Nonparametric estimation of time-variable transit time distribution and SAS function: A transfer function model approach

The transit time distribution (TTD) and the StorAge Selection (SAS) function of a catchment have served as important tools in understanding how the hydrologic system stores and releases water. However, we currently lack a method that can directly observe those functions at the catchment scale; previous studies have mainly relied on the calibration of parameters in pre-determined functional forms of those functions. Such a procedure could lead us to get the right answer from a wrong model structure. In this study, we propose a transfer function model approach to estimate the TTD, which limits the assumptions about the distribution's functional form. We also extend a transfer model estimation algorithm to consider the time variabilities in the TTD. Once we estimate the time-variable TTD, estimating the SAS function is straightforward by using the governing equation of the SAS function framework. We evaluate this method using synthetic datasets (generated by parameterized SAS functions) and an experimental dataset observed at the Landscape Evolution Observatory (LEO) hillslopes, Biosphere 2, the University of Arizona. In both cases, the proposed approach estimates the TTD and SAS functions that are close to the parameterized SAS functions (in the test with synthetic dataset) and the experimentally observed functions.