Peaks-over-threshold Series Research Articles

Change and coincidence risk analysis of floods in the Mahanadi River Basin, India

ABSTRACT Coincidence flood risk due to the simultaneous flood occurrences on both mainstream and its tributary results in downstream inundation of a confluence. Therefore, this study was taken up for coincidence flood risk analysis of Mahanadi River basin considering the annual maximum (AM) and the peak over threshold (POT) series. In this study, the Mann–Kendall trend test was performed to analyze the trend in flood magnitudes, while circular statistics was used to analyze the persistence in flood timing. The joint distributions between the streams were established using bivariate copula functions considering flood magnitudes and occurrence dates as variables. The results of MK test revealed a mixture of significant and insignificant trends for AM series for the selected stations, while the trends were insignificant for POT series. Additionally, the flood occurrence dates showed a high level of persistence. It is evident from the results that the coincidence risk is high for Seorinarayan–Bamnidhi confluence point with a risk value of 7.63 × 10−3. The coincidence risk increases mostly from late July to mid-September, and the coincidence risk is high for more frequently occurring flood events. The obtained results will help in prioritizing flood hazard zones for effective flood mitigation strategies in Mahanadi River basin.

Use of peak over threshold data for flood frequency estimation: An application at the UK national scale

This study investigates choices of statistical distributions to represent the threshold exceedance frequency and magnitude of peaks-over-threshold (POT) series from a national dataset of extreme hydrological events from 842 gauging stations in the UK. From the initial POT series, two new series were created, POT1 and POT3, representing POT series with an average of, respectively, one and three exceedances per year. Using a χ2 goodness-of-fit test, the choice of distributions for both the annual exceedance counts and the magnitude of threshold exceedances were explored for both the POT1 and POT3 datasets. The results show that the negative binomial and geometrical distributions provide a better fit to the annual exceedance count than the Poisson distribution typically assumed. These results are particularly pronounced when considering the POT3 dataset and in the South-East of the UK where many river flow series are dominated by slow responding groundwater dominated catchments. Finally, estimates of design floods with a return period of 2 and 100 years were obtained for each POT series and compared to the equivalent estimates obtained from direct at-site analysis of the annual maximum series. The results show a good alignment between the magnitude of the design floods estimated by the two methods, but a generally lower standard deviation of estimates obtained from the POT data, as quantified using a bootstrap procedure. The results presented here show that the POT series could beneficially replace the current operational guidelines based on annual maximum series for design flood estimation in the UK.

Improved Extreme Rainfall Frequency Analysis Using a Two‐Step Kappa Approach

AbstractAccurate estimation of annual exceedance probabilities (AEPs) of extreme rainfalls through rainfall frequency analysis is a critical step in engineering design for flood mitigation and disaster response. Here we show how the estimation of rainfall frequency curves can be improved by fitting a four‐parameter Kappa distribution to a peaks‐over‐threshold (POT) series. To fit the Kappa distribution to POT data we present a two‐step fitting approach based on maximum likelihood estimation which separately models storm intensity and the arrival frequency. First, a Generalized Pareto distribution (GPA) describing storm intensity is fitted, followed by a Binomial distribution for storm arrivals. We compare the performance of this two‐step Kappa approach to an analogous two‐step Generalized Extreme Value (GEV) approach and to Kappa and GEV distributions fitted to annual maxima series (AMS), using both synthetic and real‐world data representative of Australian climatic conditions. The experiments show that leveraging additional information from the POT series in the two‐step Kappa approach dramatically improves quantile estimation and reduces uncertainty compared to fitting either the GEV or the Kappa distributions to AMS, particularly for rare quantiles. When skew–kurtosis properties of extreme rainfalls are well represented by the Kappa but not the GEV, the two‐step Kappa approach yields unbiased quantiles under extrapolation, while the use of GEV can lead to highly biased estimates. From these results, we believe the two‐step Kappa approach is suitable for both at‐site and regional rainfall frequency analyses as it can accommodate distributions ranging from GPA to GEV without encountering over‐fitting problems generally associated with four‐parameter distributions.

