This is the author accepted manuscript (AAM) of the following published
article:

DOI | https://doi.org/10.1088/1748-9326/ad27b9
---|---
arXiv DOI | https://doi.org/10.48550/arXiv.2307.08909
|
author(s) |  Laurens P. Stoop, Karin van der Wiel, William Zappa, Arno Haverkamp, Ad J. Feelders, Machteld van den Broek
title |  The Climatological Renewable Energy Deviation Index (credi)
publication date | February 2024
journal | Enviromental Research Lettes
volume | 19
page numbers | 034021

This AAM version corresponds to the author’s final version of the article, as
accepted by the journal. However, it has not been copy-edited or formatted by
the journal.

This AAM is deposited under a Creative Commons Attribution–ShareAlike (CC-BY-
SA) license.

# The Climatological Renewable Energy Deviation Index (credi)

Laurens P. Stoop ,1,2,3,* Karin van der Wiel ,4 William Zappa ,3 Arno
Haverkamp ,3 Ad J. Feelders ,1 Machteld van den Broek5
1Information and Computing Science 0000-0003-2756-5653 0000-0001-9365-5759
0000-0001-6810-7224 0000-0001-6947-7892 0000-0003-4525-1949
0000-0003-1028-1742 Utrecht University the Netherlands
2Copernicus Institute of Sustainable Development Utrecht University the
Netherlands
3TenneT TSO B.V Arnhem the Netherlands
4Royal Netherlands Meteorological Institute (KNMI) the Netherlands
5Delft University of Technology Faculty Technology Policy and Management the
Netherlands
*Corresponding Author<EMAIL_ADDRESS>

###### Abstract

We propose an index to quantify and analyse the impact of climatological
variability on the energy system at different timescales. We define the
Climatological Renewable Energy Deviation Index (credi) as the cumulative
anomaly of a renewable resource with respect to its climate over a specific
time period of interest. For this we introduce the smooth, yet physical,
hourly rolling window climatology that captures the expected hourly to yearly
behaviour of renewable resources. We analyse the presented index at decadal,
annual and (sub-)seasonal timescales for a sample region and discuss
scientific and practical implications.
credi is meant as an analytical tool for researchers and stakeholders to help
them quantify, understand, and explain, the impact of energy-meteorological
variability on future energy system. Improved understanding translates to
better assessments of how renewable resources, and the associated risks for
energy security, may fare in current and future climatological settings. The
practical use of the index is in resource planning. For example transmission
system operators may be able to adjust short-term planning to reduce adequacy
issues before they occur or combine the index with storyline event selection
for improved assessments of climate change related risks.

Keywords: Resource droughts, Resource Adequacy, Renewable Energy Drought,
Dunkelflaute, Wind Drought

## 1 Introduction

The energy system is changing. This is due to the increased deployment of
renewable energy generators, like wind turbines and solar panels; changes in
electricity demand, from increased use of heat pumps and electric vehicles;
and climatic changes influencing the weather dependent parts of the system. It
is crucial to understand the full dynamics of the (future) energy system, both
for policy making and energy security reasons [1].

Knowing the impact of and link between the energy system and weather-related
variability on daily to inter-annual and decadal timescales is vital for
robust design and planning of future energy systems [2, 1, 3]. Meteorological
variability leads to temporal variability. Not only in renewable energy
production, but also in energy demand, changing the way energy systems have to
be operated and controlled [1].

Energy system models are vital to capture the impact of this variability [4].
However, their complexity results in high computational burdens that grows
exponentially with the simulation period [5, 6, 1, 7, 8]. Incorporating large
climate datasets that capture energy-meteorological variability in
_operational hourly_ energy system models is thus, as of yet, unfeasible [9,
1, 7]. Even so, understanding the scale of this variability, can aid system
operators in their task to ensure both short- and long-term energy security
[1, 7, 10]. Therefore, alternative approaches are needed to assess energy-
meteorological variability [1, 11]. While a number of methods exists to model
and/or select challenging high impact events using basic statistical
principles [[,
e.g.]]vanderwiel2019extreme,Ohlendorf2020,OteroFelipe2021,stoop2021detection,vanderMost2022,Boston2022,Hu2023,Allen2023,
we aim to define a physics based and intuitive to understand metric to
quantify energy-meteorological variability across timescales.

In developing this metric, we were inspired by the hydrological sciences. For
drought monitoring, a number of indices have proven useful for both scientific
assessment and operational use. These drought indices, such as the
Climatological Water Balance [[, CWB;]]gleick1985regional,Gleick1986, the
Standardised Precipitation Index [[, SPI;]]mckee1993, and the Standardised
Precipitation-Evapotranspiration Index [[, SPEI;]]VicenteSerrano2010), are
based on precipitation deficits (anomaly of precipitation, or anomaly of the
difference between potential evapotranspiration and precipitation) and are
used to assess the temporal development of dry or wet periods. Furthermore,
they have been used to assess the influence of inter-annual to multi-decadal
variability, and of climate change on the temporal variability of hydrological
drought [[, e.g.]]Quiring2009,Stagge2015,Cammalleri2021,vanderWiel2022. As
[18] showed, some aspects of these indices and their use in assessing
hydrological variability can be transferred to the energy-meteorological
domain. However, where [18] developed direct analogues of the SPI and SPEI
metrics using probabilistic descriptions, we took inspiration from aspects of
these metrics, their use in operational applications, and combined this with
the need for physically grounded storylines in energy system operation.

We define the Climatological Renewable Energy Deviation Index (credi) as the
cumulative anomaly of a renewable resource with respect to its climate over a
specific time period of interest (Figure 1). Given this definition, this study
addresses the following considerations: (a) how do you define the climatic
behaviour of a highly variable renewable resource, like wind or solar? and (b)
how do you analyse the credi score at different timescales; like
(sub-)seasonal, annual, or multi-decadal?

Figure 1:  Illustration of climatological renewable energy deviation index.
Given the climate of a renewable resource (black line in panel a), the
instantaneous anomaly can be calculated (orange/teal bars in panel a).
Positive anomalies (orange) increase, and negative anomalies (teal) decrease
the index, which starts at zero at the start of period of analysis (panel b).
The illustration shows solar potential anomalies for 2021 with respect to a
1991-2020 climate, and the solar credi with a starting point at 1 March. Two
meteorological forecast ensemble members converted to credi are shown to
indicate a use-case for grid-operators.

The paper is structured as follows. In Section 2, we define the hourly rolling
window climate and the index. In Section 3, we indicate the data used. In
Section 4, we analyse the index at different timescales and discuss the best
starting point. In the Section 5 we discuss our definition of the index.
Finally, in Section 6, a synthesis of our findings is presented and potential
use cases in research and/or operational application are outlined. Supporting
Information (SI) with additional figures and observational analysis is
available online.

## 2 Definition of the climatic characterisation and index

Within the atmospheric sciences the climate of a region is defined as the
statistical-mean weather conditions prevailing in that region [27]. The [[,
WMO;]]wmo2017normals has a standardised method for calculation of the
_climatological normals_ , which comes down to calculating monthly or daily
mean values over a 30-year period. The climate, or mean expected behaviour, of
renewable resources could be defined similarly. However, monthly or daily
climatological values are not suitable due to the highly variable nature of
renewable resources like wind and solar energy, and the need to balance the
power grid at shorter timescales.

We can distinguish four relevant timescales that cover the main modes of
energy-meteorological variability. Namely:

  1. 1.

annual to decadal timescales: variability caused by interactions in the
coupled ocean-atmosphere-system, e.g. modes of variability like the El-Niño-
Southern Oscillation [[, ENSO;]]ipcc6_wg1_variability or the North Atlantic
Oscillation [[, NAO;]]Wanner2001,

  2. 2.

seasonal timescale: variability caused by the revolution of the Earth around
the Sun and the directly related variation of the solar declination angle,

  3. 3.

sub-seasonal timescale: variability caused by the cumulative interplay at
various timescales, associated with the passing of weather systems and the
changes in their persistence and occurrence,

  4. 4.

daily timescale: variability caused by the revolution of the Earth around its
axis, and the directly related times of sunrise, sunset, and the solar
elevation angle.

When studying the generation potential of wind or solar, all these timescales
of variability should be considered.

