DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Some Difficulties in Modeling Water and Solute Transport in Soils Ph. ACKERER IMFS STRASBOURG With the help of B. Belfort, H. Beydoun, F. Lehmann and A. Younès.

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG 0.36 km 2, m Contact: Bruno AMBROISE (IMFS) Hillslope hydrology The Ringelbach catchment

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Saturated area Discharge (from B. Ambroise, IMFS)

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Hillslope hydrology Mathematical models – Darcy – Richards eq. – Soil hydraulic properties Parameter measurements – Direct methods – Indirect methods Numerical methods – Highly non linear PDEs – Very strong parameters contrasts – Long term simulation – ‘Flat’ geometry

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG (from UMR LISAH, Montpellier) Usual concepts and mathematical models __________________________________________________________________________________ Model concept

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Scale (m) Model scale Q1Q1 Continuum Mec. (Stokes, Hagen- Poiseuille, …) KTKT KLKL REV Darcy, Richards, Water retention curves, …. Usual concepts and mathematical models __________________________________________________________________________________

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Usual mathematical models – conservation laws __________________________________________________________________________________ Mass conservation Generalized Darcy’s law Richards’ equation

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Mualem, 1976 Van Genuchten, 1981 Pore-size distribution models Usual mathematical models – Soil hydraulic properties __________________________________________________________________________________

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Particle-size distribution (Arya & Paris, 1981) Pore radius R i : average particle radius for fraction i  b : soil density  p : particle density n : number of particle  : 1.35 – 1.40 Water content W: fraction of particle distribution Water pressure  : surface tension  : contact angle Usual mathematical models – Soil hydraulic properties __________________________________________________________________________________

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Robbez-Masson, UMR LISAH, Montpellier

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Macropores in un-colonised and colonised soil (from Pierret et al., 2002)

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Hierarchy of flow/transport models for variably-saturated structured media (after Altman et al., 1996)

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG From Tuller & Or, 2001

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG New mathematical models Richard’s equation with alternative h(  ) and K(  ) Network models Alternative models Some recent concepts __________________________________________________________________________________

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Pore-size distribution models Modified Van Genuchten, Vogel et al. (1998, 2001) Soil Hydraulic Properties, h(  ) and K(  ) __________________________________________________________________________________

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Kosugi, 1996 Soil Hydraulic Properties, h(  ) and K(  ) __________________________________________________________________________________

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Soil Hydraulic Properties, h(  ) and K(  ) __________________________________________________________________________________ Pore-scale models (Tuller & Or, 2002)

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Soil Hydraulic Properties, h(  ) and K(  ) __________________________________________________________________________________ (a) Fitted liquid saturation for silt loam soil with biological macropores. (b) Predicted relative hydraulic conductivity. (Note that 1 J kg -1 = bar.) (from Tuller & Or, 2002) Pore-scale models (Tuller & Or, 2002)

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Pedotransfer functions (Wösten, 2001) Soil Hydraulic Properties, h(  ) and K(  ) __________________________________________________________________________________

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Soil Hydraulic Properties, h(  ) and K(  ) __________________________________________________________________________________ Smooth functions Prunty & Casey, 2002 Mualem, 1976

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Kinematic–dispersive wave model ( Di Pietro et al., 2003) Network models __________________________________________________________________________________

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG From Pan et al., 2004 Alternative models __________________________________________________________________________________ Two-phase flow using Lattice Boltzmann approach

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Alternative models __________________________________________________________________________________ Water retention curve from Pan et al., 2004.

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Parameter estimation Spatial variability and scales __________________________________________________________________________________ Direct measurements and interpolation Indirect estimation by inverse approach

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG (Ptak, Teutsch, 1994) Spatial variability and scales __________________________________________________________________________________

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Measurement locations Probability distribution of indicator 1 Conditioning InterpolationConditioning Interpolation Spatial variability and scales __________________________________________________________________________________ Probability distribution of indicator 2

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Probability normalization P k = P k / (  P i ) Integrated density function Spatial variability and scales __________________________________________________________________________________

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Spatial variability and scales __________________________________________________________________________________ Experimental site in Alsace Ksat  init (30 cm)

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Spatial variability and scales __________________________________________________________________________________ Fluxes after 8 weeks Water NitrateWater Nitrate Fluxes after 16 weeks Water Fluxes after 20 weeks Nitrate

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Inverse methods __________________________________________________________________________________ Parameter identification by inverse approaches Generalized least-square approach

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Inverse methods __________________________________________________________________________________ Experimental set-up

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Computed and measured variables Inverse methods __________________________________________________________________________________

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG ParameterInit.Est.MinMax θ r (cm 3 /cm 3 ) θ s (cm 3 /cm 3 ) α (cm -1 ) n K 1 s (cm/h) K P s (cm/h) Inverse methods __________________________________________________________________________________ Parameter estimation and validation

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG First order confidence interval Sensitivity matrix Covariance matrix Parameter uncertainty Inverse methods __________________________________________________________________________________

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Inverse methods __________________________________________________________________________________ ParamètresKsKs K s (P) rr ss  n KsKs 1-0,4490,7790,1030,3360,148 K s (P) 1-0,3250,473-0,5910,212 rr 1-0,082-0,0180,543 ss 10,162-0,131  1-0,707 n1 Correlation matrix

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Inverse methods __________________________________________________________________________________ Parameters and computed variable p c,1 Y c,1 Min(J(p)) Virtual data set P, y(p) Measurements: Y m,1 = y(p) +  1 Measurements: Y m,n = y(p) +  n Parameters and computed variable p c,n Y c,n Min(J(p)) Measurements: Y m,i = y(p) +  i Parameters and computed variable p c,i Y c,i Min(J(p)) Exp. Covariance matrix First Monte Carlo approach

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Virtual data set P, y(p) Inverse methods __________________________________________________________________________________ Measurements: Y m,1 = Y o +  1 Parameters and computed variable p c,1 Y c,1 Min(J(p)) Measurements: Y m,n = Y o +  n Parameters and computed variable p c,n Y c,n Min(J(p)) Exp. Covariance matrix Parameters and computed variable p c,i Y c,i Min(J(p)) Measurements: Y m = Y o +  i Second Monte Carlo approach Observations Y o = y(p) +  

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Comparison between 1er order and Monte Carlo Approaches Inverse methods __________________________________________________________________________________

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG Conclusions __________________________________________________________________________________ Many challenges remain: Understanding of processes and their mathematical modelling Parameter scaling: from measurements to element size Soil heterogeneity description Accurate of numerical codes will be of great help

DYNAS 04 Workshop Ph. Ackerer, IMFS - STRASBOURG References Frontis Workshop on Unsaturated-Zone Modeling: Progress, Challenges and Applications, Wageningen, The Netherlands 3-5 October Arya & Paris, Soil Sci. Soc. Am. J.,1981 Binayak P. Mohanty, Water Res. Res, 1999 Di Pietro et al., J. of Hydrology,2003 Pan et al., Water Res. Res., 2004 Pierret et al., Géoderma, 2002 Prunty & Casey, Vadose Zone J, 2002 Tulle & Or, Vadose Zone J, 2002 Vogel et al., Adv. Water Res., 2001 Vogel & Roth, J of Hydrology, 2003 Wösten, J. of Hydrology., 2001