Nonstationary Generalized Extreme Value Models Research Articles

Nonstationary quantity-duration-frequency (QDF) relationships of lowflow in the source area of the Yellow River basin, China

Study regionThe source area of the Yellow River (SAYR) located in the northeastern part of the Qinghai-Tibet Plateau, China Study focusThis study attempts to produce the quantity-duration-frequency (QDF) relationships of lowflow through a nonstationary approach of the generalized extreme value (GEV) models. Detailed derivation of theoretical model of different structures and parameter estimation is presented as the central part, followed by model evaluation and recommendation. Time and two climate indices, i.e., Arctic Oscillation (AO) and Eastern Asia (EA), are selected as covariates. New hydrological insights for the regionFor the SAYR, nonstationary GEV models incorporating additional climate-informed covariates show apparent strengths over stationary GEV model. Using AO and EA as covariates, dual-covariate model has not shown apparent advantages over single-covariate model. The introduction of climate indices as critical covariates, in addition to time, is found to be a good choice in the construction of nonstationary GEV models for obtaining the QDF relationships and analyzing multivariate properties of lowflow. The results could help to guide the emergency management and regulation of water resources during the lowflow season, and to assistant the design of water engineering for the future period.

Analysis of maximum precipitation in Thailand using non‐stationary extreme value models

AbstractNon‐stationarity in heavy rainfall time series is often apparent in the form of trends because of long‐term climate changes. We have built non‐stationary (NS) models for annual maximum daily (AMP1) and 2‐day precipitation (AMP2) data observed between 1984 and 2020 years by 71 stations and between 1960 and 2020 by eight stations over Thailand. The generalized extreme value (GEV) models are used. Totally, 16 time‐dependent functions of the location and scale parameters of the GEV model are considered. On each station, a model is selected by using Bayesian and Akaike information criteria among these candidates. The return levels corresponding to some years are calculated and predicted for the future. The stations with the highest return levels are Trad, Samui, and Narathiwat, for both AMP1 and AMP2 data. We found some evidence of increasing (decreasing) trends in maximum precipitation for 22 (10) stations in Thailand, based on NS GEV models.

Importance of non-stationary analysis for assessing extreme sea levels under sea level rise

Abstract. Increased coastal flooding caused by extreme sea levels (ESLs) is one of the major hazards related to sea level rise. Estimates of return levels obtained under the framework provided by extreme-event theory might be biased under climatic non-stationarity. Additional uncertainty is related to the choice of the model. In this work, we fit several extreme-value models to two long-term sea level records from Venice (96 years) and Marseille (65 years): a generalized extreme-value (GEV) distribution, a generalized Pareto distribution (GPD), a point process (PP), the joint probability method (JPM), and the revised joint probability method (RJPM) under different detrending strategies. We model non-stationarity with a linear dependence of the model's parameters on the mean sea level. Our results show that non-stationary GEV and PP models fit the data better than stationary models. The non-stationary PP model is also able to reproduce the rate of extremes occurrence fairly well. Estimates of the return levels for non-stationary and detrended models are consistently more conservative than estimates from stationary, non-detrended models. Different models were selected as being more conservative or having lower uncertainties for the two datasets. Even though the best model is case-specific, we show that non-stationary extremes analyses can provide more robust estimates of return levels to be used in coastal protection planning.

The role of teleconnection in the occurrence probability of extreme precipitation over China based on extreme value theory