Detection of trends in flood magnitude and frequency in Canada

Changes in flood regimes in Canada were examined using a large-scale dataset of hydrometric stations from across the country. Significant trends were analysed in time series of both Annual Maximum (AMAX) and Peaks-Over-Threshold (POT) series of streamflow data. POT series were extracted from daily flows for each watershed using a semi-automated threshold selection method. Since flood regimes are complex by nature, a multi-temporal and multifaceted approach was employed to identify and properly characterize the types of changes. Common time periods of the recent 30-, 40-, 50-, and 60-years were studied. Trends were investigated both in terms of flood magnitude and frequency of these time series. Changes were examined using different groupings of sites based on dominant hydro-climatic regions, drainage area size, and land-use changes based on hydrometric reference stations. Trends were examined both at local and field scale. Notably significant trends were identified in the Atlantic, Central, Prairie, and Northern regions. Additionally, Reference Hydrometric Basin Network (RHBN) watersheds were found to have more statistically significant trends than the non-RHBN sites.New Hydrological InsightsAn increased number of threshold exceeding events was observed from this analysis. Flow magnitudes series showed more increasing trends in the most recent time windows while there are more decreasing trends in longer time periods. Different types of changes were observed for different hydro-climatic regions.

On the Exact Distribution of Correlated Extremes in Hydrology

AbstractThe analysis of hydrological hazards usually relies on asymptotic results of extreme value theory, which commonly deals with block maxima or peaks over threshold (POT) data series. However, data quality and quantity of block maxima and POT hydrological records do not usually fulfill the basic requirements of extreme value theory, thus making its application questionable and results prone to high uncertainty and low reliability. An alternative approach to better exploit the available information of continuous time series and nonextreme records is to build the exact distribution of maxima (i.e., nonasymptotic extreme value distributions) from a sequence of low‐threshold POT. Practical closed‐form results for this approach do exist only for independent high‐threshold POT series with Poisson occurrences. This study introduces new closed‐form equations of the exact distribution of maxima taken from low‐threshold POT with magnitudes characterized by an arbitrary marginal distribution and first‐order Markovian dependence, and negative binomial occurrences. The proposed model encompasses and generalizes the independent‐Poisson model and allows for analyses relying on significantly larger samples of low‐threshold POT values exhibiting dependence, temporal clustering, and overdispersion. To check the analytical results, we also introduce a new generator (called Gen2Mp) of proper first‐order Markov chains with arbitrary marginal distributions. An illustrative application to long‐term rainfall and streamflow data series shows that our model for the distribution of extreme maxima under dependence takes a step forward in developing more reliable data‐rich‐based analyses of extreme values.

Application of the non-stationary peak-over-threshold methods for deriving rainfall extremes from temperature projections

Concerns about climate change are amplifying interest in future rainfall extremes. However, there are big differences between the statistics of rainfall extremes obtained using future rainfall time series produced from various climate models. Such large uncertainties create a lot of confusion in establishing climate change adaptation measures. Looking at future rainfall extremes at a particular site yields increasing trends in some climate models and decreasing trends in others. The spatial patterns of rate of change in rainfall extremes also vary widely, depending on the climate model. As a result, they often do not gain the public’s trust. We believe that this difficulty in obtaining credibility does not come from a lack of theory or technique, but from an approach that persuades the public of uncertain future rainfall extremes. In this study, we employed a novel approach to integrate a co-variate of the not-stationary Peak-Over-Threshold (POT) – Generalized Pareto distribution (GPD) model identified at each site with its future projection information for obtaining future rainfall extreme ensembles. Rainfall extremes are obtained from the observed rainfall time series using the POT method, and the scale parameter among GPD parameters are applied as a function of surface air temperature (SAT) or dew-point temperature (DPT). At this time, the threshold of the POT series is set to match the results of frequency analysis of the annual maximum series and the POT series for each site as much as possible. The behavior of future rainfall extremes is analyzed by inputting the future SAT or DAT produced from various climate models into the non-stationary frequency model using the co-variate. As a result of comparing the rainfall extremes obtained using the future rainfall time series directly with the future rainfall extremes obtained indirectly using the proposed method, it was found that the proposed approach projected future design rainfall depths with much less variation between climate models. The spatial pattern of rate of change was also consistent regardless of climate model. The proposed method is expected to contribute to the public’s confidence in future rainfall extremes under climate change scenarios and to be of practical help in formulating reasonable climate change adaptation policies.

