Extreme Rainfall Quantiles Research Articles

A Bayesian non-asymptotic extreme value model for daily rainfall data

Motivated by the analysis of extreme rainfall data, we introduce a general Bayesian hierarchical model for estimating the probability distribution of extreme values of intermittent random sequences, a common problem in geophysical and environmental science settings. The approach presented here is derived under a set of assumptions different than those used in traditional extreme value (EV) theory. A hierarchical model structure is adopted for capturing the underlying variability in the yearly distribution of event magnitudes and occurrences, which are described through a latent temporal process. Focusing on daily rainfall extremes, the structure of the proposed model lends itself to incorporating prior geo-physical understanding of the rainfall process. By means of an extensive simulation study, we show that this methodology can significantly reduce quantile estimation uncertainty with respect to Bayesian formulations of traditional asymptotic EV methods, particularly in the case of relatively small samples. On the other hand, a negative bias is observed in estimated rainfall quantiles. We evaluate the tradeoff between bias and variance for extreme rainfall quantiles and show that the approach proposed here can be advantageous depending on the sample size available for training. The benefits of the approach are illustrated with an application to a large data set of 479 long daily rainfall historical records from across the conterminous United States. By comparing measures of in-sample and out-of-sample predictive accuracy, we find that the model structure developed here, combined with the use of all available observations for inference, can improve robustness with respect to overfitting to the specific sample in case of short datasets.

Estimation of extreme rainfall quantiles at ungauged sites in the Loess Plateau, China by regional frequency analysis

AbstractAn increase in the frequency of extreme rainfall events has caused more severe floods than before under the influence of climate change, and is receiving a lot of attention in data‐scarce areas like the Loess Plateau, especially in some small basins without hydrometeorological data, and to avert the risk of disaster needs the estimation of extreme rainfall quantiles. In this study, generalized additive models (GAM) are combined with a nonlinear canonical correlation analysis (NLCCA) procedure to estimate extreme rainfall quantiles at ungauged sites in the Wei River basin on the Loess Plateau. Also, the single inverse distance weighting (IDW) interpolation, NLCCA‐backpropagation (BP), and NLCCA‐radial basis function (RBF) models were used as comparative methods for testing the efficiency of the NLCCA‐GAM model. Because meteorological data are generally lacking in rainfall‐ungauged basins, data at ungauged sites was interpolated by IDW interpolation when NLCCA delineated homogeneous regions. Results of validation indicated that maximum daily rainfall quantiles in the Loess Plateau were well estimated by NLCCA‐GAM‐based regional frequency analysis, implying the NLCCA‐GAM is a useful tool for estimating design extreme rainfall in ungauged basins. Results of comparison demonstrated that NLCCA‐GAM was more robust and better reflected the nonlinear relationship between explanatory and response variables in the region than did comparative approaches. In addition, it was found that the NLCCA‐GAM approach made full use of the data from sites in homogeneous regions to mine the valuable nonlinear correlation between ungauged and gauged sites and estimate extreme rainfall quantiles at ungauged sites.

Climatic and altitudinal controls on rainfall extremes and their temporal changes in data-sparse tropical regions

