Modeling short duration extreme precipitation patterns using copula and generalized maximum pseudo-likelihood estimation with censoring

The paper aims to develop researches on the spatial variability of heavy rainfall events estimation using spatial copula analysis. To demonstrate the methodology, short time resolution rainfall time series from Stuttgart region are analyzed. They are constituted by rainfall observations on continuous 30 min time scale recorded over a network composed by 17 raingages for the period July 1989–July 2004. The analysis is performed aggregating the observations from 30 min up to 24 h. Two parametric bivariate extreme copula models, the Husler–Reiss model and the Gumbel model are investigated. Both involve a single parameter to be estimated. Thus, model fitting is operated for every pair of stations for a giving time resolution. A rainfall threshold value representing a fixed rainfall quantile is adopted for model inference. Generalized maximum pseudo-likelihood estimation is adopted with censoring by analogy with methods of univariate estimation combining historical and paleoflood information with systematic data. Only pairs of observations greater than the threshold are assumed as systematic data. Using the estimated copula parameter, a synthetic copula field is randomly generated and helps evaluating model adequacy which is achieved using Kolmogorov Smirnov distance test. In order to assess dependence or independence in the upper tail, the extremal coefficient which characterises the tail of the joint bivariate distribution is adopted. Hence, the extremal coefficient is reported as a function of the interdistance between stations. If it is less than 1.7, stations are interpreted as dependent in the extremes. The analysis of the fitted extremal coefficients with respect to stations inter distance highlights two regimes with different dependence structures: a short spatial extent regime linked to short duration intervals (from 30 min to 6 h) with an extent of about 8 km and a large spatial extent regime related to longer rainfall intervals (from 12 h to 24 h) with an extent of 34 to 38 km.     

Uncertainty analysis of urban sewer system using spatial simulation of radar rainfall fields: New York City case study

The goal of this study is to investigate the uncertainty of an urban sewer system’s response under various rainfall and infrastructure scenarios by applying a recently developed nonparametric copula-based simulation approach to extreme rainfall fields. The approach allows for Monte Carlo simulation of multiple variables with differing marginal distributions and arbitrary dependence structure. The independent and identically distributed daily extreme rainfall events of the corresponding urban area, extracted from nationwide high resolution radar data stage IV, are the inputs of the spatial simulator. The simulated extreme rainfall fields were used to calculate excess runoff using the Natural Resources Conservation Service’s approach. New York City is selected as a case study and the results highlight the importance of preserving the spatial dependence of rainfall fields between the grids, even for simplified hydrologic models. This study estimates the probability of combined sewer overflows under extreme rainfall events and identifies the most effective locations in New York City to install green infrastructure for detaining excess stormwater runoff. The results of this study are beneficial for planners working on stormwater management and the approach is broadly applicable because it does not rely on extensive sewer system information.     

The implications of regional variations in rainfall for reconstructing rainfall patterns using tree rings

In Australia, multidecadal periods of floods and droughts have major economic consequences. Due to the short duration of Australian instrumental precipitation records, it is difficult to determine the patterns of these multidecadal periods. Proxy records can be used to create long‐term rainfall reconstructions for regions that are lacking instrumental data. However, the spatial extent over which single‐site proxy records can be applied is poorly understood. Southeast Queensland (SEQ) is an area where tree rings can be used to reconstruct long‐term rainfall patterns, but their regional representation is unknown. In this study, the spatial variability in rainfall across SEQ is investigated from 1908 to 2007 using 140 instrumental rainfall stations. Pearson correlation analysis between stations is used to create groups at the r = 0.80, 0.85, and 0.90 correlation levels, and then annual deviations from the mean are determined. These patterns indicate that rainfall is not uniform across SEQ but can be broken into 2 main spatially consistent groups. Each of these groups is broken down into several subgroups with higher correlation levels. Long‐term streamflow records are found to be correlated to rainfall patterns local to the streamflow stations, indicating that analysis of extreme events should consider spatial precipitation variability. Finally, the only currently available proxy rainfall reconstruction for the region, a 140‐year Toona ciliata tree ring width record from Lamington National Park, is compared to rainfall groups at different correlation levels across all of SEQ. The correlation between the reconstruction and the rainfall station groupings is best for the groups within which the tree‐ring record is spatially located, and this correlation improves as rainfall group correlation increases. Correlation is nearly nonexistent for groupings located at a distance from the tree‐ring site. These results demonstrate the importance of assessing the spatial variability of precipitation so that the spatial applicability of proxy records can be assessed.     

