Spectral and cross-spectral analysis of three hydrological systems

The mean hydrological and hydrochemical behaviour is analysed from observed time series on three agricultural catchments, located in different regions of France, named respectively Kervidy, Melarchez and Mercube. The time series are considered as input data or output data. The input data for hydrology and chemistry are respectively rainfall and nitrate leaching, and the output data are represented by stream discharge and nitrate concentration in the stream. The method is based on the spectral analysis of the data. First the spectral density function of each time series is calculated. It appears that nitrate concentrations measured at the outlet of the three catchments exhibit a strong and unique one year periodicity. This periodicity is due to the hydrological regime and the time distribution of the nitrate availability in the soil. Second, we performed a cross-spectral analysis between the input and output data. The catchment is then viewed as a linear and stationary system that converts an input to an output through a transfer function. The transfer function characterizes the behaviour of the catchment and is related to the real physical and chemical processes. For each catchment, the observed transfer functions for water and nitrate are determined in the spectral domain from the data. By comparing the observed frequency transfer function with the spectral signature of the theoretical model, we identify for each catchment: (i) the major processes that govern water and nitrate transfer and (ii) the characteristic time scale of these processes. The spectral and cross-spectral method appear to be valuable in identifying the main transfer processes operating in the different catchments. (C) 2000 Elsevier Science Ltd. All rights reserved.