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Compound flooding is a multidimensional consequence of the joint impact of multiple intercorrelated drivers, such as oceanographic, hydrologic, and meteorological. These individual drivers exhibit interdependence due to common forcing mechanisms. If they occur simultaneously or successively, the probability of their joint occurrence will be higher than expected if considered separately. The copula-based multivariate joint analysis can effectively measure hydrologic risk associated with compound events. Because of the involvement of multiple drivers, it is necessary to switch from bivariate (2D) to trivariate (3D) analyses. This study presents an original trivariate probabilistic framework by incorporating multivariate hierarchal models called asymmetric or fully nested Archimedean (or FNA) copula in the joint analysis of compound flood risk. The efficacy of the derived FNA copulas model, together with symmetric Archimedean and Elliptical class copulas, are tested by compounding the joint impact of rainfall, storm surge, and river discharge observations through a case study at the west coast of Canada. The obtained copula-based joint analysis is employed in multivariate analysis of flood risks in trivariate and bivariate primary joint and conditional joint return periods. The estimated joint return periods are further employed in estimating failure probability statistics for assessing the trivariate (and bivariate) hydrologic risk associated with compound events. The statistical tests found the fully nested Frank copula outperforms symmetric 3D copulas. Our work confirms that for practical compound flood risk analysis together with bivariate or univariate return periods, it is essential to account for the trivariate joint return periods to assess the expected compound flood risk and strength of influence of different variables if they occur simultaneously or successively. The bivariate (also univariate) events produce a lower failure probability than trivariate analysis for the OR-joint cases. Thus, ignoring the compounding impacts via trivariate joint analysis can significantly underestimate failure probability and joint return period.

The interaction between oceanographic, meteorological, and hydrological factors can result in an extreme flooding scenario in the low-lying coastal area, called compound flooding (CF) events. For instance, rainfall and storm surge (or high river discharge) can be driven by the same meteorological forcing mechanisms, tropical or extra-tropical cyclones, resulting in a CF phenomenon. The trivariate distributional framework can significantly explain compound events’ statistical behaviour reducing the associated high-impact flood risk. Resolving heterogenous dependency of the multidimensional CF events by incorporating traditional 3D symmetric or fully nested Archimedean copula is quite complex. The main challenge is to preserve all lower-level dependencies. An approach based on decomposing the full multivariate density into simple local building blocks via conditional independence called vine or pair-copulas is a much more comprehensive way of approximating the trivariate flood dependence structure. In this study, a parametric vine copula of a drawable (D-vine) structure is introduced in the trivariate modelling of flooding events with 46 years of observations of the west coast of Canada. This trivariate framework searches dependency by combining the joint impact of annual maximum 24-h rainfall and the highest storm surge and river discharge observed within the time ±1 day of the highest rainfall event. The D-vine structures are constructed in three alternative ways by permutation of the conditioning variables. The most appropriate D-vine structure is selected using the fitness test statistics and estimating trivariate joint and conditional joint return periods. The investigation confirms that the D-vine copula can effectively define the compound phenomenon’s dependency. The failure probability (FP) method is also adopted in assessing the trivariate hydrologic risk. It is observed that hydrologic events defined in the trivariate case produce higher FP than in the bivariate (or univariate) case. It is also concluded that hydrologic risk increases (i) with an increase in the service design life of the hydraulic facilities and (ii) with a decrease in return periods.

The design rainfall intensity and its return period of the combined interceptor sewer is an important factor affecting combined sewer overflow (CSO) occurrence. However, we often use the interceptor ratio (or interceptor multiple, n0) to design the interceptor sewer, and its equivalent design return period is often ignored. In this study, a low return period rainfall formula modeling method was proposed to estimate this return period. First, a new rainfall event separation approach was especially developed, and the minimum interevent time (MIET) was set to time of concentration of the tributary area corresponding to the most downstream interceptor well. Second, a new rainfall intensity sampling algorithm, annual multi—event—maxima (AMEM) sampling algorithm, was put forward. For this sampling algorithm, several maxima of rainfall intensity should be sampled annually, and only one maximum is sampled for each rainfall event. In addition, the empirical frequency values of the above sampled rainfall intensities can be obtained according to the mathematical expectation formula (Weibull formula). After comparison, the lognormal distribution was selected for the theoretical probability density function. Finally, parameters of the low return period rainfall intensity formula were estimated using three-parameter Horner formula and MCMC (Markov Chain Monte Carlo) algorithm. A case study was conducted to demonstrate the proposed method based on the recorded rainfall data from a meteorological station in southwestern China and a combined sewer system. Results revealed that: (1) A MIET determination method was proposed according to independence of CSO events. (2) An annual multi-event-maxima (AMEM) sampling was proposed for collecting samples of the low return period rainfall intensity. (3) For the case study, the best-fit distribution for low return period rainfall intensity was lognormal distribution. (4) Resulted low return period rainfall intensity formula was provided.

