Reply on RC3

Abstract. Anticipating risks related to climate extremes often relies on the quantification of large return levels (values exceeded with small probability) from climate projection ensembles. Current approaches based on multi-model ensembles (MMEs) usually estimate return levels separately for each climate simulation of the MME. In contrast, using MME obtained with different combinations of general circulation model (GCM) and regional climate model (RCM), our approach estimates return levels together from the past observations and all GCM–RCM pairs, considering both historical and future periods. The proposed methodology seeks to provide estimates of projected return levels accounting for the variability of individual GCM–RCM trajectories, with a robust quantification of uncertainties. To this aim, we introduce a flexible non-stationary generalized extreme value (GEV) distribution that includes (i) piecewise linear functions to model the changes in the three GEV parameters and (ii) adjustment coefficients for the location and scale parameters to adjust the GEV distributions of the GCM–RCM pairs with respect to the GEV distribution of the past observations. Our application focuses on snow load at 1500 m elevation for the 23 massifs of the French Alps. Annual maxima are available for 20 adjusted GCM–RCM pairs from the EURO-CORDEX experiment under the scenario Representative Concentration Pathway (RCP) 8.5. Our results show with a model-as-truth experiment that at least two linear pieces should be considered for the piecewise linear functions. We also show, with a split-sample experiment, that eight massifs should consider adjustment coefficients. These two experiments help us select the GEV parameterizations for each massif. Finally, using these selected parameterizations, we find that the 50-year return level of snow load is projected to decrease in all massifs by −2.9 kN m−2 (−50 %) on average between 1986–2005 and 2080–2099 at 1500 m elevation and RCP8.5. This paper extends the recent idea to constrain climate projection ensembles using past observations to climate extremes.

Statistical modeling of hydrological extremes is significant to the construction of hydraulic engineering. This paper, taking the Yingluoxia watershed as the study area, compares the annual maximum (AM) series and the peaks over a threshold (POT) series in order to study the hydrological extremes, examines the stationarity and independence assumptions for the two series, and discusses the estimations and uncertainties of return levels from the two series using the Generalized Extreme Value (GEV) and Generalized Pareto distribution (GPD) models. For comparison, the return levels from all threshold excesses with considering the extremal index are also estimated. For the POT series, the threshold is selected by examining the mean excess plot and the stability of the parameter estimates and by using common-sense. The serial correlation is reduced by filtering out a set of dependent threshold excesses. Results show that both series are approximately stationary and independent. The GEV model fits the AM series well and the GPD model fits the POT series well. The estimated return levels are fairly comparable for the AM series, the POT series, and all threshold excesses with considering the extremal index, with the difference being less than 10% for return periods longer than 10 years. The uncertainties of the estimated return levels are the highest for the AM series, and next for the POT series and then for all threshold excesses series in turn.

Previous research shows that for limited sample sizes applying the simplified metastatistical extreme value (sMEV) distribution instead of the more commonly used general extreme value (GEV) distribution can significantly reduce the associated uncertainty in rainfall return levels. Recent literature has also highlighted the possibility to analyze the effects of climate change using the non-stationary version of the sMEV distribution. Thus, the objective of this study is to test the performance of the sMEV and GEV for hourly precipitation using a convection-permitting regional climate model. The global climate model MIROC5 is employed to drive the regional climate model COSMO over the greater Germany area for the past, near future, and distant future. It is set up at a high temporal and spatial resolution allowing it to explicitly resolve deep convection, which is important when assessing extreme hourly precipitation. No comparable time series from a convection-permitting model has previously been analyzed using the sMEV distribution. The results show that the sMEV performs much better than the GEV in terms of the uncertainty for almost all return periods regardless of the observational years available. In addition, there is a north-south gradient in the return level difference, the uncertainty difference and the adequacy of the left-censoring threshold chosen for the sMEV. Investigating non-stationary versions of the sMEV and GEV shows that the non-stationary sMEV is more suitable to describing the change in return levels. However, both implemented versions of the non-stationary distributions are limited by the complexity of the temperature dependency. Therefore, we recommend a careful application for the prediction of return levels under higher temperatures. 

