Non-stationary Extreme Value Analysis Research Articles

Modeling Return Levels of Non-Stationary Rainfall Extremes Due to Climate Change

Global warming increases evaporation and atmospheric water vapor, leading to more extreme events in both spatial and temporal domains. This study conducts a non-stationary extreme value analysis of the annual daily maximum at 36 meteorological stations over Iran from 1960 to 2021. We applied stationary and non-stationary Generalized Extreme Value (GEV) models within a Bayesian framework to estimate return levels for rainfall extremes, along with 90% confidence intervals. Our findings indicate that non-stationary models are not prominently evident based on AIC at most stations; however, non-stationary Generalized Extreme Value (GEV) models outperform stationary models based on RMSE and NSE evaluation criteria that sufficiently capture variations in extremes. Furthermore, most observed changes in extreme events exhibit a non-stationary pattern. Non-stationary analysis indicates that the frequency and severity of rainfall extremes have shown both increasing and decreasing trends, characterized by inconsistent spatial patterns.

Variability of Extreme Climate Events and Prediction of Land Cover Change and Future Climate Change Effects on the Streamflow in Southeast Queensland, Australia

The severity and frequency of extremes are changing; thus, it is becoming necessary to evaluate the impacts of land cover changes and urbanisation along with climate change. A framework of the Generalised Extreme Value (GEV) method, Google Earth Engine (GEE), and land cover patterns’ classification including Random Forest (RF) and Support Vector Machine (SVM) can be useful for streamflow impact analysis. For this study, we developed a unique framework consisting of a hydrological model in line with the Process-informed Nonstationary Extreme Value Analysis (ProNEVA) GEV model and an ensemble of General Circulation Models (GCMs), mapping land cover patterns using classification methods within the GEE platform. We applied these methods in Southeast Queensland (SEQ) to analyse the maximum instantaneous floods in non-stationary catchment conditions, considering the physical system in terms of cause and effect. Independent variables (DEM, population, slope, roads, and distance from roads) and an integrated RF, SVM methodology were utilised as spatial maps to predict their influences on land cover changes for the near and far future. The results indicated that physical factors significantly influence the layout of landscapes. First, the values of projected evapotranspiration and rainfall were extracted from the multi-model ensemble to investigate the eight GCMs under two climate change scenarios (RCP4.5 and RCP8.5). The AWBM hydrological model was calibrated with daily streamflow and applied to generate historical runoff for 1990–2010. Runoff was projected under two scenarios for eight GCMs and by incorporating the percentage of each land cover into the hydrological model for two horizons (2020–2065 and 2066–2085). Following that, the ProNEVA model was used to calculate the frequency and magnitude of runoff extremes across the parameter space. The maximum peak flood differences under the RCP4.5 and RCP8.5 scenarios were 16.90% and 15.18%, respectively. The outcomes of this study suggested that neglecting the non-stationary assumption in flood frequency can lead to underestimating the amounts that can lead to more risks for the related hydraulic structures. This framework is adaptable to various geographical regions to estimate extreme conditions, offering valuable insights for infrastructure design, planning, risk assessment, and the sustainable management of future water resources in the context of long-term water management plans.

Revealing trends in extreme heatwave intensity: applying the UNSEEN approach to Nordic countries

The increase in heatwave intensity, causing heat stress and crop failures in many regions is a concerning impact of global climate change. In northern Europe, significant interannual variability previously prevented robust assessments of trends in heat extremes. However, with a large-ensemble seasonal hindcasts and archived forecasts dataset covering 1981–2022 multiple realisations of weather patterns can be pooled and assessed. What are recent trends of extreme temperatures? Has the risk for a 100-year heatwave event increased in Northern Europe? We apply the UNSEEN (UNprecedented Simulated Extremes using ENsembles) approach to assess the credibility of the model ensemble and use non-stationary extreme value analysis to quantify recent trends in extreme 3-day heatwaves in late spring and early summer (May to July). We find significant non-stationarity and positive trends in annual maximum heatwave intensity. We also show that heatwave volatility, i.e. the risk of clearly outstanding heatwaves, is highest in central Scandinavia.

