Space-dependent continuous time random walk for soil moisture modeling

A space-dependent continuous time random walk, with waiting times between jumps following a Mittag-Leffler distribution, is considered to model soil moisture. The model is applied to daily soil moisture measurements taken as vertical average between the surface and the depths of 30, 60, and 100 cm, from an experimental site in Grugliasco (Turin, Italy), focusing on dry periods between rainfall events from 2006 to 2008. Our approach assumes that water particles in the soil start with an initial vertical distribution estimated from data after a rainfall. The waiting times between jumps are Mittag-Leffler distributed with a position-dependent parameter αk (k=1,2,3), that varies according to the layers (0–30 cm, 30–60 cm, 60–100 cm). The effect of evapotranspiration is taken into account in the first layer because the soil is covered by grass. We simulate the movement of water particles, compute the daily proportion of water in each layer, and compare the results with measured data to estimate the parameters of the Mittag-Leffler distributions. The relationship between the estimated parameters and initial soil moisture and potential evapotranspiration is then investigated. These relationships make it possible to predict the α1,α2,α3 values for each dry period and to validate the model through comparison between estimated and observed soil moisture. In conclusion, space-dependent continuous time random walks are useful for modeling soil moisture in field soils between rainfall events, requiring only a limited number of parameters and simple assumptions.