Stochastic multi-site generation of daily rainfall occurrence in south Florida

This paper presents a stochastic model to generate daily rainfall occurrences at multiple gauging stations in south Florida. The model developed in this study is a space–time model that takes into account the spatial as well as temporal dependences of daily rainfall occurrence based on a chain-dependent process. In the model, a Markovian method was used to represent the temporal dependence of daily rainfall occurrence and a direct acyclic graph (DAG) method was introduced to encode the spatial dependence of daily rainfall occurrences among gauging stations. The DAG method provides an optimal sequence of generation by maximizing the spatial dependence index of daily rainfall occurrences over the region. The proposed space–time model shows more promising performance in generating rainfall occurrences in time and space than the conventional Markov type model. The space–time model well represents the temporal as well as the spatial dependence of daily rainfall occurrences, which can reduce the complexity in the generation of daily rainfall amounts.     

Characteristics of intense rainfall over Gujarat State (India) based on percentile criteria

The study focuses on the spatial and temporal variations of intense/extreme rainfall events over Gujarat State (India) during the period 1970–2014. Average monsoon rainfall for the state shows a significant increasing trend, with an increase of 48 mm/decade. Some of the stations in the Saurashtra region show a statistically significant increasing trend but none of the stations in the state show a decreasing trend. The increasing trend in monsoon rainfall is very significant for the past three decades, with an increase of 167 mm/decade. Instead of fixed absolute threshold values, relative threshold values of rainfall corresponding to the 95th, 98th, 99th and 99.5th percentiles for each station have been proposed to represent heavy, very heavy, intense and extreme rainfall, which varied between 70–120, 105–160, 130–210 and 165–280 mm, respectively. Significant increasing trends are observed for the frequency of heavy and very heavy rainfall events over the state.     

Bayesian comparison of different rainfall depth–duration–frequency relationships

Depth–duration–frequency curves estimate the rainfall intensity patterns for various return periods and rainfall durations. An empirical model based on the generalized extreme value distribution is presented for hourly maximum rainfall, and improved by the inclusion of daily maximum rainfall, through the extremal indexes of 24 hourly and daily rainfall data. The model is then divided into two sub-models for the short and long rainfall durations. Three likelihood formulations are proposed to model and compare independence or dependence hypotheses between the different durations. Dependence is modelled using the bivariate extreme logistic distribution. The results are calculated in a Bayesian framework with a Markov Chain Monte Carlo algorithm. The application to a data series from Marseille shows an improvement of the hourly estimations thanks to the combination between hourly and daily data in the model. Moreover, results are significantly different with or without dependence hypotheses: the dependence between 24 and 72 h durations is significant, and the quantile estimates are more severe in the dependence case.     

Analysis and modeling of spatial correlation structure in small-scale rainfall in Central Oklahoma

Spatial correlation structure in small-scale rainfall is analyzed based on a dense cluster of raingauges in Central Oklahoma. This cluster, called the EVAC PicoNet, consists of 53 gauges installed in 25 measurement stations covering an area of about 3 km by 3 km. Two raingauges are placed in 24 stations and five in the central station. Three aspects of the estimated spatial correlation functions are discussed: dependence on time-scale ranging from 1 min to 24 h, inter-storm variability, and dependence on rainfall intensity. The results show a regular dependence of the correlogram parameters on the averaging time-scale, large differences of the correlograms in the individual storms, and the dominance of storms with high spatial variability on the average large sample characteristics. The authors also demonstrate and discuss the ambiguities in correlation estimates conditioned on rainfall intensities. The findings of this study have implications for raingauge network design, rainfall modeling, and conclusive evaluation of radar and satellite estimates of rainfall.     

Statistical identification of orographic effects in the regional analysis of extreme rainfall

Regional models of extreme rainfall must address the spatial variability induced by orographic obstacles. However, the proper detection of orographic effects often depends on the availability of a well‐designed rain gauge network. The aim of this study is to investigate a new method for identifying and characterizing the effects of orography on the spatial structure of extreme rainfall at the regional scale, including where rainfall data are lacking or fail to describe rainfall features thoroughly. We analyse the annual maxima of daily rainfall data in the Campania region, an orographically complex region in Southern Italy, and introduce a statistical procedure to identify spatial outliers in a low order statistic (namely the mean). The locations of these outliers are then compared with a pattern of orographic objects that has been a priori identified through the application of an automatic geomorphological procedure. The results show a direct and clear link between a particular set of orographic objects and a local increase in the spatial variability of extreme rainfall. This analysis allowed us to objectively identify areas where orography produces enhanced variability in extreme rainfall. It has direct implications for rain gauge network design criteria and has led to promising developments in the regional analysis of extreme rainfall. Copyright © 2015 John Wiley & Sons, Ltd.     

