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Vrije Universiteit Brussel

Winter is leavingYao, Yi; Thiery, Wim; Sterl, Sebastian Hendrik

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Citation for published version (APA):Yao, Y., Thiery, W., & Sterl, S. H. (2020). Winter is leaving: Reduced occurrence of extremely cold days inBelgium and implications for power system planning. Vrije Universiteit Brussel.

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WINTER IS LEAVINGREDUCED OCCURRENCE OF EXTREMELY COLD DAYS IN BELGIUM AND IMPLICATIONS FOR POWER SYSTEM PLANNING

Yi YAOWim THIERYSebastian STERL

2 / 33© 2020 Vrije Universiteit Brussel

Winter is Leaving - Reduced occurrence of extremely cold days in Belgium and implications for power system planning

COLOFON Verantwoordelijke: Wim Thiery; Department of Hydrology and Hydraulic EngineeringContact: [email protected]: 18/03/2020Status: eindversieClassificatie: publiek

DISCLAIMER

This study was commissioned by the CREG (Commissie voor de Regulering van Elektriciteit en Gas / Commission de Régulation de l’Électricité et du Gaz).

The views and assumptions expressed in this report represent the views of the authors and not necessarily those of the client.

WINTER IS LEAVING



CONTENT

Executive Summary 41. Introduction 52. Recent evidence of decreasing cold extremes in Europe 7 3. Method 114. How may cold extremes be related to LOLE in Belgium? 135. How has the probability of cold extremes changed in Belgium and its neighbours? 166. Implications for power system adequacy planning 19Bibliography 22Appendix 25



EXECUTIVE SUMMARYWinters in north-western Europe have been becoming milder on average in recent decades, which is consistent with the trend of global warming observed and documented worldwide. Both average as well as extreme temperatures have shifted to higher ranges as a symptom of this warming. Since electricity demand in north-western Europe is well-known to peak during the coldest periods, this warming trend is likely to have important implications for power systems.

In this study, we analysed observed weather data at daily resolution over Belgium (and its neighbouring countries) for the period 1980-2019 to assess the (change in) occurrence of extremely cold days. We compared this temperature information with the occurrence of Loss of Load Expectation (LOLE – moments when power demand exceeds the available capacity) as simulated in power market and adequacy modelling by Belgium’s transmission system operator, based on the country’s expected 2025 power mix and historical (1982-2015) weather conditions. We conclude that (i) there is a high degree of co-occurrence of simulated persistent LOLE events with extremely cold days, and (ii) the probability of such extremely cold days has shown robust decreases across Belgium (and its neighbouring countries) since the 1980s.

Based on this analysis, we advise that whenever simulations on power system adequacy are underta-ken to support future peak generating capacity planning, such assessments should account for climate change effects on the meteorological data used for the simulations, for instance through sensitivity tests regarding the choice of time period. Considering the robust warming trend observed in recent decades, simulations based on weather data that is no longer representative of the current (and future) climate may result in unrealistic estimations.



1. INTRODUCTIONA substantial number of studies have reported increases in near-surface air temperature over Europe in recent decades (Moberg et al., 2006; Philipona et al., 2009; Pachauri et al., 2014; Lorenz et al., 2019). Conse-quently, cold extremes have diminished in Europe, resulting in warmer-on-average winters for several sub-sequent decades (Lorenz et al., 2019). This trend is likely to continue in the near future (Seneviratne et al., 2018).

Despite this trend, some regional cold winters still occurred in recent years, for instance in France in 2010. However, their frequency and intensity have reduced consistently with the worldwide robust warming trends (Cattiaux et al., 2010; Twardosz and Kossowska-Cezak, 2016). Results from climate simulations indicate that under continued global warming, extreme cold events will continue to reduce in frequency and intensity (Seneviratne et al., 2012; Seneviratne et al., 2016).