### 2.1 A climatology of renewable resources and the use of hourly rolling
windows

The highly variable nature of the wind and solar resources makes that a
straightforward 30-year daily mean does not result in a useful definition of
their climate (see SI Section A). The same holds for an initial estimate by
averaging each ordinal hour over 30 years (Figure 2a,c). Though this simple
average-based climatology does capture the mean expected behaviour on annual
timescales, the random fluctuations from day-to-day and hour-to-hour cannot be
explained by physical processes in this climatological definition. To remove
these random fluctuations more data would be needed to obtain the desired,
physical, smooth , but physical, climatology. However, considering a period
longer than 30-years is ineffective, as climate change would start to
influence the result[28]. Applying a simple running mean to this simple
average-based climate timeseries is undesirable, as that would remove the
diurnal cycle, which has a physical origin and is of large importance for our
application in the energy sector.

We therefore define an _hourly rolling window_ climate, meaning that we first
group the same time of day, and then, for each ’hour-of-the-day’-group, we
apply a 30-year running mean (see SI Section A.2). The hourly rolling window
climate ($C$) of a renewable resource potential $P$ for hour-of-the-year $h$
is computed by:

$C_{P}(h)=\frac{1}{n}\sum_{y=1}^{n}\leavevmode\nobreak\
\sum_{h^{\prime}\in\\{h+24d\\}_{d=-\Delta}^{d=+\Delta}}\leavevmode\nobreak\
\frac{P(y,h^{\prime})}{2\Delta+1},\hskip 28.45274pth=1,2,\ldots,8760$ (1)

where $n$ is the number of years, $h$ is the hour of the year from 1 to 8760,
$\Delta$ is half the window size (days) and $P(y,h^{\prime})$ is the
generation potential for hour $h^{\prime}$ of year $y$. In line with [27] an
unweighted average and $n=$ 30 years are used. See Figure 2 for a comparison
between the different methods.

Figure 2:  Comparison of different methods for computing the climate of the
potential generation for wind (top), and solar (bottom), for the period
1991-2020. Figures (a,c) show the hourly generation potentials for each year
in this period (light blue for wind and orange for solar), the simple average-
based climate (grey, see main text for details) and the hourly rolling window
climate (blue and red, for wind, solar, respectively). Figures (b,d) show the
same, but specifically for the period 3-10 April 2003. For clarity only 13:00
for each day of the year is shown in Figure (c).

It should be noted that two details where omitted in formula 1. First, the
hour-of-the-year is cyclic in nature, meaning that the first hour of year $y$
follows the last hour of year $y-1$. While this is implemented, for reasons of
clarity this is not included. Second, to deal with leap years, we discard
February 29th when computing the climatology. The climatology of each hour of
the day for February 29th is then defined by the mean value of that hour of
the day of February 28th and March 1st. This addresses the lack of data for 29
February and keeps a simple formalism.

The choice for the size of the rolling window is somewhat arbitrary.
Sensitivity tests indicate that the window size should be bigger then 20 days
to smooth any remaining nonphysical day-to-day variability, but smaller then
60 days to avoid over-smoothing the annual cycle (SI Section A.3). Within this
range the exact size of the window does not affect the use of the index. Here,
we choose a window size of 40 days.

By using the hourly rolling window climate, both the importance of the various
timescales and the need for more data points to get a smooth climatological
function are addressed. It is essential that the climatological definition
used in the calculation of the deviation index for wind or solar energy is
physical (i.e. does not contain random fluctuations), such that anomalies
represent variability due to the weather, decoupled from the climate.

### 2.2 The Climatological Renewable Energy Deviation Index (credi)

We define the credi to be the cumulative anomaly of a renewable resource with
respect to its climate over a specific time period of interest from a chosen
starting point in two steps (Figure 1). First, we determine the anomaly of a
renewable resource, as the difference between the hourly generation potential
of that resource and its climate (i.e. its expected value), taken from the
computed hourly rolling window climate. Second, from an initial chosen
starting point we sum these anomalies over a time period of interest.

More formally: let $P(y,h)$ denote the generation potential for ordinal hour
$h$ of year $y$, and let $C_{P}(h)$ denote the climate for ordinal hour $h$
for that potential $P$. The anomaly $A_{C}(y,h)$ of a renewable resource for
ordinal hour $h$ of year $y$ is then defined as:

$A_{C}(y,h)=P(y,h)-C_{P}(h).$ (2)

The credi over a given period of time is defined as the cumulative sum (or
running total) of $A_{C}$ over that period. For example, if we align the
starting point with the start of the year, the credi on the $i$-th hour of
that year ($y$) is:

$\mbox{{\sc credi}}(y,i)=\sum_{h=1}^{i}A_{C}(y,h),\hskip
56.9055pti=1,2,\ldots,8760$ (3)

When interpreting the index, the following should be considered. A change in
credi over time is an indication of either an excess or deficit of the
renewable resource potential with respect to its climatic normal (Figure 1b).
A stable credi over a period indicates nominal renewable resource potential
with respect to its climate.

Specifically, the credi score has the unit Full Load Hours (FLH) and at a
given time informs the user of the cumulative surplus or deficit generation
potential over the period considered with respect to its nominal behaviour. So
given a fixed time window, the distribution of the credi score calculated then
provides insight into the properties of a connected storage unit, like the
(dis-)charge potential. FLHs depend on the installed capacity, therefore if
the installed capacity of a resource is known or assumed, the index allows for
direct assessment of the storage volume and power needed to always generate
nominally within the fixed time window used.

For clarity, when the index is applied to a specific resource, we first refer
to the resource before the index acronym is given. For example, the wind credi
refers to an assessment of the credi of wind energy potential, and similarly
for solar.

### 2.3 The use of storylines in analysing credi

The index can be used to assess the temporal development of anomalous
renewable energy generation. In line with the application of hydrological
drought indices, a physical storylines approach [31, 32] could be used. This
approach can use regional climate change information while avoiding the strict
limitations of a normal confidence-based approach applied in climate science.
Storylines can be used to gain more insight into the driving processes,
identify event analogues, and investigate similar events in alternative energy
systems or under future climate conditions. Utilising these insights in, for
example, resource adequacy assessments or system design studies, will likely
lead to a more robust energy system.

Selection of relevant events can be based on historical adequacy assessments
(like the [33] Adequacy Outlook). As shown by [12, 32], event analogues can
then be found in large energy-climate datasets that incorporate climate change
[1, 11]. By studying these analogues the physical processes and likelihood of
these events can be assessed.

To demonstrate the index at different timescales and to highlight relevant
considerations in the application of the credi, we selected the years 1996,
1998, 2003 and 2016 as storylines. The year 1996 was chosen specifically, as
one of the most challenging years for resource adequacy in the Netherlands and
Germany in a future net-zero emission energy system [[]p.56]tennet2023. In the
analysis of the potential for hydrogen generation from wind, 2003 and 2010
where found to be anomalously low [[]p.58-61]tennet2023. Both 1998 and 2016
where chosen as they represent the most anomalous years of the index for solar
and wind, respectively.

## 3 Data

We used the preliminary 4th version of the Pan-European Climate Database to
demonstrate the credi in this paper [[, PECDv4.0;]]Dubus2022PECD. This
database, developed by Copernicus Climate Change Services (C3S) in cooperation
with the European Network of Transmission System Operators for Electricity
(ENTSO-E) will be the new standard database used for all common Transmission
System Operator (TSO) studies. The full database will be openly available as
part of the new C3S-Energy dataset, expected in late 2023
(https://climate.copernicus.eu/energy/).

To showcase the developed index all figures show data from the preliminary
PECDv4.0 of the northern region of the Netherlands. This region is the NUTS
statistical region ‘NL1’ and covers the provinces of Groningen, Friesland and
Drenthe, see:
https://en.wikipedia.org/wiki/NUTS_statistical_regions_of_the_Netherlands.
While the region is named ‘NL01’ in the PECD dataset, the NUTS-code is used
here. While we focus in the main paper on the NL1 region, in the supplement we
show additional regions reflecting some of the diversity within Europe.
Further details in SI Section F.

## 4 Application of the credi at different timescales

In this section we show the application of the index at decadal, seasonal and
sub-seasonal timescales in the context of modelling future energy systems. The
considerations associated with choosing a starting point for the credi
calculation is especially relevant at (sub-)seasonal timescales, and will be
discussed.