Generalized distributions for modeling precipitation extremes based on the L moment approach for the Amman Zara Basin, Jordan

Extreme event magnitude and frequency are prerequisites for accurately designing and managing various water infrastructure systems. This paper studies precipitation extremes in the Amman Zara Basin (AZB) using daily precipitation records from 24 weather stations during a period that exceeds 50 years. Two extreme precipitation series (the annual maximum (AM) and the peak over threshold (POT)), four generalized probability distributions (generalized extreme value (GEV), generalized Pareto (GP), generalized lognormal (GLN), and generalized logistic (GLO)) and the L moment method for distribution parameter estimation are used. A mix of increasing and decreasing trends is observed at different stations for both the AM and POT series over the study period. Since the POT series considers up to the fifth largest precipitation in some years, in contrast to the AM series, and skips the largest precipitation in the AM series in other years, the trend analysis results for the POT series differ slightly from those for the AM series. According to the goodness-of-fit (Kolmogorov-Smirnov test and L moment diagram), the probability distributions GEV, GLN, and GLO can better fit the AM series, with no unique distribution among them consistently ranking the best for all stations, while the POT series is better fitted by the GP distribution. The calculated extreme precipitation amounts of the AM series are up to 18% greater than those of the POT series for the same return period. Additionally, the AM series can describe extreme precipitation events better than the POT series based on relative error calculations. The 50- and 100-year extreme precipitation events occurred more frequently in recent years.

Variations and Statistical Probability Characteristic Analysis of Extreme Precipitation in the Hekouzhen-Longmen Region of the Yellow River, China

Under the impact of climate change, the variation in the magnitude and frequency of extreme precipitation events has become a major issue worldwide. Based on the daily precipitation data at 9 meteorological stations and 111 precipitation stations in the Hekouzhen-Longmen region (HLR) in the middle reaches of the Yellow River Basin during 1966–2015, the spatial and temporal variations in and statistical probability characteristics of extreme precipitation were investigated. The probability distribution of extreme precipitation in the HLR was simulated with the annual maximum (AM) series and peak over threshold (POT) series by three extreme distributions, namely, generalized extreme value (GEV) distribution, generalized Pareto (GP) distribution, and gamma distribution. The parameters of the GEV, GP and gamma distributions were estimated by the L-moments method, and the best fit model was selected by the Kolmogorov-Smirnov (K-S) test. The results showed that high value area of extreme precipitation was located in the southeast part of the HLR, while the lower value area was mainly distributed in the northwestern part of the HLR and the upper reaches of the Wuding River Basin. A positive trend of annual maximum precipitation was detected at half of the stations, and the other half of the stations were found to show a negative trend from 1966 to 2015, while the changing trends of extreme precipitation at almost all of the stations were nonsignificant. From the results of the K-S test, the GEV distribution can better fit the AM series, and the GP distribution can better fit the POT series. The estimated extreme precipitation of the AM series is larger than that of the POT series with the same return period at most stations.

High-spatial-resolution probability maps of drought duration and magnitude across Spain

Abstract. Assessing the probability of occurrence of drought is important for improving current drought assessment, management and mitigation measures, and strategies across Spain. This study employed two well-established drought indices, the Standardized Precipitation Index (SPI) and the Standardized Precipitation Evapotranspiration Index (SPEI), to characterize drought duration and magnitude at different timescales over Spain. In order to map the drought hazard probability, we applied the extreme value theory and tested different thresholds to generate peak-over-threshold (POT) drought duration and magnitude series. Our results demonstrate that the generalized Pareto (GP) distribution performs well in estimating the frequencies of drought magnitude and duration. Specifically, we found a good agreement between the observed and modelled data when using upper percentiles to generate the POT series. Spatially, our estimations suggest a higher probability of extreme drought events in southern and central Spain compared to the northern and eastern regions. Also, our study found spatial differences in drought probability estimations as a function of the selected drought index (i.e. SPI vs. SPEI) and timescale (i.e. 1, 3, 6, and 12 months). Drought hazard probability maps can contribute to the better management of different sectors (e.g. agriculture, water resources management, urban water supply, and tourism) at national, regional, and even local scale in Spain.