Normally, in north-western Europe, shortfalls in electricity supply mainly occur during very cold winters when demand is high (CREG, 2016; Thornton et al., 2017). In particular, the occurrence of extreme cold can cause Loss of Load Expectation (LOLE) – measured as the expected number of hours per year in which the power demand exceeds the available power generating capacity. Warming in winter may thus alleviate shortfalls in electricity supply in some countries. As such, knowing whether, and how, the occurrence of cold extremes is changing is of importance for future power systems planning in



north-western Europe. In Belgium, for instance, estimating the historical and future change in the likeli-hood of extreme cold, potentially leading to LOLE, can be argued to be of prime importance for near- and medium-term system adequacy planning, especially in light of the announced nuclear phase-out and expected growth in variable offshore wind power generation.

This report opens with a review of recent literature pertaining to the decrease in cold extremes in Euro-pe (chapter 2). Subsequently, the method for the current study is described (chapter 3). We then present results on the correlation of simulated LOLE and low temperatures in Belgium (chapter 4) and on the recent trends in extreme temperatures in Belgium and its neighbours (chapter 5). The report closes with several conclusions (chapter 6).



Figure 1: Trends in the annual minimum value of daily minimum temperature (TNn, °C per decade) at various stations (a), histograms

of trends in TNn (b) in light red (all stations) and dark red (only stations with statistically significant trends) and from randomly bootstrapped time series in gray over Europe. The black range indicates the 5th to

95th percentile of the median area averaged trends from the bootstrapped samples.

Figure adapted from(Lorenz et al., 2019).

2. RECENT EVIDENCE OF DECREASING COLD EXTREMES IN EUROPEThe European Climate Assessment & Dataset (ECA&D) provides long-term time series of near-surface temperature data, as measured in a wide range of stations over Europe (Klein Tank et al., 2002; Klok and Klein Tank, 2009). Based on the data from 910 stations, Lorenz et al. (2019) calculated the linear trend of annual minimum temperature (TNn) for each station (Figure 1a). Over Europe, most of the stations recorded an increase in annual minimum temperature. Across these stations, annual minimum temperatures generally increased with a median value of roughly 0.50°C per decade (Figure 1b). For those stations with statistically significant trends, the recorded increase was even sharper.



Dividing the period into three parts (1950-1972, 1973-1995 and 1996-2018), Lorenz et al. (2019) also calculated the number of days per year with daily minimum and maximum temperature in different percentile bins. Both the number of days with daily minimum and daily maximum temperatures below the 10th percentile decreased with time (Figure 2a-b). Moreover, the lower the percentile, the sharper the decrease, implying that cold events that are relatively more extreme experienced a relatively stronger reduction in frequency.

Figure 2: Histograms of (a) daily minimum temperature (TX) and (b) daily maximum temperature (TX) for 1950-1972 (orange), 1973-1995 (red) and 1996-2018 (purple). The percentiles were calculated for the

whole period. The middle part of histograms was excluded in the figure. Figure adapted from Lorenz et al. (2019).

Anthropogenic activities, and especially increasing greenhouse gas emissions from fossil fuel burn-ing, are the main driver of the observed global warming over the industrial period (Bindoff et al., 2013). As the airborne fraction of CO2 emitted into the atmosphere has a long lifetime, its warming effect on cli-mate persists for decades to centuries. Past cumulative emissions have thus far induced a global mean temperature increase by about 1°C (IPCC, 2018).

Just like global historical cumulative emissions of CO2 and other greenhouse gases have controlled the historical pathway of global mean temperature, future cumulative emissions will determine the even-tual global warming level (Figure 3) (IPCC, 2013). According to different Representative Concentration Pathways (RCPs), global mean temperature may increase by 1.5°C to more than 4°C above pre-industrial levels by 2100 (IPCC, 2013; IPCC, 2018).



As global mean temperatures continue to rise, so do temperatures during cold spells. Moreover, cold extremes will generally warm faster than the global average (Figure 4a; Seneviratne et al., 2016). Over most of the land area, multi-model mean projected warming of TNn exceeds 2°C under a global 2°C warming scenario (Figure 4b); over Central Europe, it may even exceed 5°C (Figure 4a).

Figure 4: (a) Scaling between the annual coldest night-time temperature (TNn) over Central Europe (CEU) and changes in

global mean temperature, with associated global cumulative CO2 emissions targets. The solid black line denotes the

ensemble average in the historical runs until 2010 (combined with RCP8.5 for 2006–2010) and the solid blue (red) line denotes the

ensemble average of the future projections following the RCP4.5 (RCP8.5) scenario simulations, based on 22 (25) model

simulations. The red shaded area indicates the total range (minimum to maximum value) for all considered simulations and

experiments (land grid cells only). (b) Local changes associated with a global warming of 2°C for TNn.

