Last modified on Oct 09, 2023 16:14

Contributors: A. Reder (CMCC), P. Mercogliano (CMCC), G. Rianna (CMCC), M. Raffa (CMCC), M. Mancini (CMCC), G. van der Schrier (KNMI), C. de Valk (KNMI)

Acronyms

Introduction

This document serves as a Product User Guide (PUG) for the Extreme precipitation risk indicators for Europe and European cities dataset, as part of the Copernicus Climate Change Service (C3S) Sectoral Information System (SIS) to support Disaster Risk Reduction (DRR) concerning Pluvial Flood Risk Assessment in Urban Areas. More information about the project can be found at https://climate.copernicus.eu/pluvial-flood-risk-assessment-urban-areas.

Executive Summary

The dataset presents Climate Impact Indicators related to extreme precipitation across Europe.

Using gridded observations and reanalysis products, this dataset provides various metrics to evaluate the magnitude and frequency of extreme precipitation under current climate conditions. These are provided as a gridded product for the whole European region, as well as a focused, high-resolution, product for 20 cities situated across Europe.

The dataset includes a historic record of extreme precipitation, computed recurrence intervals, as well as numerous statistical measures of extreme precipitation.

This product makes use of datasets available on the Climate Data Store (CDS) combined with additional datasets which improve the spatial and temporal resolution to produce a dataset suitable for pluvial flood analysis up to city scale. Daily E-OBS observational data and hourly ERA5 reanalysis are used to create the Climate Impact Indicators and compute the magnitude of extreme precipitation events across Europe. This dataset further includes point observations from meteorological stations around Europe, from the European Climate Assessment & Dataset (ECA&D), which are processed and interpolated onto the E-OBS grid to provide expected precipitation under fixed return periods (see Appendix II for a definition of return periods). This additional layer estimates the return values at station scale; then, they are aggregated on a regular grid. On the other side, by using E-OBS and ERA5, return values are computed by using the area-averaged value on the regular grid. The comparison between the additional layer and E-OBS can help the user to clear understand the influence of the different procedures. The impact of such a difference can be assumed as limited for the other indicators while it may play a relevant role for return values. Further dynamical downscaling of the ERA5 reanalysis data is also conducted to generate a gridded dataset for the 20 European cities at the resolution of 0.02° (about 2.2 km) identified as vulnerable to urban pluvial flooding according to stakeholder requirements. Such a tailored dataset allows city stakeholders to detect and rank extreme precipitation events occurred in the city.

The bases for this dataset are the ERA5 reanalysis and the E-OBS dataset, both are provided under the C3S umbrella.

This dataset was produced on behalf of the Copernicus Climate Change Service.

Scope of Documentation

The PUG promotes the Product from a multitude of perspectives by:

1. drawing identified gaps and Users' requirements, and how the dataset may address these gaps and needs;
2. providing an overview as for key dataset characteristics as for computed variables/indicators;
3. describing used input data providing synthetic informative features;
4. providing an overview about the methodology underlying the dataset development with a special focus on how methods and resulting product may be able to address the identified gaps, and on results of tailored evaluations, addressing also benefits, limitations, and modelling assumption made in the production of the dataset.

Product Description

Product Target Requirements

The analysis of gaps and Users' requirements have been carried out using multiple modes:

• identification of key users and mobilization of the network of DRR practitioners and experts;
• desk review of surveys of users' requirements produced in the context of C3S and other projects relevant for the purpose of the Sectoral Information System concerning DRR;
• participation in relevant DRR events to inform people about the project (oral presentations, posters, side-sessions) and to initiate discussions;
• consultations via interviews, webinars, and a workshop, engaging DRR experts and policy networks.

Based on insights and caveats collected through such initiatives, three main gaps are identified:

• GAP 1: a clearer identification of the European areas more affected and impacted by heavy precipitation events, in recent dECA&Des, in terms of frequency and severity. It has been stressed the need of having available and comparing the information provided by sources and datasets. In this regard, also if the input datasets could highly differ for approach, spatial and temporal resolution, the prompt availability of different information from multiple sources could provide a clearer view about the issue of interest. Furthermore, where available, the comparison with local data (e.g., national gridded datasets or from weather stations) can permit a deeper investigation about the reliability of such datasets for different areas and periods.
• GAP2: detailed information about the severity and the probability of occurrence of heavy precipitation events inducing impacts over Europe in recent dECA&Des. Several catalogues are available at global and continental scale providing information about affected areas, event duration, cost and losses of precipitation induced events (fluvial/pluvial flooding, storms). Nevertheless, at transnational scale, they hardly supply information about the potential triggering precipitation events. The availability in CDS of datasets returning global, long- lasting, and spatially homogeneous precipitation data could enable the development of datasets coupling causes (precipitation events) and effects (costs and socio-economic losses). In this sense, expert Users ask not only the finished product but also the availability of managing precipitation data to build tailored and/or local applications.
• GAP3: a clearer understanding about the added value of very high-resolution dynamical downscaling from ERA5 reanalysis in terms of localization and magnitude of precipitation events at urban context scale. There is a growing interest, considering the activities on going on different European projects and programs, in assessing the added value of information returned by high resolution dynamical downscaling of reanalysis; specifically, it is expected that results at this resolution could be highly relevant for extreme atmospheric events (as heavy precipitations) due to the explicit representation of the deep convection phenomena that can lead intense and localized (in space and time) precipitation events. In this regard, the expected substantial increase in performances (better characterization of spatial distribution and hourly values) due, for example, could justify the required investment in time and computational resources.

Product Overview

This Product relies on the concept of climate data integration, whose main goal is to develop a strong connection between data available in CDS and data ad-hoc provided to improve spatial and temporal requirements resolution making them more suitable for pluvial flood analysis.
According to this definition, the Extreme precipitation risk indicators for Europe and European cities dataset represents a potential pillar enabling the Users to investigate extreme precipitation features and their effects thanks to a suite of tailored basic and advanced information provided at the European scale, with a further refinement for a pool of 20 European Cities, selected according to User requirements as vulnerable to urban pluvial flooding (see Figure 1).

Figure 1: Spatial distribution of 20 European Cities, selected according to User requirements as vulnerable to urban pluvial flooding, for which ERA5 are dynamically downscaled at ~ 2 km: Amadora (Portugal), Amersfoort (the Netherlands), Antwerp (Belgium), Athens (Greece), Bilbao (Spain), Birmingham (United Kingdom), Brussels (Belgium), Bucharest (Romania), Budapest (Hungary), Frankfurt am Main (Germany), Koln (Germany), London (United Kingdom), Milan (Italy), Pamplona (Spain), Paris (France), Prague (Czech Republic), Riga (Latvia), Rimini (Italy), Stockholm (Sweden), Vienna (Austria).