A two-component generalized extreme value distribution for precipitation frequency analysis

Abstract. Occurrence probabilities of extreme sea levels required in coastal planning, e.g. for calculating design floods, have been traditionally estimated individually at each tide-gauge location. However, these estimates include uncertainties, as sea-level observations typically have only a small number of extreme cases such as annual maxima. Moreover, exact information on sea-level extremes between the tide-gauge locations and incorporation of dependencies between the adjacent stations is often lacking in the analysis. In this study, we use Bayesian hierarchical modelling to estimate return levels of annual maxima of short-term sea-level variations related to storm surges in the Finnish coastal region. We use the generalised extreme value (GEV) distribution as the basis and compare three hierarchical model structures of different complexity against tide-gauge-specific fits. The hierarchical model structures allow us to share information on annual maximum sea levels between the neighbouring stations and also provide a natural way to estimate uncertainties in the theoretical estimates. The results show that compared to the tide-gauge-specific fits, the hierarchical models, which pool information across the tide gauges, provide narrower uncertainty ranges for both the posterior parameter estimates and the corresponding return levels in most locations. The estimated shape parameter of the GEV model is systematically negative for the hierarchical models, which indicates a Weibull type of behaviour for the extremes along the Finnish coast. The negative shape parameter also allows us to calculate the theoretical upper limit for the annual maximum sea levels on the Finnish coast. Depending on the tide gauge and hierarchical model considered, the median value of the theoretical upper limit was 47–73 cm higher than the highest observed sea level.

Rainfall extreme value estimates in Canada have historically been based on fitting the Gumbel distribution to annual maxima at individual sites by the method of moments (MOM). Studies have, however, shown that regional frequency analyses (RFA) may perform better than at-site methods. Also, the Fréchet rather than Gumbel form of the generalized extreme value (GEV) distribution may better describe the distribution of annual extremes. In this study, at-site Gumbel MOM and GEV extreme value analyses based on L-moment, maximum likelihood (MLE), and generalized maximum likelihood (GML) estimators are compared against RFA with L-moment methods at stations in southern British Columbia, Canada via cross-validation and Monte Carlo simulations. While GEV shape parameter estimates are predominately negative, qualitatively showing weak evidence for the Fréchet form of the GEV distribution, field significant differences from the Gumbel distribution in the region are not found. Regional frequency analysis leads to substantial reductions in error relative to at-site methods, especially for the GEV distribution and small samples. While Gumbel estimators exhibit lower variance than GEV estimators, they are also more biased, underestimating 100 year return levels. Of the at-site GEV estimators, GML tended to perform better than the L-moment estimator, in some cases nearing performance of RFA. Maximum likelihood performed worst, especially for small samples sizes.

The generalized extreme value (GEV) model has been recommended by FEMA (Federal Emergency Management Agency of the United States). In this study, we choose annual maximum water levels at two water gauging stations with long history data (more than 50 years) for flood frequency analysis. The maximum likelihood estimation (MLE) method is used to estimate the parameters of the GEV model. The return level and the probability that next year's annual maximum level exceeds all previous level are obtained.

Satellite gravimetry as realized with GRACE and GRACE‐FO provides a novel opportunity to study extreme deviations from annually varying terrestrial water storage (TWS) in all continental areas of our planet. By utilizing the generalized extreme value (GEV) distribution, we estimate return levels for events that are expected to happen once every 10 (i.e., 1‐in‐10) years. With two GRACE‐like reconstructions spanning over 40 and 114 years, respectively, we show that the currently available data record of 20 years is already sufficiently long to derive robust estimates of those return levels. When contrasting the GRACE/‐FO results to model experiments from the CMIP6 archive extending until the year 2100 by concatenating historical runs and climate projections under the SSP5‐8.5 socioeconomic pathway, we find that (a) the multi‐model median from CMIP6 has the overall best agreement with the satellite data, thereby nicely confirming the validity of a central assumption of many climate‐related studies that heavily rely on ensemble statistics. We also find that (b) CMIP6 model runs contain only modest deviations of 1‐in‐10 years return levels from the beginning of the 20th century when compared to present‐day, but predict stronger changes toward more extreme return levels by the end of the 21st century. On the other hand, we also find substantial differences between satellite data and individual model experiments, which opens new opportunities to inform, validate and/or calibrate numerical climate models with satellite gravimetry data from GRACE, GRACE‐FO, and in future also GRACE‐C.

