JUNE 2006 R I G O N E T A L . 371

GEOtop: A Distributed with Coupled Water and Energy Budgets

RICCARDO RIGON AND GIACOMO BERTOLDI Department of Civil and Environmental Engineering, CUDAM, University of Trento, Trento, Italy

THOMAS M. OVER Department of Geology/Geography, Eastern Illinois University, Charleston, Illinois

(Manuscript received 1 March 2005, in final form 11 August 2005)

ABSTRACT

This paper describes a new distributed hydrological model, called GEOtop. The model accommodates very complex topography and, besides the , unlike most other hydrological models, integrates all the terms in the surface energy balance equation. GEOtop uses a discretization of the landscape based on digital elevation data. These digital elevation data are preprocessed to allow modeling of the effect of topography on the radiation incident on the surface, both shortwave (including shadowing) and longwave (accounting for the sky view factor). For saturated and unsaturated subsurface flow, GEOtop makes use of a numerical solution of the 3D Richards’ equation in order to properly model, besides the lateral flow, the vertical structure of water content and the suction dynamics. These characteristics are deemed necessary for consistently modeling hillslope processes, initiation of landslides, snowmelt processes, and ecohydrological phenomena as well as discharges during and interstorm periods. An accurate treatment of radiation inputs is implemented in order to be able to return surface temperature. The motivation behind the model is to combine the strengths and overcome the weaknesses of forecasting and land surface models. The former often include detailed spatial description and lateral fluxes but usually lack appropriate knowledge of the vertical ones. The latter are focused on vertical structure and usually lack spatial structure and prediction of lateral fluxes. Outlines of the processes simulated and the methods used to simulate them are given. A series of applications of the model to the Little Washita basin of Oklahoma using data from the Southern Great Plains 1997 Experiment (SGP97) is presented. These show the model’s ability to reproduce the pointwise energy and water balance, showing that just an elementary calibration of a few parameters is needed for an acceptable reproduction of at the outlet, for the prediction of the spatial distribution of soil moisture content, and for the simulation of a full year’s streamflow without additional calibration.

1. Introduction: Design prerequisites and momentum exchanges between the land surface and the atmosphere at several scales (Abbott 1992; The study of basin hydrology is focused on the Reggiani et al. 1999), with the purpose of creating mod- analysis of the interactions between the near-surface els that can provide improved mid- and long-term hy- soil and the atmospheric boundary layer (ABL), which drologic forecasts and better prediction of the impacts occur mainly through the mediation of the soil itself, on the hydrologic cycle and on the earth’s ecosystems the vegetation, and the turbulent and radiative energy resulting from changes in land use and in the climate transfers taking place on the earth’s surface, and pos- (Grayson and Blöschl 2000). Though inspired by this sible feedbacks from the ABL (e.g., soil moisture– trend toward improved predictions, the initial motiva- precipitation feedback mechanisms). In recent years, tions behind the development of GEOtop were practi- hydrologic research has generally evolved toward a cal, as its development began with attempts to predict, comprehensive theory describing the water, energy, besides river discharges, landslide and ini- tiation, snowpack evolution and ablation, and the water budget (especially, accurate assessment of evapotrans- Corresponding author address: Riccardo Rigon, Dept. of Civil and Environmental Engineering, CUDAM, University of Trento, piration and the distribution of soil moisture) in small Via Mesiano, 77, Trento TN 38050, Italy. catchments and in complex mountain terrain. E-mail: [email protected] None of the above phenomena can be currently pre-

