA(http://hydro.ou.edu) and NASA SERVIR ProjectTeam (www.servir.net). The CREST model simulatesthe spatio-temporal variation of water and energyfluxes and storages on a regular grid with the gridcell resolution being user-defined, thereby enablingglobal- and regional-scale applications. The scalabil-ity of CREST simulations is accomplished throughsub-grid scale representation of soil moisture stor-age capacity (using a variable infiltration curve) andrunoff generation processes (using linear reservoirs).CREST was initially developed to provide onlineglobal flood predictions with relatively coarse reso-lution, but also applicable at small scales, even forsingle basins; this paper concentrates and tests the

model at the small scale. It can be driven either bysatellite-based precipitation estimates and datasets ofpotential evapotranspiration, or by raingauge observa-tions, remote sensing platforms such as weather radar,and quantitative precipitation forecasts from numer-ical weather prediction models. The representationof the primary water fluxes, such as infiltration androuting, are closely related to the spatially-variablelandscape characteristics (i.e. vegetation, soil typeand topography). The runoff generation componentand routing scheme are coupled, thus providing real-istic interactions between atmospheric, land surfaceand subsurface water.

This paper provides a detailed description ofeach modelling component of the CREST model inSection 2. Section 3 demonstrates a regional applica-tion of the model with its very first test basin locatedin Lake Victoria, Africa. Note that Lake Victoriabasin is the focus area of our funded NASA SERVIR-Africa project. Section 4 evaluates the CREST modelperformance for the presented case study, and a sum-mary and discussion are provided in Section 5.

2 CREST MODEL DESCRIPTION

Similar to many distributed hydrological models,CREST represents a region by dividing it into a num-ber of regular spatial elements (see Fig. 1(c)), whichwe will refer to hereafter as a “cell”. A flow diagramis given in Fig. 1 that depicts the core of the CRESTcomponents: rainfall–runoff generation, evapotran-spiration, sub-grid cell routing, downstream routing,and feedbacks between the routing and rainfall–runoffmodules. A description and the units of each symbolappearing in the figures and equations of this sectionare supplied in the Appendix.

The vertical profile of a cell in Fig. 1(a) showsthat there are four excess storage reservoirs repre-senting interception by the vegetation canopy andsubsurface water storage in the underlying threesoil layers. In addition, two linear reservoirs simu-late sub-grid cell routing of overland and subsurfacerunoff separately. In each cell, a variable infiltrationcurve, originally proposed by Zhao et al. (1980), isemployed to separate precipitation into runoff andinfiltration (see Fig. 1(b)). Figure 1(c) shows a planview of overland water movement and then channelflow based on flow direction and basin area derivedfrom a digital elevation model (DEM), and Fig. 1(d)shows two cell-to-cell routing modules that movewater overland as surface runoff and below ground assubsurface interflow. These modules run in parallel,

Downloaded At: 19:38 7 March 2011

86 Jiahu Wang et al.

A

Overland

Routing

Interflow

Routing

j th

( j + 5)th

( j + 4)th

( j + 3)th

( j + 2)th

( j + 1)th

B

R j

R jI,Out,t

R j+2R j+3

R j+4R j+5

(d)

j

th

A

B

(c)

Infiltration Capacity

im

i

i + Psoil

00

R

1

I

WU j

(b)

PSoil

I

R

PEc

Ea

ET

∑ RO,in

RI,in

RI,out

RO,out

Variable Infiltration Curve

Th

K

Atmospheric Forcing

Overland

Routing

Interflow

Routing

Canopy Layer

Soil Layer 1

Soil Layer 2

Soil Layer 3

(a)

∑

i = im1[1− (1− a) b ]

I,Out,tIn,t+1 I,In,t+1

O,In,t+1 O,In,t+1

Fig. 1 Core components of CREST: (a) vertical profile of a cell including rainfall–runoff generation, evapotranspiration,sub-grid cell routing and feedbacks from routing; (b) variable infiltration curve of a cell; (c) plan view of cells and flowdirections; and (d) vertical profile along several cells including sub-grid cell routing, downstream routing, and subsurfacerunoff redistribution from a cell to its downstream cells.

which enables a computationally efficient and realis-tic three-dimensional representation of water flux todownstream cells. The following model description isorganized according to the sequential flow of: waterentering a cell as rainfall from the atmosphere above;interception by the canopy layer and subsequent redis-tribution back to the atmosphere via evapotranspira-tion; division of rainfall reaching the soil surface intoinfiltration and surface runoff components; sub-gridrouting, routing of overland, channel and subsur-face components downstream; and, finally, feedbacksbetween routing and runoff generation components.

2.1 Rainfall–runoff generation

2.1.1 Canopy interception Once there is pre-cipitation (P) input to a cell, the rainfall–runoff

generation process will be activated. First, a por-tion of the precipitation is intercepted by the veg-etation canopy, and an excess storage reservoir isemployed here to simulate this process (see Fig. 1(a)).Maximum storage of the reservoir is the canopy inter-ception capacity (CIC): a cell’s mean value based onthe land cover classification, and modelled based onDickinson (1989) as follows:

CIC = kc · d · LAI (1)

where kc is the coefficient of the land cover’s CIC; d isthe vegetation coverage; and LAI is leaf area index.Typically, kc is set to a value of 1 if the true CICis accurately estimated from observations or ancil-lary data; otherwise this coefficient can be calibratedlater in rainfall–runoff simulation. When the reservoir

Downloaded At: 19:38 7 March 2011

The coupled routing and excess storage (CREST) distributed hydrological model 87

is full, excess precipitation will reach the soilsurface:

Psoil = P − (CIC − CI) (2)

where Psoil is the precipitation reaching the soil sur-face and CI is the depth of water intercepted by thevegetation canopy.

