Under the\u00a0RCP8.5 scenario (2070\u20132100), the\u00a0mean\u00a0relative change in The\u00a0analysis shows that uncertainty at high return periods is strongly influenced by the\u00a0estimation of\u00a0the\u00a0GEV shape parameter, where small differences lead to nonlinear growth in\u00a0extrapolated quantiles. The\u00a0detected intensification of\u00a0extreme precipitation is consistent with the\u00a0expected thermodynamic amplification of\u00a0the\u00a0hydrological cycle; however, the\u00a0ensemble spread highlights substantial structural uncertainty in\u00a0regional climate models.<\/span><\/p>\n The\u00a0results indicate that the\u00a0use of\u00a0historical IDF curves without accounting for climate change may lead to a\u00a0systematic underestimation of\u00a0design values, particularly for infrastructure with a\u00a0long service life.<\/span><\/p>\n Extreme precipitation events are of\u00a0the\u00a0most significant hydrometeorological phenomena affecting public safety, the\u00a0functioning of\u00a0technical infrastructure, and the\u00a0economic stability of\u00a0regions [1]. Under Central European\u00a0conditions, flash floods and local inundation have long been associated primarily with short-duration intense rainfall events, the\u00a0impacts of\u00a0which are intensified by urbanisation and changes in\u00a0land use. The\u00a0increasing proportion of\u00a0impervious surfaces, river channel modifications, and the\u00a0concentration of\u00a0built-up areas accelerate the\u00a0runoff response of\u00a0catchments and increase the\u00a0sensitivity of\u00a0the\u00a0landscape to extreme precipitation episodes.<\/span><\/p>\n The\u00a0design of\u00a0technical measures such as sewer systems, retention reservoirs, dry polders, and blue-green infrastructure elements is therefore based on the\u00a0statistical description of\u00a0extreme precipitation [2]. In\u00a0practice, design quantiles expressed through intensity\u2013duration\u2013frequency (IDF) curves are used as the\u00a0principal tool for the\u00a0dimensioning of\u00a0water management structures [3, 4]. These curves are usually derived from historical precipitation time series and implicitly assume a\u00a0stationary climate regime [3].<\/span><\/p>\n The\u00a0assumption of\u00a0stationarity, however, is no longer defensible in\u00a0the\u00a0context of\u00a0ongoing climate change [1]. Increasing concentrations of\u00a0greenhouse gases lead to atmospheric warming, which is associated with changes in\u00a0the\u00a0hydrological cycle [5]. Climate models as well as observed trends indicate an\u00a0intensification of\u00a0extreme precipitation in\u00a0many regions of\u00a0the\u00a0world [1, 6]. The\u00a0physical basis of\u00a0this intensification is linked to the\u00a0Clausius\u2013Clapeyron relationship, according to which the\u00a0maximum water vapour content of\u00a0the\u00a0atmosphere increases by approximately 7\u00a0% per 1 K\u00a0of\u00a0warming [5, 6]. A\u00a0higher water vapour content creates the\u00a0potential for more intense precipitation events, particularly those of\u00a0a\u00a0convective nature [6].<\/span><\/p>\n Although the\u00a0physical mechanism responsible for the\u00a0intensification of\u00a0extreme precipitation is relatively well understood, its quantification at the\u00a0regional and local levels is subject to considerable uncertainty [1]. This uncertainty arises from several sources, namely structural differences among climate models, uncertainty associated with emission scenarios, and internal climate variability [7]. From the\u00a0perspective of\u00a0water management practice, however, not only the\u00a0mean\u00a0change in\u00a0the\u00a0design quantile is important, but above all its upper bound, which represents the\u00a0potential risk of\u00a0infrastructure underdesign.