With the rapid urbanization, waterlogging losses caused by rainstorm are becoming increasingly severe. In order to reveal the correlations between rainstorm characteristic elements, and make the calculation of rainstorm return period more reasonable and objective, this study established the joint distribution models of rainstorm elements by using copula theory based on the rainfall data in a Chinese megacity, Zhengzhou. Then their combined design values of primary return period (PRP) and secondary return period (SRP) are derived by the maximum probability method and the same frequency method. Finally, the rainstorm pattern was acquired associated with Pilgrim & Cordery method (PC). The results indicate that the calculation of rainstorm return period (RRP) with SRP is more reasonable than PRP. For same RRP, the rainstorm volume (RV) of “Or” return period type is largest, while the “And” return period’s is smallest, and the RVs of Kendall return period and survival Kendall return period are between them. Concerning Kendall return period, the RVs calculated by the maximum probability method and the same frequency method are pretty close, and their relative deviations are from -5.84% to 4.69%. Compared to “Or” return period, the rainstorm patterns of Kendall return period can reduce the magnitude and investment of the stormwater infrastructure. Moreover, the rainfall with designed rainstorm pattern of survival Kendall return period mainly concentrated before the rain peak in contrast with Kendall return period.

Balochistan province is highly drought-prone and affected by almost every drought in Pakistan. This study is conducted to evaluate and project drought for the planning of water resources in Baluchistan, Pakistan. Drought characteristics of duration and severity were extracted from the standardized precipitation index (SPI). Statistical tools showed a high positive correlation and skewed nature between drought duration and severity. The sites were checked for identical drought conditions through homogeneity measures. Best-fitted regional probability distributions were selected for both drought characteristics and transformed into uniformly distributed values over [0, 1]. The bivariate Gumbel-Hougaard (G-H) copula function was selected for joint and conditional drought projections. The G-H copula function has the property to measure upper tail dependence which is highly important for measuring extreme drought conditions. Three types of joint and two types of conditional drought projections were found numerically and graphically using selected years of return periods. Contour lines were drawn for possible combinations of drought duration and severity to show the drought variability within the region. According to projections, the drought duration and severity increase with the increase in return periods. Conditional projections have high values of severity (or duration) return periods because drought at a fixed duration (or severity) takes a long time to occur. The results show changes in drought conditions and might help in drought mitigation and water planning in Balochistan, Pakistan. There is no such detailed study of drought risk assessment in the area. This effort will fill the research gap in the existing literature in the study area.

Desde hace dos décadas, la estimación de las crecientes de diseño de los embalses se aborda con el enfoque multivariado más simple: el bivariado. Lo anterior se aceptó pues se demostró que los embalses no son sensibles al tiempo al gasto máximo, y que tal gasto y volumen están correlacionados entre ellos y este último con la duración total del hidrograma de la creciente. En este estudio se ajustó la distribución Gumbel bivariada o modelo logistico a los 61 datos anuales de gasto pico y volumen de las crecientes de entrada a la presa Adolfo Ruiz Cortines (Mocúzari) en el río Mayo del estado de Sonora, México. Este proceso abarca las ocho etapas siguientes: (1) selección y prueba de los registros por procesar; (2) verificación de la aleatoriedad de los registros anuales; (3) aceptación de las funciones marginales Gumbel; (4) estimación de las probabilidades empíricas conjuntas; (5) validación del modelo Logístico; (6) verificación de las restricciones de probabilidad; (7) estimación de eventos de diseño, gasto pico y volumen, univariados híbridos, y (8) estimación de eventos de diseño conjuntos. En la etapa 1 primero se hace una selección subjetiva y después se verifica con el Test PPCC. La etapa 2 se realiza con base en el Test de Wald-Wolfowitz. Las etapas 3 y 5 utilizan el Test de Kolmogórov-Smirnov. En la etapa 7 se definen gastos de diseño, y se obtienen volúmenes por regresión y probabilidad condicional. En contraste, en la etapa 8 se obtienen diversos eventos de gasto pico y volumen que pertenecen al subgrupo de parejas criticas en las gráficas del periodo de retorno conjunto T'(Q,V). Por último, se formulan las Conclusiones, las cuales destacan las ventajas del análisis de frecuencias conjunto bivariado y la sencillez de aplicación y prueba del modelo Logístico.

