Improving the Horton infiltration equation by considering soil moisture variation

Abstract

Soil water infiltration simulation is a subject receiving great interest in hydrological cycle modelling. The traditional Horton equation is based on the curve of infiltration capacity-rainfall duration time. However, the infiltration process is directly affected by soil moisture content, rather than rainfall duration. The objective of this study was to determine a relationship between infiltration capacity and soil moisture content in order to improve the Horton infiltration equation. Artificial rainfall-infiltration experiments were used to determine a series of power functions. The improved equation was cross-validated with observations from 32 experiments of multiple rainfall intensities and antecedent soil moisture. The simulation performance and uncertainty of the improved equation were compared with those of the original Horton equation to verify its accuracy. The results showed that infiltration rate decreases nonlinearly as soil moisture increases, and finally approaches a stable infiltration rate when the soil is saturated. Overland flow simulations by the improved Horton equation closely matched the observations from all 32 experiments over a soil moisture range of 0.222–0.349 m3/m3. The simulation performance was rated as good for most of the experiments for both the calibration and validation data sets. Compared with the original Horton equation, the simulation performance of the improved equation clearly improved estimation of infiltration, particularly as quantified by the Nash-Sutcliffe efficiency coefficient (NSE) and the coefficient of determination (R2). The number of simulations with NSE values greater than 0.65 increased 11.59% and 2.50% for the calibration and validation data sets, respectively. The number of simulations with R2 values greater than 0.90 increased 31.14% and 22.50%, respectively. The uncertainty intervals of the improved Horton equation became a little greater than those of the original Horton equation. For all 32 experimental simulations, the average relative length of the uncertainty interval at the 95% confidence level increased from 40.52% with the original Horton equation to 49.17% with the improved Horton equation. The number of observations falling within the 95% confidence interval increased from 92.13% to 95.94% with the improved Horton equation. Most of the observations were accurately simulated using the improved Horton equation. The greatest improvements in simulating overland flow were seen for the experiments with low flow simulations. The study results provide insights into soil infiltration mechanisms, and also provide references to support improved infiltration simulation by considering soil moisture variation.