A wavelet transform based stationary transformation method for estimating the extreme value of the non-stationary wind speeds

The rational estimation of extreme wind speeds is crucial. As reported, in the Chinese area, the measured wind speed variation from different meteorological observatories shows a general non-stationary trend in the past 40 years due to urbanization factors or temperature variation. Thus, the non-stationary extreme value analysis (TNGEV) of the measured wind speed is required. However, TNGEV is relatively complicated. Under such a background, in this paper, a novel simplified wavelet transform-based stationary transformation method (PNGEV) is proposed for the extreme value analysis of the non-stationary wind speeds. This paper firstly derives the proposed time-varying extreme value distribution parameter form, combining the wavelet transform and moving average. Secondly, a case study is provided to illustrate and verify this proposed method (PNGEV), using the 40-year daily maximum wind speeds recorded from 1981 to 2020 in Baoshan District Shanghai, China. The effectiveness of the proposed method (PNGEV) is verified by comparing it with TNGEV in the return period and the risk of failure. By comparison, it can be figured out that the proposed PNGEV is practicable and outperforms TNGEV in the stability of the return period calculation, as well as the time-varying extreme value distribution establishment.

A Multi-Framework of Google Earth Engine and GEV for Spatial Analysis of Extremes in Non-Stationary Condition in Southeast Queensland, Australia

The frequency and severity of extremes, including extreme precipitation events, extreme evapotranspiration and extreme water storage deficit events, are changing. Thus, the necessity for developing a framework that estimates non-stationary conditions is urgent. The aim of this paper is to develop a framework using the geeSEBAL platform, Generalised Extreme Value (GEV) models and spatiotemporal analysis techniques that incorporate the physical system in terms of cause and effect. Firstly, the geeSEBAL platform has enabled the estimation of actual evapotranspiration (ETa) with an unprecedented level of spatial-temporal resolution. Following this, the Non-stationary Extreme Value Analysis (NEVA) approach employs the Bayesian method using a Differential Evolution Markov Chain technique to calculate the frequency and magnitude of extreme values across the parameter space. Station and global climate datasets have been used to analyse the spatial and temporal variation of rainfall, reference evapotranspiration (ETo), ETa and water storage (WS) variables in the Lockyer Valley located in Southeast Queensland (SEQ), Australia. Frequency analysis of rainfall, ETa, and water storage deficit for 14 stations were performed using a GEV distribution under stationary and non-stationary assumptions. Comparing the ETa, ETo and ERA5 rainfall with station data showed reasonable agreement as follows: Pearson correlation of 0.59–0.75 for ETa, RMSE of 45.23–58.56 mm for ETa, Pearson correlation of 0.96–0.97 for ETo, RMSE of 73.13–87.73 mm for ETo and Pearson correlation of 0.87–0.92 for rainfall and RMSE of 37.53–57.10 mm for rainfall. The lower and upper uncertainty bounds between stationary and non-stationary conditions for rainfall station data of Gatton varied from 550.98 mm (stationary) to 624.97 mm (non-stationary), and for ERA5 rainfall datasets, 441.30 mm (stationary) to 450.77 mm (non-stationary). The results demonstrate that global climate datasets underestimate the difference between stationary and non-stationary conditions by 9.47 mm compared to results of 73.99 mm derived from station data. Similarly, the results demonstrate less variation between stationary and non-stationary conditions in water storage, followed by a sharp variation in rainfall and moderate variation in evapotranspiration. The findings of this study indicate that neglecting the non-stationary condition in some hydrometeorological variables can lead to underestimating their amounts. This framework can be applied to any geographical area for estimating extreme conditions, providing valuable insights for infrastructure planning and design, risk assessment and disaster management.

