Multidecadal High-Resolution Hydrologic Modeling of the Arkansas–Red River Basin

Multidecadal High-Resolution Hydrologic Modeling of the Arkansas–Red River Basin

HATIM O. SHARIF

University of Texas at San Antonio, San Antonio, Texas

W. CROW

ARS–USDA Hydrology and Remote Sensing Laboratory, Beltsville, Maryland

N. L. MILLER

Lawrence Berkeley National Laboratory, Berkeley, California

E. F. WOOD

Princeton University, Princeton, New Jersey

(Manuscript received 4 October 2005, in final form 1 February 2007)

ABSTRACT

Land surface heterogeneity and its effects on surface processes have been a concern to hydrologists andclimate scientists for the past several decades. The contrast between the fine spatial scales at which het-erogeneity is significant (1 km and finer) and the coarser scales at which most climate simulations with landsurface models are generated (hundreds of kilometers) remains a challenge, especially when incorporatingland surface and subsurface lateral fluxes of mass. In this study, long-term observational land surfaceforcings and derived solar radiation were used to force high-resolution land surface model simulations overthe Arkansas–Red River basin in the Southern Great Plains region of the United States. The most uniqueaspect of these simulations is the fine space (1 km2) and time (hourly) resolutions within the model relativeto the total simulation period (51 yr) and domain size (575 000 km2). Runoff simulations were validated atthe subbasin scale (600–10 000 km2) and were found to be in good agreement with observed discharge fromseveral unregulated subbasins within the system. A hydroclimatological approach was used to assess simu-lated annual evapotranspiration for all subbasins. Simulated evapotranspiration values at the subbasin scaleagree well with predictions from a simple one-parameter empirical model developed in this study accordingto Budyko’s concept of “geographical zonality.” The empirical model was further extended to predict runoffand evapotranspiration sensitivity to precipitation variability, and good agreement with computed statisticswas also found. Both the empirical model and simulation results demonstrate that precipitation variabilitywas amplified in the simulated runoff. The finescale at which the study is performed allows analysis ofvarious aspects of the hydrologic cycle in the system including general trends in precipitation, runoff, andevapotranspiration, their spatial distribution, and the relationship between precipitation anomalies andrunoff and soil water storage anomalies at the subbasin scale.

1. Introduction

The use of long-term records of observational data todetermine the variability of land surface moisturefluxes and storages is essential for answering key sci-ence questions concerning the degree to which the glo-

bal hydrologic cycle is intensifying in response to po-tential anthropogenic climate forcings (Hornberger etal. 2001) and to assess the potential for improving pre-dictability of floods and droughts. In addition to climateanomalies, accurate characterization of land surfacestates enhances runoff predictability (Maurer et al.2004). Land surface conditions affect the global envi-ronment through various processes such as vertical andhorizontal water fluxes, land surface roughness, reflec-tivity, and emissivity, greenhouse gas emissions, andformation of aerosols.

Land surface models play an essential role in our

Corresponding author address: Hatim Sharif, Department ofCivil and Environmental Engineering, 6900 N. Loop 1604 W., SanAntonio, TX 78249-0668.E-mail: [email protected]

OCTOBER 2007 S H A R I F E T A L . 1111

DOI: 10.1175/JHM622.1

© 2007 American Meteorological Society

JHM622

understanding of the exchanges of water, carbon, andenergy between the terrestrial biosphere and atmo-sphere. Moreover, by incorporating the land surface asa lower boundary condition in atmospheric models,land surface models improve numerical weather andclimate prediction. The land surface is an importantpart of the coupled system, and inaccurate land surfaceconditions and uncertainties in land surface model pre-dictions significantly contribute to the overall uncer-tainty in climate predictions (Henderson-Sellers et al.1995). The land surface modeling community has beenpresenting new schemes or adapting existing schemesfor better conceptualization of the complex physicalprocesses that take place at the land surface–atmo-sphere interface for the past few decades. New tools forparameterizing surface energy and mass fluxes are be-ing developed and more processes are being simulated.Application of increasingly sophisticated land surfacemodels has shown that water–carbon–energy exchangesare tightly coupled and that large-scale interannualvariations in climate produce substantial variations inatmosphere–biosphere carbon exchanges.

One area of considerable modeling progress has beenin the representation of temporal and spatial heteroge-neity. Land surface heterogeneity and its effects on sur-face processes and the numerical representations havebeen a concern to hydrologists and climate scientists forthe past few decades. The contrast between the finespatial scales at which this heterogeneity is manifestand the coarser scales at which most land surface mod-els are implemented remains a challenge, especially foradequately computing lateral fluxes of mass. Spatialheterogeneities in soil moisture, which can be a mani-festation of heterogeneity in precipitation, topography,soils, and vegetation, have been shown to exert impor-tant controls on aggregated fluxes and boundary layerdevelopment (e.g., Weaver et al. 2002). As our under-standing of the atmosphere–biosphere interactions andcontrol mechanisms advance, there is a need for in-creased details in representing the transfer of mass, en-ergy, and momentum. This need becomes more impor-tant as rapid advances in computational resources re-duce computational constraints.

High-resolution land hydrology is needed to addressquestions such as identifying physiographic and climaticcontrols on the spatial variability of soil moisture andthe scales at which they are most dominant (e.g.,D’Odorico et al. 2000); developing subgrid parameter-ization approaches for soil moisture during wet and dryconditions; examining the spatial scaling properties ofsoil moisture (Crow and Wood 1999; Rodriguez-Iturbeet al. 1995); performing statistical analysis of the tele-connection between climatic variables and land surface

states and processes, such as soil moisture and evapo-transpiration (ET); and development of Observing Sys-tem Simulation Experiments (OSSE) for remote sens-ing of soil moisture (Crow et al. 2001). The recentlydeveloped Land Information System infrastructure(LIS; http://lis.gsfc.nasa.gov; Peters-Lidard et al. 2004;Kumar et al. 2006) is designed to be capable of en-semble land surface modeling on points, regions, or theglobe at spatial resolutions from 2 degrees � 2.5 de-grees down to 1 km. The 1-km capability of LIS allowsit to take advantage of the latest satellite observationsat their full resolution.