• We used the Simplified MEV to model extreme rainfall quantiles in tropical regions. • Weibull distribution well approximates the tail of daily rainfall distribution. • Statistical parameters and rainfall quantiles significantly depend on latitude. • Homogeneous patterns in regional temporal trends are related to altitude. • Extreme daily rainfall amounts in the Volta basin increased during 1978–2018. Sub-Saharan Africa’s economy and livelihood are primarily dependent on agriculture, which makes it highly vulnerable to the impacts of extreme weather events and climate change. Modelling and quantifying extreme rainfall and its temporal changes in such environments could thus provide crucial information for design, insurance, management, ecology and climate adaptation. Rain gauge networks in the area are relatively sparse, and often characterized by missing data, which hamper the use of extreme-value methods for estimating extreme precipitation quantiles. In this study, we adopted the Simplified Metastatistical Extreme Value approach for the estimation of extreme return levels based on ordinary events (i.e., all the independent realizations of the variable of interest), which was shown to be more accurate than traditional extreme-value methods in the presence of short data records. We examined data from 66 rain gauges covering diverse hydro-climatic regions across Ghana with the aim of (i) validating the robustness of the statistical approach, (ii) characterising the climatic and altitudinal controls on the occurrence, frequency and intensity of rainfall extremes, and (iii) quantifying recent changes in the characteristics of extremes. We found that a two-parameter Weibull distribution well approximates the tail of the daily rainfall distribution throughout the area. Our statistical approach can quantify extremes with largely reduced uncertainties (7–17% uncertainty in the 100-year return levels computed using 10 years of data versus 11–62% of extreme-value based methods). Extreme precipitation statistics (daily intensity distribution, number of wet days, extreme rainfall quantiles) are found to significantly depend on latitude, so that the four latitudinally layered hydro-climatic regions typically adopted in the area well represent spatial variations. Elevation significantly affects the tail heaviness of the daily intensity distribution and thus extreme rainfall quantiles. Temporal changes during the period 1978–2018 are found to be non-homogeneous in the area as well as within the four hydro-climatic regions, but are homogeneous in three altitude-based regions. We report contrasting trends in extreme return levels in low-elevation (<200 m a.s.l.) and hilly regions, related to contrasting changes in the daily intensity distribution. Statistically significant positive trends in extreme daily rainfall amounts are observed in the inland low-elevation region of the Volta river basin, which call for further investigation of changes in future precipitation extremes in this extremely important hydrological region in Sub-Saharan Africa.

Improvement of Extreme Value Modeling for Extreme Rainfall Using Large-Scale Climate Modes and Considering Model Uncertainty

Extreme value modeling for extreme rainfall is one of the most important processes in the field of hydrology. For the improvement of extreme value modeling and its physical meaning, large-scale climate modes have been widely used as covariates of distribution parameters, as they can physically account for climate variability. This study proposes a novel procedure for extreme value modeling of rainfall based on the significant relationship between the long-term trend of the annual maximum (AM) daily rainfall and large-scale climate indices. This procedure is characterized by two main steps: (a) identifying significant seasonal climate indices (SCIs), which impact the long-term trend of AM daily rainfall using statistical approaches, such as ensemble empirical mode decomposition, and (b) selecting an appropriate generalized extreme value (GEV) distribution among the stationary GEV and nonstationary GEV (NS-GEV) using time and SCIs as covariates by comparing their model fit and uncertainty. Our findings showed significant relationships between the long-term trend of AM daily rainfall over South Korea and SCIs (i.e., the Atlantic Meridional Mode, Atlantic Multidecadal Oscillation in the fall season, and North Atlantic Oscillation in the summer season). In addition, we proposed a model selection procedure considering both the Akaike information criterion and residual bootstrap method to select an appropriate GEV distribution among a total of 59 GEV candidates. As a result, the NS-GEV with SCI covariates generally showed the best performance over South Korea. We expect that this study can contribute to estimating more reliable extreme rainfall quantiles using climate covariates.

Actualization of Climatic Parameters of the Empirical Methods of ORSTOM and CIEH: Case of Ivory Coast