Extreme value modeling for extreme rainfall is one of the most important processes in the field of hydrology. For the improvement of extreme value modeling and its physical meaning, large-scale climate modes have been widely used as covariates of distribution parameters, as they can physically account for climate variability. This study proposes a novel procedure for extreme value modeling of rainfall based on the significant relationship between the long-term trend of the annual maximum (AM) daily rainfall and large-scale climate indices. This procedure is characterized by two main steps: (a) identifying significant seasonal climate indices (SCIs), which impact the long-term trend of AM daily rainfall using statistical approaches, such as ensemble empirical mode decomposition, and (b) selecting an appropriate generalized extreme value (GEV) distribution among the stationary GEV and nonstationary GEV (NS-GEV) using time and SCIs as covariates by comparing their model fit and uncertainty. Our findings showed significant relationships between the long-term trend of AM daily rainfall over South Korea and SCIs (i.e., the Atlantic Meridional Mode, Atlantic Multidecadal Oscillation in the fall season, and North Atlantic Oscillation in the summer season). In addition, we proposed a model selection procedure considering both the Akaike information criterion and residual bootstrap method to select an appropriate GEV distribution among a total of 59 GEV candidates. As a result, the NS-GEV with SCI covariates generally showed the best performance over South Korea. We expect that this study can contribute to estimating more reliable extreme rainfall quantiles using climate covariates.

Quantification of the climate change-induced variations in Intensity–Duration–Frequency curves in the Canadian Prairies

Abstract. In France, nuclear facilities were designed around very low probabilities of failure. Nevertheless, some extreme climatic events have given rise to exceptional observed surges (outliers) much larger than other observations, and have clearly illustrated the potential to underestimate the extreme water levels calculated with the current statistical methods. The objective of the present work is to conduct a comparative study of three approaches to extreme value analysis, including the annual maxima (AM), the peaks-over-threshold (POT) and the r-largest order statistics (r-LOS). These methods are illustrated in a real analysis case study. All data sets were screened for outliers. Non-parametric tests for randomness, homogeneity and stationarity of time series were used. The shape and scale parameter stability plots, the mean excess residual life plot and the stability of the standard errors of return levels were used to select optimal thresholds and r values for the POT and r-LOS method, respectively. The comparison of methods was based on (i) the uncertainty degrees, (ii) the adequacy criteria and tests, and (iii) the visual inspection. It was found that the r-LOS and POT methods have reduced the uncertainty on the distribution parameters and return level estimates and have systematically shown values of the 100 and 500-year return levels smaller than those estimated with the AM method. Results have also shown that none of the compared methods has allowed a good fit at the right tail of the distribution in the presence of outliers. As a perspective, the use of historical information was proposed in order to increase the representativeness of outliers in data sets. Findings are of practical relevance, not only to nuclear energy operators in France, for applications in storm surge hazard analysis and flood management, but also for the optimal planning and design of facilities to withstand extreme environmental conditions, with an appropriate level of risk.

Background:The geographic range of the tick Amblyomma americanum, a vector of diseases of public health significance such as ehrlichiosis, has expanded from the southeast of the United States northward during the 20th century. Recently, populations of this tick have been reported to be present close to the Canadian border in Michigan and New York states, but established populations are not known in Canada. Previous research suggests that changing temperature patterns with climate change may influence tick life cycles and permit northward range expansion of ticks in the northern hemisphere.Objectives:We aimed to estimate minimal temperature conditions for survival of A. americanum populations at the northern edge of the tick’s range and to investigate the possibility of range expansion of A. americanum into northern U.S. states and southern Canada in the coming decades.Methods:A simulation model of the tick A. americanum was used, via simulations using climate data from meteorological stations in the United States and Canada, to estimate minimal temperature conditions for survival of A. americanum populations at the northern edge of the tick’s range.Results:The predicted geographic scope of temperature suitability [ annual cumulative degree days (DD) ] included most of the central and eastern U.S. states east of longitude 110°W, which is consistent with current surveillance data for the presence of the tick in this region, as well as parts of southern Quebec and Ontario in Canada. Regional climate model output raises the possibility of northward range expansion into all provinces of Canada from Alberta to Newfoundland and Labrador during the coming decades, with the greatest northward range expansion (up to by the year 2100) occurring under the greenhouse gas (GHG) emissions of Representative Concentration Pathway (RCP) 8.5. Predicted northward range expansion was reduced by approximately half under the reduced GHG emissions of RCP4.5.Discussion:Our results raise the possibility of range expansion of A. americanum into northern U.S. states and southern Canada in the coming decades, and conclude that surveillance for this tick, and the diseases it transmits, would be prudent. https://doi.org/10.1289/EHP5668