This goal is addressed by developing a set of climate indicators related to extreme precipitation. These climate indicators allow the Users to characterize specific precipitation events and to compare different areas across the Europe, even when they feature different climatic conditions. They gather a sub-set of indicators based on CCl/WCRP/JCOMM Expert Team on Climate Change Detection and

Indices (ETCCDI¹) recommendations and others carried out by using the Extreme Value Analysis (EVA) approach (e.g., fixed and percentile thresholds, length of wet spells as well as "hard extremes", relating to return levels up to 100-year). A key novelty is represented by those indicators related to the magnitude of precipitation events: these indicators provide a direct view at gridded scale concerning the deviation of a daily precipitation event from the 95th and 99th percentile of its distribution. All the climate indicators are derived from E-OBS daily gridded data and ERA5 Reanalysis, except for indicators based on return levels that are also computed from ECA&D station network data.

Data Description

Table 1: Overview of key characteristics of the Extreme precipitation risk indicators for Europe and European cities dataset.

Figure 2: Overview image of the dataset: standardised precipitation amount over 95th percentile (11 August 2002) computed from E-OBS data. Values ≥ 1 represent grid points where precipitation exceeds the 95th percentile (the higher the values the higher the magnitude of the event)

Variable Description

Table 2: Overview (long name, short name and unit) and description of variables included in the Dataset. Specifically, the long name represents what the Users find in the catalogue entry whilst the short name is what the variables are called in the NetCDF.

Input Data

Table 3: Overview of climate model data for input to Extreme precipitation risk indicators for Europe and European cities, summarizing the model properties.

ERA5 Reanalysis

ERA5 represents the fifth global reanalysis produced by ECMWF with a horizontal resolution of ~ 31 km. A reanalysis combines numerical modelling with observations into a comprehensive global data set consistent with the laws of physics (data assimilation) that provides a picture of the current climate. The ERA5 reanalysis was produced using the 4D-Var data assimilation in CY41R2 of the


ECMWF's Integrated Weather Forecasting System (IFS), with 137 vertical levels (above 0.01 hPa). The IFS is coupled to a soil model and an ocean wave model. At present it provides, operationaly, data from 1979 to the present day at hourly resolution. As of June 2021, a preliminary version of the 1950- 1978 back extension of ERA5 has been released in the CDS.

E-OBS daily gridded

The E-OBS dataset is a daily gridded land-only observational dataset over Europe available at a horizontal resolution of 0.1° (~ 11 km) containing data for precipitation amount, mean/maximum/minimum temperature, sea level pressure, and surface shortwave downwelling radiation. Its latest version (v.21) delivered by Copernicus Climate Data Store covers the period 1950- 2019. As general information, the E-OBS relies on the 'blended' time series from the station network of the European Climate Assessment & Dataset (ECA&D) project and is calculated following a two- stage process to derive the daily field and the uncertainty in these daily estimates; further details are available from Cornes et al (2018).

European Climate Assessment & Dataset (ECA&D) station network

The ECA&D dataset (Klein Tank et al., 2002; Klok & Klein Tank, 2009) consists of observations supplied by national meteorological services and other data providers in Europe and adjacent regions in North Africa and the Middle East². The data are quality controlled by the contributing agencies, and are subjected to further quality control following incorporation into ECA&D. These data are then blended with neighbouring series to form more temporally complete series. These blended series are those used to generate the E-OBS dataset. For the scope of this Contract, they are adopted to determine precipitation values at prescribed return times over Europe. The ECA&D dataset now contains approximately 9000 stations in the case of precipitation (status summer 2020). However, there has been an increasing disparity in station density across the domain as a number of meteorological agencies have increased the number of stations in ECA&D. This means there are relatively many stations across central Europe and Scandinavia, and many fewer towards the south and east of the domain.

ERA5-2km

ERA5-2km represents an additional hourly dataset at horizontal resolution of 0.02° (~ 2.2 km) for a pool of 20 user-selected cities over 1989-2018. It is developed by dynamically downscaling ERA5 with the regional climate model COSMO-CLM (Rockel et al., 2008) switching on the module TERRA-URB to account for the urban parameterizations (Wouters et al., 2016). The downscaling activity relies on a one-step nesting strategy, in which the simulation at 2.2km is directly "one-way nested" in ERA5 (1:15 resolution jump). In ERA5-2km, observations are indirectly accounted through the atmospheric forcing of ERA5.

Method

Background

• GAP 1: several indicators providing information about occurrence and severity of extreme precipitation events have been selected following what is carried out or suggested by authoritative Research groups (e.g., ETCCDI) or suggested by Stakeholders during the users' requirements phases (see $2.1). They exploit daily data from two different reference datasets: observational gridded dataset, E-OBS and the fifth generation of ECMWF reanalysis, ERA5. The indicators return information about "moderate" rare events expected occurring one or more times for year and (ii) "rarer" events as, for example, expected precipitation for fixed return periods requiring the use of more sophisticated approaches as Extreme Value Analysis. The indicators are computed at monthly and yearly scale exploiting the entire available length of the two datasets.
• GAP 2 & GAP3: the characterization of severity and probability of occurrence of precipitation events inducing remarkable impacts in recent dECA&Des follows the approaches suggested by Ramos et al. (2014, 2018). According to such approaches, the overcoming of reference thresholds (in this case, 95th and 99th percentiles) are assumed as proxies for heavy rainfall events while the surplus compared to the threshold (in terms of ratio) represents a measure of the severity. To this aim, different precipitation datasets are exploited to limit potential weaknesses for specific areas or time spans. In this perspective, in addition to ERA5 and E- OBS, a dynamical downscaling of ERA5 reanalysis at very high resolution (about 2 km) for 20 cities, acknowledged as ERA5-2km, allows an improvement of spatial and temporal characterization of precipitation events. Furthermore, using standardised precipitation avoids misleading comparisons between the datasets and with local data sources providing information at point scale while gridded datasets return information at spatial scales consistent with their horizontal resolution. Precipitation data feed the catalogue developed as CDS application, but they are made available for building tailored or local applications.

Model / Algorithm

General Description

The dataset includes a set of 19 extreme precipitation risk indicators derived (some of them only partially) from ERA5, E-OBS, ECA&D and ERA5-2km. All the indicators are computed from realizations of daily total precipitation assumed as essential climate variable (ECV) and are delivered in Network Common Data Form (NetCDF-4) format on the grids of the native data, except for indicators derived directly from ECA&D data that are provided on the E-OBS grid.
Extreme precipitation risk indicators can be grouped into three categories:

1. indicators defined according to ETCCDI recommendations: they include a sub-set of indicators, selected according to Users' requirements, relying on fixed thresholds, cumulative and maximum values, durations, and occurrences;
2. Extreme Value Analysis (EVA) -derived indicators: they include indicators related to expected precipitation under fixed return period (5-10-25-50-100 yrs) derived by using Generalized Extreme Value (GEV) function;
3. ad hoc defined indicators: they include indicators related to the magnitude of precipitation events stated as standardised precipitation amount over 95th and 99th percentiles.

