Extreme Rainfall Series Research Articles

Modelling nonlinear trend for developing non‐stationary rainfall intensity–duration–frequency curve

ABSTRACTThe infrastructure design is primarily based on rainfall intensity–duration–frequency (IDF) curves, and the existing IDF curves are based on the concept of stationary extreme value theory (EVT) (i.e. the occurrence probability of extreme precipitation is not expected to change significantly over time). But, the extreme precipitation events are increasing due to global climate change and questioning the reliability of our current infrastructure design. Based on recent developments in the EVT, recent studies proposed a method for developing non‐stationary rainfall IDF curve by incorporating linear trend in the location parameter of the generalized extreme value (GEV) distribution. Upon detecting a significant trend in the extreme rainfall series, directly applying the linear trend to develop non‐stationary IDF curves may increase the bias of the non‐stationary model. Hence, it is important to develop non‐stationary GEV model which has less bias than the stationary model by modelling nonlinear trend in the series.In this study, we try to develop non‐stationary GEV models with less bias by modelling nonlinear trend in the series using multi‐objective genetic algorithm (MOGA). In addition, the proposed GEV model is compared with the stationary GEV model and the linear trend‐based non‐stationary GEV model. Furthermore, the Wilmington city and the Hyderabad city non‐stationary IDF curves are developed and compared with stationary IDF curves. From the study results, it is observed that the proposed MOGA‐based method is able to build the good quality and less bias non‐stationary GEV models by modelling nonlinear trend in the series. In addition, it is also observed that the usage of linear trend for modelling non‐stationarity in the time series sometimes increase the bias of non‐stationary model.

Uncertainty Analysis in the Evaluation of the DDF Curves Parameters in Climate Change Scenarios

On the global scale, there is a robust observational evidence that, over the last decades, the frequency and intensity of extreme events significantly changed, even if regional and local studies have highlighted complex and non-uniform spatial patterns. Climate change can cause increased rainfall intensities which leads to an additional impact on drainage systems, due to the alteration of magnitude and frequency of peak flows over their service life. For this reason, the design criteria of urban drainage infrastructures need to be revised and updated, in order to take into account the possible variations of extreme rainfall. In particular, the Depth-Duration-Frequency (DDF) curves, widely used in engineering to assess the return periods of rainfall events, require an adjustment for climate change. The main purpose of this study is to provide a methodology to assess the DDF curves parameters in climate change scenarios, once the evidence of a statistically significant trend in extreme rainfall was verified. Specifically, a Bayesian procedure has been applied for two cases of study located in the Sicily (Southern Italy), in order to incorporate the effects of extreme rainfall variations on the definition of DDF curve for a future climate condition and to evaluate the uncertainty related to such projection. The climate projection has been compared with a baseline scenario representative of current climate conditions. Finally, the implications of the uncertainty related to the DDF parameters estimation on the design of real detention tanks were analyzed, thus providing an evaluation of their hydraulic performance under the assumption of climate change. Results showed that the assessment of DDF parameters from historical extreme rainfall series could not be adequate to provide reliable estimations of future design storm. Therefore, the occurring climate change cannot be neglected in the design procedure based on extreme rainfall estimation.

Uncertainty Analysis in the Evaluation of Extreme Rainfall Trends and Its Implications on Urban Drainage System Design

Future projections provided by climate models suggest that the occurrence of extreme rainfall events will increase and this is evidence that the climate is changing. Because the design of urban drainage systems is based on the statistical analysis of past events, variations in the intensity and frequency of extreme rainfall represent a critical issue for the estimation of rainfall. For this reason, the design criteria of drainage systems should take into account the trends in the past and the future climate changes projections. To this end, a Bayesian procedure was proposed to update the parameters of depth–duration–frequency (DDF) curves to assess the uncertainty related to the estimation of these values, once the evidence of annual maximum rainfall trends was verified. Namely, in the present study, the historical extreme rainfall series with durations of 1, 3, 6, 12 and 24 h for the period of 1950–2008, recorded by the rain gauges located near the Paceco urban area (southern Italy), were analyzed to detect statistically significant trends using the non‐parametric Mann‐Kendall test. Based on the rainfall trends, the parameters of the DDF curves for a five‐year return period were updated to define some climate scenarios. Finally, the implications of the uncertainty related to the DDF parameters estimation on the design of a real urban drainage system was assessed to provide an evaluation of its performance under the assumption of climate change. Results showed that the future increase of annual maximum precipitation in the area of study would affect the analyzed drainage system, which could face more frequent episodes of surcharge.