2.1.2 Variable infiltration curve Next, Psoil

is separated into two parts: excess rain (R) and infil-tration water (I), according to the variable infiltrationcurve (VIC; also called tension water capacity curve),founded in the Xinanjiang model (Zhao et al., 1980;Zhao, 1992), and later employed in the Universityof Washington VIC model (Liang et al., 1996) (seeFig. 1(b)). The curve is:

i = im[1 − (1 − A)

1/bi

](3)

where i is the point infiltration capacity; im is the max-imum infiltration capacity of a cell; A is the fractionalarea of the cell corresponding to i; and bi is the expo-nent of the curve. In equation (3), im is a function ofthe cell’s maximum water capacity (Wm) of the threesoil layers, as:

im = Wm (1 + bi) (4)

Wm = Wm1 + Wm2 + Wm3 (5)

where Wm1, Wm2 and Wm3 correspond to the three soillayers and are related to soil porosity. Equation (3) canbe rewritten as a function of the cell’s total mean waterof the three soil layers (W ), as follows:

i = im

⎡⎣1 −

(1 − W

Wm

) 11+bi

⎤⎦ (6)

W = W1 + W2 + W3 (7)

where W 1, W 2 and W 3 are the mean soil water depthof each layer in the cell. The amount of water availablefor infiltration (I) is then computed as follows:

for i + Psoil ≥ im I = (Wm − W )

for i + Psoil < im

I = (Wm − W) + Wm

[1 − i + Psoil

im

]1+bi

(8)

There are three storage reservoirs in this model repre-senting three different soil layers. Infiltration water (I)enters the upper soil layer until it is full. The middleand lower soil layers are filled in sequence.

2.1.3 Runoff generation Given the partition-ing of Psoil into I using equations (3)–(8), the excessrain (R) is computed as:

R = Psoil − I (9)

A further partitioning of R into overland excess rain(RO) and interflow excess rain (RI) ensues by com-paring Psoil to the infiltration rate of the first layer(K):

for Psoil > K RI = KR

PsoilRO = R − RI

for Psoil ≤ K RI = R RO = 0(10)

where K is closely related to the soil saturatedhydraulic conductivity. The partition of overland andinterflow excess rain provides quick and slow hydro-graph responses to precipitation. The terms RO andRI are handled separately in the routing componentdescribed in Section 2.2.

2.1.4 Evapotranspiration The process ofwater flux from the land surface soils, vegetation,or directly from overland water to the atmosphere isreferred to as evapotranspiration. Potential evapo-transpiration (Ep) is the amount of evapotranspirationthat would occur if there were an unlimited supplyof land surface water, and is often estimated fromatmospheric thermodynamics, wind and radiationconditions. The method for estimating Ep in theCREST model depends on the availability of data inthe study basin. When radiation data are available,the Priestley-Taylor equation (Priestley & Taylor,1972) is recommended. If only temperature data areavailable, the Hargreaves equation (Hargreaves &Samani, 1982) can be used to estimate Ep. In situa-tions where no meteorological data (except rainfall)are available, users can defer to the 0.25-degreemonthly mean Ep data available from the FamineEarly Warning Systems Network (FEWS NET;http://igskmncnwb015.cr.usgs.gov/Global/), whichis provided with the CREST software package.

Actual evapotranspiration (Ea) is determined byboth Ep and the vertically-integrated water contents ofthe cell. The process of evapotranspiration begins toremove water from the uppermost canopy reservoirand continues until this storage tank is completely

Downloaded At: 19:38 7 March 2011

88 Jiahu Wang et al.

depleted (i.e. CI from equation (2) goes to 0), withsuccessive drying of Layer 1, and so on:

for CI > Ep Ec = Ep

for CI ≤ Ep Ec = CI(11)

where Ec is the water lost from the canopy layervia evapotranspiration. Next, we define the potentialevaporation that applies to the uppermost soil layer(EP1) as follows:

Ep1 = Ep − Ec (12)

In the process of the canopy reservoir being depleted,we see that EP1 is initially 0, and eventuallyapproaches EP when the canopy layer is completelydevoid of water. In other words, this term activates asthe storage tank empties from above. Analogous to thetreatment of the depletion of water in the canopy layerin equation (9), the rate of water evaporated from soillayer 1 (ES1) is defined as:

for W1 > Ep1 Es1 = Ep1

for W1 ≤ Ep1 Es1 = W1(13)

where W 1 is the depth of water in the upper soil layerreservoir (refer to equation (7)). The potential evap-oration that applies to the second soil layer (EP2) isdefined as:

Ep2 = (Ep1 − Es1

)√W2

Wm2(14)

From equations (13)–(14), we see that EP2 activatesin response to a depletion of water in the uppermostsoil layer (W 1); the process of drying out the soil col-umn begins from the top and proceeds downward. Areduction term has been included on the right handside of equation (14) in the calculation of EP2 so that itwill be less than or equal to EP1 (and EP). Physically,this term represents the increasing difficulty to evapo-rate water from greater depths in the soils. The rate ofactual water evaporated from layer 2 (ES2) in CRESTis calculated as:

for W2 > Ep2 Es2 = Ep2

for W2 ≤ Ep2 Es2 = W2(15)

Recall that W 2 is the depth of water in the secondsoil layer reservoir (see equation (7)). Finally, as thewater contents in the second layer are depleted, the

potential evaporation for the third soil layer (EP3) iscomputed as:

Ep3 = (Ep2 − Es2

) W3

Wm3(16)

In this case, the reduction term is larger on the right-hand side than in equation (14) so that EP3 will fallbelow EP2 at a higher rate than occurs in the secondsoil layer. Again, physically, this term represents theadditional difficulty encountered in evaporating waterwith increasing depth. The depletion of water fromsoil Layer 3 occurs at the following rates:

for W3 > Ep3 Es3 = Ep3

for W3 ≤ Ep3 Es3 = W3(17)

where ES3 is the rate of evaporation from soil Layer 3.The vertically-integrated, actual rate of evapotranspi-ration of a cell is computed as:

Ea = EC + Es1 + Es2 + Es3 (18)

The terms in equation (18) are coordinated so thatdrying and wetting begin from the canopy layer andproceed downward (see Fig. 1(a)). Evapotranspiredwater is lost to the atmosphere and is no longer con-sidered in the water budget. Deep-layer transpirationby root uptake is not considered in CREST, which cur-rently has a model structure designed for warm seasonflood simulation.

2.2 Runoff routing

2.2.1 Sub-grid-scale routing Disadvantagesof cell-to-cell routing schemes have been reported andhave, in part, motivated the present research. First,most cell-to-cell routing methods do not explicitlyaccount for routing of runoff within a cell, which werefer to herein as sub-grid-scale routing. An exampleis the modelling of braided streams which meanderat scales not easily resolved with commonly availableDEMs and must be parameterized. The representationof runoff routing at the sub-grid scale becomes muchmore problematic with coarser grid scales encom-passing global-scale applications (Naden, 1993). InCREST, we employ two linear reservoirs to simulatesub-grid cell routing.