Indicators falling into the group are derived from E-OBS and ERA5 data and provided at monthly and yearly scales, except for percentiles amount (r90p, r95p, r99p) that are evaluated assuming 30- years (1989-2018) as a reference period, to reliably account for intrinsic interannual variability, reducing the effect of external forcing that may induce statistically significant trends and thus undermine the homogeneity of the data.
Indicators falling into the group (ii) are derived considering not only E-OBS and ERA5 data but also the ECA&D collection of observations, assumed as a reference for the return levels derived from the other two datasets. These indicators are evaluated assuming 30-years (1989-2018) as reference period.
Finally, indicators falling into the group (iii) are derived from E-OBS, ERA5 and ERA5-2km data and are provided at daily scale as they serve as base for the development of the catalogue of past extreme precipitation events.

Compute Algorithms

In this section the definitions and algorithms that has been used for generating indicators are outlined. The following information are provided for each indicator:

• Description: definition of the indicator
• Units: SI units of the variable
• Temporal resolution: time frequency of the provided indicator
• Definition: algorithm for computing the indicator using daily climate data

prcptot

• Description: Total precipitation amount
• Units: mm
• Temporal resolution: monthly / yearly

• Definition: Let RR_ij be the daily precipitation amount on day i in period j. If I represents the number of days in j, then  \( prctot_{j} = \sum_{i=1}^I RR_{i,j} \)

RR1

• Description: Number of days with daily precipitation amount above 1mm
• Units: day
• Temporal resolution: monthly / yearly
• Definition:Let RR_ij be the daily precipitation amount on day i in period j. Count the number of days where 𝑅𝑅_ij ≥ 1 𝑚𝑚

rx1day

• Description: Maximum 1-day precipitation amount
• Units: mm
• Temporal resolution: monthly / yearly
• Definition: Let RR_ij be the daily precipitation amount on day i in period j. The maximum 1-day value for period j are: 𝑟𝑥1𝑑𝑎𝑦_j = max(RR_ij)

rx5day

• Description: Maximum 5-days precipitation amount
• Units: mm
• Temporal resolution: monthly / yearly
• Definition: Let RR_kj be the precipitation amount for the 5-day interval ending k, period j. Then maximum 5-day values for period j are: 𝑟𝑥1𝑑𝑎𝑦_j = max(RR_kj)

cwd

• Description: Maximum spell length of days with daily precipitation amount above 1 mm
• Units: day
• Temporal resolution: monthly / yearly
• Definition: Let RR_ij be the daily precipitation amount on day i in period j. Count the largest number of consecutive days where 𝑅𝑅_ij ≥ 1 𝑚𝑚

rr20mm

• Description: Number of days with daily precipitation amount above 20 mm
• Units: day
• Temporal resolution: monthly / yearly
• Definition: Let RR_ij be the daily precipitation amount on day i in period j. Count the number of days where 𝑅𝑅_ij ≥ 20 𝑚𝑚

rXXp (r90p, r95p, r99p)

• Description: Daily precipitation amount corresponding to the XXth percentile
• Units: mm
• Temporal resolution: 1989-2018

• Definition: Let RR_wj be the daily precipitation amount on a wet day w (RR ≥ 1.0mm) in period i and let RR_wnXX be the XX^th percentile of precipitation on wet days in the 1989-2018 period. If W represents the number of wet days in the period, then:  \( rXXp_{j} = \sum_{w=1}^W RR_{wj} where RR_{wj} > RR_{wn}XX \)

rXXpday (r90pday, rp95pday, r99pday)

• Description: Frequency of rainy days exceeding the XX^th percentile
• Units: day
• Temporal resolution: monthly / yearly
• Definition: Let RR_ij be the daily precipitation amount on day i in period j. Count the number of days where 𝑅𝑅_ij ≥ rXXp_j

rZZyrRP (r5yRP, r10yRP, r25yRP, r50yRP, r100yRP)

• Description: Precipitation amount for a ZZ-year return period
• Units: mm
• Temporal resolution: 1989-2018
• Definition: At each grid point, return values of 24h precipitation sums over 1989- 2018 are derived from estimates of the distribution function of annual maxima of 24h precipitation sums, approximated by a Generalized Extreme Value (GEV) distribution. These estimates are derived from a model of a spatially and temporally varying GEV distribution, which is estimated from data of annual maxima of 24h precipitation sums, separately from ERA5, E-OBS, ECA&D (see Appendix III).

nrrXXp (nrr95p, nrr99p)

• Description: Magnitude of precipitation amount standardised over XX^th percentile
• Units: dimensionless
• Temporal resolution: daily

• Definition: Let RR_ij be the daily precipitation amount on day i in period j and let RR_wnXX be the XX^th percentile of precipitation on wet days w (RR ≥ 1.0mm) in the 1989-2018 period. The standardised precipitation amount over XX^th percentile value for period j are:  \( nrrXXp_{j} = \frac{RR_{ij}}{RR_{wn}XX} \)

Validation

Indicators based on percentiles

For indicators based on percentiles, the percentiles are derived from the data over a reference period. The reference period is 1989-2018. Possibly, these indicators are subject to bias as the percentiles themselves are estimated and hence uncertain: due to nonlinearity of the distribution function, the probability of exceeding the estimated per-centile is not equal to the probability of exceeding the exact percentile. This bias is proportional to the variance of the estimator of the percentile. It may be visible in the time-series of the index as a jump at the beginning and/or the end of the reference period (see Zhang et al, 2005).

Indicators based on return value

Temporally and spatially varying parameters of the Generalized Extreme Value (GEV) distribution of annual maxima of the 24-hour precipitation over Europe are estimated. Data from three sources are used, the station dataset ECA&D, the gridded observational dataset E-OBS and the reanalysis dataset ERA5. There is a fundamental difference between the station data of ECA&D, which are point measurements, and the data on a regular grid of E-OBS and ERA5, which should be considered as area-averages. The E-OBS and ERA5 datasets are therefore more likely to be similar in character and a difference is likely between these datasets and ECA&D.

Figure 3: Estimates of the 1yr return value of 24h precipitation in mm (left) and its relative standard deviation (right) from ERA5 reanalysis (top) and ECA&D observations (bottom).

For return periods from 1 to 100 years, maps of return value estimates averaged over 20yr intervals with their standard deviations were computed, and maps of differences between averages over different intervals are produced. As expected, the precision and spatial variability of estimates from ECA&D observations depend strongly on station density, but bias does not. Overall, estimates from ERA5 data have smaller random error and the precision is more uniform. However, they are much lower than estimates from ECA&D, and more so for a return period of 100 years than for 1 year. Furthermore, spatial patterns are generally smoother, in areas with high station density. Return value estimates from E-OBS data exhibit a large downward bias, which is dependent on station density in the original ECA&D data. Figure 3 illustrates this showing the estimates of the 1yr return value of 24h precipitation in mm averaged over the years 2000-2019 and its relative standard deviation from ERA5 reanalysis and ECA&D observations.