<b>Is the Conditional Density Network more suitable than the Maximum likelihood for fitting the Generalized Extreme Value Distribution?

The Generalized Extreme value Distribution (GEV) has been widely used to assess the probability of extreme weather events and the parameter estimation method is a key factor for improving its quantile estimates. On such background, this study aimed to indicate under which conditions (sample size and tail behavior) the Conditional Density Network (CDN) leads to better GEV quantile estimates than the widely used Maximum likelihood method (MLE) does. With Monte Carlo simulations and rainfall series of several Brazilians regions, we highlight the following results: the return period and the tail behavior of the GEV (specified by the shape parameter) are two of the main factors affecting the quantile estimates. For -0.1 ≤ shape ≤ 0.1 and sample size ≤ 50, the CDN outperformed the MLE. For shape ≥ 0.20 the CDN outperformed the MLE for all sample sizes (30-90). The results also suggested that the CDN is more suitable than the MLE for fitting the GEV parameter to the Brazilian extreme rainfall series. We conclude that when the shape parameter are equal to or greater than -0.1 the CDN should be preferred over the MLE.

From pointwise testing to a regional vision: An integrated statistical approach to detect nonstationarity in extreme daily rainfall. Application to the Sahelian region

Global warming is expected to intensify the hydrologic cycle. Documenting whether significant changes in the extreme precipitation regimes have already happened is consequently one of the challenging topics in climatic research. The high natural variability of extreme precipitation often prevents from obtaining significant results when testing changes in the empirical distribution of extreme rainfall at regional scale. A regional integrated approach is proposed here as one possible answer to this complex methodological problem. Three methods are combined in order to detect regionally significant trends and/or breakpoints in series of annual maximum daily rainfall: (1) individual stationarity tests applied to the raw point series of maxima, (2) a maximum likelihood testing of time‐dependent generalized extreme value (GEV) distributions fitted to these series, and (3) a heuristic testing of a regional time‐dependent GEV distribution. This approach is applied to a set of 126 daily rain gauges covering the Sahel over the period 1950–1990. It is found that only a few stations are tested as nonstationary when applying classical tests on the raw series, while the two GEV‐based models converge to show that the extreme rainfall series indeed underwent a negative breakpoint around 1970. The study evidences the limits of the widely used classical stationarity tests to detect trends in noisy series affected by sampling uncertainties, while using a parametric space and time‐dependent GEV efficiently reduces this effect. Showing that the great Sahelian drought was accompanied by a significant decrease of extreme rainfall events is the other main result of this study.

The climatic characteristics of extreme precipitations for short-term intervals in the watershed of Lake Maggiore

Alpine and Mediterranean areas are undergoing a profound change in the typology and distribution of rainfall. In particular, there has been an increase in consecutive non-rainy days, and an escalation of extreme rainy events. The climatic characteristic of extreme precipitations over short-term intervals is an object of study in the watershed of Lake Maggiore, the second largest freshwater basin in Italy (located in the north-west of the country) and an important resource for tourism, fishing and commercial flower growing. The historical extreme rainfall series with high-resolution from 5 to 45 min and above: 1, 2, 3, 6, 12 and 24 h collected at different gauges located at representative sites in the watershed of Lake Maggiore, have been computed to perform regional frequency analysis of annual maxima precipitation based on the L-moments approach, and to produce growth curves for different return-period rainfall events. Because of different rainfall-generating mechanisms in the watershed of Lake Maggiore such as elevation, no single parent distribution could be found for the entire study area. This paper concerns an investigation designed to give a first view of the temporal change and evolution of annual maxima precipitation, focusing particularly on both heavy and extreme events recorded at time intervals ranging from few minutes to 24 h and also to create and develop an extreme storm precipitation database, starting from historical sub-daily precipitation series distributed over the territory. There have been two-part changes in extreme rainfall events occurrence in the last 23 years from 1987 to 2009. Little change is observed in 720 min and 24-h precipitations, but the change seen in 5, 10, 15, 20, 30, 45, 60, 120, 180 and 360 min events is significant. In fact, during the 2000s, growth curves have flattened and annual maxima have decreased.