The floods in our country every year cause damage and endanger the reservoirs. Therefore, its hydrological dimensioning is based on the hydrograph of the design flood, and its most straightforward estimation is based on the joint frequency analysis of the annual peak flow and volume. In this study, the bivariate general extreme values distribution (GVEb) was adjusted to the record of the 55 annual floods at the La Cuña hydrometric station on the Río Verde of Hydrological Region No. 12-3, Mexico. This study encompasses the following nine stages: (1) selection and testing of annual records; (2) verification of the randomness of the records; (3) estimation of the joint empirical probabilities; (4) adjustment of the GVEb function through the maximum likelihood method; (5) validation of the GVEb function; (6) ratification of GVE marginal functions; (7) verification of probability constraints; (8) estimation of hybrid univariate design events, and (9) estimation of joint design events and selection of the critical subgroup. In stage 1, a simple test is applied based on the shape parameter of the marginal GVE. Stage 2 is carried out based on the Wald-Wolfowitz Test. In stage 4, the Complex algorithm is used. Stages 5 and 6 use the Kolmogorov-Smirnov Test. In stage 9, the graphs of the joint return period of type AND are used. Finally, conclusions are formulaated, which highlight the maximization approach adopted and the advantages of the bivariate joint frequency analysis through the GVEb.

Human impacts on fire regimes accumulated slowly with the evolution of modern humans able to ignite fires and manipulate landscapes. Today, myriad voices aim to influence fire in grassy ecosystems to different ends, and this is complicated by a colonial past focused on suppressing fire and preventing human ignitions. Here, I review available evidence on the impacts of people on various fire characteristics such as the number and size of fires, fire intensity, fire frequency and seasonality of fire in African grassy ecosystems, with the intention of focusing the debate and identifying areas of uncertainty. Humans alter seasonal patterns of fire in grassy systems but tend to decrease total fire emissions: livestock have replaced fire as the dominant consumer in many parts of Africa, and fragmented landscapes reduce area burned. Humans alter the season and time of day when fires occur, with important implications for fire intensity, tree–grass dynamics and greenhouse gas (GHG) emissions. Late season fires are more common when fire is banned or illegal: these later fires are far more intense but emit fewer GHGs. The types of fires which preserve human livelihoods and biodiversity are not always aligned with the goal of reducing GHG concentrations. Current fire management challenges therefore involve balancing the needs of a large rural population against national and global perspectives on the desirability of different types of fire, but this cannot happen unless the interests of all parties are equally represented. In the future, Africa is expected to urbanize and land use to intensify, which will imply different trajectories for the continent's fire regimes. This article is part of the themed issue ‘The interaction of fire and mankind.

The Paris agreement focused global climate mitigation policy on limiting global warming to 1.5 or 2 °C above pre-industrial levels. Consequently, projections of hazards and risk are increasingly framed in terms of global warming levels rather than emission scenarios. Here, we use a multimethod approach to describe changes in extreme sea levels driven by changes in mean sea level associated with a wide range of global warming levels, from 1.5 to 5 °C, and for a large number of locations, providing uniform coverage over most of the world’s coastlines. We estimate that by 2100 ~50% of the 7,000+ locations considered will experience the present-day 100-yr extreme-sea-level event at least once a year, even under 1.5 °C of warming, and often well before the end of the century. The tropics appear more sensitive than the Northern high latitudes, where some locations do not see this frequency change even for the highest global warming levels.Combining previous estimates in a multimethod approach, extreme sea levels are assessed under global warming levels of 1.5–5 °C at over 7,000 coastal sites worldwide. By 2100 or before, about 50% of locations exhibit present-day 100-year extreme sea levels at least once per year, even at 1.5 °C of warming.

In June 2021, the Pacific Northwest experienced a heatwave that broke all previous records. Estimated return levels based on observations up to the year before the event suggested that reaching such high temperatures is not possible in today's climate. We here assess the suitability of the prevalent statistical approach by analyzing extreme temperature events in climate model large ensemble and synthetic extreme value data. We demonstrate that the method is subject to biases, as high return levels are generally underestimated and, correspondingly, the return period of low‐likelihood heatwave events is overestimated, if the underlying extreme value distribution is derived from a short historical record. These biases have even increased in recent decades due to the emergence of a pronounced climate change signal. Furthermore, if the analysis is triggered by an extreme event, the implicit selection bias affects the likelihood assessment depending on whether the event is included in the modeling. Plain Language Summary In June 2021, the Pacific Northwest experienced a record‐breaking heatwave event. Based on historical data, the scientific community has applied statistical models to understand how likely this event was to occur. However, due to the record‐shattering nature of this particular heatwave, the model suggested that reaching such high temperatures should not have been possible. In this study, we evaluate the accuracy of these statistical models in describing the occurrence probability of extreme events. We find that the current models tend to underestimate the occurrence probability and that the bias has become more pronounced in recent years due to climate change. Finally, we assess how the way extreme events are included in the model can also affect the accuracy of estimates. Key Points Standard return period estimates of temperature extremes are systematically overestimated in short records under non‐stationary conditions The small‐sample bias in maximum likelihood estimates is found both for extremes in climate model data and in synthetic data experiments Future analysis should account for the statistical implications of the selection bias if the analysis is triggered by an extreme event