Statistical Determination of Rainfall-Runoff Erosivity Indices for Single Storms in the Chinese Loess Plateau

Correlation analysis is popular in erosion- or earth-related studies, however, few studies compare correlations on a basis of statistical testing, which should be conducted to determine the statistical significance of the observed sample difference. This study aims to statistically determine the erosivity index of single storms, which requires comparison of a large number of dependent correlations between rainfall-runoff factors and soil loss, in the Chinese Loess Plateau. Data observed at four gauging stations and five runoff experimental plots were presented. Based on the Meng’s tests, which is widely used for comparing correlations between a dependent variable and a set of independent variables, two methods were proposed. The first method removes factors that are poorly correlated with soil loss from consideration in a stepwise way, while the second method performs pairwise comparisons that are adjusted using the Bonferroni correction. Among 12 rainfall factors, I (30) (the maximum 30-minute rainfall intensity) has been suggested for use as the rainfall erosivity index, although I (30) is equally correlated with soil loss as factors of I (20), EI (10) (the product of the rainfall kinetic energy, E, and I (10)), EI (20) and EI (30) are. Runoff depth (total runoff volume normalized to drainage area) is more correlated with soil loss than all other examined rainfall-runoff factors, including I (30), peak discharge and many combined factors. Moreover, sediment concentrations of major sediment-producing events are independent of all examined rainfall-runoff factors. As a result, introducing additional factors adds little to the prediction accuracy of the single factor of runoff depth. Hence, runoff depth should be the best erosivity index at scales from plots to watersheds. Our findings can facilitate predictions of soil erosion in the Loess Plateau. Our methods provide a valuable tool while determining the predictor among a number of variables in terms of correlations.