© 2006 American Meteorological Society

JHM497 372 JOURNAL OF HYDROMETEOROLOGY VOLUME 7 dicted with enough accuracy and consistency to be op- floods but do not provide enough hydrological infor- erationally useful (Committee on Hydrologic Science mation for forecasting other processes. 2002). It is known that such phenomena are affected by Vice versa, the land surface models (LSMs), unlike heterogeneity in soil hydraulic properties, land use, the flood-forecasting models, are usually one- landscape, topography and geological properties, and dimensional (1D) vertical models that represent soil– soil moisture profile and surface–subsurface interac- atmosphere interactions with a great degree of com- tions, but it has not been quantitatively assessed to what plexity and accuracy, but they are usually not endowed extent. This cannot be explicitly obtained without a with a detailed representation of runoff and lateral small-scale distributed model that is capable of explic- fluxes (Warrach et al. 2002), as they have been devel- itly accounting for these characteristics. Furthermore, it oped mainly to provide a land surface interface in sup- would require that both the water and energy balances port of atmospheric general circulations models be solved (Grayson and Blöschl 2000). Solving the en- (GCMs). Reviews of LSMs are presented in Garratt ergy balance means, among other things, being able to (1992, 1993) and Lakshmi et al. (2001). State-of-the-art estimate surface temperature Ts, and it also requires LSMs, inclusive of the ability to model snowmelt, freez- proper treatment of radiation physics (including the ef- ing soil, and multilayer canopy models are, to mention fect of the view angle and shadowing in complex ter- a few, the biosphere–atmosphere transfer scheme ) (Blo¨ schl et al. 1991). However, since temperature (BATS; Dickinson et al. 1986), the surface energy and is absolutely necessary in modeling snowpack evolution water balance (SEWAB; Mengelkamp et al. 1999), the (e.g., Zanotti et al. 2004; Pomeroy et al. 2003), its simu- Noah LSM (Chen et al. 1996), and the National Center lation should be included in the design of such a model. for Atmospheric Research (NCAR) LSM (Bonan 1996). Finally, the proper description of many of the hydro- GEOtop is designed to be an integration of the char- logic phenomena on hillslopes (including hill- acteristics of both LSMs and flood-forecasting models slope stability) and of water fluxes in the absence of and to include a detailed treatment of topographic in- significant slopes, such as in plains or in riparian zones, teraction with radiation, which is not usually available requires an adequate treatment of suction head in un- in other models. Thus GEOtop is a distributed model; saturated soils. it is a terrain-based model; it simulates not only the Just a few distributed hydrological models have all water balance but also the energy balance; and it is built the necessary characteristics. Since the blueprint of for remote sensing data because it provides surface Freeze and Harlan (1969), many “distributed” hydro- temperature and an accurate treatment of radiation and logical models (Beven 2000) have been implemented to moisture in the upper soil (Troch et al. 2003). predict the lateral distribution of water, ranging from This paper is organized as follows. Section 2 contains more conceptualized descriptions (e.g., Beven and the description of model components, which begins Kirkby 1979; Franchini and Pacciani 1991) to fully dis- with a description of the discretization of the landscape tributed approaches, such as the Syste`me Hydrologique in GEOtop, followed by a description of local water Europe´en (SHE; Abbott et al. 1986), topographic ki- and energy budgets, and concluding with a description nematic approximation and integration model (TOP- of the processes driving the water and energy fluxes. KAPI; Ciarapica and Todini 2002), THALES (Grayson Section 3 contains three case studies based on the 1997 et al. 1992), and others (Vertessy et al. 1993; Garrote Southern Great Plains Hydrology Experiment (SGP97) and Bras 1995; Bronstert and Plate 1997). At the catch- dataset. The case studies show the reproduction of the ment scale, distributed approaches range from a three- water and energy balance at a point, a calibration of the dimensional integration of the Richards’ equations as in model on a flood event on the Little Washita basin in Paniconi and Putti (1994) or in the catchment hydro- Oklahoma, the spatial soil moisture distribution over logical model (CATHY; Paniconi and Wood 1993; Pa- the basin, and the subsequent simulation of a yearlong niconi et al. 2003a) to a distributed description of the surface discharge with no additional cali- hydrological effects of vegetation as in the Distributed bration. Conclusions follow in section 4. Hydrological Soil Vegetation Model (DHSVM) (Wig- mosta et al. 1994). Nevertheless, the Distributed Mod- 2. Description of model components els Intercomparison Project (DMIP) (Reed et al. 2004) GEOtop simulates the fluxes and budgets of energy provides a recent, clear example of the continued em- and water on a landscape defined by three-dimensional phasis in hydrologic modeling on ; the grid boxes, whose surfaces come from a digital eleva- models involved, with a few exceptions (Liang and Xie tion model (DEM) and whose lower boundaries are 2001; Ivanov et al. 2004), were mostly event-oriented located at some specified spatially varying depth. If rainfall-runoff models, which are successful in modeling snow accumulates on top of the land surface, a new JUNE 2006 R I G O N E T A L . 373 layer is added on top of the DEM as described in Zan- and in the soil otti et al. (2004). Surface boundary conditions are given Ѩ␪͑x, t͒ by hydrometeorological measurements (rainfall, tem- ϩ ٌ · q ͑x, t͒ ϭϪS͑x, t͒, ͑2͒ Ѩt sub perature, wind velocity), regionalized as described in Bertoldi (2004). where vectors are in bold characters, x is the position We present here the components of the first public (L), t is time (T), qsup is the runoff discharge per unit Ϫ1 version of GEOtop. Information on previous versions surface area [in units of L (length) T (time)], c(x) the Ϫ1 ٌ ϭ can be found in Bertoldi and Rigon (2004). spatially varying kinematic wave celerity (L T ), · Ϫ1 ץץϩ ץץϩ ץ ץ ( / x / y / z) is the divergence operator (L ), qL Ϫ a. Landscape and equation discretization (T 1) is the unit volume flow exchange with the soil [inflow from the soil (exfiltration) if positive, outflow to GEOtop requires preprocessing of the catchment the soil () if negative], ␪ is the volumetric ٌ -DEM for which a special set of routines has been imple water content in the soil (or snow), and · qsub is the mented in an open source GIS, the Java Geographic Ϫ flux divergence of water per unit volume (T 1), which Resource Analysis Support System (JGRASS; http:// includes the water fluxes from adjacent cells, regulated www.hydrologis.com). The outputs of these routines in- Ϫ by Richards’ Eq. (6) below. The term S (T 1) includes clude estimation of directions, slopes, curva- the exchanges between atmosphere and soil (evapora- ture, the channel network structure, shadowing, and the tion and transpiration) according to Eqs. (15)–(19). The sky view factor. is modeled to follow the treatment of the boundary conditions is derived from terrain surface according to a so-called D8 topology as Bixio et al. (2000) and allows for surface flow to infil- in Orlandini et al. (2003). Advantages and disadvan- trate (when possible) and subsurface flow to return to tages of various methodologies for carrying out these the surface (exfiltration and return flow). When chan- computations are thoroughly discussed in Rodriguez- nel pixels are present, surface runoff eventually turns Iturbe and Rinaldo (1997) and in Orlandini et al. (2003) into channel flow, which is routed with a separate nu- and are not further discussed here. Soil thickness can be merical scheme as described below. Bottom boundary defined either using field data or the model by Heim- conditions can be defined either by a flux at the bed- sath et al. (1997), as discussed Bertoldi et al. (2006a). rock–soil interface or by the conductivity of the deeper The DEM identifies also the plan view of a three- bedrock. Except for , water vapor dimensional grid on which all the model’s equations are fluxes are neglected in the present implementation of discretized. The thickness of the discretized soil layers the model. is set up at run time; it is usually appropriate to assume that the top layer is quite thin (e.g., 5 cm thick). Ac- 2) ENERGY BUDGET cording to criteria that the user can specify (e.g., The fluxes of energy for a unit volume of water in the Prosser and Abernethy 1996), some of the grid cells can earth’s gravitational field are given by the sum of a be identified as river network cells. River network cells “thermal” part, which is a function of the net radiation are treated the same as hillslope cells except for the R , the thermal fluxes into the ground G , energy inputs routing of surface runoff, which is modeled as described n r deriving from precipitation P, sensible heat flux H, la- in section 2c. ␭ ␭ tent heat flux ET (where is the latent heat of vapor- b. Water and energy budgets in GEOtop ization per unit mass), and a fluid-mechanical part (de- pendent on the hydraulic head). The action of the me- The budgets of mass and energy in GEOtop may be chanical part in producing internal energy by friction is divided into three parts: the water budget, the energy neglected in GEOtop according to the common prac- budget, and the radiation budget. The radiation budget tice. This results in a partial decoupling of the water and is presented separately from the energy budget, as it energy balances, which however remain strongly con- creates the link between the model and remotely nected through the evapotranspiration term and the de- sensed data. pendence of hydraulic conductivity on temperature. The energy balance is computed with respect to vol- 1) WATER BUDGETS umes where the energy content of the water and soil are GEOtop calculates the conservation of water accord- considered together and for the same grid boxes as the ing to discretized versions of the continuity equations soil water balance. In continuous form, the energy bal- for liquid water on the surface ance is written as Ѩ ͑ ͒ Ѩ ͑ ͒ qsup x, t U x, t ϩ c͑x, tٌ͒ · q ͑x, t͒ ϭ c͑x, t͒q ͑x, t͒ ͑1͒ ϩ ٌ · g͑x, t͒ ϭ 0, ͑3͒ Ѩt sup L Ѩt 374 JOURNAL OF HYDROMETEOROLOGY VOLUME 7 where U (E/L3) is the internal energy density and g is are expressed through the sky view factor V(x), which the energy flux per unit area (E LϪ2 TϪ1). In the actual indicates the sky fraction visible at a point. The rel- numerical implementation of Eq. (3), lateral energy evance of V(x) for the radiative balance in mountain fluxes have been neglected, as they are usually much areas has been underlined, for instance, by Blo¨ schl et smaller than the vertical fluxes, even though at small al. (1991). Many models neglect shadowing and the sky spatial scales (ϳ10 m) lateral energy advection can be view factor, causing large errors in the local energy nonnegligible (Albertson and Parlange 1999). Radia- balance estimation in mountainous catchments. The al- tion, sensible heat, and precipitation energy input are gorithms for estimating these terms are fully docu- ϭ ϩ ٌ effective only on the surface layer, that is, g Rn mented in Bertoldi and Rigon (2004). Taking into ac- ϩ ϩ ϩ ␭ ٌ ϭ P Gr H ET on the surface layer and only g count the effects of shadowing and of the sky view fac- ϩ ␭ ␭ Gr ET on the other soil layers. The ET term in- tor, the flux of net radiation Rn is cludes both bare soil evaporation (only for the first ϭ ͓ ͑ ͒ ϩ ͑ ͒ ͔͓ Ϫ ͑ ͒ ͔ Rn sh x, t R↓SW P V x R↓SW D 1 V x a layer) and canopy transpiration (depending from root ϩ ͑ ͒␧ Ϫ ͑ ͒␧ ␴ 4 ͑ ͒ density of each layer), as explained later. The top layer V x aR↓LW V x s T s, 5 Ϫ2 Ϫ1 can be the snowpack, if present, and can have any thick- where R↓SW (E L T ) is the shortwave net radiation ness. In this case, the internal energy content U is di- at the surface obtained by correcting the solar radiation vided between energy of the ice component and energy incoming at the atmosphere top (the subscript P refers of the water component (Zanotti et al. 2004). Heat to the direct component and D to the diffuse; note the fluxes in the ground between the layers, diffuse component is not influenced by shadowing but is proportional to the sky view factor), a is the short- ѨT͑x, t͒ ϭϪ␭ ͑ ␪͒ ͑ ͒ wave albedo, ␧ is the atmospheric emissivity, ␧ is the Gr s x, t, Ѩ , 4 a s z longwave soil (or snow) emissivity, ␴ is the Stefan– Ϫ8 2 4 Ϫ1 are a function of the soil temperature gradient accord- Boltzman constant {5.6704 10 [W(m K ) ]}, R↓LW ing to the Fourier heat diffusion equation where the the incoming longwave radiation, calculated according ␭ to Brutsaert (1975), depending on air temperature, air thermal conductivity s(x, t) depends on the mineral properties of the soil and on the actual (time varying) humidity, and cloud cover, and Ts is surface tempera- Ϫ water content ␪ in the grid element. Freezing soil pro- ture. The factor [1 V(x)a] accounts for the shortwave cesses are included as described in Bertoldi et al. radiation reflected by the surfaces surrounding the (2006b). The boundary condition in the deepest soil point. The last two terms of Eq. (5) are multiplied by layer is the soil temperature obtained from the analyti- V(x) to account for the longwave radiation emitted by cal solution of the Fourier law, using an annual sinu- the surfaces surrounding the point, under the hypoth- soidal forcing. The soil temperature in Eq. (4) is ob- esis of radiative equilibrium. tained in the model by the integration of the full surface Remote sensors detect only limited bands of the ra- energy budget (Best 1998), solving the system given by diation spectrum and not the whole integrated infrared the partial differential Eqs. (3) describing the soil tem- (LW) and visible parts (SW) of it as in (5). The radia- perature profile. tion budget code was separated in GEOtop from the energy budget code because future versions of the model will be able to return the radiative intensity sepa- 3) RADIATION BUDGET rated into optical radiation bands where remote sensors An accurate calculation of the net radiation is essen- operate. tial for a hydrological model working in complex ter- rain (Dubayah et al. 1990). Solar radiation geometry is c. Dynamic hydrology in GEOtop treated in GEOtop as in Iqbal (1983), and all the ra- Water and energy fluxes, which control the budgets diative corrections needed for complex topography, in- described above, are computed according to gradients cluding shadowing of direct solar radiation by sur- of energy potentials as described below. A more de- rounding mountains and the effect of topography on tailed description of the dynamics including complete diffuse radiation, are included. Shadowing is expressed equations can be found in Bertoldi and Rigon (2004). by the dimensionless factor sh(x, t), which is 0 if the grid The snow module and its preliminary application to a cell is in shadow (no direct radiation) and 1 if radiation case study are described in Zanotti et al. (2004). from the sun hits the surface. The shadowing factor is calculated for any position, x, and for any instant, t, 1) SUBSURFACE SATURATED–UNSATURATED FLOW depending on the interplay of solar position and topog- To model soil moisture dynamics properly in the soil raphy. The effects of topography on diffuse radiation layers, GEOtop utilizes the integration of Richards’ JUNE 2006 R I G O N E T A L . 375

