Study of three subsurface hydrologic systems based on spectral and cross-spectral analysis of time series

Abstract

Estimating the major hydrological processes and their characteristic time scale is important when studying the hydrology of a catchment. However, in general, only limited data are available, namely climatic data and stream discharge. In this paper, the catchment is viewed as a system that converts the rainfall to the stream discharge through a transfer function (TF). The observed TF calculated from the rainfall and the specific stream discharge depends on the hydrological processes operating in the catchment. By comparing the observed TF to simulated TF, these processes and their time scale are identified. The simulated TF are developed from the Dupuit and linear representations of the aquifer. The identification of the TF is based on the stochastic method using a spectral representation of the rainfall and stream-discharge time series. The novelty of this work is to extend the stochastic approach to the one-order catchment hydrology and to develop a model, which takes into consideration both the aquifer discharge and the rapid flows. The method was applied to three first-order agricultural catchments. For each site, the theoretical results are in accordance with reality. These results show that the stream discharge is dominated by the aquifer flow, the fast transfer accounting for 3–8% of the total discharge depending on the catchment. The stochastic approach based on spectral analysis of the temporal variation of global observations appears useful to extract significant information about dominant processes occurring in the catchment and their characteristic time scale.