Statistical tools are crucial for a variety of hydrological applications, whether to model processes and enhance understanding and knowledge or to design infrastructure systems. Given the rapid evolution of statistical methods and the need for a solid theoretical foundation for their correct application, a multidisciplinary community STAtistics in HYdrology Working Group (STAHY-WG) aggregated under the International Association of Hydrological Sciences (IAHS) umbrella to contribute to this research field. Now, more than 15 years since its inception, this paper summarizes the main achievements of this productive community collaboration in four (of many) branches of statistical hydrology: extreme value analysis, multivariate analysis, time series analysis, and regionalization. The aim is to provide an overview of recent developments, offer practical suggestions (e.g. software packages), and outline future challenges to support scientists and practitioners in their endeavours within the realm of statistical hydrology studies.@en

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.

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Coastal regions have experienced significant environmental changes and increased vulnerability to floods caused by the combined effect of multiple flood drivers such as storm surge, heavy rainfall and river discharge, i.e., compound floods. Hence, for a sustainable development of coastal cities, it is necessary to understand the spatiotemporal dynamics and future trends of compound flood hazard. While the statistical dependence between flood drivers, i.e., rainfall and storm surges, has been extensively studied, the sensitivity of the inundated areas to the relative timing of a driver's individual peaks is less understood and location dependent. To fill this gap, here we propose a framework combining a statistical dependence model for compound event definition and a hydrodynamic model to assess inundation maps of compound flooding from storm surge and rainfall during typhoon season in Shanghai. First, we determine the severity of the joint design event, i.e., peak surge and precipitation, based on the copula model. Second, we use the same frequency amplification (SFA) method to transform the design event values in hourly time series so that they represent boundary conditions to force hydrodynamic models. Third, we assess the sensitivity of inundation maps to the time lag between storm surge peak and rainfall. Finally, we define flood zones based on the primary flood driver, and we delineate flood zones under the worst compound flood scenario. The study highlights that the temporal delay between storm surge and rainfall plays a pivotal role in shaping the dynamics of flooding events. More specifically, that the peak rainfall occurs 2 h before the peak storm surge would cause the deepest average cumulative inundation depth. At the same time, the results show that in Shanghai surge is the primary flood driver. High storm surge at the eastern part of the city (Wusongkou tidal gauge) propagates upstream in the Huangpu River, resulting in fluvial flooding in Shanghai city center and several surrounding districts. This calls for a better fluvial flooding control system hinging on the backwater effect during high surge in the upper and middle Huangpu River and in the newly added urbanized areas to ensure flood resilience. The proposed framework is useful to evaluate and predict flood hazard in coastal cities, and the results can provide guidance for urban disaster prevention and mitigation.@en

The Netherlands has traditionally focused on managing flood risk. However, the frequent occurrence of droughts in recent years has brought attention to managing both extremes. Transitions between these opposite extremes pose additional challenges to water management, requiring a trade-off between water storage during dry periods and flood control during wet periods. In this study, we develop a framework to define wet and dry meteorological events and study their transitions using timeseries of meteorological data namely, precipitation, temperature and potential evapotranspiration. The magnitudes of event characteristics are retained, which presents a different approach to the normalized climate indices (like the Standardized Precipitation Index) commonly used in literature. We apply this framework to the Dutch part of the Meuse River basin in northwestern Europe using climate observations between 1951 and 2022. Our analysis shows a statistically significant increase in the amount of water lost from potential evapotranspiration compared to water gained from precipitation between April and September of the water year and an increase in the length of this drying period over the past decades. Such trends in the drying period are related to variability in potential evapotranspiration caused by rising temperatures in the region, indicating the potential for increased water shortage in Spring and Summer due to future temperature increases. We also identify abrupt transitions between opposite extreme events where there is a lack of water at the end of the second event as meteorological situations that challenge water management due to overlapping impacts like flash flooding, less time for water storage, and reduced water availability. We see such conditions occur in 6% of the wet-dry transitions and 20% of the dry-wet transitions, highlighting meteorological scenarios to which the hydrological response of the catchment can be simulated to increase our understanding of the combined risk of floods and droughts.@en

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.

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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.

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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.

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In this paper we discuss PyBanshee, which is a Python-based open-source implementation of the MATLAB toolbox BANSHEE. PyBanshee constitutes the first fully open-source package to quantify, visualize and validate Non-Parametric Bayesian Networks (NPBNs). The architecture of PyBanshee is heavily based on its MATLAB predecessor. It presents the full implementation of existing tools and introduces new modules. Specifically, PyBanshee allows for: (i) choosing fully parametric one-dimensional margins, (ii) choosing different sample sizes for the model-validation tests based on the Hellinger distance, (iii) drawing user-defined sample sizes of the NPBN, (iv) sample-based conditioning sampling (similarly to the closed-source proprietary package UNINET by LightTwist Software) and (v) visualizing the comparison between the histograms of the unconditional and conditional marginal distributions. New detailed examples demonstrating new features are provided.@en

Non-parametric Bayesian networks (NPBNs) are graphical tools for statistical inference widely used for reliability analysis and risk assessment and present several advantages, such as the embedded uncertainty quantification and limited computational time for the inference process. However, their implementation in hydrological studies is still scarce. Hence, to increase our understanding of their applicability and extend their use in hydrology, we explore the potential of NPBNs to reproduce catchment-scale hydrological dynamics. Long-term data from 240 river catchments with contrasting climates across the United States from the Catchment Attributes and Meteorology for Large-sample Studies (CAMELS) data set will be used as actual means to test the utility of NPBNs as descriptive models and to evaluate them as predictive models for maximum daily river discharge in any given month. We analyse the performance of three networks, one unsaturated (hereafter UN-1), one saturated (hereafter SN-1), both defined only by hydro-meteorological variables and their bivariate correlations, and one saturated network (hereafter SN-C), consisting of the SN-1 network and including physical catchments' attributes. The results indicate that the UN-1 network is suitable for catchments with a positive dependence between precipitation and discharge, while the SN-1 network can also reproduce discharge in catchments with negative dependence. The latter can reproduce statistical characteristics of discharge (tested via the Kolmogorov–Smirnov statistic) and have a Nash–Sutcliffe efficiency (NSE) ≥0.5 in ∼40 % of the catchments analysed, receiving precipitation mainly in winter and located in energy-limited regions at low to moderate elevation. Further, the SN-C network, based on similarity of the catchments, can reproduce discharge statistics in ∼10 % of the catchments analysed. We show that once a NPBN is defined, it is straightforward to infer discharge and to extend the network itself with additional variables, i.e. going from the SN-1 network to the SN-C network. However, the results also suggest considerable challenges in defining a suitable NPBN, particularly for predictions in ungauged basins. These are mainly due to the discrepancies in the timescale of the different physical processes generating discharge, the presence of a “memory” in the system, and the Gaussian-copula assumption used for modelling multivariate dependence.@en

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.

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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.

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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.

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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.

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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.

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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.

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