Figure adapted from Seneviratne et al. (2016).

Figure 3: Simulated global mean surface temperature increase as a function of cumulative total global CO2 emissions. Multi-model results from a hierarchy of climate-carbon cycle models for each RCP until 2100 are shown with coloured lines and decadal means (dots). Model results over the historical period (1860 to 2010) are indicated in black. The coloured plume illustrates the multi-model spread over the four RCP scenarios and fades with the decreasing number of available models in RCP8.5. The multi-model mean and range simulated by CMIP5 models, forced by an indealised CO2 increase of 1% per year, is given by the thin black line and grey area. For a specific amount ofcumulative CO2 emissions, the 1% per year CO2 simulations exhibit lower warming than those driven by RCPs, which include additional non-CO2 forcing. Temperature values are given relative to the 1861−1880 base period, emissions relative to 1870. Figure from IPCC (2013).



As a consequence, cold extremes will continue to decrease in frequency towards the future (Seneviratne et al., 2018). For instance, both cold days (days with daily maximum temperature below the 10th percentile) and cold nights (nights with minimum temperature below the 10th percentile) are projected to decrease in frequency from 10% during the reference period (1981–2000) to less than 4% and 5%, respectively, towards the end of the century even under an optimistic emission scenario, and with higher emissions leading to a stronger reduction in their frequency of occurrence (Figure 5; Sillmann et al. (2013)). These results indicate that cold extremes substantially diminish under projected future warming scenarios.

Figure 5: Global averages of temperature percentile indices (a) cold nights (TN10p) and (b) cold days (TX10p) over land as simulated by the

CMIP5 ensemble for the low-emission scenario RCP2.6 (blue), a middle-of-the-road scenario RCP4.5 (green), and a high-emission

scenario RCP8.5 (red) displayed as the probability of occurrence versus time. The reference period for computing the temperature values

associated with TN10p and TX10p was 1981–2000. Solid lines indicate the ensemble median and the shading indicates the interquartile

ensemble spread (25th and 75th quantiles). Time series are smoothed with a 20-year running mean filter.

Figure adapted from Sillmann et al. (2013).



3. METHODTo better understand how cold extremes may correlate with LOLE, and how the occurrence of such cold extremes has changed in the previous decades as a result of climate change in Belgium as well as in neighbouring countries, we analysed (i) observed temperature data across Belgium and its neighbou-ring countries in the period 1980-present, and (ii) daily LOLE data from electricity market and adequacy simulations used in a recent assessment of Belgium’s capacity adequacy by the Belgian Transmission System Operator (TSO) (ELIA, 2019). The latter assessment was based on the assumed future (2025-2030) power generating fleet, including the announced Belgian nuclear phase-out and strong growth in offsho-re wind power capacity, as well as historical (1982-2015) weather data. The LOLE data for Belgium was provided by the Commission for Electricity and Gas Regulation (CREG) for the purpose of this analysis. For observed temperature, we used gridded daily data from the E-OBS dataset (version 20.0e) developed by the ECA&D project (Cornes et al., 2018; ECA&D, 2019)1. Over Belgium (BE), the Netherlands (NL), France (FR), Germany (DE) and the United Kingdom (UK), the stations are evenly distributed in a dense network, especial-ly for NL and UK (Cornes et al., 2018). These data have been evaluated and used in many studies over Europe and consistently showed high reliability (Hofstra et al., 2009; Lorenz et al., 2019).

