Joint Return Periods Research Articles

Multivariate analysis of compound hail, wind and rainfall extremes in Alberta's hail alley

Hailstorms are severe weather events with the potential for devastating impacts. The consequences can be significantly worsened when hail events are accompanied by strong winds, intensifying both hail momentum and damage to property sidings and windows. Additionally, rainfall extremes during hailstorms can disrupt the drainage systems, potentially leading to flash flooding. Therefore, understanding the inter-dependencies and joint behaviour of these hazards is crucial for developing effective risk mitigation strategies. In this study, we conduct a multivariate probabilistic assessment of concurrent hail, wind, and rainfall extremes over the Alberta's “hail alley” using radar and ground-based observations. The analysis comprehensively explores individual hazards, as well as bivariate and trivariate scenarios using a vine copula approach. We quantify individual, conditional, and joint return periods (JRPs) for the various scenarios. Findings indicate that in both wind-driven hail and hail-rainfall extreme hazards, the joint occurrences based on JRP, can be underestimated by 20% and 70% when assuming independence, respectively, which has substantial implications for risk assessment and management, as well as infrastructure design and maintenance. The analysis of the trivariate case suggests the potential for the concurrent occurrence of multiple hazards in the region. Furthermore, results show that Archimedean copula families outperform elliptical copulas in simulating extreme variables related to compound events associated with hailstorms. The study stresses the importance of assessing the joint behaviour of these hazard components in hailstorms, with the objective of mitigating potential impacts on vulnerable regions.

Joint Occurrence of Extreme Water Level and River Flows in St. Lawrence River Coasts Under Present and Sea Level Rise Conditions

AbstractIn low‐lying coastal regions, the joint occurrence of high river flow and high water levels can cause coastal flooding with substantial economic and social implications. Recent studies over Canada's coasts have shown that neglecting the interdependency between flood drivers can underestimate the risk of flooding by up to 50%. However, to date, such interdependency has not been investigated for the coasts of the St. Lawrence River, Estuary and Gulf system (StL), where Sea Level Rise (SLR), along with intensified river peaks, are already threatening these communities. In this study, a copula‐based bivariate frequency analysis was applied to quantify the likelihood of occurrence of flooding events under dependent and independent assumptions, for 26 sites along the StL. Furthermore, to quantify the impact of anthropogenic climate change, the joint return period in historical period was compared with that of projected SLR associated with RCP 8.5 for the year 2100. Results show that (a) the independence assumption can underestimate the likelihood of occurrence of flooding event in the Fluvial Section of the StL by up to 30 times and (b) the SLR can increase the likelihood of occurrence of flooding event by up to 50 times in the Estuary and the Gulf and by up to 5 times in the Fluvial Section of the StL. This study highlights the need for explicit consideration of the dependence between flood drivers and of SLR in the delineation of flood maps along the coast of the St. Lawrence.

Comprehensive evaluation of the response relationship between meteorological drought and hydrological drought in the Yalong River Basin, China

Extreme climate events are becoming increasingly severe owing to global warming. In recent years, the Yalong River has experienced frequent droughts, which has seriously hindered the development of hydropower. Based on standardized precipitation evapotranspiration index (SPEI) and standardized runoff index (SRI) values, this study employed transfer entropy, multivariate Copula functions, and a cloud model to study the response relationship and risk situation between meteorological and hydrological droughts. The results showed that: (1) The smaller the scale of SPEI and SRI, the more sensitive the identification of drought and the faster the detection of drought trend changes. (2) Combined with small-scale drought index analyses, the trend and severity of meteorological and hydrological droughts propagating from the upper and middle reaches to the lower reaches is increasing from year to year. (3) The Gumbel-Hougaard Copula function reveals the relationship between meteorological and hydrological drought, with the longest joint return period of 13–15 months. (4) In cloud model risk evaluation, the degree, uncertainty and stochasticity of drought risk in the basin are increasing, and the risk degree of interannual meteorological and seasonal hydrological droughts in the basin was high. This study provides theoretical support for optimizing water resource allocation and drought risk situation analysis in the basin.

