Last modified on Feb 27, 2024 15:04

Contributors: Else van den Besselaar (KNMI)

Issued by: Else van den Besselaar (KNMI)

Issued Date: 16/05/2022

Acronyms

Introduction

Executive Summary

Indices of extremes are derived indicators that can be used to monitor the climate. Examples of these indices are the number of frost days in winter or the annual number of rainy days. Some indices have a fixed threshold and therefore only useful in certain areas, at certain times, such as the number of ice days which reflect the number of days when the maximum daily temperature is below zero. Other indices are calculated with respect to the local climate, such as the number of very heavy precipitation days, calculated as the number of days when the daily precipitation is higher than the 95^th percentile for a reference period at that specific location. A large number of indices uses only temperature or only precipitation as input, while a few others require more than one variable as input. The indices dataset presented here uses the E-OBS gridded dataset as the input from which the indices are derived.

Scope of Documentation

This Product User Guide describes the indices dataset derived from E-OBS. Background information is given on why certain choices have been made and how the dataset might be affected by that. The E-OBS dataset is available from the CDS: https://cds.climate.copernicus.eu/cdsapp#!/dataset/insitu-gridded-observations-europe?tab=overview

Version History

The version of the indices based on E-OBSv23.1e is the first version available from the CDS. Differences between subsequent E-OBS versions due to increases in the number of station data and density of the network, will propagate into this indices dataset as well. The number of indices is too large to give a complete overview of what has changed between the indices versions, but comparisons between subsequent E-OBS versions are available. The PUG for E-OBS will give general information on what changes might be expected for the indices with a new version. However, the main change between versions of the indices datasets will usually be the length of the dataset.

 Data access information

Product Description

Product Target Requirements

The indices dataset will be updated once per year using E-OBS versions that cover complete calendar years.

Product Overview

Data Description

Figure 1: Anomaly in the number of ice days (days with maximum temperature below 0°C) in winter 2020 with respect to the corresponding climatology for 1981-2010. For this 'best-estimate', the ensemble median derived from 20 ensemble members is used. This figure features in the European State of the Climate 2020 report (https://climate.copernicus.eu/esotc/2020).

Table 1: Overview of key characteristics of the indices derived from E-OBS

Variable Description

Table 2: Overview and description of variables.

Input Data

The input data for the indices described here is the E-OBS dataset. E-OBS is a daily gridded land-only observational dataset over Europe. The blended time series from the station network of the European Climate Assessment & Dataset (ECA&D) form the basis for the E-OBS gridded dataset. All station data are sourced directly from the European National Meteorological and Hydrological Services (NMHSs) or other data holding institutions. For a considerable number of countries, the number of stations used is that from their complete national networks, which are therefore much denser than the station networks that are routinely shared among NMHSs (which are the basis of other gridded datasets). The density of stations gradually increases, with the lowest number of stations available in the 1950s, to much higher numbers in more recent periods. The meteorological station dataset which is the basis of the E-OBS dataset is not static - for both the historical period and the most recent period, sometimes new stations are added with new releases of E-OBS, through collaborations with NMHSs.

Initially, in 2008, this gridded dataset was developed to provide validation for the suite of Europe-wide climate model simulations produced as part of the European Union ENSEMBLES project. While E-OBS remains an important dataset for model validation, it is also used more generally for monitoring the climate across Europe, particularly with regard to the assessment of the magnitude and frequency of daily extremes.

The position of E-OBS is unique in Europe because of the relatively fine spatial horizontal grid spacing, the daily resolution of the dataset, the provision of multiple variables and the length of the dataset. Finally, the station data on which E-OBS is based are available through the ECA&D webpages (where the owner of the data has given permission to do so). In these respects, it contrasts well with other datasets.

The temporal resolution of the dataset is daily, meaning the observations cover 24 hours per time step. The exact 24-hour period can be different per region. The reason for this is that some data providers measure from midnight to midnight while others might measure from morning to morning. Since E-OBS is an observational dataset, no attempts have been made to adjust time series for this 24-hour offset. However, it is made sure, where known, that the largest part of the measured 24-hour period corresponds to the day attached to the time step in E-OBS (and ECA&D).