A spatio-temporal analysis of the role of climatic drivers influencing extreme precipitation events in a Costa Rican basin

Regional patterns of rainfall are changing around the world, putting pressure on social, economic, and environmental systems, and changing the outlook for food, water, and health security. This is the case in the Tempisque-Bebedero River Basin (TBRB), located on the Pacific slope of northwest Costa Rica, which relies heavily on water resources for tourism, agriculture, ranching, and fish farming. In this study, we use non-stationary extreme value analysis to characterize the climatic drivers of extreme precipitation in the TBRB. Daily extreme precipitation events at stations across the TBRB are selected using a peak-above-threshold approach, and interannual climate variability is included as time-varying covariates in a non-stationary point process model, using three regional climate indices: the Caribbean Low-Level Jet (CLLJ) index, the Oceanic Niño Index (ONI), representative of the El Niño Southern Oscillation (ENSO), and the Atlantic Multidecadal Oscillation (AMO) index. We find that the magnitude and frequency of precipitation extremes in the basin are driven by the CLLJ and the AMO. The ONI is only a significant driver of extreme precipitation in the northwestern region of the basin. This is likely because ENSO controls the strength of the CLLJ, thus the dominant impact of ENSO on precipitation in the TBRB may be incorporated within the CLLJ component of our model.

Application of nonstationary extreme value analysis in the coastal environment – A systematic literature review

Coastal zones are among the most complex and dynamic areas on earth. Many marine and hydrologic processes act individually or combined in these areas and can lead to extreme events impacting coastal communities. Since coastal areas are densely populated and host many significant economic activities, understanding how these extremes are changing is crucial for integrated coastal zone management. More reliable and appropriate estimations of future extreme conditions in nearshore areas are urgently needed in light of the projected increases in the severity of future loading conditions combined with the limited residual service life of many existing coastal infrastructures. Considering the ever-growing adoption of nonstationary extreme value analysis as a reliable tool to study the evolution of extremes in coastal regions, this paper provides a systematic and comprehensive literature review on this topic. For this purpose, an automated search algorithm is used to retrieve the most relevant literature form the SCOPUS database. Then, after a careful review of the full texts, a set of articles and conference papers that fully match the purpose of the article are selected and classified based on 14 different categories. Moreover, research challenges and future research pathways regarding nonstationary extreme value analysis are highlighted and discussed.

Uncertainties in estimating the effect of climate change on 100-year return value for significant wave height

The process of estimating the effect of a changing climate on the severity of future ocean storms is plagued by large uncertainties; for safe design and operation of offshore structures, it is nevertheless important that best possible estimates of climate effects is made given the available data. We explore the variability in estimates of 100-year return value of significant wave height (HS), and changes in estimates over a period of time, for output of WAVEWATCH-III models from 7 representative Coupled Model Intercomparison Project (CMIP) Phase 5 General Circulation Models (GCMs), and the FIO-ESM v2.0 CMIP Phase 6 GCM. Non-stationary extreme value analysis of peaks-over-threshold and block maxima using Bayesian inference provide posterior estimates of return values as a function of time; MATLAB software for the extreme value analysis is provided. Best overall estimates for return values, and changes in return value over the period 1979-2100, are calculated by averaging estimates for individual GCMs. We focus attention on neighbourhoods of locations east of Madagascar and south of Australia where a previous study of CMIP5-derived output reported significant decrease and increase in HS respectively, under Representative Concentration Pathway (RCP) scenarios RCP4.5 and RCP8.5. There is large variation between return value estimates from different GCMs, and with longitude and latitude within each neighbourhood for estimates based on samples corresponding to ≤ 165 years of model output; these sources of uncertainty tend to be larger than those due to typical modelling choices (such as choice of threshold for peaks over threshold, or block length for block maxima). However, we also find that careful threshold choice and block length are critical east of Madagascar, because of the presence of a mixed population of storms there. Nevertheless, there is general evidence supporting the trends reported by others, but these findings are conditional on the choice of 8 GCMs being representative of climate evolution. We use simple randomisation testing to identify “significant” departures from steady climate. The long 700-year pre-industrial control (piControl) output of the CMIP6 GCM offers an excellent opportunity to quantify the apparent inherent variability in return value as a function of time, estimated using a subsample of output corresponding to a continuous time interval of between 20 and 160 years in length, where no climate forcing is present. We find large variation in return value estimates of approximately ±15% made from samples corresponding to periods of time of around 50 years drawn from piControl data.