Virtual reservoirs have been incorporated inhydrological modelling studies to account for flood-plain storage, groundwater flow, storage by lakes andwetlands, and simulation of operations of real reser-voirs (Vörösmarty et al., 1989; Liston et al., 1994;

Downloaded At: 19:38 7 March 2011

The coupled routing and excess storage (CREST) distributed hydrological model 89

Coe, 1997; Hagemann & Dümenil, 1997). Interflowand overland excess rain (RI and RO; refer to Section2.1.3) enter the two linear reservoirs separately asshown in Fig. 1(a), and the reservoir depths arecomputed as follows:

SO,t+1 = SO,t + RO,t (19)

SI ,t+1 = SI ,t + RI ,t (20)

where the subscript t indicates the time step; SO

is the overland reservoir depth; and SI is the inter-flow reservoir depth. Discharge from the overlandand subsurface reservoirs, referred to hereafter asoverland runoff (RO,out) and interflow runoff (RI,out),are calculated separately based on a linear model asfollows:

RO,out = kO · SO (21)

RI ,out = kI · SI (22)

where kO and kI are the overland and interflow reser-voir discharge parameters, which are a function ofthe watershed characteristics (such as basin area andslope) and modelling cell size. However, these param-eters are often determined through parameter calibra-tion. The outputs from the reservoirs, RO,out and RI,out

are passed into the downstream routing module.

2.2.2 Downstream routing The typicalapproach to routing involves determining the depthand momentum of overland water that flows fromeach cell to a neighbouring cell downstream andcontinuing this process down to the river networkwhere it is considered open channel flow (Vörösmartyet al., 1989; Liston et al., 1994; Miller et al., 1994;Sausen et al., 1994; Coe 1997; Hagemann & Dümenil1997; Branstetter & Famiglietti 1999). The routingcomponent in CREST is based on a two-layer schemedescribing overland runoff and interflow from onecell to the next one downstream, with considerationof open channel flow. Advantages of cell-to-cellrouting schemes include the ease with which theycan be implemented globally (e.g. Miller et al.,1994; Sausen et al., 1994; Coe 1997; Hagemann &Dümenil 1997; Branstetter & Famiglietti 1999); andthe explicit accounting of the volume of river waterin each cell. This second advantage enables hydro-graph computation at any interior cell. Furthermore,when the volume of river water stored in a cell istransformed into a fraction of land area covered by

the surface water (i.e. wetlands, floodplain storage,rivers, lakes, or reservoirs as in Coe, 1997), thenthe effect of that surface water on land–atmosphereinteraction can have feedbacks to climate simulations(Bates et al., 1993; Hostetler et al., 1993; Bonan,1995; Kundzewicz and Stakhiv, 2010).

The concentration time (T) for RI,out and RO,out iscalculated as follows:

Tj = lj

KX

√Sj

(23)

where the superscript j refers to the spatial index of acell, as illustrated in Fig. 1(c) and (d); Tj is the con-centration time from the jth cell to its downstream(j + 1)th cell; lj is the distance between the cen-tres of the jth and (j + 1)th cells; Sj is the slopefrom the jth to the (j + 1)th cell; and KX is definedas the runoff velocity coefficient. The value of Kx

varies from cell to cell and within cells dependingon the following three processes that it represents:for interflow runoff (RI,out), KX is set to a valuerepresentative of the soil saturated hydraulic conduc-tivity; for overland runoff (RO,out), KX corresponds tothe land surface roughness; and for overland runoff(RO,out) where the drainage area of the jth cell exceedsan experimentally-found threshold (Th) (i.e. channelflow), KX is a channel velocity coefficient determinedby the channel roughness and hydraulic radius.

Figure 1(d) illustrates how runoff from inter-flow, overland flow and channel flow contribute tocells downstream from the jth cell after a time stepdT . The RI,out moves more slowly in response to arelatively small value of KX, corresponding to soil sat-urated hydraulic conductivity, and provides runoff tothe nearby (j + 2)th and (j + 3)th cells. In contrast,RO,out contributes runoff to the (j + 4)th and (j + 5)thcells further downstream due to a larger value of KX.All values for KX, which control the timing of peakflow, can be provided a priori using land cover maps,soil surveys and channel cross-sections, but typicallymust be optimized through calibration.

2.3 Coupling rainfall–runoff generationand routing

For each cell, the water balance is computed asfollows:

dSto

dt= P − Ea +

∑RO,in − RO,out

+∑

RI ,in − RI ,out

(24)

Downloaded At: 19:38 7 March 2011

90 Jiahu Wang et al.

where Sto is the total cell water storage, whichincludes all water stored in the overlying vegetationcanopy, the three soil layers, and in the two linearreservoirs (see Fig. 1(a)). The summations for inter-flow and overland flow in equation (24) correspondto contributing runoff of multiple upstream cells (asdetermined from values of KX; see Fig. 1(d)) and fromeight possible flow directions (as determined from aDEM-derived flow direction map; see Fig. 1(c)).

In CREST, routed water from a cell impacts therainfall–runoff generation as well as routing com-ponents of downstream cells, thus coupling theseprocesses in the following three ways. First, overlandrunoff coming from upstream cells is treated the sameas adding precipitation directly on the uppermost soillayer, so that Psoil calculated from equation (2) isadjusted as follows:

Psoil = Psoil +∑

RO,in (25)

where Psoil is the adjusted Psoil as dictated by the totalamount of overland flow from upstream cells. Thisadditional water is available to enter the soil layersfrom above, as described in Section 2.1.2. Secondly,soil moisture is increased by lateral interflow comingfrom upstream cells, so the amount of water availablefor infiltration in equation (8) is adjusted as:

I = I +∑

RI ,in (26)

where I is the adjusted I determined by the sum ofinterflow from upstream cells. Finally, channel runoffcoming from upstream cells contributes to the cell’soverland reservoir depth, so that SO in (19) is modifiedas follows:

St+1O = St

O + RtO +

∑RO,in (27)

where St+1O is the adjusted St+1

O , increased by con-tributing channel runoff.