Past and future joint return period of precipitation extremes over South Asia and Southeast Asia

Climate change is one of the major reasons for the increased intensity and frequency of precipitation extremes in tropical regions. This will have a significant impact on underdeveloped countries in South Asia and Southeast Asia. Therefore, this study analyzes changes in spatiotemporal patterns and the joint behavior of precipitation extremes across South Asian and Southeast Asian countries for the historical period (1975 to 2014) and future periods (2021–2060 (F1) and 2061–2100 (F2)). This study develops bias-corrected precipitation data and ranks General Circulation Models (GCMs) using the Empirical Quantile Mapping method and TOPSIS method, respectively. A multi-model ensemble of precipitation extremes is created using the top five GCMs. The Mann Kendall test is used to analyze trends in precipitation extremes. Joint probabilistic analysis is also conducted for different combinations of ETCCDI precipitation-based indices using Archimedes and Elliptical copulas. The results of the trend analysis indicate significant positive trends for R20mm (19.26%), R95pTOT (18.40%), Rx5Day (11.53%), and CWD (10.46%), while CDD (5.07%) shows a significant negative trend across the study area during historical period (1975–2014). The results of R20mm, R95pTOT, and Rx5Day under SSP585 shows almost 19 to 39% of area comes under significant positive trend during the F1 period. This becomes more evident in F2, with trends under SSP585 rising between 32% and 61%. The high-emissions scenario SSP585 reveals an increase in these positive trends compared to SSP126 in both the future periods (F1 and F2). These results indicating a noticeable rise in extreme precipitation events. The analysis of changes in the joint return period of precipitation extremes indicates that the South Peninsular India, North East India, West Central India and Central Northeast India, as well as most parts of Southeast Asian countries, will experience very heavy intensify precipitations in the future. In addition, persistent co-occurrence of dry and wet conditions will be observed in Pakistan, North West India, and Central Northeast India. This study provides useful information on the distribution of precipitation extremes in different regions of the study area.

Drought and its ecological risk bundle from the perspective of watershed hydrological cycle

The mechanisms underlying the impacts of climate change and vegetation dynamics on hydrological drought in humid regions are still lacking. In this study, we connected the four components of meteorology-soil-vegetation-runoff to investigate the spatio-temporal response relationship between vegetation growth and different drought types. Based on the Variable Infiltration Capacity model and the Self-organizing Map Algorithm, we proposed ecological risk bundles at the grid scale to characterize the potential impacts of different types and levels of drought on vegetation. Furthermore, we quantified the driving impact of temporal and spatial changes in vegetation coverage on the propagation of meteorological-hydrological drought. The study found that the centers of gravity for the occurrence frequencies of extreme and mild drought shifted towards regions where vegetation growth was influenced by climate change. In certain regions of the watershed, vegetation exhibits significant spatial and temporal heterogeneity in its response to stress caused by different drought types. From 2004 to 2014, the stress on vegetation caused by moderate and mild meteorological droughts weakened, while soil moisture stress intensified after 2014. Simultaneously, the impacts of climate change and vegetation growth on runoff reached 48.25 % and 35.13 % respectively, and their synergistic effects triggered changes in the risk of co-concurrent return periods for hydrological drought events. Under the 100-year design return period, the co-occurrence return period of runoff shifted from its natural state of 162.9 years to 52.8 years, and the joint return period reversed its scenario, becoming shorter than the co-occurrence return period.

Propagation process‐based agricultural drought typology and its copula‐based risk

AbstractDetermining the risks associated with different drought event types can be beneficial for related scientific research and management strategies. In this study, we proposed an agricultural drought event pair and typology based on the governing drought propagation processes in the Yellow River basin at the catchment scale. In total, seven agricultural drought event pairs were distinguished, namely single meteorological drought event pair (MDonly), single soil moisture drought event pair (SDonly), single agricultural drought event pair (ADonly), soil moisture and meteorological drought event pair (SDMD), agricultural and meteorological drought event pair (ADMD), agricultural and soil moisture drought event pair (ADSD) and agricultural, soil moisture and meteorological drought event pair (ASMD). The SDMD and ADMD events had the highest copula‐based risk probabilities with the shortest joint return periods. Six agricultural drought types were distinguished in this study, namely classical rainfall deficit, rain‐to‐snow‐season, wet‐to‐dry‐season, cold snow season, warm snow season and composite drought events. The classical rainfall deficit, wet‐to‐dry season and composite drought events were the major agricultural drought types in the Yellow River basin. The agricultural drought typology results of the present study provide a comprehensive understanding of drought propagation and improvement of drought forecasting and management.