Climate change is a reality that affects several climate variables including precipitation. This change and the variability of the climate are considered to be the greatest challenges facing humanity in the decades to come, on all geographic scales and in all economic sectors. In this context of severe climate change, it will be judicious to review the sizing parameters of hydraulic structures. The determination of hydrological standards is necessary within the framework of development projects for the design of hydraulic structures and the storm water management. The objective of this study is to update the parameters of the ORSTOM and CIEH methods. These are annual rainfall normals, extreme rainfall norms, extreme rainfall quantiles as well as the extreme rainfall gradex. The study carried out was based on annual maximum daily rainfall data and annual rainfall data collected over the period 1931-2020 from twenty-six (26) rainfall stations. The methodological approach is based on the one hand on the evaluation of the normals (normals of annual rainfall, norms of extreme rainfall) and on the other hand on the determination of the quantiles of the daily maximum annuals. These quantiles were used to assess the extreme rainfall gradex. The annual rainfall norms evaluated over the period 1931-2020 vary between 1,180 and 1,457.4 mm. As for the normals of the maximum daily rains, they oscillate between 73.61 mm (Agnibilékro) and 136.59 mm (Tabou) with an average of 94.57 mm. The 10-year return period quantiles evaluated over the period 1931-2020 vary between 103 mm (Dimbokro) and 222 mm (Tiassalé) with an average of 143.6 mm. As for the centennial quantiles, they oscillate between 132 mm (Dimbokro) and 326 mm (Tiassalé) with an average of 211.5 mm. An analysis of the extreme rainfall gradex revealed values fluctuating between 0.28 (Dimbokro) and 0.71 (Guiglo) with an average of 0.47 on Ivorian territory. The gradex coefficients determined are all greater than the regional value of 0.38 defined by ORSTOM except for the Dimbokro station (0.28). Indeed, the calculated gradex coefficient biases are all positive (ranging from +2.63 to + 86.84%) except that of Dimbokro (-26.32%). The use of the regional value of 0.38 reflects an under designing of the values of the gradex coefficient for the whole country except the Dimbokro station.

A New Look at Storm Separation Technique in Estimation of Probable Maximum Precipitation in Mountainous Areas

Storm separation is a key step when carrying out storm transposition analysis for Probable Maximum Precipitation (PMP) estimation in mountainous areas. The World Meteorological Organization (WMO) has recommended the step-duration-orographic-intensification-factor (SDOIF) method since 2009 as an effective storm separation technique to identify the amounts of precipitation caused by topography from those caused by atmospheric dynamics. The orographic intensification factors (OIFs) are usually developed based on annual maximum rainfall series under such assumption that the mechanism of annual maximum rainfalls is close to that of the PMP-level rainfall. In this paper, an alternative storm separation technique using rainfall quantiles, instead of annual maximum rainfalls, with rare return periods estimated via Regional L-moments Analysis (RLMA) to calculate the OIFs is proposed. Based on Taiwan’s historical 4- and 24-h precipitation data, comparisons of the OIFs obtained from annual maximum rainfalls with that from extreme rainfall quantiles at different return periods, as well as the PMP estimates of Hong Kong from transposing the different corresponding separated nonorographic rainfalls, were conducted. The results show that the OIFs obtained from rainfall quantiles with certain rare probabilities are more stable and reasonable in terms of stability and spatial distribution pattern.

Quantile-based downscaling of rainfall extremes: Notes on methodological functionality, associated uncertainty and application in practice

Local characteristics of extreme rainfall quantiles, manifested through Intensity-Duration-Frequency (IDF) curves, are key to infrastructure design. Due to climate change, rainfall extremes are subject to changes, it is, therefore, crucial to explore the potential impacts these changes will have on design storms. A new strain of methodologies, quantile-based downscaling approaches, have recently been proposed to exclusively downscale extreme rainfall quantiles obtained from Global Climate Models (GCMs). These approaches, however, have not been systematically intercompared and the uncertainties related to assigning future design storms are poorly understood. This study evaluates the functionality of three quantile-based downscaling methods during the historical and future periods in Montreal, Canada. Results show that the performance of quantile-based downscaling approaches in reproducing observed extreme quantiles can be divergent. At lower return periods, however, differences between the three schemes are not significant. Similar performances for reproducing historical rainfall extremes, however, does not necessarily imply similar future projections due to the different functionalities of the three approaches in mapping GCM projections into finer scales. Despite these uncertainties, the total projection range of future rainfall extremes are, in many cases, comparable to the confidence interval of the parametric probability distribution when fitted to the observed annual maximum rainfall series. A risk-based approach to accommodate this uncertainty in vulnerability assessments through evaluating potential alterations in historical rainfall extremes using an ensemble projection coming from multiple downscaling approaches is suggested. This allows for the selection of design storms based on the acceptable level of risk and given budgetary and operational restrictions.