Non-stationarity of extreme climate events has been reported worldwide in recent decades, and traditional stationary analysis methods are no longer sufficient to properly reveal the occurrence probability of climate extremes. Based on the 0.25°C × 0.25°C gridded precipitation data (i.e., CN05.1), stationary and non-stationary models of generalized extreme value (GEV) and generalized Pareto (GP) distributions are adopted to estimate the occurrence probability of extreme precipitation over China during 1961–2018. Low-frequency oscillation (LFO) indices, such as El Niño-Southern Oscillation (ENSO), Indian Ocean Dipole (IOD), North Atlantic Oscillation (NAO), Southern Annular Mode (SAM), and Pacific Decadal Oscillation (PDO), are included as time-varying covariates in the non-stationary GEV and GP models. Results illustrate that the occurrence probability of extreme precipitation estimated from the stationary GEV and GP distributions shows a significant increasing trend in northwestern and southeastern China, and the opposite trend in southwestern, central, and northeastern China. In comparison with stationary model, the fitness of extreme precipitation series is improved for both the GEV and GP distributions if these LFO indices are used as time-varying covariates. Positive ENSO, IOD and PDO tend to cause negative anomalies in the occurrence probability of extreme precipitation in northeastern China and Tibet Plateau, and positive anomalies in southern China. Positive NAO and SAM phases mainly tend to cause positive anomalies in southern China. The circulation patterns of extreme precipitation anomalies associated with these LFO indices are discussed from aspects of precipitable water, vertical integrated moisture transport, 500-hPa geopotential height and 850-hPa wind field.

Estimating the impact of urbanization on non-stationary models of extreme precipitation events in the Yangtze River Delta metropolitan region

Rapid urbanization has significantly increased the proportion of impervious surfaces in Yangtze River Delta urban agglomeration (YRDUA), hence quantifying its impact on extreme precipitation events is essential for waterlogging control and urban planning. The spatiotemporal evolution patterns of extreme precipitation indices (EPIs) based on a non-stationary Generalized Extreme Value (GEV) model are analyzed in urban, suburban, and rural stations. Additionally, the degree of change of the recurrence levels are calculated to evaluate the effect of the urbanization process on EPIs in these stations. The results indicated that (1) Except for CWD, other EPIs show an increasing trend and EPIs with significantly increasing trend distributed in the downwind direction of the YRD. The percentages of significantly positive trends in EPIs, accounted for more than 85%, are mainly in the urban and suburban stations. (2) The optimal non-stationary GEV model with urbanization factor is predominately distributed in the highly urbanized areas. Urbanization factor has a significant impact on short-term, high-intensity precipitation and PRCPTOT in urban areas. (3) While the proportion of urban impervious areas in the urban area increased from 0.11 in 1985 to 0.63 in 2016, the effect of urbanization on EPIs changes from negative to positive and R95p, R25, R50, PRCPTOT in urban are much higher than those in rural after 2000. Urbanization significantly affects the recurrence levels of Rx5day in the rural, urban, and suburban stations, which increased by 27%, 29%, and 29%, respectively. The degree of change in the recurrence level in the suburban and urban areas is greater than that in the rural areas.

Uncertainty of Rate of Change in Korean Future Rainfall Extremes Using Non-Stationary GEV Model

Interest in future rainfall extremes is increasing, but the lack of consistency in the future rainfall extremes outputs simulated in climate models increases the difficulty of establishing climate change adaptation measures for floods. In this study, a methodology is proposed to investigate future rainfall extremes using future surface air temperature (SAT) or dew point temperature (DPT). The non-stationarity of rainfall extremes is reflected through non-stationary frequency analysis using SAT or DPT as a co-variate. Among the parameters of generalized extreme value (GEV) distribution, the scale parameter is applied as a function of co-variate. Future daily rainfall extremes are projected from 16 future SAT and DPT ensembles obtained from two global climate models, four regional climate models, and two representative concentration pathway climate change scenarios. Compared with using only future rainfall data, it turns out that the proposed method using future temperature data can reduce the uncertainty of future rainfall extremes outputs if the value of the reference co-variate is properly set. In addition, the confidence interval of the rate of change of future rainfall extremes is quantified using the posterior distribution of the parameters of the GEV distribution sampled using Bayesian inference.

