Linear system model of water flow and oxygen-18 transport on a steep hillslope

Abstract

The purpose of this model was to assist with the determination of the nature of water flow processes on steep (≈35°) hillslopes in a 3.8 ha forested catchment. The soils are sufficiently permeable that, for most rainstorms, streamflow responds rapidly without significant surface runoff occurring. Scientific debate had focused on whether "old water" held within the soil could be rapidly mobilised by incoming "new water" from storm rainfall. A linear system approach was taken to the analysis of the dynamic response of water flow and concentration of the natural isotope oxygen-18 in the stream to the input series of rainfall and associated oxygen-18 content from one storm. The candidate system components were bounded and unbounded water storages with first-order water flow dynamics, and bounded storages with zero-order dynamics. The upper limits on the bounded storages allow for nonlinearities in flow processes. The dynamic effect on transport of the isotopic tracer was assumed to be due to perfect mixing within each of the water storage components. The model was implemented on spreadsheet software in the form of difference equations and logical expressions. Analysis of the rainfall and streamflow data showed that the hydrometric response could be simulated with one bounded (8.5 mm) zero-order storage to account for initial rainfall loss, followed by a bounded (25.6 mm) and an unbounded first-order storage in parallel. However, this model provided insufficient attenuation of the oxygen-18 signal. Satisfactory simulation of oxygen-18 in the stream was achieved by including a bounded zero-order storage (250 mm) of specified oxygen-18 concentration. The same model structure was fItted to additional data from measurement of subsurface flow conected by troughs at four locations on the hillslopes. The results support the hypothesis that mobilisation of old water is an important component of water flow on the hillslopes. However, the degree of mixing within the old water storage has not been conclusively determined on the basis of the one storm event.