To shed light on the relation between extremely cold days and LOLE, we first extracted (i) the daily mean

1 We acknowledge the E-OBS dataset from the EU-FP6 project UERRA (http://www.uerra.eu) and the Copernicus Climate Change Service, and the data providers in the ECA&D project (https://www.ecad.eu)



temperature averaged over Belgium in the period 1980-2019 from E-OBS and (ii) the number of LOLE hours per day from the Belgian TSO’s simulations based on the expected 2025 power generating fleet and the historical weather period 01/09/1982 – 31/08/2015. As these simulations contain 10 realisations per calendar day, corresponding to different “Monte Carlo” years combining historical weather data with (uncorrelated) power plant and HVDC (High Voltage Direct Current) line availability, we considered the average number of LOLE hours per day across the 10 realisations. Second, we analysed the co-occurrence of low temperatures and LOLE and the correlation between these two quantities, as well as changes in their temporal distribution across the analysed period. To this end, we binned all days in the period 1980-2019 into six categories, based on the empirical percentile rank (0-0.1, 0.1-0.2, 0.2-1, 1-2, 2-5 and 5-100) of their daily mean average temperature across Belgium. Subsequently, we calculated the average number of simulated LOLE hours per day in each category to elucidate the co-occurrence of extremely cold days and LOLE hours in the period 1982-2015. The results of this analysis are provided in chapter 4.

Having analysed the relationship between extreme cold and LOLE, we then calculated the change in occurrence of cold extremes over time for Belgium as well as four of its neighbouring countries (FR, DE, UK and NL). We used the probability ratio ( PR ) of the temperature bins as a metric, denoting the relative change in occurrence of extreme cold between a present-day period and a past period:

where Pnew refers to the occurrence rate of the type of event under scrutiny in the present-day period, and Pref to the same probability in the reference (past) period. PR<1 indicates that the occurrence rate of such a type of event decreased in the new period as compared to the reference period. For instance, a PR=1/4 for a given temperature bin implies that days categorised in that bin occurred four times less often in the new period than in the reference period. The results of this analysis are provided in chapter 5. This index has been used in several studies (Stott et al., 2004; Fischer and Knutti, 2015; Thiery et al., 2020).

Concluding remarks related to power system adequacy planning are given in chapter 6.

PnewPref

PR= (1)



4. HOW MAY COLD EXTREMES BE RELATED TO LOLE IN BELGIUM?The simulated daily LOLE hours are graphically shown against the corresponding mean daily temperatu-re in Figure 6 for the period 1982-2015. The results indicate that (i) LOLE did not occur exclusively during cold days, and (ii) extremely cold days do not guarantee LOLE. Despite this, the data suggest that (iii) the likelihood of LOLE increases with decreasing mean daily temperature, as nearly all simulated LOLE hours occur during days with sub-zero average temperature.

To better understand this relation, we calculated the average number of LOLE hours per day for each percentile rank category of daily mean temperature, the results of which are shown in Figure 7. (Similar re-sults using indices other than daily mean temperature can be found in the Appendix; see Figure A1.) A strong correlation between LOLE occurrence and daily mean temperature is evident: the average amount of LOLE hours stands at 10.98 hours/day for days in the lowest bin (percentile rank 0-0.1, that is, cold days occurring less than once every 1000 days), at 1.32 hours/day for the second lowest (0.1-0.2, that is, cold days occur-ring once every 500 to 1000 days), 0.74 hours/day for the third lowest (0.2-1, that is, cold days occurring once every 100 to 500 days), 0.11 hours/day for the fourth lowest (1-2), 0.08 hours/day for the fifth lowest (2-5), and near-zero for all other days (5-100).



This clear decrease in LOLE hours per day with the mean temperature percentile rank indicates a strong concurrence between extreme cold days on the one hand, and LOLE occurrence on the other. While there clearly exist other factors related to LOLE occurrence besides low temperatures, this leads us to conclude that the occurrence of a daily mean temperature in the lowest percentile ranks can indicate an increased risk of LOLE.

All days with more than 6 hours of simulated LOLE (Figure 6) occurred in the weather years 1982-1990, with a single exception (one day in the weather years 2000-2009), consistent with the occurrence of extreme cold days during this period (especially 1984-1985 and 1986-1987, see Figure A2). In the most recent period 2009-2015, LOLE, when recorded, mostly lasted for less than three hours per day and without a clear correlation to temperature. We thus deduce that the period 1982-1990 is the most extreme peri-od in the dataset both in terms of extremely cold days and in extremely long-lasting LOLE, with the latter tending to occur during the former.

Figure 6: Simulated average LOLE hours per day versus observed average daily mean temperature (Tmean) during 1982-2015 over

Belgium. Every data point represents one day of historical weather / simulated LOLE. The data points have been grouped by historical time

period (1982-1990, 1990-2000, 2000-2009, 2009-2015).



