# Towards a global dynamic wind atlas: A multi-country validation of wind
power simulation from MERRA-2 and ERA-5 reanalyses bias-corrected with the
Global Wind Atlas

Katharina Gruber, Peter Regner, Sebastian Wehrle, Marianne Zeyringer, Johannes
Schmidt

(December 2020)

###### Abstract

Reanalysis data are widely used for simulating renewable energy and in
particular wind power generation. While MERRA-2 has been a de-facto standard
in many studies, the newer ERA5- reanalysis recently gained importance. Here,
we use these two datasets to simulate wind power generation and evaluate the
respective quality in terms of correlations and errors when validated against
historical wind power generation. However, due to their coarse spatial
resolution, reanalyses fail to adequately represent local climatic conditions.
We therefore additionally apply mean bias correction with two versions of the
Global Wind Atlas (GWA) and assess the respective quality of resulting
simulations. Potential users of the dataset can also benefit from our analysis
of the impact of spatial and temporal aggregation on simulation quality
indicators. While similar studies have been conducted, they mainly cover
limited areas in Europe. In contrast, we look into regions, which globally
differ significantly in terms of the prevailing climate: the US, Brazil,
South-Africa, and New Zealand. Our principal findings are that (i) ERA5
outperforms MERRA-2, (ii) no major improvements can be expected by using bias-
correction with GWA2, while GWA3 even reduces simulation quality, and (iii)
temporal aggregation increases correlations and reduces errors, while spatial
aggregation does so only consistently when comparing very low and very high
aggregation levels.

##  1 Introduction

Decarbonising global energy systems is at the core of climate change
mitigation. The expansion of renewable energies is one important measure to
attain this goal [1, 2].

Globally, wind power and solar PV have been the renewable energy sources with
the highest growth rates in recent years. While the installed capacity on a
global level is similar for PV (579 GW) and wind power (594 GW), wind power
generation (1195 TWh) is substantially higher than electricity generation from
PV (550 TWh) [3]. This trend of a higher share of wind power generation is
likely to continue for some world regions, e.g. Europe [4]. Scenarios have
explored the importance of wind power in future energy systems, with shares of
around 50% of global power demand in 2030 [5], 74% in Europe by 2050 [6], or
even 80% to 90% of the European VRES mix [7].
For an adequate assessment of the impacts of high shares of renewable
electricity and in particular of wind power generation on power systems, long
spatially and temporally highly resolved renewable power generation time
series are necessary to represent short and long term changes in resource
availability [8]. At least one climatological normal of 30 years should be
used to understand variability [9].

Reanalysis climate data sets are frequently used to generate such time series.
Two of the most prominent global reanalyses are NASA’s MERRA and MERRA-2 and
the more recent ERA5 provided by the European Centre for Medium-Range Weather
Forecasts. The MERRA reanalyses were used for example for estimating the
global technical onshore and offshore wind power generation potentials [10,
11], or the integration of renewables into the European power system [12].
Also correlations between wind power generation in European countries [13],
extreme events in Britain [14], or the impacts of uncertainty factors [15] and
ageing [16] in wind power simulation were studied. With ERA5 global [16] and
Lebanese [17] offshore wind power potential, as well as electricity demand and
renewable generation in Europe [18] and West Africa [19] were estimated. While
global reanalysis data sets offer the advantage of conducting multi-country or
global analyses without the need for country or region-specific climate data
sources, they also come with their drawbacks. Although the temporal resolution
is usually high at one hour or even less, the spatial resolution is rather
coarse at a grid size of several kilometres (eg. MERRA-2 about 50 km).
Therefore, those data sets, in contrast to regional reanalyses such as COSMO-
REA [20], are limited in representing local climatic conditions in sufficient
detail, as required for the simulation of wind power generation [21]. It is
known that reanalysis data are subject to bias [14, 22, 13]. To increase
simulation quality, efforts should be made to correct the bias [15, 23], as
the bias of reanalysis data may result in differences in model-derived
installed capacities of up to 20% difference [23]. In many cases, however,
reanalysis data is used directly [24, 15, 14, 25, 26, 27, 28]. If it is
corrected, observed wind power generation data is mostly used [29, 21, 30, 13,
31]. This approach is not globally applicable, as observations of wind power
generation are unavailable for many world regions. Additionally, data quality
and the level of temporal and spatial aggregation varies between countries.
Therefore, other forms of bias correction are required when conducting global
analysis [21]. Here, we aim at reducing the bias in reanalysis data by
applying the Global Wind Atlas [32]. Recently, the Global Wind Atlas Version
3.0 has been released and we put a particular focus on assessing the quality
of this latest version compared to the previous version 2.1. GWA 3.0 has - at
the moment- only been assessed for Pakistan, Papua New Guinea, Vietnam, and
Zambia for wind speeds [33], however not for the purpose of wind power
simulation.