These runoff routing-generation feedback mech-anisms (i.e. water routed from upper grids couldpotentially increase runoff generation of the lowergrids), via linking the runoff generation and rout-ing modules in CREST, mark it as a distinguish-ing characteristic from other hydrological models.Because a cell is pre-determined as being a channelcell based on its basin area, only one of the over-land runoff processes can occur (i.e. the process in(25) cannot occur simultaneously with that in (27),but either can occur along with (26)). These feedbacks

cause downstream cells to become more readily sat-urated than upstream cells; a desirable characteristicin excess storage theory is the expansion of the soilsaturation area beginning downstream and workingits way up (Zhao, 1992). The CREST approach ofmodule coupling enables realistic fluxes of water bothhorizontally and vertically through the soil structureand laterally overland. Nevertheless, the actual mod-elling performance also depends upon the accuratequality of soil information such as depth and types.

2.4 Parameter estimation

Many of the parameters in the CREST model canbe estimated based on the availability of field sur-vey data, such as soil surveys, land cover maps andvegetation coverage. Other parameters, such as flowdirection, slope and drainage area, are derived directlyfrom a DEM. These physically-based parameters arelisted in the Appendix (Table A1), along with a sug-gested source of data to estimate them. There areapproximately ten parameters that are much more dif-ficult to estimate from ancillary data and need tobe calibrated either manually, automatically, or usingcombined approaches given observations of rainfalland streamflow. Table A2 in the Appendix lists theseparameters, their units and default values.

Conceptual hydrological models are tailored toa specific application through a process of calibra-tion (e.g. Linsley et al., 1986; Beven & Binley, 1992;Gupta et al., 1998; Vrugt et al., 2005). In this pro-cess, model parameters are adjusted in successivemodel simulations until the model output matches theobservations to within a previously determined errorcriterion or multiple criteria. While initial parameterestimates are supplied with the model, we recom-mend further optimization using either manual cali-bration or an automatic calibration routine (such as inReichold, et al., 2010), the latter being supplied withthe model. The auto-calibration routine embedded inCREST performs global optimization of the param-eter values based on an Adaptive Random Searchmethod (ARS) (Brooks, 1958).

2.5 Inputs and outputs

The two input data sources required to run CRESTare: rainfall data and potential evapotranspiration(Ep). The CREST software package comes with aglobal, climatologically-averaged Ep data set (i.e.FEWS NET). As discussed in Section 2.1.4, betteraccuracy in estimating Ep can be accomplished with

Downloaded At: 19:38 7 March 2011

The coupled routing and excess storage (CREST) distributed hydrological model 91

the availability of atmospheric observations such astemperature, humidity, wind speed, and radiation.

The CREST outputs consist of several variables,all of which are listed in the Appendix (Table A3),including storage depths of the vegetation canopy, thethree soil layers, and two linear reservoirs, relativechange of the six reservoir levels representing actualevapotranspiration from the canopy and soil layers,overland and interflow excess rain, and overland andinterflow runoff. Each variable to be output is selectedin a control file and is subsequently written to a 2-D fileat a designated frequency. In addition, other variablesthat are not listed in Table A3 (e.g. re-distributioncoefficient) can also be output with a simple modifi-cation to the CREST source code, which is providedwith the software package written in Fortran 95 andC. The output variables listed in Table A3 can supporthydrological research as envisaged by the authors.

3 CREST MODEL IMPLEMENTATION

The CREST model was designed to enable multi-scale hydrological modelling and hence is suited forsimulations ranging from coarse scale (grid size oftens of kilometres) to relatively fine resolution (grid

size of 1 km to a few kilometres). In this section wedemonstrate the utility of CREST for a regional 1-kmfine scale application focusing on the Nzoia Basin inEast Africa, which is the first test basin of the CRESTmodel.

3.1 Nzoia River basin

Frequent flooding is a serious problem in East Africa,particularly in the Lake Victoria basin, which affectsthe lives of 30 million people (Osano et al., 2003).The region around Lake Victoria is prone to highsocietal impacts from flooding because of the concur-rence of extreme rainfall, overflowing tributary riversand streams, and a high population density. People inthe heavily populated regions of Kenya, Uganda andTanzania live under a threat of flooding almost everyyear. In late May of 2002 alone, widespread floodingthroughout Kenya displaced up to 60 000 people.

The Nzoia River basin, a sub-basin of the LakeVictoria basin, was chosen as the study area becauseof its territorial, geographic and epidemiologicalimportance for the region (Li et al., 2009). The NzoiaRiver basin, situated in East Africa, covers approx-imately 12 696 km2, and drains into Lake Victoria(Fig. 2). It is bounded by the latitudes 34◦–36◦E

Fig. 2 Study area and rain gauge stations.

Downloaded At: 19:38 7 March 2011

92 Jiahu Wang et al.

and longitudes 0◦03′–1◦15′N, and the basin elevationranges from 1134 to 2700 m. It encompasses threegeographical regions: the highlands around MountElgon and the Cherangany Hills, the upper plateau,which includes Eldoret, and the lowlands. The low-lands are characterized by clayey soils, typical of thegreater area, while the highland and upper plateausoils are deeper and well-drained. The predominantsoil texture on the basin is clay soils at 77% followedby sandy soils at 14%. The region as a whole receivesan average of 1350 mm of rain annually Annual rain-fall in the lowlands is smaller with average amountsof 1076 mm, which increases with elevation reach-ing 2235 mm in the highlands. The seasonality of therainfall is predominantly controlled by the movementof the inter-tropical convergence zone (ITCZ). Marchto May are the primary rainy months while there isa secondary rainy season from October to December.Crop production in the Nzoia basin is important for itscereal and sugar cane yield, producing at least 30% ofthe national output of both maize and sugar. The totallength of the river is 252 km with an average gradientof 4 m km-1.

3.2 Data and model implementation

The key data sets enabling the implementation of theCREST distributed hydrological model in the Nzoiabasin in 30 arc-second-resolution, DEM from theShuttle Radar Topography Mission (SRTM; Rabuset al., 2003; http://www2.jpl.nasa.gov/srtm/),SRTM-derived hydrological parameter files ofHydroSHEDS (Lehner et al., 2008), soil parametersprovided by the Food and Agriculture Organization ofthe United Nations (FAO; http://www.fao.org/AG/

agl/agll/dsmw.htm) and the Moderate ResolutionImaging Spectroradiometer (MODIS) land classifi-cation map. The latter is used as a surrogate for landuse/cover, with 17 classes of land cover according tothe International Geosphere–Biosphere Programmeclassification (Friedl et al., 2002).