Only physically based distributed models take advan-tage of high-resolution forcings. However, at regionalscales, much simpler models are, up to now, the mostfrequently used tools for understanding how the energyand water cycles are coupled. For example, empiricalformulas are used to describe how the amount of avail-able energy and precipitation for a given basin or re-gion control the annual mean evapotranspiration andrunoff rates (e.g., Budyko 1950). A very common analy-sis technique in the geophysical sciences is to use acomplex model, such as the one used in this study, togain insight into the accuracy of a much less complexmodel (e.g., a linear model or an empirical relation-ship). Thus, one of the main benefits of complex physi-cally based simulations is that they can be used toevaluate and validate much simpler modeling ap-proaches.

In this study, long-term observational land surfaceforcings and derived solar radiation were used to forcehigh-resolution land surface model simulations over theArkansas–Red River (AR) basin in the Southern GreatPlains (SGP) region of the United States. The mostunique aspect of these simulations is the fine space andtime resolutions (1 km2 and hourly) within the modelrelative to the total simulation period and domain size(51 yr and 575 000 km2, respectively). A description ofthe study area, the land surface model used, the simu-lation setup, forcing data and outputs, validation of wa-ter and energy flux simulation, and an assessment of thesimulation results are presented. A diagnostic hydrocli-matological analysis of the annual water budget at thesubbasin scale is performed, including development ofnew empirical models to predict annual runoff andevapotranspiration and their sensitivity to precipitationvariations. Variations at the monthly time scale werealso examined.

2. The study area

The model domain in this study is the 576 000-km2

area of the U.S. SGP defined by the confluence of the

1112 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 8

Arkansas and Red Rivers. The two rivers are treated asone system because of similar climatologies. The head-waters of the basins come from the continental divideof the Rocky Mountains. Both rivers, with almost par-allel courses, flow eastward to the Mississippi River.The Arkansas River joins the Mississippi near LittleRock, Arkansas, and the Red River joins near Shreve-port, Louisiana.

Figure 1 shows the location of the AR system and itssubbasins in the SGP region. Rainfall climatologies ofthis basin display a strong east–west gradient with drierconditions prevailing in the western part of the basin.The region generally receives its maximum precipita-tion in the spring and fall and has a relatively dry latesummer. Significant orographic summer precipitationat the highest elevations in the west near the continen-tal divide is an exception. Winter snow accumulationhas a significant contribution to the headwaters butcovers a relatively limited area in the west and does nothave a significant overall influence on the climatologyand hydrology of the basin. Climatological runoff ratios(the ratio between runoff and precipitation) in the ba-sin are generally on the order of 10% to 20%, implying

that evaporation and infiltration dominate runoff. Typi-cal seasonal cycles of soil moisture exhibit maximumsduring the late spring and minimums during the latesummer and early fall as a result of the seasonality inprecipitation and temperature. Late growing seasonminimums can be pronounced, and the soil moisturecontrol on evapotranspiration is common during thesummer months.

Following the precipitation gradient, vegetation gen-erally ranges from grassland in the drier western partsof the basin to deciduous forests in the east, although alarge portion of the eastern region is cultivated. Theforested eastern portion has small areas of remainingnative tall grass prairie. Moving west, forest cover be-comes gradually lighter and agricultural areas moreprevalent—most notably the band of winter wheat bi-secting central Oklahoma from north to south. WesternOklahoma and the panhandle region of Texas are gen-erally covered with short grass and sparse shrublandwith some patches of irrigated agriculture in easternColorado. Forest cover briefly reemerges in the farwestern portion of the basin along the foothills of theRocky Mountains.

The AR basin has extensive meteorological and hy-drological data collection networks. For this reason,these basins were the first large-scale areas studiedunder the Global Energy and Water Experiments(GEWEX; http://www.gewex.org) Continental-ScaleInternational Project (GCIP; http://www.ogp.noaa.gov/mpe/gapp/gcip/). The AR basin contains a number ofU.S. Department of Agriculture–Agricultural ResearchService (USDA–ARS) experimental catchments; theU.S. Department of Energy Atmospheric RadiationCloud and Radiation Test bed (ARM-CART) site; andthe Cooperative Atmosphere–Surface Exchange Study(CASES) boundary layer facility. Portions of the basinwere the site of the 2002 International H2O Project(IHOP; Weckwerth et al. 2004), and the Department ofEnergy Intensive Observing Period 2002 (Miller et al.2005) experiments. In addition, the National WeatherService’s Arkansas–Red River Forecast Center was thefirst prototype site for modernized River Forecast Cen-ter’s technologies and operations. The River ForecastCenter provides hydrologic forecasting, hydrometeoro-logical analysis and support functions, and quality con-trol of associated data.

3. The model

The TOPMODEL-based Land Surface AtmosphereTransfer Scheme (TOPLATS; Famiglietti 1992;Famiglietti and Wood 1994; Peters-Lidard et al. 1997)incorporates a TOPMODEL (Beven and Kirkby 1979)

FIG. 1. Location of the Arkansas–Red River basin in the South-ern Great Plains region of the United States. The basin was di-vided into 314 subbasins shown on the inset.


framework to account for lateral redistribution of sub-surface water based on the local topography and soiltransmissivity. Famiglietti and Wood (1994) describedetails of a water balance system for two soil layers anda full surface energy balance system incorporated in themodel. The water and energy balance is solved for eachcombination of topographic index class and land coverclass. The model can be run in a distributed or a statis-tical mode. In the distributed mode the water and en-ergy balances are directly solved for each pixel, while inthe statistical mode a distribution of the topographicindex is used to describe the spatial variability of to-pography, and fractional representation of land covertypes within a lumped domain. Peters-Lidard et al.(1997) made additional modifications and addressedearlier deficiencies in the model representation ofground heat flux, soil column geometry, soil evapora-tion, transpiration, and the effect of atmospheric stabil-ity on surface energy fluxes. The addition of snow, un-derstory, lakes, moss, and frozen soil modules (Pauwelsand Wood 1999) makes it possible to apply the model inboreal environments. The version of TOPLATS used inthis study contains several additional model enhance-ments, including the use of four soil layers and a morerobust numerical scheme for soil water balance and im-proved numerical stability. Lateral subsurface flow iscontrolled mainly by topography and soil propertiesand defines the spatial pattern of water table depths.The local water table, in turn, affects local soil moisturestorage and thus the root zone moisture content andeventually surface fluxes. Initial water table depths areinput to TOPLATS at the start of simulation, and varia-tions at each time step are recorded. Local variations inwater table depths due to pumping are not simulated.TOPLATS computations at locations that are affectedby significant groundwater pumping, or where initialwater depths are not reasonably accurate, may be un-reliable.