Nonstationary bayesian modeling of precipitation extremes in the Beijing-Tianjin-Hebei Region, China

This paper investigates the nonstationarity of precipitation extremes by incorporating time-varying and physical-based explanatory covariates, using daily precipitation data across the Beijing-Tianjin-Hebei (BTH) region, China. We perform the stationary and nonstationary generalized extreme value (GEV) models based on the Bayesian framework to estimate the expected return levels of precipitation extremes with the 90% credible intervals. Results reveal that the nonstationarity of precipitation extremes is not prominently visible for the majority of sites in BTH. However, the nonstationary GEV models exhibit better performance to capture the variations of precipitation extremes by comparison to the stationary models based on four evaluation criteria. Further, this work attempts to determine the best covariate to illustrate the possible effects of environmental changes on the frequency analysis. Results indicate that the El Nino-Southern Oscillation (ENSO) is the top of the best covariates, followed by the East Asian summer monsoon, North Atlantic Oscillation (NAO) and local temperature anomaly. Moreover, the best covariates are dominated by the physical-based covariates, and the best models with nonlinear functions of covariates are found in the majority of sites. Finally, the best-fitted models are used to estimate the design values of return levels in precipitation extremes. Results illustrate that the differences between the stationary modeling and nonstationary modeling in the median condition of covariates are not significant for most of the sites. But the discrepancies will be enhanced if the covariates locate in a high (95-percentile) or low (5-percentile) value. Our findings suggest that the nonstationary modeling of precipitation extremes might prove more useful and reliable, especially in the uncommon conditions of physical-based covariates.

Modeling power loss during blackouts in China using non-stationary generalized extreme value distribution

Power loss during blackouts shows an increasing complexity with the increase in the size of power grids. Traditional statistical methods based on the assumption of stationarity can lead to inappropriate assessments of blackouts. This study builds on the generalized extreme value (GEV) distribution by introducing time as a covariate to account for possible non-stationarities. The location, scale, and shape parameters of GEV are modeled step-by-step through the one-factor-at-a-time experiment. The results indicate that the GEV model of the annual maximum power loss in China exhibits a significant change of the scale parameter. By contrast, changes in location and shape parameters are not significant. Overall, the power loss during blackouts is tested to change with time, which reflects the sustained increase in the variability of power loss due to the growing size of power grids. The mean tends to be stable and the distribution type remains the same, which can be related to technological advances that improve the reliability of power grids. The non-stationary GEV model with time as a covariate can effectively analyze power loss during blackouts in China. It has the potential to be extended to describe non-stationary high-dimensional characteristics of power grids.

21st Century flood risk projections at select sites for the U.S. National Park Service

Assessing flood risk using stationary flood frequency analysis techniques is commonplace. However, it is increasingly evident that the stationarity assumption of these analyses does not hold as anthropogenic climate change could shift a site’s hydroclimate beyond the range of historical behaviors. We employ nonstationary flood frequency models using the generalized extreme value (GEV) distribution to model changing flood risk for select seasons at twelve National Parks across the U.S. In this GEV model, the location and/or scale parameters of the distribution are allowed to change as a function of time-variable covariates. We use historical precipitation and modeled flows from the Variable Infiltration Capacity model (VIC), a land-surface model that simulates land–atmosphere fluxes using water and energy balance equations, as covariates to fit a best nonstationary GEV model to each site. We apply climate model projections of precipitation and VIC flows to these models to obtain future flood probability estimates. Our model results project a decrease in flood risk for sites in the southwestern U.S. region and an increase in flood risk for sites in northern and eastern regions of the U.S. for the selected seasons. The methods and results presented will enable the NPS to develop strategies to ensure public safety and efficient infrastructure management and planning in a nonstationary climate.

