Frequency analysis of precipitation extremes in Heihe River basin based on generalized Pareto distribution

Precipitation extremes could cause a series of social, environmental and ecological problems. This paper, taking Heihe River basin, the second largest inland river basin in China, as the study area, focused on the frequency analysis of precipitation extremes based on the historical daily precipitation records (1960–2010) at nine stations. Generalized Pareto distribution (GPD) was employed for fitting the peaks over threshold (POT) series, in which Hill plot, percentile method and the average annual occurrence number were used to select the threshold in GPD. Maximum likelihood estimate and L-moment were used to estimate the parameters. The inherent assumptions for POT series were investigated by auto-correlation coefficient, Mann–Kendall test, Spearman’s ρ test, cumulative deviation test and Worsley likelihood ratio test. 10, 20, 50 and 100 year precipitation extremes for Heihe River basin were calculated and analyzed as well. It was found the POT series derived from several methods involved were approximately independent and stationary, and GPD could give a satisfactory fit to the POT series for each station. For the upper and lower reaches, the frequency of precipitation extremes at long return periods (20, 50 year or longer) presented increasing in recent years, and the intensity of the highest precipitation were getting stronger as well. The intensity of the highest precipitation extremes for the lower reach (21 and 35 %) increased higher than those for the upper reach (10 and 11 %). For the middle reach, the frequency of precipitation extremes (over 20 year return level) was not found to be increased. The uneven spatial and temporal distribution of precipitation extremes for the basin especially for the upper and lower reaches were getting more and more serious, which would bring great challenges for the local water allocation and management.     

Statistical analysis of extreme events in a non-stationary context via a Bayesian framework: case study with peak-over-threshold data

Statistical analysis of extremes currently assumes that data arise from a stationary process, although such an hypothesis is not easily assessable and should therefore be considered as an uncertainty. The aim of this paper is to describe a Bayesian framework for this purpose, considering several probabilistic models (stationary, step-change and linear trend models) and four extreme values distributions (exponential, generalized Pareto, Gumbel and GEV). Prior distributions are specified by using regional prior knowledge about quantiles. Posterior distributions are used to estimate parameters, quantify the probability of models and derive a realistic frequency analysis, which takes into account estimation, distribution and stationarity uncertainties. MCMC methods are needed for this purpose, and are described in the article. Finally, an application to a POT discharge series is presented, with an analysis of both occurrence process and peak distribution.     

Frequency analysis of climate extreme events in Zanjan, Iran

In this study, generalized extreme value distribution (GEV) and generalized Pareto distribution (GPD) were fitted to the maximum and minimum temperature, maximum wind speed, and maximum precipitation series of Zanjan. Maximum (minimum) daily and absolute annual observations of Zanjan station from 1961 to 2011 were used. The parameters of the distributions were estimated using the maximum likelihood estimation method. Quantiles corresponding to 2, 5, 10, 25, 50, and 100 years return periods were calculated. It was found that both candidate distributions fitted to extreme events series, were statistically reasonable. Most of the observations from 1961 to 2011 were found to fall within 1–10 years return period. Low extremal index (θ) values were found for excess maximum and minimum temperatures over a high threshold, indicating the occurrence of consecutively high peaks. For the purpose of filtering the dependent observations to obtain a set of approximately independent threshold excesses, a declustering method was performed, which separated the excesses into clusters, then the de-clustered peaks were fitted to the GPD. In both models, values of the shape parameters of extreme precipitation and extreme wind speed were close to zero. The shape parameter was less negative in the GPD than the GEV. This leads to significantly lower return period estimates for high extremes with the GPD model.     

Rainfall frequency analysis using a mixed GEV distribution: a case study for annual maximum rainfalls in South Korea

Extreme rainfalls in South Korea result mainly from convective storms and typhoon storms during the summer. A proper way for dealing with the extreme rainfalls in hydrologic design is to consider the statistical characteristics of the annual maximum rainfall from two different storms when determining design rainfalls. Therefore, this study introduced a mixed generalized extreme value (GEV) distribution to estimate the rainfall quantile for 57 gauge stations across South Korea and compared the rainfall quantiles with those from conventional rainfall frequency analysis using a single GEV distribution. Overall, these results show that the mixed GEV distribution allows probability behavior to be taken into account during rainfall frequency analysis through the process of parameter estimation. The resulting rainfall quantile estimates were found to be significantly smaller than those determined using a single GEV distribution. The difference of rainfall quantiles was found to be closely correlated with the occurrence probability of typhoon and the distribution parameters.     