␪ equations (Richards 1931; Freeze and Harlan 1972) in where r is the residual water content (dimensionless), three dimensions (3D). For some of the processes esti- and ␣(LϪ1), m, and n (both dimensionless) are param- mation, simpler approaches could have been used such eters. Such parameters, as well as the saturated hydrau- as the hillslope-storage Boussinesq (hsB) equation de- lic conductivity, are 3D fields in the model and many veloped by Troch et al. (2003), Paniconi et al. (2003b), different strategies for their assignment are possible. and Hilberts et al. (2004), which has been shown to For instance, they can be derived from the soil texture work generally very well as compared to the 3D Rich- by means of the pedotransfer functions proposed, for ards’ equation for simulation of saturated subsurface example, by Vereecken et al. (1989) and Leij et al. flow dynamics and to be much more computationally (2004) or by regionalization of the appropriate field efficient. However, GEOtop is intended to simulate measurements. The relative hydraulic conductivity is also the suction dynamics, and, in this, solving Rich- expressed as a function of the water content as in ards’ equation is necessary. Mualem (1976). Even though we did not pursue a com- The numerical scheme used is new and is described in plete thermodynamic treatment of saturated– Tamanini (2003) and in Bertoldi and Rigon (2004). The unsaturated flow as in Milly (1974), saturated hydraulic use of Richards’ equation removes the need to make an conductivity is made dependent on soil temperature assumption of stationary conditions in subsurface flows through viscosity, which increases by a factor 2 from 10° [as is assumed, e.g., in Beven and Kirkby (1979)], and to 40°C, allowing the treatment of soil freezing and therefore it is possible to describe the transients of flow seasonal variation of hydraulic characteristics that oth- and infiltration. Richards’ equation is here written ac- erwise require multiple calibrations of soil parameters cording to Paniconi and Putti (1994) as through the year. The description of vertical infiltration in GEOtop ͒ ͑ ϭϪ ͑ ٌ͒͑␩ ϩ ␺͒ qsub KsKr SW z , 6 takes into account the surface fraction actually covered in water, assuming the presence of microrelief in the Ѩ␺ terrain, which is parameterized by a surface roughness ,␴͑S ͒ ϭ ٌ · ͓K ͑T͒K ͑S ٌ͒͑␺ ϩ ␩ ͔͒ Ϫ S W Ѩt s r W z parameter according to Smith (2002) as ϭ Ն ͑ ͒ ͑7͒ I I0 if d h0, 9 ϭ ր Ͻ ͑ ͒ I I0d h0 if d h0, 10 where the dependence from space and time of the vari- where I is the effective infiltration rate, I is the infil- ables has been dropped for notational simplicity, ␴ (S ) 0 W tration rate with no microrelief, d is the ␺ is the storage term (LϪ1), S (␺) ϭץ/ Sץ ϭ S S ϩ ␾ W s W W depth, and h is the microrelief height. ␪/␪ is the relative water saturation (the ratio between 0 s Runoff at the surface is generated because the pre- the volumetric soil moisture content ␪ and the saturated cipitation intensity is greater than the soil surface infil- moisture content ␪ ), ␾ is the porosity (dimensionless), s tration capacity (infiltration excess runoff; Horton S is the aquifer specific storage coefficient (LϪ1), ␺ is s 1933) or the level rises above the soil sur- -the pressure hydraulic head (L), ٌ is the gradient op face (saturation excess runoff; Dunne 1978). Both of erator, K (T) is the saturated hydraulic conductivity, s these possibilities are dealt with the Richards’ equation and T is the temperature (K). Here, K (S ) ϵ K(S )/ r W W solver and are implemented according to the compre- K (T) is the relative hydraulic conductivity, z is the S hensive analysis of boundary conditions made by Pani- vertical upward coordinate, and S represents the modu- coni and Putti (1994). In addition, Richards’ equation lus of the source or sink volumetric flow per unit vol- allows for water to redistribute laterally and even move ume [the same as in Eq. (2)]. The saturated hydraulic uphill or exfiltrate according to local suction. conductivity Ks(T) has in fact two components, the ver- tical, Ks ␷(T), and the lateral Ksh(T) grid-averaged val- 2) SURFACE RUNOFF ues (Kumar 2004). In the model they are considered proportional according to an anisotropy ratio given by Runoff is routed according to a kinematic scheme ␣ ϭ that also accounts for subgrid-scale rilling and hetero- K Ksh/Ks ␷, which is used as a calibration parameter. The relation between ␺ and ␪ [e.g., Eq. (2)] in geneity in roughness: Ѩ ͑ ͒ Ѩ ͑ ͒ GEOtop is given through the van Genuchten (1980) qsup x, t qsup x, t ϩ c͑x, t͒ ϭ c͓͑x, t͔͒q , ͑11͒ schematization, Ѩt Ѩs L ϭ ͑ ͒␥ ٌ͓ ͑ ͔͒0.5 ͒ ͑ 1 ␪ Ϫ ␪ 1րm 1րn c x, t Cmd x, t z x , ␺ ϭ ͫͩ r ͪ Ϫ ͬ ͑ ͒ ␣ ␪ Ϫ ␪ 1 , 8 ͑ ͒ s r 12 376 JOURNAL OF HYDROMETEOROLOGY VOLUME 7