Accounting for possible extremes in LOLE is of importance for system adequacy planning. Given (i) the strong observed correlation between extremely cold days and LOLE, (ii) the prevalence of both during the beginning of the analysis period (1982-1990), and (iii) the widespread observed increase in average and extreme temperatures as a result of anthropogenic greenhouse gas emissions (Seneviratne et al., 2016), the question arises to what extent the probability of extremely cold days (and by extension, the probabi-lity of cold-related LOLE) may since have changed. This question, carrying implications regarding which weather period would be most representative of present-day conditions for system adequacy modelling in Belgium, is dealt with in the next chapter.

Figure 7: Simulated average LOLE hours per day (rounded to two decimal values) for different percentile rank bins of daily average temperature over Belgium. Bar width reflects the number of days in each category.



5. HOW HAS THE PROBABILITY OF COLD EXTREMES CHANGED IN BELGIUM AND ITS NEIGHBOURS?For the analysis of changes in the probability of occurrence of cold extremes, we focused on winter days (i.e. days in December, January and February) for the periods 1981-1990 and 2010-2019. First, we calculated the average temperature across Belgium on each winter day for these two periods; the histogram of these values is shown in Figure 8. There is a clear rightward shift to higher temperatures from the first period (1981-1990) to the second one (2010-2019), reflecting an increase in both the average and the coldest temperatures in winter, with the change of the latter clearly the more drastic of the two. For reference, the values corresponding to 1-in-1000, 1-in-500 and 1-in-100-day events2 in daily average temperature across Belgium are also shown3.

To quantify the changes in the occurrence of cold extremes, we calculated the PR for these three categories of events using equation (1), using 1981-1990 as reference period and 2010-2019 as new period, and considering all days of the year. In Belgium, the PR of the three event categories is respectively 0.08, 0.21 and 0.43, which means that the occurrence in the new period was respectively ~12 times, ~5 times and ~2 times less than in the reference period (Figure 9). This implies that cold extremes which occurred less than once every 1000 days on average in the last four decades, actually happened

2 Cf. the lowest one, lowest two, and lowest three temperature bins in Figure 7.3 For instance, one-in-1000 days events are characterised by average daily temperatures of below -10°C.



nearly 12 times less often during the 2010s than during the 1980s. It also indicates that the more extre-me the events under consideration, the more their occurrence decreased from the period 1981-1990 to 2010-2019.

It is important to note that these factors denote “best estimate” values which do not include confidence intervals, and that confidence intervals increase with decreasing sample sizes (i.e. the rarer the event, the larger the confidence interval). These values should therefore be considered as indicating overall trends, rather than providing highly accurate estimations of probability reduction.

Comparable results are found for Belgium’s neighbouring countries, for which this analysis was repeated (except for Luxembourg). The corresponding PR values are shown in Figure 9; histograms and tabulated data for all countries are provided in the Appendix (Figure A3 and Table A1). The results highlight that the probability of cold extremes occurrence reduced for all considered countries and temperature percentile bins. Moreover, the results generally confirm that the more extreme the temperature percentile, the stronger the reduction in probability of occurrence. Note however that we did not verify whether daily mean tempera-tures below the 1st percentile value imply high risk of LOLE in neighbouring countries.

Figure 8: Histogram of the average daily mean temperature across Belgium during winter. The shift towards higher temperatures between the period 1981-1990 and 2010-2019 is clear, as is the decrease in the

amount of days with extremely low temperatures. The temperature values corresponding to 1-in-1000, 1-in-500 and 1-in-100-day events for

the period 1980-2019 are plotted as vertical lines. The corresponding histograms for neighbouring countries are shown in Figure A3.



Figure 9: Change, as quantified by the Probability Ratio (PR), between the reference period 1981-1990 and the new period 2010-2019 in the occurrence of events representing values of Tmean reached on average less than once every 1000, 500 and 100 days in the last four decades, respectively.