On daily timescales the weather is extremely variable, but it depends on local
conditions and short-term battery storage comes into play [34]. For most
regions the maximum cost-effective storage based on the surplus charging
capacity from wind and/or solar is in the order of 8 hours to 4 days [35, 36,
34]. For these reasons, we make no assessment on daily timescales here.
However, due to the relevance of short-term events for the energy system, an
example of a 8-day study window in credi is provided.

### 4.1 Annual to decadal variability in credi

At annual to decadal timescales the index can be used to assess the impact of
large scale oscillations in the ocean and atmosphere on the availability of a
renewable energy resource. These long-term deviations from the climate are
relevant, e.g., because they offer sources of meteorological predictability
[37, 38], or because stakeholders look at 10 year time periods to estimate
return of investments [33].

Over the past 30 years, large inter-annual variation is observed in the wind
credi (Figure 3a). The cumulative effect of variations at seasonal scales
resulted in higher than expected wind generation potential from 1991 to 2002,
while from 2010 onwards wind credi declined indicating lower than expected
wind generation potential. These general variations are in line with those
found by [39, 15].

Similarly, the solar credi shows inter-annual variability. From 1991 to 2003
solar credi shows a general decrease, indicating less than average potential
generation from solar. Within this period, a strong reduction in the periods
1993-1995 and 1998-2002 is observed (Figure 3b). In the period 2005-2018,
solar credi is flat, showing that the solar potential was as expected from
climate. After this period a steady increase in the solar credi is observed,
indicating higher than expected potential generation.

Figure 3:  Hourly Wind (a) and Solar (b) credi over the period 1991-2020 for
‘NL1’. As the climate was calculated over the same period, by definition the
credi sums to zero over the full period.

The values of solar credi are generally lower than those of the wind credi.
This is directly related to the diurnal cycle, which by definition gives zero
solar potential at night and low values in the morning and evening.
Consequently, the sum of the anomalies over a given period is smaller than for
wind potential, which has values for all 24 hours in a day.

Finally, while the impact of the relative observed variability depends on the
ratio of installed capacities, we observe that the inter-annual energy-
meteorological variability is mainly driven by the wind resource in the
analysed region (i.e., the northern of the Netherlands). And though the wind
and solar credis show strong anti-correlated behaviour during some years (e.g.
from 1991 to 2002), in others this is not the case (e.g. from 2004 to 2005).
At decadal timescales, wind and solar balance the system somewhat, but they
are not suited to fully negate the variability of their counterpart.

### 4.2 Seasonal variability in credi

When assessing the seasonal energy-meteorological variability using the credi,
the starting point determines the way the temporal development of the index is
perceived. In line with definitions of hydrological drought, the starting
point determines the separation between energy surplus (wet) and deficit (dry)
years. As the index is intended to capture the energy-meteorological
variability, the start date is picked such that the biggest range if credi at
the end of, and throughout, the year is observed.

Comparing credi starting points for each month of the year, we found that
these should _not_ be the same for wind and solar (SI Section B). We use May
1st as the starting point for wind, as it gives the widest distribution of the
index at the end of the analysis window in this particular region. For solar
no clear distinction is found between a December or January starting point, we
chose to use January 1st here.

For the yearly wind credi, it is obvious that an individual year can either be
anomalously positive or negative, and that variations throughout a year are
large (Figure 4a). This results in a wide range of yearly storylines. The
25-75% spread of the index grows to $\pm 180$ FLH over a year (Figure 4b). The
most extreme negative year in the period considered for wind credi was 2016.
In that year, from about September onwards, the wind potential was almost
consistently below expected with $350$ less FLHs at the end of the analysed
period.

Figure 4:  Hourly wind credi per analysis year over the period May 1991 to
April 2021 for ‘NL1’. Figure a) shows the specific progression of wind credi
for each year (blue lines). Figure b) shows the distribution of the wind credi
for each hour of the year, namely the 50th percentile (blue line), the 25-75,
10-90 percentile and min-max range (shaded blue, see legend). Four exemplary
storylines are shown, namely 1996 (red), 1998 (green), 2003 (purple) and 2016
(black).

As an example of the use of wind credi for storyline analysis we look at 1996.
From May to October the index is relatively flat, indicating that the wind
potential was as expected from its climate (red line in Figure 4b). Then, a
strong reduction is observed in the wind credi from December to the end of
January, indicating much lower then average potential generation from wind.
Part of this deviation is compensated by higher than normal generation
potential in February of 1997.

As noted earlier, values of yearly solar credi are smaller than of wind credi
(Figure 5a), with an average spread (25-75%) of $\pm 18$ FLHs, and uncommon
spread (10-90%) of $\pm 35$ FLHs spread over a year (Figure 5b). This
indicates that ~18 FLHs of total energy is needed to cover the deficit of the
installed solar capacity in 50 % of years and ~35 FLHs to cover 80% of years
(Figure 5).

The most extreme year of high solar potential was 2003; the most extreme year
of low solar potential was 1998. Especially 2003 is remembered for its
extremely warm and sunny summer [40].

Figure 5:  Hourly solar credi per year over the period 1991-2020 for ‘NL1’. As
shown in Figure 4, but the solar credi is shown in orange hues.

### 4.3 Sub-seasonal variability in credi

At sub-seasonal timescales, similar to seasonal, the start point determines
the way the temporal development of the index is perceived. We use
’energy’-seasons to capture the large scale changes on sub-seasonal
timescales. For wind we define two seasons of interest: September to March,
and April to August. For brevity, only the results found for wind in the
winter ‘energy’-season are shown here, see SI Section C for the other and
solar. Alternative definitions of ’energy’-seasons can be relevant, especially
for regions that have different sub-seasonal behaviour then the ‘NL1’-region
shown here.

It is obvious that different years show quite different characteristics
(Figure 6a) and individual winter seasons can differ greatly. As expected, the
sub-seasonal timescale is emphasised more. For instance, the anomalous index-
development in 1996 described in Section 4.2 is more clearly visible.
Especially the strong reduction in wind credi from December to the end of
January stands out as a period of much lower than normal wind generation
potential.

Figure 6:  Hourly winter wind credi per season (Sep.-Apr.) for 1991-2021 for
‘NL1’. Figure a) shows the specific progression of wind credi for each summer
season (blue lines). In addition, four example storylines are represented,
namely those starting in 1996 (red), 1998 (green), 2003 (purple) and 2016
(black). Figure b) shows two storylines (1996, 2003) and the hourly
distribution of the wind credi, namely the 50th percentile (blue line), the
25-75, 10-90 percentile, and min-max range (shaded blue, see legend).

### 4.4 A short-term study window for event-based credi

Finally, short-term events, e.g. _Dunkelflautes_ , can pose significant risk
to highly renewable energy systems [41, 42, 12, 43, 44]. A 8-day window for
credi aligns with previous work [33], and is investigated here, see SI Section
D for additional figures and the top 50 8-day events.

For short-term event analysis we do not pre-define the start point, all 8-day
windows are considered. Overlapping events that share a five or more days, are
removed from the analysis. While we only consider the lowest final credi value
for our event selection, other impact selection methods as described by [32]
can be used.

Again we noted the large weather-caused variability between different 8-day
periods (Figure 7a). The computed spread in Figure 7b considers events
throughout the year. This can also be investigated on a seasonal basis for
winter or summer-specific event information, or for shorter or longer events.

The most extreme event is from 16-24 jan. 2017 and the analysis year 2016 is
present 3 times in the top 50 events. While the specific 8-day event found in
[33] is not the most extreme event, the analysis year 1996 does show up four
times in the top 50 events. Indicating that the analysis year 1996 indeed
stands out as quite exceptional.

Figure 7:  Hourly winter wind credi during 8-days for all events with less
then 5 days overlapping in the period May 1991 to April 2021 for ‘NL1’. The
storylines show the analysis years 1996 (red, 4x), 1998 (green, 1x), 2003
(purple, 1x) and 2016 (black, 3x). Further formatting as shown in Figure 6.

## 5 Discussion

The presented index is defined as the cumulative anomaly of a renewable
resource with respect to its climate. The method of determining the climate is
thus vital and, as shown, should take into account the strong diurnal and
annual cycle present in renewable energy resources. The calculation of the
climate used here has a dependence on the size of the rolling window, which
was primarily based on expert judgement. A longer timeseries, covering many
decades, could be used for a cross-validation check to obtain the optimum
_rolling window_ size, but the data source should be selected with great care,
due to potential inconsistencies [39, 45, 46]. In previous work a climatic
definition on harmonics has been effective [47, 48, 49], but we found it
unsuitable here (see SI Section A.3).

credi should not be confused with the standardised energy indices recently
introduced by [18]. While we have been inspired by indices for monitoring
hydrological droughts, their standardised energy indices are direct analogues.
Meaning that those indices are a pure statistical assessment of the observed
variance that rely heavily on the empirical distribution functions used [[,
See Section 2]p.2-3]Allen2023. However, in energy system operation and
control, the specific sequence of observations and the deviation with respect
to the expected patterns matter. The credi presented incorporates these
aspects.

