Compound events, arising from the combinations of multiple interacting underlying physical drivers, have gained increasing attention over the past decade with a wide range of applications, including floods, droughts, and wildfires. This growing body of research has advanced both the conceptual understanding and statistical modeling of compound events, often emphasizing the role of dependence between underlying drivers. Building on this foundation, we recognize the need to further describe hydrological and climate phenomena not only through the overall tendency of contributing physical drivers to interact but also by considering the individual combinations of drivers leading to compound events, regardless of whether these drivers are statistically dependent. Here, we introduce the concepts of structural and transient compoundness as system properties of compound events. Structural compoundness quantifies the overall contribution of each driver to the generative mechanism of the compound variable, while transient compoundness captures the role of each driver in the individual realization of the compound variable. This will ultimately improve risk assessment and mitigation strategies. Indeed, by applying these concepts to two types of compound events, river discharge at confluences and hot and dry events, we show that structural and transient compoundness can inform modeling choices and enhance system understanding, with both the dependence and magnitude of the drivers playing critical roles in shaping compound events. Incorporating structural and transient compoundness enhances scientific modeling and, at the same time, improves risk assessment, guiding adaptation strategies for persistent (structural) and temporary (transient) risks.

Study Region: The study examines the Geul River basin in the southern Netherlands, a small (343 km²), hilly, rain-fed catchment characterised by a rapid rainfall-runoff response and exposure to both floods and droughts. Recent extremes, including the July 2021 flood and multiple dry summers, make the basin a relevant case study for understanding transitions between these opposite hydrological conditions. 

Study Focus: Transitions between drought-flood and flood-drought events were analysed using observations and hydrological simulations for 1982–2018. Floods and droughts were defined from meteorological thresholds and extended by an empirically derived catchment response time to capture hydrological effects. The role of antecedent precipitation, temperature, streamflow, soil moisture, and groundwater storage on subsequent event’s hydrological response was assessed using correlation and distribution (Kolmogorov–Smirnov) analyses. 

New Hydrological Insights for the Region: Antecedent droughts were associated with lower flood peaks, likely reflecting greater absorption of rainfall by dry soils prior to runoff generation. In contrast, antecedent floods were not associated with a consistent mitigation of streamflow response during subsequent droughts, consistent with continued streamflow recession from prior high flows. Groundwater showed a slower and more gradual adjustment than surface fluxes at the event scale, consistent with sub-seasonal storage buffering. Overall, opposite antecedent conditions in the Geul basin tend to moderate, rather than amplify, subsequent extremes. These findings emphasise the importance of considering antecedent catchment conditions and longer-term subsurface storage when evaluating flood and drought interactions in regional water management.

Rock groins in the Elbe Estuary are constructed to maintain proper water levels for navigation and for embankment erosion protection. At certain localities, significant damages to rock groins have been observed due to the primary ship-generated waves. Primary waves are generated along the ship's hull and then propagate toward the river banks and groin fields, appearing in the interaction with the structures as a turbulent overflow phenomenon. Eventually, this overflowing may cause damages mainly to the crest and leeward side of the groins. Since this overflowing is the most pronounced with large primary waves at certain water levels, the estimation of the probabilities of extreme primary waves is a key element for a safe and reliable design of groins. For this goal, nonparametric Bayesian networks (NPBNs) are used here to infer the probability distribution function of the extreme primary wave heights at the tip of a groin in the Elbe Estuary. Results demonstrate the suitability of the NPBN in their prediction. The model framework allows the designer to predict the probabilities of primary ship-generated waves at groins when the information of ship dimensions, nautical parameters, and waterway geometry is available. These probabilities can later be used for design purposes for current and future conditions.

Coastal flooding events pose a critical risk in delta areas, since they are characterized by population growth and urban expansion. A better understanding of Extreme Water Levels (EWLs), the mechanisms generating them, and their components, i.e., astronomical tide and storm surge is of great importance as they drive the maintenance and design of flood protection systems. Therefore, a statistical investigation of them can provide new insights for more reliable flood risk mitigation infrastructures. In this study, we analyse these components and compare different probabilistic methods i.e., univariate extreme value analysis, copula functions, and Joint Probability Method (JPM) for the better estimation of EWLs. We use Hoek van Holland (NL) as a representative case study, since the dynamic conditions of this deltaic environment with man-made infrastructures render the area of strategic importance. The results indicate that a more accurate estimate of the declustering time between extreme events can be achieved using correlation of high surges and high wind speeds, taking into consideration also the wind direction. In the Southwest Delta this time estimated to be around 4 days. Furthermore, the EWLs components, i.e., surge and astronomical tide, show negative dependence. From the comparison between statistical approaches to model EWLs, results show that EWLs estimated via EVA and JPM do not vary significantly, while copulas’ seems to outperform the other methods. However, the selection of the proper copula to show the dependence is critical. As a conclusion, the analysis of the dependence between tides and storm surges can lead to more robust inferences of EWLs.