A penalised piecewise-linear model for non-stationary extreme value analysis of peaks over threshold

Metocean extremes often vary systematically with covariates such as direction and season. In this work, we present non-stationary models for the size and rate of occurrence of peaks over threshold of metocean variables with respect to one- or two-dimensional covariates. The variation of model parameters with covariate is described using a piecewise-linear function in one or two dimensions, defined with respect to pre-specified node locations on the covariate domain. Parameter roughness is regulated to provide optimal predictive performance, assessed using cross-validation, within a penalised likelihood framework for inference. Parameter uncertainty is quantified using bootstrap resampling. The models are used to estimate extremes of storm-peak significant wave height with respect to direction and season for a site in the northern North Sea. A covariate representation based on a triangulation of the direction-season domain with six nodes gives good predictive performance. The penalised piecewise-linear framework provides a flexible representation of covariate effects at reasonable computational cost.

Effect of nonstationary extreme wind speeds and ground snow loads on the structural reliability in a future Canadian changing climate

Extreme wind speeds and ground snow loads for many regions across North America exhibit non-stationarity in projected future climates. The adequacy of conventional return period design values estimated in the past for the future design life needs to be investigated. Nonstationary extreme value analysis methods were used in several previous studies to evaluate the nonstationarity of extreme wind and snow loads based on the latest future projections for Canada in the RCP8.5 (where RCP denotes the representative concentration pathway) emission scenario. These methods have not been considered in nonstationary reliability analyses. This study will examine the effect of including these nonstationary extreme value analysis methods in the reliability analysis. Investigations were conducted by applying the design value estimated in past stationary climate to the reliability analysis considering nonstationary climatic load effects in the future design life. Two non-stationary extreme value analysis methods were then used to determine the design level value in the nonstationary future climates for mitigating the climate change impact. These two approaches target different risk levels. Both nonstationary methods provide design level values greater than the conventional return period values and can maintain the probability of failure close to the target value at the end of the design life. Analyses were also conducted to examine the climate change impact on the structural reliability for considering principal wind load effects or snow load effects with the companion live load effects.

Application of Non-stationary Extreme Value Analysis to Satellite-Observed Sea Surface Temperature Data for Past Decades

Extreme value analysis (EVA) has been extensively used to understand and predict long-term return extreme values. This study provides the first approach to EVA using satellite-observed sea surface temperature (SST) data over the past decades. Representative EVA methods were compared to select an appropriate method to derive SST extremes of the East/Japan Sea (EJS). As a result, the peaks-over-threshold (POT) method showed better performance than the other methods. The Optimum Interpolation Sea Surface Temperature (OISST) database was used to calculate the 100-year-return SST values in the EJS. The calculated SST extremes were 1.60–3.44°C higher than the average value of the upper 5th-percentile satellite-observed SSTs over the past decades (1982–2018). The monthly distribution of the SST extremes was similar to the known seasonal variation of SSTs in the EJS, but enhanced extreme SSTs exceeding 2°C appeared in early summer and late autumn. The calculated 100-year-return SSTs were compared with the simulation results of the Coupled Model Intercomparison Project 5 (CMIP5) climate model. As a result, the extreme SSTs were slightly smaller than the maximum SSTs of the model data with a negative bias of –0.36°C. This study suggests that the POT method can improve our understanding of future oceanic warming based on statistical approaches using SSTs observed by satellites over the past decades.