Spatial distribution and temporal trends of mean precipitation and extremes in the arid region,northwest of China,during 1960–2010

On the basis of daily precipitation records at 76 meteorological stations in the arid region, northwest of China, the spatial and temporal distribution of mean precipitation and extremes were analysed during 1960–2010. The Mann–Kendall trend test and linear least square method were utilized to detect monotonic trends and magnitudes in annual and seasonal mean precipitation and extremes. The results obtained indicate that both the mean precipitation and the extremes have increased except in consecutive dry days, which showed the opposite trend. The changes in amplitude of both mean precipitation and extremes show seasonal variability. On an annual basis, the number of rain days (R0.1) has significantly increased. Meanwhile, the precipitation intensity as reflected by simple daily intensity index (SDII), number of heavy precipitation days (R10), very wet days (R95p), max 1‐day precipitation amount (RX1day) and max 5‐day precipitation amount (RX5day) has also significantly increased. This suggests that the precipitation increase in the arid region is due to the increase in both precipitation frequency and intensity. Trends in extremes are very highly correlated with mean trends of precipitation. The spatial correlation between trends in extremes and trends in the mean is stronger for winter (DJF) than for annual and other seasons. The regional annual and seasonal precipitation and extremes are observed the step jump in mean in the late 1980s. Overall, the results of this study are good indicators of local climate change, which will definitely enhance human mitigation to natural hazards caused by precipitation extremes. Copyright © 2012 John Wiley & Sons, Ltd.     

Nonstationary extreme value analysis of temperature extremes in China

In a changing climate, the common assumption of stationarity of climate extremes has been increasingly challenged, raising the need to incorporate non-stationarity in extreme value modeling. In this study, quantile regression is used to identify the trends of annual temperature extremes and their correlations with two large climate patterns, the western Pacific subtropical high (WPSH) and the Arctic Oscillation (AO) at 357 stations in China. Statistical significant positive trends and correlations between warm (or cold) temperature extremes and WPSH (or AO) have been detected at most stations. The influence of WPSH on warm extremes is significant in southern China, while the AO mainly affects the cold extremes in northern and eastern China. Then, annual temperature extremes are fitted to generalized extreme value (GEV) distributions with time-varying parameters. The summer (or winter) mean daily maximum (or minimum) temperatures and two climate indices, the WPSH index and the AO index, are chosen as covariates. In total, 16 candidate GEV distribution models are constructed, and the best fitting model with the lowest Bayesian information criterion (BIC) is selected. The 20-year return levels of annual warm (or cold) extremes in the period 1961–1980 and 1991–2010 are computed and compared. The changes of 20-year return levels of annual warm and cold extremes are jointly determined by trend and distributional changes of annual temperature extremes. Analysis of large scale atmospheric circulation changes indicate that a strengthening anticyclonic circulation and increasing geopotential height in recent decades may have contributed to the changes in temperature extremes in China.     

Application of bivariate frequency analysis to the derivation of rainfall–frequency curves

Bivariate distributions have been recently employed in hydrologic frequency analysis to analyze the joint probabilistic characteristics of multivariate storm events. This study aims to derive practical solutions of application for the bivariate distribution to estimate design rainfalls corresponding to the desired return periods. Using the Gumbel mixed model, this study constructed rainfall–frequency curves at sample stations in Korea which provide joint relationships between amount, duration, and frequency of storm events. Based on comparisons and analyses of the rainfall–frequency curves derived from univariate and bivariate storm frequency analyses, this study found that conditional frequency analysis provides more appropriate estimates of design rainfalls as it more accurately represents the natural relationship between storm properties than the conventional univariate storm frequency analysis.     