Of course, the GWA may not necessarily decrease bias. It is therefore of great
interest to validate simulated wind power simulation data against observed
generation - for both, raw reanalysis data and reanalysis data corrected with
the GWA. Other work has mainly focused on validating raw wind power simulation
data: [21] validate wind power simulations derived from MERRA and MERRA-2
against observed generation data for 23 European countries and find
significant bias. [30] [30] used the MERRA data set to model Swedish wind
power generation, and production data from the Swedish TSO to validate and
bias-correct their modelled data. In a comparison of MERRA-2 and ERA5 for the
use of wind power simulation, time series for four European countries and one
region in the USA were validated[29]. [34] compared MERRA-2 and ERA5 [34] to
simulations of French wind power generation based on two high-resolution
models (COSMO-REA6 and AROME) and a mesoscale model (NEWA) and validated all
datasets against observed wind speed and power generation data.
Since most of the previous analyses only assessed one particular reanalysis
data set, we focus on the comparison of ERA5 and MERRA-2, on results quality
and the additional use of the GWA for bias-correction. As Europe has already
been studied in several other analyses [21, 30, 34, 15, 35] and to cover
different global climatic conditions, we study the following non-European
countries: Brazil, USA, South Africa and New Zealand. These countries are
spatially very diverse, host significant wind power capacities, and provide
timeseries of wind power generation that can be used for validation.
Furthermore, we contribute to a better understanding of the role of spatial
and temporal resolution by assessing simulation quality on different levels of
spatial and temporal aggregation. This is highly relevant information for
users in power- and energy system models [36].

In particular, we answer the following research questions: (1) Does the newer
reanalysis ERA5 with higher spatial resolution perform better than the older
MERRA-2 when validated against historical wind power generation data? (2) Does
bias-correction with the spatially highly resolved GWA increase simulation
quality? (3) Does the GWA 3.0 perform better than the previous GWA 2.1.? (4)
Does aggregating single wind parks to larger systems decrease the error due to
spatial complementarity and error compensation effects, as indicated by Goić
et al. [37] and Santos-Alamillos et al. [38]? (5) Does temporal aggregation
reduce errors? We assess those questions by simulating wind power generation
in the four countries for all wind parks, using both ERA5 and MERRA-2 with and
without bias-correction with the GWA. We validate simulated against observed
generation on different spatial levels and compare quality between all
simulations.

##  2 Data

We use several data sets for simulation, bias correction and validation: wind
speeds are taken from the MERRA-2 and ERA5 reanalysis data sets. The GWA is
used for mean bias correction. Information on wind park locations and the used
turbine technology is collected from different country specific data sources
(see section 2.3). Similarly, country specific wind power generation data is
gathered to perform the final validation.

###  2.1 Reanalysis data

From MERRA-2 [39], we use the time-averaged, single-level, assimilation,
single-level diagnostics (tavg1_2d_slv_Nx) dataset, while we use hourly data
on single levels from 1950 to present from ERA5[40]. MERRA-2 reanalysis data
are provided by the National Aeronautics and Space Administration via the
Goddard Earth Sciences Data and Information Services Center and follow the
earlier version of MERRA, while ERA5 is the follow-up product of ERA-Interim
provided by the European Centre for Medium Range Weather Forecast (ECMWF).
MERRA-2 is available for circa 40 years (since 1980), while ERA5 has recently
been extended to reach back to 1950. While both exhibit a temporal resolution
of one hour, the spatial resolution is higher in the more recent ERA5 data set
( 31 km) than in MERRA-2 ( 50 km).
The climate input data is downloaded for time periods corresponding to the
temporal availability of validation data. Spatial boundaries are defined by
the size of the respective country. The downloaded parameters are eastward (u)
and northward (v) wind speeds at two different heights for each reanalysis
data set (ERA5: 10 m and 100 m above surface, MERRA-2: 10 m above displacement
height and 50 m above surface), as well as the displacement height for
MERRA-2.