where Eq. (11) is the continuity Eq. (1) written along through the bulk turbulent heat transfer coefficient CH

the drainage direction coordinate s (L), qsup is the run- (dimensionless), the wind speed uw, and the gradient Ϫ1 off discharge per unit surface area (L T ) along s, c(x) between the surface soil/snow temperature Ts and the is the spatially varying kinematic wave celerity module air temperature Ta as (L TϪ1), C is a resistance coefficient, [LϪ(1Ϫ␥) TϪ1], d m Q ϭ ␳c C u ͑T Ϫ T ͒, ͑14͒ is the surface water depth (L), ٌz(x) is the local slope s p H w s a ␥ ␳ (dimensionless), the exponent (dimensionless) is vari- where is the density of the air, and cp is the specific able as a function of the runoff phenomena geometry, heat of the air at constant pressure. Here, Ts is obtained Ϫ1 and qL (T ) is the unit volume vertical inflow (posi- from solving the energy balance, and Ta is a measured tive: exfiltration) or outflow (negative: infiltration) external forcing; CH is a bulk turbulent transfer coeffi- from any surface cell to the soil. The qL term contains cient that accounts for the turbulent transfer processes the term Si from Eq. (7) and allows for runoff to rein- and the different roughness length zT of the various filtrate downhill. The exponent 0.5 in Eq. (12) is cali- surfaces through a mapping of the land use and a pa- brated or specified according to the literature (e.g., rameterization of the stability of the ABL. In particu-

Smith 2002). lar, CH is determined using similarity theory (Garratt 1992) and is expressed according the theory of Louis 3) CHANNEL FLOW (1979), which uses the Richardson number (a function GEOtop does not need a channel network to be of the potential temperature gradient between soil and identified since water can move downhill according to atmosphere) as a stability parameter. Similarity func- (12). However, channel geometry and roughness adjust tions are given by the approach of Kot and Song (1998). themselves to maintain certain mean flow characteris- The total evapotranspiration is a sink in (7) made up tics (e.g., Rodriguez-Iturbe et al. 1992) and thus it is of the sum of evaporation or sublimation from the soil generally useful to separate channel flow routing from or snow surface EG, transpiration from the vegetation the hillslope runoff routing. In the channels, surface ETC, and evaporation of the precipitation intercepted water flow is described by the convolution of the in- by the vegetation EVC, that is, ϭ ϩ ϩ ͑ ͒ coming discharge with the solution of the de Saint- ET ETC EG EVC. 15 Venant parabolic equation using a constant celerity in the whole network as proposed in Mesa and Mifflin Every cell has a fraction covered by vegetation and a (1986), Rinaldo et al. (1991), and D’Odorico and Rigon fraction covered by bare soil, and the vegetation frac- (2003): tion contains an interception store, modeled as in Men- gelkamp et al. (1999). The model uses a single-layer t Lmax sW͑␶,s͒ canopy model, and the leaf temperature is assumed to ͑ ͒ ϭ ͵ ͵ Qc t AT exp 3 be equal to soil temperature, as in Garratt (1992). The 0 0 ͌4␲D͑t Ϫ ␶͒ green vegetation fraction is static, and there is not a ͑ Ϫ ͑ Ϫ ␶͒͒2 s uc t mechanism to automatically vary the leaf area index ͫϪ ͬ ds d␶, ͑13͒ 4D͑t Ϫ ␶͒ (LAI) to model plant development, but it may be