Methodology and uncertainty estimate

The best-estimate for the various climate impact indices, like the E-OBS-based temperature and precipitation indices, is given as the ensemble median of the dataset which is constructed by calculating the indices using all of the ensemble members of the E-OBS dataset. Where users require a single measure of the E-OBS-based indices, then this 'best-estimate' value should be used. Nevertheless, the general recommendation relating to uncertainty is that users ought to consult the uncertainty information as this can be considerable and will change in space and time. The uncertainty is ultimately determined by the station coverage which varies across the domain and in time.

To address uncertainty in the temperature and precipitation indices, all 20 E-OBS ensemble members are used to calculate an ensemble of indices, propagating the spread in the E-OBS ensemble to a spread in the indices. The size of this spread is captured by the values for the 2.5 and 97.5 percentiles of the indices ensemble. Although the full E-OBS ensemble will be made available, the full ensemble of the indices is not made available.
The spatial maps of the 2.5 and 97.5 percentiles of the indices ensemble and how these vary in time for the various aggregation levels (annual, half-yearly, seasonal, monthly) are made available as two variables in a netcdf file. The ensemble median is available in a separate file.

For indices that use multiple elements as input (e.g. Potential EvapoTranspiration (PET), Universal Thermal Climate Index (UTCI) and self-calibrating Palmer Drought Severity Index (scPDSI)), only the best-estimate is available (daily values for PET and UTCI, monthly values for scPDSI). These indices are derived using the E-OBS ensemble mean rather than the individual ensemble members as propagating the ensemble uncertainty in derived indices based on multiple input streams - each with their own ensemble spread - quickly becomes computationally prohibitive.

An example of the use of the available uncertainty files is given in Figure 2, where a map of the 100-member ensemble-median of the number of rainy days for November 2011 is shown, with a large area in Central Europe showing no rainy days at all, and a time series of the number of rainy days, averaged over the Danube catchment, for the ensemble median (in red) and the ensemble spread quantified by the 2.5^th and 97.5^th percentiles (in grey). This latter plot clearly shows the low value for November 2011 - even when the spread in the ensemble is taken into account - but it also shows the considerable spread for more typical months or wetter months, like April 2010. Note that the median (the red line in Figure 2) is expected to be nearer the 2.5^th percentile value as opposed to the 97.5^th percentile value. This happens more for precipitation-based indices as the data are much more skewed than for temperature.

Figure 2: Map showing the ensemble median of the R1mm index (number of rainy days) for November 2011 (a) and a time series of the number of rainy days averaged over the Danube basin (b). The latter plot shows the ensemble median value (red line) and the spread in the ensemble (grey shading) as quantified by the 2.5^th and 97.5^th percentile values as provided in the netcdf files. These figures are based on the 100-ensemble member version of E-OBSv18.0e.

Why not use all E-OBS ensemble members?

The range of uncertainty in earlier versions of the E-OBS derived indices (version 19.0e and earlier) was described by a 100 member ensemble. However, it was observed that the uncertainty in derived indices saturated at a much lower number of ensemble members and it turned out to be possible to use fewer ensemble members to reliably estimate the uncertainty in the indices of extremes. From these experiments, it was decided that a 20 member ensemble is sufficient to span the uncertainty and from then on, only 20 ensemble members were produced for the E-OBS indices. The uncertainty saturated at a much lower number of ensemble members, as we try to explain here. As these experiments were performed before the E-OBS indices were available through the CDS, the text and figures of this Product User Guide that cover the reasons why only 20 ensemble members were chosen, are based on an older E-OBS indices version instead of the latest version. Note, that from E-OBSv24.0e onwards, the E-OBS dataset itself has been created with only 20 ensemble members instead of the earlier 100 ensemble members.

