Evapotranspiration Impact on Diurnal Discharges in a Small Catchment

Abstract

This paper describes a new application of the Fourier series for a detailed simulation of runoff in a small catchment in dry periods, when the streamflow is significantly impacted by evapotranspiration, particularly during daytime hours. The catchment was considered as a dynamic system, in which evapotranspiration has an impact on the day–night fluctuation of discharges. Measurements of these discharges were accomplished by a high-resolution water-level sensor attached to a V-notch. In parallel, the free water evaporation and also the soil moisture content have been measured nearby. The paper describes three runoff recession episodes in dry periods. Using short time step measurements and calculations, it was not difficult to analyze the diurnal streamflow fluctuations as harmonic waves. An application of the finite Fourier series model (FSM) to a quasi-periodic hydrologic data series clearly shows how the actual evapotranspiration influences surface runoff from small catchments. The method was verified by direct numerical evaluation of the convolution integral. The Fourier transformation works better if the number of discharge points (n) is large. The method allows computing the missing discharges in order to bridge accidental data gaps. The automatic measurement of free water evaporation multiplied by the measured soil water content compared semiquantitatively with the Fourier transformation function derived backward from the discharge hydrograph. Hence, this measurement can, to some extent, substitute the actual evapotranspiration on the catchment scale. The observation has been carried out with a time delay of the stream discharges behind the water evaporation, caused by the unsaturated zone processes and the hydraulic resistance to water flow, both in the saturated zone and in the streambed.