Pooled flood frequency analysis: a comparison based on peaks-over-threshold and annual maximum series

ABSTRACTDespite some theoretical advantages of peaks-over-threshold (POT) series over annual maximum (AMAX) series, some practical aspects of flood frequency analysis using AMAX or POT series are still subject to debate. Only minor attention has been given to the POT method in the context of pooled frequency analysis. The objective of this research is to develop a framework to promote the implementation of pooled frequency modelling based on POT series. The framework benefits from a semi-automated threshold selection method. This study introduces a formalized and effective approach to construct homogeneous pooling groups. The proposed framework also offers means to compare the performance of pooled flood estimation based on AMAX or POT series. An application of the framework is presented for a large collection of Canadian catchments. The proposed POT pooling technique generally improved flood quantile estimation in comparison to the AMAX pooling scheme, and achieved smaller uncertainty associated with the quantile estimates.

Change and Climatic Linkage for Extreme Flows in Typical Catchments of Middle Tianshan Mountain, Northwest China

Due to an absence of an essential daily data set, changing characteristics, and cause of flow extremes in the Tianshan Mountains are rarely explored in depth. In this study, daily based long-term meteorological and hydrological observation data were collected in four typical watersheds in the middle Tianshan Mountains; Manne-Kendall trend analysis and Pettit’s test were used to detect the trends and alterations of extreme flow series; Generalized Extreme Value distribution (GEV) and General Pareto distribution (GDP) models were used to describe the probability distributions of annual maximum (AM) and peaks over threshold (POT) series based on daily discharge; and the relationship between extreme flow and climate indices, were also investigated. The findings indicated that, change of the AM series at five hydrological stations experienced positive trends; the POT series generally showed no significant trends, while the peaks over threshold number (POTN) present a positive trend at the five stations. Change points exist in the POT and occurrence time of maximum daily discharge in spring (AM-SPR) series at the Kensiwate (KSWT) station in Manas watershed; the mean extreme flow decreased after 1986, and the occurrence time the annual maximum daily flow in spring significant forward after 1978. The AM series can well fit the GEV distribution, while the POT series fit the GDP distribution better; the GEV model performed worse in estimating flood events with high return period than low return period events. Moreover, acceleration of glacier melting lead to the magnitude and frequency increments of flood in the north slope; intensifying and frequent precipitation extremes are dominate factors of extreme flow variations in south slope watersheds which without large amount of glacier coverage; and continually temperature rising in spring and increased precipitation in winter lead to the change on magnitude and timing of spring extreme floods.

Influence of climate change on flood magnitude and seasonality in the Arga River catchment in Spain

Climate change projections suggest that extremes, such as floods, will modify their behaviour in the future. Detailed catchment-scale studies are needed to implement the European Union Floods Directive and give recommendations for flood management and design of hydraulic infrastructure. In this study, a methodology to quantify changes in future flood magnitude and seasonality due to climate change at a catchment scale is proposed. Projections of 24 global climate models are used, with 10 being downscaled by the Spanish Meteorological Agency (Agencia Estatal de Meteorologia, AEMET) and 14 from the EURO-CORDEX project, under two representative concentration pathways (RCPs) 4.5 and 8.5, from the Fifth Assessment Report provided by the Intergovernmental Panel on Climate Change. Downscaled climate models provided by the AEMET were corrected in terms of bias. The HBV rainfall-runoff model was selected to simulate the catchment hydrological behaviour. Simulations were analysed through both annual maximum and peaks-over-threshold (POT) series. The results show a decrease in the magnitude of extreme floods for the climate model projections downscaled by the AEMET. However, results for the climate model projections downscaled by EURO-CORDEX show differing trends, depending on the RCP. A small decrease in the flood magnitude was noticed for the RCP 4.5, while an increase was found for the RCP 8.5. Regarding the monthly seasonality analysis performed by using the POT series, a delay in the flood timing from late-autumn to late-winter is identified supporting the findings of recent studies performed with observed data in recent decades.

Detection of trends in magnitude and frequency of flood peaks across Europe

ABSTRACTThis study analyses the differences in significant trends in magnitude and frequency of floods detected in annual maximum flood (AMF) and peak over threshold (POT) flood peak series, for the period 1965–2005. Flood peaks are identified from European daily discharge data using a baseflow-based algorithm and significant trends in the AMF series are compared with those in the POT series, derived for six different exceedence thresholds. The results show that more trends in flood magnitude are detected in the AMF than in the POT series and for the POT series more significant trends are detected in flood frequency than in flood magnitude. Spatially coherent patterns of significant trends are detected, which are further investigated by stratifying the results into five regions based on catchment and hydro-climatic characteristics. All data and tools used in this study are open-access and the results are fully reproducible.

