A physically based distributed model at the REW scale and application to Oklahoma regionMurugesu SivapalanFuqiang TianHongyi Li

Department of Geography & Civil and Environmental Engineering, UIUC09/11/2007

ContentsREW approach and THREW modelSpatial discretization and temporal resolutionParameter calibration strategy Discussions on the seasonally switching pattern

REW approachRepresentative Elementary Watershed (REW) approach first proposed by Reggiani, Sivapalan, et al. (1998, 1999): REV, REA, and REWWatershed is viewed as an open thermodynamic system which exchange mass, momentum, and energy with its environmentAfter a rigorous definition of REW, the universal conservative law is applied to different materials at micro-scale, then averaged over control volume and characteristic time scale. Finally the scale adaptable Ordinary Differential Equations (ODEs) are derived.Consistent and scale adaptableIntroduction to THREW model

REW approachConstitutive relationships lie in the heart of REW approach: the universal principles and the properties of materialsConstitutive relationship at point scale: Darcys law; Chezy formula; soil characteristics curveThe constitutive relationships for REW approach are required to developed at macro-scale.Introduction to THREW model

A extended frameworkFrom Tian F., 2006Introduction to THREW model

A extended frameworkMass balance equation:Momentum balance equation:heat balance equation: energy related processes are incorporated, i.e., evaporation and transpiration, glacier/snow accumulation and depletion, soil freezing and thawing general form of time-averaged conservation laws flexible framework which can be extended to include new zones and phases, such as human impact components, e.g. reservoir, well, pump station, etc.Introduction to THREW model

Numerical solutionsODEs & PDEs: REW model is based on ODEs, while FH69 models are based on PDEs.CREW: by Haksu LeeREWASH: by Paolo ReggianiTHREW: by Fuqiang TianBackward Differential Formulas for iterative formula of ODEsNewtonian Iteration for nonlinear equationsPreconditioned GMRES algorithm for linear equationsCVODE solverIntroduction to THREW model

Hydrological processesIntroduction to THREW modelFrom Lee et al., 2007

Principle closure relationshipsCanopy interception & depression: exponential functionInfiltration & Hortons runoff: spatial averaged Green-Ampt modelSub-stream-network zone & Dunnian runoff: tension water capacity distribution curve proposed in Xinanjiang modelIntroduction to THREW model

Principle closure relationshipsExfiltration & evapotranspirationSeepage outflow: nonlinear to storageRecharge & capillary risingRiver channel routing: sub-stream-network & main channel, kinematicsIntroduction to THREW model

Principle closure relationshipsSoil matrix potential Soil hydraulic conductivity Introduction to THREW model

DiscretizationTime step: 1 hourSpatial discretization

Spatial discretization

General principlesTotally THREW model has more than 40 parameters, the number of calibrated parameters is 15All REWs have the same calibrated parameters, the model is not calibrated for each REW separately but for all REWs togetherWarm-up period: 1 yearManual calibration Parameter calibration strategy

Model parametersParameter calibration strategy

Data usedTopography: DEM, 30*30mRainfall: radar precipitation data, re-distributed at each REWPotential evaporation: 3 hour resolution data from NOAA website, re-distributed at each REW, http://nomads.ncdc.noaa.gov/NARR/Soil data: from STATSGO, hydraulic conductivity, porosity, soil pore distribution index, and air entry value of soil matrix potential Vegetation: DMIP2 websiteParameter calibration strategy

Calibration stepsGroup the parameters: most of the parameters are from investigation or literature, only some of them are subject to the calibration based on initial valueCalibrate surface flow and subsurface flow separately. fixed subsurface flow, calibrate the surface runoff: software developed by Arnold J.G., et al.When the streamflow matches the observed one well and overall water balance is reasonable, calibrate the baseflow then.The objective functions are: Nash-Sutcliffe efficiency coefficient and water balance index.

Seasonally switching patternRunoff generation mechanism shifts from Hortornian dominating in summer to Dunnian dominating in winter-springWater table and soil moisture fluctuate abruptly from one season to another.Simulation in summer is not as good as that in winterThe governing factor of switching pattern maybe lies in the variability of climatic forcing and vegetation growing.

Illinois River at talo2hydrographHydrograph at Talo2 station

Soil moisture dynamicsAveraged soil moisture dynamics

Water table fluctuationAveraged water table depth

Hortornian runoffHortornian runoffrainfall

Dunnian runoffDunnian runoff

What are the possible reasons of switching runoff generation pattern?

Mean monthly precipitation and evaporationMean monthly precipitation and evaporation

Monthly runoff coefficientMean monthly runoff coefficient

Monthly greenness values

Rainfall-runoff event analysis We analysis about 90 events during 7 years (1995-2002). Runoff coefficient is lower in summer, and higher in winter-spring deficit of tension water is higher in summer, and lower in spring water table level is lower in summer, and higher in spring

Monthly analysisOct.Nov.Dec.Jan.Feb.Good correlation betweenrunoff coefficient and event rainfall volume

Monthly analysisMar.Apr.May.Jun.Jul.Aug.Sep.

seasonal analysis dry seasonwet season

DiscussionsThree period can be classified according to event analysis: wet, transition, and dryModel diagnostic:Better results in winter and spring, and worse results in summer may suggest that infiltration excess runoff generation component in our model should be improvedTwo layers model: VIC-3L

Thanks!