An innovative technique based on the use of environmental DNA was proposed by Ficetola et al. (2008) for performing biodiversity assessment. Applications of this technique in rivers are still scarce, due to the limited knowledge on the dynamics of eDNA traces. Here, using the open source dataset by Carraro et al. 2020, we investigate the transport of eDNA. We first investigate the ability of eDNA to capture species abundance observed by classical methods via correlation measures. Finally, we setup a numerical simulation for evaluating the transport induced by advection and diffusion and the eDNA decay coefficient.

Extreme surges and rainfall represent major driving factors for compound flooding in estuary regions along the Chinese coast. The combined effect of extreme surges and rainfall (that is, compound floods) might lead to greater impacts than if the drivers occurred in isolation. Hence, understanding the frequency and severity of compound flooding is important for improving flood hazard assessment and compound flood resilience in coastal cities. In this study, we examined the dependence between extreme surges and corresponding rainfall events in 26 catchments along the Chinese coastline during typhoon and non-typhoon seasons using copula functions, to identify where the two drivers more often occur together and the implication for flood management in these locations. We found that the interaction between flood drivers is statistically significant in 10 catchments located around Hainan Island (south) and Shanghai, where surge peaks occur mainly during the typhoon season and around the Bohai Sea (north), where surge peaks occur mainly during the non-typhoon season. We further applied the copula-based framework to model the dependence between surge peaks and associated rainfall and estimate their joint and conditional probability in two specific locations—Hainan Island and the Bohai Sea, where the correlation between flood drivers is statistically significant. We observed that in Hainan Island where most of the surge peaks occur during the typhoon season, extreme rainfall events during the typhoon season are generally more intense compared to annual maxima rainfall. In contrast, around the Bohai Sea where surge peaks occur mainly outside the typhoon season, rainfall is less intense than annual maxima rainfall. These results show that the interaction between extreme surges and rainfall can provide valuable insight when designing coastal and urban infrastructure, especially in highly populated urban areas prone to both coastal and pluvial flooding, such as many Chinese coastal cities.

Coastal hazards represent an existential threat to Italian coastal regions since they host important economic centers related to manufacturing and tourism. Knowledge of potential extreme sea levels (ESL), their component, and their interactions are essential to better evaluate potentially hazardous future extreme events in a changing climate and possible effects on the design of coastal structures. Hence, in this study, we investigate the interaction between tide and surge for extreme conditions of sea level in 9 locations along the Italian coastline facing both the Adriatic and the Tyrrhenian Seas and all in a semi-diurnal tidal regime. First, we introduce a novel dependence metric, i.e., the β factor, in support of the classical Kendall's τ to preliminary assess the effect of the dependence between tide and surge when conditioned on ESL on the variance of ESL, and then we quantify such effect using a copula-based framework. Here, the surge component is determined via the concept of skew surge, i.e., the difference within a tidal cycle between the maximum observed sea level and the predicted high tide (irrespective of the time of occurrence), to remove any random effect in the interaction due to the timing of the tidal peak. Our results show that ESL components, i.e., tide and skew surge, are negatively dependent, i.e., high/low values of the surge are associated with low/high values of the tide, in all the stations investigated, and that higher values of dependence, measured with Kendall's τ, can be observed in the Adriatic Sea, around −0.6, while lower values in the Tyrrhenian Sea, around −0.45, with the exception of Palermo. In general, an increase in ESL for higher quantiles is observed when the negative dependence between tide and surge is explicitly modeled. Moreover, our results show that the β factor can help quantify the relative contribution of tide and surge on the variability of ESLs. More specifically, small β refers to cases when tide and surge are similar in their magnitude, e.g., Palermo, while values of β close to 1 refer to the case when one component dominates the other. In the former case, ESLs obtained from a model that does not account for the dependence between tide and surge will result in ESL estimates with larger variability. On the other hand, when one component dominates the other, the variability of ESLs is slightly influenced by the model used for tide and surge, i.e., dependent or independent. We can then conclude that by explicitly modeling the dependence between tide and skew surge we can improve estimates and inference of ESLs.

Compound flooding is generated when two or more flood drivers occur simultaneously or in close succession. Multiple drivers can amplify each other and lead to greater impacts than when they occur in isolation. A better understanding of the interdependence between flood drivers would facilitate a more accurate assessment of compound flood risk in coastal regions. This study employed the D-Flow Flexible Mesh model to simulate the historical peak coastal water level, consisting of the storm surge, astronomical tide, and relative sea level rise (RSLR), in Shanghai over the period 1961-2018. It then applies a copula-based methodology to calculate the joint probability of peak water level and rainfall during historical tropical cyclones (TCs) and to calculate the marginal contribution of each driver. The results indicate that the astronomical tide is the leading driver of peak water level, followed by the contribution of the storm surge. In the longer term, the RSLR has significantly amplified the peak water level. This study investigates the dependency of compound flood events in Shanghai on multiple drivers, which helps us to better understand compound floods and provides scientific references for flood risk management and for further studies. The framework developed in this study could be applied to other coastal cities that face the same constraint of unavailable water level records.