Regional frequency analysis of rainfall extremes in Southern Malawi using the index rainfall and L-moments approaches

Rainfall extremes often result in the occurrence of flood events with associated loss of life and infrastructure in Malawi. However, an understanding of the frequency of occurrence of such extreme events either for design or disaster planning purposes is often limited by data availability at the desired temporal and spatial scales. Regionalisation, which involves “trading time for space” by pooling together observations for stations with similar behavior, is an alternative approach for more accurate determination of extreme events even at ungauged areas or sites with short records. In this study, regional frequency analysis of rainfall extremes in Southern Malawi, large parts of which are flood prone, was undertaken. Observed 1-, 3-, 5- and 7-day annual maximum rainfall series for the period 1978–2007 at 23 selected rainfall stations in Southern Malawi were analysed. Cluster analysis using scaled at-site characteristics was used to determine homogeneous rainfall regions. L-moments were applied to derive regional index rainfall quantiles. The procedure also validated the three rainfall regions identified through homogeneity and heterogeneity tests based on Monte Carlo simulations with regional average L-moment ratios fitted to the Kappa distribution. Based on assessments of the accuracy of the derived index rainfall quantiles, it was concluded that the performance of this regional approach was satisfactory when validated for sites not included in the sample data. The study provides an estimate of the regional characteristics of rainfall extremes that can be useful in among others flood mitigation and engineering design.     

Cokriging for enhanced spatial interpolation of rainfall in two Australian catchments

Rainfall data in continuous space provide an essential input for most hydrological and water resources planning studies. Spatial distribution of rainfall is usually estimated using ground‐based point rainfall data from sparsely positioned rain‐gauge stations in a rain‐gauge network. Kriging has become a widely used interpolation method to estimate the spatial distribution of climate variables including rainfall. The objective of this study is to evaluate three geostatistical (ordinary kriging [OK], ordinary cokriging [OCK], kriging with an external drift [KED]), and two deterministic (inverse distance weighting, radial basis function) interpolation methods for enhanced spatial interpolation of monthly rainfall in the Middle Yarra River catchment and the Ovens River catchment in Victoria, Australia. Historical rainfall records from existing rain‐gauge stations of the catchments during 1980–2012 period are used for the analysis. A digital elevation model of each catchment is used as the supplementary information in addition to rainfall for the OCK and kriging with an external drift methods. The prediction performance of the adopted interpolation methods is assessed through cross‐validation. Results indicate that the geostatistical methods outperform the deterministic methods for spatial interpolation of rainfall. Results also indicate that among the geostatistical methods, the OCK method is found to be the best interpolator for estimating spatial rainfall distribution in both the catchments with the lowest prediction error between the observed and estimated monthly rainfall. Thus, this study demonstrates that the use of elevation as an auxiliary variable in addition to rainfall data in the geostatistical framework can significantly enhance the estimation of rainfall over a catchment.     

Estimation of tail dependence coefficient in rainfall accumulation fields

Extreme rainfall events are of particular importance due to their severe impacts on the economy, the environment and the society. Characterization and quantification of extremes and their spatial dependence structure may lead to a better understanding of extreme events. An important concept in statistical modeling is the tail dependence coefficient (TDC) that describes the degree of association between concurrent rainfall extremes at different locations. Accurate knowledge of the spatial characteristics of the TDC can help improve on the existing models of the occurrence probability of extreme storms. In this study, efficient estimation of the TDC in rainfall is investigated using a dense network of rain gauges located in south Louisiana, USA. The inter-gauge distances in this network range from about 1 km to 9 km. Four different nonparametric TDC estimators are implemented on samples of the rain gauge data and their advantages and disadvantages are discussed. Three averaging time-scales are considered: 1 h, 2 h and 3 h. The results indicate that a significant tail dependency may exist that cannot be ignored for realistic modeling of multivariate rainfall fields. Presence of a strong dependence among extremes contradicts with the assumption of joint normality, commonly used in hydrologic applications.     