Non-stationary frequency analysis of heavy rainfall events in southern France

Abstract

Heavy rainfall events often occur in southern French Mediterranean regions during the autumn, leading to catastrophic flood events. A non-stationary peaks-over-threshold (POT) model with climatic covariates for these heavy rainfall events is developed herein. A regional sample of events exceeding the threshold of 100 mm/d is built using daily precipitation data recorded at 44 stations over the period 1958–2008. The POT model combines a Poisson distribution for the occurrence and a generalized Pareto distribution for the magnitude of the heavy rainfall events. The selected covariates are the seasonal occurrence of southern circulation patterns for the Poisson distribution parameter, and monthly air temperature for the generalized Pareto distribution scale parameter. According to the deviance test, the non-stationary model provides a better fit to the data than a classical stationary model. Such a model incorporating climatic covariates instead of time allows one to re-evaluate the risk of extreme precipitation on a monthly and seasonal basis, and can also be used with climate model outputs to produce future scenarios. Existing scenarios of the future changes projected for the covariates included in the model are tested to evaluate the possible future changes on extreme precipitation quantiles in the study area.

Editor Z.W. Kundzewicz; Associate editor K. Hamed

Citation Tramblay, Y., Neppel, L., Carreau, J., and Najib, K., 2013. Non-stationary frequency analysis of heavy rainfall events in southern France. Hydrological Sciences Journal, 58 (2), 280–294.     

Constructing rainfall depth-frequency curves considering a linear trend in rainfall observations

Comprehensive flood prevention plans are established in large basins to cope with recent abnormal floods in South Korea. In order to make economically effective plans, appropriate design rainfalls are critically determined from the rainfall depth-frequency curves which take the occurrence of abnormal floods into consideration. Conventional approaches to construct the rainfall depth-frequency curves are based on the stationarity assumption. However, this assumption has a critical weak aspect in that it cannot reflect non-stationarities in rainfall observations. As an alternative, this study suggests the non-stationary Gumbel model (NSGM) which incorporates a linear trend of rainfall observations into rainfall frequency analysis to construct the rainfall depth-frequency curves. A comparison of various schemes employed in the model found that the proposed NSGM permits the estimation of the distribution parameters even when shifted in the future by using linear relationships between rainfall statistics and distribution parameters, and produces more acceptable estimates of design rainfalls in the future than the conventional model. The NSGM was applied at several stations in South Korea and then expected the design rainfalls to increase by up to 15–30% in 2050.     

Single station and regional analysis of daily rainfall extremes

A peaks over threshold (POT) method of analysing daily rainfall values is developed using a Poisson process of occurrences and a generalised Pareto distribution (GPD) for the exceedances. The parameters of the GPD are estimated by the method of probability weighted moments (PWM) and a method of combining the individual estimates to define a regional curve is proposed.     

Trends in frequency of precipitation extremes in the Yangtze River basin,China: 1960–2003 / Tendances d'évolution de la fréquence des précipitations extrêmes entre 1960 et 2003 dans le bassin versant du Fleuve Yangtze (Chine)

Abstract

The spatial distribution and trends in the frequency of precipitation extremes over the last 44 years (1960–2003), especially since 1990, have been analysed using daily precipitation data from 147 stations in the Yangtze River basin. The research results are as follows: (1) The 15 mm precipitation isohyet approximately divides the precipitation extremes (corresponding to the 95th percentile) of the stations in the middle and lower Yangtze reaches (higher) from those of the upper Yangtze reaches (lower). Also the starting time of the precipitation extremes in the middle and lower Yangtze reaches is earlier than of those in the upper Yangtze reaches. Precipitation extremes are concentrated mostly in June in the middle and lower Yangtze reaches, and July in the upper Yangtze reaches. (2) During the period 1960–2003, the first two decades had fewer precipitation extremes than the last two decades. There have been significant increasing trends and step changes in frequency of annual total precipitation extremes and precipitation extremes with a 1–5 day gap in the middle and lower Yangtze reaches. Precipitation extremes occur more frequently in shorter periods, separated by a few days. Precipitation extremes are also becoming more concentrated in the month with the highest frequency of extremes (June) in the middle and lower Yangtze reaches. In the upper Yangtze reaches, there is an upward tendency of extreme events in June. Increasing precipitation extremes in June for both the middle and lower, and the upper Yangtze reaches will increase the probability of flooding if the observed trends of the last 40 years continue into the future.     