Lohmann et al. (1998) evaluated the performance of16 Soil–Vegetation–Atmosphere Transfer (SVAT)schemes over the AR system for the 1980–86 period atvery coarse model grid resolution (1 degree) and foundsignificant differences among streamflow and evapo-transpiration values predicted by different models.TOPLATS is particularly well suited for the analysispresented in this paper, since it combines a detailedrepresentation of surface water and energy balanceprocesses while capturing the topographically inducedhorizontal redistribution of subsurface water. Point-scale TOPLATS predictions of surface energy flux, sur-face soil moisture, and surface temperature have beenextensively validated within the SGP region (Famigli-etti and Wood 1994; Peters-Lidard et al. 1997, 2001).

Crow (2001) and Crow and Wood (2002) performedhigh-resolution TOPLATS simulations over the entireAR domain for the period from 1 April to 31 July 1994,with energy and water balance modeling on a 1-kmgrid.

4. The datasets

Soil and topographic information were based on1-km data of depth-to-bedrock estimations, 1-km StateSoil Geographic database (USDA Natural ResourcesConservation Service; http://www.ncgc.nrcs.usda.gov/products/datasets/statsgo/) soil texture data (STATSGO),and 1-km USDA digital elevation maps (DEMs) of thebasin. STATSGO data includes soil texture, residualmoisture, and total soil depth, from which other prop-erties were derived. The main source for the valuesused for the soil hydraulic conductivity parameter isRawls et al. (1982), while other soil parameters weretaken from Cosby et al. (1984). Land cover was takenfrom a 1-km classification map derived from observa-tions by the Advanced Very High Resolution Radiom-eter (AVHRR) sensor. Land cover and vegetation pa-rameters were obtained from several sources: leaf areaindex (Pielke 1984); surface albedo (Pielke 1984; Stull1995; Dingman 1994); stomatal conductance (Peters-Lidard et al. 1997; Jacquemin and Noilhan 1990); sur-face emissivity and momentum roughness (Brutsaert1982; Pielke 1984); internal plant resistance (Federer1979; Choudhury and Federer 1984; Choudhury andIdso 1985); and seasonal variation of vegetation param-eters (Tian et al. 2004). It has to be noted that landuse/cover changes within the simulation period werenot included because of lack of data. Changes due toprecipitations trends are modeled only within the verylimited vegetation dynamics included in the model. Ex-amples of high-resolution TOPLATS inputs are sownin Fig. 2.

The dataset used to force the land surface modelconsists of precipitation, wind speed, near-surface airtemperature, dewpoint temperature, shortwave radia-tion, longwave radiation, and surface pressure, all athourly time steps and a spatial resolution of 1 km. Themain source of this forcing data is a 51-yr (January1949–July 2000) daily 1/8° gridded meteorological (pre-cipitation, maximum and minimum temperature, andwind speed) input forcing data compiled by the SurfaceWater Modeling Group at the University of Washing-ton (Maurer et al. 2002; http://www.hydro.washington.edu/SurfaceWaterGroup/DataInfo.html). To interpo-late hourly precipitation from the daily data, we applieda disaggregation procedure (Maurer et al. 2002) thatuses observed hourly precipitation data from the near-


est precipitation station to the grid center for determin-ing the cumulative distribution function (CDF) ofhourly precipitation occurrence and the CDF of hoursof duration for events in different rainfall categories.The Mountain Climate Simulator Model (MT-CLIM;Thornton and Running 1999; Thornton et al. 2000) wasused to compute the diurnal temperature range, dew-point temperature, and incoming radiation. MT-CLIMis a computer program that uses observations of dailymaximum temperature, minimum temperature, andprecipitation from one location to estimate the tem-perature, precipitation, radiation, and humidity at an-other location. Humidity estimates are based on theobservation that daily minimum temperature is usuallyvery close to dewpoint temperature. Radiation esti-mates are based on the observation that the diurnaltemperature range (from minimum temperature tomaximum temperature) is closely related to the dailyaverage atmospheric transmittance.

Using information about the latitude, elevation,slope, and aspect of the site, this relationship can beused to estimate radiation. Air pressure data weretaken from the spatial interpolation of measurementsmade at 72 National Climate Data Center (NCDC) sta-tions within the south-central United States. Other thanadjustment performed within MT-CLIM, dynamic forc-ings were downscaled to 1 km assuming uniform distri-bution.

5. Long-term simulations

Using the 1-km DEM data, ARCInfo GeographicInformation System (GIS) software (www.esri.com/software/arcgis/arcinfo/) was used to compute flow di-rections, flow accumulations, and terrain slopes. Thederived drainage network was used to delineate 314(see the inset in Fig. 1) subcatchments that range in sizebetween 10 and 7000 km2. The outlets of many of thesubcatchments coincide with stations managed by theU.S. Geological Survey (USGS). Flow accumulationsand slopes were used to build a topographic index(Beven and Kirkby 1979) map at 1-km resolution. Crow(2001) and Crow and Wood (2002) performed exten-sive calibration and validation of TOPLATS over theAR basin. The water balance component of the modelwas calibrated over several subcatchments in themiddle and eastern portion of the basin, because theparameters affected by calibration (baseflow and satu-rated runoff parameters) are more important in thesubregions where most of the runoff from the system isgenerated. The forcing data used for calibration, at1-km resolution, were obtained from datasets con-structed during phase 2c of the Project for the Inter-comparison of Land Surface Parameterization Schemes(PILPS-2c) study of the AR basin (Wood et al. 1998).The main differences between this study and the onedescribed by Wood et al. (1998) and subsequent papersis that for this study the temporal domain is about oneorder of magnitude larger and the model grid area isfour orders of magnitude smaller. Thus, the parameter-ization in this study is much more physically based, andthe water and energy budgets are more tied together,and without that most of the analysis presented in thispaper would not have been possible.