Probability distribution of extreme precipitation in Beijing based on extreme value theory

In this study, the statistical characteristics of the probability distribution in precipitation extremes in Beijing were explored and discussed based on the extreme value theory. The extreme precipitation series were filtered from the daily precipitation data (45 rain gauge stations) in the warm season during 1960–2012 based on the annual maximum (AM) and peak-over-threshold (POT) method. The generalized extreme distribution (GEV) and generalized Pareto distribution (GPD) were used to fit the two precipitation series and to investigate their statistic characteristics. The parameters of GEV and GPD distribution were estimated by the L-moment method. The best distribution was determined by the Kolmogorov-Smirnov test and then the best distribution was used to estimate the precipitation extremes in different return periods. The results showed that the mean values of AM series for all the rain gauges apart from Banbidian and Yanhecheng were larger than that of POT series, whereas the minimum values of AM series were lower than that of POT series. Furthermore, the optimal distribution of 40 sites for the AM series were GEV distribution, and the best distribution 38 sites for the POT series were GPD distribution, based on the results of the Kolmogorov-Smirnov test. Finally, the distributions of precipitation extremes in different return periods for this two series were similar, with the high value in the south and east and the low value in the north and west. Overall, the estimated precipitation amounts by the AM series were larger than that of POT series in the different return periods, which means the precipitation extremes based on the AM series will be relatively safer when it was used in the engineering design.

A similarity index for storm runoff due to saturation excess overland flow

• We propose and demonstrate an index for similarity in the storm event response of catchments to rainfall. • The similarity index is based on the steady state assumption. • The index is applicable to catchments where runoff is generated by saturation excess overland flow. • The index was applied to 236 independent storm events on eight catchments in southeast Australia. • The index’s effectiveness was assessed by comparing its groupings with those obtained from a flood frequency analysis. An index for the determination of hydrologic similarity is proposed and demonstrated. The index is based on the steady state assumption and is applicable for small- to medium-sized catchments where storm runoff is generated principally by the saturation excess mechanism – a key runoff generation mechanism in humid regions. The index uses variables that can be derived from rainfall and streamflow measurements and topographic and soil hydraulic attributes. The index is applied to eight gauged catchments located in southeast Australia. Comparisons of similarity index values with groupings obtained from a peaks-over-threshold (POT) analysis of daily maxima of hourly runoff series show good agreement. A sensitivity analysis of the index and the POT series indicated that these results are reasonably robust provided catchments are allowed to have partial memberships in all of the groupings identified.

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.

Regional estimates of intense rainfall based on the Peak-Over-Threshold (POT) approach

The Peak-Over-Threshold (POT) approach is an interesting alternative to the one based on Annual Maxima (AM) series since it gives the opportunity to take into consideration extreme events that would not be considered otherwise. It has also been recognized that the regional approach improves statistical inference when compared to the local approach, assuming that the region is statistically homogeneous. A regional POT approach was developed and applied to the network stations located in southern Quebec. POT series for 5-, 10-, 15-, 30-min and 1-, 2-, 6- and 12-h durations were constructed assuming a fixed exceedance rate. An analysis of local POT series showed that the intra-annual variability of the Generalized Pareto Distribution (GPD) parameters needs to be taken into consideration. Models of various complexities were defined combining local and regional representations as well as the intra-annual variability of GPD parameters. Regional likelihood was estimated and models were compared based on the Akaike Information Criterion (AIC). Models with regional shape and scale parameters and accounting for intra-annual variability were selected for all durations. Spatial covariates were also introduced through a simple model linking GPD parameters to latitude, longitude and altitude. The sensitivity of results to threshold values and selected models was also investigated. Interpolated maps of intense rainfall over the studied area are finally proposed.