Regionalization of precipitation characteristics in the Canadian Prairie Provinces using large-scale atmospheric covariates and geophysical attributes

Observed data at most stations are often inadequate to obtain reliable estimates of many hydro-meteorological variables that not only define water availability across a region but also the vulnerability of social infrastructure to climatic extremes. To overcome this, data from neighboring sites with similar statistical characteristics are often pooled. The pooling process is based on partitioning of a larger region into smaller sub-regions with homogeneous features of interest. The established approaches rely heavily on statistics computed from observed precipitation data rather than the covariates that play a significant role in modulating the regional and local climate patterns at various temporal and spatial scales. In this study, a new approach for identifying homogeneous regions for regionalization of precipitation characteristics is proposed for the Canadian Prairie Provinces. This approach incorporates information about large-scale atmospheric covariates, teleconnection indices and geographical site attributes that impact spatial patterns of precipitation in order to delineate homogeneous precipitation regions through combined use of multivariate approaches—principal component analysis, canonical correlation analysis and fuzzy C-means clustering. Results of the analyses suggest that the study area can be partitioned into five homogeneous regions. These partitions are validated independently for homogeneity using statistics computed from monthly and seasonal precipitation totals, and seasonal extremes from a network of observation stations. Furthermore, based on the identified regions, precipitation magnitude-frequency relationships of warm and cold season single- and multi-day precipitation extremes, developed through regional frequency analysis, are mapped spatially. Such estimates are important for numerous water resources related activities.     

Trends in precipitation extremes over the Yellow River basin in North China: Changing properties and causes

The Mann–Kendall test, composite analysis, and 68 high‐quality meteorological stations were used to explore the spatiotemporal variations and causes of precipitation extremes over the Yellow River basin (YRB) during the period of 1960–2011. Results showed that (a) the YRB is characterized by decreases of most precipitation indices, excluding the simple daily intensity index, which has increasing trends in most locations, suggesting that the intensity of rainfall and the probability of occurrence of droughts have increased during the last decades. (b) Trends of extreme precipitation show mixed patterns in the lower reach of the YRB, where drought–flood disasters have increased. The increases in heavy rainfall and decreases in consecutive wet days in recent years over the northwestern portions of the YRB indicate that the intensity and frequency of above‐normal precipitation have been trending upward in domains. In the central‐south YRB, the maximum 1‐day precipitation (RX1day) and precipitation on extremely wet days (R99p) have significantly increased, whereas the number of consecutive dry days has declined; these trends suggest that the intensity of precipitation extremes has increased in those regions, although the frequency of extreme and total rainfall has decreased. (c) The spatial distributions of seasonal trends in RX1day and maximum 5‐day precipitation (RX5day) exhibited less spatial coherence, and winter is becoming the wettest season regionwide, particularly over the central‐south YRB. (d) There were multiple and overlapping cycles of variability for most precipitation indices, indicating variations of time and frequency. (e) Elevation is intimately correlated with precipitation indices, and a weakening East Asian summer monsoon during 1986–2011 compared to that in 1960–1985 may have played an important role in the declines in most indices over the YRB. Therefore, the combined effects from local and teleconnection forcing factors have collectively influenced the variations in precipitation extremes across the YRB. This study may provide valuable evidence for the effective management of water resources and the conduct of agricultural activities at the basin scale.     