In the following subsection, the motivation for moving to the use of a smaller 20-member ensemble for the indices is documented.
In order to assess how the spread in the E-OBS ensemble propagates to a spread in derived data, climate impact indicator data from 17 selected grid boxes across Europe are selected. For temperature, the six indices looked at are:

• TNn (minimum value of the daily minimum temperature)
• TXx (maximum value of the daily maximum temperature)
• TN10p (cold nights, percentage of days with daily minimum temperature below the 10^th percentile of daily minimum temperatures)
• TX90p (warm day-times, percentage of days with daily maximum temperature above the 90^th percentile of daily maximum temperatures)
• WSDI (warm spell duration index)
• CSDI (cold spell duration index)

For precipitation the three indices looked at are:

• R95pTOT (precipitation fraction due to very wet days (exceeding the 95^th percentile))
• RX5day (maximum 5-day accumulated precipitation sum)
• CDD (Consecutive Dry Days)

The motivation to look into these indices is that they are expected to show maximum spread, given a spread in the input temperature or precipitation data, because of their focus on the extreme end of possible events.

Spread in temperature indices

Figure 3 shows the 2.5^th and the 97.5^th percentiles for annual TN10p, for the grid boxes in the E-OBS dataset nearest to Munich (Germany) and Kiev (Ukraine). Together, these two percentiles capture 95% of the spread in TN10p and so provide a measure of that spread. It can be seen that this spread is about the same whichever set of 20 E-OBS ensemble members is used. This illustrates the rapid saturation of the spread with ensemble size. Figure 3 also shows that the spread in TN10p is modest (as we will see later with examples showing TX90p as well). The relatively narrow spread is related to the use of 10% of the values in the temperature distribution, which is apparently not sufficiently extreme to maximize the spread.

Figure 3: The 2.5^th (a & b) and 97.5^th (c & d) percentiles for the spread in annual TN10p (percentage of cold nights) for the grid boxes in the E-OBS dataset nearest to Munich (Germany) (a & b) and Kiev (Ukraine) (c & d). The colour coding relates to the use of five different subsets of 20 members from the 100-member E-OBS ensemble.

The spread in the ensemble is larger using the TNn index, showing the spread in estimates of the coldest night in the year (Figure 4). Such a relatively large spread in the ensemble is observed for TXx (warmest daily temperature of the year) for grid boxes close to Perugia (Italy) and Brno (Czech Republic) as well (Figure 5). There appears to be slightly more diversity between the 20-member sets than for those in Figure 3. Figure 6 shows the 2.5^th (top) and 97.5^th (bottom) percentiles for TX90p (percentage of warm day-times) for the grid boxes in the E-OBS dataset nearest to Perugia (Italy) (left) and Brno (Czech Republic) (right).

Similarly to the plots for the coldest nights (Figure 3), the spread is modest.

The Warm Spell Duration Index (and the Cold Spell Duration Index - not shown), as shown in Figure 7, has more spread. There are, as is to be expected, quite a few years having no warm or cold spells.

Figure 4: The 2.5^th (a & b) and 97.5^th (c & d) percentiles for the spread in annual TNn (minimum of the daily minimum temperature - coldest night) for the grid boxes in the E-OBS dataset nearest to Munich (Germany) (a & c) and Kiev (Ukraine) (b & d). The colour coding relates to the use of five different subsets of 20 members from the 100-member E-OBS ensemble.

Figure 5: The 2.5^th (a & b) and 97.5^th (b & d) percentiles for the spread in annual TXx (maximum of the daily maximum temperature - warmest day-time) for the grid boxes in the E-OBS dataset nearest to Perugia (Italy) (a & c) and Brno (Czech Republic) (b & d). The colour coding relates to the use of five different subsets of 20 members from the 100-member E-OBS ensemble.

Figure 6: The 2.5^th (a & b) and 97.5^th (c & d) percentiles for the spread in annual TX90p (percentage of warm day-times) for the grid boxes in the E-OBS dataset nearest to Perugia (Italy) (a & c) and Brno (Czech Republic) (b & d). The colour coding relates to the use of five different subsets of 20 members from the 100-member E-OBS ensemble.

Figure 7: The 2.5^th (a & b) and 97.5^th (c & d) percentiles for the spread in annual WSDI (Warm Spell Duration Index) for the grid boxes in the E-OBS dataset nearest to Munich (Germany) (a & c) and Brno (Czech Republic) (b & d). The colour coding relates to the use of five different subsets of 20 members from the 100-member E-OBS ensemble.