###  2.2 Global Wind Atlas

The Global Wind Atlas [32] provided by the Technical University of Denmark
(DTU) is used to spatially downscale the reanalysis data to a resolution of
250 m, in order to take into account local variations of mean wind speeds. The
current version, GWA 3.0 was derived from the ERA5 reanalysis and provides
mean wind speeds and mean power densities at five different heights (10, 50,
100, 150 and 200 m), as well as mean capacity factors for three different
turbine classes according to IEC111 International Electrotechnical Commission
for the period 2008-2017. Furthermore, there are layers describing the terrain
surface and a validation layer showing in which countries and for which wind
measurement stations the GWA has been validated.
The previous version, GWA 2.1, which is also used in this analysis, provides
wind speeds at only three heights (50, 100 and 200 m) at the same spatial
resolution and was derived from ERA-Interim, the preceding data set of ERA5
[41] for the period 1987-2016.
For the purpose of mean bias correction, the wind speed layers at 50 m and 100
m height are downloaded for each country. They correspond to the upper layer
of reanalysis wind speeds in MERRA-2 and ERA5, respectively. Since the GWA2 is
no longer available at the official GWA homepage, data were extracted from the
stored global data set [42] around the country boundaries.

###  2.3 Wind park information

For the simulation of wind power generation, we use turbine specific
information on location, installed capacity, hub height and rotor diameter.
The spatial distribution of wind power plants is shown in Figure 1. In
countries where turbine specific location information is not available, we use
wind park specific data. This information is retrieved from freely available
country level data sets (see Table 1).
For Brazil, two data sets, the Geographic Information System of the Electrical
Sector (SIGEL) [43] and the Generation Database (BIG) [44], from the National
Electrical Energy Agency (ANEEL) [45] are combined using the wind park codes.
The use of both datasets is necessary, as SIGEL data contains only the
location, installed capacity, hub height and rotor diameter, while the state
and the commissioning dates are added from the BIG database. Two wind turbines
in the BIG dataset have a hub height and rotor diameter of 0 meters. They are
replaced by values from turbines with similar capacity.
The information on ten wind parks with available production data is collected
from the New Zealand Wind Energy Association [46]. Similarly, the information
on 39 wind parks in South Africa is gathered from the Renewable Energy Data
and Information Service (REDIS) [47], while rotor diameters, hub heights and
capacities are complemented with information from The Wind Power[48]. Since
several data points were obviously erroneous or missing, the database was
completed with an online search (see Table 4). The resulting South Africa wind
park data set is available online for further use [49].
The information on the over 60 000 wind turbines in the USA is obtained from
the US Wind Turbine Data Base (Version 3.2) [50], which comprises most of the
necessary data. Missing information222Lacking data of commissioning date: 1540
turbines, turbine capacity: 5530 turbines, hub height: 7790 turbines, and
rotor diameter: 6728 turbines is replaced by the yearly mean (installed
capacities, hub heights) or the overall mean (commissioning year) and rotor
diameters are completed by fitting a linear model to the hub heights. In some
cases the specific power calculated from rotor diameter and capacity is too
low (below 100 W/m2) resulting in unrealistic power curves, and thus replaced
by the mean specific power of turbines with the same capacity 333This applies
to 49 wind turbines, of which 48 have incomplete turbine specifications.

Figure 1: Locations of wind parks in Brazil, New Zealand, USA and South Africa
Table 1: Wind turbine and wind park data sets applied for simulation

Country Source Avail-ability turbines parks total capacity [MW] avg. park
capacity [MW] avg. turbine capacity [kW] avg. rotor diameter [m] avg. hub
height [m] Brazil ANEEL (BIG, SIGEL) [45, 44, 43] turbines 7438 603 15190 25
2031 98 87 New Zealand NZWEA [46] wind parks 405 10 564 56 1719 61 53 South
Africa REDIS [47] and various wind parks 1466 39 3545 90 1719 84 95 USA USWTDB
[50] turbines 63002 1565 108301 69 2525 105 75