The CREST model was implemented at 1-kmgrid cell resolution for the Nzoia basin and drivenby daily precipitation from 12 stations in the basin(see Fig. 2). Observed discharge data from one down-stream station (Fig. 2) was employed as a bench-mark. Station-based precipitation data were interpo-lated to the model grid cells based on the Thiessenpolygon method. The observed discharge data isavailable for the period of 1985–2004 at a dailytime step.

4 CREST MODEL EVALUATION ANDDEMONSTRATION

4.1 Performance in discharge simulation

4.1.1 Evaluation indices CREST simulationperformance was assessed using three commonly-used statistical indices. First, for statistical goodnessof fit of simulated flows, we utilized the Nash-Sutcliffe coefficient of efficiency (NSCE; Nash &Sutcliffe, 1970):

NSCE = 1 −∑(

Qi,o − Qi,c)2

∑(Qi,o − Qo

)2(28)

where Qi,o is the observed discharge of the ith day;Qi,c is the simulated discharge of ith day; and Qo isthe average of all the daily observed discharge val-ues. If NSCE ≤ 0, then the model provides no skillin relation to using the observed mean as a predictor.Second, the Pearson Correlation Coefficient (CC) isused to assess the agreement between simulated andobserved discharge as follows:

CC =∑(

Qi,o − Qo

) (Qi,c − Qc

)√∑ (

Qi,o − Qo

)2 (Qi,c − Qc

)2(29)

where Qc is the average of all daily simulated dis-charge values. Third, relative bias ratio assesses thesystematic bias of the simulated discharge:

Bias =∑

Qi,c − ∑Qi,o∑

Qi,o× 100% (30)

The best skill occurs with NSCE = 1, CC = 1, andBias = 0%.

4.1.2 Model calibration and validationCREST was calibrated using daily observed dis-charge data for the period between 1985 and 1999. Aone-year period (1984) was used for warming up themodel states. CREST calibration, performed usingthe ARS method described in Sec. 2.4, resulted ingood performance with NSCE = 0.72, CC = 0.89 andBias = –0.07%. Figure 3(a) shows the precipitationand streamflow time series during the calibration andvalidation time periods, and Fig. 3(b) shows accumu-lated discharge of observation and simulation. AfterCREST parameters were calibrated and then fixed,simulations during the validation period from 2000–2004 were excellent as compared to observationswith only minor reductions in the NSCE, CC and Bias

Downloaded At: 19:38 7 March 2011

The coupled routing and excess storage (CREST) distributed hydrological model 93

Model calibration (1985–1–1 to 1999–12–31, NSCE = 0.72, CC = 0.89, Biasp = –0.07%)and validation (2000–1–1 to 2004–12–31, NSCE = 0.71, CC = 0.84, BiasP = –0.47%)

0

140

280

420

560

700

1985–1

Dis

char

ge (

m3 /s

)

0

2

4

6

8

10

Prec

ipita

tion

(mm

/ h)

PrecipitationObservation

Simulation

(a)

1987–1 1989–1 1991–1 1993–1 1995–1 1997–1 2003–11999–1 2001–1

Model calibration (1985–1–1 to 1999–12–31, NSCE = 0.72, CC = 0.89, Biasp = –0.07%)and validation (2000–1–1 to 2004–12–31, NSCE = 0.71, CC = 0.84, BiasP = –0.47%)

0

200000

400000

600000

800000

Acc

umul

ated

Dis

char

ge (

m3 /s

) ObservationSimulation

(b)

1985–1 1987–1 1989–1 1991–1 1993–1 1995–1 1997–1 2003–11999–1 2001–1

Fig. 3 Comparison of simulated and observed discharge during the calibration and validation periods: (a) discharge timeseries, and (b) accumulated discharge time series.

error statistics from the values obtained during thecalibration period. The error metrics (NSCE = 0.71,CC = 0.84 and Bias = –0.47%) indicate that theCREST model can effectively and robustly reproduceobserved discharge in the Nzoia basin.

4.2 Spatially distributed discharge simulation

An important advantage of spatially distributedhydrological models, such as CREST, is that they notonly provide estimates of hydrological variables at thebasin outlet, but also at any location (represented bya cell) within the basin. As described in Section 2.5,CREST can output any of the variables listed in theAppendix (Table A3) as a raster grid for any timeperiod. As an example, we show in Fig. 4(a) how dailyrainfall of the order of 80 mm impacted the upper part

of the Nzoia basin on 22 April 2003. This displayof the model inputs also shows the unnatural rain-fall patterns that can result from the Thiessen polygoninterpolation method. Figure 4(b) shows the cell-by-cell discharge response throughout the basin. We cansee how relatively high flows were being experiencednear the basin outlet from previous rainfall, with anew flood peak responding to the recent rainfall in theupper part of the basin. If observations are availablewithin the basin, such as soil moisture, then differentcomponents of the CREST model can be evaluated.

4.3 Impacts of coupling rainfall–runoffgeneration and routing components

Most distributed hydrological models consider rout-ing as a separate process following the rainfall–runoff

Downloaded At: 19:38 7 March 2011

94 Jiahu Wang et al.

Fig. 4 Example of CREST’s display of input data and simulation results in raster format: (a) precipitation on 22 April 2003(interpolated by Thiessen polygon method), and (b) simulated discharge on every 1-km cell.

generation component. In a synthetic setting in whichrain falls uniformly over cells with the same initialsoil moisture contents and potential evapotranspira-tion rates, the excess rain simulated across the basinwill be homogenous. This overland and subsurfacerunoff will be transferred to the routing componentwhich will then move the water overland and in chan-nels until it leaves the basin. In most hydrologicalmodels, once surface runoff enters the routing compo-nent it no longer is capable of contributing to the soilmoisture contents of downstream cells. CREST cou-ples these components so that overland runoff fromupstream cells enter the soil moisture reservoirs ofdownstream cells, and have the effect of saturatingcells in low-lying areas (e.g. valleys) first and thenpropagating upstream.