Stationary and Nonstationary Generalized Extreme Value Models for Monthly Maximum Rainfall in Sabah

Generalized Extreme Value (GEV) model is the combination of three types of distribution class namely Gumbel, Fréchet and Weibull distributions of the Extreme Value Theory (EVT). In hydrological studies, GEV model is widely applied in the modelling of extreme rainfall. The nature of hydrological variables is highly complex, especially with the changing climate and frequent occurrences of extreme events. As such, some rainfall models assume rainfall series as stationary, while some as nonstationary. In this study, GEV models based on stationary and nonstationary data are used to assess monthly maximum rainfall data within Sabah, Malaysia and performance comparison between both GEV models is conducted. Theoretically both stationary and nonstationary GEV models are based on the same foundation, however nonstationary GEV model allows the location and scale parameters to be expressed as cyclic function of time. In this study, the stationary and the nonstationary GEV models are individually fitted to rainfall data at selected stations. Monthly maximum rainfall is blocked, and the estimated location (μ), scale (σ) and shape (ξ) parameters are estimated by using Maximum Likelihood Estimation method. Performance of both GEV models are compared based on the Akaike Information Criterion, Bayesian Information Criterion and the likelihood ratio goodness of fit tests. Results showed that nonstationary GEV model is the best fit. The inclusion of cyclic covariates in the GEV model gives improvement on the stationary GEV model at the study region. It is also concluded that, Gumbel is identified as the significant distribution for monthly maximum rainfall in Sabah at 5% significance level.

Modelling spatial variation of extreme precipitation over Ho Chi Minh City under nonstationary condition

Understanding the magnitude and spatial variation of extreme rainfall events are required for decision making and adaptation strategies for flood risk. In Ho Chi Minh City (HCMC), heavy rainfall, which is considered as a main cause of floods, witnessed an increase in frequency and magnitude in last few decades. Although nonstationarity in extreme rainfall has been proved in many places of the world, research into nonstationarity feature in extreme rainfall in HCMC has not been paid attention thoroughly. In this study, the spatial variation of extreme precipitation over Ho Chi Minh City is modelled under nonstationary condition. The generalized extreme value (GEV) distribution with location made a nonlinear function of time is applied to annual maximum daily rainfall. The study results show that the nonstationary GEV model is found to be superior in capturing extreme precipitation events when compared to the stationary GEV model. The extreme rainfall estimates under the stationary condition are lower than those under the nonstationary condition in most stations. Besides, the spatial variation of extreme rainfall under nonstationary condition shows a significant difference in extreme estimates between the periods of 1980–1984 and 2010–2014 in study area.

The assessment of return probability of maximum ozone concentrations in an urban environment of Delhi: A Generalized Extreme Value analysis approach

High ozone episodes have become a serious issue specially in megacities of developing countries. In this study an attempt has been made to understand the changes in the extreme ozone concentration due to different precursor compounds and meteorological variables in a given time period by applying Generalized Extreme Value (GEV) theory. The return probabilities of the extreme ozone concentrations were estimated for both classical stationary assumption as well as nonstationary assumption given the fact that ozone time series have both trend and multiple periodicities. Under stationary case, the distribution parameters were allowed to remain stationary, but in nonstationary case, distribution parameters were allowed to vary as a function of precursor compounds (Benzene, Toluene, mp-Xylene, NO, NO2) and meteorological variables (temperature and relative humidity). Daily maximum ozone concentrations were found to follow heavy tailed Fréchet distribution in both stationary and nonstationary conditions. The inclusion of covariate into the classical model explains the dynamic nature of ozone depending on its precursor variables. Principal components were also used as covariates in nonstationary GEV distribution model. The estimated return levels of ozone from the stationary model, were found to be 97.89, 144.34, 188.44, 232.10, 310.33, 366.47 and 429.97 μg/m3 for 3, 7, 15, 30, 90, 180 and 365-day return period, respectively. In case of non-stationary GEV model the estimated return levels for 3, 7, 15, 30, 90, 180 and 365-day period were in the range 38.38–140.96, 84.31–184.35, 115.92–225.26, 166.61–337.21, 189.46–388.30 and 214.98–445 μg/m3, respectively. The highest median return level of O3 for 3-day return period (100.35 μg/m3) was observed due to temperature as covariate, for 7-day (146.04 μg/m3) and 15- day (189.85 μg/m3) return period, it was observed due to Benzene as a covariate and for rest of the 4 different return periods, NO was found responsible for the highest median return level of O3 (233.52, 312.40, 369.02 and 433.06 μg/m3 for 30, 90, 180 and 365-day respectively). Seasonal analysis finds O3 extremes to be high in monsoon and premonsoon seasons and low in winter period. The impact of nonstationary condition is exemplified by the fact that the 365 day return level of maximum ozone concentration was found to exceed within just 20 days for a lower concentration of precursor Benzene (i.e. 214.48 μg/m3). Results underline the role of the principal components of the precursor compounds in governing the maximum ozone concentration in any city.

