On the compounding of nitrate loads and discharge

Compound extremes can arise from combinations of multiple drivers, and even non-extreme univariate events can combine to cause large societal and economic impacts. In this study, we model multivariate compound events focusing on the potential interaction of nitrate loads and discharge. We use daily discharge and nitrate loads at seven US Geological Survey sites in the state of Iowa. We apply a two-sided conditional sampling method, which derives two joint probabilities conditioning on discharge and nitrate loads, respectively. Our results show that there is a dependence between discharge and nitrate loads, which can be described through bivariate modeling and the subsequent estimation of their joint annual exceedance probabilities (AEPs). The magnitude of the joint AEPs to extreme discharge and extreme nitrate loads exhibit different structures across the different sites, highlighting the different roles of these two quantities in controlling their compounding. In examining the ranges in design values for a given AEP, we found that the largest variability in highly likely values was generally associated with high agricultural intensity, high hog density, and fertilizer expenditures.