Joseph A. P. POLLACCO USA , Paolo NASTA ITALY , Binayak P. MOHANTY USA

1. GENERALIZED FRAMEWORK TO REDUCE THE NON-UNIQUENESS OF THE INVERTED PARAMETERS Joseph A. P. POLLACCOUSA, Paolo NASTAITALY, Binayak P. MOHANTYUSA AOGS 2011: Challenges in Hydrologic Modeling Joseph@pollaccowater.org www.pollaccowater.org Department of Agricultural Engineering and Agronomy, Division of Water Resources and Biosystems Engineering - University of Napoli Federico II, Italy Past position

2. LONG-TERM RESEARCH OBJECTIVESTaking advantage of data retrieved at different scales Time series ET from RS Point measurements Geophysics Transpiration Storage Runoff Time series streamflow Time series surface θ (5 cm)from RS Recharge

3. UNCERTAINTIES OF THE INVERTED HYDRAULIC PARAMETERS Non-uniqueness of the inverted parameters causes uncertainties of the forwarded water fluxes. Methods needs to be developed to increase the sensitivity of the parameters and decrease the uncertainties of forwared water fluxes.This is the objective of the presentation. Pollacco J.A.P., Mohanty B.P., (2010b) Maximum uncertainty simulator algorithm that derives the water fluxes uncertainties by inverting soil moisture and evapotranspiration retrieved from remote sensing Vadose Zone Journal

4. SCHEME TO REDUCE THE NON-UNIQUENESS OF THE INVERTED PARAMETERS & MODEL OUTPUTS Observations calibration Potential Evapotranspiration Precipitation MODEL saturate hydraulic conductivity: Ks Ks HYDROLOGICAL MODEL suitable for inverse modeling hm, , s hm, , s Selecting best period Yes Water fluxes Is the parameter set physical? No Multiple Objective Functions parameterization depending on hydroclimate INVERSE MODELING modified Water fluxess Parameterss DYNAMIC RANGE parameters MEMORY PEDOTRANSFERfunctions SELECTING feasible Outputs Bulk density Texture UNCERTAINTIES water fluxes & parameters

5. SCHEME TO REDUCE THE NON-UNIQUENESS OF THE INVERTED PARAMETERS & MODEL OUTPUTS Observations calibration Potential Evapotranspiration Precipitation MODEL saturate hydraulic conductivity: Ks Ks HYDROLOGICAL MODEL suitable for inverse modeling hm, , s hm, , s Selecting best period Yes Water fluxes Is the parameter set physical? No Multiple Objective Functions parameterization depending on hydroclimate INVERSE MODELING modified Water fluxess Parameterss DYNAMIC RANGE parameters MEMORY PEDOTRANSFERfunctions SELECTING feasible Outputs Bulk density Texture UNCERTAINTIES water fluxes & parameters

6. DESIGNING HYDROLOGICAL MODELS SUITABLE FOR INVERSE MODELING Extinc. Coef. Solar Rad. PARTITIONING Beer-Lambert law LAI POT. TRANSPIRATION POT. EVAPORATION POT. TRANSPIRATION OF WET CANOPY EVAPORATION TRANSPIRATION INTERCEPTION SOIL MOISTURE HYDRAULIC PARAMETERS

7. SCHEME TO REDUCE THE NON-UNIQUENESS OF THE INVERTED PARAMETERS & MODEL OUTPUTS Observations calibration Potential Evapotranspiration Precipitation MODEL saturate hydraulic conductivity: Ks Ks HYDROLOGICAL MODEL suitable for inverse modeling hm, , s hm, , s Selecting best period Yes Water fluxes Is the parameter set physical? No Multiple Objective Functions parameterization depending on hydroclimate INVERSE MODELING modified Water fluxess Parameterss DYNAMIC RANGE parameters MEMORY PEDOTRANSFERfunctions SELECTING feasible Outputs Bulk density Texture UNCERTAINTIES water fluxes & parameters

8. SELECTING THE PERIOD TO AVOID DECOUPLING DECOUPLING THEORY: Capehart, W. J., and T. N. Carlson (1997), Decoupling of surface and near-surface soil water content: A remote sensing perspective, Water Resources Research, 33(6), 1383-1395.