Evaluation of a spatial rainfall generator for generating high resolution precipitation projections over orographically complex terrain

Space–time variability of precipitation plays a key role as driver of many environmental processes. The objective of this study is to evaluate a spatiotemporal (STG) Neyman–Scott Rectangular Pulses (NSRP) generator over orographically complex terrain for statistical downscaling of climate models. Data from 145 rain gauges over a 5760-km² area of Cyprus for 1980–2010 were used for this study. The STG was evaluated for its capacity to reproduce basic rainfall statistical properties, spatial intermittency, and extremes. The results were compared with a multi-single site NRSP generator (MSG). The STG performed well in terms of average annual rainfall (+1.5 % in comparison with the 1980–2010 observations), but does not capture spatial intermittency over the study area and extremes well. Daily events above 50 mm were underestimated by 61 %. The MSG produced a similar error (+1.1 %) in terms of average annual rainfall, while the daily extremes (>50-mm) were underestimated by 11 %. A gridding scheme based on scaling coefficients was used to interpolate the MSG data. Projections of three Regional Climate Models, downscaled by MSG, indicate a 1.5–12 % decrease in the mean annual rainfall over Cyprus for 2020–2050. Furthermore, the number of extremes (>50-mm) for the 145 stations is projected to change between ?24 and +2 % for the three models. The MSG modelling approach maintained the daily rainfall statistics at all grid cells, but cannot create spatially consistent daily precipitation maps, limiting its application to spatially disconnected applications. Further research is needed for the development of spatial non-stationary NRSP models.     

Trend detection in river flow series: 2. Flood and low-flow index series / Détection de tendance dans des séries de débit fluvial: 2. Séries d'indices de crue et d'étiage

Abstract

Major floods in Europe and North America during the past decade have provoked the question of whether or not they are an effect of a changing climate. This study investigates changes in observational data, using up to 100-year-long daily mean river flow records at 21 stations worldwide. Trends in seven flood and low-flow index series are assessed using Mann-Kendall and linear regression methods. Emphasis was on the comparison of trends in these flow index series, particularly in peak-over-threshold (POT) series as opposed to annual maximum (AM) river flow series. There is a larger number of significant trends in the AM than in the POT flood magnitude series, probably relating to the way the series are constructed. Low flood peaks occurring at the beginning or end of a time series with trend may be too low to be selected for the POT analysis. However, one peak per year will always be selected for the AM series, making the slope steeper and/or the series longer, resulting in a more significant trend. There is no general pattern of increasing or decreasing numbers or magnitudes of floods, but there are significant increases in half of the low-flow series.     

A sample reconstruction method based on a modified reservoir index for flood frequency analysis of non-stationary hydrological series

Flood extremes, affected by climate change and intense human activities, exhibit non-stationary characteristics. As a result, the stationarity assumption of traditional flood frequency analysis (FFA) cannot be satisfied. Generally, the impacts of human activities, especially water conservancy projects (i.e., reservoirs), on extreme flood series are much greater than those of climate change; therefore, new FFA methods must be developed to address the non-stationary flood extremes associated with large numbers of reservoirs. In this study, a new sample reconstruction method is proposed to convert the reservoir-influenced annual maximum flow (AMF) series from non-stationary to stationary, thus warranting the feasibility of the traditional FFA approach for non-stationary cases. To be more specifically, a modified reservoir index (MRI(t)) is proposed and the original non-stationary AMF series are converted to stationary series by multiplying by a scalar factor 1/(1 ? MRI(t)), and thus traditional FFA can be adopted. Besides, Bayesian theory was applied to analyze the effect of uncertainty on the designed reconstructed AMF. As an example, the proposed method was applied to observations from Huangzhuang station located on the Hanjiang River. The original AMF observations from Huangzhuang displayed nonstationarity for the continuous construction of reservoirs in the basin. After applying the new method of sample reconstruction, the original AMF observations became stationary, and the designed AMFs were estimated using the reconstructed series and compared with those estimated based on the original observation series. In addition, Bayesian theory is adopted to quantify the uncertainty of designed reconstructed AMF and provide the expectation of the sampling distribution.     