A synthetic experiment was designed in CRESTin order to demonstrate the impacts of coupling therainfall–runoff generation and routing modules. Thespatial distribution of the model parameters and sub-sequent analysis of raster-based outputs will havevariability that results from spatially distributed soiltypes, land cover, etc.; i.e. variability that is not dueto process coupling. In order to highlight impacts dueto coupling alone, we designed the experiment underthe condition of spatially uniform parameter values,with the exception of the DEM-derived parameters(refer to Appendix, Table A1). The experiment wasperformed with initial soil moisture contents at zerofor all grid cells, spatially homogenous soil types andland cover, and Ep of 5 mm/d. Forcing was from uni-form rainfall at a rate of 10 mm/d for 200 consecutivehours, and then turned off. Spatially uniform values

of the parameters in the Appendix (Table A2) weredetermined from the automatic calibration performedin Section 4.1.2. Figure 5(a)–(c) shows the spatial dis-tribution of grid cells with saturated soil states (asdefined by W > 0.95Wm; refer to Section 2.1.2 andTable A2) after 72, 120 and 168 h of constant rain-fall, respectively. At 72 h only a small number of gridcells (less than 1%) begin to become saturated in val-leys. As rainfall proceeds, the number of grid cellsbeing saturated increases at a linear rate up to 170 h(see Fig. 6). The saturation rate increases from 170to 194 h; afterwards, all grid cells in the basin reachsaturation. We also computed the spatial average ofsoil moisture values, plotted in a time series as a per-centage of the maximum soil moisture storage (i.e.(W

/W m) · 100; see Fig. 6). This curve shows a linear

increase in the regional soil moisture contents untilapproximately 120 h. After this time, the regional soilmoisture in the basin increases more gradually untilall grid cells reach saturation at 194 h. After the rain-fall is turned off at 200 h, we can see the numberof saturated grid cells drops exponentially, and theregional soil moisture in the basin decreases linearlyin response to the constant Ep of 5 mm/d.

In distributed hydrological models, soil mois-ture contents are typically determined by the spatialdistribution and intensity of precipitation, infiltra-tion characteristics and depth of the soil, land cover,and vegetation. The CREST model has demonstratedits ability to couple the rainfall–runoff generationto routing processes with the end result being arealistic pattern of grid cells becoming saturated inlow-lying valleys first and then propagating upstream,

Downloaded At: 19:38 7 March 2011

The coupled routing and excess storage (CREST) distributed hydrological model 95

Fig. 5 Spatial distribution of grid cells with saturated soil states (as defined by W > 0.95Wm) after (a) 72, (b) 120 and(c) 168 h. This synthetic experiment assumed: (1) dry initial soil moisture conditions everywhere, (2) uniform precipitationat a rate of 10 mm/d in the first 200 h, (3) constant daily Ep = 5 mm/d, and (4) spatially uniform soil type and land cover.

100

80

60

40

20

01 25 49 73 97 12

114

516

919

321

724

126

528

931

333

736

138

540

943

345

748

150

552

955

357

7

Perc

enta

ge o

f Sa

tura

ted

Gri

d C

ells

Sapa

tial A

vera

ge o

f So

il M

oist

ure

(%)

Percentage of Saturated Grid Cells

Spatial Average of Soil Moisture Values

Fig. 6 Time series of percentage of saturated grid cells (as defined by W > 0.95Wm; solid line) and spatial average ofsoil moisture values (as defined by W/W m · 100; dashed line). Note that after uniform rainfall was input at a constant rateof 10 mm/d, it was suddenly stopped at the 200th hour. After this time, the percentage of saturated grid cells decreasesexponentially due to runoff processes, while the spatial average of soil moisture values decreases more gradually in responseto a 5 mm/d potential evapotranspiration rate.

Downloaded At: 19:38 7 March 2011

96 Jiahu Wang et al.

patterns quite similar to the dynamic simulation studyreported in Beven & Freer (2001). In essence, CRESTaccounts for the terrain dependence of soil moisturein addition to the other physical properties mentionedabove. Future research will compare simulated soilmoisture values with remotely-sensed or in situ valuesto determine whether the simulated soil moisture dis-tribution is reasonably well represented by the CRESTmodel and will guide further improvements if deemednecessary.

5 SUMMARY AND DISCUSSION

This paper describes the Coupled Routing and ExcessSTorage (CREST) model; a flexible spatially dis-tributed hydrological model that is designed to sim-ulate the spatiotemporal distribution of streamflowand soil moisture (and other hydrological variables)within a basin using data from remote sensing plat-forms (e.g. precipitation, land cover, elevation, etc.)and in situ instruments (e.g. raingauges, soil moisturesensors, etc.). CREST was implemented in the Nzoiabasin near Lake Victoria, Africa, and streamflow mea-surements were used to calibrate model parametersvia an automatic calibration routine embedded in theCREST model code. The results during the valida-tion period indicated very good performance withNSCE, Bias and correlation coefficient values of 0.71,–0.47% and 0.84, respectively. The display of spa-tially distributed flood information was demonstratedby showing the discharge at each grid cell in the basin.Future studies will examine the model performance inother basins where there are stream gauges at interiorpoints. Another demonstration was provided to showthe impact of coupling the rainfall–runoff generationand routing components on the spatiotemporal distri-bution of soil moisture values. The evolution of thesoil moisture values appeared physically realistic withsaturation occurring first in low-lying areas and prop-agating upstream. The validity of this behaviour willbe further tested in a future study.

In summary, CREST has four desirable charac-teristics that contribute to its usefulness:

(1) distributed rainfall–runoff generation and cell-to-cell routing;

(2) coupling between the runoff generation androuting components via three feedback mecha-nisms; and

(3) scalability through the representation of soilmoisture variability (using a variable infiltration

curve) and routing processes (using linear reser-voirs) at the sub-grid scale.

These characteristics make the CREST modelsuitable for multi-scale hydrological modelling appli-cations ranging from global coverage (grid size oftens of kilometres) to regional coverage (grid size of1 km to a few kilometres). The authors are currentlyimplementing the CREST model for near-real timeglobal streamflow simulations driven by remotelysensed precipitation estimates (http://oas.gsfc.nasa.gov/CREST/global/). More thorough validation ofthe model at multiple scales is required to assess itsregional and global applicability.

