Non-stationary GEV Research Articles

Robustness of design flood estimates under nonstationary conditions: parameter sensitivity perspective

The changing frequency of flooding in global watersheds, driven by various human and natural factors like land use/cover changes and global warming, necessitates innovative approaches in flood frequency analysis and risk assessment. Nonetheless, the reliability of nonstationary frequency analysis models remains a concern given challenges in accurately measuring the uncertainty introduced by these methods and the impact on design flood values. In this study, deviation-based differential sensitivity indices, including single-parameter (SDDSI) and entire-parameter (EDDSI) measures were developed to assess the influence of parameter uncertainty in nonstationary models using Bayesian statistics and "equivalent reliability" nonstationary design. The Weihe River, the largest tributary of the Yellow River which is experiencing both climate change and heavy impact of human activities, is chosen to be the study area to investigate the impact of precipitation change and land use change on nonstationary flood frequency. Results show that in the One-At-A-Time (OAT) sensitivity analysis under a small uncertainty scenario (SUS) for parameter inputs, the shape parameter stands out as the most influential factor (SDDSI_SUS = 0.347) affecting the 100-year design flood in the Stationary Generalized Extreme Value (SGEV) model. For the Non-Stationary GEV (NGEV) models, the influence of this parameter is less pronounced, with SDDSI_SUS values of 0.095 and 0.093 for the SSP126 and SSP585 scenarios, respectively. Instead, attention turns to the regression coefficient of the grassland area, associated with the GEV scale parameter. In global sensitivity analysis under the posterior uncertainty scenario (PUS) for parameter inputs, the EDDSI_PUS values for SGEV, NGEV_SSP126, and NGEV_SSP585 models were 0.52, 1.41, and 1.30, respectively, inferring heightened sensitivity of NGEV models to perturbations from entire parameters. It is anticipated that incorporating additional evidence, such as historical flood data, is essential for accurate nonstationary hydrological design to mitigating the influence of parameter uncertainty. The sensitivity indices in this study provide significant insights for assessing the robustness of nonstationary hydrological design in flood risk management and applications.

Non-Stationary Flood Discharge Frequency Analysis in West Africa

With climate change and intensification of the hydrological cycle, the stationarity of hydrological variables is becoming questionable, requiring appropriate flood assessment models. Frequency analysis is widely used for flood forecasting. This study aims to determine the most suitable models (stationary and non-stationary) for estimating the maximum flows observed at some stations spread across West Africa. A statistical analysis of the annual maximum flows in terms of homogeneity, stationarity, and independence was carried out through the Pettitt, modified Mann–Kendall, and Wald–Wolfowitz tests, respectively, to identify the stations whose flows are non-stationary. After that, the best-correlated climate covariates with the annual maximum flows of the non-stationary stations were determined. The covariates explored are the climatic indices of sea surface temperatures (SST). Finally, different non-stationary GEV models were derived by varying the scale and position parameters of the best-correlated index for each station. The results indicate that 56% of the annual maximum flow series are non-stationary. As per the Bayes information criterion (BIC) values, the performance of the non-stationary models (GEV, generalized extreme values) is largely greater than that of the stationary models. These good performances of non-stationary models using climatic indices open perspectives for the prediction of extreme flows in the study area.

Severe Precipitation Phenomena in Crimea in Relation to Atmospheric Circulation

The increase in the frequency and intensity of hazardous hydrometeorological phenomena is one of the most dangerous consequences of climate instability. In this study, we summarize the data on severe weather phenomena using the data from 23 meteorological stations in Crimea from 1976 to 2020. Particular attention was paid to the precipitation phenomena descriptions. For the last 45 years, a significant positive trend of interannual variability of the annual occurrence of severe weather phenomena was estimated to be +2.7 cases per decade. The trend for severe precipitation phenomena was estimated to be +1.3 cases per decade. The probable maximum annual daily precipitation as a quantitative indicator of hazardous events was estimated for each station by using both the stationary and the non-stationary GEV models. For at least half of the meteorological stations, a non-stationary GEV model was more appropriate for the estimation of the precipitation extremes. An analysis of the main synoptic processes that drive severe weather phenomena of precipitation was carried out. The greatest contribution to the formation of severe precipitation was made by Mediterranean–Black Sea cyclones. At the same time, half of all of the cases of extreme precipitation were caused by cyclones generated over the Black Sea only, in all seasons apart from winter. In the mid-troposphere, four types of meridional circulation were identified depending on the location of troughs and ridges, with respect to the Black Sea region. More than 42% of severe precipitation phenomena were accompanied by an isolated high-altitude cyclone in the mid-troposphere over the Black Sea region. The main recommendation that can be drawn from this study is that long-term climatic non-stationarity should be taken into account whenever the risk assessment or hazard analysis is to be carried out. The results can also favor the designing of drainage and sewerage systems in urban areas. The findings of atmospheric patterns can be used for the improvement of extreme precipitation forecasts.