Spread in precipitation indices

Figure 8 shows the 2.5^th percentile and the 97.5^th percentile for annual R95pTOT (precipitation fraction due to very wet days (exceeding 95th percentile)) for the grid boxes in the E-OBS dataset nearest to the city centre of Linköping (Sweden) and Porto (Portugal). This figure shows that for precipitation, as for temperature, a rapid saturation of the spread with ensemble size is present.

Figure 8: The 2.5^th (a & b) and 97.5^th (c & d) percentiles for the spread in annual R95pTOT (precipitation amount related to very heavy precipitation days) for the grid boxes in the E-OBS dataset nearest to Linköping (Sweden) (a & c) and Porto (Portugal) (b & d). The colour coding relates to the use of five different subsets of 20 members from the 100-member E-OBS ensemble.

Figure 9, which shows RX5day (annual maximum of the 5-day accumulated precipitation amount), shows a similarly rapid saturation of the spread with the increase of the number of ensemble members. This figure, as well as Figure 8, shows a strong correlation between the 2.5^th and 97.5^th 'trends' for R95pTOT and RX5day.

Figure 9. The 2.5^th (a & b) and 97.5^th (c & d) percentiles for the spread in annual RX5day (5-day precipitation amount) for the grid boxes in the E-OBS dataset nearest to Linköping (Sweden) (a & c) and Porto (Portugal) (b & d). The colour coding relates to the use of five different subsets of 20 members from the 100-member E-OBS ensemble.

Figure 10 shows CDD (Consecutive Dry Days) for the grid boxes close to Norwich (UK) and Murcia (Spain). CDD has hardly any spread for the 2.5^th percentile but this is to be expected. Assessments of the annual maximum length of a dry spell will vary strongly when for a day in this dry spell an ensemble member indicates rainfall. This will make estimates of the length of the longest dry spells vary more wildly, whereas the estimates of the annual maximum length at the low-end of the spectrum will consist of those days for which all members show an absence of rainfall.

Figure 10: The 2.5^th (a & b) and 97.5^th (c & d) percentiles for the spread in annual CDD (consecutive dry days) for the grid boxes in the E-OBS dataset nearest to Norwich (United Kingdom) (a & c) and Murcia (Spain) (b & d). The colour coding relates to the use of five different subsets of 20 members from the 100-member E-OBS ensemble.

In order to look a little deeper into the loss of information when a 100-member ensemble is replaced by a 20-member ensemble set, Figure 11a shows the median values of R95pTOT for the various sets of 20-member ensembles and (in grey) the median value based on the full 100-member ensemble, for the period 1990-2018. Clearly, the correlation between the medians is large, except for a few years when variations between the 20-member sets and the 100-member ensemble can be substantial.

The ratio between the median of the 20-member sets and the median of the full 100-member set (Figure 11b) shows that for some years a 20-member median value may underestimate the 100-member median by as much as 20%. A similar analysis is made for the uncertainty in the gridding. Figures 11c and 11d show the ratio between the 2.5^th (c) and 97.5^th (d) percentiles based on the various 20-member ensembles and those percentiles based on the full 100-member ensemble. For the 2.5^th percentile, this ratio can be as large as 1.5. For the upper percentile, this ratio is smaller, as can be expected.

Figure 11: The R95pTOT medians of the various 20-member ensembles and the full 100-member ensemble set (in grey) (a & b). (a) shows the medians for the 1990-2018 period and (b) shows the ratios of the medians between the 20-member sets and the full 100-member set. (c & d) show similar ratios, but for the 2.5^th percentile (c) and the 97.5^th percentile (d). This figure relates to a grid box close to Munich.

