Assessing multivariate effect of best management practices on non-point source pollution management using the coupled Copula-SWAT model

Best management practices (BMPs) have wide application in non-point source (NPS) pollution abatement in agricultural watersheds. Multivariate analysis of BMPs reduction effects taking their randomness and correla-tions into account is significant to spatial optimization of BMPs configuration. However, quantifying the cor-relations among high-dimensional random variables of BMPs effects is challenging and remains unexplored thoroughly. This study coupled the SWAT with the Vine Copula model to conduct multivariate analysis of BMPs reduction effects considering their randomness caused by hydro-meteorological variability along with correla-tions among different indicators (ammonium nitrogen, NH3-N; and total phosphorus, TP) and BMPs. The coupled model was applied to evaluate the multi-indicator effect of individual BMP and combined effect of various BMPs in the upper Boyang River basin, China. Results showed that bivariate copulas and three-dimensional vine copulas can efficaciously describe the dependence of BMPs effects. Simulation results indicate 43-100% prob-abilities of 45% NH3-N loads reduction, while 0-79% probabilities of 45% TP loads reduction for combined BMPs scenarios. Besides, the joint probabilities of different indicators in combined BMPs scenarios are generally lower than separate probabilities with 0-21% decrease, which is similar to individual BMP. Generally, joint proba-bilities using copulas can provide more accurate and factual knowledge of the risk and dependability of implementation of BMPs than univariate variables. The proposed model can conduct multivariate analysis of BMPs reduction effects and has great prospect in the future risk-based decision-making of NPS pollution management.