3 changed by external input to the model. where Qc(t) is the discharge at the basin outlet (L The components of the total evapotranspiration are Ϫ1 ␶ Ϫ1 T ), AT is the basin area, W( , s)(T ) is the inflow of computed as functions of the potential evapotranspira- the water from the hillsides into the channel network at tion E , which is computed as a function of the gradient ␶ P a distance s (L) from the outlet and at a time [i.e., it between saturation-specific moisture at the soil surface is a dynamical width function (Rodriguez-Iturbe and Ϫ1 temperature q*(Ts) and the atmospheric specific mois- Rinaldo 1997)], uc is a mean celerity (L T ), D is a 2 Ϫ1 ture q(Ta) (M/M) as hydrodynamic dispersion coefficient (L T ), and Lmax ␭ ϭ ␭␳ ͓ ͑ ͒ Ϫ ͑ ͔͒ ͑ ͒ is the maximum distance from the outlet measured EP CE uw q* Ts q Ta , 16 along the network (L). where the bulk turbulent water vapor transfer coeffi-

cient CE is taken as equal (though a simplification) to 4) TURBULENT FLUXES CH. GEOtop does not contain a special parameteriza- ␭ Sensible H and latent ET heat fluxes are determined tion of the wind profile inside the canopy cover, but it by similarity theory (Monin and Obukhov 1954). The uses a displacement height to properly parameterize Ϫ1 Ϫ2 vertical sensible heat flux H (E T L ) is expressed in vegetation roughness. Bare soil evaporation EG is re- a form integrated between the surface and a reference lated to the water content of the first layer through the height as a function of the atmospheric turbulence soil resistance analogy (Bonan 1996) as JUNE 2006 R I G O N E T A L . 377

r tained starting with a saturated profile and running the ϭ ͑ Ϫ ͒ a ͑ ͒ EG 1 s␷ EP ϩ , 17 model several times on the meteorological forcings of ra rs the period analyzed until the spatial average surface where s␷ (dimensionless) is the fraction of soil covered Ϫ soil moisture reached the same value as the Electrically by the vegetation and r (L2 TM 1) is the aerodynamic a Steered Thinned Array Radiometer (ESTAR) average. resistance; r ϭ 1/(␳ C u ). The soil resistance r is a a E w s This set of simulations is further used for a simple pa- function of the water content of the first layer as in rameter sensitivity study. The third simulation (C), fi- Feddes et al. (2001). The evaporation from wet vegeta- nally, forecasts a yearlong record of measured dis- tion is calculated as charges without any further calibration, using the pa- ϭ ␦ ͑ ͒ EVC s␷ EP W, 18 rameters derived from simulations A and B. Two ␦ where W is the wet vegetation fraction, computed fol- versions of this simulation were performed. One was lowing Deardorff (1978). The transpiration is calcu- performed without any additional calibration, and in lated as the other, an adjustment of the vegetation cover frac-

n i tion was made. f rootra E ϭ s␷E ͑1 Ϫ ␦ ͚͒ . ͑19͒ TC P W ϩ i i ra r c a. The dataset i The root fraction f root of each soil layer is calculated SGP97 took place from 18 June to 17 July 1997 in decreasing linearly from the surface to a maximum root central Oklahoma and is discussed in detail by Jackson depth zroot, depending on the vegetation type. The et al. (1999), Mohanty et al. (2002), and Mohr et al. i canopy resistance r c in soil layer i depends on solar (2000). The basin primarily investigated was the Little radiation, vapor pressure deficit, temperature as in Best Washita watershed, which has been the focus of exten- (1998), and on water content in the root zone as in sive hydrologic research by the Agricultural Research Wigmosta et al. (1994). Service (ARS) (Allen and Naney 1991). The modeled portion of the watershed (i.e., upstream of U.S. Geo- d. Numerics logical Survey gauge 07327550, east of Ninne- GEOtop equations are discretized according to a fi- kah) covers an area of 603 km2. The topography of the nite-volume method, and time resolution is the smallest region is moderately rolling with a maximum relief over required for the numerical stability of all the processes the basin of less than 200 m (Fig. la). Land use is domi- described (or by the time step of the forcings), usually nated by rangeland and pasture (63%), with significant between 1 and 5 min. Grid cell horizontal dimensions areas of winter wheat and other crops concentrated in can range from 2 to 500 m, and the number of soil layers the and western portions of the watershed and the maximum soil thickness is arbitrary. All the area. As part of the ARS Micronet, there are a total of processes are solved using the same time step. GEOtop 42 recording rain gauges distributed at a 5-km spacing is coded in ANSI C and is compiled to run on Linux, over the watershed (Fig. 1b); these provided the pre- Mac OS X, and Windows. The first public version was cipitation data used in this analysis. For meteorological released in December 2005 under a General Public Li- data other than precipitation, the three Oklahoma Me- cense (GPL), and can be downloaded from http:// sonet stations, Acme (ACME), Apache (APAC), and bedu.ing.unitn.it/GEOtopWiki. The code will be thor- Ninnekah (NINN), located inside or very near the basin oughly documented with doxygen (http://www. were used. Moreover, at the National Oceanic and At- doxygen.org). Further information about the numerics mospheric Administration (NOAA) (LW02) flux site of the model can be found in Bertoldi et al. (2006b). (marked in Fig. 1b), measurements of soil properties, soil moisture and temperature, and surface energy 3. Tests of GEOtop in the Little Washita fluxes are available. watershed b. Simulations set A: Pixel-scale simulations of the An opportunity to validate and analyze the perfor- vertical profile dynamics at the NOAA (LW02) mance of GEOtop is offered by the SGP97 dataset. flux site Three different kinds of simulations were performed. The first set of simulations (A) uses GEOtop to repro- The purpose of these simulations is to test the pixel- duce the energy and water fluxes at the pixel scale to scale behavior of GEOtop. Because of this, the lateral assess the physical realism present in the model. The water fluxes have been inhibited (but infiltration is al- second set of simulations (B) reproduces a flood event lowed). The model was initialized with the measured and soil moisture evolution and calibrates some routing soil moisture and temperature profiles. Calibration was parameters. The initial water content profile was ob- performed only on the following parameters related to 378 JOURNAL OF HYDROMETEOROLOGY VOLUME 7