Frequency analysis of precipitation extremes under a changing climate: a case study in Heihe River basin, China

Abstract The stationary assumption for the traditional frequency analysis of precipitation extremes has been challenged due to natural climate variability or human intervention. To overcome this challenge, this paper, taking Heihe River basin as the case study, performed the frequency analysis by developing a nonstationary GEV model for those seasonal maximum daily precipitation (SMP) time series with nonstationary characteristics by employing the GEV conditional density estimation network. In addition, the confidence intervals (CIs) of estimated return levels were also investigated by using the residual bootstrap technique. Results showed that, 7 of 12 SMP series were nonstationary. The parameters in the nonstationary model were specified as functions of time varying or correlated climate indices varying covariates. The frequency analysis showed that the return levels varied linearly or nonlinearly with covariates. Precipitation extremes with the same magnitude in the study area were found to be occurring more frequently in the future. The CIs of such return levels increased with time passing, especially those from the more complex GEV11 model, embedding a nonlinear increasing trend in model scale parameters. It implied that the increase of model complexity is likely to result in the increase of uncertainty in estimates.

Delta Change Method with Cyclic Covariate Generalized Extreme Value Model for Downscaling Extreme Rainfall

In meteorological data, lots of variables have annual, seasonal or diurnal cycles. These would be based on different climatic patterns in different seasons rising sea levels. The delta change approach is one of the statistical downscaling methods that used to downscale global climate model data in order to use it as a future input for hydrological models and flood risk assessment. In this work, a non-stationary GEV model with cyclic covariate structure for modelling magnitude and variation of data series with some degrees of correlation for real-world applications is proposed. All extreme events were calculated assuming that maximum annual daily precipitations follow the GEV distribution. The method makes it possible to identify and estimate the impacts of multiple time scales-such as seasonality, interdecadal variability, and secular trends-throughout the area, scale, and shape parameters of extreme sea level probability distribution. The incorporation of seasonal effects describes a huge amount of data variability, permitting the methods involved to be estimated more efficiently. Next, the technique of deltachange was implemented to the mean annual rainfall and also the regular rainfall occurrences of 5, 10, 20, 50 and 100 years of return. The capability of the proposed model will be tested to one rainfall station in Sabah. The new model suggesting improvement over the stationary model based on the p-value which is highly significant (approximate to 0). GEV model with cyclic covariate on both location and scale parameters is able to capture the seasonality factor in rainfall data. Hence, a reliable delta-change model has been developed in this study. This could produce more accurate projection of rainfall in the future

Non-stationary analysis of the frequency and intensity of heavy precipitation over Canada and their relations to large-scale climate patterns

In recent years, because the frequency and severity of floods have increased across Canada, it is important to understand the characteristics of Canadian heavy precipitation. Long-term precipitation data of 463 gauging stations of Canada were analyzed using non-stationary generalized extreme value distribution (GEV), Poisson distribution and generalized Pareto (GP) distribution. Time-varying covariates that represent large-scale climate patterns such as El Nino Southern Oscillation (ENSO), North Atlantic Oscillation (NAO), Pacific decadal oscillation (PDO) and North Pacific Oscillation (NP) were incorporated to parameters of GEV, Poisson and GP distributions. Results show that GEV distributions tend to under-estimate annual maximum daily precipitation (AMP) of western and eastern coastal regions of Canada, compared to GP distributions. Poisson regressions show that temporal clusters of heavy precipitation events in Canada are related to large-scale climate patterns. By modeling AMP time series with non-stationary GEV and heavy precipitation with non-stationary GP distributions, it is evident that AMP and heavy precipitation of Canada show strong non-stationarities (abrupt and slowly varying changes) likely because of the influence of large-scale climate patterns. AMP in southwestern coastal regions, southern Canadian Prairies and the Great Lakes tend to be higher in El Nino than in La Nina years, while AMP of other regions of Canada tends to be lower in El Nino than in La Nina years. The influence of ENSO on heavy precipitation was spatially consistent but stronger than on AMP. The effect of PDO, NAO and NP on extreme precipitation is also statistically significant at some stations across Canada.

Spatial analysis of trend in extreme daily rainfall in southern France

This paper makes a regional evaluation of trend in yearly maxima of daily rainfall in southern France, both at point and spatial scales on a regular grid of 8 × 8 km2. In order to filter out the high variability of rainfall maxima, the current analysis is based on a non-stationary GEV modeling in which the location parameter is allowed to vary with time. Three non-stationary models are considered for each series of maxima by constraining the location parameter to vary either linearly, linearly after a given date or linearly up to a final date. Statistical criteria are used to compare these models and select the best starting or final point of putative trends. The analysis shows that, at regional scale, the best distribution of maxima involves a linear trend starting in year 1985 and that this trend is significant in half the region, including most of the mountain ranges and part of the Rhone valley. Increases in yearly maxima are considerable since they reach up more than 60 mm/day in 20 years, which is more than 40 % of the average maximum in this area.

