Estimating effective model parameters for heterogeneous unsaturated flow using error models for bias correction

Estimates of effective parameters for unsaturated flow models are typically based on observations taken on length scales smaller than the modeling scale. This complicates parameter estimation for heterogeneous soil structures. In this paper we attempt to account for soil structure not present in the flow model by using so-called external error models, which correct for bias in the likelihood function of a parameter estimation algorithm. The performance of external error models are investigated using data from three virtual reality experiments and one real world experiment. All experiments are multistep outflow and inflow experiments in columns packed with two sand types with different structures. First, effective parameters for equivalent homogeneous models for the different columns were estimated using soil moisture measurements taken at a few locations. This resulted in parameters that had a low predictive power for the averaged states of the soil moisture if the measurements did not adequately capture a representative elementary volume of the heterogeneous soil column. Second, parameter estimation was performed using error models that attempted to correct for bias introduced by soil structure not taken into account in the first estimation. Three different error models that required different amounts of prior knowledge about the heterogeneous structure were considered. The results showed that the introduction of an error model can help to obtain effective parameters with more predictive power with respect to the average soil water content in the system. This was especially true when the dynamic behavior of the flow process was analyzed.