When combined with weather forecasts, indices for hydrological drought can
help policy makers make early decisions regarding societal risks [23, 24, 25,
26]. However, the operation of the electricity grid requires balance on very
short timescales [1, 33]. While we presented our index with an hourly
resolution, further research is needed to investigate if the credi can also be
applied on these very short timescales. The examples provided, however, do
already show credi’s usefulness in resilience planning, resource adequacy
assessments, and as a metric for selecting events for robustness analysis.

In this introduction of the index, we applied it to the northern region of the
Netherlands. However, as shown by [50], energy-meteorological variability is
strongly region dependent. Therefore, the credi should be calculated and
analysed for each region separately. Due to the ease of application, and the
intuitive analysis and interpretation of the index, this application to other
regions is relatively straightforward (see SI Section E for a few additional
regions).

## 6 Conclusion

Drawing inspiration from the work on drought monitoring indices, we have
presented the hourly rolling window climatology and Climatological Renewable
Energy Deviation Index (credi). Given the relevance of both the diurnal and
annual cycle in meteorology for energy applications, we recommend a simple but
suitable definition of the background climate using an hourly rolling window
approach. This new index is meant as an analytical method for researchers and
stakeholders to help them understand and explain the impact of the variable
nature of the weather on the energy system. The index computes the cumulative
deviation or anomaly from the climatology for a chosen period.

The index can be used when understanding of energy-meteorological variability
is key. For example, the credi can be used as part of a resource adequacy
analysis from TSOs to identify events which are likely to be a challenge in
maintaining security of supply in a (future) power system driven by renewable
energy sources. At the same time, the credi could be used to assess the volume
and power output of back-up resources needed for a given timescale, region,
and energy system design. Then, by using the event selection and analysis, as
e.g. in [32] for hydrological extremes, detailed event descriptions can be
developed, systems can be stress tested, and further insight could be gained
into energy-meteorological variability.

## CRediT Author Statement

Conceptualisation, Formal Analysis and Visualisation: LPS, Investigation,
Methodology and Writing - Original Draft: LPS, KvdW, Writing - Review &
Editing: _All listed authors_ , Supervision and Funding acquisition: _AJF,
MvdB_.

## Acknowledgments

Laurens P. Stoop received funding from the Dutch Research Council (NWO) under
grant number 647.003.005. The content of this paper and the views expressed in
it are solely the author’s responsibility, and do not necessarily reflect the
views of TenneT TSO B.V..

## Open research

The implementation of the credi, its use at different timescales, all code
used to generate the figures, the data from the ‘NL1’ region discussed and the
full list of the most extreme short-term events found as presented in this
study are available at Github via https://github.com/laurensstoop/ccmetrics
with the MIT license.

The full preliminary dataset of the PECDv4 containing the regional renewable
resource potential for other technological definitions of wind and solar, or
regions, then used in this study are not available due to ongoing validation.
In due time the full PECDv4, including raw gridded and aggregated
regional/national renewable resource potentials for a wide range of
technological definitions, will be made available as part of the C3S Energy
dataset and can be found through https://climate.copernicus.eu/operational-
service-energy-sector. The framework describing the new C3S-Energy dataset,
part of which is the PECDv4, can be found on:
https://climate.copernicus.eu/c3s2412-enhanced-operational-services-energy-
sector.

