1. Oslo Gardermoen Oslo N12 N10 N18 N20 N34 N32 N30 N40 N38 N36 N46 N44 N42 N12 N10 N18 N20 N34 N32 N30 N40 N38 N36 N46 N44 N42 GPR(44)GPR(46) GPR(47) GPR(45) 5 m Oslo airport Gardermoen 500m Moreppen research site railway runways utm-E utm-N 614 000616 000618 000 6672500 6674500 6676500 6678500 Ground Penetrating Radar profiles Figure 1. The Moreppen research site INVERSE MODELLING OF UNSATURATED FLOW COMBINED WITH STOCHASTIC SIMULATION USING EMPIRICAL ORTHOGONAL FUNCTIONS (EOF) Nils-Otto Kitterød University of Oslo, Department of Geophysics, Norway e-mail: nilsotto@geofysikk.uio.no Background Oslo Airport is a potential hazard to the unconfined groundwater aquifer at Gardermoen (fig. 1). Biological remediation may prevent serious pollution of the groundwater, but this protection requires that the transport to the groundwater is not too fast. Spatial and temporal variation in unsaturated flow properties however, make short cuircuiting and preferential flow very likely under extreme conditions. Stefan Finsterle University of California, Lawrence Berkeley National Laboratory Berkeley, California, USA The Forward Flow Model: The numerical code TOUGH2 (Preuss, 1991) is used to solve Richards equation with constitutive relations between pressure p, permeability k r and saturation S according to the van Genuchten model (fig.2): where S e is effective saturation, S e = (S- S r )/(1- S r ), S r is called residual liquid saturation, 1/  is called air entry value, and m=1-1/n where n is called the pore size distribution index. Conditional simulation of the parameter set p can be done according to the Proper Orthogonal Decomposition Theorem (Loève, 1977): and: Uncertainty propagation analysis by Empirical Orthogonal Eigenfunctions Given the covariance matrix C pp of the best-estimate parameter set p (Carrera and Neuman, 1986): where  is the eigenvector derived from: where  is the eigenvalue, and  ij = 0 if i  j, else 1. Conclusions: EOF simulation reproduces C pp, and thereby automatically avoides unlikely parameter combinations EOF simulation does not rely on second order stationarity Truncation of p reduces the quality of C pp reproduction Geological architecture is critical Liquid saturation data can be used to estimate optimal parameters for flow simulation, but a priori information is necessary Non-steady infiltration improves parameter estimation Figure 5. Local Sedimentological Architecture 105 0 Depth 0 1 2 3 Top 1 Top 2 Dip 1 Dip 2 lp4 West-East 105 0 Depth 0 1 2 3 sp4 c11c16 Figure 6. Liquid saturation, May 11, 1995 2D flow test Inverse modeling: The code iTOUGH2 (Finsterle, 1999) is used. The general inverse modeling procedure is illustrated in fig.3. In this case the inverse problem is to estimate the parameter p in such a way that the residual vector r is minimized: where y* j is observation of liquid saturation in space and y i (p) is the forward model response, p={k i, S ri 1/  i,n i }, i=1,2,…,number of sedimentological units, in this case equal to 4 (top1, top2, dip1 and dip2) Figure 2. Constitutive relations between pressure p, permeability k r and saturation S Use liquid saturation as primary data for Bayesian Maximum Likelihood Inversion of unsaturated flow parameters. Simulate parameter uncertainties by Karhunen- Loève expansion. The purpose of this study is to: Estimate sedimentological architecture and liquid saturation by Ground Penetrating Radar. Input data Sedimentological architecture from Ground Penetrating Radar (fig.4 and 5) Liquid saturation measured by Neutron Scattering and interpolated by kriging (fig.6) A priori statistical data on flow parameters Effective infiltration (fig. 7) Figure 7. Effective Infiltration rate Results Main character of observed liquid saturation is simulated (fig. 8 and 9) and absolute permeabilities are estimated according to independent observations (fig. 10) Simulation by EOF reproduce C pp (fig. 11) Neglecting C pp imply unphysical parameter combinations and overestimation of parameter uncertainty (fig. 12) Figure 8. Reproduction of observed liquid saturation in location c11 and c16 (cf.fig 6) Figure 9. Difference between observed and calculated liquid saturation Figure 10. Observed and estimated hydraulic conductivities Figure 11. C pp reproduced by EOF- simulation Figure 12. Improved simulation by EOF p47 p45 Figure 4. Ground Penetrating Radar foresets p43 Ground- water- table Delta - topsets Flow model p41 Figure 3. Inverse modeling procedure true unknown system response measured system response TOUGH2 model calculated system response stopping criteria minimization algorithm objective function best estimate of model parameters maximum- likelihood theory a posteriori error analysis uncertainty propagation analysis prior information corrected parameter estimate