Compound Flooding Potential from the Joint Occurrence of Precipitation and Storm Surge in the Qiantang Estuary, China

Abstract In coastal regions, compound flooding, driven by multiple flood hazard sources, can cause greater damage than when the flood drivers occur in isolation. This study focuses on compound flooding from extreme precipitation and storm surge in China’s Qiantang Estuary. We quantify the potential of compound flooding by measuring bivariate joint statistical dependence and joint return period (JRP). We find a significant positive dependence between the two flood drivers considered, as indicated by Kendall’s rank correlation coefficients. Compound events occur frequently, with an average of 2.65 events per year from 1979 to 2018, highlighting the significant concern of compound flooding for this estuary. Using a copula model, we demonstrate that considering the dependence between the two flood drivers shortens the JRP of compound flooding compared to the JRP assuming total independence. For a 1-in-10-yr precipitation event and 1-in-10-yr storm surge event, the JRP is 1 in 100 years when assuming total independence. However, it decreases to 1 in 32.44 years when considering their dependence. Ignoring the dependence between flood drivers can lead to an increase in the JRP of compound events, resulting in an underestimation of the overall flood risk. Our analysis reveals a strong link between the weather patterns creating compound events and extreme storm surge only events with tropical cyclone activity. Additionally, the extreme precipitation only events were found to be connected with the frontal system of the East Asian summer monsoon. This study highlights the importance of considering the dependence between multiple flood drivers associated with certain types of the same weather systems when assessing the flood risk in coastal regions.

Using Copula functions to predict climatic change impacts on floods in river source regions

Flood frequency in river source regions is significantly affected by rainfall and snowmelt as part of climatic changes. A traditional univariate flood frequency analysis cannot reflect the complexity of floods, and when used in isolation, it can only underestimate flood risk. For effective flood prevention and mitigation, it is essential to consider the combined effects of precipitation and snowmelt. Copula functions can effectively quantify the joint distribution relationship between floods and their associated variables without restrictions on their distribution characteristics. This study uses copula functions to consider a multivariate probability distribution model of flood peak flow (Q) with cumulative snowmelt (CSm) and cumulative precipitation (CPr) for the Hutubi River basin located in northern Xinjiang, China. The joint frequencies of rainfall and snowmelt floods are predicted using copula models based on the Coupled Model Intercomparison Project Phase 6 data. The results show that Q has a significant positive correlation with 24-d CSm (r = 0.559, p = 0.002) and 23-d CPr (r = 0.965, p < 0.05). Flood frequency will increase in the future, and mid- (2050–2074) and long-term (2075–2099) floods will be more severe than those in the near-term (2025–2049). The probability of flood occurrence is higher under the SSP2-4.5 and SSP1-2.6 scenarios than under SSP5-8.5. Precipitation during the historical period (1990–2014) led to extreme floods, and increasing future precipitation trends are found to be insignificant. Snowmelt increases with rising temperatures and occurs earlier than estimated, leading to an earlier flood period in the basin and more frequent snowmelt floods. The Q under the joint return period is larger than that during the same univariate return period. This difference indicates that neglecting the interaction between precipitation and snowmelt for floods leads to an underestimation of the flood risk (with underestimations ranging from 0.3% to 22%). The underestimations decrease with an increase in the return period. The joint risks of rainfall or snowmelt according to various flood periods should be considered for rivers with multi-source runoff recharge in flood control design. This study reveals the joint impact of precipitation and snowmelt on extreme floods under climate change in river source regions. This study also provides a scientific basis for regional flood prevention and mitigation strategies, as well as for the rational allocation of water resources.