## References

  * [1] Michael T. Craig et al. “Overcoming the disconnect between energy system and climate modeling” In _Joule_ , 2022 DOI: 10.1016/j.joule.2022.05.010
  * [2] H.. Bloomfield et al. “The Importance of Weather and Climate to Energy Systems: A Workshop on Next Generation Challenges in Energy–Climate Modeling” In _Bulletin of the American Meteorological Society_ , 2021 DOI: 10.1175/bams-d-20-0256.1
  * [3] Russell McKenna et al. “High-resolution large-scale onshore wind energy assessments: A review of potential definitions, methodologies and future research needs” In _Renewable Energy_ , 2022 DOI: 10.1016/j.renene.2021.10.027
  * [4] David EHJ Gernaat et al. “Climate change impacts on renewable energy supply” In _Nature Climate Change_ , 2021 DOI: 10.1038/s41558-020-00949-9
  * [5] Rogier H. Wuijts, J.M. van den Akker and Machteld Broek “Effect of modelling choices in the unit commitment problem” In _Energy Systems_ , 2023 DOI: 10.1007/s12667-023-00564-5
  * [6] James Price and Marianne Zeyringer “highRES-Europe: The high spatial and temporal Resolution Electricity System model for Europe” In _SoftwareX_ , 2022 DOI: 10.1016/j.softx.2022.101003
  * [7] Rogier H. Wuijts et al. “Linking Unserved Energy to Weather Regimes” In _Submitted to: Earth’s Future_ , 2023 DOI: 10.48550/arXiv.2303.15492
  * [8] Aleksander Grochowicz, Koen van Greevenbroek, Fred Espen Benth and Marianne Zeyringer “Intersecting near-optimal spaces: European power systems with more resilience to weather variability” In _Energy Economics_ , 2023 DOI: 10.1016/j.eneco.2022.106496
  * [9] Inès Harang, Fabian Heymann and Laurens P. Stoop “Incorporating climate change effects into the European power system adequacy assessment using a post-processing method” In _Sustainable Energy, Grids and Networks_ , 2020 DOI: 10.1016/j.segan.2020.100403
  * [10] Jing Hu et al. “Implications of a Paris-proof scenario for future supply of weather-dependent variable renewable energy in Europe” In _Advances in Applied Energy_ , 2023 DOI: 10.1016/j.adapen.2023.100134
  * [11] Laurent Dubus et al. “Towards a future-proof climate database for European energy system studies” In _Environmental Research Letters_ , 2022 DOI: 10.1088/1748-9326/aca1d3
  * [12] K. Van der Wiel et al. “Meteorological conditions leading to extreme low variable renewable energy production and extreme high energy shortfall” In _Renewable and Sustainable Energy Reviews_ , 2019 DOI: 10.1016/j.rser.2019.04.065
  * [13] Nils Ohlendorf and Wolf-Peter Schill “Frequency and duration of low-wind-power events in Germany” In _Environmental Research Letters_ , 2020 DOI: 10.1088/1748-9326/ab91e9
  * [14] Noelia Otero Felipe et al. “A Copula-Based Assessment of Renewable Energy Droughts Across Europe” In _SSRN Electronic Journal_ , 2021 DOI: 10.2139/ssrn.3980444
  * [15] Laurens P. Stoop, Erik Duijm, Ad Feelders and Machteld van den Broek “Detection of Critical Events in Renewable Energy Production Time Series” In _Advanced Analytics and Learning on Temporal Data_ , 2021 DOI: 10.1007/978-3-030-91445-5\\_7
  * [16] L. Van der Most et al. “Extreme events in the European renewable power system: Validation of a modeling framework to estimate renewable electricity production and demand from meteorological data” In _Renewable and Sustainable Energy Reviews_ , 2022 DOI: 10.1016/j.rser.2022.112987
  * [17] Andy Boston, Geoffrey D Bongers and Nathan Bongers “Characterisation and mitigation of renewable droughts in the Australian National Electricity Market” In _Environmental Research Communications_ , 2022 DOI: 10.1088/2515-7620/ac5677
  * [18] Sam Allen and Noelia Otero “Standardised indices to monitor energy droughts” In _Renewable Energy_ , 2023 DOI: 10.1016/j.renene.2023.119206
  * [19] Peter H Gleick et al. “Regional hydrologic impacts of global climatic changes” In _Arid Lands: Today and Tomorrow_ , 1985
  * [20] Peter H. Gleick “Methods for evaluating the regional hydrologic impacts of global climatic changes” In _Journal of Hydrology_ , 1986 DOI: 10.1016/0022-1694(86)90199-x
  * [21] Thomas B McKee, Nolan J Doesken and John Kleist “The relationship of drought frequency and duration to time scales” In _Proceedings of the 8th Conference on Applied Climatology_ , 1993 Boston URL: https://climate.colostate.edu/pdfs/relationshipofdroughtfrequency.pdf
  * [22] Sergio M. Vicente-Serrano, Santiago Begueria and Juan I. Lopez-Moreno “A Multiscalar Drought Index Sensitive to Global Warming: The Standardized Precipitation Evapotranspiration Index” In _Journal of Climate_ , 2010 DOI: 10.1175/2009jcli2909.1
  * [23] Steven M. Quiring “Monitoring Drought: An Evaluation of Meteorological Drought Indices” In _Geography Compass_ , 2009 DOI: 10.1111/j.1749-8198.2008.00207.x
  * [24] James H. Stagge, Irene Kohn, Lena M. Tallaksen and Kerstin Stahl “Modeling drought impact occurrence based on meteorological drought indices in Europe” In _Journal of Hydrology_ , 2015 DOI: 10.1016/j.jhydrol.2015.09.039
  * [25] Carmelo Cammalleri et al. “The effects of non-stationarity on SPI for operational drought monitoring in Europe” In _International Journal of Climatology_ , 2021 DOI: 10.1002/joc.7424
  * [26] K. Van der Wiel, T.J. Batelaan and N. Wanders “Large increases of multi-year droughts in north-western Europe in a warmer climate” In _Climate Dynamics_ , 2022 DOI: 10.1007/s00382-022-06373-3
  * [27] Anthony Arguez and Russell S. Vose “The Definition of the Standard WMO Climate Normal: The Key to Deriving Alternative Climate Normals” In _Bulletin of the American Meteorological Society_ , 2011 DOI: 10.1175/2010bams2955.1
  * [28] World Meteorological Organization “WMO guidelines on the calculation of climate normals”, 2017 URL: https://library.wmo.int/doc%5C_num.php?explnum%5C_id=4166
  * [29] IPCC “Annex IV: Modes of Variability [Cassou, C., A. Cherchi, Y. Kosaka (eds.)]” In _Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change_ , 2021 DOI: 10.1017/9781009157896.018
  * [30] Heinz Wanner et al. “North Atlantic Oscillation – Concepts And Studies” In _Surveys in Geophysics_ , 2001 DOI: 10.1023/a:1014217317898
  * [31] Theodore G. Shepherd “Storyline approach to the construction of regional climate change information” In _Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences_ , 2019 DOI: 10.1098/rspa.2019.0013
  * [32] K. Van der Wiel, G. Lenderink and H. De Vries “Physical storylines of future European drought events like 2018 based on ensemble climate modelling” In _Weather and Climate Extremes_ , 2021 DOI: 10.1016/j.wace.2021.100350
  * [33] TenneT “Adequacy Outlook”, 2023 URL: https://www.tennet.eu/nl/nieuws/leveringszekerheid-van-elektriciteit-een-volledig-duurzaam-elektriciteitssyteem
  * [34] Maximilian Parzen, Davide Fioriti and Aristides Kiprakis “The Value of Competing Energy Storage in Decarbonized Power Systems”, 2023 arXiv:2305.09795 [physics.soc-ph]
  * [35] Hannah G. Livingston and Julie K. Lundquist “How many offshore wind turbines does New England need?” In _Meteorological Applications_ , 2020 DOI: 10.1002/met.1969
  * [36] Nestor A. Sepulveda et al. “The design space for long-duration energy storage in decarbonized power systems” In _Nature Energy_ , 2021 DOI: 10.1038/s41560-021-00796-8
  * [37] Ed Hawkins and Rowan Sutton “The Potential to Narrow Uncertainty in Regional Climate Predictions” In _Bulletin of the American Meteorological Society_ , 2009 DOI: 10.1175/2009bams2607.1
  * [38] A.. Scaife et al. “Skillful long-range prediction of European and North American winters” In _Geophysical Research Letters_ , 2014 DOI: 10.1002/2014gl059637
  * [39] Jan Wohland, Nour Eddine Omrani, Noel Keenlyside and Dirk Witthaut “Significant multidecadal variability in German wind energy generation” In _Wind Energy Science_ , 2019 DOI: 10.5194/wes-4-515-2019
  * [40] R. Garcia-Herrera et al. “A Review of the European Summer Heat Wave of 2003” In _Critical Reviews in Environmental Science and Technology_ , 2010 DOI: 10.1080/10643380802238137
  * [41] Paulina Tedesco, Alex Lenkoski, Hannah C Bloomfield and Jana Sillmann “Gaussian copula modeling of extreme cold and weak-wind events over Europe conditioned on winter weather regimes” In _Environmental Research Letters_ , 2023 DOI: 10.1088/1748-9326/acb6aa
  * [42] Fabian Mockert, Christian M. Grams, Tom Brown and Fabian Neumann “Meteorological conditions during Dunkelflauten in Germany: Characteristics, the role of weather regimes and impacts on demand”, 2022 DOI: 10.48550/ARXIV.2212.04870
  * [43] Bowen Li, Sukanta Basu and Simon J. Watson “Automated Identification of “Dunkelflaute” Events: A Convolutional Neural Network–Based Autoencoder Approach” In _Artificial Intelligence for the Earth Systems_ , 2022 DOI: 10.1175/aies-d-22-0015.1
  * [44] Srihari Sundar et al. “Meteorological Drivers of Resource Adequacy Failures in Current and High Renewable Western U.S. Power Systems”, 2022 DOI: 10.31223/x57d2g
  * [45] Jan Wohland “Process-based climate change assessment for European winds using EURO-CORDEX and global models” In _Environmental Research Letters_ , 2022 DOI: 10.1088/1748-9326/aca77f
  * [46] Clara Deser and Adam S. Phillips “A range of outcomes: the combined effects of internal variability and anthropogenic forcing on regional climate trends over Europe” In _Nonlinear Processes in Geophysics_ , 2023 DOI: 10.5194/npg-30-63-2023
  * [47] A.. Sabziparvar et al. “Geographical factors affecting variability of precipitation regime in Iran” In _Theoretical and Applied Climatology_ , 2014 DOI: 10.1007/s00704-014-1174-3
  * [48] M. Fischer, H.W. Rust and U. Ulbrich “A spatial and seasonal climatology of extreme precipitation return-levels: A case study” In _Spatial Statistics_ , 2019 DOI: 10.1016/j.spasta.2017.11.007
  * [49] Matthew D. Rayson, Nicole L. Jones, Gregory N. Ivey and Yankun Gong “A Seasonal Harmonic Model for Internal Tide Amplitude Prediction” In _Journal of Geophysical Research: Oceans_ , 2021 DOI: 10.1029/2021jc017570
  * [50] Bryn Pickering, Christian M Grams and Stefan Pfenninger “Sub-national variability of wind power generation in complex terrain and its correlation with large-scale meteorology” In _Environmental Research Letters_ , 2020 DOI: 10.1088/1748-9326/ab70bd
  * [51] P.. Bett, H.. Thornton and R.. Clark “European wind variability over 140 yr” In _Advances in Science and Research_ , 2013 DOI: 10.5194/asr-10-51-2013
  * [52] Yves-Marie Saint-Drenan et al. “An approach for the estimation of the aggregated photovoltaic power generated in several European countries from meteorological data” In _Advances in Science and Research_ , 2018 DOI: 10.5194/asr-15-51-2018
  * [53] Hans Hersbach et al. “The ERA5 global reanalysis” In _Quarterly Journal of the Royal Meteorological Society_ , 2020 DOI: 10.1002/qj.3803
  * [54] Juan Pablo Murcia et al. “Validation of European-scale simulated wind speed and wind generation time series” In _Applied Energy_ , 2022 DOI: 10.1016/j.apenergy.2021.117794
  * [55] Mads M. Pedersen et al. “PyWake 2.5.0: An open-source wind farm simulation tool”, 2023 URL: https://gitlab.windenergy.dtu.dk/TOPFARM/PyWake
  * [56] Juan Pablo Murcia Leon, Matti Juhani Koivisto, Poul Sørensen and Philippe Magnant “Power fluctuations in high-installation- density offshore wind fleets” In _Wind Energy Science_ , 2021 DOI: 10.5194/wes-6-461-2021
  * [57] Graziela Luzia, Koivisto Matti and Andrea N. Hahmann “Validating Euro-Cordex Climate Simulations For Modelling European Wind Power Generation”, 2023 DOI: 10.2139/ssrn.4401025

##  Appendix A Comparison of Climatic Definitions of the Renewable Resources

Section 2 in the main text describes the four relevant timescales of energy-
meteorological variability and shows the use of the hourly rolling window
climate for renewable resources. Here we provide some additional detail on the
observed variability of wind and solar potential (Section A.1) and an analysis
on the specific behaviour during each hour of the day (Section A.2). We also
highlight the use of different climate definitions (Section A.3) and discuss
the sensitivity of the hourly rolling window climate on its window size
(Section A.4).

