Annual Extreme Rainfall Research Articles

Investigating common trends of annual maximum rainfalls during heavy rainfall events in southern Taiwan

Summary Typhoons or heavy rainfall events account for a significant portion of annual extreme rainfall in southern Taiwan. This study built a dynamic time series model for long duration extreme rainfalls to investigate common trends in annual maximum precipitation. The annual maximum rainfall depths for 24-h duration (AM24 h) and annual maximum rainfall depths for 1-h duration (AM1 h) of the same event were observed at 16 rainfall stations in the Kaoping River watershed, Southern Taiwan. The relationship between short and long duration observations is difficult to directly evaluate from comparative statistical techniques. Dynamic factor analysis (DFA, a dimension reduction technique and can be adopted for analysis of non-stationary time series) was therefore used to identify underlying common trends of AM24 h time series and significant explanatory variables (AM1 h) contributing to variations of AM24 h. The results of best dynamic factor models (DFMs) show that the AM1 h of nearby rainfall stations at both high elevation (coefficient of efficiency, C eff = 0.924) and low elevation ( C eff = 0.909) successfully describe the AM24 h in the Kaoping River watershed. The AM1 h observed at high elevation, close to the study area center significantly relates to the AM24 h of most rainfall stations. The common trends of extreme precipitation at most stations are upward in the Kaoping River watershed. Due to this successful application of DFA, predicting AM24 h in the Kaoping River watershed should account for the dominant rainfall stations with annual maximum rainfalls for short durations, to provide important information to determine precipitation trends for long-term planning.

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.

Weighted likelihood copula modeling of extreme rainfall events in Connecticut

Summary Copulas have recently emerged as a practical method for multivariate modeling. To date, only limited amount of work has been done to apply copula-based modeling in the context of extreme rainfall analysis, and no work exists on modeling multiple characteristics of rainfall events from data at resolutions finer than hourly. In this study, trivariate copula-based modeling is applied to annual extreme rainfall events constructed from 15-min time series precipitation data at 12 stations within the state of Connecticut. Three characteristics (volume, duration, and peak intensity) are modeled by a multivariate distribution specified by three marginal distributions and a dependence structure via copula. A major issue in this application is that, because the 15-min precipitation data are only available fairly recently, the sample size at most stations is small, ranging from 10 to 33 years. For each station, we estimate the model parameters by maximizing a weighted likelihood, which assigns weight to data at stations nearby, borrowing strengths from them. The weights are assigned by a kernel function whose bandwidth is chosen by cross-validation in terms of predictive loglikelihood. The fitted model and sampling algorithms provide new knowledge on design storms and risk assessment in Connecticut.

Bayesian Changepoint Analysis for Extreme Events (Typhoons, Heavy Rainfall, and Heat Waves): An RJMCMC Approach

Abstract A hierarchical Bayesian framework is developed to identify multiple abrupt regime shifts in an extreme event series. Specifically, extreme events are modeled as a Poisson process with a gamma-distributed rate. Multiple candidate hypotheses are considered, under each of which there presumably exist a certain number of abrupt shifts of the rate. A Bayesian network involving three layers—data, parameter, and hypothesis—is formulated. A reversible jump Markov chain Monte Carlo (RJMCMC) algorithm is developed to calculate posterior probability for each hypothesis as well its associated within-hypothesis parameters. Based on the proposed RJMCMC algorithm, a simulated example is designed to illustrate the effectiveness of the method. Subsequently, the algorithm is applied to three real, rare event time series: the annual typhoon counts over the western North Pacific (WNP), the annual extreme heavy rainfall event counts at the Honolulu airport, and the annual heat wave frequency in the Chicago area. Results indicate that the typhoon activity over the WNP is very likely to have undergone a decadal variation, with two change points occurring around 1972 and 1989 characterized by the active 1960–71 epoch, the inactive 1972–88 epoch, and the moderately active 1989–2006 epoch. For the extreme rainfall case, only one shift around 1970 is found and heavy rainfall frequency has remained stationary since then. There is no evidence that the rate of the annual heat wave counts in the Chicago area has had any abrupt change during the past 50 years.

