Using high-resolution regional climate models to estimate return levels of daily extreme precipitation over Bavaria

Extreme daily rainfall is an important trigger for floods in Bavaria. The dimensioning of water management structures as well as building codes is based on observational rainfall return levels. In this study, three high-resolution regional climate models (RCMs) are employed to produce 10- and 100-year daily rainfall return levels and their performance is evaluated by comparison to observational return levels. The study area is governed by different types of precipitation (stratiform, orographic, convectional) and a complex terrain, with convective precipitation also contributing to daily rainfall levels. The Canadian Regional Climate Model version 5 (CRCM5) at a 12 km spatial resolution and the Weather and Forecasting Research (WRF) model at a 5 km resolution both driven by ERA-Interim reanalysis data use parametrization schemes to simulate convection. WRF at a 1.5 km resolution driven by ERA5 reanalysis data explicitly resolves convectional processes. Applying the generalized extreme value (GEV) distribution, the CRCM5 setup can reproduce the observational 10-year return levels with an areal average bias of +6.6 % and a spatial Spearman rank correlation of ρ=0.72. The higher-resolution 5 km WRF setup is found to improve the performance in terms of bias (+4.7 %) and spatial correlation (ρ=0.82). However, the finer topographic details of the WRF-ERA5 return levels cannot be evaluated with the observation data because their spatial resolution is too low. Hence, this comparison shows no further improvement in the spatial correlation (ρ=0.82) but a small improvement in the bias (2.7 %) compared to the 5 km resolution setup. Uncertainties due to extreme value theory are explored by employing three further approaches. Applied to the WRF-ERA5 data, the GEV distributions with a fixed shape parameter (bias is +2.5 %; ρ=0.79) and the generalized Pareto (GP) distributions (bias is +2.9 %; ρ=0.81) show almost equivalent results for the 10-year return period, whereas the metastatistical extreme value (MEV) distribution leads to a slight underestimation (bias is −7.8 %; ρ=0.84). For the 100-year return level, however, the MEV distribution (bias is +2.7 %; ρ=0.73) outperforms the GEV distribution (bias is +13.3 %; ρ=0.66), the GEV distribution with fixed shape parameter (bias is +12.9 %; ρ=0.70), and the GP distribution (bias is +11.9 %; ρ=0.63). Hence, for applications where the return period is extrapolated, the MEV framework is recommended. From these results, it follows that high-resolution regional climate models are suitable for generating spatially homogeneous rainfall return level products. In regions with a sparse rain gauge density or low spatial representativeness of the stations due to complex topography, RCMs can support the observational data. Further, RCMs driven by global climate models with emission scenarios can project climate-change-induced alterations in rainfall return levels at regional to local scales. This can allow adjustment of structural design and, therefore, adaption to future precipitation conditions.

Frequency of winter temperature extremes over northern Eurasia dominated by AMOC

Widespread observed and projected increases in warm extremes, along with decreases in cold extremes, have been confirmed to be consistent with global and regional warming. However, in our study, decadal variations in surface air temperature (SAT) extremes over northern Eurasia in winter are primarily dominated by the Atlantic Meridional Overturning Circulation (AMOC), rather than an anthropogenically forcing. Based on reanalysis and state-of-the-art model simulations, we highlight that the decadal weakening of AMOC narrowed the generalized extreme value (GEV) distribution of winter SAT via diminishing its variance, and thus inducing fewer SAT extremes. On the contrary, the decadal enhancing of AMOC corresponded to the increase in the SAT variance over northern Eurasia, making a milder GEV distribution and generating more warm and cold extremes. These AMOC induced variations in SAT extremes may depend on the ocean heat transported into the atmosphere for air motion over northern Eurasia and the Arctic amplification caused by the heat advection from the northward-flowing Atlantic water.

Study of Unbiased Plotting Position Formulae for the Generalized Extreme Value (GEV) Distribution

The determination of appropriate quantile relations between the magnitude of extreme events and the corresponding exceedance probabilities is a prerequisite for optimum design of hydraulic structures. Various plotting position formulae have been proposed for estimating the exceedance probabilities or recurrence in. In this study, eight plotting position formulae recommended for GEV distribution were used for estimating the exceedance probabilities of annual maximum series of River Niger at Baro, Kouroussa and Shintaku hydrological stations. The performance measures of PPCC, RRMSE, PBIAS, MAE and NSE were calculated by applying their individual equations to each pair of observed AMS, arranged in ascending order, and exceedance probabilities calculated using each plotting positions. The result of the study show that Weibull was the best plotting position formula, seconded by Beard and thirdly, In – na and Ngugen. This study underscores the necessity to accurately size water infrastructure. In a recent paper, the author found GEV distribution the best – fit probability distribution model in Nigeria. Thus, the need to develop indepth understanding and accurate estimation of exceedance probabilities and return periods using the GEV distribution. Furthermore, this paper recommends similar studies to be conducted for Pearson Type 3(PR3) and Log Pearson Type 3 (LP3) distributions.

