A nonlinear filtering approach for determining hydraulic conductivity functions in field soils

A nonlinear Extended Kalman Filter approach is used to explicitly account for measurement and model uncertainty in field soil hydraulic conductivity function determination. The standard deviation that such a procedure provides for hydraulic conductivity, as a function of water content, is estimated from water content and matric potential measurements. These measurements were obtained following 43 days of water redistribution in a two-layer soil profile previously ponded with water. Except for a brief initial period during redistribution, water content changes can be described with a single exponential conductivity function. Also, reducing the frequency of measurements by 50% and 80% would change the mean hydraulic conductivity function less than ±1. standard deviation, i.e., half an order of magnitude. The filtering scheme, which accounts for both model and measurement uncertainty, provides an improved description of in situ hydraulic conductivity functions when compared with previous methods, which fail to supply fiducial limits of uncertainty.