These estimates are well constrained by the annual maxima from which the estimates were derived; the relative error is quite small for both datasets. Figure 4 shows the same for estimates of the 100yr return value. Patterns are very similar; the main differences are the average magnitudes of the return value and of its relative error.

For the analysis of Figure 3 and Figure 4 we find that the spatial patterns of the return value estimates from ERA5 and ECA&D are similar. However, estimates from ERA5 are about one third lower than estimates from ECA&D. This is most likely due to the approximations involved in the simulation of convective precipitation by present global-scale numerical weather prediction models.

Figure 4: Estimates of the 100yr return value of 24h precipitation in mm from ERA5 reanalysis (top left), ECA&D observations (top right), and E-OBS data (bottom). The relative standard deviations of estimates from ERA5 and ECA&D are identical to those in Figure 3

The relative standard deviation of the estimates from ERA5 is almost uniform. This is expected, as the ERA-5 data density is uniform, and data over sea were also used (for consistency, estimates over sea are not shown). For estimates from ECA&D, the relative standard deviation varies strongly with station density (Figure 5). For example, the station density is high in Germany and the Netherlands, and much lower in Belgium, France, and most of Spain. However, the relative error in data-sparse regions is amplified near the boundary of a data-dense region (e.g., in France, near the German border). The explanation is that when both regions are in the same tile, then the estimated degrees of freedom of the spline representing the spatial dependence of the location and scale parameters is high (to match variability in the data-dense region), which results in some overparameterization in the adjacent part of the data-sparse region. Given the variable station density, the estimates are still close to optimal, as they provide high resolution and low variance in data dense regions and low resolution and low variance at some distance in data sparse regions far from data-dense regions.

Figure 5: Sites of precipitation measurements in ECA&D with valid annual maxima in more than half of the years 1950- 2019 (see also text). The white area is the E-OBS grid.

Overall, the estimates from E-OBS are considerably lower than the estimates from ECA&D data, and similar in magnitude to the estimates from ERA5. In addition, the bias appears to be related to the station density of the original ECA&D data. In particular, in Germany and the Netherlands where station density is high, estimates from E-OBS are higher than those from ERA5, whereas they are somewhat lower in most regions with low station density. These findings are consistent with the expected effect of interpolation of in-situ data in preparing the E-OBS data product: a precipitation value in E-OBS should be regarded as an effective average over some domain of a size depending on the local spatial density of the observations in ECA&D. It means that E-OBS precipitation data are not suitable as reference for the evaluation of extreme precipitation statistics from climate models or reanalyses. Results for other return periods are in line with those for a return period of 100 years.

Exploiting (extreme) precipitation indicators to investigate historical flood events: 2002 European floods

In August 2002, an exceptional series of flood events caused by over a week of continuous heavy precipitation affected the Central Europe (specifically the Czech Republic, Austria, Germany, Slovakia, Poland, Hungary, Romania, and Croatia), killing dozens and inducing huge damages. Such a historical sequence of events can be properly characterized by using (extreme) precipitation indicators extracted from the Extreme precipitation risk indicators for Europe and European cities dataset. In the following, a demonstration of the added value of this dataset is provided; the analyses rely on indicators derived from E-OBS data and ERA5-2km data. To characterize this sequence of events, the following indicators are adopted:

Table 4. List of indicators deployed to investigate the sequence of events occurred in August 2002 over Central Europe

Figure 6. maximum number of consecutive wet days (a) and count of days with daily precipitation exceeding the 90th percentile of wet day precipitation (b) over Europe in August 2002 carried out by using E-OBS derived data. The Figure shows an exceptional sequences of precipitation events in the Central part of Europe, most of ones exceed the 90th percentile distribution

Figure 7. magnitude distribution of precipitation events occurred on 07 August determined through the standardised precipitation amount over 95th percentile (a) based on E-OBS data; by enlarging the map (b), it is possible to clearly identify the most affected areas: according to EM-DAT data, Barredo (2007) and Brakenridge (2017), empirical damages and losses can be retrieved in Austria, Czech Republic and Germany as consequence of these sequences of extreme precipitation events

Figure 8. magnitude distribution of precipitation events occurred on 11 August determined through the standardised precipitation amount over 95th percentile (a) based on E-OBS data; by enlarging the map (b), it is possible to clearly identify the most affected areas: according to EM-DAT data, Barredo (2007) and Brakenridge (2017), empirical damages and losses can be retrieved in Austria, Czech Republic and Germany as consequence of these sequences of extreme precipitation events

Figure 9. magnitude distribution of precipitation events occurred on 12 August determined through the standardised precipitation amount over 95th percentile (a) based on E-OBS data; by enlarging the map (b), it is possible to clearly identify the most affected areas: according to EM-DAT data, Barredo (2007) and Brakenridge (2017), empirical damages and losses can be retrieved in Austria, Czech Republic and Germany as consequence of these sequences of extreme precipitation events

Figure 10. detailed magnitude distribution of precipitation events occurred on 11 August over Vienna (a) and on 12 August over Prague (b) determined through the standardised precipitation amount over 95th percentile based on ERA5-2km

Concluding Remarks

The dataset "Extreme precipitation risk indicators for Europe and European cities" provides a set of Climate Impact Indicators under current climate conditions related to extreme precipitation across Europe to improve the spatial and temporal resolution with the aim of producing a dataset suitable for pluvial flood analysis up to city scale.

Such a dataset includes a series of historic records, computed recurrence intervals, as well as numerous statistical measures and metric to evaluate the magnitude and frequency of extreme precipitation. It is provided as a gridded product (e.g., daily -OBS observational data for the period 1950-2019, hourly ERA5 reanalysis for the period 1979-2019, and point observations from meteorological stations from ECA&D for the period 1989-2018) for the whole European region, as well as a focused, high-resolution product (i.e., dynamical downscaling of ERA5 at the resolution of 0.02°, ~2.2 km, for the period 1989-2018) for 20 cities situated across Europe.

At European scale, all the indicators are computed by adopting E-OBS and ERA5 data. Some of these ones (e.g., fixed thresholds, cumulative and maximum values, durations, and occurrences) are provided at monthly or yearly scale; others (e.g., percentiles amount and expected precipitation under fixed return period) are provided by assuming a reference (30-years) climatological period (i.e., 1989-2018); finally, the standardised magnitude of extreme precipitation events is carried out at daily scale. Regarding expected precipitation under fixed return periods, the dataset also accounts for point observations from meteorological stations around Europe included in the ECA&D station network. These data are processed to estimate the return values at station scale and then are interpolated onto the regular E-OBS grid.