###  2.4 Wind power generation data for validation

The validation of the simulated wind power generation time series is based on
observed generation at different spatial and temporal resolutions, gathered
from country specific data sources. While there is data available on all time
scales (hourly, daily and monthly) for each of the four studied countries or
regions in those countries, historical wind power generation records on the
level of wind parks are available only for Brazil and New Zealand. In South
Africa, the country’s observed power generation is only available per Cape
(Eastern, Northern and Southern Cape), while for the USA the smallest level of
spatial disaggregation available is the state level.
Temporal availability of the generation time series varies depending on the
data source and commissioning dates of wind parks. The highest resolution of
data is given in Brazil, where the National Electrical System Operator (ONS)
[51] provides data on three temporal (hourly, daily, monthly), as well as four
spatial levels (wind park, state, subsystem, country). Of the 174 wind parks
in Brazil for which hourly data are available in the ONS dataset, 70 can be
matched by their name to simulated wind parks based on ANEEL data, and 42 show
sufficient data quality (also see Table 3). They are consequently used for the
further analysis. Due to data quality issues and the requirement of
consistency only hourly data on the wind park level were used and aggregated
spatially and temporally (also see section 2.5). In New Zealand, wind park
specific generation data is also available, however only for ten wind parks.
The information on historical wind power and other generation is provided by
the Electricity Market Information (EMI) [52] half hourly and aggregated to
hourly production values for validation against hourly simulated values.
In South Africa, generation data is provided by REDIS [53] as capacity
factors. For observed power generation in the USA, several data sources are
used. The U.S. Energy Information Administration (EIA) [54] provides monthly
resolved generation data for the USA, its 51 states and 10 sub-regions444New
England, Mid-Atlantic, East North Central, West North Central, South Atlantic,
East South Central, West South Central, Mountain, Pacific Continental and
Pacific Non-Continental. For New England555Connecticut, New Hampshire, Maine,
Massachusetts, Rhode Island and Vermont, monthly data are retrieved from ISO
New England [55]666Data from EIA were discarded due to poor quality (nearly
constant/fluctuating generation instead of seasonal pattern and some very low
production months, see Figure 20) and instead ISO New England data are used.
The Electric Reliability Council of Texas (ERCOT) [56] provides hourly
generation data for Texas. The 5-minute wind power generation data in the
Bonneville Power Administration (BPA) [57], which is responsible for 49 wind
parks in the regions of Oregon and Washington, is aggregated to hourly output.
Table 2 summarises the data sources used for validation.

Table 2: Data sets applied for validation Country | Regions | Temporal resolution | Source
---|---|---|---
Brazil | 42 wind parks, 4 states, country | hourly, daily, monthly | ONS [51]
New Zealand | 10 wind parks, country | hourly, daily, monthly | EMI [52]
South Africa | 3 capes, country | hourly, daily, monthly | REDIS [53]
USA | 25 states, 8 regions, country | monthly | EIA [54]
| Texas | hourly, daily, monthly | ERCOT [56]
| New England | monthly | ISO New England [55]
| BPA | hourly, daily, monthly | BPA [57]

###  2.5 Data cleaning

In a preliminary screening, parts of the available observed wind power
generation time series showed long sequences of missing data and unlikely
generation patterns, such as long periods of constant output. We therefore
applied a thorough cleaning procedure.

####  2.5.1 Brazil

First, wind park names in the ANEEL and the ONS data set have to be machted in
order to validate the simulation with observed generation from the according
wind park. Due to the large number of available wind park data, this step is
performed using fuzzy matching, ignoring special characters and case
sensitivity. Only wind parks with a matching score of 100 are used for
validation. From a total of 174 parks, only 72 satisfied this criterion.
For these wind parks, leading and trailing series of zero production are
removed from hourly generation time series at wind park level. For constant
parts of time series, two different approaches are taken. If those parts are
0, they either indicate (a) a long period of very low or very high wind speeds
(i.e. either below cut-in or above cut-out wind speed), (b) a downtime of the
turbine due to e.g. maintenance, and (c) an error in the observed data.
Filtering out all instances of 0 wind power production would remove all three
events, however, this would be inconsistent with other countries, where this
approach cannot be taken (as wind power generation on the level of wind parks
is not available). We therefore opted for removing constant parts of the
timeseries with periods of 0 generation larger than the largest period of 0
generation in the simulated timeseries which accounts to 180 hours.
For other constant parts of the timeseries, which are above 0, we removed them
if the period was longer than 24 hours. Time series which contain less than 2
years of data are excluded from the analysis to guarantee capturing seasonal
effects. We stress that the two years of data do not necessarily occur
consecutively. Furthermore, the data are assessed with respect to their
capacity factors. We removed all instances in the timeseries where capacity
factors above 1 where observed. Table 3 gives an overview how many locations
where affected by the performed data cleaning in Brazil.