On the late twentieth century decrease in Australian east coast rainfall extremes

AbstractA change from negative to positive circulation anomalies over New South Wales (NSW) during the 1970s resulted in a decrease in east coastal low‐pressure systems and accompanying rain. Negative pressure anomalies over eastern Australia, anomalous onshore low‐level winds and larger NSW rainfall totals since 1950, occur in the cool phase of the IPO rather than the warm phase (post‐1976). Larger NSW extreme annual rainfall totals occurred prior to 1977 and were characterized by negative mean sea level pressure (MSLP) anomalies over eastern Australia. In contrast, extreme annual rainfall totals from 1977 were smaller and characterized by positive MSLP anomalies. Copyright © 2008 Royal Meteorological Society

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

Assessment of future change in intensity–duration–frequency (IDF) curves for Southern Quebec using the Canadian Regional Climate Model (CRCM)

Intensity–duration–frequency curves are used extensively in engineering to assess the return periods of rainfall events. The estimation and use of IDF curves rely on the hypothesis of rainfall series stationarity, namely that intensities and frequencies of extreme hydrological events remain unchanged over time. It is however expected that global warming will modify the occurrence of extreme rainfall events. In order to assess how extreme rainfall events will be modified in a future climate, an analysis of the Canadian Regional Climate Model (CRCM) simulations under control (1961–1990) and future (2041–2070) climates was performed. May to October annual maximum (MOAM) rainfall for 2-, 6-, 12- and 24-h durations were extracted and analyzed using regional frequency analysis for grid boxes covering the Southern Quebec region. Comparison with available rainfall records shows that CRCM estimates are consistent with those based on observed data considering the different spatial scales related to observed data (meteorological stations) and to simulated ones (grid boxes). Comparison of regional estimates in control and future climate at the grid box scale reveals that return periods of 2- and 6-h events will approximately halve in future climate while they will decrease by a third for 12- and 24-h events. Regional IDF curves at the grid box and the station scales are proposed. The analysis of spatial correlation of simulated MOAM series in control and future climates for the region under study suggests that, for a given duration, spatial correlations will decrease in a future climate suggesting that annual extreme rainfall events may result from more convective (and thus more localized) weather systems. Multi-model ensemble systems (different GCMs with different RCMs) as well as multi-member ensembles (investigation of possible sensitivity to initial conditions) are needed to investigate the impact of model structures on future change in extreme rainfalls.

Climatological Extremes of Simulated Annual Mean Rainfall

Abstract The Commonwealth Scientific and Industrial Research Organisation (CSIRO) Mark 2 global coupled climatic model has been used to generate a 10 000-yr simulation of “present” climate. The resultant dataset has been used to investigate a number of aspects of extremes associated with annual mean rainfall. Multimillennial time series of normalized rainfall amounts for selected points are used to highlight secular variability, spatial variations, and the differences between pluvial and drought conditions. Global distributions are also presented for selected rainfall characteristics, including the frequency of occurrence of specified rainfall anomalies with annual durations, the frequency of occurrence of 5-yr sequences of specified rainfall anomalies, and the maximum and minimum normalized rainfall amounts attained in the simulation. Such features cannot be obtained from observations because of their limited duration. A case study is also made of a megadrought over the southwestern United States, together with an analysis of the associated causal mechanisms. Given the exclusion of all external forcing from the model, it is concluded that the extreme annual mean rainfall extremes presented in the paper are attributable to stochastic events.

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.

Detection of trends in annual extreme rainfall

AbstractInformation on intensity–duration–frequency of rainfall is commonly required for a variety of hydrologic applications. In this study, trends are estimated for different durations of annual extreme rainfall using the regional average Mann–Kendall S trend test. The method of L‐moments was employed to delineate homogeneous regions. The trend test was modified to account for observed autocorrelation, and a bootstrap methodology was used to account for the observed spatial correlation.Numerical analysis was performed on 44 rainfall stations from the province of Ontario, Canada, for a 20 year time frame. This was done using data from homogeneous regions established using the L‐moments procedure for the annual maximum observations for the following durations: 5, 10, 15 and 30 min, and 1, 2, 6 and 12 h. Depending on different rainfall durations, four or five homogeneous regions were delineated.Based on a 5% significance level, approximately 23% of the regions tested had a significant trend, predominantly for short‐duration storms. Serial dependency was observed in 2·3% of data sets and spatial correlation was found in 18% of the regions. The presence of serial and spatial correlation had a significant impact on trend determination. Copyright © 2003 John Wiley & Sons, Ltd.