Modeling of short duration extreme rainfall events over Lower Yamuna Catchment

Short duration rainfall estimates and their intensities for different return periods are required for many purposes such as for designing flood for hydraulic structures, urban flooding etc. An attempt has been made in this paper to Model extreme rainfall events of Short Duration over Lower Yamuna Catchment. Annual extreme rainfall series and their intensities were analysed using EVI distribution for rainstorms of short duration of 5, 10, 15, 30, 45 & 60 minutes and various return periods have been computed. The Self recording rainguage (SRRGs) data for the period 1988-2009 over the Lower Yamuna Catchment (LYC) have been used in this study. It has been found that EVI distribution fits well, tested by Kolmogorov-Smirnov goodness of fit test at 5 % level of significance for each of the station.

Probabilistic structure of an annual extreme rainfall series of a coastal area of the State of São Paulo, Brazil

This study aimed to describe the probabilistic structure of the annual series of extreme daily rainfall (Preabs), available from the weather station of Ubatuba, State of São Paulo, Brazil (1935-2009), by using the general distribution of extreme value (GEV). The autocorrelation function, the Mann-Kendall test, and the wavelet analysis were used in order to evaluate the presence of serial correlations, trends, and periodical components. Considering the results obtained using these three statistical methods, it was possible to assume the hypothesis that this temporal series is free from persistence, trends, and periodicals components. Based on quantitative and qualitative adhesion tests, it was found that the GEV may be used in order to quantify the probabilities of the Preabs data. The best results of GEV were obtained when the parameters of this function were estimated using the method of maximum likelihood. The method of L-moments has also shown satisfactory results.

Frequency analyses of annual extreme rainfall series from 5 min to 24 h

The parameter estimation methods of (1) moments, (2) maximum-likelihood, (3) probability-weighted moments (PWM) and (4) self-determined PWM are applied to the probability distributions of Gumbel, general extreme values, three-parameter log-normal (LN3), Pearson-3 and log-Pearson-3. The special method of computing parameters so as to make the sample skewness coefficient zero is also applied to LN3, and hence, altogether 21 candidate distributions resulted. The parameters of these distributions are computed first by original sample series of 14 successive-duration annual extreme rainfalls recorded at a rain-gauging station. Next, the parameters are scaled by first-degree semi-log or log-log polynomial regressions versus rainfall durations from 5 to 1440 min (24 h). Those distributions satisfying the divergence criterion for frequency curves are selected as potential distributions, whose better-fit ones are determined by a conjunctive evaluation of three goodness-of-fit tests. Frequency tables, frequency curves and intensity–duration–frequency curves are the outcome. Copyright © 2010 John Wiley & Sons, Ltd.

Technical Note: Probability Distribution of Extreme Rainfall Series for Conservation Planning in a Sub-Humid Climate

The magnitude of a design storm, which is defined as the rainfall depth expected at a specified location for a given storm duration and probability of occurrence, is usually estimated by analyzing the extreme value rainfall data. A reliable estimate of the design storm, typically expressed in terms of return period, is essential for the design of conservation structures and efficiently managing the water resources. This problem is generally addressed by employing appropriate probability distributions describing the events in a given location. In this study, the annual extreme daily rainfall data of four stations was collected and analyzed in a sub-humid climate. Six two-parameter probability distributions, namely extreme value I, extreme value II, log-normal, gamma, logistic, log-logistic, and four three-parameter probability distributions, namely log-normal, extreme value II, gamma and log-logistic were compared for selecting appropriate distribution(s) to adequately describe the annual maximum one-day rainfall data. Maximum likelihood estimation technique was employed for obtaining parameter estimates of these distributions. The study on suitability of additional parameter in a three-parameter distribution over the two-parameter distribution of the same family revealed that no three-parameter distribution described the present data adequately. Two-parameter extreme value I along with log-normal and log-logistic distributions was found to be the best-fit for annual extreme daily rainfall data of Sahastradhara, Mussoorie, and Fakot stations in Uttarakhand state of India. Analysis of similar data of another station namely, Selakui revealed that two-parameter probability distributions, such as log-normal, extreme value I, gamma and log-logistic were found to describe the data almost equally well. On the basis of smallest variance of estimated extreme rainfall values in different return period and sample size combinations, extreme value I probability distribution was found to be most appropriate, and provided most stable estimate for describing annual extreme daily rainfall data. Annual extreme daily rainfall was estimated for 5-, 10-, 15-, 20-, 25-, and 30-year return periods using the best-fit two-parameter probability distributions for different stations. The region was found to be homogeneous. The best-fit distribution used to compute annual extreme daily rainfall values is an essential pre-requisite for designing soil and water conservation structures economically and efficiently.