Table 3: Data cleaning steps and remaining wind parks for validation in Brazil | Applies to | Remaining
---|---|---
|  | wind parks
\- total number of observed wind park time series |  | 174
1\. matching of ONS and ANEEL |  | 72
\- keep only 100 matching score |  | 70
2\. data cleaning |  |
\- remove constant parts of time series except 0 ($>$24h) | 50 | 70
\- remove constant parts of 0 generation ($>$180h) | 28 | 70
\- remove capacity factors $>$ 1 | 59 | 70
\- remove short time series ($<$2y) | 17 | 53

In order to ensure consistent data quality throughout the evaluation, instead
of applying the temporally and spatially aggregated data sets provided by ONS,
we aggregate the hourly wind power generation time series on wind park level
spatially and temporally. This is necessary since daily data are equal to
aggregated hourly data on the ONS site. However, this approach ignores missing
or erroneous data, resulting in lower power generation in periods where
generation data are missing in at least one of the wind parks in a particular
region. We remove time steps from simulation data, when the data are missing
in some wind parks in the validation data and aggregate after this correction.
Furthermore, hourly and daily data are not consistent with monthly data. As
the applied aggregation method is not made explicit, the reason for the
inconsistency remains unclear. To overcome the inconsistency, aggregation of
validation data is performed starting at the highest spatio-temporal
resolution of the available data, i.e. at the hourly wind park data. This
approach allows to remove missing data from all spatial and temporal scales,
improving the fit of observed and simulated data.

####  2.5.2 USA

In the USA, different measures were applied depending on the data source. In
the EIA data set, leading zero production is removed. Since before 2010 the
fit of simulation to validation data is low, the installed capacity in the USA
from the USWTDB is compared to the yearly cumulative installed wind power
capacity as provided by IRENA [58]. This comparison shows large
inconsistencies (see Figure 7). Therefore, wind power generation is analysed
for the past ten years only, starting in 2010. This approach notably improves
results (see Figure 24). Despite the cleaning measures, several regions still
result in unusually low correlations and high errors. A visual inspection of
the monthly time series shows that the observed generation of several states
and regions is nearly constant or repetitively fluctuating between different
generation levels for long time series. This contrasts with our expectation of
observing seasonal patterns (see section A.7). Due to this reason, seven
states and three regions affected by this approach are discarded for further
use, while in nine states, only part of the time series is used for
validation. These are indicated in Figure 21. In the BPA data set, some
observations are missing. As the data is available at a 5 minutes resolution,
the missing values are interpolated. The maximum consecutive missing
observations is one hour.

####  2.5.3 New Zealand and South Africa

In New Zealand, constant output over more than 24 hours is removed from the
time series. No further data cleaning operations are applied. In South Africa,
a limited amount of capacity factors larger than 1 are observed. These time
steps are removed.

##  3 Methods

###  3.1 Wind power simulation

Wind power is simulated based on reanalysis data and mean wind speeds in the
GWA. In a preparatory step, effective wind speeds are calculated from eastward
(u) and northward (v) wind speed components in reanalysis data according to
the Pythagorean theorem for the two heights available. From the effective wind
speed, the Hellmann exponent $\alpha$, describing the structure of the
surface, is calculated. Using the location information of wind turbines or
wind parks, reanalysis and GWA wind speeds are interpolated to the nearest
neighbour and extrapolated to the hub height using Hellmann’s power law.
When bias correction is applied, mean wind speeds are retrieved from the GWA
at the location closest to the wind park or turbine and divided by the average
of the reanalysis wind speed time series at the specific locations at the same
height, i.e. 50 m for MERRA-2 and 100 m for ERA5, as these are the heights
closer to hub height. This quotient is used as a bias correction factor to
shift reanalysis wind speeds interpolated to hub height up or down according
to the GWA.
In order to convert wind speeds to wind power, the power curve model
introduced by Ryberg et al. [59] is applied and scaled to the installed
capacity of the turbines.

This model estimates power curves empirically from the specific power, i.e.
the installed capacity per rotor swept area, of wind turbines. It therefore
does take into account differences in the power output according to specific
power, but additional technology or turbine specific effects are not
considered. We follow this approach, as otherwise we would have to manually
research power curves for 283 different turbine models, and as additionally
turbine models are not know for 865 cases. Wind power generation is simulated
for the whole country-specific time period, but generation is set to 0 for
periods before the commissioning date of the respective wind park. If only the
month of commissioning is known, we assume the middle of the month as
commissioning date. For the USA, only the commissioning year is known. In
order to avoid large increments of wind power generation on any particular
date, the capacity installed within a year is linearly interpolated from the
1st of January to the end of the year.