At city scale, the standardised magnitude of extreme precipitation events is provided (daily scale) for a pool of 20 European cities identified as vulnerable to urban pluvial flooding according to stakeholder requirements. Such a tailored dataset allows city stakeholders to detect and rank extreme precipitation events occurred in the city.
When using data included in "Extreme precipitation risk indicators for Europe and European cities", several aspects should be considered:

• Extreme precipitation risk indicators are assessed at different spatial scales (e.g., 31 km for ERA5, 12 km for E-OBS and ECA&D, and 2.2 km for ERA5-2km); in this sense, differences in values of these indicators could be related to the different nature of the native datasets.
• The additional data layers for the expected precipitation under fixed return periods based on ECA&D data help Users to quantify the key role of computational and interpolation processes from point station to gridded data. In general, E-OBS (sharing the same grid with ECA&D- processed data) and ERA5 return values data are more likely to be similar in character and a difference is likely between these data and ECA&D-based data for these indicators. The impact of such a difference can be assumed as limited for the other indicators while it may play a relevant role for return values. Specifically, expected precipitation under fixed return periods based on ECA&D data return higher values in comparison with the same variables estimated with E-OBS and ERA5. The estimations based on ECA&D are highly reliable if an extensive number of station points are considered for the assessment of expected precipitation under fixed return periods.
• Indicators based on percentiles could be subject to bias as the percentiles themselves are estimated and hence uncertain: due to nonlinearity of the distribution function, the probability of exceeding the estimated per-centile is not equal to the probability of exceeding the exact percentile. This bias is proportional to the variance of the estimator of the percentile. It may be visible in the time-series of the index as a jump at the beginning and/or the end of the reference period.
• Standardised magnitude of extreme precipitation events provides a reliable metric to detect and rank extreme events at different scales. Its magnitude (i.e., deviation from a fixed threshold defined as 95th or 99th percentile over 1989-2018) strictly depends on the native dataset; for this reason, values provided from different datasets cannot be comparable. Regarding data at city scale, in general the higher is the spatial resolution, the higher is the value returned by percentile assessment (in line with the estimation of precipitation at fixed return periods with ECA&D data). It is worth nothing that at city scale, data are provided for each city considering a specific Nomenclature of Territorial Units for Statistics level (NUTS3, in the case in hand) or, in specific cases (e.g., Athens, or London) an aggregation of NUTS3.

Appendix I: Variable Description

This section provides a more detailed analysis for each indicator, including variable in this section and include information on the valid and real range of values of the variable, the flag values for missing data, and further descriptive statistics.

Total precipitation amount (prcptot)

• Description: Total precipitation amount
• Units: mm
• Temporal resolution: monthly / yearly

• Definition: Let RR_ij be the daily precipitation amount on day i in period j. If I represents the number of days in j, then  \( prcptot_{j} = \sum_{i=1}^I RR_{ij} \)

• Flag values for missing data: 0

Table 5: Percentile values carried out by merging E-OBS (1950-2019) data and ERA5 data (1979-2019) for prcptot (mm)

Figure 11: prcptot mean (a-c) and standard deviation (b-d) over 1989-2018 obtained by E-OBS (a-b) and ERA5 (c-d) data (white area = NaN value)

Number of days with daily precipitation amount above 1mm (RR1)

• Description: Number of days with daily precipitation amount above 1mm
• Units: day
• Temporal resolution: monthly / yearly
• Definition: Let RR_ij be the daily precipitation amount on day i in period j. Count the number of days where 𝑅𝑅_ij ≥ 1 𝑚𝑚
• Flag values for missing data: 0

Table 6: Percentile values carried out by merging E-OBS (1950-2019) data and ERA5 data (1979-2019) for RR1 (day)

Figure 12: RR1 mean (a-c) and standard deviation (b-d) over 1989-2018 obtained by E-OBS (a-b) and ERA5 (c-d) data (white area = NaN value)

Maximum 1-day precipitation amount (rx1day)

• Description: Maximum 1-day precipitation amount
• Units: mm
• Temporal resolution: monthly / yearly
• Definition: Let RR_ij be the daily precipitation amount on day i in period j. The maximum 1-day value for period j are: rx1day_j = max(RR_ij)
• Flag values for missing data: NaN

Table 7: Percentile values carried out by merging E-OBS (1950-2019) data and ERA5 data (1979-2019) for rx1day (mm)

Figure 13: rx1day mean (a-c) and standard deviation (b-d) over 1989-2018 obtained by E-OBS (a-b) and ERA5 (c-d) data (white area = NaN value)

Maximum 5-days precipitation amount (rx5day)

• Description: Maximum 5-days precipitation amount
• Units: mm
• Temporal resolution: monthly / yearly
• Definition: Let RR_kj be the precipitation amount for the 5-day interval ending k, period j. Then maximum 5-day values for period j are: rx5day_j = max(RR_kj)
• Flag values for missing data: NaN

Table 8: Percentile values carried out by merging E-OBS (1950-2019) data and ERA5 data (1979-2019) for rx5day (mm)

Figure 14: rx5day mean (a-c) and standard deviation (b-d) over 1989-2018 obtained by E-OBS (a-b) and ERA5 (c-d) data (white area = NaN value)

Maximum spell length of days with daily precipitation amount above 1 mm (cwd)

• Description: Maximum spell length of days with daily precipitation amount above 1 mm
• Units: day
• Temporal resolution: monthly / yearly
• Definition: Let RR_ij be the daily precipitation amount on day i in period j. Count the largest number of consecutive days where 𝑅𝑅_ij ≥ 1 𝑚𝑚
• Flag values for missing data: 0

Table 9: Percentile values carried out by merging E-OBS (1950-2019) data and ERA5 data (1979-2019) for cwd (day)

Figure 15: cwd mean (a-c) and standard deviation (b-d) over 1989-2018 obtained by E-OBS (a-b) and ERA5 (c-d) data (white area = NaN value)

Number of days with daily precipitation amount above 20 mm (rr20mm)

• Description: Number of days with daily precipitation amount above 20 mm
• Units: day
• Temporal resolution: monthly / yearly
• Definition: Let RR_ij be the daily precipitation amount on day i in period j. Count the number of days where 𝑅𝑅_ij ≥ 20 𝑚𝑚
• Flag values for missing data: 0

Table 10: Percentile values carried out by merging E-OBS (1950-2019) data and ERA5 data (1979-2019) for rr20mm (day)

Figure 16: rr20mm mean (a-c) and standard deviation (b-d) over 1989-2018 obtained by E-OBS (a-b) and ERA5 (c-d) data (white area = NaN value)

Frequency of rainy days exceeding the 90th percentile (r90pday)

• Description: Frequency of rainy days exceeding the 90th percentile
• Units: day
• Temporal resolution: monthly / yearly
• Definition: Let RR_ij be the daily precipitation amount on day i in period j. Count the number of days where 𝑅𝑅_ij ≥ r90p_j
• Flag values for missing data: 0