Global Projection of Flood Risk With a Bivariate Framework Under 1.5–3.0°C Warming Levels

AbstractGlobal warming increases the atmospheric water‐holding capacity, consequently altering the frequency, and intensity of extreme hydrological events. River floods characterized by large peak flow or prolonged duration can amplify the risk of social disruption and affect ecosystem stability. However, previous studies have mostly focused on univariate flood magnitude characteristics, such as flood peak or volume, and there is still limited understanding of how these joint flood characteristics (i.e., magnitude and duration) might co‐evolve under different warming levels. Here, we develop a systematical bivariate framework to project future flood risk in 11,528 catchments across the globe. By constructing the joint distribution of flood peak and duration with copulas, we examine global flood risk with a bivariate framework under varying levels of global warming (i.e., within a range of 1.5–3.0°C above pre‐industrial levels). The flood projections are produced by driving five calibrated lumped hydrological models (HMs) using the simulations with bias adjustment of five global climate models (GCMs) under three shared socioeconomic pathways (SSP126, SSP370, and SSP585). On average, global warming from 1.5 to 3.0°C tends to amplify flood peak and lengthen flood duration across almost all continents, but changes are not unidirectional and vary regionally around the globe. The joint return period (JRP) of the historical (1985–2014) 50‐year flood event is projected to decrease to a median with 36 years under a medium emission pathway at the 1.5°C warming level. Finally, we evaluate the drivers of these JRP changes in the future climate and quantify the uncertainty arising from the different GCMs, SSPs, and HMs. Our findings highlight the importance of limiting greenhouse gas emission to slow down global warming and developing climate adaptation strategies to address future flood hazards.

Bivariate regional drought frequency analysis using multivariate approaches: a case study in southwestern Iran

Abstract Bivariate approaches in Regional Frequency Analysis (RFA) address two issues: first, to evaluate the homogeneity of regions, and second, to estimate the joint return periods. This study was conducted to investigate the joint return period of a severe historical drought in southwestern Iran. Fifty-nine rain gauges were first clustered into three, four, and five regions using the fuzzy c-means clustering (FCM) algorithm. Then bivariate discordancy and homogeneity tests were applied to adjust the initial clusters. The results showed that only in the case of three clusters were all the regions homogeneous. Therefore, it can be inferred that combining clustering analysis and discordancy test is insufficient to form homogeneous regions. Finally, the joint return period, by choosing Generalized Logistic and Wakeby as marginal distributions and Clayton as a copula, was estimated for all the sites in the three regions. Since no three-parameter distribution function fitted well to the variable severity, the bivariate homogeneity index does not necessarily attest to region homogeneity regarding the marginal distribution functions. It is also deduced that sites with higher mean annual precipiataion (MAP) and, correspondingly, higher elevation are more likely to experience shorter return periods of same drought events, in contrast to sites with lower MAP or lower elevation.

Global increase in future compound heat stress-heavy precipitation hazards and associated socio-ecosystem risks

Compound extremes of lethal heat stress-heavy precipitation events (CHPEs) seriously threaten social and ecological sustainability, while their evolution and effects at the global scale under climate warming remain unclear. Here we develop the global picture of projected changes in CHPEs under various scenarios and investigate their socioeconomic and ecosystem risks combining hazard, exposure, and vulnerability through the composite indicator approach. We find a high percentage of heat stress is followed by heavy precipitation, probably driven by atmospheric conditions. Global average frequency and intensity of CHPEs are projected to increase in the future under high-emission scenarios. Joint return periods of CHPEs are projected to decrease globally, predominantly driven by changes in heat stress extremes. In the long-term future, over half of the population, gross domestic product, and gross primary productivity may face high risk in most regions, with developed regions facing the highest risks under SSP5-8.5 and developing regions facing the highest risks under SSP3-7.0.

A composite approach to document a century of overwash events in a high tide environment of southern Brittany, France

