Supplementary material to "Multivariate statistical modelling of extreme coastal water levels and the effect of climate variability: a case study in the Netherlands"

Abstract. The co-occurrence of (not necessarily extreme) precipitation and surge can lead to extreme inland water levels in coastal areas. In a previous work the positive dependence between the two meteorological drivers was demonstrated in a case study in the Netherlands by empirically investigating an 800-year time series of water levels, which were simulated via a physical-based hydrological model driven by a regional climate model large ensemble. In this study, we present and test a multivariate statistical framework to replicate the demonstrated dependence and the resulting return periods of inland water levels. We use the same 800-year data series to develop an impact function, which is able to empirically describe the relationship between high inland water levels (the impact) and its driving variables (precipitation and surge). In our study area, this relationship is complex because of the high degree of human management affecting the dynamics of the water level. By event sampling and conditioning the drivers, an impact function was created that can reproduce the water levels maintaining an unbiased performance at the full range of simulated water levels. The dependence structure between the driving variables is modeled using two- and three-dimensional copulas. These are used to generate paired synthetic precipitation and surge events, transformed into inland water levels via the impact function. The compounding effects of surge and precipitation and the return water level estimates fairly well reproduce the earlier results from the empirical analysis of the same regional climate model ensemble. The proposed framework is therefore able to produce robust estimates of compound extreme water levels for a highly managed hydrological system. In addition, we present a unique assessment of the uncertainty when using only 50 years of data (what is typically available from observations). Training the impact function with short records leads to a general underestimation of the return levels as water level extremes are not well sampled. Also, the marginal distributions of the 50-year time series of the surge show high variability. Moreover, compounding effects tend to be underestimated when using 50 year slices to estimate the dependence pattern between predictors. Overall, the internal variability of the climate system is identified as a major source of uncertainty in the multivariate statistical model.