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 managed water system 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 an impact-focused multivariate statistical framework to model the dependence between these flooding drivers and the resulting return periods of inland water levels. This framework is applied to the same managed water system using the aforementioned large ensemble. Composite analysis is used to guide the selection of suitable predictors and to obtain an impact function that optimally describes the relationship between high inland water levels (the impact) and the explanatory predictors. This is complex due to the high degree of human management affecting the dynamics of the water level. Training the impact function with subsets of data uniformly distributed along the range of water levels plays a major role in obtaining an unbiased performance. The dependence structure between the defined predictors is modelled 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. Regarding the return levels, this is quantified by a root-mean-square deviation of 0.02gm. The proposed framework is able to produce robust estimates of compound extreme water levels for a highly managed hydrological system. Even though the framework has only been applied and validated in one study area, it shows great potential to be transferred to other areas. 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.

Compound weather and climate events are combinations of climate drivers and/or hazards that contribute to societal or environmental risk. Studying compound events often requires a multidisciplinary approach combining domain knowledge of the underlying processes with, for example, statistical methods and climate model outputs. Recently, to aid the development of research on compound events, four compound event types were introduced, namely (a) preconditioned, (b) multivariate, (c) temporally compounding, and (d) spatially compounding events. However, guidelines on how to study these types of events are still lacking. Here, we consider four case studies, each associated with a specific event type and a research question, to illustrate how the key elements of compound events (e.g., analytical tools and relevant physical effects) can be identified. These case studies show that (a) impacts on crops from hot and dry summers can be exacerbated by preconditioning effects of dry and bright springs. (b) Assessing compound coastal flooding in Perth (Australia) requires considering the dynamics of a non-stationary multivariate process. For instance, future mean sea-level rise will lead to the emergence of concurrent coastal and fluvial extremes, enhancing compound flooding risk. (c) In Portugal, deep-landslides are often caused by temporal clusters of moderate precipitation events. Finally, (d) crop yield failures in France and Germany are strongly correlated, threatening European food security through spatially compounding effects. These analyses allow for identifying general recommendations for studying compound events. Overall, our insights can serve as a blueprint for compound event analysis across disciplines and sectors.

Bayesian Networks (BNs) are probabilistic, graphical models for representing complex dependency structures. They have many applications in science and engineering. Their particularly powerful variant – Non-Parametric BNs – are for the first time implemented as an open-access scriptable code, in the form of a MATLAB toolbox “BANSHEE”.¹ The software allows for quantifying the BN, validating the underlying assumptions of the model, visualizing the network and its corresponding rank correlation matrix, and finally making inference with a BN based on existing or new evidence. We also include in the toolbox, and discuss in the paper, some applied BN models published in most recent scientific literature.

Warming temperatures and severe droughts have contributed to increasing fire activity in California. Decadal average summer temperature in California has increased by 0.8 °C during 1984–2014, while the decadal total size of large fires has expanded by a factor of 2.5. This study proposes a multivariate probabilistic approach for quantifying changes to fire risk given different climatic conditions. Our results indicate that the risk of large fires in California increases substantially in response to unit degree changes in summer temperature. The probability of annual mean fire size exceeding its long-term average increases by 30% when summer temperature anomaly increases by 1 °C (from −0.5 °C to + 0.5 °C). Furthermore, the probability of annual average fire size exceeding its long-term average doubles when the annual precipitation decreases from the 75th (wet) to the 25th (dry) percentile. The proposed model can help manage fire-prone regions where fire activity is expected to intensify under projected global warming.

Climate extremes threaten human health, economic stability, and the well-being of natural and built environments (e.g., 2003 European heat wave). As the world continues to warm, climate hazards are expected to increase in frequency and intensity. The impacts of extreme events will also be more severe due to the increased exposure (growing population and development) and vulnerability (aging infrastructure) of human settlements. Climate models attribute part of the projected increases in the intensity and frequency of natural disasters to anthropogenic emissions and changes in land use and land cover. Here, we review the impacts, historical and projected changes,and theoretical research gaps of key extreme events (heat waves, droughts, wildfires, precipitation, and flooding). We also highlight the need to improve our understanding of the dependence between individual and interrelated climate extremes because anthropogenic-induced warming increases the risk of not only individual climate extremes but also compound (co-occurring) and cascading hazards. Climate hazards are expected to increase in frequency and intensity in a warming world. Anthropogenic-induced warming increases the risk of compound and cascading hazards. We need to improve our understanding of causes and drivers of compound and cascading hazards.