Extreme precipitation time trends in Ontario, 1960–2010

The impact of climate change on the behaviour of intensity–duration–frequency curves is critical to the estimation of design storms, and thus to the safe design of drainage infrastructure. The present study develops a regional time trend methodology that detects the impact of climate change on extreme precipitation from 1960 to 2010. The regional time trend linear regression method is fitted to different durations of annual maximum precipitation intensities derived from multiple sites in Ontario, Canada. The results show the relationship between climate change and increased extreme precipitation in this province. The regional trend analysis demonstrates, under nonstationary conditions arising from climate change, that the intensity of extreme precipitation increased decennially between 1.25% for the 30‐min storm and 1.82% for the 24‐h storm. A comparison of the results with a regional Mann–Kendall test validates the found regional time‐trend results. The results are employed to extrapolate the intensity–duration–frequency curves temporally and spatially for future decades across the province. The results of the regional time trend assessment help with the establishment of new safety margins for infrastructure design in Ontario. Copyright © 2016 John Wiley & Sons, Ltd.     

Daily extreme precipitation and trends over China

Based on daily precipitation data of more than 2000 Chinese stations and more than 50 yr, we constructed time series of extreme precipitation based on six different indices for each station: annual and summer maximum(top-1) precipitation,accumulated amount of 10 precipitation maxima(annual, summer; top-10), and total annual and summer precipitation.Furthermore, we constructed the time series of the total number of stations based on the total number of stations with top-1 and top-10 annual extreme precipitation for the whole data period, the whole country, and six subregions, respectively. Analysis of these time series indicate three regions with distinct trends of extreme precipitation:(1) a positive trend region in Southeast China,(2) a positive trend region in Northwest China, and(3) a negative trend region in North China. Increasing(decreasing)ratios of 10–30% or even 30% were observed in these three regions. The national total number of stations with top-1 and top-10 precipitation extremes increased respectively by 2.4 and 15 stations per decade on average but with great inter-annual variations.There have been three periods with highly frequent precipitation extremes since 1960:(1) early 1960 s,(2) middle and late 1990 s,and(3) early 21 st century. There are significant regional differences in trends of regional total number of stations with top-1 and top-10 precipitation. The most significant increase was observed over Northwest China. During the same period, there are significant changes in the atmospheric variables that favor the decrease of extreme precipitation over North China: an increase in the geopotential height over North China and its upstream regions, a decrease in the low-level meridional wind from South China coast to North China, and the corresponding low moisture content in North China. The extreme precipitation values with a50-year empirical return period are 400–600 mm at the South China coastal regions and gradually decrease to less than 50 mm in Northwest China. The mean increase rate in comparison with 20-year empirical return levels is 6.8%. The historical maximum precipitation is more than twice the 50-year return levels.     

On the use of partial probability weighted moments in the analysis of hydrological extremes

The use of partial probability weighted moments (PPWM) for estimating hydrological extremes is compared to that of probability weighted moments (PWM). Firstly, estimates from at‐site data are considered. Two Monte Carlo analyses, conducted using continuous and empirical parent distributions (of peak discharge and daily rainfall annual maxima) and applying four different distributions (Gumbel, Fréchet, GEV and generalized Pareto), show that the estimates obtained from PPWMs are better than those obtained from PWMs if the parent distribution is unknown, as happens in practice. Secondly, the use of partial L‐moments (obtained from PPWMs) as diagnostic tools is considered. The theoretical partial L‐diagrams are compared with the experimental data. Five different distributions (exponential, Pareto, Gumbel, GEV and generalized Pareto) and 297 samples of peak discharge annual maxima are considered. Finally, the use of PPWMs with regional data is investigated. Three different kinds of regional analyses are considered. The first kind is the regression of quantile estimates on basin area. The study is conducted applying the GEV distribution to peak discharge annual maxima. The regressions obtained with PPWMs are slightly better than those obtained with PWMs. The second kind of regional analysis is the parametric one, of which four different models are considered. The congruence between local and regional estimates is examined, using peak discharge annual maxima. The congruence degree is sometimes higher for PPWMs, sometimes for PWMs. The third kind of regional analysis uses the index flood method. The study, conducted applying the GEV distribution to synthetic data from a lognormal joint distribution, shows that better estimates are obtained sometimes from PPWMs, sometimes from PWMs. All the results seem to indicate that using PPWMs can constitute a valid tool, provided that the influence of ouliers, of course higher with censored samples, is kept under control. Copyright © 2007 John Wiley & Sons, Ltd.