FIG. 1. Spatial properties of the Little Washita watershed. (upper left) Topography, (upper right) precipitation on 10 Jul 1997 with the location of the meteorological stations used in GEOtop simulations, (bottom right) soil texture (data from Mohanty et al. 2002), and (bottom left) land cover (data from Goddard Earth Sciences Data and Information Services Center).

the energy budget: the thermal roughness length zT eterization of the nocturnal stable boundary layer. (Garratt 1993), of which the turbulent transport coeffi- There is also a systematic overestimation of the ground

cients [CH and CE in Eq. (14)] are a function; the frac- heat flux during early morning, resulting from the mod- tion of the cell covered by canopy [s␷ in Eq. (15)], which el’s energy balance closure constraints, which is also controls the rate between bare soil evaporation and reflected by a slight overestimation of the soil tempera- ␭ transpiration; and the soil thermal conductivity s. Cali- ture as shown in Fig. 3. Moreover, negative values of ϭ ϭ brated values for this location are zT 8.6 mm, s␷ 0.9, sensible heat flux H in the dataset could be due to the ␭ ϭ Ϫ1 Ϫ1 and s 0.077 J kg K . Other soil properties have procedure chosen to process the measurements. A been kept equal to local field values as derived from model structural change could be then suggested that, Mohanty et al. (2002). The pixel-scale hourly evolution for instance, used a two-layer canopy model to provide of energy balance components are illustrated in Fig. 2, a more accurate estimation of the diurnal cycle of soil and rainfall, surface soil moisture, and temperature temperature. variations are illustrated in Fig. 3. The model is capable c. Simulation set B: Calibration and parameter of simulating infiltration related to small rainfall events sensitivity of discharge for the period from and daily soil moisture evaporation cycles, as shown in 26 June to 16 July 1997 Fig. 3. The model outputs show a good agreement with the local energy fluxes measured with eddy correlation The goal of this set of simulations is to determine the systems, except for a slight overestimation of nocturnal surface and subsurface flow parameters later used in a sensible heat fluxes (Fig. 2), which perhaps reveals longer simulation, and to do some sensitivity analysis. some deficiencies of the Kot and Song (1998) param- During the simulated period the weather was quite fair,

Fig 1 live 4/C JUNE 2006 R I G O N E T A L . 379

FIG. 2. Comparison between modeled and observed energy balance components at the NOAA flux site, 27 Jun to 17 Jul 1997. with mostly hot sunny days, during which the soil dried the meteorological forcing from 26 June to 16 July 1997 quickly as result of intense summer evaporation. A until the spatial-averaged surface soil moisture reached strong convective storm on 11 July (Fig. 1b) with more the same value as the ESTAR average. than 50 mm of rainfall in 7 h (averaged over the basin) Surface values of hydraulic conductivity and the van caused a flood with a peak discharge of 60 m3 sϪ1. Rain Genuchten parameters [see Eq. (8)] were obtained patterns for this event were reconstructed by means of from soil texture data from Mohanty et al. (2002) using kriging techniques. Simulations were performed with a the Vereecken et al. (1989) pedotransfer function ap- grid resolution of 200 m and five soil layers of increasing proach. To assign the 3D field structure of the saturated thickness (the first one of 5 cm). Soil depth was given by hydraulic conductivity, an exponential decay with Ϫ Ј ϭ fz z Ј field measurements by the Oklahoma State University for depth was assumed according to Ks e , where z Ϫ1 Application of Remote Sensing Laboratory and ranges is the cell depth below the surface; the factor fz (L ) from 0.5 to 1.5 m. As a lower boundary condition, an was determined by calibration. The canopy fraction S␷, impermeable surface was imposed. Heat fluxes at the the root depth zroot, the roughness length zT, and the bottom were regulated on the mean annual surface albedo a are assigned according to the land-cover map temperature and excursion, as explained in section 2b. (data available from Goddard Earth Sciences Data and Surface soil moisture maps with a resolution of 800 Information Services Center; Fig. 1c). Global param- m, derived from Jackson et al. (1999) from the flights of eters related to the water budget were calibrated the National Aeronautics and Space Administration against the measured discharges: the channel celerity

(NASA) P-3B aircraft fitted with the ESTAR, an L- uc, the hydraulic diffusivity D, the surface runoff resis- band (1.413 GHz) passive microwave sensor, were used tance coefficient Cm [all in Eq. (13)], and the anisotropy ␣ for model initialization and verification. The initial wa- ratio k [in Eq. (6)]. Values of the spatial average of the ter content profile was obtained starting with a satu- parameters are given in Table 1. rated profile and running the model several times using Comparison of the measured and calibrated dis- 380 JOURNAL OF HYDROMETEOROLOGY VOLUME 7

FIG. 3. (top) Observed rainfall and comparison between modeled and observed (middle) surface soil moisture and (bottom) temperature at the NOAA flux site, 27 Jun to 17 Jul 1997.

charge hydrograph is shown in Fig. 4a, and the ESTAR The sensitivity of the discharge during the major ␪ measured and simulated basin-average soil moisture is storm event on 11 July of the parameters Ksh, Ks ␷, r, ␪ ␣ shown in Fig. 4b. It can be seen that it was possible to s, , m, n, and S␷ is shown in Fig. 6. Among the cali- obtain a good calibration to the main flood hydrograph. brated parameters summarized in Table 1, the vertical Also fairly good is the uncalibrated forecasting of the hydraulic conductivity (Fig. 6a) determines the maxi- average soil moisture, which implies that, on average, mum infiltration capacity and greatly influences the evapotranspiration (ET) was properly simulated. Cu- surface runoff formation, because it controls the mulative water balance simulation results (Fig. 5) show amount of Hortonian-type runoff, and therefore the

that total evaporation ET flux dominates the water magnitude of the peak discharge. The horizontal hy- losses during this period compared to discharge Qc;in draulic conductivity, Ksh, on the contrary, primarily in- particular, only a small fraction of the 11 July storm fluences the flood tail because it determines the sub-

precipitation became runoff. surface runoff quantity (Fig. 6b). A large value of Ksh,

TABLE 1. Basin-averaged values of the parameters in the application of GEOtop to the Little Washita basin.