<\/span><\/p>\n Another significant problem is the limited availability of long-term high-quality precipitation measurements. In many locations, sufficiently long time series enabling reliable estimation of high return periods are not available. The extrapolation of a 100-year or 200-year quantile from a short time series is statistically unstable and sensitive to individual extreme events [2, 8]. Regional frequency analysis (RFA) represents a methodological approach that mitigates this problem through the sharing of information among climatically similar locations [9]. By separating the regional shape of the distribution from the local\u00a0<\/span>scale, it enables a\u00a0more robust estimation of\u00a0extreme quantiles even in\u00a0areas without direct measurements or with limited data availability [9].<\/span><\/p>\n The\u00a0literature contains numerous studies addressing changes in\u00a0extreme precipitation in\u00a0the\u00a0context of\u00a0climate change; however, fewer studies systematically combine regional frequency analysis with a\u00a0multi-model ensemble of\u00a0climate projections and explicitly quantify the\u00a0uncertainty associated with high return periods [3, 10, 11]. In\u00a0particular, insufficient attention has been paid to the\u00a0question of\u00a0how large the\u00a0uncertainty of\u00a0the\u00a0100-year design quantile is and how its structure changes depending on the\u00a0time horizon and emission scenario [7].<\/span><\/p>\n The\u00a0present study aims to partially fill this gap. The\u00a0methodology described below was applied to three pilot locations (Bukovno, Pe\u010dky, and B\u011bchovice). The\u00a0main\u00a0research questions can\u00a0be formulated as follows:<\/span><\/p>\n \u00a0<\/span>Answers to these questions are of\u00a0direct relevance to the\u00a0dimensioning of\u00a0water management infrastructure as well as to the\u00a0strategic planning of\u00a0adaptation measures. The\u00a0study therefore combines regional frequency analysis with a\u00a0multi-model ensemble of\u00a0regional climate projections and focuses not only on the\u00a0estimation of\u00a0future IDF curves, but especially on the\u00a0systematic quantification of\u00a0their uncertainty [7, 10, 11].<\/span><\/p>\n Observed data on short-duration precipitation totals from the\u00a0network of\u00a0stations operated by the\u00a0Czech Hydrometeorological Institute (CHMI) were used for the\u00a0construction of\u00a0reference IDF curves for the\u00a0three pilot locations [12,\u00a013]. Only stations with time series exceeding 30 years in\u00a0length were included in\u00a0the\u00a0analysis, representing the\u00a0minimum duration required for a\u00a0more robust estimation of\u00a0high return periods within\u00a0the\u00a0framework of\u00a0block maxima analysis [2, 8]. The\u00a0selection of\u00a0stations was further restricted to locations with sufficient measurement continuity and a\u00a0minimal proportion of\u00a0missing data.<\/span><\/p>\n The\u00a0primary criterion for station selection was their spatial proximity to the\u00a0analysed locations, defined as a\u00a0circular buffer with a\u00a0radius of\u00a030 km. Only stations located within\u00a0this radius and simultaneously meeting the\u00a0requirement of\u00a0a\u00a0time series of\u00a0annual maxima of\u00a0at least 30 years were included in\u00a0the\u00a0regional analysis. The\u00a0minimum record length was selected with regard to the\u00a0stability of\u00a0the\u00a0estimation of\u00a0the\u00a0parameters of\u00a0the\u00a0GEV (General Extreme Value) distribution and to the\u00a0limitation of\u00a0uncertainty associated with the\u00a0extrapolation of\u00a0high return periods. This approach assumes that stations meeting both criteria exhibit sufficient climatic similarity and statistical robustness for the\u00a0application of\u00a0regional frequency analysis. The\u00a0stations used are shown and described in\u00a0Fig.<\/span>\u00a01<\/span><\/em> and Tab.<\/span>\u00a01<\/span><\/em>.