Abstract. In this study we detect and quantify changes in the distribution of the annual maximum daily maximum temperature (TXx) in a large observation-based gridded data set of European daily temperature during the years 1950–2018. Several statistical models are considered, each of which analyses TXx using a generalized extreme-value (GEV) distribution with the GEV parameters varying smoothly over space. In contrast to several previous studies which fit independent GEV models at the grid-box level, our models pull information from neighbouring grid boxes for more efficient parameter estimation. The GEV location and scale parameters are allowed to vary in time using the log of atmospheric CO2 as a covariate. Changes are detected most strongly in the GEV location parameter, with the TXx distributions generally shifting towards hotter temperatures. Averaged across our spatial domain, the 100-year return level of TXx based on the 2018 climate is approximately 2 ∘C (95 % confidence interval of [2.03,2.12] ∘C) hotter than that based on the 1950 climate. Moreover, averaged across our spatial domain, the 100-year return level of TXx based on the 1950 climate corresponds approximately to a 6-year return level in the 2018 climate.

The study examines the impacts of climate change on the operation and capacity of the combined sewer network in the historic center of Thessaloniki, Greece. Rainfall data from three high-resolution Regional Climate Models (RCMs), namely (a) the Cosmo climate model (CCLM), (b) the regional atmospheric climate model (RACMO) and (c) the regional model (REMO), from the MED-CORDEX initiative with future estimations based on Representative Concentration Pathway (RCP) 4.5, are first corrected for bias based on existing measurements in the study area. Intensity–duration–frequency (IDF) curves are then constructed for future data using a temporal downscaling approach based on the scaling of the Generalized Extreme Value (GEV) distribution to derive the relationships between daily and sub-daily precipitation. Projected rainfall events associated with various return periods are subsequently developed and utilized as input parameters for the hydrologic–hydraulic model. The simulation results for each return period are compared with those of the current climate, and the projections from various RCMs are ranked according to their impact on the combined sewer network and overflow volumes. In the short term (2020–2060), the CCLM and REMO project a decrease in CSO volumes compared to current conditions, while the RACMO predicts an increase, highlighting uncertainties in short-term climate projections. In the long term (2060–2100), all models indicate a rise in combined sewer overflow volumes, with CCLM showing the most significant increase, suggesting escalating pressure on urban drainage systems due to more intense rainfall events. Based on these findings, it is essential to adopt mitigation strategies, such as nature-based solutions, to reduce peak flows within the network and alleviate the risk of flooding.

Downscaling of future projections of climatic variables from global climate models (GCMs) to urban catchment scales is required for stormwater studies as existing GCMs are unable to predict the rainfall at high temporal and spatial resolutions. In the current study, the capability of dynamical and statistical downscaling methods is evaluated and compared using the rainfall data of current climate and future extreme events at a small urban catchment scale. Regional climate model (RCM) and statistical downscaling model (SDSM) are utilized to downscale rainfall data from twelve GCMs under three representative concentration pathways (RCPs) (i.e., RCP2.6, RCP 4.5 and RCP 8.5). The daily rainfall data (1985–2015) of Lucas Creek catchment located in Auckland, New Zealand is used as a baseline/current climate. The future downscaled rainfall data is analyzed in the 2090s (2071–2100). The results showed that both the methods performed well in downscaling the current climate. For future projections, SDSM underestimated mean daily rainfall at the start of the annual cycle and overestimated towards the middle of the year compared to RCM. Similarly, monthly variance and skewness were overestimated for some months by SDSM. The GCMs of both the methods also showed variations in the future rainfall projections amongst themselves. However, significant alterations in the future rainfall were observed compared to the current climate. Rainfall frequency analysis was performed by applying the Gumbel distribution to the baseline and downscaled data for 1, 2, 3, 4, 5, 10, 20, 30, 50 and 100 years return periods. The investigation revealed that RCM and SDSM show similar results for low return periods and different results for high return periods for the current and future climate. Both the methods forecasted an increase in magnitudes of future events however, RCM projections were lower compared to SDSM. The results illustrate the downscaling abilities of both the methods at a small urban catchment scale however, the contrasting implication in downscaling the rainfall data is related to their different downscaling mechanisms.