Spectral Analysis of Hydrological Signals to Estimate Watershed Properties Considering Impacts of Unsaturated Zone

Understanding responses of stream discharge to precipitation in a watershed is important in gaining insights into watershed hydrology and estimating hydraulic parameters. Transfer functions in the spectral domain are commonly used to quantify the relationship between precipitation and discharge, and estimate watershed hydraulic parameters. However, previous models have not adequately accounted for the impact of the unsaturated zone. To address this, we have developed a novel analytical model that considers the effect of the unsaturated zone to obtain transfer functions within watersheds. These transfer functions are derived by the spectral method and verified through numerical simulations. The results indicate that the transfer functions are influenced significantly by the relative hydraulic conductivity exponent α_k in the moisture characteristic curve. A higher α_k results in a lower transfer function, indicating more robust filtering of hydrological signals. A thicker unsaturated zone results in lower transfer functions at higher frequencies. The traditional transfer functions, which neglect the retention capacity of the unsaturated zone, tend to overestimate hydrological responses at high frequencies. Our transfer functions agree well with integrated watershed-scale flow models and are also applied to observed data from four watersheds in Iowa, providing reasonable estimates for the hydraulic parameters. This study contributes to a deeper understanding of watershed behavior and offers an enhanced tool for estimating hydraulic parameters with practical applications.