A New Scaled Inverse Modeling Method to Estimate Hydraulic Parameter Variations in a Deep Vadose Zone

Simulating flow and transport in the deep vadose zone requires accurate estimation of three-dimensional hydraulic parameter variations based on limited field and laboratory data. Traditional inverse modeling methods that are commonly used to establish parameter fields usually suffer such limitations as: 1) need of assumption of material homogeneity; 2) large computation times that rise with the number of “free” parameterse; 3) strongly correlated parameters resulting in equifinality problems and “unreasonable” final parameters at predefined minimum or maximum values. In this research we develop a new scaled inverse modeling method with which hydraulic parameters are not optimized directly, instead, output from site-specific and other pedotransfer function are bias corrected by optimizing parameter a and b in the equation: ξi’= ai + biξi where ξi’ and ξi refer to the ith hydraulic parameter after and before optimization. In our case there are 5 hydraulic parameters (residual water content θr, saturated water content θs, van Genuchten parameter α and n, and saturated hydraulic conductivity Ks), each has a pair of a and b (i.e.10 parameters in total). Then the optimized a and b can be used to calibrate hydraulic parameters for each point via the above equation. Our results indicate the lowest estimation bias and uncertainty, and the most accurate representation of observed variations in water content, compared to other methods such as traditional inverse modeling, Bayesian Updating and site-specific PTFs, are achieved with this advanced inverse modeling (decrease RMSE by 64%). The new method also possesses such advantages as: 1) no need of assumption of simplified homogeneous layers; 2) reduce number of calibrated parameters (from 25 to 10) so save computer time; and 3) optimize hydraulic parameters of each point so represent 3-D heterogeneity and variations across the site.