Understanding and precisely dating the sedimentological imprint of storm-induced back-barrier washover deposits is challenging, even more so in macro-tidal environments. Indeed, in such a situation, significant storms may not lead to any washover deposits, for instance if they occurred during low tide. To tackle this challenge, we propose a method based on crossing sedimentology, historical impacts from archives and weather-marine data, together with dating, statistics and modeling technique. We chose the Petite Mer de Gâvres (PMG) site, in southern Brittany, along the French Atlantic coast, as a demonstration site in a macro tidal environment. The sediment core analyses led to the identification of six washover deposits, dated back to 1905 ± 10 yr, 1931 ± 8 yr, 1946 ± 7 yr, 1973 ± 1.5 yr, 1990 ± 3 yr, and 2000 ± 2 yr. The crossing with reanalysis weather-marine data and historical (local and regional impact) sources suggested that they have been caused by the 1896, 1924, 1950, 1974, 1990 (four storms) and 1999 (two storms) events. The post-processing made on the reanalysis data leading to this event list included the computation of the joint return period of exceedance RP (accounting for the tide, surge and wave height) and the use of the Stockdon formula to estimate whether the water level (including the wave runup) may have exceeded the dune crest level and led to overwash events. The storm on January 9, 1924 seemed to have induced the most extreme conditions, with a joint return period RP estimated to 1000 years, giving way to a “vision of desolation” according to historical documents. For all the identified storms at the origin of washover deposits, the wave height was always exceptionally strong, highlighting the key effect of this parameter. However, we need to keep in mind that the tide level should be high enough to allow overwash phenomena on such a macro tidal site. Finally, we underlined the benefits and limits of our composite method to document historical storms.

Impact of Anthropogenic Warming on Future Unprecedented Droughts in California: Insights From Multiple Indices and Multi‐Model Projections

AbstractSo‐called hot droughts are seen as one of the very foreseeable extremes amid the faster‐than‐expected pace of global warming. In particular, the western part of North America has been pummeled by severe droughts due to a lack of precipitation as well as record‐breaking hot temperatures. This study assesses the joint return period of drought severity and duration using the COordinated Regional Climate Downscaling EXperiment‐COmmon Regional Experiment (CORDEX‐CORE) simulations over the California domain. Six dynamically downscaled simulations with 25 km resolution are analyzed for the historical (1956–2005) and future (2050–2099) periods, whose warming sensitivities differ based on three global climate models (GCMs) driving two regional climate models (RCMs). Our focus is on estimating the joint probabilities of the drought duration and severity constructed from multiple drought indices such as the Palmer Drought Severity Index (PDSI) (with original temperature (PDSI) and its detrended counterpart (PDSI_detrended)) and Standardized Precipitation Index (SPI). Under the RCP8.5 scenario, an unprecedented level of droughts in terms of both duration and severity is likely to emerge only when the drought is characterized by PDSI. A comparison of PDSI and PDSI_detrended explicitly reveals that the occurrence of severe and prolonged droughts is mainly attributed to the warming trend of temperature. Both PDSI_detrended and SPI, which do not incorporate the warming effect explicitly, barely differentiate the joint distributions from the historical and future simulations. Unlike the PDSI based on water budget, the SPI, based on solely accumulated precipitation, shows a loosely coupled joint structure between the severity and duration of droughts, with marked differences in their marginal distributions.

Univariate and bivariate spatiotemporal characteristics of heat waves and relative influence of large-scale climate oscillations over India

Heat waves (HWs) have grown in frequency, duration, and intensity in last few decades globally and even the latest climate projections (CMIP6) reveal these to get worsen under enhanced global warming. HWs have adverse impacts over biophysical and human systems, therefore, to analyse the impacts of HWs accurately, it is required to understand the regional trend and variability associated with HWs. We carried out a bivariate copula-based joint exceedance probabilistic analysis of HW characteristics to better assess the vulnerability of Indian regions. The regions with comparatively higher HW frequency, higher intensity, longer duration, and lower joint return period of HW frequency and intensity were selected as vulnerable to HWs. Rajasthan, Madhya Pradesh, Uttar Pradesh, Punjab, Bihar, Chhattisgarh, Gujrat, Karnataka, Maharashtra, Telangana, Andhra Pradesh, and Odisha states of India have been found vulnerable and are projected to get even more vulnerable in the future as per the recent climate projections. To unveil the spatiotemporal variability in HW characteristics, we investigated the relative influence of crucial large-scale climate oscillations (LSCOs) i.e., ENSO, IOD, and AMO on HW by introducing these atmospheric variables as covariates in nonstationary extreme value theory (EVT)-based models. The statistical analysis from generalized extreme value distribution of temperature extreme with LSCOs reveals that ENSO and IOD simultaneously have been influencing the extreme in 21.2%, 25.9% and 23.1% of total region taken into consideration in April, May and June month respectively.