TOPLATS long-term simulations began 1 January1949 at 00:00 UTZ and ended on 31 July 2000 at 24:00UTZ. One of the main challenges in this study is thehandling of the massive (100s GB) input and outputdata, and the computing power needed to performthese model runs. Several utility programs and scriptswere developed to compress, decompress, and reformatthe input data. The model was run in a semiparallelizedmode making use of the domain decomposition into314 subbasins. All water and energy fluxes were com-puted for all subcatchments, as well as a lumped calcu-lation representing the entire basin at hourly time steps.These fluxes include infiltration excess and saturationexcess runoff, baseflow, depth to groundwater table,vertical water fluxes, canopy water balance, evapo-transpiration, sensible, latent, and ground heat fluxes,and surface and soil temperature. In addition, hourlysoil moisture states for the four soil layers were pro-

FIG. 2. High-resolution vegetation and soil inputs.


duced at the 1-km resolution for the entire temporaland spatial domain.

6. Streamflow validation and evaluation

The physical mechanisms controlling runoff genera-tion and evapotranspiration are connected together viathe available soil moisture. Therefore, accurate compu-tations of surface runoff simulations are important be-cause they directly affect simulations of the water andenergy balance relationships. Long-term stream dis-charge is recorded by the USGS at hundreds of stationswithin the AR system, but water management and di-versions affect the vast majority of records. As part ofthe international Model Parameter Estimation Experi-ment (MOPEX), sponsored by the National Oceanicand Atmospheric Administration (NOAA) and otherorganizations (http://www.nws.noaa.gov/oh/mopex),precipitation, streamflow, and physiographic data were

compiled for 23 unregulated watersheds within the ARsystem. These watersheds were used in this study tovalidate runoff simulations.

TOPLATS runoff simulations (no stream routingwas applied) compare very well with observed streamdischarge for these watersheds. In Fig. 3 observed andsimulated monthly stream discharge accumulations areplotted for Caney River near Elgin, Kansas; Bird Creeknear Sperry, Oklahoma; Spring River near Waco, Mis-souri; and Illinois River near Tahlequah, Oklahoma.For all these four watersheds observed discharge isavailable for the entire simulation period, 1949–2000.Comparisons of observed and simulated monthly dis-charge for these four watersheds over different 10-yrperiods are shown in Fig. 4. In addition, two statistics,the relative discharge bias (Brel) and the Nash and Sut-cliffe (1970) coefficient (NS), were computed to quan-tify the comparison between observed and simulatedstream discharge for these unregulated subbasins:

FIG. 3. Observed (solid lines) and simulated (dotted lines) monthly stream discharge accumulation for fourunregulated MOPEX watersheds: (a) Caney River near Elgin, KS (USGS station 07172000; average monthlydischarge of 20.42 mm), (b) Bird Creek near Sperry, OK (USGS station 07177500; 18.69 mm), (c) Illinois Rivernear Tahlequah, OK (USGS station 07196500; 29.03 mm), and (d) Spring River near Waco, MO (USGS station07186000; 23.87 mm).


Brel ��Qs � Qo�

Qo

100% �1�

NS � 1 �

�i�1

n

�Qs,i � Qo.i�2

�i�1

n

�Qo,i � Qo�2

, �2�

where Qs,i and Qo,i are simulated and observed monthlydischarge for month i, n is the number of months simu-lated, and Q is the mean discharge. It has to be notedthat the NS coefficient is a measure of how the simu-lations compare to long-term means. A discussion onthe limitations of NS coefficient as a measure is pro-vided by Legates and McCabe (1999).

These statistics were computed for all watersheds.For the Caney River near Elgin, at USGS station07172000 (1153 km2), the relative discharge bias is 11%while the Nash–Sutcliff coefficient is 0.88. For BirdCreek near Sperry, at USGS station 07177500 (2344km2), the Spring River near Waco, at USGS station

07186000 (3015 km2), and the Illinois River near Tah-lequah, at USGS station 07196500 (2484 km2), the sta-tistics are 5.7% and 0.84, 1.71% and 0.85, and 2.8% and0.89, respectively. As seen in Figs. 3 and 4, the monthlydischarge compares well for all watersheds except for afew months when the observed discharge is exception-ally high. Accuracy and resolution limitations in the pre-cipitation dataset may be responsible for these anoma-lies. Nevertheless, the Nash–Sutcliffe coefficients for thefour watersheds are quite high, indicating a good agree-ment between observed and simulated discharge. Thisis generally true for other MOPEX basins examinedbut not included in Figs. 3 and 4. Locations of all un-regulated watersheds used in validation, together withmagnitudes of relative bias, are shown in Fig. 5. Areasof these watershed range between 600 and 10 000 km2.

7. Spatial distributions of the water balancecomponents

Figure 6 shows the spatial distribution of climatologi-cally averaged 1949–2000 annual precipitation, runoff,

FIG. 4. Observed (solid lines) and simulated (dotted lines) monthly stream discharge of the same watersheds inFig. 3 over different 10-yr periods.


and ET over the whole AR domain at 1-km resolution.Figure 6a suggests a strong east-to-west precipitationgradient with higher precipitation in the eastern part ofthe basin. The mean annual precipitation varies fromless than 300 mm yr�1 in the arid and semiarid west tomore than 1300 mm yr�1 in the dominantly humid east-ern subbasins. The mean annual precipitation on theeastern half of the AR basin is approximately twice aslarge as that on the western half. The basin-averagedmean annual precipitation during 1949–2000 ranges be-tween less than 500 mm yr�1 to nearly 1000 mm yr�1.Figure 7 shows the spatial distribution of mean monthlyprecipitation averaged over the 1949–2000 period. Theeast-to-west precipitation gradient prevails throughoutmost of the year, except for the period from June toAugust, when the precipitation gradient tends to have anorth–south orientation in the eastern part of the basin.The spatial pattern of monthly precipitation shows sig-nificant month-to-month differences for the periodfrom March to October, but the spatial pattern is basi-cally constant for the December–February period. Spa-tial patterns of monthly wetness of the root zone aresimilar, to a large extent, to those of precipitation ex-cept for the effects of temperature and local topogra-phy.