Observed and Projected Scaling of Daily Extreme Precipitation with Dew Point Temperature at Annual and Seasonal Scales across the Northeast United Sates

AbstractThis study investigates how extreme precipitation scales with dew point temperature across the Northeast U.S., both in the observational record (1948-2020) and in a set of downscaled climate projections in the state of Massachusetts (2006-2099). Spatiotemporal relationships between dew point temperature and extreme precipitation are assessed, and extreme precipitation – temperature scaling rates are evaluated on annual and seasonal scales using non-stationary extreme value analysis for annual maxima and partial duration series, respectively. A hierarchical Bayesian model is then developed to partially pool data across sites and estimate regional scaling rates, with uncertainty. Based on the observations, the estimated annual scaling rate is 5.5% per °C, but this varies by season, with most non-zero scaling rates in summer and fall and the largest rates (∼7.3% per °C) in the summer. Dew point temperatures and extreme precipitation also exhibit the most consistent regional relationships in the summer and fall. Downscaled climate projections exhibited different scaling rates compared to the observations, ranging between -2.5 and 6.2% per °C at an annual scale. These scaling rates are related to the consistency between trends in projected precipitation and dew point temperature over the 21st century. At the seasonal scale, climate models project larger scaling rates for the winter compared to the observations (1.6% per °C). Overall, the observations suggest that extreme daily precipitation in the Northeast U.S. only thermodynamic scales with dew point temperature in the warm season, but climate projections indicate some degree of scaling is possible in the cold season under warming.

Assessment of temporal probability for rainfall-induced landslides based on nonstationary extreme value analysis

Climate change may alter the frequency and intensity of rainfall, and thereby significantly affect the frequency and magnitude of shallow landslides. To accurately evaluate the temporal probability of landslide initiation, it is therefore important to consider the effect of climate variation. Although various approaches have been proposed to estimate the temporal probability of landslides to date, most of them were based on the stationary assumption, i.e., that the statistical properties of the historical rainfall data are time-invariant. However, if historical rainfall data show nonstationary characteristics such as a trend or an abrupt change, the stationary assumption is no longer valid and induces a miscalculation. In this study, we propose a new approach that can estimate the temporal probability of future rainfall-induced landslide occurrence while incorporating the nonstationary characteristics of the rainfall data. In assessing such data, a nonstationary generalized extreme value distribution was used to evaluate the temporal probability. Then, by combining the derived nonstationary temporal probability with landslide susceptibility results obtained from the random forest model, probabilities of landslide occurrence were calculated for future periods, from 1 to 50 years, and compared with the results based on a stationary model. The results showed that the stationary model underestimated the landslide probability compared with the nonstationary approach. This is because an increasing trend in local rainfall, taken from a gauge in the study area, was not considered in the stationary analysis. Thus, climate change has ongoing consequences for landslide occurrence. To reflect the impacts of climate change, a nonstationary approach capable of coping with climate variation should therefore be considered in any landslide hazard analysis.

Nonstationary Extreme Value Analysis of Nearshore Sea-State Parameters under the Effects of Climate Change: Application to the Greek Coastal Zone and Port Structures

In the present work, a methodological framework, based on nonstationary extreme value analysis of nearshore sea-state parameters, is proposed for the identification of climate change impacts on coastal zone and port defense structures. The applications refer to the estimation of coastal hazards on characteristic Mediterranean microtidal littoral zones and the calculation of failure probabilities of typical rubble mound breakwaters in Greek ports. The proposed methodology hinges on the extraction of extreme wave characteristics and sea levels due to storm events affecting the coast, a nonstationary extreme value analysis of sea-state parameters and coastal responses using moving time windows, a fitting of parametric trends to nonstationary parameter estimates of the extreme value models, and an assessment of nonstationary failure probabilities on engineered port protection. The analysis includes estimation of extreme total water level (TWL) on several Greek coasts to approximate the projected coastal flooding hazard under climate change conditions in the 21st century. The TWL calculation considers the wave characteristics, sea level height due to storm surges, mean sea level (MSL) rise, and astronomical tidal ranges of the study areas. Moreover, the failure probabilities of a typical coastal defense structure are assessed for several failure mechanisms, considering variations in MSL, extreme wave climates, and storm surges in the vicinity of ports, within the framework of reliability analysis based on the nonstationary generalized extreme value (GEV) distribution. The methodology supports the investigation of future safety levels and possible periods of increased vulnerability of the studied structure to different ultimate limit states under extreme marine weather conditions associated with climate change, aiming at the development of appropriate upgrading solutions. The analysis suggests that the assumption of stationarity might underestimate the total failure probability of coastal structures under future extreme marine conditions.