Wakeby distribution for representing annual extreme and partial duration rainfall series

AbstractIn this study, to measure the upper right tail estimate performances for representing annual extreme and partial duration precipitation series at 31 stations in the northeastern and southeastern United States, the results of five‐parameter Wakeby‐L moments distribution were compared to those by beta‐κ, and beta‐P distributions. The statistics of modified Anderson‐Darling and average deviation (AD) and the bootstrap resampling to extrapolate the right tail beyond the data showed that the Wakeby distribution gave mostly better results than beta‐κ and beta‐P, and sometimes it produced comparable results to those by beta‐κ and beta‐P. Copyright © 2007 Royal Meteorological Society

Extreme rainfall analysis of Andhra Pradesh using a probability distribution model : A regional estimate

The study is an attempt to analyze the extreme rainfall events of Andhra Pradesh, a coastal state of Peninsular India, where both monsoon and post-monsoon seasons contribute significant rain. A network of 155 stations having data of seventy years or more during the period 1901-2000 has been used for the study. These stations are well distributed over the state. One-day, two-day and three-day extreme annual rainfall series are made and the isohyetal analysis demarcates three heavy rainfall receiving zones. Probability distribution functions have been fitted for the regional estimates of climate changes in extreme rainfall series of each station. Both the extreme value distribution viz., Gumbel and log normal distribution fit well with latter one giving slightly better fit over the former. Goodness of fit of the distribution is tested with Kolmogorov - Smirnov Statistic.

Detecting trends of extreme rainfall series in Sicily

Abstract. The objective of the study is to assess the presence of linear and non linear trends in annual maximum rainfall series of different durations observed in Sicily. In particular, annual maximum rainfall series with at least 50 years of records starting from the 1920’s are selected, and for each duration (1, 3, 6, 12 and 24 h) the Student’s t test and theMann- Kendall test, respectively, for linear and non linear trend detection, are applied also by means of bootstrap techniques. The effect of trend on the assessment of the return period of a critical event is also analysed. In particular, return periods related to a storm, recently occurred along the East Coast of Sicily, are computed by estimating parameters based on several sub-series extracted from the whole observation period. Such return period estimates are also compared with confidence intervals computed by bootstrap. Results indicate that for shorter durations, the investigated series generally exhibit increasing trends while as longer durations are considered, more and more series exhibit decreasing trends.

Divergence criteria in extreme rainfall series frequency analyses

Extreme rainfall series (ERS) are treated as successive-duration events of from 5 min to 24 h in most parts of the world. In Turkey, as in European countries, the ERS of standard durations of 5, 10, 15, 30, 60 min, and 2, 3, 4, 5, 6, 8, 12, 18, 24 h are recorded, and these sample series are analysed to ultimately determine the depth—duration—frequency (DDF) relationships. If a probability distribution function (pdf) is used for these ERS, the frequency curves in the form of graphical quantile functions may intersect each other at high return periods, due to possible data recording errors, and an extreme rainfall magnitude of a longer duration may turn out to be smaller than that of a shorter duration beyond some high return period. In this study: (a) the criteria of divergence of the quantile functions of various pdfs used in frequency analyses of ERS are depicted; (b) necessary and sufficient conditions for divergence of the quantile functions and ultimately of the DDF curves are analytically deduced; (c) scaling relationships between conventional statistics and rainstorm durations, and between probability-weighted moments and rainstorm durations, are investigated; (d) necessary adjustments to the parameters of four commonly-used pdfs are shown; and (e) a comprehensive example using rainfall data recorded at the Florya gauging station (Istanbul, Turkey) is presented.

Extreme rainfall in a changing climate: regional analysis and hydrological implications in Tuscany

AbstractA comprehensive analysis of the extreme rainfalls in Tuscany, Italy, is carried out with the aim of understanding and quantifying the uncertainties connected with the estimation of the design storms, which is very important for a sound basin management at urban or larger scales. The historical extreme rainfall series of durations 1, 3, 6, 12 and 24 h collected at 81 rain gauges located at representative sites in Tuscany are computed to detect a possible trend by means of two tests: the Pearson linear correlation coefficient and the Mann–Kendall test. The generalized extreme value distribution is employed to compute design storms with a 30 years return period; hence a preliminary map of the most hazardous areas is built up. The design storms are then computed for several consecutive 20 year moving time windows (1 year step) to evaluate intrinsic (climatological) uncertainties in the series. A regionalization of the difference between the design storms calculated for different periods is performed. The hydrological consequences of this kind of climate variability are demonstrated to have a major impact on the design of hydraulic works in a basin. Copyright © 2002 John Wiley & Sons, Ltd.