The spatial pattern of 1949–2000 averaged runoff(Fig. 6b) was extracted from the 1 km � 1 kmTOPLATS-simulated data and has a pattern similar tothat of observed precipitation. The relative spatial vari-ability of the basin-averaged runoff is higher than thatof precipitation; ranging from 40 to 190 mm yr�1. Theaverage runoff of the eastern half of the basin is 5 timesthe average of the western half. This is a direct result of

FIG. 5. Locations of the unregulated watersheds used in runoffdischarge validation. The size of the circle indicates the magnitudeof the bias in accumulated discharge over the simulation period(or period of available record). The sizes of the symbols, fromsmallest to largest, represent absolute bias magnitudes of 0.0%–3.0%, 3.0%–6.0%, 6.0%–9.0%, 9.0%–12.0%, and 12.0%–15%.

FIG. 6. Spatial distribution of mean annual (a) precipitation, (b)runoff, and (c) evapotranspiration (mm yr�1) for the 1949–2000period. (Note the different scales.)


the east–west trend of decreasing runoff ratio (Fig. 8).Runoff ratio ranges from more than 35% for very hu-mid subbasins in the east to less than 5% in some of thearid and semiarid subbasins in the west. The total basin-averaged climatological runoff ratio for 1949–2000 is14.7%. This sharp contrast in the spatial distribution ofthe runoff ratio can be attributed to several physi-ographic and climatic factors, for example, topography,

soil types, temperature, and precipitation. However, byfar, the contrast in precipitation is the main factor.

The fact that an increase in precipitation results in anincrease in runoff ratio is supported by studies ofmonthly discharges (e.g., Sankarasubramanian and Vo-gel 2002) and event-based runoff (e.g., Sharif et al.2002). The dependence of the runoff ratio on precipi-tation is very distinct in Fig. 9, which plots the relation-

FIG. 7. Spatial patterns of mean monthly precipitation (mm month�1) for the 1949–2000 period.


ship between daily precipitation and runoff ratio for theIllinois River at Tenkiller Reservoir, a 4000-km2 water-shed. The scatter of the points around the regressionline is due to the fact that many other factors, such asspatial and temporal distribution of precipitation, andantecedent soil moisture, affect the runoff off ratio. Thespatial distribution of the 1949–2000 averaged precipi-tation has a consistent trend that agrees with publishedclimatology values (e.g., Korzun et al. 1978)—note thatthe climatology provided by Korzun et al. (1978) wasfor a different time period (1930–60). The gradient ofmonthly surface runoff does not show a distinct north–south orientation over the summer months as seen forthe precipitation gradient (Fig. 7). The distinct month-to-month variability in the spatial pattern of runoff isonly seen in the eastern part of the basin. Most of thewestern part remains relatively dry throughout theyear.

The spatial pattern of ET, illustrated in Fig. 6c, showsa less pronounced east–west gradient than that of pre-cipitation. However, the annual variability of basin-averaged ET is similar to that of precipitation, and thecoefficient of variation of annual ET (0.099) is signifi-cantly smaller than that of precipitation and surfacerunoff. The fact that vegetation cover may have virtu-ally the same ET for a range of humidity conditions canbe an important factor causing the decreased variabilityof ET, for example, ET cannot exceed its potentialvalue, and physiography dictates how much precipita-tion can be transformed into surface runoff. Climato-logical ET maps are typically smoother than TOPLATSoutput plotted in Fig. 6c. However, climatology mapsdo not reflect local variations in land cover type andtopography. Figure 6c is based on 1 km � 1 km data

computed at an hourly time step with forcing data thatis approximately 140-km2 in resolution. Average ETvalues are approximately 5 times as large as runoff val-ues.

8. Annual hydroclimatology at the subbasin scale

Energy fluxes and precipitation control runoff andET rates. In arid and semiarid regions where availableenergy supply is greater than the latent heat required toevaporate total precipitation, ET equals or approachestotal precipitation. On the other hand, in more humidregions the available energy supply can be less than thelatent heat required to evaporate all the precipitationand hence actual ET approaches potential ET. Valida-tion of TOPLATS-simulated energy fluxes were limitedby the relative scarcity of energy flux observationwithin the domain. However, Crow and Wood (2002)spatially averaged TOPLATS flux predictions duringthe 1994 growing season over the ARM-CART SGPsite and validated them against spatially interpolatedflux measurements made with nine Bowen ratio towerslocated in Oklahoma and Kansas. Errors in TOPLATSenergy flux predictions were comparable to typical lev-els of systematic closure errors in the surface energybudget measured by eddy covariance (Twine et al.2000); see Crow and Wood (2002) for further discus-sion.

Another way to examine model simulations is tostudy how they reflect the control of precipitation andavailable energy, manifested by potential ET (PET), onthe mean annual ET at the subbasin scale. To obtainunbiased results, observed PET values are used ratherthan estimates by the land surface model. These values

FIG. 9. Relationship between daily precipitation and runoff ra-tio for the Illinois River at the Tenkiller Reservoir subbasin. Thesolid line represents the regression line.FIG. 8. Spatial distribution of mean runoff ratio for the

1949–2000 period.


of PET are based on maps from the NOAA Evapo-transpiration Atlas (Farnsworth et al. 1982) for the re-gion, which were digitized to obtain gridded values.Several empirical formulas that compute mean annualET for a basin as a function of the ratio of mean annualprecipitation and PET have been derived based on theassumption that interannual change in soil moisturestorage is insignificant compared to P and ET. Amongthe most frequently cited are those suggested bySchreiber (1904), Ol’dekop (1911), and Budyko (1948).These three formulas are listed in Table 1. Budyko’sformula, the most widely used, is simply the geometricmean of the formulas suggested by Schreiber (1904)and Ol’dekop (1911). All these formulas express ET asa function of the humidity index, which is the ratiobetween precipitation and PET [Eq. (4) below].