<\/span><\/p>\n The\u00a0block maxima method was used for the\u00a0application of\u00a0extreme value theory [2, 8]. For each duration (5\u00a0minutes to 24 hours), annual maxima were extracted from the\u00a0time series. This approach is consistent with the\u00a0classical formulation of\u00a0EVT (Extreme Value Theory) and allows the\u00a0direct application of\u00a0the\u00a0GEV distribution [8]. The\u00a0resulting set of\u00a0annual maxima constituted the\u00a0input for the\u00a0regional frequency analysis and for the\u00a0estimation of\u00a0the\u00a0parameters of\u00a0the\u00a0GEV distribution in\u00a0the\u00a0reference period [8, 9].<\/span><\/p>\n Future changes in\u00a0design precipitation were derived from regional climate projections of\u00a0the\u00a0CORDEX (Coordinated Regional Climate Downscaling Experiment) initiative [14]. Models from the\u00a0European\u00a0EUR-11 (horizontal resolution of\u00a0approximately 11 km) and EUR-22 (resolution of\u00a0approximately 22 km) domains were used [15]. The\u00a0higher spatial resolution allows a\u00a0more detailed representation of\u00a0orography and regional circulation processes influencing extreme precipitation.<\/span><\/p>\n The\u00a0ensemble included multiple combinations of\u00a0global climate models (GCMs) and regional climate models (RCMs). This multi-model approach makes it possible to capture structural uncertainty arising from differences in\u00a0the\u00a0dynamical cores of\u00a0the\u00a0models, the\u00a0parameterisation of\u00a0cloud processes and convection, and atmosphere\u2013surface interactions [7, 16]. Each GCM\u2013RCM combination represents one realisation of\u00a0future climate, while the\u00a0complete set of\u00a0realisations constitutes the\u00a0ensemble. An\u00a0overview of\u00a0the\u00a0ensemble combinations used is presented in\u00a0Tab.\u00a02<\/span><\/em>.<\/span><\/p>\n Three time periods were evaluated:<\/span><\/p>\n For future projections, the\u00a0RCP2.6, RCP4.5, and RCP8.5 emission scenarios were analysed, representing different trajectories of\u00a0greenhouse gas concentration development [17, 18]. The\u00a0RCP2.6 scenario assumes rapid stabilisation of\u00a0emissions, RCP4.5 an\u00a0intermediate stabilisation trajectory, and RCP8.5 a\u00a0scenario of\u00a0continuing emission growth [18].<\/p>\n Hourly precipitation data from climate models, expressed in units of\u00a0kg\u2009\u2219\u2009m-2<\/sup>\u2009\u2219\u2009s-1<\/sup>, were used and converted to precipitation totals before being aggregated to the\u00a0required durations. For each grid point corresponding to the\u00a0analysed pilot sites, a\u00a0time series of\u00a0annual maxima was extracted from the\u00a0regional models using a\u00a0procedure analogous to that applied to the\u00a0observed data [8].<\/p>\n \u00a0<\/em>To reduce the\u00a0influence of\u00a0systematic model biases, the\u00a0future change in\u00a0the\u00a0design quantile was expressed in\u00a0relative form [3]:<\/p>\n This approach assumes that the\u00a0systematic model bias is largely consistent between the\u00a0historical and future periods, thereby allowing the\u00a0analysis to focus on the\u00a0relative change in\u00a0extremes rather than\u00a0on their absolute values [16]. The\u00a0relative changes were subsequently applied to the\u00a0reference IDF curves derived from observed data, yielding future design values for the\u00a0individual emission scenarios for both projection periods [12, 13]. This procedure made it possible to link the\u00a0local statistical behaviour of\u00a0extreme values derived from observed data with future climate projections, while simultaneously systematically quantifying the\u00a0ensemble spread as a\u00a0measure of\u00a0model uncertainty [7].