Investigating the changes in extreme rainfall series recorded in an urbanised area

The aim of this study is to investigate and quantify changes in the rainfall regime of the metropolitan area of Palermo characterised by increasingly strong urbanisation. The rainfall data, considered in this study, were collected on a yearly basis from eight rain gauges within and outside the metropolitan area of Palermo, Sicily, Italy. A preliminary analysis made on the annual total rainfall depths showed a global reduction of total annual rainfall, with two different trends: more regular for the series observed in the rain gauges within the urbanised area and more variable for the series observed in the rain gauges outside the area. A further analysis has been performed using the series of maximum intensity for fixed duration (1, 3, 6, 12, 24 hrs) and annual daily maxima. The analysis of the trend in the extreme rainfall series has been performed by estimating the maximum rainfall depth corresponding to a fixed return period using the EV1 distribution with parameters estimated using L-moments. The analysis of all series indicates a global reduction of rainfall intensities, both for internal and external series, in disagreement with the results obtained by other authors.

Selecting a probability distribution for extreme rainfall series in Malaysia

This paper discusses the comparative assessment of eight candidate distributions in providing accurate and reliable maximum rainfall estimates for Malaysia. The models considered were the Gamma, Generalised Normal, Generalised Pareto, Generalised Extreme Value, Gumbel, Log Pearson Type III, Pearson Type III and Wakeby. Annual maximum rainfall series for one-hour resolution from a network of seventeen automatic gauging stations located throughout Peninsular Malaysia were selected for this study. The length of rainfall records varies from twenty-three to twenty-eight years. Model parameters were estimated using the L-moment method. The quantitative assessment of the descriptive ability of each model was based on the Probability Plot Correlation Coefficient test combined with root mean squared error, relative root mean squared error and maximum absolute deviation. Bootstrap resampling was employed to investigate the extrapolative ability of each distribution. On the basis of these comparisons, it can be concluded that the GEV distribution is the most appropriate distribution for describing the annual maximum rainfall series in Malaysia.

Uncertainties and trends in extreme rainfall series in Tuscany, Italy: effects on urban drainage networks design

Sound basin management at urban or greater scale needs reliable design storm definition. A statistical analysis is carried out on extreme annual rainfall series for durations of 1, 3, 6 and 12 hours occurring at two gauges in Tuscany, Italy. Kendall's test is applied to the extremal series to detect a definite increasing (or decreasing) trend. A special form of an ARIMA model is also fitted to the series to quantify possible linear trends and their respective significance. Results show a clearly increasing trend at shortest duration at both gauges, no trend at longer ones. Time evolution of design storms for all durations and return periods up to 25 years is derived and analysed based on Gumbel distribution. Applications are presented concerning impacts of uncertainties for the design of urban drainage networks.

Uncertainties and trends in extreme rainfall series in Tuscany, Italy: Effects on urban drainage networks design

Sound basin management at urban or greater scale needs reliable design storm definition. A statistical analysis is carried out on extreme annual rainfall series for durations of 1, 3, 6 and 12 hours occurring at two gauges in Tuscany, Italy. Kendall's test is applied to the extremal series to detect a definite increasing (or decreasing) trend. A special form of an ARIMA model is also fitted to the series to quantify possible linear trends and their respective significance. Results show a clearly increasing trend at shortest duration at both gauges, no trend at longer ones. Time evolution of design storms for all durations and return periods up to 25 years is derived and analysed based on Gumbel distribution. Applications are presented concerning impacts of uncertainties for the design of urban drainage networks.

Trends in the annual extreme rainfall events of 1 to 3 days duration over India

In this paper, the annual extreme rainfall series in the time scale of 1 to 3 days duration at 316 stations, well distributed over the Indian region, covering 80-years of rainfall data from 1901 to 1980 were analysed for trend and persistence using standard statistical tests. It has been found that the annual extreme rainfall records of most stations are free from trend and persistence. However, the extreme rainfall series at stations over the west coast north of 12°N and at some stations to the east of the Western Ghats over the central parts of the Peninsula showed a significant increasing trend at 95% level of confidence. Stations over the southern Peninsula and over the lower Ganga valley have been found to exhibit a decreasing trend at the same level of significance. The data series of the stations which showed trends were subjected to a 10-year moving average and the resulting smoothed series have been discussed. It may be said that this increasing or decreasing trend in the annual extreme rainfall events at a few places will have tremendous implications in the hydrologic studies and dam design projects.