Drought Occurrence Probability Analysis Using Multivariate Standardized Drought Index and Copula Function Under Climate Change

This study aims to investigate the effect of climate change on the probability of drought occurrence in central Iran. To this end, a new drought index called Multivariate Standardized Drought Index (MSDI) was developed, which is composed of the Standardized Precipitation Evapotranspiration Index (SPEI) and the Standardized Soil Moisture Index (SSI). The required data included precipitation, temperature (from CRU TS), and soil moisture (from the ESA CCA SM product) on a monthly time scale for the 1980–2016 period. Moreover, future climate data were downloaded from CMIP6 models under the latest SSPs-RCPs emission scenarios (SSP1-2.6 and SSP5-8.5) for the 2020–2056 period. Based on the NRMSE, Sn, and NS evaluation criteria, the Galambos and Clayton functions were selected to derive copula-based joint distribution functions in both periods. The results showed that more severe droughts and longer will occur in the future compared to the historical period and in particular under the SSP5-8.5 scenario. From the derived joint return period, a drought event with defined severity or duration will happen in a shorter return period as compared with the historical period. In other words, joint return period indicated a higher probability of drought occurrence in the future period. Moreover, the joint return period analysis revealed that the return period of mild droughts will remain the same, while it decresed over extreme droughts in the future.

A maximum entropy copula-based frequency analysis method for assessing bivariate drought risk: a case study of the Kaidu River Basin

In this study, a maximum entropy copula-based frequency analysis (MECFA) method is developed through integrating maximum entropy, copulas and frequency analysis into a general framework. The advantages of MECFA are that the marginal modeling requires no assumption and joint distribution preserves the dependence structure of drought variables. MECFA is applied to assessing bivariate drought frequency in the Kaidu River Basin, China. Results indicate that the Kaidu River Basin experienced 28 drought events during 1958–2011, and drought inter-arrival time is 10.8 months. The average duration is 6.2 months (severity 4.6), and the most severe drought event lasts for 35 months (severity 41.2) that occurred from June 1977 to March 1980. Results also disclose that hydrological drought index (HDI) 1 is suitable for drought frequency analysis in target year of return periods of 5 and 10, HDI 3, HDI 6 and HDI 12 are fit for the target year of return periods of 20, 50 and 100. The joint return period can be used as the upper bound of the target return period, and the joint return period that either duration or severity reaches the drought threshold can be used as the lower bound of the target return period.

Swell wave progression in the English Channel: implications for coastal monitoring

Energetic swell waves, particularly when they coincide with high water levels, can present significant coastal hazards. To better understand and predict these risks, analysis of the sea levels and waves that generate these events and the resulting coastal impacts is essential. Two energetic swell events, neither of which were predicted by modelled flood forecasts, occurred in quick succession in the English Channel. The first event, on 30 January 2021, produced moderate significant wave heights at or just below the 0.25 year return period along the southwest English coast, but combined with significant swell caused overtopping at East Beach in West Bay and at Chesil Beach. The second event, on 1 February 2021, generated the highest wave energy periods measured at many locations along the southern English coastline and, at high water, caused waves to run up over the promenades at Poole Bay and Christchurch Bay and caused overtopping at Hayling Island. Both events are described in detail, and their spatial footprints are mapped through a joint return period analysis using a copula function. It is found that typical joint return period analysis of water level and significant wave height underestimates potential impacts, while a joint consideration of water level and wave power (P) describes the 31 January event better and a joint consideration of water level and energy period (Te) best describes the 1 February event. Therefore, it is recommended that Te and P are adopted for coastal monitoring purposes, and that future studies further explore the use of both parameters for swell monitoring.

Time-varying copula and design life level-based nonstationary risk analysis of extreme rainfall events

Due to global climate change and urbanization, more attention has been paid to decipher the nonstationary multivariate risk analysis from the perspective of probability distribution establishment. Because of the climate change, the exceedance probability belonging to a certain extreme rainfall event would not be time invariant any more, which impedes the widely-used return period method for the usual hydrological and hydraulic engineering practice, hence calling for a time dependent method. In this study, a multivariate nonstationary risk analysis of annual extreme rainfall events, extracted from daily precipitation data observed at six meteorological stations in Haihe River basin, China, was done in three phases: (1) Several statistical tests, such as Ljung-Box test, and univariate and multivariate Mann-Kendall and Pettist tests were applied to both the marginal distributions and the dependence structures to decipher different forms of nonstationarity; (2) Time-dependent Archimedean and elliptical copulas combined with the Generalized Extreme Value (GEV) distribution were adopted to model the distribution structure from marginal and dependence angles; (3) A design life level-based (DLL-based) risk analysis associated with Kendall's joint return period (JRPken)and AND's joint return period (JRPand) methods was done to compare stationary and nonstationary models. Results showed DLL-based risk analysis through the JRPken method exhibited more sensitivity to the nonstationarity of marginal and bivariate distribution models than that through the JRPand method.

Estimations of statistical dependence as joint return period modulator of compound events – Part 1: Storm surge and wave height

The possibility of utilizing statistical dependence methods in coastal flood hazard calculations is investigated since flood risk is rarely a function of just one source variable but usually two or more. Source variables in most cases are not independent as they may be driven by the same weather event, so their dependence, which is capable of modulating their joint return period, has to be estimated before the calculation of their joint probability. Dependence and correlation may differ substantially from one another since dependence is focused heavily on tail (extreme) percentiles. The statistical analysis between surge and wave is performed over 32 river ending points along European coasts. Two sets of almost 35-year hindcasts of storm surge and wave height were adopted, and results are presented by means of analytical tables and maps referring to both correlation and statistical dependence values. Further, the top 80 compound events were defined for each river ending point. Their frequency of occurrence was found to be distinctly higher during the cold months, while their main low-level flow characteristics appear to be mainly in harmony with the transient nature of storms and their tracks. Overall, significantly strong values of positive correlations and dependencies were found over the Irish Sea; English Channel; and south coasts of the North Sea, Norwegian Sea, and Baltic Sea, with compound events taking place in a zero-lag mode. For the rest, mostly positive moderate dependence values were estimated even if a considerable number of them had correlations of almost zero or even a negative value.

Estimations of statistical dependence as joint return period modulator of compound events. Part I: storm surge and wave height

The possibility of utilising statistical dependence methods in coastal flood hazard calculations is investigated, since flood risk is rarely a function of just one source variable but usually two or more. Source variables in most cases are not independent as they may be driven by the same weather event, so their dependence, which is capable of modulating their joint return period, has to be estimated before the calculation of their joint probability. Dependence and correlation may differ substantially from one another since dependence is focused heavily on tail (extreme) percentiles. The statistical analysis between surge and wave is performed over 32 river ending points along European coasts. Two sets of almost 35-year hindcasts of storm surge and wave height were adapted and results are presented by means of analytical tables and maps referring to both correlation and statistical dependence values. Further, the top 80 compound events were defined for each river ending point. Their frequency of occurrence was found to be distinctly higher during the cold months while their main low-level flow characteristics appear to be mainly in harmony with the transient nature of storms and their tracks. Overall, significantly strong values of positive correlations and dependencies were found over the Irish Sea, English Channel, south coasts of the North Sea, Norwegian Sea and Baltic Sea, with compound events taking place in a zero-lag mode. For the rest, mostly positive moderate dependence values were estimated even if a considerable number of them had correlations of almost zero or even negative value.