Estimating runoff probability from precipitation data: A binomial regression analysis

The runoff threshold of a catchment is often reported in the literature as a measure used to evaluate the effectiveness of low-impact development (LID) techniques and is oftentimes determined using linear regression. However, due to the heteroscedastic nature of precipitation and runoff data, linear regression analyses can result in invalid conclusions, so the use of a binomial regression model was investigated. Precipitation and runoff data collected from five studies were assessed for homoscedasticity and applied to four linear regression models for the evaluation of the linear regression runoff threshold (LRRT) and the associated 95% bootstrapping confidence intervals. Log-transformation corrected the heteroscedasticity of two of the five precipitation and runoff datasets. While mixed-effect linear models accounted for heteroscedasticity, these models often resulted in extremely large confidence intervals. A binomial regression model was created to determine the likelihood of runoff based on precipitation depth. For each catchment, the 10%-90% runoff probability range (p10-p90) is reported to provide the user with a more comprehensive understanding of when a catchment produces runoff than the LRRT. The p10-p90 range reflects the effects that environmental factors may have on runoff generation. For example, impervious catchments with limited interaction with the vegetation and soil produce a narrow p10-p90 range. Conversely, LID practices encourage the interaction of runoff with environmental factors and result in a wider p10-p90 range. Utilization of the binomial regression methodology presented herein is recommended for evaluation of the likelihood of runoff for each precipitation depth. Linear regression models of precipitation and runoff data are heteroscedastic and violate the assumption of homoscedasticity. The best method to analyse precipitation and runoff is modelling the runoff likelihood based on precipitation depth with binomial regression.image