Table 11: Percentile values carried out by merging E-OBS (1950-2019) data and ERA5 data (1979-2019) for r90pday (day)

Figure 17: r90pday mean (a-c) and standard deviation (b-d) over 1989-2018 obtained by E-OBS (a-b) and ERA5 (c-d) data (white area = NaN value)

Frequency of rainy days exceeding the 95th percentile (r95pday)

• Description: Frequency of rainy days exceeding the 95th percentile
• Units: day
• Temporal resolution: monthly / yearly
• Definition: Let RR_ij be the daily precipitation amount on day i in period j. Count the number of days where 𝑅𝑅_ij ≥ r95p_j
• Flag values for missing data: 0

Table 12: Percentile values carried out by merging E-OBS (1950-2019) data and ERA5 data (1979-2019) for r95pday (day)

Figure 18: r95pday mean (a-c) and standard deviation (b-d) over 1989-2018 obtained by E-OBS (a-b) and ERA5 (c-d) data (white area = NaN value)

Frequency of rainy days exceeding the 99th percentile (r99pday)

• Description: Frequency of rainy days exceeding the 99th percentile
• Units: day
• Temporal resolution: monthly / yearly
• Definition: Let RR_ij be the daily precipitation amount on day i in period j. Count the number of days where 𝑅𝑅_ij ≥ r99p_j
• Flag values for missing data: 0

Table 13: Percentile values carried out by merging E-OBS (1950-2019) data and ERA5 data (1979-2019) for r99pday (day)

Figure 19: r99pday mean (a-c) and standard deviation (b-d) over 1989-2018 obtained by E-OBS (a-b) and ERA5 (c-d) data (white area = NaN value)

Daily precipitation amount corresponding to the 90th percentile (r90p)

• Description: Daily precipitation amount corresponding to the 90th percentile
• Units: mm
• Temporal resolution: 1989-2018

• Definition: Let RR_wj be the daily precipitation amount on a wet day w (RR ≥ 1.0mm) in period i and let RRwn90 be the 90^th percentile of precipitation on wet days in the 1989-2018 period. If W represents the number of wet days in the period, then:  \( r90p_{j} = \sum_{w=1}^W RR_{wj} where RR_{wj} > RR_{wn}90 \)

• Flag values for missing data: Not expected

Table 14: Percentile values carried out by merging E-OBS (1989-2018) data and ERA5 data (1989-2018) for r90p (mm)

Figure 20: r90p over 1989-2018 obtained by E-OBS (a) and ERA5 (b) data (white area = NaN value)

Daily precipitation amount corresponding to the 95th percentile (r95p)

• Description: Daily precipitation amount corresponding to the 95th percentile
• Units: mm
• Temporal resolution: 1989-2018

• Definition: Let RR_wj be the daily precipitation amount on a wet day w (RR ≥ 1.0mm) in period i and let RR_wn95 be the 95^th percentile of precipitation on wet days in the 1989-2018 period. If W represents the number of wet days in the period, then:  \( r95p_{j} = \sum_{w=1}^W RR_{wj} where RR_{wj} > RR_{wn}95 \)

• Flag values for missing data: Not expected

Table 15. Percentile values carried out by merging E-OBS (1989-2018) data and ERA5 data (1989-2018) for r95p (mm)

Figure 21: r95p over 1989-2018 obtained by E-OBS (a) and ERA5 (b) data (white area = NaN value)

Daily precipitation amount corresponding to the 90th percentile (r99p)

• Description: Daily precipitation amount corresponding to the 99th percentile
• Units: mm
• Temporal resolution: 1989-2018

• Definition: Let RR_wj be the daily precipitation amount on a wet day w (RR ≥ 1.0mm) in period i and let RRwn99 be the 99^th percentile of precipitation on wet days in the 1989-2018 period. If W represents the number of wet days in the period, then:  \( r99p_{j} = \sum_{w=1}^W RR_{wj} where RR_{wj} > RR_{wn}99 \)

• Flag values for missing data: Not expected

Table 16. Percentile values carried out by merging E-OBS (1989-2018) data and ERA5 data (1989-2018) for r99p (mm)

Figure 22. r99p over 1989-2018 obtained by E-OBS (a) and ERA5 (b) data (white area = NaN value)

Precipitation amount for a 5-year return period (r5yrRP)

• Description: Precipitation amount for 5-year return period
• Units: mm
• Temporal resolution: 1989-2018
• Definition: At each grid point, return values of 24h precipitation sums over 1989- 2018 are derived from estimates of the distribution function of annual maxima of 24h precipitation sums, approximated by a Generalized Extreme Value (GEV) distribution. These estimates are derived from a model of a spatially and temporally varying GEV distribution, which is estimated from data of annual maxima of 24h precipitation sums, separately from ERA5, E-OBS, ECA&D.
• Flag values for missing data: Not expected

Table 17: Percentile values carried out by merging E-OBS, ERA5 and ECA&D data over 1989-2018 for r5yrRP (mm)

Figure 23: r5yrRP over 1989-2018 obtained by E-OBS (a), ERA5 (b) and ECA&D (c) data (white area = NaN value)

Precipitation amount for a 10-year return period (r10yrRP)

• Description: Precipitation amount for 10-year return period
• Units: mm
• Temporal resolution: 1989-2018
• Definition: At each grid point, return values of 24h precipitation sums over 1989- 2018 are derived from estimates of the distribution function of annual maxima of 24h precipitation sums, approximated by a Generalized Extreme Value (GEV) distribution. These estimates are derived from a model of a spatially and temporally varying GEV distribution, which is estimated from data of annual maxima of 24h precipitation sums, separately from ERA5, E-OBS, ECA&D.
• Flag values for missing data: Not expected

Table 18. Percentile values carried out by merging E-OBS, ERA5 and ECA&D data over 1989-2018 for r10yrRP (mm)

Figure 24: r10yrRP over 1989-2018 obtained by E-OBS (a), ERA5 (b) and ECA&D (c) data (white area = NaN value)

Precipitation amount for a 25-year return period (r25yrRP)

• Description: Precipitation amount for 25-year return period
• Units: mm
• Temporal resolution: 1989-2018
• Definition: At each grid point, return values of 24h precipitation sums over 1989- 2018 are derived from estimates of the distribution function of annual maxima of 24h precipitation sums, approximated by a Generalized Extreme Value (GEV) distribution. These estimates are derived from a model of a spatially and temporally varying GEV distribution, which is estimated from data of annual maxima of 24h precipitation sums, separately from ERA5, E-OBS, ECA&D.
• Flag values for missing data: Not expected

Table 19. Percentile values carried out by merging E-OBS, ERA5 and ECA&D data over 1989-2018 for r25yrRP (mm)

Figure 25: r25yrRP over 1989-2018 obtained by E-OBS (a), ERA5 (b) and ECA&D (c) data

Precipitation amount for a 50-year return period (r50yrRP)