Using indices for trend analysis

A strong argument for using climate indices stems from their ability to reveal changes in climate, thereby enabling a means of climate monitoring. The inspection of the trends in these indices is part of this monitoring. The calculation of trends based on the ensemble median of the indices (which is provided) is a good starting point. However, the quantification of the uncertainty in the trend, due to the uncertainty in the gridding of the underlying temperature or precipitation fields, by calculating trends in the 2.5^th and 97.5^th percentiles does not fully capture this uncertainty. Nevertheless, calculating trends using these percentiles (which are provided) should provide an estimate of the uncertainty of the trends, in the absence of the assessment of uncertainty based on calculating trends on each of the ensemble members of the climate indices. This consideration may be an argument to provide full ensembles of the indices in the future. However, the practical consequences of having to analyse an ensemble of trends, each having its own uncertainty as well, are large since these different type of uncertainties need to be combined. For these type of issues, it is suggested that a Bayesian approach may be useful as the output of one model is uncertain, which is then input to the next model. Bayesian inference expresses uncertainty with posterior distributions (not p values). The many distributions from the complete ensemble can be combined in to one. The keyword is 'Bayesian predictive distribution', sometimes simply 'predictive distribution', an elegant concept to translate uncertainty from one model into another (Hoff, 2009). The challenge left is then to conduct trend analysis Bayesian style. Hoff (Chapter 5, 2009) shows how to do linear regression Bayesian style.

Concluding Remarks

In the figures above, it is shown how the the ensemble-based uncertainty estimates of the E-OBS dataset propagate into the climate impact indices. All of the extreme indices, both for temperature and precipitation, show a rapid saturation of the ensemble spread with increasing ensemble size. This means that, for these type of indices, using a 100-member ensemble of E-OBS to assess uncertainty in the indices is generally not required. It has been found that an overall valid estimate of the uncertainty can be obtained by reducing the number of ensemble members to about 20. Note, that the smaller the number of values used to calculate the extremes (like TXx or RX1day, which show values for one day only), the greater the differences between ensemble members are likely to be. Also note, that for individual years in the smaller ensembles, a substantial difference with a 100-member ensemble may exist, both in the median but more so in the estimates of the spread of the ensemble. Note, that from E-OBSv24.0e onwards, only 20 members are created for the E-OBS dataset itself instead of the earlier 100 members.

Earlier work (Cornes et al. 2018) showed that the uncertainty quantified by the ensemble spread appears to be an underestimation of the real uncertainty, especially in data sparse regions, although the uncertainty in the current E-OBS dataset is more closely related to station density than uncertainty values in the original data set (Haylock et al. 2008). The modest range of values spanned by the ensemble and the necessity to use the more extreme indices to show a reasonable uncertainty relate to this. Improvements may be made in this estimate through the quantification of other sources of uncertainty such as instrumentation error (Cornes et al., 2018, Yang et al., 1999).

The underestimation of uncertainty may be related to the use of a single variogram across the domain, as an assumption is made that the correlation structure is only dependent on the spatial lag, and not the location. This assumption is often made in such applications (e.g., Haylock et al., 2008; Newman et al., 2015) but can be an oversimplification for continental-scale data as the spectral characteristics of the true fields can vary considerably across the domain, particularly for precipitation. This assumption of stationarity may also be unrealistic in the present application on account of the varying characteristics of the spatial trend captured by the Generalized Additive Model, which results from the large variations in station coverage across the domain. An approach to remedy this is to use different variograms across the domain; this, however, introduces artefacts in the gridded data, and particularly in the ensemble spread and this approach is no longer pursued (Cornes et al. 2018). A possible way forward is to use approaches explored from non-stationary co-variance modelling by Douglas Nychka (e.g. Nychka et al., 2018).

Nevertheless, the main recommendation relating to uncertainty is that users ought to use results from all 20 members as the uncertainty will vary in space and time, reflecting the changing station density. Although the spread in the uncertainty estimate of the E-OBS dataset is probably too small, the results shown in this report clearly indicate that (even for this modest ensemble of twenty) the spread in the climate indices can be considerable.

Appendix I

Input Data Description

E-OBS dataset

Table 3: Overview of key characteristics of E-OBS as used to derive the E-OBS indices

References

https://www.ecad.eu/documents/ECAD_datapolicy.pdf

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Cornes, R., G. van der Schrier, E.J.M. van den Besselaar, and P.D. Jones. 2018: An Ensemble Version of the E-OBS Temperature and Precipitation Datasets, J. Geophys. Res. Atmos., 123. doi:10.1029/2017JD028200

De Bruin, H.A.R. 1987: From Penman to Makkink. In: Evaporation and Weather (C. Hooghardt, editor), Commission for Hydrological Research TNO, The Hague, the Netherlands, Proceedings and Informations 39, pages 5-31

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