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Abstract. The low-lying Netherlands is at risk from multiple threats of sea level rise, storm surges and extreme river discharges. Should these occur simultaneously, a catastrophe will be at hand. Knowledge about the likelihood of simultaneous occurrence or the so-called "compound effect" of such threats is essential to provide guidance on legislation for dike heights, flood barrier design and water management in general. In this study, we explore the simultaneous threats of North Sea storm surges and extreme Rhine river discharge for the current and future climate in a large 17-member global climate model ensemble. We use a simple approach, taking proxies of north-northwesterly winds over the North Sea and multiple~day precipitation averaged over the Rhine basin for storm surge and discharge respectively, so that a sensitivity analysis is straightforward to apply. By investigating soft extremes, we circumvent the need to extrapolate the data and thereby permit the model's synoptic development of the extreme events to be inspected. Our principle finding based on the climate model data is that, for the current climate, the probability of extreme surge conditions following extreme 20-day precipitation sums is around 3 times higher than that estimated from treating extreme surge and discharge probabilities as independent, as previously assumed. For the future climate (2070–2100), the assumption of independence cannot be rejected, at least not for precipitation sums exceeding 7 days.

Political decisions, adaptation planning, and impact assessments need reliable estimates of future climate change and related uncertainties. To provide these estimates, different approaches to constrain, filter, or weight climate model projections into probabilistic distributions have been proposed. However, an assessment of multiple such methods to, for example, expose cases of agreement or disagreement, is often hindered by a lack of coordination, with methods focusing on a variety of variables, time periods, regions, or model pools. Here, a consistent framework is developed to allow a quantitative comparison of eight different methods; focus is given to summer temperature and precipitation change in three spatial regimes in Europe in 2041–60 relative to 1995–2014. The analysis draws on projections from several large ensembles, the CMIP5 multimodel ensemble, and perturbed physics ensembles, all using the high-emission scenario RCP8.5. The methods' key features are summarized, assumptions are discussed, and resulting constrained distributions are presented. Method agreement is found to be dependent on the investigated region but is generally higher for median changes than for the uncertainty ranges. This study, therefore, highlights the importance of providing clear context about how different methods affect the assessed uncertainty—in particular, the upper and lower percentiles that are of interest to risk-averse stakeholders. The comparison also exposes cases in which diverse lines of evidence lead to diverging constraints; additional work is needed to understand how the underlying differences between methods lead to such disagreements and to provide clear guidance to users.