An at-site flood estimation method in the context of nonstationarity I. A simulation study

Summary The stationarity of annual flood peak records is the traditional assumption of flood frequency analysis. In some cases, however, as a result of land-use and/or climate change, this assumption is no longer valid. Therefore, new statistical models are needed to capture dynamically the change of probability density functions over time, in order to obtain reliable flood estimation. In this study, an innovative method for nonstationary flood frequency analysis was presented. Here, the new method is based on detrending the flood series and applying the L-moments along with the GEV distribution to the transformed “stationary” series (hereafter, this is called the LM-NS). The LM-NS method was assessed through a comparative study with the maximum likelihood (ML) method for the nonstationary GEV model, as well as with the stationary (S) GEV model. The comparative study, based on Monte Carlo simulations, was carried out for three nonstationary GEV models: a linear dependence of the mean on time (GEV1), a quadratic dependence of the mean on time (GEV2), and linear dependence in both the mean and log standard deviation on time (GEV11). The simulation results indicated that the LM-NS method performs better than the ML method for most of the cases studied, whereas the stationary method provides the least accurate results. An additional advantage of the LM-NS method is to avoid the numerical problems (e.g., convergence problems) that may occur with the ML method when estimating parameters for small data samples.

Comparison of nonstationary generalized logistic models based on Monte Carlo simulation

Abstract. Recently, the evidences of climate change have been observed in hydrologic data such as rainfall and flow data. The time-dependent characteristics of statistics in hydrologic data are widely defined as nonstationarity. Therefore, various nonstationary GEV and generalized Pareto models have been suggested for frequency analysis of nonstationary annual maximum and POT (peak-over-threshold) data, respectively. However, the alternative models are required for nonstatinoary frequency analysis because of analyzing the complex characteristics of nonstationary data based on climate change. This study proposed the nonstationary generalized logistic model including time-dependent parameters. The parameters of proposed model are estimated using the method of maximum likelihood based on the Newton-Raphson method. In addition, the proposed model is compared by Monte Carlo simulation to investigate the characteristics of models and applicability.

비정상성 GEV 모형을 이용한 행정구역별 미래 확률강우량 산정

국내에서는 설계강우량을 산정하기 위해서 정상성 강우빈도해석법이 일반적으로 적용되고 있다. 그러나, 기후변화 또는 기후 변동으로 인한 극치사상의 증가 등으로 최근의 강우패턴은 과거와는 다른 양상을 보여주고 있으며, 이러한 경향은 수문학적 설계를 위한 확률강우량 산정에 고려될 필요가 있다. 본 연구에서는 행정구역별 비정상성 강우빈도해석을 수행하였다. 이를 위하여 1973년부터 2012년까지 관측된 지점강우량을 이용하여 행정구역별 연최대강우량 자료를 구축하였다. 25년 이동평균방법으로 관측자료의 통계량과 GEV 분포함수의 모수 사이의 상관성을 검토한 후, 미래 특정 시점에 대한 분포함수의 모수를 추정할 수 있는 비선형 회귀식을 유도하였다. 본 연구에서 제시한 방법은 관측된 연최대강우량에 대하여 검증을 하였으며, 강우패턴의 변화를 정상성 강우빈도해석법에 비해 보다 적절히 반영하는 것으로 나타났다. 따라서, 본 연구에서 제시하는 행정구역별 비정상성 강우빈도해석법은 가까운 미래의 확률강우량 산정과 최근에 도입된 행정구역별 방재성능 목표강우량 산정에 유용할 것으로 판단된다. In South Korea, stationary frequency analysis methods are generally used for estimating design rainfalls in practice. However, due to climate change and/or variability, recent rainfall observations have significantly different patterns from the past so that the recent trends need to be considered to estimate extreme rainfall quantiles for hydrologic design. This study focused on estimating extreme rainfall quantiles in administrative districts across South Korea, after building nonstationary GEV model using annual maximum rainfall (AMR) datasets for 228 administrative districts from point rainfall measures from 1973 to 2012. A moving average method with 25-year window was used for investigating time-dependent statistics of AMR, such as mean, variance and skewness, and parameters of GEV distribution. From the analyses of relationships between statistics and distribution parameters, this study derived nonlinear regression equations for distribution parameters, which provide the estimates of distribution parameters at any future time. The overall results achieved in this study illustrate that the nonlinear regression equations can be easily incorporated into the hydrologic frequency analysis and provide appropriate estimates of design rainfalls in the near future.

