Reduced complexity models for probabilistic forecasting of infiltration rates

Soil heterogeneity and data sparsity combine to render estimates of infiltration rates uncertain. We develop reduced complexity models for the probabilistic forecasting of infiltration rates in heterogeneous soils during surface runoff and/or flooding events. These models yield closed-form semi-analytical expressions for the single- and multi-point infiltration-rate PDFs (probability density functions), which quantify predictive uncertainty stemming from uncertainty in soil properties. These solutions enable us to investigate the relative importance of uncertainty in various hydraulic parameters and the effects of their cross-correlation. At early times, the infiltration-rate PDFs computed with the reduced complexity models are in close agreement with their counterparts obtained from a full infiltration model based on the Richards equation. At all times, the reduced complexity models provide conservative estimates of predictive uncertainty.

Research highlights
► We derive single- and multi-point Probability Density Functions of infiltration rates.
► These PDFs are exact and free of linearization errors required by Richards’ equation.
► The PDFs serve to quantify parametric uncertainty in arbitrary hydraulic functions.
► Multi-point PDFs can be used to facilitate data assimilation.