Future Joint Probability Characteristics of Extreme Precipitation in the Yellow River Basin

The relationship between climate change and extreme precipitation is extremely complex. From a probabilistic perspective, a proper understanding of the response of extreme precipitation to climate change is of significant importance. This study was based on daily precipitation provided by CMIP6 climate models and employed copula functions to construct joint distributions of precipitation amount and precipitation intensity indices at different quantile levels. A spatial–temporal assessment of the susceptibility areas for extreme precipitation in the Yellow River Basin was conducted while considering bivariate return periods and design values. The results indicate that there were significant spatial differences in the bivariate return periods. Taking the R90P-SDII (90) index for a 20a return period as an example, the difference between the maximum and minimum joint return periods within the Yellow River Basin was 1.4 times, while the co-occurring return period was 7.0 times, and the Kendall return period was 4 times. Moreover, this difference increased with the increase in the return period. The magnitude order of the four return periods is as follows: TAnd &gt; TKendall &gt; TSingle-variable &gt; TOr. Joint return periods (Or) and co-occurring return periods (And) could be considered as the extreme cases under single-variable return periods, serving as an estimation interval for actual return periods. Under the influence of climate change, the bivariate design values for future periods exhibited a variability increase of 6.76–28.8% compared to historical periods, and this increase grew with higher radiative forcing scenarios, ranking as SSP126 &lt; SSP245 &lt; SSP585. The bivariate design values showed a noticeable difference in variability compared to the single-variable design values, ranging from −0.79% to 18.67%. This difference increased with higher quantile values, with R95P-SDII (95) &gt; R90P-SDII (90) &gt; PRCPTOT-SDII.

Multivariate Drought Risk Analysis for the Weihe River: Comparison between Parametric and Nonparametric Copula Methods

This study analyzed the multivariate drought risks for the Wei River basin by characterizing the interdependence between the standardized precipitation index (SPI) and the standardized precipitation evapotranspiration index (SPEI). Both parametric and nonparametric copulas were adopted to quantify the dependence between the SPI and SPEI. The results indicated that the Gaussian copula demonstrated the best fit in most cases, while the nonparametric copula method showed superiority over the parametric models at only one out of eighteen meteorological stations. The joint return periods (TOR, TAND, and TKendall) were computed through copula modeling, providing valuable insights into the co-occurrence of extreme drought events. For the SPI and SPEI with a 50-year return period, the TOR values range from 25.5 to 37.9 years, the TAND values fluctuate between 73.4 and 1233 years, and the TKendall values range from 60.61 to 574.71 years, indicating a high correlation between the SPI and SPEI in the study area. The spatial analysis revealed varying patterns across the basin with some regions more prone to experiencing simultaneous drought conditions characterized by both the SPI and SPEI. Furthermore, our results indicated that the SPEI exhibited more severity in drought characterization than the SPI due to its consideration of temperature effects. The disparities in the spatial features of the SPI and SPEI underscore the importance of incorporating multiple meteorological factors for a comprehensive drought risk analysis. This research contributes to a better understanding of the drought patterns and their joint risks in the Wei River basin, offering valuable information for drought preparedness and water resource management.

Copula-Based Joint Flood Frequency Analysis: The Case of Guder River, Upper Blue Nile Basin, Ethiopia

The univariate analysis of hydrological extremes is a well-established practice in developing countries such as Ethiopia. However, for the design of hydrological and hydraulic systems, it is essential to have a thorough understanding of flood event characteristics, including volumes, peaks, time of occurrence, and duration. This study utilizes copula functions for bivariate modeling of flood peak and volume characteristics, examining the performance of four Archimedean copulas in the Guder basin located in Ethiopia from 1987 to 2017. Flood peak and volume were extracted using the theory of runs for analysis of their joint characteristics with the truncation level chosen as equal to the lowest annual maximum event. Univariate distributions with the best fitness on both variables were determined, and results showed that gamma and GEV-fitted flood peaks and lognormal-fitted flood volumes are the most suitable. Four Archimedean copulas were evaluated, and the Gumbel-Hougaard copula was found to be the best fit for the data based on graphical and measurable tests. Bivariate probability and return period were computed in “AND” and “OR” states. The joint return period for flood peak (97.49 m3/s) and volume (77.35 m3/s) was found to be 15 years in the “AND” state and approximately 4 years in the “OR” state. The study also evaluates univariate and conditional return periods, comparing them with the primary one. The copula method was an effective method for distributing marginal variables, highlighting its potential as a valuable tool in flood management.

