Prediction of the subsurface flow of hillslopes using a subsurface time-area model

Prediction of subsurface flow (SF) in hillslopes is more complicated than prediction of surface flow; hence, a simple and practical SF model would interest hydrogeologists. For the first time, the time-area method is employed to estimate the SF of hillslopes. The locations of the isochrone curves for complex hillslopes were determined using SF travel-time equations. Some equations were developed to delineate the isochrones and the subsurface time area (STA). The analytic equations suggested by the characteristics method of solving a hillslope-storage kinematic wave were used for validation of the STA method results in complex hillslopes. The average values of the coefficient of efficiency (CE), correlation coefficient ( R ), error of peak flow (EPF) and root-mean-square error (RMSE) of the STA method for the nine defined hillslopes are, respectively, 0.96, 0.96, 1.35, and 0.076. To further verify the results, a laboratory rainfall simulator with sandy loam soil was employed, which was conditioned under artificial rainfall intensities of 31.7, 4.6 and 63.46 mm/hr, and slopes of 3°, 6° and 9°. The STA model results were compared with those of a laboratory model of subsurface flow. The average values of CE, R , EPF and RMSE of the STA method for the nine events are, respectively, 0.81, 0.85, 0.98, and 0.017, which are regarded as good values. For the final evaluation of the STA model, the subsurface flow rates obtained from the Richards’ equation using HYDRUS were also used. The proposed STA model has good agreement with the results of the laboratory and HYDRUS models.