Using high-resolution regional climate models to estimate return levels of daily extreme precipitation over Bavaria

Extreme daily rainfall is an important trigger for floods in Bavaria. The dimensioning of water management structures as well as building codes are based on observational rainfall return levels. In this study, three high-resolution regional climate models (RCMs) are employed to produce 10-year daily rainfall return levels and their performance is evaluated by comparison to observational return levels. The study area is governed by different types of precipitation (stratiform, orographic, convectional) and a complex terrain, with convective precipitation also contributing to daily rainfall levels. The Canadian Regional Climate Model version 5 (CRCM5) at 12 km spatial resolution and the Weather and Forecasting Research model (WRF) at 5 km resolution both driven by ERA-Interim reanalysis data use parametrization schemes to simulate convection. The WRF at 1.5 km resolution driven by ERA5 reanalysis data explicitly resolves convectional processes. Applying the Generalized Extreme Value (GEV) distribution, all three model setups can reproduce the observational return levels with an areal average bias of +6.6 % or less and a spatial Spearman rank correlation of ρ > 0.72. The increase of spatial resolution between the 12 km CRCM5 and the 5 km WRF setup is found to improve the performance in terms of bias (+6.6 % and +3.2 %) and spatial correlation (ρ = 0.72 and ρ = 0.82). However, the finer topographic details of the WRF-ERA5 return levels cannot be evaluated with the observation data because their spatial resolution is too low. Hence, this comparison shows no great further improvement (bias = +1.1 %, ρ = 0.82) of the overall performance compared to the 5 km resolution setup. Uncertainties due to extreme value theory are explored by employing three different approaches for the highest-resolution WRF-ERA5 setup. The GEV distribution with fixed shape parameter (bias = +0.9 %, ρ = 0.79) and the Generalized Pareto (GP: bias = +1.3 %, ρ = 0.81) show almost equivalent results for the 10-year return period, whereas the Metastatistical Extreme Value (MEV) distribution leads to a slight underestimation (bias = -6.2 %, ρ = 0.86). From these results, it follows that high-resolution regional climate models are suitable for generating spatially homogeneous rainfall return level products. In regions with a sparse rain gauge density or low spatial representativeness of the stations due to complex topography, RCMs can support the observational data. Further, RCMs driven by global climate models with emission scenarios can project climate change-induced alterations in rainfall return levels at regional to local scales. This would allow adjustment of structural design and, therefore, adaption to future precipitation conditions.

Extreme Storm Surge estimates and projection through the Metastatistical Extreme Value Distribution

<p>Storm surges caused by extreme meteorological conditions are a major natural risk in coastal areas, especially in the context of global climate change. The increase of future sea-levels caused by continuing global warming, may endanger human lives and infrastructure through inundation, erosion and salinization.<br>Hence, the reliable estimation of the occurrence probability of these extreme events is crucial to quantify risk and to design adequate coastal defense structures. The probability of event occurrence is typically estimated by modelling observed sea-level records using one of a few statistical approaches.<br>The traditional Extreme Value Theory is based on the use of the Generalized Extreme Value distribution (GEV),  fitted either by considering block (typically yearly) maxima, or values exceeding a high threshold (POT). This approach does not make full use of all observational information, and thereby does not minimize estimation uncertainty.<br>The recently proposed Metastatistical Extreme Value Distribution (MEVD), instead, makes use of most of the available observations and has been shown to outperform the classical GEV distribution in several applications, including hourly and daily rainfall, flood peak discharge and extreme hurricane intensity.<br>Here, we comparatively apply the MEVD and the GEV distribution to long time series of sea-level observations distributed along European coastlines (Venice (IT), Hornbaek (DK), Marseille (FR), Newlyn (UK)). A cross-validation approach, dividing available data in separate calibration and test sub-samples, is used to compare their performances in high-quantile estimation.<br>The MEVD approach is based on the definition of an “ordinary values” distribution (here a Generalized Pareto distribution), whose parameters are estimated using the Probability Weighted Moments method on non-overlapping sub-samples of fixed size (5 years). To address the problems posed by observational samples of different sizes, we explore the effect on uncertainty of different calibration sample sizes, from 5 to 30 years. In this application, we find that the GEVD-POT and MEVD approaches perform similarly, once the above parameter choices are optimized. In particular, when considering short samples (5 years) and events with a high return time, the estimation errors show no significant differences in their median value across methods and sites, all approaches producing a similar underestimation of the actual quantile. When larger calibration sample sizes are considered (10-30 yrs), the median error of MEVD estimates tends to be closer to zero than those obtained from the traditional methods.<br>Future projections of sea-level rise until 2100 are also analyzed, with reference to intermediate and extreme representative concentration pathways (RCP 4.5 and RCP 8.5). The probability of future storm surges along European coastlines are then estimated assuming a changing mean sea-level and an unchanged storm regime. The projections indicate future changes in mean sea-level lead to increases in the height of storm surges for a fixed return period that are spatially heterogeneous across the coastal locations explored.</p>