Given that countries differ in size, and cold extremes may also occur locally (and potentially lead to risk of LOLE) especially in large countries such as France and Germany, we additionally created histograms of daily mean winter temperature for all grid cells in Belgium and its neighbours (Figure A4) instead of the country averages (Figure 8). These results again show a robust warming of the cold tail of the distribution and are consistent with the above. We also calculated three alternative PR values based on the occurrence of cold ex-tremes in all grid cells (Table A2-4 and Figure A5-7) instead of on country-average values (Figure 9 and Table A1). While these alternative PR definitions at times yield slightly different values, the results overall corrobo-rate the patterns shown in Figure 9.

Based on the data presented in this chapter, we conclude that a substantial and robust decreasing trend in the occurrence of cold extremes (Figure 9) that tend to be most correlated to high risk of LOLE (Figure 7) has taken place during the last few decades in Belgium, and a comparable trend has been observed in Belgium’s neighbouring countries.

The implications of this finding for power system adequacy planning are discussed in the next and final chap-ter of this report.



6. IMPLICATIONS FOR POWER SYSTEM ADEQUACY PLANNINGIn this report, we (i) explored the relation between extremely cold days and the amount of LOLE hours simulated to occur on such days in Belgium based on its projected 2025 power generating fleet and demand, and (ii) analysed the changes in probability of occurrence of different types of extreme cold events from 1981-1990 to 2010-2019. Our results indicate (i) that very cold days (occurring less than once every 1000 days) tend to indicate the highest risk of LOLE in the considered electricity market and adequacy simulations, with a clear decrease in risk of LOLE when moving to less extreme temperature ca-tegories (Figure 7), and (ii) the occurrence rate of such events has decreased substantially in Belgium as well as in its neighbouring countries from the 1980s to the present day (Figure 9). These results are highly consistent with recent scientific studies focusing on the decrease in cold extremes in the context of global warming (chapter 2).

This result may have important ramifications for power system adequacy planning in Belgium. Given the continued trends of global warming, it is to be expected that the occurrence of very cold days (Figure 8) will continue to decrease in the next decades (Lenton et al., 2019). This suggests that the risk of persistent LOLE events is also likely to continue its decreasing trend (Figure 6).



Since the decrease in occurrence of cold extremes is observed to have been the sharpest for the “most extreme” extremes, and less sharp for the “less extreme” events (Figure 9), we hypothesize that in the future, a continued reduction in the risk of LOLE events related to temperature increase is most likely for the most extreme LOLE cases, and less evident for moderate LOLE cases.

As should be evident, a decrease in probability of occurrence does not mean a zero probability of occurrence. Cold extremes such as observed in the 1980s, and the associated risk of LOLE for prolon-ged periods, can still occur under today’s climate and that of the future, albeit likely less often. For power system adequacy planning, the important question is therefore not whether or not such events can occur (they can, and theoretically one cannot even rule out more extreme cold events than any observed in the pe-riod 1980-2019 with complete certainty), but against events of what likelihood the robustness of the future system should be planned.

The higher the reserve margins, the more secure a power system will be, and the lower the risk of failure. This statement applies generally to any power system. The question is: up to which level would extra peaking capacity have a substantial effect on system adequacy, and beyond which level would it become ineffective—in terms of cost or another relevant quantity—by proofing the system to events so unli-kely (“overbuilding”) that the investment in extra capacity may no longer be justified (Pietzcker et al., 2017).

In the case of Belgium, this means that system adequacy planning should consider the fact that the probability of cold extremes and the associated high risk of persistent LOLE appear to have substan-tially decreased since the 1980s. Results of economic optimisation models will depend on the weather years used as input data; therefore, a sensitivity test to different weather periods (e.g. covering the 5 to 20 most recent years), taking into account the climatic changes observed since the 1980s, could lead to more robust assessments of the estimated peak generating capacity needed to proof the system to ex-treme events in the future according to the legally defined adequacy criteria, while avoiding “overbuilding”. Considering the balance between statistical robustness (i.e. a large enough sample size) and re-presentativeness of the climate of the planning period (i.e. avoiding years representing a different climate) is key in this context, and may be informed by extreme value statistics accounting for global mean temperature changes (Philip et al., 2017; Vautard et al., 2019).