<\/span><\/p>\n Extreme value theory<\/span><\/span><\/strong><\/span><\/p>\n Extreme value theory (EVT) represents a\u00a0statistical approach based on the\u00a0asymptotic properties of\u00a0extremes, intended for modelling the\u00a0behaviour of\u00a0maxima of\u00a0random variables [2, 8]. Whereas the\u00a0classical central limit theorem describes the\u00a0limiting behaviour of\u00a0sums, EVT focuses on the\u00a0limiting properties of\u00a0extremes. For independent and identically distributed random variables X1<\/sub><\/span>,\u2026, Xn<\/sub><\/span>, it holds that for suitably normalised maxima Mn<\/sub><\/span> = max\u00a0(X1<\/sub><\/span>, …, Xn<\/sub><\/span>), the\u00a0corresponding distribution function converges to the\u00a0Generalised Extreme Value (GEV) distribution [8].<\/span><\/p>\n The\u00a0distribution function of\u00a0the\u00a0GEV distribution is given by the\u00a0following equation:<\/span><\/p>\n where:<\/p>\n \u03be\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 is\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 the\u00a0location parameter<\/p>\n \u03b1 > 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 the\u00a0scale parameter<\/p>\n \u03ba\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 the\u00a0shape parameter [8]<\/p>\n <\/p>\n The\u00a0shape parameter determines the\u00a0thickness of\u00a0the\u00a0right tail of\u00a0the\u00a0distribution. For \u03ba > 0, the\u00a0distribution has a\u00a0heavy tail (Fr\u00e9chet type); for \u03ba = 0, it reduces to the\u00a0Gumbel type; and for \u03ba < 0, it has a\u00a0finite upper bound (Weibull type) [8]. Estimation of\u00a0this parameter is crucial for the\u00a0extrapolation of\u00a0high quantiles, because small changes in\u00a0\u03ba may lead to substantial differences in\u00a0the\u00a0estimation of\u00a0100-year or 200-year extremes [2, 8].<\/p>\n Quantiles of\u00a0the\u00a0GEV distribution can\u00a0be expressed by inversion of\u00a0the\u00a0distribution function:<\/p>\n where:<\/p>\n T<\/em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 is\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 the\u00a0return period [8].<\/p>\n <\/p>\n This explicit formulation allows the\u00a0direct calculation of\u00a0design values following parameter estimation.<\/p>\n Regional frequency analysis<\/span><\/span><\/strong><\/span><\/p>\n Regional frequency analysis (RFA) is a\u00a0methodology developed to increase the\u00a0robustness of\u00a0the\u00a0estimation of\u00a0extreme quantiles in\u00a0situations with limited time-series length [9]. The\u00a0basic idea is the\u00a0sharing of\u00a0information among stations exhibiting similar statistical behaviour of\u00a0extremes [9].<\/span><\/p>\n The\u00a0index-flood concept assumes:<\/span><\/p>\n where:<\/p>\n Qi<\/sub>(F)\u00a0\u00a0\u00a0\u00a0\u00a0 is\u00a0\u00a0\u00a0\u00a0 the\u00a0quantile at location<\/p>\n \u00b5i<\/sub>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 the local scaling factor<\/p>\n q(F)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 the\u00a0dimensionless regional growth curve common to\u00a0the\u00a0entire region [9]<\/p>\n The\u00a0scaling factor \u00b5i<\/sub> is typically defined as the\u00a0first L-moment (analogous to the\u00a0sample mean) of\u00a0annual maxima [9, 19]. For the\u00a0pilot locations without direct measurements, the\u00a0scaling factor was estimated using the\u00a0IDW (Inverse Distance Weighting) method. This method allows the\u00a0interpolation of\u00a0quantile values from surrounding gauged stations on the\u00a0basis of\u00a0a\u00a0weighted average of\u00a0the\u00a0values, where the\u00a0weight assigned to each station is inversely proportional to the\u00a0distance from the\u00a0analysed location. The\u00a0distances of\u00a0the\u00a0individual stations used for the\u00a0three pilot locations are presented in\u00a0Tab.\u00a01. By normalising the\u00a0data from individual stations by their local scale, a\u00a0dimensionless dataset is obtained, from which the\u00a0regional shape of\u00a0the\u00a0distribution is subsequently estimated [9].