Parameter symbol Description Units Basin-averaged value Source u Channel celerity m sϪ1 2.0 Calibration D Channel diffusivity m2 sϪ1 1000 Calibration

Ksh/Ks ␷ Hydraulic conductivity anisotropy ratio 50 Calibration Ϫ1 fz Hydraulic conductivity decay factor m 0.5 Calibration 1/3 Ϫ1 Cm Hydraulic surface resistance m s 0.1 Calibration ␪ r Residual water content 0.06 Literature ␪ s Saturated water content 0.41 Literature ␣ van Genuchten parameter cmϪ1 0.035 Literature m van Genuchten parameter 1.0 Literature n van Genuchten parameter 0.98 Literature ␭ Ϫ1 Ϫ1 s Thermal soil conductivity J kg K 0.077 Calibration S␷ Canopy fraction 0.78 Literature

zroot Root depth m 0.82 Literature zT Roughness length m 0.021 Literature a Albedo 0.2 Literature JUNE 2006 R I G O N E T A L . 381

FIG. 5. Cumulative water balance of the Little Washita water- shed, 27 Jun to 17 Jul 1997, as determined by GEOtop model simulations with parameters indicated in Table 1.

the model do not show the influence of land use; how- ever, on the contrary, the soil texture (and by inference hydraulic conductivity) patterns become evident during the dry periods (3 and 16 July), as can be seen from the comparison of Fig. 7 with Fig. 1. The spatial distribution FIG. 4. Comparison between GEOtop simulations and measure- of precipitation, as pointed out by the comparison of ments in the Little Washita watershed from discharge 27 Jun to 17 Jul 1997. The parameters used in the GEOtop simulations are the precipitation field of 10 July in Fig. 1 to the soil given in Table 1. (a) Discharge at the outlet; (b) basin-averaged moisture map of 11 July reported in Fig. 7, strongly surface soil moisture, simulated in surface soil layer (top 5 cm) determines the spatial distribution of the soil surface compared to ESTAR estimated value. water content, mostly in the first hour immediately fol- lowing the rainfall. According to the simulations, as however, causes soil drainage that is too rapid, leading qualitatively shown in the 11 July map of Fig. 7, topog- to water content values that are too low compared to raphy starts exerting its influence only some hours ␪ the measured values. Residual water content r, which later, by concentrating moisture in the topographic con- controls the total basin storage capacity, has a greater vergence zones. influence on discharge than the water content value at The simulated averaged surface soil moisture values ␪ saturation s (Figs. 6c and 6d). The van Genuchten pa- are very similar to those estimated by ESTAR, as was rameters ␣, n, and m [Eq. (8)] have also a significant shown in Fig. 4b. However, the frequency distribution influence on peak discharge (Figs. 6e–g). In particular, of global measured and simulated water content are very low values of ␣ (which means increased suction somewhat different (Fig. 8). In particular, GEOtop pre- potential for the same saturation) lead to a bimodal dicted a larger soil moisture variance than ESTAR behavior of the hydrograph. These simulations of this measured (especially in the case of rain events: see 11 event are not significantly affected by the vegetation- and 16 July in Fig. 8). To understand the reason for this cover fraction S␷ (Fig. 6h), which, however, plays a ma- discrepancy, we also ran some simulations on the same jor role in the energy budget calibration. Other sensi- dataset (using a coarser 1000-m grid) with the Variable tivity analyses on soil thickness and river network ex- Infiltration Capacity (VIC) model (Liang et al. 1994), tension are the subject of Bertoldi et al. (2006). obtaining distributions, which at least show that the difference is not simply an effect of grid resolution (re- d. Surface soil moisture evolution in the basin call that ESTAR has a resolution of 800 m). In fact, The soil moisture distribution derived from the these differences among model simulation results and ESTAR data by Jackson et al. (1999), available for the ESTAR products may be caused not only by errors in same period in which we performed the calibration, was the model but also in the data assimilation used to ob- compared to that produced by the top 5-cm layer of tain the ESTAR product. In fact, in the computation of the model. As shown in Fig. 7, GEOtop predicted sur- the ESTAR soil moisture product soil dielectric prop- face moisture patterns that appear visually similar to erties, which themselves depend on moisture content, ESTAR estimates. The soil moisture maps produced by must be assumed. 382 JOURNAL OF HYDROMETEOROLOGY VOLUME 7

FIG. 6. Sensitivity of the flood hydrograph of 11 Jul 1997 in the Little Washita watershed, simulated with ␪ ␪ ␣ GEOtop, to different parameters: (a) Ks ␷ , (b) Ksh, (c) r, (d) s, (e) , (f) n, (g) m, and (h) S␷. Here Ks ␷ and ␪ ␪ Kshare vertical and lateral saturated hydraulic conductivity at the surface, respectively; r and s are residual and saturated water content; ␣, n, and m are parameters of the van Genuchten (1980) curve; and S␷ is the averaged fractional canopy cover. The measured value of the peak discharge was 60 m3 sϪ1.

e. Simulation set C: The forecasting of the 1997 been kept constant. Only the three Oklahoma Mesonet streamflow stations (Fig. 1) had precipitation data available for the whole year; therefore the model was forced only with In this simulation for the whole year of 1997, the these three stations. The model was initialized by forc- calibrated parameters of the previous simulations have ing it repeatedly with the meteorological conditions of

Fig 6 live 4/C JUNE 2006 R I G O N E T A L . 383

flow also appeared in summer, which could be ex- plained with a lower actual ET than was simulated. This missing evaporation in the simulation was small in terms of total volumes but presented a definite trend in summer that eventually could be strongly decreased by changing the average fractional vegetation cover from s␷ ϭ 0.78 to s␷ ϭ 0.89, in accord with Mohanty et al. (2000), who showed that bare soil evaporates more than vegetation cover in a mixed vegetation pixel. The upper limit of the gray band of Fig. 9 shows the evolu- tion of the discharge once s␷ has been raised since the beginning of the year. It emphasizes that an incorrect evapotranspiration estimation results in an incorrect average soil moisture content with possible increasing errors as time elapses (Fig. 10). Eventually the pattern of soil moisture would also depart from actual, since ET is heterogeneous in the presence of heterogeneous to- pography, and hydraulic conductivity presents a strong nonlinear dependence on soil moisture volumetric con- tent.