Flood frequency analysis for annual maximum streamflow using a non-stationary GEV model

Under changing environment, the streamflow series in the Yangtze River have undergone great changes and it has raised widespread concerns. In this study, the annual maximum flow (AMF) series at the Yichang station were used for flood frequency analysis, in which a time varying model was constructed to account for non-stationarity. The generalized extreme value (GEV) distribution was adopted to fit the AMF series, and the Generalized Additive Models for Location, Scale and Shape (GAMLSS) framework was applied for parameter estimation. The non-stationary return period and risk of failure were calculated and compared for flood risk assessment between stationary and non-stationary models. The results demonstrated that the flow regime at the Yichang station has changed over time and a decreasing trend was detected in the AMF series. The design flood peak given a return period decreased in the non-stationary model, and the risk of failure is also smaller given a design life, which indicated a safer flood condition in the future compared with the stationary model. The conclusions in this study may contribute to long-term decision making in the Yangtze River basin under non-stationary conditions.

Penalized maximum likelihood estimators for the nonstationary Pearson type 3 distribution

The climate change and human activities can principally doubt the frequency analysis methods which assume that the hydrological events are stationary. The Pearson type 3 (P3) distribution, which has been widely applied in frequency analysis under the stationary condition, was developed for the nonstationary cases. The distribution parameters can be expressed as exponential or polynomial functions with time or other covariates. Parameter estimation for the nonstationary P3 model was done with the penalized maximum likelihood estimation (PMLE) method in which we applied a restrictive penalty on the location parameter to avoid unreasonable results. The results of the nonstationary P3 model were compared to that of the generalized extreme value (GEV) distribution, in which the generalized maximum likelihood estimation (GMLE) method was applied to estimate the parameters. The Monte Carlo simulations indicated that the nonstationary P3 model provided better results than the nonstationary GEV model for different sample sizes. Both models were also applied in hydrological series with various trends and record lengths to prove the feasibility of the nonstationary P3 model in practical applications. The applications showed that the nonstationary P3 model performed better than the nonstationary GEV model in most of the studied cases.

Modelling extreme dry spells in the Mediterranean region in connection with atmospheric circulation

Long droughts periods can affect the Mediterranean region during the winter season, when most of annual precipitation occurs, and consequently have strong impacts on agriculture, groundwater levels and water resources. The goal of this study is to model annual maximum dry spells lengths (AMDSL) that occur during the extended winter season (October to April). The spatial patterns of extreme dry spells and their relationships with large-scale atmospheric circulation were first investigated. Then, AMDSL were modelled using Generalized Extreme Value (GEV) distributions incorporating climatic covariates, to evaluate the dependences of extreme dry spells to synoptic patterns using an analogue approach. The data from a network of 160 rain gauges having daily precipitation measurements between 1960 and 2009 are considered together with the ERA-20C reanalysis of the 20th century to provide atmospheric variables (geopotential heights, humidity, winds). A regional classification of both the occurrence and the duration of AMDSL helped to distinguish three spatially contiguous regions in which the regional distributions were found homogeneous. From composite analysis, significant positive anomalies in geopotential height (Z500) and negative anomalies in zonal wind (U850) and relative and specific humidity (S850, R850) were found to be associated with AMDSL in the three regions and provided the reference to build analogue days. Finally, non-stationary GEV models have been compared, in which the location and scale parameters are related to different atmospheric indices. Results indicates, at the whole Mediterranean scale, that positives anomalies of the North Atlantic Oscillation index and to a lesser extent the Mediterranean Oscillation index are linked to longer extreme dry spells in the majority of stations. For the three regions identified, the frequency of U850 negative anomalies over North Africa is significantly associated with the magnitude of AMDSL. AMDL are also associated with the frequency of S850 negative anomalies for the southeastern region, and with positive Z500 anomalies for the Western and North-eastern Mediterranean regions.

