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.

Exploring the Potential for Multivariate Fragility Representations to Alter Flood Risk Estimates.

In flood risk analysis, limitations in the multivariate statistical models adopted to model the hydraulic load have restricted the probability of a defense suffering structural failure to be expressed conditionally on a single hydraulic loading variable. This is an issue at the coastal level where multiple loadings act on defenses with the exact combination of loadings dictating their failure probabilities. Recently, a methodology containing a multivariate statistical model with the flexibility to robustly capture the dependence structure between the individual loadings was used to derive extreme nearshore loading conditions. Its adoption will permit the incorporation of more precise representations of a structure's vulnerability in future analyses. In this article, a fragility representation of a shingle beach, where the failure probability is expressed over a three-dimensional loading parameter space-water level, wave height, and period-is derived at two localities. Within the approach, a Gaussian copula is used to capture any dependencies between the simplified geometric parameters of a beach's shape. Beach profiles are simulated from the copula and the failure probability, given the hydraulic load, determined by the reformulated Bradbury barrier inertia parameter model. At one site, substantial differences in the annual failure probability distribution are observed between the new and existing approaches. At the other, the beach only becomes vulnerable after a significant reduction of the crest height with its mean annual failure probability close to that presently predicted. It is concluded that further application of multivariate approaches is likely to yield more effective flood risk management.