Compound events (CEs) are multivariate extreme events in which the individual contributing variables may not be extreme themselves, but their joint – dependent – occurrence causes an extreme impact. Conventional univariate statistical analysis cannot give accurate information regarding the multivariate nature of these events. We develop a conceptual model, implemented via pair-copula constructions, which allows for the quantification of the risk associated with compound events in present-day and future climate, as well as the uncertainty estimates around such risk. The model includes predictors, which could represent for instance meteorological processes that provide insight into both the involved physical mechanisms and the temporal variability of compound events. Moreover, this model enables multivariate statistical downscaling of compound events. Downscaling is required to extend the compound events' risk assessment to the past or future climate, where climate models either do not simulate realistic values of the local variables driving the events or do not simulate them at all. Based on the developed model, we study compound floods, i.e. joint storm surge and high river runoff, in Ravenna (Italy). To explicitly quantify the risk, we define the impact of compound floods as a function of sea and river levels. We use meteorological predictors to extend the analysis to the past, and get a more robust risk analysis. We quantify the uncertainties of the risk analysis, observing that they are very large due to the shortness of the available data, though this may also be the case in other studies where they have not been estimated. Ignoring the dependence between sea and river levels would result in an underestimation of risk; in particular, the expected return period of the highest compound flood observed increases from about 20 to 32 years when switching from the dependent to the independent case.

Societally relevant weather impacts typically result from compound events, which are rare combinations of weather and climate drivers. Focussing on four event types arising from different combinations of climate variables across space and time, here we illustrate that robust analyses of compound events — such as frequency and uncertainty analysis under present-day and future conditions, event attribution to climate change, and exploration of low-probability-high-impact events — require data with very large sample size. In particular, the required sample is much larger than that needed for analyses of univariate extremes. We demonstrate that Single Model Initial-condition Large Ensemble (SMILE) simulations from multiple climate models, which provide hundreds to thousands of years of weather conditions, are crucial for advancing our assessments of compound events and constructing robust model projections. Combining SMILEs with an improved physical understanding of compound events will ultimately provide practitioners and stakeholders with the best available information on climate risks.

Climate models are the major tools to study the climate system and its evolutions in the future. However, climate simulations often present statistical biases and have to be corrected against observations before being used in impact assessments. Several bias correction (BC) methods have therefore been developed in the literature over the last 2 decades, in order to adjust simulations according to historical records and obtain climate projections with appropriate statistical attributes. Most of the existing and popular BC methods are univariate, i.e., correcting one physical variable and one location at a time and, thus, can fail to reconstruct inter-variable, spatial or temporal dependencies of the observations. These remaining biases in the correction can then affect the subsequent analyses. This has led to further research on multivariate aspects for statistical postprocessing BC methods. Recently, some multivariate bias correction (MBC) methods have been proposed, with different approaches to restore multidimensional dependencies. However, these methods are not yet fully apprehended by researchers and practitioners due to differences in their applicability and assumptions, therefore leading potentially to different results. This study is intended to intercompare four existing MBCs to provide end users with aid in choosing such methods for their applications. For evaluation and illustration purposes, these methods are applied to correct simulation outputs from one climate model through a cross-validation method, which allows for the assessment of inter-variable, spatial and temporal criteria. Then, a second cross-validation method is performed for assessing the ability of the MBC methods to account for the multidimensional evolutions of the climate model. Additionally, two reference datasets are used to assess the influence of their spatial resolution on (M)BC results. Most of the methods reasonably correct inter-variable and intersite correlations. However, none of them adjust correctly the temporal structure as they generate bias-corrected data with usually weak temporal dependencies compared to observations. Major differences are found concerning the applicability and stability of the methods in high-dimensional contexts and in their capability to reproduce the multidimensional changes in the model. Based on these conclusions, perspectives for MBC developments are suggested, such as methods to adjust not only multivariate correlations but also temporal structures and allowing multidimensional evolutions of the model to be accounted for in the correction.