Finally, it is important to note that the trend of higher temperatures potentially leading to lower need for peak generating capacity applies specifically to the situation of north-western Europe. In the United States, for in-stance, the inverse is likely to be the case: peak load in the United States is mostly correlated with extremely hot instead of extremely cold days and the temperature shifts resulting from climate change are thus likely to increase, instead of decrease, the need for peak generating capacity there (Auffhammer et al., 2017).

4 While the risk of transgressing tipping points in the climate system increases as anthropogenic global warming continues , such changes occur at time scales (multiple decades up to centuries) not relevant for near-term adequacy planning.



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APPENDIXWe analysed the correlation of average LOLE hours per day and percentile rank categories for four indices (T1, T2, T3 and T4) other than the daily mean temperature (Tmean). The main reason for exploring different indices that LOLE may be correlated not only to instantaneously low temperatures, but also to persistent cold periods spreading over several days. The four indices considered here are:

Here, Ti denotes the daily mean temperature on day i. These indices therefore reflect different weighted averages of daily temperatures, including days preceding those with or without LOLE. The average LOLE hours for different categories based on percentile values of T1, T2, T3 and T4 are shown in Figure A1 (cf. Figure 6).

T1, i = (6Ti + 3Ti-1 + Ti-2)110

T2, i = (Ti + Ti-1 + Ti-2)13

T3, i = (Ti + Ti-1 + Ti-2 + Ti-3)14

T4, i = (Ti + Ti-1 + Ti-2 + Ti-3 + Ti-4)15



The histograms of average daily temperature observed for Belgium’s neighbouring countries during winter for the periods 1981-1990 and 2010-2019 are shown in Figure A3 (cf. Figure 8).

Figure A1: Simulated average LOLE hours per day for different percentile rank categories of different indices (T1, T2, T3 and T4) over Belgium. The width of each bar represents the number of days in each category.



Figure A3: Same as Figure 3 for France (FR), Germany (DE), the United Kingdom (UK) and the Netherlands (NL).

Figure A2: Number of days with average mean temperature over Belgium in the categories “1-in-1000-days” (top), “1-in-500-days” (middle), and “1-in-100-days” (bottom) categories over the period 1980-2019.



The PR values of events with country-average daily mean temperature in winter falling into three different extreme categories (occurring less than 1-in-1000, 1-in-500, and 1-in-100 days) have been tabulated in Table A1.

< 1-in-1000 days Pref Pnew PR

BE 0.33% 0.03% 0.08

FR 0.41% 0.00% 0.00

DE 0.25% 0.08% 0.33

UK 0.19% 0.14% 0.71

NL 0.30% 0.03% 0.09


BE 0.52% 0.11% 0.21

FR 0.58% 0.14% 0.24

DE 0.47% 0.16% 0.35

UK 0.41% 0.30% 0.73

NL 0.52% 0.08% 0.16


BE 1.73% 0.74% 0.43

FR 1.29% 1.01% 0.79

DE 1.78% 0.68% 0.38

UK 1.86% 0.88% 0.47

NL 1.59% 0.66% 0.41

Table A1: Probability ratio PR (reference period: 1981-1990, new period: 2010-2019) of the days with mean temperature across Belgium (BE), France (FR), Germany (DE), the United Kingdom (UK) and the Netherlands (NL) occurring, on average, less than once in 1000, once in 500, and once in 100 days during the period 1980-2019. Shown are the probabilities for the two periods and the corresponding PR.



We also calculated the histograms of daily mean winter temperature for all grid cells of a country—the “spatiotemporal” histogram (Figure A4), as opposed to the “temporal” histogram (spatially averaged; Figure 8). Based on this, we also calculate the “spatiotemporal” PR for the same three events, which is shown in Figure A5 and Table A2.

Figure A4: Histograms of the winter daily temperature (spatiotemporal histograms) during 1981-1990 and 2010-2019 in all grids across Belgium (BE), France (FR), Germany (DE), the United Kingdom (UK) and the Netherlands (NL).