Investigation of the propagation of meteorological to hydrological drought and water required to recover from drought over Ethiopian basins

Abstract This study investigates drought propagation from meteorological to hydrological and streamflow required to recover from drought in four sub-basins: Genale, Tekeze, Awash, and Baro basins of Ethiopia. Due to limited observed streamflow data, the soil moisture accounting and routing (SMAR) model was used to extend the streamflow data for each sub-basin from 1985 to 2017. Drought characteristics in terms of duration, severity, and onset/offset of drought and propagation time at different time scales are investigated using run theory and Pearson correlation, respectively. Two Archimedean copulas (Clayton and Gumbel) are used to identify the joint return period between drought duration and severity and the amount of streamflow required to recover from hydrological drought for each sub-basin. Our results revealed that drought frequency has increased over most sub-basins over the last two decades. The propagation time from meteorological drought to hydrological drought is shorter over the Tekeze sub-basin (1–3 months); however, Genale and Awash sub-basin show 3- to 6-month propagation time. The more extended propagation time is seen over the Baro sub-basin (6–9 months). The required amount of water for drought recovery estimation shows a linear relationship between the duration of the drought and the amount required.

Effect of intense rainfall and high riverine water level on compound flood hazards in a river-valley city: A case study of Yingde, China

River-valley cities are susceptible to compound floods induced by intense rainfall and high riverine water level, especially where design standard of levees is low and overtopping-induced fluvial flood are very likely to run into urban area. However, the holistic impact of high riverine water level and intense rainfall on a river-valley city still needs to be assessed within a quantitative analyzing framework. In this study, a typical river-valley city named Yingde in Guangdong Province of China is selected as the study area. A framework combining multivariate statistical analysis and numerical hydrodynamic modeling is proposed to quantitatively assess the compound flood hazard in river valley cities. To be specific, a compound flood numerical model that can integrate rainfall and overtopping flow processes is first developed and validated based on historical observations. Then, the joint probability distribution of rainfall and riverine water level is established based on the copula function. After that, the compound flood scenarios corresponding to different joint return periods are simulated and compared. Considering only one factor may underestimate the probability of flooding occurrence. The compound flood severity in terms of both inundation area and depth for the study area is majorly dominated by intense rainfall, but the extra contribution from upstream water level cannot be ignored. An inundation amplification factor can be used to assess the amplification effect of high upstream water level on the flood hazard of the riparian area. For a site that is quite near the river, the inundation amplification factor can be drastically decreased as the levee crest elevation is heightened. Without the contribution from the fluvial floods, the rainfall-induced inundation could be several times smaller than the compound floods.

Joint probability analysis of storm surges and waves caused by tropical cyclones for the estimation of protection standard: a case study on the eastern coast of the Leizhou Peninsula and the island of Hainan in China

Abstract. The impact of natural hazards such as storm surges and waves on coastal areas during extreme tropical cyclone (TC) events can be amplified by the cascading effects of multiple hazards. Quantitative estimation of the marginal distribution and joint probability distribution of storm surges and waves is essential to understanding and managing tropical cyclone disaster risks. In this study, the dependence between storm surges and waves is quantitatively assessed using the extreme value theory (EVT) and the copula function for the Leizhou Peninsula and the island of Hainan of China, based on numerically simulated surge heights (SHs) and significant wave heights (SWHs) for every 30 min from 1949 to 2013. The steps for determining coastal protection standards in scalar values are also demonstrated. It is found that the generalized extreme value (GEV) function and Gumbel copula function are suitable for fitting the marginal and joint distribution characteristics of the SHs and SWHs, respectively, in this study area. Secondly, the SHs show higher values as locations get closer to the coastline, and the SWHs become higher further from the coastline. Lastly, the optimal design values of SHs and SWHs under different joint return periods can be estimated using the nonlinear programming method. This study shows the effectiveness of the bivariate copula function in evaluating the probability for different scenarios, providing a valuable reference for optimizing the design of engineering protection standards.