The MELBS team winning entry for the EVA2017 competition for spatiotemporal prediction of extreme rainfall using generalized extreme value quantiles

We present our winning entry for the EVA2017 challenge on spatiotemporal prediction of extreme precipitation. The aim of the competition is to predict extreme rainfall quantiles that score as low as possible on the competition error metric. Good or bad predictions are defined only by the metric used. Our methodology was simple and produced accurate predictions under this metric. This outcome emphasizes the importance of cross-validation and identifying model over-fitting.

Constructing confidence intervals of extreme rainfall quantiles using Bayesian, bootstrap, and profile likelihood approaches

Hydrological risk is highly dependent on the occurrence of extreme rainfalls. This fact has led to a wide range of studies on the estimation and uncertainty analysis of the extremes. In most cases, confidence intervals (CIs) are constructed to represent the uncertainty of the estimates. Since the accuracy of CIs depends on the asymptotic normality of the data and is questionable with limited observations in practice, a Bayesian highest posterior density (HPD) interval, bootstrap percentile interval, and profile likelihood (PL) interval have been introduced to analyze the uncertainty that does not depend on the normality assumption. However, comparison studies to investigate their performances in terms of the accuracy and uncertainty of the estimates are scarce. In addition, the strengths, weakness, and conditions necessary for performing each method also must be investigated. Accordingly, in this study, test experiments with simulations from varying parent distributions and different sample sizes were conducted. Then, applications to the annual maximum rainfall (AMR) time series data in South Korea were performed. Five districts with 38-year (1973–2010) AMR observations were fitted by the three aforementioned methods in the application. From both the experimental and application results, the Bayesian method is found to provide the lowest uncertainty of the design level while the PL estimates generally have the highest accuracy but also the largest uncertainty. The bootstrap estimates are usually inferior to the other two methods, but can perform adequately when the distribution model is not heavy-tailed and the sample size is large. The distribution tail behavior and the sample size are clearly found to affect the estimation accuracy and uncertainty. This study presents a comparative result, which can help researchers make decisions in the context of assessing extreme rainfall uncertainties.

A framework for regional estimation of intensity–duration–frequency (IDF) curves

AbstractA regional, or pooled, approach to frequency analysis is explored in the context of the estimation of rainfall quantiles required for the formation of intensity–duration–frequency (IDF) curves. Resampling experiments are used, in conjunction with two rainfall data sets with long record lengths, to explore the merits of a pooled approach to the estimation of extreme rainfall quantiles. The width of the 95% confidence interval for quantile estimates is used as the primary basis to evaluate the relative merits of pooled and single site estimates of rainfall quantiles. Recommendations are formulated for applying the regional approach to frequency analysis, and these recommendations are used in the application of the regional approach to 40 sites with IDF data in southern Ontario, Canada. The results demonstrate that the regional approach is preferred to single site analysis for estimating extreme rainfall quantiles for conditions and data availability commonly encountered in practice. Copyright © 2014 John Wiley &amp; Sons, Ltd.