• Description: Precipitation amount for 50-year return period
• Units: mm
• Temporal resolution: 1989-2018
• Definition: At each grid point, return values of 24h precipitation sums over 1989- 2018 are derived from estimates of the distribution function of annual maxima of 24h precipitation sums, approximated by a Generalized Extreme Value (GEV) distribution. These estimates are derived from a model of a spatially and temporally varying GEV distribution, which is estimated from data of annual maxima of 24h precipitation sums, separately from ERA5, E-OBS, ECA&D.
• Flag values for missing data: Not expected

Table 20. Percentile values carried out by merging E-OBS, ERA5 and ECA&D data over 1989-2018 for r50yrRP (mm)

Figure 26: r50yrRP over 1989-2018 obtained by E-OBS (a), ERA5 (b) and ECA&D (c) data (white area = NaN value)

Precipitation amount for a 100-year return period (r100yrRP)

• Description: Precipitation amount for 100-year return period
• Units: mm
• Temporal resolution: 1989-2018
• Definition: At each grid point, return values of 24h precipitation sums over 1989- 2018 are derived from estimates of the distribution function of annual maxima of 24h precipitation sums, approximated by a Generalized Extreme Value (GEV) distribution. These estimates are derived from a model of a spatially and temporally varying GEV distribution, which is estimated from data of annual maxima of 24h precipitation sums, separately from ERA5, E-OBS, ECA&D.
• Flag values for missing data: Not expected

Table 21: Percentile values carried out by merging E-OBS, ERA5 and ECA&D data over 1989-2018 for r100yrRP (mm)

Figure 27: r100yrRP over 1989-2018 obtained by E-OBS (a), ERA5 (b) and ECA&D (c) data (white area = NaN value)

Magnitude of precipitation amount standardised over 95th percentile (nrr95p)

• Description: Magnitude of precipitation amount standardised over 95th percentile
• Units: dimensionless
• Temporal resolution: daily

• Definition: Let RR_ij be the daily precipitation amount on day i in period j and let RR_wn95 be the 95^th percentile of precipitation on wet days w (RR ≥ 1.0mm) in the 1989-2018 period. The standardised precipitation amount over 95th percentile value for period j are:  \( nrr95p_{j} = \frac{RR_{ij}}{RR_{wn}95} \)

• Flag values for missing data: NaN

Table 22. Percentile values carried out by merging E-OBS (1950-2019) data and ERA5 data (1979-2019) for nrr95p (dimensionless) considering only values ≥ 1

Figure 28: nrr95p mean (a-c) and standard deviation (b-d) over 1989-2018 obtained by E-OBS (a-b) and ERA5 (c-d) data considering only values ≥ 1 (white area = NaN value)

Magnitude of precipitation amount standardised over 99th percentile (nrr99p)

• Description: Magnitude of precipitation amount standardised over 99th percentile
• Units: dimensionless
• Temporal resolution: daily

• Definition: Let RR_ij be the daily precipitation amount on day i in period j and let RR_wn99 be the 99^th percentile of precipitation on wet days w (RR ≥ 1.0mm) in the 1989-2018 period. The standardised precipitation amount over 99th percentile value for period j are:  \( nrr99p_{j} = \frac{RR_{ij}}{RR_{wn}99} \)

• Flag values for missing data: NaN

Table 23. Percentile values carried out by merging E-OBS (1950-2019) data and ERA5 data (1979-2019) for nrr99p (dimensionless) considering only values ≥ 1

Figure 29. nrr99p mean (a-c) and standard deviation (b-d) over 1989-2018 obtained by E-OBS (a-b) and ERA5 (c-d) data considering only values ≥ 1 (white area = NaN value)

Appendix II: Definition of return periods

For a correct understanding of the concept of Intensity – Duration – Frequency curves, it is worth providing the main definitions involved in the probabilistic interpretation of the extreme rainfall regime.

Under the assumption of stationarity, the return period T of a given event is defined as the average time elapsing between two successive realizations of the event itself; alternatively, the return level (or return value) is the value expected to be exceeded, on average, once every return period, or with probability 1/T in any given unitary T (e.g., every year if T is measured in years) (WMO 2009). More generally, the return period T can be defined as:

where 𝐹(𝑥) is the Cumulative Distribution Function, or CDF, describing the non-exceedance probability, ranging between 1 and 0, associated to x, and 𝜇_T is the average waiting time between two events.
In the present document, variable x is the annual maximum rainfall depth associated to a specific duration d; therefore, by definition, the average waiting time between two successive events is equal to 1 year and the return period can be simplified in the following:

The return level can be defined as the annual maximum rainfall value exceeded, on average, once every T years, and it coincides with the inverse function of CDF:

Notice that the uncertainty in the estimation of return periods associated to specific rainfall values, or, alternatively, the estimation of return values associated to specific return periods, depends on the reliability associated to the estimation of the CDF, which, in turn, largely depends on the sample size
N. The higher the sample size, the more robust the estimation of 𝐹(𝑥).

Appendix III: Generalized Extreme Value (GEV) approach

The distribution function 𝐹 of annual maxima of 24h precipitation at a fixed site is approximated by a Generalized Extreme Value (GEV) distribution:

with 𝜇 the offset, 𝜎 the scale, and 𝛾 the shape parameter. This approximation has the form of the limiting distribution function of the affinely normalised maximum over a long time-interval, as the length of this interval tends to infinity (e.g. Leadbetter et al, 1983). In fact, only 𝛾 is a parameter in the normal sense; 𝜇 and 𝜎 are functions of the length of the time interval, which is fixed at one year in our case. Defining 𝑑 = 𝜎/𝜇, the (nondimensional) dispersion coefficient, we obtain the expression on the right-hand side of (1).

The return value 𝑟_T of 24h precipitation for a return of period of 𝑇 years is defined as the precipitation level exceeded one average once per year. It is given by

 
To estimate temporally and spatially varying parameters of the GEV distribution of annual maxima of the precipitation accumulated over 24 hours over Europe, we model the temporal and spatial variation of the GEV parameters and the resulting return values of precipitation separately over spatial tiles of 10°x10° arranged in a regular pattern, with neighbouring tiles overlapping by 50%. This is done primarily for computational reasons. For each location (𝑥, 𝑦), return value estimates and their estimated standard deviations obtained from all tiles containing this location are merged by weighted averaging: let 𝐿 be the width of a tile in degrees, and

Then the weight 𝑤_ij(𝑥, 𝑦)of the return value estimate 𝑟_T,ij(𝑥, 𝑦) based on the tile with centre (𝑥_i, 𝑦_j) is given by

Observe that the sum in the denominator equals 1 for locations (𝑥, 𝑦) further than 𝐿/2 from a boundary of the domain.

For the GEV model for a single tile, we assume a uniform shape 𝛾 and uniform dispersion coefficient
𝑑 , so only the offset 𝜇 can vary in space and time. This assumption is conventionally applied in hydrology and is known there as index flood approach; a similar approach was pursued in Hanel et al (2009).