4. Conclusions In this paper, a new distributed hydrological model, GEOtop, is presented. This model is an attempt to cre- ate a catchment simulator that not only accounts for water redistribution in a very detailed fashion (solving the 3D Richards’ equation), but also includes a coupled

FIG. 7. Volumetric surface soil water content of the Little energy and radiation budget. The model accommodates Washita watershed. (left) Estimated using the ESTAR remote very complex topography and its effects on the incident sensor. (right) Simulated using the GEOtop model. For (top) 3, radiation, both shortwave (with shadowing) and long- (middle) 11, and (bottom) 16 July 1997. wave (with accounting for the sky view factor). The application of the model to the Little Washita the year (periodic forcing) until a dynamical equilib- basin leads to the following conclusions. The set of rium was achieved after various periodic cycles had simulations A shows that the model is capable of accu- passed. rately reproducing the local energy budget and the local The comparison between the daily measured and the infiltration once initialized with measured parameters GEOtop-simulated streamflow with no additional cali- and calibrated for the roughness length, the fraction of bration (the gray band bottom) is shown in Fig. 9 for cell covered by canopies, and the heat capacity of the the whole year of 1997. The model preserves fairly well soil. The set of simulations B shows that GEOtop, with the total streamflow volume, but tends to overestimate calibration and accurate initialization, gives a precise peak discharges, except for the event of late May when reproduction of a peak flow, with no more calibration there is a considerable underestimation of the mea- than a typical rainfall-runoff model would require (i.e., sured flood. The underestimation for this event, how- adjusting the river network celerity, the surface and ever, could be caused by inadequate rainfall inputs, subsurface celerity on the hillsides). This result con- since the runoff ratio of that event is considerably firms the common belief that it is not necessary to have larger that that of the others. Unfortunately, more de- a detailed evapotranspiration estimation for flood fore- tailed rainfall data was not available to assess this issue. casting. However, since the initial soil moisture condi- The July event used for calibration is simulated slightly tions were obtained with a dynamical procedure, and differently in this simulation compared with the calibra- the set of simulations C show that flood peaks can be tion simulation because here different initial conditions sensitive to such conditions, more investigation is and rainfall are used. needed to assess the interplay between initialization As Fig. 9b underlines, an increased difference in base procedures and parameter identification.

Fig 7 live 4/C 384 JOURNAL OF HYDROMETEOROLOGY VOLUME 7

FIG. 8. Volumetric surface (top 5 cm) soil water content frequency distributions, comparison between ESTAR data, GEOtop model, and VIC model. (upper left) 29 Jun, (upper right) 3 Jul, (bottom right) 11 Jul, and (bottom left) 16 Jul 1997.

At the basin scale, the model is capable of capturing Washita basin the main controlling factors on the soil the spatial distribution of the surface soil moisture, with moisture spatial distribution are soil properties during no additional calibration, and it can be used as a tool to dry periods and precipitation during wet periods, con- understand what the major controls on soil moisture firming the finding by Mohr et al. (2000). A few hours patterns are. Simulated data show that in the Little after precipitation, the topographic redistribution of

FIG. 9. Comparison between measured discharge and the GEOtop simulated discharge in the Little Washita watershed for the whole 1997 year: (a) linear scale; (b) logarithmic scale. The black line is the measured discharge; the upper limit of the gray band is the simulated discharge with s␷ ϭ 0.89 (with less bare soil evaporation and more transpiration); the lower limit of the gray band is the simulated discharge with s␷ ϭ 0.78. JUNE 2006 R I G O N E T A L . 385

FIG. 10. Comparison between simulations in the Little Washita watershed for the whole 1997 year with different averaged canopy fraction S␷ : (a) evapotranspiration, (b) total soil column saturation. The black lines refer to the simulation with s␷ ϭ 0.89, the gray one with s␷ ϭ 0.78. soil moisture also exerts a slight influence. A compari- Satellite Land Surface Climatology Project (ISLSCP) son of soil moisture obtained from simulations with Field Experiment (FIFE; Sellers et al. 1992), the Pro- ESTAR data brings some confirmation of the model gram for Intercomparison of Land Surface Parameter- behavior and calls for further investigations in which ization Schemes (PILPS; Henderson-Sellers et al. remotely sensed data will be assimilated concurrently 1993; Wood et al. 1999), the Hydrological Atmospheric (i.e., in parallel) with the model simulations. Pilot Experiment-Modelisation du Bilan Hydrique The set of simulations C, a yearlong simulation of (HAPEX-MOBILHY; Andre et al. 1988), SGP97 (Jack- streamflow with no additional calibration, shows an son et al. 1999), Tarrawarra (Western et al. 1998), overestimation of some flow peak discharges, giving Mahurangi River Variability Experiment (MARVEX; however the proper total flow volumes. This simulation Woods et al. 2001), and other experiments, however, have also shows that the vegetation dynamics can have, dur- already provided integrated data based on combined sat- ing the simulated period, a small but systematic effect ellite, remote sensing, ground-based soil moisture and on the water budget partition and that a correct esti- vegetation mapping, eddy correlation measurements of mation of evapotranspiration is essential to have a cor- turbulent fluxes, and boundary layer profiling at a hierar- rect total discharge volume, the most important param- chy of scales. As digital terrain and remotely sensed sur- eter being the transpiration rate. An adjustment of a face radiation data of higher resolution and better quality controlling parameter was adequate to correct the bud- become increasingly available and computer perfor- get partition. However, using the same parameter for mances continue to increase, physically based, distributed the entire year (either the first or the second) resulted models such as GEOtop will become increasingly useful in increasingly incorrect average soil moisture contents and more easily connected to climate and limited-area with possible increasing departures from actual and meteorological models, and they may become accepted as causing increasing errors in base flow estimations. Re- the standard tool for river basin hydrology. sults underline the importance of incorporating an ad- equate description of evapotranspiration processes for Acknowledgments. This research has been partially an accurate prediction of long-term discharge and soil supported by the Italian Ministry of University and Re- moisture patterns and suggest the value of implement- search (MIUR Prin 2003) and by the TIDE fifth frame- ing a dynamic vegetation model. work and AQUATERRA sixth framework European A fully distributed model predicts throughout the Projects. We thank the Civil and Environmental Engi- catchment (and not only at the outlet of the basin) a neering Department of the University of Illinois at Ur- larger number of observable processes than traditional bana–Champaign and the Illinois Water Sciences Cen- lumped models. However, it also requires a corre- ter of the U.S. Geological Survey for their hospitality sponding increase in input data and parameters. Field during the visit of the second author during the course measurement campaigns like the First International of this research. Davide Tamanini designed and wrote 386 JOURNAL OF HYDROMETEOROLOGY VOLUME 7 the code for the integration of the Richards’ equations. and soil moisture dynamics for hillslopes and microcatch- The Agricultural Research Service, Grazinglands Re- ments. J. Hydrol., 198, 177–195. search Laboratory (ARS-GRL), El Reno, Oklahoma, Brutsaert, W., 1975: On a derivable formula for long-wave radia- tion from clear skies. Water Resour. Res., 11, 742–744. provided the Little Washita precipitation data, and the Chen, F., and Coauthors, 1996: Modeling of land surface evapo- ARS-GRL, in cooperation with the U.S. Geological ration by four schemes and comparison with FIFE observa- Survey and the Oklahoma Water Resources Board, tions. J. Geophys. Res., 101 (D3), 7251–7268. provided the Little Washita discharge data. Ciarapica, L., and E. Todini, 2002: TOPKAPI: A model for the representation of the rainfall-runoff process at different scales. Hydrol. Processes, 16, 207–229. 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