Analytical Solution for Field Soil Water Content Profiles

Abstract

AbstractQuantifying the spatial and temporal dynamics of soil moisture is an important subject in vadose zone hydrology. Although progress has been made to measure soil water content, soil water flow needs to be simulated for many applications. An analytical solution for soil water content, resulting from vertical flow and simplified mathematical conditions and hydraulic properties, was derived with the Cole‐Hopf transformation. The solution serves as a transfer function with the calibrated boundary condition and water content as respective input and output. This transfer function was applied to time series of soil water content, obtained from weekly observations with a neutron probe over a 1282‐day period at five depths and 16 locations. Water retention and saturated hydraulic conductivity were measured on soil samples in the laboratory. The transfer function was calibrated to observed time series of soil water content θ(t) with a median coefficient of determination R2 = 0.980. It was then used to predict θ(t) using constants from the calibration location and hydraulic parameters from the prediction location. There was a fairly good correspondence between predicted and observed θ(t) using calibrations elsewhere (R2 = 0.783). As an alternative, an observed time series θ(t) was scaled by multiplying it by the ratio of experimental saturated water contents for prediction and observation location. This scaling approach led to poorer predictions (R2 = 0.651). The analytical solution provides a flexible approach to quantify soil moisture for a variety of scenarios regarding available data on topography, climate, soil properties, and soil hydraulic parameters.