城镇化对极端降水的影响及其贡献率研究——以太湖平原地区为例

城镇化背景下极端降水事件频发,洪涝灾害问题日益突出,探讨城镇化对极端降水的影响已成为热点与难点问题.本文以长江下游太湖平原地区为例,基于区内40个雨量站长序列的逐日资料(1976-2015年),结合城镇化下土地利用/覆被和社会经济等数据,对比分析了不同城镇化阶段极端降水相关指标的时空变化规律,并定量评估不同城镇化水平对...     

Hydroclimatology of the Upper Madeira River basin: spatio-temporal variability and trends

Rising in the Andes, the Madeira River drains the southwestern part of the Amazon basin, which is characterized by high geographical, biological and climatic diversity. This study uses daily records to assess the spatio-temporal runoff variability in the Madeira sub-basins. Results show that inter-annual variability of both discharge and rainfall differs between Andean and lowland tributaries. High-flow discharge variability in the Andean tributaries and the Guaporé River is mostly related to sea surface temperature (SST) in the equatorial Pacific in austral summer, while tropical North Atlantic (TNA) SST modulates rainfall and discharge variability in the lowlands. There also is a downward trend in the low-flow discharge of the lowland tributaries which is not observed in the Andes. Because low-flow discharge values at most lowland stations are negatively related to the SST in the tropical North Atlantic, these trends could be explained by the warming of this ocean since the 1970s.

EDITOR A. Castellarin

ASSOCIATE EDITOR A. Viglione     

Impact of climate change on 24‐h design rainfall depth estimation in Qiantang River Basin,East China

The frequency and magnitude of extreme meteorological or hydrological events such as floods and droughts in China have been influenced by global climate change. The water problem due to increasing frequency and magnitude of extreme events in the humid areas has gained great attention in recent years. However, the main challenge in the evaluation of climate change impact on extreme events is that large uncertainty could exist. Therefore, this paper first aims to model possible impacts of climate change on regional extreme precipitation (indicated by 24‐h design rainfall depth) at seven rainfall gauge stations in the Qiantang River Basin, East China. The Long Ashton Research Station‐Weather Generator is adopted to downscale the global projections obtained from general circulation models (GCMs) to regional climate data at site scale. The weather generator is also checked for its performance through three approaches, namely Kolmogorov–Smirnov test, comparison of L‐moment statistics and 24‐h design rainfall depths. Future 24‐h design rainfall depths at seven stations are estimated using Pearson Type III distribution and L‐moment approach. Second, uncertainty caused by three GCMs under various greenhouse gas emission scenarios for the future periods 2020s (2011–2030), 2055s (2046–2065) and 2090s (2080–2099) is investigated. The final results show that 24‐h design rainfall depth increases in most stations under the three GCMs and emission scenarios. However, there are large uncertainties involved in the estimations of 24‐h design rainfall depths at seven stations because of GCM, emission scenario and other uncertainty sources. At Hangzhou Station, a relative change of ?16% to 113% can be observed in 100y design rainfall depths. Copyright © 2012 John Wiley & Sons, Ltd.     

Rainfall network design using kriging and entropy

The spatial distribution of rainfall is related to meteorological and topographical factors. An understanding of the weather and topography is required to select the locations of the rain gauge stations in the catchment to obtain the optimum information. In theory, a well‐designed rainfall network can accurately represent and provide the needed information of rainfall in the catchment. However, the available rainfall data are rarely adequate in the mountainous area of Taiwan. In order to provide enough rainfall data to assure the success of water projects, the rainfall network based on the existing rain gauge stations has to be redesigned. A method composed of kriging and entropy that can determine the optimum number and spatial distribution of rain gauge stations in catchments is proposed. Kriging as an interpolator, which performs linear averaging to reconstruct the rainfall over the catchment on the basis of the observed rainfall, is used to compute the spatial variations of rainfall. Thus, the rainfall data at the locations of the candidate rain gauge stations can be reconstructed. The information entropy reveals the rainfall information of the each rain gauge station in the catchment. By calculating the joint entropy and the transmitted information, the candidate rain gauge stations are prioritized. In addition, the saturation of rainfall information can be used to add or remove the rain gauge stations. Thus, the optimum spatial distribution and the minimum number of rain gauge stations in the network can be determined. The catchment of the Shimen Reservoir in Taiwan is used to illustrate the method. The result shows that only seven rain gauge stations are needed to provide the necessary information. Copyright © 2007 John Wiley & Sons, Ltd.     