Zhang et al. (2001) suggest a formula with an addi-tional parameter to take into account the dominantvegetation type:

E

EP�

� � w

1 � � � w��, �3�

� �P

Ep, �4�

where P is the mean annual precipitation, E is the meanannual ET, Ep is annual PET, w is a plant-availablewater coefficient that has a value that varies between0.5 and 2.0 for grassy and forest regions, respectively,and � is denoted as the basin’s humidity index.Whereas Zhang et al. (2001) cited several studies indi-cating the effect of the plant type on ET, Budyko (1950)and others classified regions into desert, steppe, forest,or tundra according to the value of �. None of theformulas in Table 1 explicitly take into account the ef-fect of vegetation type. However, the formula in Eq. (3)does not work properly when � approaches 2.0 (e.g., forvery wet forested regions the value of ET/Ep can ex-ceed 1.0). Since vegetation type is a function of � and wis a function of the vegetation type, the formula of Eq.(3) can be simplified by assuming that w varies linearly

with vegetation type, that is, between the end of thedesert region where � is equal to 0.5 and into the forestregion for � being less that 2.0. According to this sim-plification the value of w will be equal to the value of �in this region and the formula of Eq. (3) will reduce to

E

EP�

2�

2 � �. �5�

For values of � less than 0.5 the curve of Eq. (5) isclosest to Schreiber’s, and as � approaches 2.0, it isclosest to Ol’dekp’s. These formulas can be used whenEq. (5) is not applicable, as seen in Fig. 10.

Figure 10 displays the three empirical curves pre-dicted by the formulas of Table 1 and the curve pre-dicted by Eq. (5) (solid line) together with the datacomputed for all 314 subbasins. The values of the in-dex � were computed after constructing a PET mapbased on the NOAA Evapotranspiration Atlas (Farns-worth et al. 1982) and using observed precipitation.TOPLATS-simulated ET was used to compute theevapotranspiration efficiency (E/Ep) values. All formu-las have high values of the coefficient of determina-tion (R2) with the formula of Eq. (5) having the high-est value of 0.96 while Schreiber’s, Ol’dekop’s, andBudykoe’s have values of 0.92, 0.94, and 0.95, respec-tively. As seen in Fig. 10, the formula of Eq. (5) fallsbetween Schreiber’s and Ol’dekop’s curves, as Budykoobserved for real data, but it fits the simulated databetter than Budyko’s curve. Interestingly, Eq. (5) stillagrees with Budyko’s (1950) assumptions when he firstdiscussed the concept of “geographical zonality”: that(a) the biome type is determined by the aridity (orhumidity) index and (b) the evaporation efficiency (E/Ep) is a function only of the aridity (or humidity) index.

TABLE 1. Definition of three empirical formulas for the rela-tionships between the ratio of actual to potential evapotranspira-tion and ratio of precipitation to potential evapotranspiration

Author Formula

Schreiber (1904) E

Ep� ��1 � e�1��

Ol’dekop (1911) E

Ep� tanh��

Budyko (1948) E

Ep� �tanh��1 � e�1��1�2

FIG. 10. Empirical relationships curves predicted by the formu-las of Table 1 and Eq. (5) (solid line) together with the datacomputed for all 314 subbasins.


9. Analysis of hydrologic variability

a. Precipitation

The interannual variability of basin-averaged ob-served precipitation is very significant, as seen in Fig.11. The year-to-year change in precipitation exceeded25% of the maximum annual precipitation severaltimes. The minimum and maximum precipitation oc-curred in two consecutive years, the difference beingmore than 50% of the maximum annual precipitation.The basin-averaged precipitation has a mean value of725.8 mm yr�1 and a standard deviation of 113.5 mmyr�1. Basin-averaged precipitation follows an increas-ing trend for the 1949–99 period. Simple linear regres-sion indicates that the average precipitation increasedby about 20% during the simulation period. Trendanalysis using Kendall’s nonparametric test results in aconfidence level of 99.35%, a very strong indicator thatthe observed trend is an actual trend in the data, ratherthan an artifact. While annual precipitation follows adistinct increasing trend, the annual variability in pre-cipitation decreases with time and stays within 12% ofthe maximum annual value for the last decade of thestudy. This increasing trend in precipitation is alsodominant for monthly precipitation. For 10 months ofthe year, excluding May and July, monthly precipitationincreased over the simulation period—based on linearregression. There is a slight decrease in May precipita-tion, but July precipitation decreased by about 18% forthis period—dropping July from being the second wet-test month to the sixth wettest. Winter and springmonths witnessed significant increases in average pre-cipitation—November precipitation increased by about95%, on average, and March precipitation increased byabout 80%. December went from being the driestmonth of the year to the third driest.

It has to be noted that gridded data based on theNational Climatic Data Service’s Cooperative Observer(Co-op) network might not be the best for accurateanalysis of long-term trends in the western UnitedStates due to changes in instrumentation in the 1940s(e.g., Groisman and Legates 1994). For example, Ham-let and Lettenmaier (2005) found some inconsistenciesin the data for the period before 1950. However, theCo-op data had been used in trend analysis by severalresearchers (e.g., Groisman and Easterling 1994; Boylesand Raman 2003). The authors are not aware of anystudy indicating spurious trends inferred from Co-opdata over the AR basin for the 1949–2000 period.Moreover, our results agree well with the findings ofGroisman et al. (2004) and others who analyzed trendsof the hydrologic cycle components over the contiguousUnited States.