### A.1 Observed variability of wind and solar energy potential

Examples of typical behaviour of wind and solar energy are shown in Figure S1.
For wind, at seasonal timescales, we observe lower mean generation potential
in the summer period (Figure S1a, 2a. when weather conditions are more stable.
The higher and more variable generation potential in the autumn and winter
period is associated with the quicker succession of storms in Europe (Figure
S1a,b).

For solar the difference between summer and winter is more pronounced, which
is predominantly due to seasonal changes in the angle of declination of the
sun (Figure S1d and 2c For both wind and solar the succession of large-scale
high and low pressure systems can be observed (Figures S1b,e). Additionally,
as the efficiency of solar panels declines with increasing air temperature, a
reduced solar generation potential is observed around noon after the summer
solstice (Figure S2).

On daily timescales the inherent diurnal cycle of the solar energy generation
potential is very prominent and changes due to cloudiness are noticeable
(Figure S1f). For the wind generation potential no diurnal cycle is evident
(Figure S3), but large intra- to multi-day changes associated with the passing
of weather systems can clearly be observed (Figure S1b,c).

Figure S1:  Timeseries of hourly generation potential of wind (top) and solar
(bottom). Showing variability on yearly (a,d), sub-seasonal (b,e) and daily
(c,f) timescales. This example shows data for the Dutch zone ‘NL1’ from
2002-2004.

The observed variability of wind and solar energy potential is in line with
the large ensemble used by [12] and the decadal observations align with [51]
and [39].

It is clear that both wind and solar show strong variability at daily to
yearly timescales (Figure S1). To define a practically useful climate of the
prevalent behaviour for the wind or solar energy resources, all these
timescales of variability should be taken into account.

### A.2 Climatic characterisation for each hour of the day

Section 2.1 in the main text describes the observed variability of wind and
solar energy potential. Here we provide some additional figures (Figure S2 and
S3) show the climatic behaviour throughout the year, for each hour of the day
separately.

For solar, the strong annual and diurnal cycle are very clearly visible. In
addition, a few peculiarities can be observed related to how solar panels
function. The efficiency of solar panels declines with increasing air
temperature [52], leading to a reduced solar generation potential around noon
after the summer solstice from the higher temperatures at this time of the
year.

Figure S2:  The climatological definitions for the solar potential generation
is shown for each hour of the day over a year for the period 1991-2020 for
‘NL1’. The figures show the simple average-based, initial, climate definition
(grey), the hourly rolling window climate (red) and also include the full
range of generation potentials in 1991-2020 (light orange).

For wind energy generation potential only the annual cycle of the seasonal
variability of wind is clear and no clear distinction for the hour of the day
can be made. The climatology for each hour of the day does not match perfectly
and there are some minor differences observed.

Figure S3:  The climatological definitions for the wind potential generation
is shown for each hour of the day over a year for the period 1991-2020 for
‘NL1’. The figures show the simple average-based, initial, climate definition
(grey), the hourly rolling window climate (dark blue) and also include the
full range of generation potentials in 1991-2020 (light blue).

### A.3 Comparison of climate definitions

Section 2.2 in the main text discusses the climate of a renewable resource.
Here we provide some additional figures showing that both a daily [28] and
harmonic description of the climate are unsuitable for use in energy-
meteorological applications (Figures S4 & S5). For the latter see the work of
[47, 48, 49] for their use of the harmonic climate definition.

While the climate definitions are unsuitable, their impact on the crediis
limited (Figure S6).

Figure S4:  Comparison of windows for the hourly rolling window (HRW) climate
for wind during the period 1991-2020 for ‘NL1’. In light blue the yearly
generation potentials from 1991 to 2020 are shown. The simple average-based,
initial, climate (grey, see main text for details) and various windows sizes
(10,20,40,60,90,120 days) of the hourly rolling window climate (in purple,
green, dark blue, yellow, black and orange, respectively) are shown. Figure
S5:  Comparison of windows for the hourly rolling window (HRW) climate for
solar during the period 1991-2020 for ‘NL1’. As shown in Figure S4, see legend
for colours.  Figure S6:  Comparison of the impact of a different climate
definition on the resulting credi for wind during the period 1991-2020 for
‘NL1’.

### A.4 Sensitivity of window size for Hourly Rolling Window climate
definitions

A comparison of windows for the hourly rolling window climate is shown in
Figure S7 & S8 for solar and Figure S9 & S10 for wind.

Figure S7: Comparison of windows for the hourly rolling window (HRW) climate
for solar during the period 1991-2020 for ‘NL1’. In light orange the yearly
generation potentials from 1991 to 2020 are shown. The simple average-based,
initial, climate (grey, see main text for details) and various windows sizes
(10,20,40,60,90,120 days) of the hourly rolling window climate (in purple,
green, red, yellow, black and orange, respectively) are shown. For clarity
only 13:00 for each day of the year is shown.

For solar potential the hourly rolling window climate for a 10 day window is
not suited as variations are observed on daily to weekly timescales that have
no physical reason to be a recurrent over the years (see Figure S7). Similar
to the climate for wind, these fluctuations observed at the 10 day window
would not constitute as a good definition of a climate. On the other hand,
very large windows like those using the 60, 90 or 120 window, are very smooth
throughout the year, underestimating for instance the peak of maximum solar
potential near the end of April/start of May (see Figure S8) and severely over
estimating the winter dip in solar potential (Figure S7). Again, inline with
what was found with wind this indicates an over-smoothing of the yearly cycle
and thus using these windows within the hourly rolling window climate would
thus not be a good indicator of likely weather. A window size in the range of
20-60 days is adequate in capturing the persistent weather fluctuations and
the annual peak solar potential, without underestimating the annual cycle.

Figure S8: Comparison of windows for the hourly rolling window climate for
solar, as shown in Figure S7, but specifically for the period from March to
June 2003.

For wind potential the hourly rolling window climate for a 10 day window is
not suited as variations are observed on daily to monthly timescales that have
no physical reason to be a recurrent over the years (see Figure S10). As a
climate is defined as the statistically-mean weather conditions _prevailing_
in a region, the short-term nature of the fluctuations observed at the 10 day
window would not constitute as a good definition of a climate as the climate
fluctuates on short timescales. The same holds for the 20 day window, albeit
to a lesser extent. On the other hand, very large windows like those using the
90 or 120 window, are very smooth throughout the year. For most of the mid-
winter period their climate is well below the initial, simple average-based,
climate and during the summer above (see Figure S9). This indicates an over-
smoothing of the yearly cycle and thus using these windows within the hourly
rolling window climate would thus not be a good indicator of likely weather. A
window size in the range of 20-90 days is adequate in capturing the persistent
weather fluctuations throughout the year, without underestimating the annual
cycle.

Figure S9: Comparison of windows for the hourly rolling window (HRW) climate
for wind during the period 1991-2020 for ‘NL1’. In light blue the yearly
generation potentials from 1991 to 2020 are shown. The simple average-based,
initial, climate (grey, see main text for details) and various windows sizes
(10,20,40,60,90,120 days) of the hourly rolling window climate (in purple,
green, dark blue, yellow, black and orange, respectively) are shown. Figure
S10: Comparison of windows for the hourly rolling window climate for wind for
‘NL1’, as shown in Figure S9, but specifically for the period from March to
June 2003.

##  Appendix B Annual start date analysis for credi

Section 4 in the main text describes the application of the credi at different
timescales. Here we show how the hourly distribution of credi changes over a
year if a different starting point is used (Figures S11 & S12). In line with
the main text four exemplary storylines are shown, namely 1996 (red), 1998
(green), 2003 (purple) and 2016 (black).

From Figure S12, the impact of choosing a different starting point becomes
very clear. For the storylines shown you can see that they change from one of
the highest, to on of the lowest depending on the start point. To a lesser
degree, the same holds for the solar resource shown in Figure S11.