Multivariate density model comparison for multi-site flood-risk rainfall in the French Mediterranean area

The French Mediterranean area is subject to intense rainfall events which might cause flash floods, the main natural hazard in the area. Flood-risk rainfall is defined as rainfall with a high spatial average and encompasses rainfall which might lead to flash floods. We aim to compare eight multivariate density models for multi-site flood-risk rainfall. In particular, an accurate characterization of the spatial variability of flood-risk rainfall is crucial to help understand flash flood processes. Daily data from eight rain gauge stations at the Gardon at Anduze, a small Mediterranean catchment, are used in this work. Each multivariate density model is made of a combination of a marginal model and a dependence structure. Two marginal models are considered: the Gamma distribution (parametric) and the Log-Normal mixture (non-parametric). Four dependence structures are included in the comparison: Gaussian, Student t, Skew Normal and Skew t in increasing order of complexity. They possess a representative set of theoretical properties (symmetry/asymmetry and asymptotic dependence/independence). The multivariate models are compared in terms of three types of criteria: (1) separate evaluation of the goodness-of-fit of the margins and of the dependence structures, (2) model selection with a leave-one-out evaluation of the Anderson-Darling and Cramer-Von Mises statistics and (3) comparison in terms of two hydrologically interpretable quantities (return periods of the spatial average and conditional probabilities of exceedances). The key outcome of the comparison is that the Skew Normal with the Log-Normal mixture margins outperform significantly the other models. The asymmetry introduced by the Skew Normal is an added-value with respect to the Gaussian. Therefore, the Gaussian dependence structure, although widely used in the literature, is not recommended for the data in this study. In contrast, the asymptotically dependent models did not provide a significant improvement over the asymptotically independent ones.     

Regionalization of heavy rainfall to improve climatic design values for infrastructure: case study in Southern Ontario,Canada

Abstract

Southern Ontario, Canada, has been impacted in recent years by many heavy rainfall and flooding events that have exceeded existing historical estimates of infrastructure design rainfall intensity–duration–frequency (IDF) values. These recent events and the limited number of short-duration recording raingauges have prompted the need to research the climatology of heavy rainfall events within the study area, review the existing design IDF methodologies, and evaluate alternative approaches to traditional point-based heavy rainfall IDF curves, such as regional IDF design values. The use of additional data and the regional frequency analysis methodology were explored for the study area, with the objective of validating identified clusters or homogeneous regions of extreme rainfall amounts through Ward's method. As the results illustrate, nine homogeneous regions were identified in Southern Ontario using the annual maximum series (AMS) for daily and 24-h rainfall data from climate and rate-of-rainfall or tipping bucket raingauge (TBRG) stations, respectively. In most cases, the generalized extreme value and logistic distributions were identified as the statistical distributions that provide the best fit for the 24-h and sub-daily rainfall data in the study area. A connection was observed between extreme rainfall variability, temporal scale of heavy rainfall events and location of each homogeneous region. Moreover, the analysis indicated that scaling factors cannot be used reliably to estimate sub-daily and sub-hourly values from 24- and 1-h data in Southern Ontario.

Citation Paixao, E., Auld, H., Mirza, M.M.Q., Klaassen, J. & Shephard, M.W. (2011) Regionalization of heavy rainfall to improve climatic design values for infrastructure: case study in Southern Ontario, Canada. Hydrol. Sci. J. 56(7), 1067–1089.     

Hydrological analysis of extreme rainfall events and severe rainstorms over Uttarakhand,India

ABSTRACT

Following the June 2013 disaster in the Uttarakhand Himalayas, many discussions are ongoing with regard to how climate change is seeking revenge on mankind by endowing us with disasters! The event was mostly linked with the occurrence of an extreme event due to climate change. In view of this, an attempt has been made in this paper to analyse the extreme rainfall events experienced by the Uttarakhand during 1901–2013 using more than 100 stations’ daily rainfall data. The study revealed that during the 113-year period, the highest numbers of extreme events were recorded during the decade 1961–1970, and to some extent in the decade 1981–1990. Thereafter, there is a decrease in extreme rainfall events. The comparative study of extreme events prior to 1901 showed that on 17–18 September 1880, a rainstorm which occurred in close vicinity to Uttarakhand caused serious floods and damage to lives and properties. The extreme rainfall recorded by some stations during this unprecedented rainstorm has not been surpassed to date.