Revisiting the link between extreme sea levels and climate variability using a spline-based non-stationary extreme value analysis

Non-stationary extreme value analysis is a powerful framework to address the problem of time evolution of extremes and its link to climate variability as measured by different climate indices CI (like North Atlantic Oscillation NAO index). To model extreme sea levels (ESLs), a widely-used tool is the non-stationary Generalized Extreme Value distribution (GEV) where the parameters (location, scale and shape) are allowed to vary as a function of some covariates like the month-of-year or some CIs. A commonly used assumption is that only a few CIs impact the GEV parameters by using a linear model, and most of the time by focusing on two GEV parameters (location or/and the scale parameter). In the present study, these assumptions are revisited by relying on a data-driven spline-based GEV fitting approach combined with a penalization procedure. This allows identifying the type (non- or linear) of the CI influence for any of the three GEV parameters directly from the data, and evaluating the significance of this relation, i.e. without making any a priori assumptions as it is traditionally done. This approach is applied to the monthly maxima of sea levels derived from eight of the longest (quasi century-long) tide gauge dataset (Brest, France; Cuxhaven, Germany; Gedser, Denmark; Halifax, Canada; Honolulu, US; Newlyn, UK; San Francisco, US; Stockholm, Sweden) and by accounting for four major CIs (the North Atlantic Oscillation, the Atlantic Multidecadal Oscillation, the Niño 1 + 2 and the Southern Oscillation indices). From this analysis, we show that: (1) the links between CIs and different parameters of a GEV distribution fitted to ESL data are most of the time linear, but some of them present significant non-linear shapes; (2) multiple CIs should be considered to predict ESLs, and (3) the CI influence of the GEV distribution is not limited to the location parameter. These results are useful to understand current modes of variability of ESLs, and ultimately to improve coastal resilience through more precise extreme water level assessments.

Nonstationary analysis of the extreme temperatures in Turkey

Record-breaking extreme temperatures have been measured in the last two decades all over Turkey, with recent studies detecting positive trends in extreme temperature time series. In this study, nonstationary extreme value analysis was performed on extreme temperature time series obtained from fifty stations scattered over the seven geographical regions of Turkey. Basic characterization of the data set was defined through outlier detection, homogeneity, trend detection, and stationarity tests. Trend-including non-stationary extreme temperature time series were analyzed with non-stationary Generalized Extreme Value distribution. Three main physical drivers were considered as the leading causes that trigger the observed trends in extreme temperatures over Turkey: time, teleconnection patterns of the Arctic Oscillations, and those of the North Atlantic Oscillations. The results showed that most of the absolute annual minimum and maximum temperature time series are inhomogeneous while the possible breakpoints date back to the1970s and 1990s, respectively. More than half of the absolute annual maximum time series (26/50 and many of the absolute annual minimum time series (21/50) showed a positive trend. No negative trend was detected in the extreme temperature time series. Based on the frequency analysis of the 21 annual maximum time series, the non-stationary estimations of 50-year return levels were detected to be higher than in the stationary model (between 0.44 °C and 3.73 °C). The return levels in 15 of the 20 minimum temperature time series increased from 0.11 °C up to 12.28 °C. Elevation increases the nonstationarity impact on absolute minimum temperatures and decreases it on absolute maximums. The findings in this study indicate that the consideration of non-stationarity in extreme temperature time series is a necessity during return level estimations over the study area.

Projected incremental changes to extreme wind-driven wave heights for the twenty-first century

Global climate change will alter wind sea and swell waves, modifying the severity, frequency and impact of episodic coastal flooding and morphological change. Global-scale estimates of increases to coastal impacts have been typically attributed to sea level rise and not specifically to changes to waves on their own. This study provides a reduced complexity method for applying projected extreme wave changes to local scale impact studies. We use non-stationary extreme value analysis to distil an incremental change signal in extreme wave heights and associate this with a change in the frequency of events globally. Extreme wave heights are not projected to increase everywhere. We find that the largest increases will typically be experienced at higher latitudes, and that there is high ensemble model agreement on an increase (doubling of events) for the waters south of Australia, the Arabian Sea and the Gulf of Guinea by the end of the twenty-first century.