(a) January

(b) Febuary

(c) March

(d) April

(e) May

(f) June

(g) July

(h) August

(i) September

(j) October

(k) November

(l) December

Figure S11:  Comparison of the distribution of the solar credi with different
the monthly starting points of the annual period. The distribution is shown
with the 50th percentile (orange line), the 25-75, 10-90 percentile and min-
max range (shaded orange, see legend) for each hour of the year for the years
1991-2020 in the ‘NL1’ region. Four exemplary storylines are shown, namely
1996 (red), 1998 (green), 2003 (purple) and 2016 (black), see main text for
details and analysis.

(a) January

(b) Febuary

(c) March

(d) April

(e) May

(f) June

(g) July

(h) August

(i) September

(j) October

(k) November

(l) December

Figure S12:  Comparison of the distribution of the wind credi with different
the monthly starting points of the annual period. The distribution is shown
with the 50th percentile (blue line), the 25-75, 10-90 percentile and min-max
range (shaded blue, see legend) for each hour of the year for the years
1991-2020 in the ‘NL1’ region. Four exemplary storylines are shown, namely
1996 (red), 1998 (green), 2003 (purple) and 2016 (black), see main text for
details and analysis.

##  Appendix C Additional seasonal analysis figures of credi

Section 4.3 in the main text shows the seasonal variability in credi. Here we
provide some additional figures representing a different season for either
wind or solar credi (Figures S13-S16).

Figure S13:  Hourly summer wind credi throughout the season over the period
1991-2020 for ‘NL1’. Figure a) shows the specific progression of wind credi
for each summer season (blue lines). In addition, four example storylines are
represented, namely 1996 (red), 1998(green), 2003(purple) and 2016 (black),
see main text for details and analysis. Figure b) shows two storylines (1996,
2003) and the hourly distribution of the wind credi, namely the 50th
percentile (blue line), the 25-75, 10-90 percentile, and min-max range (shaded
blue, see legend).  Figure S14:  Hourly winter wind credi throughout the
season over the period 1991-2020 for ‘NL1’. As shown in Figure S13.  Figure
S15:  Hourly summer solar credi throughout the season over the period
1991-2020 for ‘NL1’. Figure a) shows the specific progression of solar credi
for each summer season (orange lines). In addition, four example storylines
are represented, namely 1996 (red), 1998(green), 2003(purple) and 2016
(black), see main text for details and analysis. Figure b) shows two
storylines (1996, 2003) and the hourly distribution of the solar credi, namely
the 50th percentile (orange line), the 25-75, 10-90 percentile, and min-max
range (shaded orange, see legend).  Figure S16:  Hourly winter solar credi
throughout the season over the period 1991-2020 for ‘NL1’. As shown in Figure
S15.

##  Appendix D Additional short-term analysis figures of credi

Section 4.4 in the main text shows an example of the short-term credi event
selection. Here we provide some additional figures related to the event
selection and the observed behaviour. Figure S17 shows the wind distribution
of the generation potential during the analysis period and for the selected
events.

Figure S17:  Hourly winter wind credi per 8-days for all events with less then
5 days overlapping in the period May 1991 to April 2021 for ‘NL1’. The
storylines show the analysis years 1996 (red, 4x), 1998 (green, 1x), 2003
(purple, 1x) and 2016 (black, 3x). Figure a) shows the specific progression of
wind credi for each summer season (blue lines). To highlight the behaviour
during an event, Figure b) shows the hourly distribution of the wind
generation potential, namely the 50th percentile (blue line), the 25-75, 10-90
percentile, and min-max range (shaded blue, see legend).  Figure S18:
Histogram of the solar credi (Figure a) and wind credi (Figure b) at 8-days
for all events with less then 5 days overlapping in the period May 1991 to
April 2021 for ‘NL1’.

The distribution of all non-overlapping events in the analysed period for both
solar credi and wind crediis shown in Figure S18. This is then further
detailed by looking at the wind credi and solar credi values at the end of the
selected events for both wind and solar in Figures S19 and S20, where the
latter only shows the top 50 events for both wind and solar. A Table with all
top 50 events for both wind and solar credi 8-day events is provided in Table
LABEL:tab:Top50longtable, see the _Open Research_ section for the details of
the code repository that contains the full list of all events.

Figure S19:  The 8-days wind credi and associated solar credi for all wind credi (blue) and solar credi (orange) events with less then 5 days overlapping in the period May 1991 to April 2021 for ‘NL1’. The highlighted events are for those used in the analysis 1996 (red, 4x), 1998 (green, 1x), 2003 (purple, 1x) and 2016 (black, 3x).  Figure S20:  As Figure S19, but then only the top 50 wind credi and solar credi events are shown.  Table S1:  Overview of the index value and event date for the top 50 8-day events selected both for wind and solar credi. Only those events are selected which have less then 5-days of overlap. The full list of the all 8-day events can be found as listed in the _Open Research_ section. Event Rank | solar credi | Event date | wind credi | Event date
---|---|---|---|---
1 | -15,49 | 23/05/2013 | -67,36 | 24/01/2017
2 | -13,98 | 18/05/1996 | -65,88 | 27/12/2006
3 | -13,80 | 07/06/2012 | -65,75 | 30/12/1992
4 | -12,97 | 06/05/2002 | -62,68 | 18/01/2013
5 | -12,55 | 08/07/2002 | -62,30 | 30/01/1991
6 | -11,82 | 26/05/2016 | -60,45 | 15/02/1993
7 | -11,75 | 11/07/2020 | -59,27 | 01/02/1992
8 | -11,30 | 18/06/1995 | -58,73 | 06/02/2006
9 | -11,16 | 23/05/1994 | -57,74 | 13/12/1996
10 | -10,93 | 28/05/2006 | -55,27 | 21/01/2001
11 | -10,89 | 14/05/2010 | -54,99 | 15/12/2001
12 | -10,88 | 28/07/2005 | -53,80 | 31/01/1997
13 | -10,82 | 31/07/1993 | -53,39 | 18/02/2008
14 | -10,44 | 21/03/1997 | -52,57 | 22/12/2007
15 | -10,44 | 31/07/2011 | -52,30 | 28/01/2004
16 | -10,43 | 13/06/1998 | -52,03 | 26/02/1994
17 | -10,30 | 17/03/2019 | -50,96 | 26/01/1997
18 | -10,12 | 12/05/2012 | -50,88 | 04/01/1993
19 | -10,07 | 09/04/1993 | -50,61 | 02/03/2019
20 | -10,00 | 12/05/2014 | -50,54 | 26/01/2019
21 | -9,92 | 13/08/1993 | -50,41 | 03/02/2001
22 | -9,88 | 14/06/2010 | -50,34 | 13/01/1997
23 | -9,84 | 22/07/1993 | -50,13 | 13/01/2002
24 | -9,74 | 26/03/2016 | -50,08 | 07/03/2021
25 | -9,67 | 09/05/2010 | -49,91 | 17/02/1991
26 | -9,65 | 05/04/2000 | -49,82 | 24/11/2011
27 | -9,63 | 20/07/2011 | -49,03 | 21/12/2016
28 | -9,39 | 13/07/2000 | -48,58 | 11/01/2003
29 | -9,34 | 01/07/1996 | -48,47 | 14/12/2004
30 | -9,17 | 03/07/1991 | -48,29 | 24/12/2021
31 | -9,14 | 21/04/1992 | -48,21 | 22/11/1998
32 | -9,01 | 06/05/2005 | -48,19 | 23/12/2017
33 | -9,00 | 20/06/1993 | -48,14 | 16/10/1994
34 | -8,99 | 10/09/1995 | -47,60 | 03/11/1997
35 | -8,97 | 03/05/2019 | -47,44 | 05/12/2004
36 | -8,97 | 31/05/1998 | -47,20 | 04/12/1991
37 | -8,97 | 17/07/1998 | -46,51 | 07/02/2015
38 | -8,95 | 31/03/2015 | -46,47 | 26/01/2015
39 | -8,95 | 31/05/2014 | -46,44 | 04/02/1991
40 | -8,93 | 02/06/2007 | -46,38 | 09/12/1991
41 | -8,92 | 17/06/1991 | -46,31 | 09/01/2010
42 | -8,89 | 08/03/2012 | -46,30 | 23/02/2013
43 | -8,88 | 25/05/2003 | -46,24 | 29/01/2017
44 | -8,86 | 14/08/2001 | -45,76 | 13/01/2013
45 | -8,85 | 20/04/2005 | -45,51 | 18/02/2003
46 | -8,84 | 01/07/2017 | -45,25 | 16/01/2001
47 | -8,82 | 30/09/1991 | -45,16 | 17/03/1991
48 | -8,82 | 09/10/1998 | -44,90 | 24/02/2018
49 | -8,81 | 26/07/2011 | -44,87 | 27/01/2010
50 | -8,80 | 08/05/1991 | -44,46 | 17/10/1995

##  Appendix E Application of credi to other regions

Section 5 in the main text discusses the use of the credi for other regions.
Here selected additional figures on the application of the index and very
limited analysis for some other regions is provided. Due to the preliminary
version of the PECDv4.0 used, caution is advised on the exact interpretation
of the results and no data is provided for these regions. In addition, for the
analysis only the seasonal and annual to decadal variability is discussed as
the analysis of the short-term and sub-seasonal variability depends on the
choice of the storylines which depend on the region considered and are kept
consistent with the main text for reference.