Hydrological consistency between the upstream and downstream estimates of Q1000 flood on the upper Rhine River, using historical series in Basel (1808-2017) and Maxau (1815-2018)

<div> <p>Estimation of extreme design floods with a short series of a few decades remains challenging because the statistical extrapolation of observed floods to extreme floods induces great uncertainties. Several alternative methods take advantage of the use of additional information: regional methods (e.g. the index flood method), Monte Carlo rainfall-runoff simulation methods, or specific statistical methods adapted to historical series. Here we present a flood frequency analysis on the upper Rhine River, using long historical series in Basel (1808-2017) and Maxau (1815-2018). We used a Bayesian framework to fit the parameters of the GEV distribution. Each value of the annual maximum discharge has uncertainties, which vary from ± 5-7% for the last decades to ± 22-42% for the oldest period depending on the station. At the local scale, without prior assumption on the three parameters of a GEV distribution, we found that the credibility intervals of the Basel and Maxau flood distributions are consistent. However, beyond a 1000-year return period, flood quantiles are incoherent with Q(Maxau) < Q(Basel) although Maxau (50 000 km<sup>2</sup>) is located downstream of Basel (36 000 km<sup>2</sup>). The floods at Basel are almost Gumbel distributed (shape parameter k = 0.066), whereas the floods at Maxau are Weibull distributed (shape parameter k = 0.219) with an asymptotic maximum value. Assuming that the shape parameter k has a certain regional consistency, we have performed a second iteration, with a prior interval [-0.1; +0.4] on k. The width of this interval corresponds to the union of the posterior distribution of k parameter of each local distribution: [-0.1; +0.2] at Basel and [0.0; +0.4] at Maxau. The second version of each distribution is almost the same up to a return period of 100 years, but there is no more crossing for extreme values. Using the predictive distribution with a regional prior on the shape parameter of the GEV distribution, the result is hydrologically consistent from upstream to downstream.</p> </div>

Paradigm Shift in distribution preferences for Flood Frequency Analysis and the ‘LMoFit’ R-Package

<p>Safe and economical design of dams, highways, bridges, and other infrastructures require accurate estimates of the magnitude and frequency of peak floods obtained by flood frequency analysis (FFA). The Generalized Extreme Value (GEV) distribution is the traditional preference for FFA along with other distributions having location, scale, and shape parameters. In this poster, two alternative power-type distributions comprising one location and two shape parameters are explored, these are Burr type III (BrIII) and Burr type XII (BrXII) distributions. The performances of BrIII and BrXII are compared against that of GEV in describing annual maximum streamflow records at 1088 sites across Canada. A generic L-moment algorithm is developed to fit these distributions regardless of the unavailability of some of their analytical L-moment expressions. This algorithm is devised in the R package “LMoFit” on CRAN. The latter comparison shows that: (1) the three distributions perform equally-well in describing the observed peaks; (2) the BrIII and the BrXII distributions predict larger streamflow peaks increasing the heaviness of their right tails compared to that of the GEV distribution; (3) the predictions of the GEV distribution reach the upper limits of the distribution in 39% of the sites, while the corresponding predictions of BrIII and BrXII are not limited and exceed the reached limits of GEV; (4) the GEV distribution might be underestimating the risk of extreme events, especially for large return periods. Accordingly, there are potential limitations in using the GEV distribution for FFA and the findings suggest BrIII and BrXII distributions as consistent alternatives for future FFA practices. The “LMoFit” R package is devised to facilitate the future application of the suggested distributions.</p>

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.

Modelling Unusual Behaviour of Rainfall Using Truncated GEV Distribution in a Mixture Framework

A truncated generalised extreme value (GEV) distribution in a mixture framework is proposed for the analysis of abnormal rare events in heterogeneous data representing environmental phenomena. The proposed extremal mixture model produced a better understanding of the extremal rainfall behaviour in the Mula-Mutha-Bhima subbasin in India. It gave some realistic extrapolation of quantiles corresponding to a very low probability of exceedance useful in water resources planning and design of civil infrastructure. The proposed model could be useful for the class of problems characterising extreme events and heterogeneity in fields like hydrology, environment and so on.