Non-stationary extreme value analysis of sea states based on linear trends. Analysis of annual maxima series of significant wave height and peak period in the Mediterranean Sea

Non-stationary Extreme Value Analysis (NEVA) allows to determine the probability of exceedance of extreme sea states taking into account trends in the time series of data at hand. In this work, we analyse the reliability of NEVA of significant wave height (Hs) and peak period (Tp) under the assumption of linear trend for time series of annual maxima (AM) Hs in the Mediterranean Sea. A methodology to assess the significance of the results of the non-stationary model employed is proposed. Both the univariate long-term extreme value distribution of Hs and the bivariate distribution of Hs and Tp are considered. For the former, a non-stationary Generalized Extreme Value (GEV) probability is used, and a methodology to compute the parameters of the distribution based on the use of a penalty function is explored. Then, non-stationary GEV is taken as a reference to compute the Environmental Countours of Hs and Tp, assuming a conditional model for the latter parameter. Several methods to compute linear trends are analysed and cross-validated on the series of AM Hs at more than 20,000 hindcast nodes. Results show that the non-stationary analysis provides advantages over the stationary analysis only when all the considered metrics are consistent in indicating the presence of a trend. Moreover, both the univariate return levels of Hs and bivariate return levels of Hs and Tp show a marked dependence to the time window considered in the GEV distribution formulation. Therefore, when applying NEVA for coastal and marine applications, the hypothesis of linear trend and the length of the reference data used for the non-stationary distribution should be carefully considered.

The Optimization of Bayesian Extreme Value: Empirical Evidence for the Agricultural Commodities in the US

Bayesian extreme value analysis was used to forecast the optimal point in agricultural commodity futures prices in the United States for cocoa, coffee, corn, soybeans and wheat. Data were collected daily between 2000 and 2020. The estimation of extreme value can be empirically interpreted as representing crises or unusual time series trends, while the extreme optimal point is useful for investors and agriculturists to make decisions and better understand agricultural commodities future prices warning levels. Results from the Non-stationary Extreme Value Analysis (NEVA) software package using Bayesian inference and the Newton-optimal methods provided optimal interval values. These indicated extreme maximum points of future prices to inform investors and agriculturists to sell the contract and product before the commodity prices dropped to the next local minimum values. Thus, agriculturists can use this information as an advanced warming of alarming points of agricultural commodity prices to predict the efficient quantity of their agricultural product to sell, with better ways to manage this risk.

A novel analysis of COVID 19 risk in India incorporating climatic and socioeconomic Factors

This study investigates the influence of climate variables (pressure, relative humidity, temperature and wind speed) in inducing risk due to COVID 19 at rural, urban and total (rural and urban) population scale in 623 pandemic affected districts of India incorporating the socioeconomic vulnerability factors. We employed nonstationary extreme value analysis to model the different quantiles of cumulative COVID 19 cases in the districts by using climatic factors as covariates. Wind speed was the most dominating climatic factor followed by relative humidity, pressure, and temperature in the evolution of the cases. The results reveal that stationarity, i.e., the COVID 19 cases which are independent of pressure, relative humidity, temperature and wind speed, existed only in 148 (23.7%) out of 623 districts. Whereas, strong nonstationarity, i.e., climate dependence, was detected in the cases of 474 (76.08%) districts. 334 (53.6%), 200 (32.1%) and 336 (53.9%) districts out of 623 districts were at high risk (or above) at rural, urban and total population scales respectively. 19 out of 35 states were observed to be under high (or above) Kerala, Maharashtra, Goa and Delhi being the most risked ones. The study provides high-risk maps of COVID 19 pandemic at the district level and is aimed at supporting the decision-makers to identify climatic and socioeconomic factors in augmenting the risks.