비정상성 GEV 모형을 이용한 행정구역별 미래 확률강우량 산정

국내에서는 설계강우량을 산정하기 위해서 정상성 강우빈도해석법이 일반적으로 적용되고 있다. 그러나, 기후변화 또는 기후 변동으로 인한 극치사상의 증가 등으로 최근의 강우패턴은 과거와는 다른 양상을 보여주고 있으며, 이러한 경향은 수문학적 설계를 위한 확률강우량 산정에 고려될 필요가 있다. 본 연구에서는 행정구역별 비정상성 강우빈도해석을 수행하였다. 이를 위하여 1973년부터 2012년까지 관측된 지점강우량을 이용하여 행정구역별 연최대강우량 자료를 구축하였다. 25년 이동평균방법으로 관측자료의 통계량과 GEV 분포함수의 모수 사이의 상관성을 검토한 후, 미래 특정 시점에 대한 분포함수의 모수를 추정할 수 있는 비선형 회귀식을 유도하였다. 본 연구에서 제시한 방법은 관측된 연최대강우량에 대하여 검증을 하였으며, 강우패턴의 변화를 정상성 강우빈도해석법에 비해 보다 적절히 반영하는 것으로 나타났다. 따라서, 본 연구에서 제시하는 행정구역별 비정상성 강우빈도해석법은 가까운 미래의 확률강우량 산정과 최근에 도입된 행정구역별 방재성능 목표강우량 산정에 유용할 것으로 판단된다. In South Korea, stationary frequency analysis methods are generally used for estimating design rainfalls in practice. However, due to climate change and/or variability, recent rainfall observations have significantly different patterns from the past so that the recent trends need to be considered to estimate extreme rainfall quantiles for hydrologic design. This study focused on estimating extreme rainfall quantiles in administrative districts across South Korea, after building nonstationary GEV model using annual maximum rainfall (AMR) datasets for 228 administrative districts from point rainfall measures from 1973 to 2012. A moving average method with 25-year window was used for investigating time-dependent statistics of AMR, such as mean, variance and skewness, and parameters of GEV distribution. From the analyses of relationships between statistics and distribution parameters, this study derived nonlinear regression equations for distribution parameters, which provide the estimates of distribution parameters at any future time. The overall results achieved in this study illustrate that the nonlinear regression equations can be easily incorporated into the hydrologic frequency analysis and provide appropriate estimates of design rainfalls in the near future.

Quantile-Based Downscaling of Precipitation Using Genetic Programming: Application to IDF Curves in Saskatoon

AbstractIntensity-duration-frequency (IDF) curves are commonly used in engineering planning and design. Considering the possible effects of climate change on extreme precipitation, it is crucial to analyze potential variations in IDF curves. This paper presents a quantile-based downscaling framework to update IDF curves using the projections of future precipitation obtained from general circulation models (GCMs). Genetic programming is applied to extract duration-variant and duration-invariant mathematical equations to map from daily extreme rainfall quantiles at the GCM scale to corresponding daily and subdaily extreme rainfall quantiles at the local scale. The proposed approach is applied to extract downscaling relationships and to investigate possible changes in the IDF curves for the City of Saskatoon, Canada. The results show that genetic programming is a promising tool for extracting mathematical mappings between extreme rainfall quantiles at the GCM and local scales. The duration-variant mappings w...

Adjustment of extreme rainfall statistics accounting for multidecadal climate oscillations

Summary Rainfall extremes exhibit temporal clustering at multi-decadal time scales, most probably as a result of persistence in large scale atmospheric circulation over such time scales. Analysis of a 107-year time series of 10 min rainfall intensities since 1898 at Uccle, Brussels, has shown that the 1960s and the 1990–2000s had a higher frequency and amplitude of high rainfall intensities at various time scales in the range between 10 min and 1 month. These periods are alternated with periods of lower rainfall quantiles, e.g. in the 1970–1980s. The climate oscillations have to be accounted for when calculating extreme rainfall statistics, e.g. IDF relationships and synthetic storms commonly applied on the basis of urban drainage systems design. The importance of this and how this climate oscillation accounting can be done is demonstrated in this paper based on the Uccle rainfall data. Old and new IDF statistics, based on, respectively, shorter and longer rainfall series have been compared. It is shown that recent increases in rainfall statistics should not necessarily be attributed to climate change but may also be due to a different positioning of the periods with available rainfall data in comparison with the climate oscillation high and low periods. Comparison of old IDF statistics based on the period 1967–1993 versus new statistics based on the full period 1898–2007 or the period 1970–2007 covering one climate oscillation cycle, shows 7.5% difference in extreme rainfall quantiles for return periods higher than 1 year. Adjustment with +7.5% is required to remove the bias in the old rainfall design values in comparison with the long-term statistics.