ERA-40 reanalyses, and simulations from three regional climate models (RCMs) (ALADIN, LMDZ, and WRF) and from one statistical downscaling model (CDF-t) are used to evaluate the uncertainty in downscaling of wind, temperature, and rainfall cumulative distribution functions (CDFs) for eight stations in the French Mediterranean basin over 1991–2000. The uncertainty is quantified using the Cramer-von Mises score (CvM) to measure the "distance" between the simulated and observed CDFs. The ability of the three RCMs and CDF-t to simulate the "climate" variability is quantified with the explained variance, variance ratio and extreme occurrence. The study shows that despite their differences, the three RCMs display very similar performance. In terms of global distributions (i.e. CvM), all models perform better than ERA-40 for both seasons and variables. However, looking at variance criteria, RCMs are not always much better than ERA-40 reanalyses, whereas CDF-t produces accurate results when applied to ERA-40. In a second step, a combined statistical/dynamical downscaling approach has been used, consisting in applying CDF-t to the RCM outputs. It shows that CDF-t applied to the RCM outputs does not necessarily produce better results than those from CDF-t directly applied to ERA-40. It also shows that CDF-t applied to RCMs generally improves the downscaled CDFs and that the "additional" added value of CDF-t applied to the RCMs is independent of the performance of the RCMs in terms of CvM, explained variance, variance ratio and extreme occurrence.

This study focuses on how the treatment of the rainfall occurrences in bias correction (BC) contexts may affect the resulting precipitation, both in terms of occurrence and intensity. Three methodologies are compared—the “direct approach” (DA), the “Threshold Adaptation” approach (TA), and the “Positive Approach” (Pos)—as well as a method called “Singularity Stochastic Removal” (SSR) specifically developed for precipitation, all based on the same adjustment technique. Unlike the three other models, SSR allows dealing in the same way with the situations where the precipitation model has too many wet days or not with respect to the reference data. SSR also avoids separating the correction of the occurrence from that of the intensity, which constitutes a flexible tool. First, the four approaches are applied to a historical regional climate model precipitation run. Evaluations are realized through occurrence‐ and intensity‐related criteria. Although SSR, DA, and Pos may be close to each other depending on the criterion, in general, SSR provides the best results when all criteria are accounted for. This is even more true when the classical assumption that “the model precipitation had too many wet days” does not hold. The BC methods are also intercompared over the 2071–2100 period. The different BC methods are in agreement with previous studies, with relatively equivalent evolutions from 1976–2005 to 2071–2100, although nuances are present from one BC method to another. As a global conclusion, the SSR method for precipitation is a good compromise to correct both occurrences and intensities.

Climate simulations often suffer from statistical biases with respect to observations or reanalyses. It is therefore common to correct (or adjust) those simulations before using them as inputs into impact models. However, most bias correction (BC) methods are univariate and so do not account for the statistical dependences linking the different locations and/or physical variables of interest. In addition, they are often deterministic, and stochasticity is frequently needed to investigate climate uncertainty and to add constrained randomness to climate simulations that do not possess a realistic variability. This study presents a multivariate method of rank resampling for distributions and dependences (R²D²) bias correction allowing one to adjust not only the univariate distributions but also their inter-variable and inter-site dependence structures. Moreover, the proposed R²D² method provides some stochasticity since it can generate as many multivariate corrected outputs as the number of statistical dimensions (i.e., number of grid cell × number of climate variables) of the simulations to be corrected. It is based on an assumption of stability in time of the dependence structure – making it possible to deal with a high number of statistical dimensions – that lets the climate model drive the temporal properties and their changes in time. R²D² is applied on temperature and precipitation reanalysis time series with respect to high-resolution reference data over the southeast of France (1506 grid cell). Bivariate, 1506-dimensional and 3012-dimensional versions of R²D² are tested over a historical period and compared to a univariate BC. How the different BC methods behave in a climate change context is also illustrated with an application to regional climate simulations over the 2071–2100 period. The results indicate that the 1d-BC basically reproduces the climate model multivariate properties, 2d-R²D² is only satisfying in the inter-variable context, 1506d-R²D² strongly improves inter-site properties and 3012d-R²D² is able to account for both. Applications of the proposed R²D² method to various climate datasets are relevant for many impact studies. The perspectives of improvements are numerous, such as introducing stochasticity in the dependence itself, questioning its stability assumption, and accounting for temporal properties adjustment while including more physics in the adjustment procedures.