The offset 𝜇 is modelled as a product of a smooth function of space and a smooth function of time, both positive. This assumption was checked on a small part of the data. The resulting model is an example of a generalized additive model (gam): it specifies the spatially-temporally varying distribution function 𝐹of the annual maxima as (1) with 𝛾 and 𝑑 uniform, and

in which the 𝑠_l,1 and 𝑠_k,2 are thin-plate spline basis functions on the line and on the plane, respectively; see e.g. Wahba (1990). The coefficients 𝑎₃ and 𝑏₂are to be estimated jointly with 𝛾 and
d. A common approach is to maximize the logarithm of the likelihood function of the observed annual maxima minus additional thin-plate spline penalty terms (one for the second, and one for the third term in (5)), which favour smooth solutions for 𝑙𝑜𝑔𝜇. Each penalty term contains a positive weight factor controlling the degree of smoothness of the solution. Modern methods for gam fitting can simultaneously estimate the model parameters and the weight factors of the penalty terms. In this way, parameters and smoothness are estimated simultaneously to deliver high spatial resolution where station density allows it, and smoothness in data-sparse regions. We applied the residual maximum likelihood (REML) method (Woods, 2011) implemented for the GEV distribution in the function gam of the R-package mgcv. Using the function predict.gam from the same package, the covariance of all model parameters for a tile can be computed. It is easy to extend this to approximate the variance of the return value for any return period and any position on the tile and for any year, or of the average return value over any time-interval.

Formally, the likelihood-based approach described above assumes that the annual maxima at neighbouring locations are independent. Although this assumption is questionable, it produces valid estimates; however, estimates of standard deviations derived from the model may be biased low.
A modification is required for tiles where annual maxima of 0 mm are observed. There, the average probability 𝑝₄ of a zero value is determined first, and the GEV distribution is fitted to the nonzero values. Then to compute a return value, (2) is applied with the return period 𝑇 substituted for

Appendix IV: Input Data Description

Input Data 1: ERA5 Reanalysis

Table 24: Overview of key characteristics of ERA5 Reanalysis.

Input Data 2: E-OBS

Table 25: Overview of key characteristics of E-OBS daily gridded data

Input Data 3: ECA&D

Table 26. Overview of key characteristics of ECA&D station network data

Input Data 4: ERA5-2km

Table 27: Overview of key characteristics of ERA5-2km Reanalysis

References

Barredo J. I. (2007). Major flood disasters in Europe: 1950-2005. Natural Hazards 42(1): 125-148, doi: 10.1007/s11069-006-9065-2.

Brakenridge G. R. (2017). Global active archive of large flood events. Dartmouth Flood Observatory, University of Colorado. http://floodobservatory.colorado.edu/Archives/index.html

Copernicus Climate Data Store (2018). ERA5 hourly data on single levels from 1979 to present. Copernicus Climate Change Service Climate Data Store. https://doi.org/10.24381/cds.adbb2d47 [Publication 14th June 2018].

Copernicus Climate Data Store (2020). E-OBS daily gridded meteorological data for Europe from 1950 to present derived from in-situ observations. Copernicus Climate Change Service Climate Data Store. https://doi.org/ 10.24381/cds.151d3ec6 [Publication 15th February 2020].

Coppola E., Sobolowski S., Pichelli E., et al. (2020). A first-of-its-kind multi-model convection permitting ensemble for investigating convective phenomena over Europe and the Mediterranean. Climate Dynamics 55: 3-34, doi:10.1007/s00382-018-4521-8.

Cornes R. C., van der Schrier G., van den Besselaar E. J. M. & Jones P. D. (2018). An Ensemble Version of the E-OBS Temperature and Precipitation Data Sets. Journal of Geophysical Research: Atmospheres 123(17): 9391-9409, doi:10.1029/2017JD028200.

Hanel M., Buishand T. A. & Ferro C. A. (2009). A nonstationary index flood model for precipitation extremes in transient regional climate model simulations. Journal of Geophysical Research: Atmospheres 114(D15), doi: 10.1029/2009JD011712.

Klein Tank A. M. G., Wijngaard J. B., Können G. P., Böhm R., et al. (2002). Daily dataset of 20th-century surface air temperature and precipitation series for the European Climate Assessment. International Journal of Climatology 22: 1441–1453, doi: 10.1002/joc.773.

Klok E. J. & Klein Tank A. M. G. (2008). Updated and extended European dataset of daily climate observations. International Journal of Climatology 29: 1182-1191, doi: 10.1002/joc.1779.

Leadbetter M.R., Lindgren G. & Rootzén H. (1983). Extremes and Related Properties of Random Sequences and Processes. Springer Nature, https://link.springer.com/book/10.1007/978-1-4612-5449-2.

Ramos A. M., Martins M. J., Tomé R. & Trigo R. M. (2018). Extreme Precipitation Events in Summer in the Iberian Peninsula and Its Relationship with Atmospheric Rivers. Frontiers in Earth Science 6: 110, 10.3389/feart.2018.00110.

Ramos A. M., Trigo R. M. & Liberato M. L. R. (2014). A ranking of high-resolution daily precipitation extreme events for the Iberian Peninsula. Atmospheric Science Letters 15(4): 328-334, doi: 10.1002/asl2.507.

Rockel B., Will A. & Hense  A. (2008). The regional climate model COSMO-CLM (CCLM). Meteorologische Zeitschrift 17:347-348, doi: 10.1127/0941-2948/2008/0309.

Wahba G. (1990). Spline models for observational data. SIAM, Society for Industrial and Applied Mathematics, https://doi.org/10.1137/1.9781611970128.

Wood S. N. (2011). Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. Journal of the Royal Statistical Society (B) 73(1):3-36, doi: 10.1111/j.1467-9868.2010.00749.x.

Wouters H., Demuzere M., Blahak U., Fortuniak K., Maiheu B., Camps J., Tielemans D., & van Lipzig N. M. (2016). The efficient urban canopy dependency parametrization (SURY) v1.0 for atmospheric modelling: description and application with the COSMO-CLM model for a Belgian summer. Geoscientific Model Development 9, 3027–3054, doi:10.5194/gmd-9-3027-2016.

Zhang X., Hegerl G., Zwiers F. & Kenyon J. (2005). Avoiding inhomogeneity in percentile-based indices of temperature extremes .Journal of Climate 18(11):1641-1651, doi: 10.1175/JCLI3366.1.

Related articles

• Page:
  NEMO-ERSEM and POLCOMS-ERSEM: User Guides for Products (v1.1)
• Page:
  Sea level and ocean wave time series and indicators
• Page:
  Product user guide for sea level and ocean wave products - time series and indicators
• Page:
  ECDE indicators catalogue entry: Product User Guide
• Page:
  Climate variables for cities in Europe from 2008 to 2017 documentation