1. 1 A physically based distributed model at the REW scale and application to Oklahoma region Murugesu Sivapalan Fuqiang Tian Hongyi Li Department of Geography & Civil and Environmental Engineering, UIUC 09/11/2007

2. 2 Contents 1.REW approach and THREW model 2.Spatial discretization and temporal resolution 3.Parameter calibration strategy 4.Discussions on the seasonally switching pattern

3. 3 REW approach 1.Representative Elementary Watershed (REW) approach first proposed by Reggiani, Sivapalan, et al. (1998, 1999): REV, REA, and REW 2.Watershed is viewed as an open thermodynamic system which exchange mass, momentum, and energy with its environment 3.After 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. 4.Consistent and scale adaptable Introduction to THREW model

4. 4 REW approach 1.Constitutive relationships lie in the heart of REW approach: the universal principles and the properties of materials 2.Constitutive relationship at point scale: Darcy ’ s law; Chezy formula; soil characteristics curve 3.The constitutive relationships for REW approach are required to developed at macro-scale. Introduction to THREW model

5. 5 A extended framework From Tian F., 2006 Introduction to THREW model

6. 6 A extended framework Mass 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

7. 7 Numerical solutions 1.ODEs & PDEs: REW model is based on ODEs, while FH69 models are based on PDEs. 2.CREW: by Haksu Lee 3.REWASH: by Paolo Reggiani 4.THREW: by Fuqiang Tian  Backward Differential Formulas for iterative formula of ODEs  Newtonian Iteration for nonlinear equations  Preconditioned GMRES algorithm for linear equations  CVODE solver Introduction to THREW model

8. 8 Hydrological processes Introduction to THREW model From Lee et al., 2007

9. 9 Principle closure relationships 1.Canopy interception & depression: exponential function 2.Infiltration & Horton ’ s runoff: spatial averaged Green-Ampt model 3.Sub-stream-network zone & Dunnian runoff: tension water capacity distribution curve proposed in Xin ’ anjiang model Introduction to THREW model

10. 10 Principle closure relationships 4.Exfiltration & evapotranspiration 5.Seepage outflow: nonlinear to storage 6.Recharge & capillary rising 7.River channel routing: sub-stream- network & main channel, kinematics Introduction to THREW model

11. 11 Principle closure relationships 8.Soil matrix potential 9.Soil hydraulic conductivity Introduction to THREW model

12. 12 Discretization 1.Time step: 1 hour 2.Spatial discretization

13. 13 Spatial discretization (Km 2 ) BlueIllinois Baron Fork ElkNum55832789 min0.10.20.10.1 max59.5148.8132.485.2 avg22.429.629.624.5

14. 14 General principles 1.Totally THREW model has more than 40 parameters, the number of calibrated parameters is 15 2.All REWs have the same calibrated parameters, the model is not calibrated for each REW separately but for all REWs together 3.Warm-up period: 1 year 4.Manual calibration Parameter calibration strategy

15. 15 Model parameters Parameter calibration strategy No.typeSymbol Blue RiverIllinois River Note Init.Cali.Init.Cali. 1 Soil 1.0 1.1Exponential index for soil matrix potential 21.0 Exponential index for soil hydraulic conductivity 31.0 0.3Saturated hydraulic conductivity of u-zone 41.0 0.3Saturated hydraulic conductivity of s-zone 5 Routing 0.40.30.10.18 Manning roughness coefficient of t-zone, the initial value is determined from literature 60.2 0.050.08Manning coefficient of r-zone 7 Infiltration & exfiltration 1.010.01.015.0Spatial heterogeneity parameter of infiltration capacity 81.013.01.00.05Spatial heterogeneity parameter of exfiltration capacity 9Recharge1.01.51.0 Recharge/capillary rising 10 Dunnian runoff 0.50.350.5 Capacity value of tension water storage 1122.0 Shape parameter of tension water capacity distribution curve 12 Subsurface runoff 1.00.021.06.0Coefficient for fast subsurface runoff 137.0 8.0Exponential index for fast subsurface runoff 145.05.55.0 Coefficient for slow subsurface runoff 150.010.030.010.25Exponential index for slow subsurface runoff

16. 16 Data used Parameter calibration strategy 1.Topography: DEM, 30*30m 2.Rainfall: radar precipitation data, re- distributed at each REW 3.Potential evaporation: 3 hour resolution data from NOAA website, re-distributed at each REW, http://nomads.ncdc.noaa.gov/NARR/ 4.Soil data: from STATSGO, hydraulic conductivity, porosity, soil pore distribution index, and air entry value of soil matrix potential 5.Vegetation: DMIP2 website

17. 17 Calibration steps 1.Group the parameters: most of the parameters are from investigation or literature, only some of them are subject to the calibration based on initial value 2.Calibrate 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. 3.The objective functions are: Nash- Sutcliffe efficiency coefficient and water balance index.

18. 18 Seasonally switching pattern 1.Runoff generation mechanism shifts from Hortornian dominating in summer to Dunnian dominating in winter-spring 2.Water table and soil moisture fluctuate abruptly from one season to another. 3.Simulation in summer is not as good as that in winter 4.The governing factor of switching pattern maybe lies in the variability of climatic forcing and vegetation growing.

19. 19 Illinois River at talo2 hydrograph Hydrograph at Talo2 station

20. 20 Soil moisture dynamics Averaged soil moisture dynamics

21. 21 Water table fluctuation Averaged water table depth

22. 22 Hortornian runoff rainfall

23. 23 Dunnian runoff

24. 24 What are the possible reasons of switching runoff generation pattern?

25. 25 Mean monthly precipitation and evaporation

26. 26 Monthly runoff coefficient Mean monthly runoff coefficient

27. 27 Monthly greenness values

28. 28 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

29. 29 Monthly analysis Oct.Nov.Dec. Jan.Feb. Good correlation between runoff coefficient and event rainfall volume

30. 30 Monthly analysis Mar.Apr.May. Jun.Jul. Aug. Sep.

31. 31 seasonal analysis dry season wet season

32. 32 Discussions 1.Three period can be classified according to event analysis: wet, transition, and dry 2.Model 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 improved  Two layers model: VIC-3L

33. 33 Thanks!