Implications of changes in seasonal and annual extreme rainfall

Future projections from climate models and recent observations show a worldwide increase in both the frequency and intensity of heavy rainfall, coinciding with widespread flooding and landslides in Europe. It is estimated, using regional frequency analysis, that the magnitude of extreme rainfall has increased two‐fold over parts of the UK since the 1960s. Intensities previously experienced, on average, every 25 years now occur at 6 year intervals; a consequence of both increased event frequency and changes in seasonality. These climatic changes may be explained by persistent atmospheric circulation anomalies and have huge economic and social implications in terms of increased flooding.

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.

Synthetic Generation of Tropical Rainfall Time Series Using an Event-Based Method

An algorithm for simulating tropical rainfall using an event-based method has been developed. The simulation process uses a one-step Markov chain model. The driving mechanism of the model is based on the statistics derived from rainfall recorded using the event-based method of recording proposed by Tan and Chiew. These statistics are expressed in terms of a transition matrix that can be used to generate the next event after the occurrence of the first. The model was applied to rainfall recorded in Singapore. Despite the relatively sparse source data, the results show that the synthetic rainfall time series reproduces the essential characteristics of tropical rainfall in terms of mean and total rainfall, and the internal characteristics of tropical rainfalls. Furthermore, this methodology is capable of generating plausible estimates of extreme annual rainfall.

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.

Estimation of probable maximum precipitation for a 2-day duration: Part 2 ? north Indian region

In a previous study the authors have estimated the probable maximum precipitation (PMP) for a 2-day duration using Hershfield's formulaXPMP =Xn +kmσn for stations in the southern Indian region. In this paper, the study is extended to estimate the PMP for stations in the north Indian region, north of 20°N. Maximum annual 2-day rainfall data for an 80-year period, from 1901, were obtained for 286 stations in the region. A mathematical relationship between the frequency factor (km) and the mean annual extreme rainfall (Xn) was developed to bekm = 18.15 exp (−0.0448Xn). This equation was used to obtainkm for different values ofXn and, subsequently, to estimate 2-day PMP values for the 286 stations. Using these PMP estimates, a generalised chart was prepared, showing the spatial distribution of 2-day PMP. It was found that 2-day PMP over the north Indian region varied from 60 cm to 130 cm, and the average ratio of the 2-day PMP to the highest observed 2-day rainfall was found to be 1.91. The results show that there have been instances when almost 2-day point PMP have occurred at some of the stations in the region. These results indicate that the statistically estimated PMP rainall are not therefore, mere theoretical estimates, but they can occur under optimum meteorological conditions.

Hydroclimatic fluctuations of the Upper Narmada catchment and its association with break-monsoon days over India

In this paper, hydroclimatic fluctuations of the Upper Narmada catchment (upto Narmadasagar damsite) have been studied by examining the time series (1901–80) of (i) 1-to 10-day annual extreme rainfall; (ii) seasonal total rainfall between May and October; (iii) the precipitation concentration index (PCI); (iv) a modified version of PCI(MPCI); and (v) parameters of the periods contributing specified percentages of rainfall to annual total. Most of these parameters followed the normal distribution and did not show any significant long-term trend. However, some dominant long period oscillations have been noticed in extreme rainfall, seasonal rainfall, PCI and MPCI series. Influence of break-monsoon days over India during July and August on the rainfall activities of the Upper Narmada catchment has also been investigated and salient findings discussed.

Deriving rainfall intensity-duration-frequency relationships and estimates for regions with inadequate data

Type 1 extreme-value distribution (Gumbel) was applied to the annual extreme rainfall data sets generated by 11 rainfall zones to estimate the parameters and hence the intensity-duration-frequency (IDF) rainfall. The chi-square test confirmed the appropriateness of the fitted distribution. Gumbel graphical plots and the computed confidence limits also showed that the Gumbel EV-1 function fits well the empirical distribution.

A Pilot study for the estimation of probable maximum precipitation using Hershfield Technique

Statistical technique developed by Hershfield has been used in this note to determine one-day PMP estimates for the plain areas of Uttar Pradesh. Extreme annual one-day rainfall data was collected for 230 stations in this region from the scrutiny of daily rainfall data of 60 to 70 years from 1891 to 1960. The enveloping value for the frequency factor Km in the modified Chow's general formula was found to be 12 for this region. This value was utilized in obtaining PMP values for 230 stations in this region. On the basis of this data a generalized chart of PMP was prepared for the plain areas of Uttar Pradesh for one-day duration. It has been seen that on an average in this region one-day PMP values obtained by this technique are 2.4 times the highest observed one-day rainfall during the past 60 to 70 years.