A similarity approach to determine response times to steady-state saturation in landscapes

Relationships describing response times for landscape saturation and subsurface flow for idealised hillslopes after a change in water balance are derived in terms of similarity parameters given by their topographic, soil and climatic attributes. The study was carried out under a set of specific assumptions. The work quantitatively describes effects of each of these attributes on travel time. For example, divergent hillslopes can exhibit travel times that are double those of convergent hillslopes, and concave slopes tend to have lower travel times than planar or convex slopes. It is shown that the hillslope travel time T is dependent on hillslope length L, hydraulic conductivity K and slope S such that T = f(L/KS, B, CR, Δq/smd) and if saturation does not occur in the lower reaches of a hillslope, this can be simplified to T = f(L/KS, B). Here, Δq is change in net external flux and smd is soil moisture deficit; CR and B are the convergence ratio and profile factor respectively. The relative importance of these attributes on response time is discussed. It is shown that subsurface flow hydrographs of simple hillslopes of different scale, derived numerically, can be collapsed into a single curve by normalising them by means of a form of response time, the time constant. Results from the analytical derivation were compared with numerical analysis with good agreement. The theory was applied to a natural catchment using observed data from a bushfire event. Comparison of analytically calculated response time with observed response time for the event showed a large discrepancy. The reason is discussed.