Exploring Rainfall-Runoff Relationship at Hillslope Scale through Virtual Experiments

Abstract:

Hillslope is an intermediate scale bridging the micro-scale (e.g., soil pore and representative elementary volume) at which hydraulic processes are described and the macro-scale at which the hydrological processes are described. The rainfall-runoff relationship at a hillslope scale can serve as hydrological constitutive relationship by integrating micro-scale processes and heterogeneous properties (observations not accessible), which can be further up-scaled by integrating macro-scale processes and heterogeneous properties for hydrological modeling (observations accessible). We tried to explore such relationships by designing dedicate virtual experiments targeting headwater hillslope.A hillslope can be defined by specific characteristics, including geomorphology, topography, soil, etc. Climate forcing is another factor controlling rainfall-runoff relationship at hillslope scale. We chose a series of parameters to represent the characteristics dominating the hydrological responses at hillslope scale. For example, the size, slope, and longitude shape represent geomorphology and topography of hillslope; soil depth, distribution and hydraulic conductivity represent the soil characteristics; bedrock topography and leakage rate represent the bedrock characteristics. Also, storm size, precipitation intensity and initial soil moisture represent climate forcing and initial wet conditions of hillslope. With the verification of field observation, we fixed a range for each of above eleven factors and picked out 3~5 values within each range representing different situations of a real hillslope. More than 40,000 scenarios were obtained with different combinations of the eleven factors.

A calibrated dynamic numerical model (THRM) is employed to simulate the hydrological processes at hillslope scale. The THRM model integrates Saint-Venant equation for surface runoff with Richard's equation for variably saturated soil water movement. THRM model presents a high computational efficiency and stability in simulating subsurface flow of the experimental hillslope. THRM was validated by the field experiments at the Panola hillslope in Georgia of U.S.

Our numerical experiments show that when the soil profile reaches steady state, only a finite layer above the soil-bedrock interface is saturated rather than the whole soil profile. This proves the so-called “fill and spill” hypothesis for subsurface flow generation. The rainfall threshold for runoff generation from hillslope is composed of bedrock depression capacity, bedrock leakage to deeper bedrock layer, and soil moisture deficit. We define the threshold as 'hillslope storage capacity'. Most headwater hillslope has relatively higher hydraulic conductivity than normal rainfall intensity. The runoff generation mechanism belongs to the runoff excess saturation. The 'steady saturated' status would be attained when the threshold is exceeded and the capacity is filled up. The excess rainfall turns into runoff. For a specific hillslope with identical initial conditions and storage capacity, deep leakage increases linearly with the excess of rainfall to storage capacity. The same behaviors exist in the flux at the outlet with the regulation of water balance. The gradient of the linear relationship is defined as 'hillslope runoff generation ratio'. This phenomenon (threshold-linear behavior) has been mentioned in previous observation-based studies and is confirmed but extended to a general situation by numerical simulations in this study.

(following results contain equations and are listed in image file)