극치수문자료의 계절성 분석 개념 및 비정상성 빈도해석을 이용한 확률강수량 해석

수문자료의 계절성은 수자원관리의 관점에서 매우 중요한 요소로서 계절성의 변동은 댐의 운영, 홍수조절, 관개용수 관리 등 다양한 분야와 밀접한 관계를 가지고 있다. 수문빈도해석을 위해 POT 자료와 같은 부분기간치계열을 사용함으로써 자료의 확충, 계절성 확보, 발생빈도모형의 구축 등이 가능하다. 본 연구에서는 POT 자료의 장점을 효과적으로 빈도해석에 연계시키는 방법론으로서 POT 자료로부터 계절성을 추출하고 이를 빈도해석과 연계시켜 Bayesian 기법을 기반으로 하는 비정상성 빈도해석 모형을 구축하였다. 서울지점의 관측 자료로부터 98% Threshold를 적용하여 POT 자료를 추출하였으며, GEV 분포에 대한적합성을 검토하였다. 위치 및 규모매개변수의 계절적변동성을 Fourier 급수로 표현하고, Bayesian Markov Chain Monte Carlo 모의를 통해 매개변수들의 사후분포를 추정하였으며, 사후분포와 Quantile 함수를 이용하여 재현기간에 따른 확률강수량을 추정하였다. 계절성을 고려한 비정상성빈도해석 결과 7~8월의 비정상성 확률강수량과 기존 정상성빈도해석의 결과가 유사한 값을 나타내고 있으며 동시에 계절성을 반영한 확률강수량의 거동을 효과적으로 모의가 가능하였다. Seasonality of hydrologic extreme variable is a significant element from a water resources managemental point of view. It is closely related with various fields such as dam operation, flood control, irrigation water management, and so on. Hydrological frequency analysis conjunction with partial duration series rather than block maxima, offers benefits that include data expansion, analysis of seasonality and occurrence. In this study, nonstationary frequency analysis based on the Bayesian model has been suggested which effectively linked with advantage of POT (peaks over threshold) analysis that contains seasonality information. A selected threshold that the value of upper 98% among the 24 hours duration rainfall was applied to extract POT series at Seoul station, and goodness-fit-test of selected GEV distribution has been examined through graphical representation. Seasonal variation of location and scale parameter (<TEX>$\mu$</TEX> and <TEX>$\sigma$</TEX>) of GEV distribution were represented by Fourier series, and the posterior distributions were estimated by Bayesian Markov Chain Monte Carlo simulation. The design rainfall estimated by GEV quantile function and derived posterior distribution for the Fourier coefficients, were illustrated with a wide range of return periods. The nonstationary frequency analysis considering seasonality can reasonably reproduce underlying extreme distribution and simultaneously provide a full annual cycle of the design rainfall as well.

L-moment estimation using annual maximum (AM) and peak over threshold (POT) series in regional analysis of flood frequencies

This article is a contribution to the development of robust approaches for frequency analysis in hydrology based on regional datasets. It focuses on finding relations between flood estimates based on Annual Maximum Series (AMS) and Peak Over Threshold Series (POTS). A consistent rule is elaborated for changing between the AMS and POTS representations for the individual observed values, for the choice of index flood and for parameter estimation. The point of departure for the analysis is the Langbein formula. The median related to AM as index flood is recommended, because, besides being robust, this characteristic can be estimated from both AMS and POTS. The methodology allows a direct comparison between L-moments of the annual maximum based on AMS and POTS, respectively, when the PWM method for estimating L-moments is applied. A conclusion of the analysis is that AM and POT data give identical results for estimation of AM L-moments but the latter has the smallest estimation errors.

The POT model described by the generalized Pareto distribution with Poisson arrival rate

The use of the peaks over threshold (POT) model described by the generalized Pareto distribution with Poisson arrival rate, which results in the generalized extreme value (GEV) distribution for the annual maximum (AM) series for flood frequency analysis, is discussed. Estimation of the generalized Pareto distribution by the method of probability weighted moments (PWM) is formulated for both known and unknown thresholds. The effect of raising the threshold of the POT series on high quantile estimation is investigated. A comparison of the efficiencies of the POT and AM models in high quantile estimation is made. It is shown that the threshold of the POT series can be raised to a reasonably high level without affecting the efficiency of high quantile estimation. This property is useful in practice. When one cannot be certain that both small and large values in a sample are well described by a single simple distribution or that peaks are independent of each other, a relatively high threshold can be introduced to overcome these difficulties without reduction in efficiency. It is also shown that the POT and AM models are of similar efficiency even when a relatively high threshold is used for the POT series. It is suggested that there is no theoretical reason to use the AM model in preference to the POT model.