Modeling nonstationary extreme value distributions with nonlinear functions: An application using multiple precipitation projections for U.S. cities

Climate extremes, such as heavy precipitation events, have become more common in recent decades, and nonstationarity concepts have increasingly been adopted to model hydrologic extremes. Various issues are associated with applying nonstationary modeling to extremes, and in this study, we focus on assessing the need for different forms of nonlinear functions in a nonstationary generalized extreme value (GEV) model of different annual maximum precipitation (AMP) time series. Moreover, we suggest an efficient approach for selecting the nonlinear functions of a nonstationary GEV model. Based on observed and multiple projected AMP data for eight cities across the U.S., three separate tasks are proposed. First, we conduct trend and stationarity tests for the observed and projected data. Second, AMP series are fit with thirty different nonlinear functions, and the best functions among these are selected. Finally, the selected nonlinear functions are used to model the location parameter of a nonstationary GEV model and stationary and nonstationary GEV models with a linear function. Our results suggest that the simple use of nonlinear functions might prove useful with nonstationary GEV models of AMP for different locations with different types of model results.

Appropriate model selection methods for nonstationary generalized extreme value models

Several evidences of hydrologic data series being nonstationary in nature have been found to date. This has resulted in the conduct of many studies in the area of nonstationary frequency analysis. Nonstationary probability distribution models involve parameters that vary over time. Therefore, it is not a straightforward process to apply conventional goodness-of-fit tests to the selection of an appropriate nonstationary probability distribution model. Tests that are generally recommended for such a selection include the Akaike’s information criterion (AIC), corrected Akaike’s information criterion (AICc), Bayesian information criterion (BIC), and likelihood ratio test (LRT). In this study, the Monte Carlo simulation was performed to compare the performances of these four tests, with regard to nonstationary as well as stationary generalized extreme value (GEV) distributions. Proper model selection ratios and sample sizes were taken into account to evaluate the performances of all the four tests. The BIC demonstrated the best performance with regard to stationary GEV models. In case of nonstationary GEV models, the AIC proved to be better than the other three methods, when relatively small sample sizes were considered. With larger sample sizes, the AIC, BIC, and LRT presented the best performances for GEV models which have nonstationary location and/or scale parameters, respectively. Simulation results were then evaluated by applying all four tests to annual maximum rainfall data of selected sites, as observed by the Korea Meteorological Administration.

What are the best covariates for developing non-stationary rainfall Intensity-Duration-Frequency relationship?

Present infrastructure design is primarily based on rainfall Intensity-Duration-Frequency (IDF) curves with so-called stationary assumption. However, in recent years, the extreme precipitation events are increasing due to global climate change and creating non-stationarity in the series. Based on recent theoretical developments in the Extreme Value Theory (EVT), recent studies proposed a methodology for developing non-stationary rainfall IDF curve by incorporating trend in the parameters of the Generalized Extreme Value (GEV) distribution using Time covariate. But, the covariate Time may not be the best covariate and it is important to analyze all possible covariates and find the best covariate to model non-stationarity. In this study, five physical processes, namely, urbanization, local temperature changes, global warming, El Niño-Southern Oscillation (ENSO) cycle and Indian Ocean Dipole (IOD) are used as covariates. Based on these five covariates and their possible combinations, sixty-two non-stationary GEV models are constructed. In addition, two non-stationary GEV models based on Time covariate and one stationary GEV model are also constructed. The best model for each duration rainfall series is chosen based on the corrected Akaike Information Criterion (AICc). From the findings of this study, it is observed that the local processes (i.e., Urbanization, local temperature changes) are the best covariate for short duration rainfall and global processes (i.e., Global warming, ENSO cycle and IOD) are the best covariate for the long duration rainfall of the Hyderabad city, India. Furthermore, the covariate Time is never qualified as the best covariate. In addition, the identified best covariates are further used to develop non-stationary rainfall IDF curves of the Hyderabad city. The proposed methodology can be applied to other situations to develop the non-stationary IDF curves based on the best covariate.