b. Runoff

Basin-averaged surface runoff computed byTOPLATS shows trends similar to those of the aver-aged precipitation over the study period although therelationship between the two is highly nonlinear. Notonly does modeled runoff increase with increasing pre-cipitation but the runoff ratio also increases with pre-cipitation, as mentioned earlier. Consequently, relativeinterannual variability in precipitation is amplified inthe simulated surface runoff (Fig. 11). For example, themaximum year-to-year change is more than 80% of themaximum modeled annual surface runoff and the in-crease in average surface runoff over the study periodwas about 28%. The coefficient of variation of modeledannual surface runoff is more than twice as large whencompared to that of annual precipitation (0.332 and0.15). Similar to precipitation, the variability in mod-eled annual surface runoff decreased with time. Theconfidence level of the runoff trend, using Kendall’stest, is at 99.86%.

c. Modeling of runoff sensitivity

The formula described in section 8 can be extendedto develop empirical expressions of runoff sensitivity tointerannual variability in precipitation. For example,the derivative of ET as a function of the derivative ofprecipitation can be obtained from Eq. (5). Expressionsfor the relationship between the means and variances ofthe two variables can also be derived. Assuming that(a) interannual variability of soil moisture is insignifi-cant compared to P and (b) the PET is constant overtime, the following expression for the relationship be-tween the coefficients of variation of annual precipita-tion and runoff, CVP and CVR, respectively, can bederived (see the appendix):

FIG. 11. Time series of observed average annual precipitation,modeled surface runoff, and modeled evapotranspiration for theArkansas–Red River basin for the 1949–2000 period.


CVR

CVP�

4 � �

2 � �. �6�

Similar expressions can be derived from the formulasin Table 1. Figure 12 shows the ratio of coefficients ofvariation computed for the data for the 314 subbasins.The solid line represents the curve predicted by Eq. (6).For small values of the humidity index the curve of Eq.(6) is joined with the one predicted by Schreiber’s for-mula. Figure 12 shows that runoff sensitivity to precipi-tation variability increases for drier basins. The datapoints follow the predicted curve reasonably well.However, the scatter of data points is higher for drybasins, which can be due to the fact that these basins aremore affected by the precipitation frequency and thesize of individual events. In addition, the soil type andsoil storage may play a higher role in precipitation par-titioning, even at the annual time scale for drier water-sheds. The coefficient of determination, R2, for thecurve is 0.4.

d. Evaporation

Comparing the average increase in annual precipita-tion and modeled surface runoff indicates that ET inthe basin has also increased during the simulation pe-riod, as seen in Fig. 11. The increase in modeled ET issignificant (about 1.4 mm yr�1), but much less than theincrease in precipitation. However, the confidence levelof the modeled ET trend, using Kendall’s test, is still at99.0%. It has to be noted that observed discharge(USGS 2007) for the 1949–82 period, although not adirect measure of the actual runoff as mentioned earlierbecause of the effects of water management, shows adecreasing trend. Increased modeled ET over the ARbasin agrees with results reported in previous observa-

tion-based studies for several regions of the UnitedStates (e.g., Szilagyi et al. 2001; Walter et al. 2004). Itcan be expected that an increase in precipitation willresult in an increase in runoff and soil moisture, whichin turn would lead to increased ET, except under PETconditions. In fact, Berger and Entekhabi (2001) foundthat, for a given value of potential evaporation, in-creased precipitation is the most important variablethat leads to increased evaporation, when they com-pared the effect of several variables related to a basin’sclimate, geomorphology, and lithology. It is worth men-tioning here that several studies have indicated decreas-ing trends in pan evaporation over wide regions in Asia,Europe, and South and North America (Lawrimoreand Peterson 2000; Chattopadhyay and Hulme 1997;Quintana-Gomez 1997). However, Brutsaert and Par-lange (1998) showed that decreasing pan evaporationcould actually be an indicator of increased terrestrialevaporation.

Equation (5), and other equations in Table 1, can beextended to show that the interannual variance in ET isalways smaller than the variance in precipitation. Againby differentiating Eq. (5), squaring, and averaging overtime, the following expression can be obtained, assum-ing that PET is constant:

�E

�P�

4

�2 � ��2 . �7�

Equation (7) suggests that the ET variance decreaseswith increase of the basin wetness for a given precipi-tation variance. For very dry basins, where ET is con-trolled by available moisture from precipitation, the ETvariance approaches the precipitation variance. Forvery wet basins, where ET approaches its potentialvalue, the variance becomes negligible. In Fig. 13, theratio of standard deviations of computed ET values andobserved precipitation for the 314 subbasins are plottedtogether with the curve predicted by Eq. (7), joinedwith Schreiber’s formula for very small values of thehumidity index. It is clear from Fig. 13 that the empiri-cal formula reasonably predicts the relationship be-tween the precipitation and ET variabilities with an R2

value of 0.86.

e. Monthly variations

Although changes in soil moisture storage at themonthly time scale are still very small compared to pre-cipitation changes, they are not negligible, which makesit impossible to develop monthly analogies for the an-nually averaged expressions in Eqs. (6), (7), and (8).This is illustrated in Fig. 14, which shows the monthlytime series of anomalies in precipitation, runoff, and

FIG. 12. Computed ratios of coefficients of variation of annualrunoff and precipitation for the 314 subbasins (circles) and thecurve predicted by the empirical relationship (solid line).


soil water storage for a 1000-km2 watershed. Theanomalies were computed after the series have beendetrended to remove the effect of the long-term trendin precipitation. The contrasts in the temporal variabil-ity between the three variables can be read from thedifference in coefficients of variations for the originalseries: 0.758, 0.902, and 0.078 for monthly precipitation,runoff, and soil water storage, respectively. A distinctdifference between the runoff and soil storage series isthat the largest anomalies in runoff are positive (fol-lowing those of precipitation) while the largest anoma-lies in soil water storage are negative. This is due to thefact that runoff is forced directly by precipitation, andan increase in precipitation implies an increase (oftenlarger increase) in runoff while an increase in precipi-tation leads to a smaller increase in soil storage becauseinfiltration rate decreases with time during a precipita-tion event. On the other hand, when precipitation isrelatively low (negative anomalies), the decrease in soilwater storage may be exacerbated by ET, which de-pends mainly on temperature and land cover. Analysisof water budget anomalies shows similar trends for allsubbasins.