Tmean below the 1.0 percentile value Pref Pnew PR

BE 1,63% O,80% O,49

FR 1.21% 0.73% 0.60

DE 1,61% O,77% O,47

UK 1.45% 0.72% 0.49

NL 1,57% O,68% O,43

Tmean below the 0.2 percentile value

Pref Pnew PR

BE 0.51% 0.11% 0.22%

FR 0.38% 0.12% 0.31

DE 0.40% 0.16% 0.40%

UK 0.39% 0.16% 0.41

NL 0.48% 0.09% 0.19%

Tmean below the 0.1 percentile value

Pref Pnew PR

BE 0.28% 0.04% 0.14

FR 0.22% 0.05% 0.23

DE 0.21% 0.07% 0.35

UK 0.22% 0.08% 0.36

NL 0.25% 0.04% 0.15

Table A2: “Spatiotemporal” Probability Ratio (PR). Probability of occurrence during the reference period (1981-1990) and the new period (2010-2019) of days with the daily mean temperature of a grid cell across Belgium (BE), France (FR), Germany (DE), the United Kingdom (UK) and the Netherlands (NL) below the 0.1, 0.2 and 1.0 percentile values of the daily mean temperature in all grid cells of the country for the period 1980-2019. Shown are the probabilities for the two periods and the corresponding PR.

Finally, Table A3 and Figure A6 show the median value of the PR when calculated separately for all grid cells in a country, and Table A4 and Figure A7 show the mean probability of all grid cells for the three percentile bins over every country and the corresponding PR, as the ‘spatial mean PR’.



< 1-in-1000 days PRBE 0.00

FR 0.08

DE 0.21

UK 0.41

NL 0.12

< 1-in-500 days PRBE 0.21

FR 0.23

DE 0.34

UK 0.43

NL 0.17

< 1-in-100 days PRBE 0.46

FR 0.66

DE 0.47

UK 0.50

NL 0.42

Table A3: “Spatial median” Probability Ratio (PR). Median value over Belgium (BE), France (FR), Germany (DE), the United Kingdom (UK) and the Netherlands (NL) of the pixel-level (reference period: 1981-1990, new period: 2010-2019) of the days with mean temperature below the 0.1, 0.2 and 1.0 percentile values for the period 1980-2019.

< 1-in-1000 days Pref Pnew PRBE 0.31% 0.02% 0.05

FR 0.32% 0.03% 0.08

DE 0.24% 0.06% 0.25

UK 0.22% 0.10% 0.44

NL 0.25% 0.03% 0.13

Table A4: “Spatial mean” Probability Ratio (PR). Mean value of the probability during the reference period (1981-1990) and new period (2010-2019) of the days with daily mean temperature across every grid cell of Belgium (BE), France (FR), Germany (DE), the United Kingdom (UK) and the Netherlands (NL) below the 0.1, 0.2 and 1.0 percentile values for the period 1980-2019. Shown are the probabilities for the two periods and the corresponding PR.

< 1-in-100 days Pref Pnew PRBE 1,66% 0,76% 0,46

FR 1.30% 0,84% 0.65

DE 1,62% 0,79% 0,48

UK 1.60% 0.85% 0.53

NL 1,67% 0,65% 0,39

< 1-in-500 days Pref Pnew PRBE 0.51% 0.11% 0.21

FR 0.50% 0.13% 0.24

DE 0.44% 0.15% 0.35

UK 0.43% 0.20% 0.73

NL 0.47% 0.09% 0.27



Figure A5: ‘Spatiotemporal’ probability ratio (PR), which is calculated based on the daily mean temperature in each grid cell across Belgium (BE), France (FR), Germany (DE), the United Kingdom (UK) and the Netherlands (NL) during new period (2010-2019) and reference period (1981-1990).

Figure A6: ‘Spatial median’ probability ratio (PR), which is the median value of the PR in all grid cells across Belgium (BE), France (FR), Germany (DE), the United Kingdom (UK) and the Netherlands (NL) during new period (2010-2019) and reference period (1981-1990).

Figure A7: ‘Spatial mean’ probability ratio (PR), which is calculated based on the average probability of events in all grid cells across Belgium (BE), France (FR), Germany (DE), the United Kingdom (UK) and the Netherlands (NL) during new period (2010-2019) and reference period (1981-1990).



© PHOTO'S IMAGGEO:

Niels ClaesTapani RepoRoshanak TootoonchiMichał KudKatja BiggeKatarzyna WalczakJulien SeguinotAdrian Navas Montilla

AUTHORS:

Yi YaoWim ThierySebastian Sterl

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