Nonstationary modeling of extreme precipitation in China

The statistical methods based on extreme value theory have been traditionally used in meteorology and hydrology for a long time. Due to climate change and variability, the hypothesis of stationarity in meteorological or hydrological time series was usually not satisfied. In this paper, a nonstationary extreme value analysis was conducted for annual maximum daily precipitation (AMP) at 631 meteorological stations over China for the period 1951–2013. Stationarity of all 631 AMP time series was firstly tested using KPSS test method, and only 48 AMP time series showed non-stationarity at 5% significance level. The trends of these 48 nonstationary AMP time series were further tested using M-K test method. There were 25 nonstationary AMP time series mainly distributed in southern and western China showing significant positive trend at 5% level. Another 5 nonstationary AMP time series with significant negative trends were near northern urban agglomeration, Sichuan Basin, and central China. For these nonstationary AMP time series with significant positive or negative trends, the location parameter in generalized extreme value (GEV) distribution was assumed to be time-varying, and the trends were successfully characterized by the nonstationary GEV models. For the remaining 18 nonstationary AMP time series mainly in the eastern portion of China, no significant trend was detected. The correlation analysis showed that only 5 nonstationary AMP time series were significantly correlated with one or two of the four climate indices EASMI, WPI, SOI, and PDO. Then, the location and scale parameters in the GEV distribution were modeled as functions of the significantly correlated climate indices. The modeling results in this study showed that the nonstationary GEV distributions performed better than their stationary equivalents. Finally, 20-year and 50-year return levels of precipitation extremes at all 631 stations were estimated using the best fitting distribution for the year 1961 and 2013, respectively.

Non-stationary frequency analysis of extreme precipitation in South Korea using peaks-over-threshold and annual maxima

The conventional approach to the frequency analysis of extreme precipitation is complicated by non-stationarity resulting from climate variability and change. This study utilized a non-stationary frequency analysis to better understand the time-varying behavior of short-duration (1-, 6-, 12-, and 24-h) precipitation extremes at 65 weather stations scattered across South Korea. Trends in precipitation extremes were diagnosed with respect to both annual maximum precipitation (AMP) and peaks-over-threshold (POT) extremes. Non-stationary generalized extreme value (GEV) and generalized Pareto distribution (GPD) models with model parameters made a linear function of time were applied to AMP and POT respectively. Trends detected using the Mann–Kendall test revealed that the stations showing an increasing trend in AMP extremes were concentrated in the mountainous areas (the northeast and southwest regions) of South Korea. Trend tests on POT extremes provided fairly different results, with a significantly reduced number of stations showing an increasing trend and with some stations showing a decreasing trend. For most of stations showing a statistically significant trend, non-stationary GEV and GPD models significantly outperformed their stationary counterparts, particularly for precipitation extremes with shorter durations. Due to a significant-increasing trend in the POT frequency found at a considerable number of stations (about 10 stations for each rainfall duration), the performance of modeling POT extremes was further improved with a non-homogeneous Poisson model. The large differences in design storm estimates between stationary and non-stationary models (design storm estimates from stationary models were significantly lower than the estimates of non-stationary models) demonstrated the challenges in relying on the stationary assumption when planning the design and management of water facilities. This study also highlighted the need of caution when quantifying design storms from POT and AMP extremes by showing a large discrepancy between the estimates from those two approaches.