The additional regions used are Slovakia (‘SK00’), the southern tip of Sweden
(‘SE02’) and one of the south-east regions of France (‘FR10’). The choice for
these regions was made to reflect some of the diversity within Europe. Not all
regions are shown for all figures provided in the main text, the figures not
shown can be found as listed in the _Open Research_ section on github.

### E.1 Observed variability of wind and solar energy potential — Other
regions

Similar observations can be made on the timescales of variability for the
other regions then the ‘NL1’ region discussed in the main text (Figure S21).
While the distribution of the values differs between regions, similar
characteristics are observed. For wind at seasonal timescales a lower mean
generation potential is observed in all three regions (‘SK00’ not shown). Some
shifts in the characteristic behaviour can be observed. For instance, there is
lower solar generation in winter for more northern regions, and a more
strongly pronounced skewness of the solar generation potential throughout the
year is seen for ‘SE02’.

(a) South-East of France (‘FR10’)

(b) Southern tip of Sweden (‘SE02’)

Figure S21:  As Figure 2 in the main text, but then for the regions as listed
for 2002-2004. Timeseries of hourly generation potential of wind (top) and
solar (bottom). Showing variability on yearly (a,d), sub-seasonal (b,e) and
daily (c,f) timescales.

### E.2 A hourly rolling windows climate — Other regions

The _hourly rolling window_ climate defined in Section 2.2 of the main text
was applied without any changes to the other regions considered. As can be
seen in Figure S22, this climate provides a smoother description of the
expected behaviour on annual timescales and reduces the random fluctuations.

In line with the observations for the northern region of the Netherlands, the
initial, simple average-based climate does capture the annual timescales, but
shows random fluctuations from day-to-day and hour-to-hour. For both Slovakia
and the part of Sweden shown some consistent daily variation is observed for
their wind generation potential, whether this is from a physical driver is
unknown and should be further studied before using the climatic description
for these regions.

(a) Slovakia (‘SK00’)

(b) Southern tip of Sweden (‘SE02’)

Figure S22:  As Figure 3 in the main text, but then for the regions as listed.
Comparison of different methods for computing the climate of the potential
generation for wind (top), and solar (bottom), for the period 1991-2020.
Figures (a,c) show the hourly generation potentials for each year in this
period (light blue for wind and orange for solar), the initial, simple
average-based climate (grey, see main text for details) and the hourly rolling
window climate (blue and red, for wind, solar, respectively). Figures (b,d)
show the same, but specifically for the period 3-10 April 2003. For clarity
only 13:00 for each day of the year is shown in Figure (c).

### E.3 Annual to decadal variability — Other regions

Section 4.1 in the main text discusses annual to decadal variability observed
in the credi, here we shortly discuss the same for other regions.

Over the past 30 years, large and consistent inter-annual variation is
observed in the wind credi for the ‘FR10’ region (Figure S23), while the
‘SE02’ region shows more variable behaviour on annual and seasonal timescales
(Figure S24). For the French region, some cumulative effect over the whole
period can be observed, while the Swedish region shows a more oscillating
pattern.

Similar to the ‘NL1’ region, more inter-annual periods with a flat solar credi
can be observed then for wind. For the French region a general decrease of the
solar credi, thus anomalous low generation potential, is observed in the
period 1992-2004 and a very consistent increase from 2018 to 2021. For the
Swedish region a yearly flat solar credi is observed, likely related to the
very limited solar generation potential in the winter.

Figure S23:  As Figure 4 in the main text, but then for the South-East of
France (‘FR10’). Hourly Wind (a) and Solar (b) credi over the period 1991-2020
for ‘NL1’. As the climate was calculated over the same period, by definition
the credi sums to zero over the full period. Figure S24:  As Figure 4 in the
main text, but then for the Southern tip of Sweden (‘SE02’) region. Hourly
Wind (a) and Solar (b) credi over the period 1991-2020 for ‘NL1’. As the
climate was calculated over the same period, by definition the credi sums to
zero over the full period.

### E.4 Seasonal variability — Other regions

Section 4.2 in the main text discusses seasonal variability in the credi, here
we shortly discuss the same for the ‘SE02’ region as it shows the most
interesting properties (see Figure S25).

The wind credi in this Swedish region shows similar behaviour as the Dutch
region discussed in the main text, but while the 2016 storyline is considered
to be the most extreme for the northern region of the Netherlands, this is not
the case for the ‘SE02’ region. In addition, the shape of the distribution of
the wind credi is different throughout the year and the 1996 storyline shows
the highest wind credi value. This stark opposition to the behaviour observed
in that storyline for the Netherlands indicates some possible balancing for
this specific storyline.

The solar credi in the southern Swedish region ‘SE02’ shows a very flat value
in the period from October to March. This is likely due to the very clearly
limited solar generation potential in this region during the wintertime period
and the reasons for the limited annual to decadal variability observed for
this region (see Figure S24). At the same time large seasonal differences
between the different March to September periods are observed. As for the
‘NL1’ region, the year 1998 is the most extreme storyline for solar credi.

(a) wind credi

(b) solar credi

Figure S25:  As Figure 5 (here Figure (a), blue shades) and 6 (here Figure
(b), orange shades) in the main text, but then for the Southern tip of Sweden
(‘SE02’). Hourly wind credi per analysis year over the period May 1991 to
April 2021 for ‘NL1’. Figure a) shows the specific progression of wind credi
for each year. Figure b) shows the distribution of the wind credi for each
hour of the year, namely the 50th percentile, the 25-75, 10-90 percentile and
min-max range (see legend). Four exemplary storylines are shown, namely 1996
(red), 1998 (green), 2003 (purple) and 2016 (black).

##  Appendix F Extended Data section

We used the preliminary 4th version of the Pan-European Climate Database to
demonstrate the credi in this paper [[, PECDv4.0;]]Dubus2022PECD. This
database, developed by Copernicus Climate Change Services (C3S) in cooperation
with the European Network of Transmission System Operators for Electricity
(ENTSO-E) will be the new standard database used for all common Transmission
System Operator (TSO) studies. The full database will be openly available as
part of the new C3S-Energy dataset, expected in late 2023
(https://climate.copernicus.eu/energy/). To showcase the developed index all
figures show data from the preliminary PECDv4.0 of the northern region of the
Netherlands (‘NL1’).

Within PECDv4.0 a range of technological properties have been modelled for
both wind turbines and photovoltaic solar panels [11]. Only the historic
hourly generation potential (or capacity factor) timeseries are used for solar
and wind with the properties of ‘existing technologies’. Our subset uses the
ERA5 reanalysis for its meteorological forcing [53]. The wind power plant
conversion model is the generic power curve model presented in [54] that is
implemented in PyWake [55]. For the property parameterisation it uses the 2020
data from the WindPowerNet (https://www.thewindpower.net/). Storm shut down
behaviour is modelled after [56], while wakes are modelled as part of the
generic power curve and for other losses a 10% reduction factor is applied
[57]. The regional solar photo-voltaic (PV) potential is derived following
[52]. A distribution of near optimal tilt and azimuth angles was used that
reflects current installed capacities. For aggregation to the modelled zones
in the PECDv4.0 database, the gridded ERA5 data was weighted by the cover of
protected areas, regions with high slopes and/or high elevation.