<\/p>\n Homogeneity of\u00a0the\u00a0region was evaluated within\u00a0the\u00a0framework of\u00a0regional frequency analysis based on L-moments according to [9]. For each duration, the\u00a0L-moment ratios of\u00a0individual stations were first calculated, and the\u00a0expected variability of\u00a0a\u00a0homogeneous region of\u00a0the\u00a0same size was subsequently estimated using Monte Carlo simulations (1,000 realisations). On this basis, H-statistics (H1<\/sub>, H2<\/sub>, H3<\/sub>) were determined (a\u00a0summary is provided in\u00a0Tab.\u00a03) quantifying the\u00a0deviation of\u00a0the\u00a0observed inter-station variability from the\u00a0variability of\u00a0the\u00a0simulated homogeneous region.<\/p>\n According to the\u00a0interpretation criteria of\u00a0[9], H < 1 indicates a\u00a0homogeneous region, 1 \u2264 H < 2 weak heterogeneity, and H \u2265 2 a\u00a0heterogeneous region.<\/p>\n To identify potentially inconsistent stations, the\u00a0discordancy measure was applied. Its values remained, in\u00a0most cases, below the\u00a0critical threshold (1.33 for the\u00a0three-member subregion and 2.33 for the\u00a0broader region), indicating no pronounced outliers in\u00a0the\u00a0L-moment space. Overall, the\u00a0region can\u00a0be considered sufficiently homogeneous for the\u00a0application of\u00a0regional frequency analysis, while acknowledging slightly increased variability for longer durations.<\/p>\n \u00a0<\/em>The\u00a0overall assessment indicates that the\u00a0Bukovno area is predominantly homogeneous from the\u00a0perspective of\u00a0regional frequency analysis, although with locally increased heterogeneity, particularly according to the\u00a0statistic H1<\/sub> and marginally also H3<\/sub>. The\u00a0Pe\u010dky area appears to be the\u00a0most homogeneous of\u00a0the\u00a0three locations, with no exceedance of\u00a0the\u00a0critical discordancy threshold and only indications of\u00a0weak to moderate heterogeneity in\u00a0H2<\/sub> and H3<\/sub>. In\u00a0contrast, B\u011bchovice exhibits the\u00a0highest degree of\u00a0spatial heterogeneity, reflected both by isolated exceedances of\u00a0the\u00a0critical discordancy threshold and by elevated values of\u00a0the\u00a0H2<\/sub> and H3<\/sub> statistics.<\/p>\n The\u00a0theoretical framework based on the\u00a0GEV distribution and regional frequency analysis made it possible to translate climate projections into changes in\u00a0the\u00a0design quantiles of\u00a0extreme precipitation. The\u00a0following section therefore presents a\u00a0quantification of\u00a0these changes, focusing on the\u00a0magnitude of\u00a0the\u00a0100-year quantile and on the\u00a0structure of\u00a0uncertainty arising from the\u00a0multi-model ensemble.<\/span><\/p>\n The\u00a0relative change in\u00a0the\u00a0100-year hourly quantile Q<\/span>100<\/sub> exhibits a\u00a0systematic dependence on both the\u00a0emission scenario and the\u00a0time horizon. In\u00a0the\u00a0period 2035\u20132065, differences among the\u00a0RCP scenarios are smaller than\u00a0the\u00a0internal variability among individual realisations within\u00a0the\u00a0same scenario. In\u00a0the\u00a0distant period 2070\u20132100, a\u00a0pronounced divergence among the\u00a0scenarios becomes apparent.<\/span><\/p>\n Under the\u00a0RCP8.5 scenario (2070\u20132100), the\u00a0mean\u00a0relative change in Q<\/span>100<\/sub>\u00a0amounts to 52\u00a0% with a\u00a0standard deviation of\u00a041\u00a0%. The\u00a0interval between the\u00a05th and 95th percentiles ranges from \u22127\u00a0% to +126\u00a0%. The\u00a0median\u00a0change is approximately 47\u00a0%. Approximately 80\u00a0% of\u00a0the\u00a0realisations exhibit a\u00a0positive change.<\/span><\/p>\n For the\u00a0RCP2.6 scenario (2070\u20132100), the\u00a0mean\u00a0change is approximately 19\u00a0%, and the\u00a0uncertainty interval is substantially narrower. The\u00a0difference between the\u00a0mean\u00a0changes under the\u00a0RCP8.5 and RCP2.6 scenarios in\u00a0the\u00a0second half of\u00a0the\u00a0century exceeds 30 percentage points.