Extreme rainstorms: Comparing regional envelope curves to stochastically generated events

The depth‐duration envelope curves (DDECs) are regional upper bounds on observed rainfall maxima for several durations. Recently, a probabilistic interpretation has been proposed in the literature in order to associate a recurrence interval T to the DDECs and, consequently, to retrieve point rainfall quantiles for ungauged sites. Alternatively, extreme rainfall quantiles can be retrieved from long synthetic rainfall series obtained with stochastic rainfall generators calibrated to local time series of rainfall events. While DDECs are sensitive to outliers and data errors, the stochastic rainfall generator performance is affected by the limited record lengths used for calibration. The objective of this study is to assess the reliability of the two alternative methods by verifying if they give consistent results for a wide study region in Austria. Relative to previous studies, we propose some generalizations of the DDEC procedure in order to better represent the Austrian data. The comparison of rainfall quantiles estimated with the two methods for large T shows an excellent agreement for intermediate durations (from 1 to 6 h), while the agreement worsen for very short (15 min) and long (24 h) durations. The results are scrupulously analyzed and discussed in light of the exceptionality of rainfall events that set the regional envelopes and the characteristics of the stochastic generator used. Our study points out that the combined use of these regional and local methods can be very useful for estimating reliable point rainfall quantiles associated with large T within regions where many rain gauges are available, but with limited record lengths.

Reliability and robustness of rainfall compound distribution model based on weather pattern sub-sampling

Abstract. A new probabilistic model for daily rainfall, named MEWP (Multi Exponential Weather Pattern) distribution, has been introduced in Garavaglia et al. (2010). This model provides estimates of extreme rainfall quantiles using a mixture of exponential distributions. Each exponential distribution applies to a specific sub-sample of rainfall observations, corresponding to one of eight typical atmospheric circulation patterns that are relevant for France and the surrounding area. The aim of this paper is to validate the MEWP model by assessing its reliability and robustness with rainfall data from France, Spain and Switzerland. Data include 37 long series for the period 1904–2003, and a regional data set of 478 rain gauges for the period 1954–2005. Two complementary properties are investigated: (i) the reliability of estimates, i.e. the agreement between the estimated probabilities of exceedance and the actual exceedances observed on the dataset; (ii) the robustness of extreme quantiles and associated confidence intervals, assessed using various sub-samples of the long data series. New specific criteria are proposed to quantify reliability and robustness. The MEWP model is compared to standard models (seasonalised Generalised Extreme Value and Generalised Pareto distributions). In order to evaluate the suitability of the exponential model used for each weather pattern (WP), a general case of the MEWP distribution, using Generalized Pareto distributions for each WP, is also considered. Concerning the considered dataset, the exponential hypothesis of asymptotic behaviour of each seasonal and weather pattern rainfall records, appears to be reasonable. The results highlight : (i) the interest of WP sub-sampling that lead to significant improvement in reliability models performances; (ii) the low level of robustness of the models based on at-site estimation of shape parameter; (iii) the MEWP distribution proved to be robust and reliable, demonstrating the interest of the proposed approach.

Connaissance régionale des pluies extrêmes.: Comparaison de deux approches appliquées en milieu méditerranéen

This study compares different methods used to estimate extreme rainfall quantiles in an area with a Mediterranean climate. The first method (M1) is based on a stochastic model of hourly rainfall, which provides hourly rainfall series. The cumulative distribution functions (cdf) of extreme rainfall over various durations are deduced from the simulations. The second method (M2) is a regional approach based on the construction of a regional cdf of maximum annual daily rainfall. In the third method (M3), an exponential cdf is fitted to observed rainfall at a given gauging station. The three methods are compared with their parameters calibrated locally using the information observed at a given gauge, and using regionalised parameters. Comparison of M1 and M2 showed good agreement, with only relatively small differences between the rarest quantiles, less than 20% for the 1000-year return period. These differences can be explained by the regionalisation of the parameters. With both methods, a heavy tail of the daily maxima annual rainfall cdf deviates from the exponential cdf. Moreover, the regionalisation of M1 and M2 is more robust than with M3, which is much more influenced by sampling uncertainties.