9. SCHEME TO REDUCE THE NON-UNIQUENESS OF THE INVERTED PARAMETERS & MODEL OUTPUTS Observations calibration Potential Evapotranspiration Precipitation MODEL saturate hydraulic conductivity: Ks Ks HYDROLOGICAL MODEL suitable for inverse modeling hm, , s hm, , s Selecting best period Yes Water fluxes Is the parameter set physical? No Multiple Objective Functions parameterization depending on hydroclimate INVERSE MODELING modified Water fluxess Parameterss DYNAMIC RANGE parameters MEMORY PEDOTRANSFERfunctions SELECTING feasible Outputs Bulk density Texture UNCERTAINTIES water fluxes & parameters

10. SELECTING THE BEST MULTIPLE OBJECTIVE FUNCTION Loamy sand/ Temperate / Shallow roots MOF* = W . OFsm + (1-W) OFet Pollacco J.A.P., Mohanty B.P., (2010a) Multiple objective function simulator algorithm which improves the inverted hydraulic parameters estimated by surface soil moisture and evapotranspiration, Vadoze zone journal

11. SCHEME TO REDUCE THE NON-UNIQUENESS OF THE INVERTED PARAMETERS & MODEL OUTPUTS Observations calibration Potential Evapotranspiration Precipitation MODEL saturate hydraulic conductivity: Ks Ks HYDROLOGICAL MODEL suitable for inverse modeling hm, , s hm, , s Selecting best period Yes Water fluxes Is the parameter set physical? No Multiple Objective Functions parameterization depending on hydroclimate INVERSE MODELING modified Water fluxess Parameterss DYNAMIC RANGE parameters MEMORY PEDOTRANSFERfunctions SELECTING feasible Outputs Bulk density Texture UNCERTAINTIES water fluxes & parameters

12. REDUCING DYNAMICALLY THE FEASIBLE PARAMETER SPACE (UNSODA data) X Capillary Young-Laplace relation X

13. SCHEME TO REDUCE THE NON-UNIQUENESS OF THE INVERTED PARAMETERS & MODEL OUTPUTS Observations calibration Potential Evapotranspiration Precipitation MODEL saturate hydraulic conductivity: Ks Ks HYDROLOGICAL MODEL suitable for inverse modeling hm, , s hm, , s Selecting best period Yes Water fluxes Is the parameter set physical? No Multiple Objective Functions parameterization depending on hydroclimate INVERSE MODELING modified Water fluxess Parameterss DYNAMIC RANGE parameters MEMORY PEDOTRANSFERfunctions SELECTING feasible Outputs Bulk density Texture UNCERTAINTIES water fluxes & parameters

14. USING PEDOTRANSFERT FUNCTIONS TO REDUCE THE NON-UNIQUENESS * Sand * Silt * Clay * Bulk density * Sand * Silt * Clay * Bulk density

15. SCHEME TO REDUCE THE NON-UNIQUENESS OF THE INVERTED PARAMETERS & MODEL OUTPUTS Observations calibration Potential Evapotranspiration Precipitation MODEL saturate hydraulic conductivity: Ks Ks HYDROLOGICAL MODEL suitable for inverse modeling hm, , s hm, , s Selecting best period Yes Water fluxes Is the parameter set physical? No Multiple Objective Functions parameterization depending on hydroclimate INVERSE MODELING modified Water fluxess Parameterss DYNAMIC RANGE parameters MEMORY PEDOTRANSFERfunctions SELECTING feasible Outputs Bulk density Texture UNCERTAINTIES water fluxes & parameters

16. SATURATED HYDRAULIC CONDUCTIVITY MODEL (UNSODA data) FLOW RATE Darcy law FLOW RATE Hagen-Poisseuille ρ (g cm-3) water density; g (cm s-2) gravity, μ (g cm-1 s-1) dynamic viscosity; l (cm) length of tube; NUMBER OF PORES Kosugi log-transf. pore radius ln Rmmean;  standard deviation of log-transformed pore radius ln R.

17. CONCLUSIONS AND FUTURE WORK There is a need to develop inverse methods which can optimize parameters at different scales e.g.,surface soil moisture & ET retrieved from remote sensing, streamflow, soil pedotransfer functions, infiltration test, soil moisture profile etc… To upscale and downscale one must work with unique parameter sets in order to compare the parameters retrieved at different scales. To be successful one needs to work with uncorrelated inverted parameters. METHODS TO REDUCE THE CORRELATION OF THE INVERTED PARAMETERS: Build models with a reduced number of parameters which compute multiple water fluxes; Reduce the range of the inverted parameters for example from pedotransfer functions; Reject parameter sets which are unphysical; Reduce the number of hydraulic parameters by applying soil physics for example by estimating the saturated hydraulic parameters from parameters describing the characteristic curves. Determine the best period to calibration the model which ironically for SVAT models may not include the full range from very dry to very wet; Select the optimal weighting of a multiple objective calibration to reduce the uncertainties of the forwarded water fluxes;

18. THANK YOU Joseph@pollaccowater.org