Estimating soil water flux from single-depth soil moisture data

Finding a relationship between soil moisture and soil water flux at a single soil depth has been of particular interest in recent years. Such a relationship, however, is challenging to derive due to a high degree of nonlinearity of the soil water flow governing equation, known as Richards equation. This paper presents a new algebraic soil moisture-flux relationship based on an approximate analytical solution of Richards equation with arbitrary soil hydraulic functions. This solution accounts for the groundwater contributions to soil moisture variations along the unsaturated zone. The new solution was evaluated using numerical solutions of Richards equation via the HYDRUS-1D model. Despite its simplicity, the new solution could reproduce HYDRUS-1D simulations for a homogeneous soil profile with coefficient of determination (R2) higher than 0.9 in most cases. The new solution offers a potential approach to modeling groundwater recharge in existing groundwater models. In particular, this model can potentially provide a more realistic recharge estimate compared to the kinematic-wave approximation of Richards equation, that neglects upward flows through the vadose zone. Future research is needed to account for soil layering and root water uptake in the soil moisture-flux relationship.