As a newly developed model further research isrequired in many directions to enhance CREST, suchas utilizing remote sensing data for developing dis-tributed calibration strategies, detailed adjustment ofthe model parameters with the availability of field sur-vey data, and further testing of the model performancein various hydro-climatic regions. Source code and areadme file for the Linux version of CREST are pub-licly accessible via email request or by visiting theNASA-SERVIR project website at www.servir.net orUniversity of Oklahoma site at http://hydro.ou.edu/

CREST_downloads.html.

Acknowledgements The financial support fromNASA Applied Science Program SERVIR-AfricaProject, from University of Oklahoma and NOAA/

NSSL Director’s Discretionary Research Fund isgratefully acknowledged. The authors also thank theRCMRD for providing gauged rainfall and stream-flow observations over the Nzoia basin. The authorswould like to extend their appreciation for supportfrom grants no. 40801012, no. 40830639 of the NSFC(National Natural Science Foundation of China), andthe Fundamental Research Funds for the CentralUniversities. Finally, we wish to thank the review-ers and editors for their encouraging and constructivecomments.

REFERENCES

Bates, G. T., F. Giorgi & S. W. Hostetler (1993) Toward the simula-tion of the effects of the Great Lakes on regional climate. Mon.Weather Rev. 121, 1373–1387.

Beck, M. B. (1987) Water quality modeling: a review of the analysisof uncertainty. Water Resour. Res. 23, 1393–1442.

Bergström, S. (1995) The HBV model. In: Computer Models ofWatershed Hydrology (V. Singh, ed.), 443–476. HighlandsRanch, CO: Water Resources Publications.

Beven, K. J. & Binley, A. M. (1992) The future of distributed models:model calibration and uncertainty prediction. Hydrol. Processes6, 279–298.

Downloaded At: 19:38 7 March 2011

The coupled routing and excess storage (CREST) distributed hydrological model 97

Beven, K. & Freer, J. (2001) A dynamic TOPMODEL. Hydrol.Processes 15(10), 1993–2011, doi:10.1002/hyp.252.

Bonan, G. B. (1995) Sensitivity of a GCM simulation to inclusion ofinland water surfaces. J. Climate 8, 2691–2704.

Branstetter, M. L. & Famiglietti, J. S. (1999) Testing the sensitivityof GCM-simulated runoff to climate model resolution usinga parallel river transport algorithm. In: Proc. 14th Conf. onHydrology, 391–392. Boston, MA: Am. Met. Soc.

Brooks, S. H. (1958) A discussion of random methods for seekingmaxima. Operations Research 6, 244–254.

Burnash, R. J. C. (1995) The NWS river forecast system—catchment modeling. In: Computer Models of WatershedHydrology (V. Singh, ed.), 311–366. Highlands Ranch, CO:Water Resources Publications.

Coe, M. T. (1997) Simulating continental surface waters: an applica-tion to Holocene Northern Africa. J. Climate 10, 1680–1689.

Dickinson, R. E. (1989) A regional climate model for the westernunited states. Climate Change 15(1), 383–422.

Friedl, M. A., McIver, D. K., Hodges, J. C. F., Zhang, X. Y.,Muchoney, D., Strahler, A. H., Woodcock, C. E., Gopal, S.,Schneider, A. & Cooper, A. (2002) Global land cover map-ping from MODIS: algorithms and early results. J. Remote Sens.Environ. 83(1-2), 287–302.

Gupta, J. V., Sorooshian, S. & Yapo, P. O. (1998) Toward improvedcalibration of hydrologic models: multiple and noncommen-surable measures of information. Water Resour. Res. 34,751–763.

Hagemann, S. & Dümenil, L. (1998) A parameterization of thelateral waterflow for the global scale. Climate Dynamics 14,17–31.

Hargreaves, G. H. & Samani, Z. A. (1982) Estimating poten-tial evaporation. J. Irrig. Drain. Engng ASCE 108(IR3),223–230.

Hostetler, S. W., Bates, G. T. & Giorgi, F. (1993) Interactive cou-pling of a lake thermal model with a regional climate model.J. Geophys. Res. 98, 5045–5057.

Kundzewicz, Z. W. & Stakhiv, E. Z. (2010) Are climate models“ready for prime time” in water resources management appli-cations, or is more research needed? Editorial. Hydrol. Sci. J .55(7), 1085–1089.

Lehner, B., Verdin, K. & Jarvis, A. (2008) New global hydrogra-phy derived from spaceborne elevation data. Eos, Trans. Am.Geophys. Un. 89(10), 93–94.

Li, L., Hong, Y., Wang, J., Adler, R., Policelli, F., Habib, S., Irwn, D.,Korme, T. & Okello, L. (2009) Evaluation of the real-timeTRMM-based multi-satellite precipitation analysis for an oper-ational flood prediction system in Nzoia basin, Lake Victoria,Africa. J. Natural Hazards 50(1), 2009, 109–123.

Liang, X., Lettenmaier, D. P. & Wood, E. F. (1996) One-dimensionalstatistical dynamic representation of subgrid spatial variabilityof precipitation in the two-layer variable infiltration capacitymodel. J. Geophys. Res. 101(D16), 21,403–21,422.

Linsley, R. K., Kohler, M. A. & Paulhus, J. L. H. (1986) Hydrologyfor Engineers, 339–356. New York: McGraw-Hill.

Liston, G. E., Sud, Y. C. & Wood, E. F. (1994) Evaluating GCMland surface hydrology parameterizations by computing riverdischarges using a runoff routing model. J. Appl. Met. 33,394–405.

Miller, J., Russell, G. & Caliri, G. (1994) Continental scale river flowin climate models. J. Climate 7, 914–928.

Naden, P. S. (1993) A routing model for continental-scale hydrology.In: Macroscale Modeling of the Hydrosphere (W. B. Wilkinson,ed.) (Proc. Yokohama Symp., July 1993), 67–79. Wallingford:IAHS Press, IAHS Publ. 214.

Nash, J. & Sutcliffe, J. (1970) River flow forecasting through concep-tual models. Part I: A discussion of principles. J. Hydrol. 10,282–290.

Osano, O., Nzyuko, D., Tole, M. & Admiraal, W. (2003) The fateof chloroacetanilide herbicides and their degradation productsin the Nzoia Basin, Kenya. Ambio: J. Hum. Environ. 32(6),424–427.