<\/span><\/p>\n Values exceeding 100\u00a0% are generated by a\u00a0limited number of\u00a0realisations and correspond to cases with a\u00a0positive shape parameter\u00a0\u03ba, implying a\u00a0heavy right tail of\u00a0the\u00a0GEV distribution. The\u00a0distribution of\u00a0changes across scenarios and periods is shown in\u00a0Fig.\u00a02<\/span>, which illustrates the\u00a0pronounced widening of\u00a0the\u00a0ensemble spread under the\u00a0RCP8.5 scenario (2070\u20132100).<\/span><\/p>\n The relative change in extreme precipitation exhibits a decreasing trend with increasing duration. Under the RCP8.5 scenario, representing a high-emission scenario used primarily to illustrate the upper bound of climate impacts (2070\u20132100), the\u00a0mean\u00a0change is approximately:<\/span><\/p>\n This gradient is also evident from the\u00a0IDF curves for the\u00a0same scenario variant shown in\u00a0Fig.\u00a0<\/em>3<\/span>, where the\u00a0intensification is more pronounced for shorter durations.<\/span><\/p>\n
\nthe\u00a0100-year hourly quantile is approximately 52\u00a0%, with the\u00a05th\u201395th percentile range spanning from \u22127\u00a0% to +126\u00a0%. In\u00a0the\u00a0period 2035\u20132065, differences among emission scenarios are smaller than\u00a0the\u00a0internal variability of\u00a0the\u00a0models, whereas in\u00a0the\u00a0second half of\u00a0the\u00a0century the\u00a0emission trajectory becomes the\u00a0dominant source of\u00a0projection divergence. Relative amplification is greater for shorter durations, indicating a\u00a0disproportionate sensitivity of\u00a0short-term extremes.<\/span><\/p>\nINTRODUCTION<\/h2>\n
\n
DATA<\/h2>\n
Observed precipitation data<\/h3>\n
<\/h6>\n
![\"\"](\"https:\/\/www.vtei.cz\/wp-content\/uploads\/2026\/06\/Strnadova-fig-1-1.jpg\")
<\/a><\/h6>\nFig. 1. Selection of\u00a0stations for RFA \u2013 locations marked with a\u00a0star indicate pilot sites, points marked with a\u00a0dot represent rain\u00a0gauge stations CHMI, and circles denote the\u00a030km buffer<\/h6>\n
Tab.\u00a01. Meteorological stations used for RFA, their distances to the\u00a0pilot locations, and the\u00a0length of\u00a0the\u00a0annual maxima time series<\/h5>\n
<\/a>\nCORDEX climate projections<\/h3>\n
Tab.\u00a02. Composition of\u00a0the\u00a0ensemble of\u00a0projections used (number of\u00a0unique GCM\u2013RCM combinations) by RCP scenario and domain<\/h5>\n
<\/a>\n\n
<\/a>\nTheoretical framework<\/h3>\n
<\/a>\n<\/a>\nTab. 3. Summary of regional statistics for the Bukovno, Pe\u010dky, and B\u011bchovice regions; ranges of heterogeneity metrics are reported<\/h5>\n
<\/a>\nRESULTS<\/h2>\n
Change in\u00a0the\u00a0100-year hourly quantile<\/h3>\n
<\/a><\/h6>\nFig. 2. Relative change in\u00a0the\u00a0100-year hourly quantile (Q\u2081\u2080\u2080, 1 h) across RCP scenarios and time horizons for three pilot areas. Box plots represent individual GCM\u2013RCM realizations (37\u00a0in\u00a0total) within\u00a0the\u00a05th\u201395th percentile range; the\u00a0box indicates the\u00a0interquartile range and the\u00a0black line denotes the\u00a0median. Time horizons are distinguished by colour \u2013 dark\u00a0blue (2035\u20132065) and light blue (2070\u20132100). The\u00a0ensemble spread is substantially wider under the\u00a0RCP8.5 scenario (2070\u20132100), where the\u00a0upper bound exceeds 100\u00a0%<\/h6>\n
Dependence on duration<\/h3>\n
\n
<\/a><\/h6>\nFig. 3. Comparison of historical and future IDF curves (T = 100 years) for the pilot locations Bukovno, Pe\u010dky, and B\u011bchovice. The solid line represents the median of the RCP8.5 (2070\u20132100) projections, while the\u00a0dashed line corresponds to the\u00a0reference period. The\u00a0lighter blue area indicates the\u00a05th\u201395th percentile range of\u00a0the\u00a0ensemble, and\u00a0the\u00a0darker blue area shows the\u00a025th\u201375th percentile range<\/h6>\n