Climate change impacts on extreme floods II: improving flood future peaks simulation using non-stationary frequency analysis

In the companion paper, Seidou et al. (2011, submitted) have shown that when adequate meteorological data are available to calibrate rainfall-runoff models, using a non-stationary GEV model with the simulated flows can provide a better description of flood peaks distributions than directly using the simulated peaks. Their methodology is extended in this paper to improve future flood peaks simulation under a changing climate. In this case, the rainfall-runoff model is forced with the downscaled outputs of the Canadian General Circulation Model CGCM3. Special attention is paid to the statistical downscaling of precipitations, as the choice of the transfer function has a significant influence on the performance of non-stationary GEV model. Stepwise regression was initially used to describe precipitation occurrence and intensity, but the patterns of the simulated hydrographs were found to be unsatisfactory. After precipitation occurrence model was successfully replaced with an ensemble of regression trees, the non-stationary GEV model was shown to provide a better description of flood peaks in the observation period. The non-stationary GEV model shows that exceedance probabilities on the Kemptville Creek will gradually rise up to 34% above current levels in 2100 for a 20-year service life.

Climate change impacts on extreme floods I: combining imperfect deterministic simulations and non-stationary frequency analysis

Flood quantiles are routinely used in hydrologic engineering to design hydraulic structures, optimize erosion control structure and map the extent of floodplains. As an increasing number of papers are pointing out cycles and trends in hydrologic time series, the use of stationary flood distributions leads to the overestimation or underestimation of the hydrologic risk at a given time. Several authors tried to address this problem by using probability distributions with time-varying parameters. The parameters of these distributions were assumed to follow a linear or quadratic trend in time, which may be valid for the short term but may lead to unrealistic long-term projections. On the other hand, deterministic rainfall-runoff models are able to successfully reproduce trends and cycles in stream flow data but can perform poorly in reproducing daily flows and flood peaks. Rainfall-runoff models typically have a better performance when simulation results are aggregated at a larger time scale (e.g. at a monthly time scale vs. at a daily time scale). The strengths of these two approaches are combined in this paper where the annual maximum of the time-averaged outputs of a hydrologic model are used to modulate the parameters of a non-stationary GEV model of the daily maximum flow. The method was applied to the Kemptville Creek located in Ontario, Canada, using the SWAT (Soil and Water Assessment Tool) model as rainfall-runoff model. The parameters of the non-stationary GEV model are then estimated using Monte Carlo Markov Chain, and the optimal span of the time windows over which the SWAT outputs were averaged was selected using Bayes factors. Results show that using the non-stationary GEV distribution with a location parameter linked to the maximum 9-day average flow provides a much better estimation of flood quantiles than applying a stationary frequency analysis to the simulated peak flows.

Incorporating climate trends in the stochastic modeling of extreme minimum air temperature series of Campinas, state of São Paulo, Brazil

Under the hypothesis that the presence of climate trends in the annual extreme minimum air temperature series of Campinas (Tminabs; 1891-2010; 22º54'S; 47º05'W; 669 m) may no longer be neglected, the aim of the work was to describe the probabilistic structure of this series based on the general extreme value distribution (GEV) with parameters estimated as a function of a time covariate. The results obtained by applying the likelihood ratio test and the percentil-percentil and quantil-quantil plots, have indicated that the use of a time-dependent model provides a feasible description of the process under evaluation. In this non-stationary GEV model the parameters of location and scale were expressed as time-dependent functions. The shape parameter remained constant. It was also verified that although this non-stationary model has indicated an average increase in the values of the analyzed data, it does not allow us to conclude that the region of Campinas is now free from frost occurrence since this same model also reveals an increasing trend in the dispersions of the variable under evaluation. However, since the parameters of location and scale of this probabilistic model are significantly conditioned on time, the presence of climate trends in the analyzed time series is proven.

Generalized maximum likelihood estimators for the nonstationary generalized extreme value model

The objective of the present study is to develop efficient estimation methods for the use of the GEV distribution for quantile estimation in the presence of nonstationarity. Parameter estimation in the nonstationary GEV model is generally done with the maximum likelihood estimation method (ML). In this work, we develop the generalized maximum likelihood estimation method (GML), in which covariates are incorporated into parameters. A simulation study is carried out to compare the performances of the GML and the ML methods in the case of the stationary GEV model (GEV0), the nonstationary case with a linear dependence of the location parameter on covariates (GEV1), the nonstationary case with a quadratic dependence on covariates (GEV2), and the nonstationary case with linear dependence in both location and scale parameters (GEV11). Simulation results show that the GLM method performs better than the ML method for all studied cases. The nonstationary GEV model is also applied to a case study to illustrate its potential. The case study deals with the annual maximum precipitation at the Randsburg station in California, and the covariate process is taken to be the Southern Index Oscillation.