10. Summary and conclusions

A 51-yr simulation of water and energy fluxes overthe entire Arkansas–Red River basin was performedusing the fully distributed TOPLATS land surfacemodel. The simulations were performed at fine tempo-ral (hourly) and spatial (1 km2) resolutions in an effortto bridge the gap between traditional hydrologic mod-eling, typically at fine temporal and spatial resolutions

on relatively small catchments, and regional land sur-face modeling, typically performed at much coarserresolutions. The land surface model used in this study isparticularly well suited for this purpose as it combines adetailed representation of surface water and energybalance processes while capturing the topographicallyinduced horizontal redistribution of subsurface water.Our approach in model validation was to focus on boththe accuracy of streamflow simulations at the subbasinscale and an appropriate physically based description ofheat and water exchange at the land surface–atmo-sphere interface because only when runoff is appropri-ately computed can other fluxes and storage terms berealistically estimated (Koster and Milly 1997). We alsochose to evaluate TOPLATS simulations againststreamflow observations since it was the single high-quality measurement type available throughout themodeling period. Of course, such comparisons do notconstitute a rigorous model “validation” exercise.Given known difficulties with the calibration of inher-ently multiobjective land surface model output and thelack of available observations at time and fine spacescomparable to that of model output, fine-resolutionvalidation of a distributed land surface model is gener-ally regarded as extremely difficult.

Forcing data (precipitation, incoming radiation, andsurface meteorology) were interpolated from meteoro-logical and rain gauge observations, made available bythe University of Washington. For this study an archiveof various forcing data for 314 subbasins at 1 km � 1km spatial and hourly temporal resolution spanning theperiod 1949–2000 was assembled. This archive is avail-able for interested researchers. Analysis of the simula-tions showed that the spatial patterns of temporally av-eraged water balance components are similar to pub-lished climatological patterns and clearly illustrate the

FIG. 14. Time series of monthly anomalies of precipitation,runoff, and soil water storage for a 1000-km2 subbasin.FIG. 13. Computed ratios of standard deviation of annual

evapotranspiration and precipitation for the 314 subbasins(circles) and the curve predicted by the empirical relationship(solid line).


strong east–west gradients of precipitation, runoff, andET. Streamflow validation at the subbasin scale showedgood agreement between simulated and observedstreamflow for several unregulated watersheds withinthe Arkansas–Red River system. Analysis of the spatialdistribution of precipitation and runoff highlights thesimilarities and differences between the two. A notabledifference is that surface runoff did not show a distinctshift of the east–west gradient during the summermonths observed for precipitation.

A new empirical model that predicts the control ofavailable energy and precipitation in determining val-ues of ET was developed. The model is a very simpleone-parameter formula that takes into account the ex-pected dominant vegetation type while maintainingBudyko’s assumptions related to the concept of “geo-graphical zonality.” Computed ET values for 314 sub-basins agreed reasonably well with the empirical modelpredictions. The model was extended to develop twoother formulas that were used successfully to predictthe sensitivity of runoff and ET to precipitation varia-tions. The empirical model can serve as a useful tool toestimate the changes in various components of the hy-drologic cycle as a result of climate change.

The variability of interannual basin-averaged precipi-tation was strong and decreased with time over thestudy period. Precipitation variability was amplified insimulated runoff but also decreased with time. Bothobserved basin-averaged precipitation and computedsurface runoff increased over the study period, on av-erage, at different rates, which indicates that ET hasincreased over this period. This conclusion is supportedby analysis of ET at the subbasin scale and observeddischarge. Results agree with the mounting evidence ofan accelerating hydrologic cycle over the conterminousUnited States. Monthly precipitation and runoff havealso increased over the study period, with the exceptionof May and July. The relationship between precipita-tion anomalies and runoff and soil water storageanomalies was examined. While more pronounced run-off anomalies correspond to positive anomalies in pre-cipitation, anomalies of soil water storage reflect andexaggerate negative precipitation anomalies.

This is an ongoing study and additional subbasin vali-dations and analyses are planned. Forcing data athigher resolutions, for example, reliable radar-esti-mated precipitation, will be used as they become avail-able. The preliminary results presented in this papermake us comfortable with the quality of soil moistureand surface and latent heat flux simulations, which arebeing analyzed for an upcoming paper because the ac-curacy achieved in surface runoff simulations impliesthat simulations of the water and energy balance rela-

tionships are adequate. The correlation between mean-monthly, seasonal, and annual variations in surface en-ergy fluxes, soil moisture, and streamflow and large-scale atmospheric patterns is also being examined. It ishoped that the results of this analysis will help clarifythe sources of long-term hydrologic variability withinthe basin.

Acknowledgments. This work was supported underNASA Grant 0965-G-CB625, “Applications of Re-motely Sensed land Surface Data for Seasonal and In-ter-Annual Hydroclimate Predictions,” and AwardNA17RJ2612 from the National Oceanic and Atmo-spheric Administration (NOAA), U.S. Department ofCommerce. The statements, findings, conclusions, andrecommendations are those of the authors and do notnecessarily reflect the views of NASA, NOAA, or theU.S. Department of Commerce. This manuscript isLawrence Berkeley National Laboratory Report No.LBNL-58746.

APPENDIX

Derivation of Eq. (6)

Assuming that change in water storage is small, on anannual time scale, compared to water fluxes,

R � P � E. �A1�

Using Eqs. (4) and (5),

R

EP� � �

2�

2 � ��

�2

2 � �� f��. �A2�

Assuming that potential evapotranspiration is virtuallyconstant and taking derivatives,

�� P

EP�A3�

�R

EP� f ��

4� � �2

�2 � ��2 ��P

EP�. �A4�

Squaring and taking the average over time,

��R�2 � �4� � �2

�2 � ��2�2

��P�2. �A5�

The ratio of coefficients of variations can be derivedfrom Eqs. (4), (A2), and (A5) as

CVR

CVP�

4 � �

2 � �. �A6�


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Multidecadal High-Resolution Hydrologic Modeling of the Arkansas–Red River Basin

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