Priestley, C. H. B. & Taylor, R. J. (1972) On the assessment of surfaceheat flux and evaporation using large-scale parameters. Mon.Weather Rev. 100, 81–92.

Rabus, B., Eineder, M., Roth, A. & Bamler, R. (2003) The shut-tle radar topography mission—a new class of digital elevationmodels acquired by spaceborne radar. Photogramm. RemoteSens. 57, 241–262.

Refsgaard, J. C. (1996) Terminology, modelling, protocol andclassification of hydrological model codes. In: DistributedHydrological Modelling (M. B. Abbott & J. C. Refsgaard,eds), 17–39. Amsterdam: Kluwer Academic Publishers, WaterScience and Technology Library.

Refsgaard, J. C. & Storm, B. (1995) MIKE SHE. In: ComputerModels of Watershed Hydrology (V. Singh, ed.), 809–846.Highlands Ranch, CO: Water Resources Publications.

Reichold, L., Zechman, E., Brill, E. & Holmes, H. (2010) Simulation–optimization framework to support sustainable watershed devel-opment by mimicking the predevelopment flow regime. J. WaterResour. Plan. Manage. 136, 366.

Singh, V. P. (ed.) (1995) Computer Models of Watershed Hydrology.Highlands Ranch, CO: Water Resources Publications.

Sausen, R., Schubert, S. & Dumenil, L. (1994) A model of river runofffor use in coupled atmosphere–ocean models. J. Hydrol. 155,337–352.

Vörösmarty, C. J., Moore, B., Grace, A., Gildea, M., Melillo, J.,Peterson, B., Rastetter, E. & Steudler, P. (1989) Continental-scale model of water balance and fluvial transport: an appli-cation to South America. Global Biogeochem. Cycles 3,241–265.

Vrugt, J. A., Diks, C. G. H., Gupta, H. V., Bouten, W. &Verstraten, J. M. (2005) Improved treatment of uncertainty inhydrologic modeling: combining strengths of global optimiza-tion and data assimilation. Water Resour. Res. 41, W01017,doi:10.1029/2004WR003059.

Woolhiser, D. A., Smith, R. E. & Goodrich, D. C. (1990) KINEROS,Kinematic Runoff and Erosion Model: Documentation and UserManual. US Dept of Agriculture – Agric. Research Service,USDA-ARS no. 77.

Yilmaz, K. K., Vrugt, J. A., Gupta, H. V. & Sorooshian, S.(2010) Model calibration in watershed hydrology. Chapter 4 in:Advances in Data-based Approaches for Hydrologic Modelingand Forecasting (B. Sivakumar & R. Berndtsson, eds), 137–182. World Scientific Publishing.

Zhao, R. J. (1992) The Xianjiang model applied in China. J. Hydrol.135(3), 371–381.

Zhao Renjun, Zhang Yilin, Fang Leren, Liu Xinren & ZhangQuansheng (1980) The Xinanjiang Model. In: HydrologicalForecasting (Proc. Oxford Symp., April 1980), 351–356.Wallingford: IAHS Press, IAHS Publ. 129.

Downloaded At: 19:38 7 March 2011

98 Jiahu Wang et al.

APPENDIX

Table A1 Physically-based parameters.

Symbol Unit Brief description Source forestimation

ACC - Accumulationgrids

Derived fromDEM

d - Vegetationcoverage

Remote sensing

DEM m Digital elevationmodel

Remote sensing

Dire - Flow direction Derived fromDEM

K mm h-1 Cell meaninfiltration rate

Soil survey

l m Distance betweencells

Derived fromDEM

LAI m2 m2 Leaf area index Remote sensingS degree Slope between

cellsDerived from

DEM

Table A2 Parameters requiring optimization.

Symbol Unit Brief description Default value

B - Exponent of variableinfiltration curve

0.2

Kc - Coefficient of land cover’sCIC

0.5

kI - Interflow reservoirdischarge parameter

0.1

kO - Overland reservoirdischarge parameter

0.5

kX - Runoff velocitycoefficient varying inoverland, channel andinterflow

50/100/15

Th km2 Threshold betweenoverland and channel

30

Wm1 mm Maximum cell mean watercapacity of soil layer 1

20

Wm2 mm Maximum cell mean watercapacity of soil layer 2

50

Wm3 mm Maximum cell meanwater capacity of soillayer 3

80

Table A3 Inputs and outputs of the CREST model.

Symbol Unit Description

A - Upstream point of profile alongseveral cells

CI mm Intercepted water in canopy layerCIC mm Canopy interception capacityEa mm h-1 Actual evaporation of bare soilEc mm h-1 Actual evaporation from intercepted

water in canopy layerEp mm h-1 Potential evapotranspirationEp1 mm h-1 Potential evaporation from soil layer 1Ep2 mm h-1 Potential evaporation from soil layer 2Ep3 mm h-1 Potential evaporation from soil layer 3Es1 mm h-1 Actual evaporation from soil layer 1Es2 mm h-1 Actual evaporation from soil layer 2Es3 mm h-1 Actual evaporation from soil layer 3im mm Maximum i of a cellI mm h-1 Infiltration water simulated from

variable infiltration curveI mm h-1 Adjusted I considering horizontal

input water from routingP mm h-1 PrecipitationPsoil mm h-1 Precipitation input to soil surfacePsoil mm h-1 Adjusted Psoil considering horizontal

input water from routingR mm h-1 Excess rain generated by variable

infiltration curveRO mm h-1 Overland excess rainRI mm h-1 Interflow excess rainRI, in mm h-1 Interflow runoff entering a cell from

routingRI,out mm h-1 Interflow runoff leaving a cellRO,in mm h-1 Overland runoff entering a cell from

routingRO,out mm h-1 Overland runoff leaving a cellSI mm Interflow reservoir storageSO mm Overland/channel reservoir storageSO mm Adjusted SO considering horizontal

input water from routingSto mm Total cell water storage, including soil

water and free waterT h Concentration time from cell to its

downstream adjoining cellW mm Total cell mean water of three soil

layersW 1 mm Cell mean water in soil layer 1W 2 mm Cell mean water in soil layer 2W 3 mm Cell mean water in soil layer 3Wm mm Maximum cell mean water capacity

Downloaded At: 19:38 7 March 2011