###  3.2 Validation

218 different data sets of observed generation are suitable for validation. 10
data sets are on country scale, 58 on state or regional scale, and 150 on wind
park scale. 62 of those have hourly resolution, 62 daily, and 94 monthly. Due
to data quality issues, not all available time series could be used (see
section 2.5). In order for results to be comparable between different levels
of spatial and temporal aggregation, as well as countries, generation time
series are normalised to capacity factors.
Validation of the simulated time series was performed using three statistical
parameters to assess quality. Pearson correlation, RMSE (root mean square
error) and MBE (mean biased error) were used, as suggested by Borsche et al.
[60].

The RMSE is an indicator that increases if (a) there is a significant
difference in the level of simulated and observed timeseries, and (b) if there
is a temporal mismatch between the two. As we use capacitiy factors which are
comparable in scale between regions, the RMSE does not have to be normalized.
To assess the different components of mismatch, i.e. temporal mismatch and
mismatch in level of production, we additionally calculate the Pearson
correlation which indicates if the temporal profile of simulated and observed
generation are similar. To assess differences in levels including over- or
underestimation, we determine the MBE.

Since the proposed model does not consider losses due to wakes or down-times
due to maintenance, a slight overestimation of generation is expected. I.e.
slightly overestimating models tend to represent actual generation better than
underestimating ones. Results for different regions and temporal aggregation
levels are compared in notched boxplots. The notches indicate if the median’s
differ significantly at the 95% level 777The notches are determined according
to $M\pm 1.57\cdot IQR\cdot\sqrt{n}$, with M being the median, IQR the
interquartile range and n the number of samples. If the notches of two boxes
do not overlap, the difference between their medians is statistically
significant at the 0.05 level [61]. As we cannot assume that our sample of
wind parks and regions represents a random sample of global wind power
generation locations and as there is a bias in the amount of timeseries
available for different regions, we report on different results for different
countries whenever they deviate from the generally observed pattern.
Respective figures are put into the appendix.
In order to estimate the effect of system size on simulation quality, a system
size parameter is introduced. It measures the number of reanalysis grid cells
occupied by wind turbines or parks, e.g. per wind park or region (see Figure
2). Individual wind turbines therefore always have size 1. Wind parks can have
a size larger 1, if they cover more than one grid cell, but this is mostly not
the case. Countries cover always more than one grid cell.

Figure 2: System sizes per country and data set (non-normalised)

##  4 Results

In this section we first present how the choice of the reanalysis dataset
affects simulation quality. Subsequently, we investigate whether the use of
the GWA for mean bias correction can improve our simulation’s goodness of fit.
Finally, we assess the effect of spatial and temporal aggregation of wind
power generation on simulation quality.

###  4.1 Impact of choice of reanalysis dataset on simulation quality

Here we assess the difference in simulation quality as implied by using
different reanalysis data sets, i.e. MERRA-2 and the more recent ERA5.

Figure 3 presents a comparison of statistical parameters between simulations
based on ERA5 and MERRA-2 reanalyses for all analysed regions, i.e. wind
parks, states, regions, and countries. While ERA5 correlations (median: 0.82)
are higher than the ones achieved with MERRA-2 (median: 0.77) and while
MERRA-2 has a larger spread of correlations, one of them being even negative,
the difference in correlations is not significant. Overall, there is a
significant (notches do not overlap) difference in RMSEs (median ERA5: 0.15,
MERRA-2: 0.19). Regarding the MBEs, there is a significant difference between
the median MBE of ERA5 (-0.05) and MERRA-2 (0.09), with ERA5 MBEs slightly
underestimating generation on average, while MERRA-2 overestimating generation
quite substantially (by approx. 1%). Underestimation of ERA5 can be as low as
almost 40% for some locations, while MERRA2 overestimates generation by as
much as 40%. In general, both data sets seem to underestimate wind power
generation in New Zealand, which is the only region where this occurs.
On a country level (see Figure 8), these results are replicated with the
exception of New Zealand, where all indicators, i.e. correlations, RMSE, and
MBE are better for MERRA-2. However, only the MBE shows a significant
improvement when comparing MERRA-2 with ERA5. The differences in correlations
between countries indicate that the ERA5 based simulation in most regions has
a higher correlation than the one based on MERRA-2, except for New Zealand
(see also Figure 10). In summary, using ERA5 as data source for wind power
simulations will result in better or at least as good timeseries as using
MERRA-2. On average, quality indicators are reasonable, but extreme outliers
are observed for both data sets. As they mostly occur for both reanalysis data
sets, this may also be a problem of lacking data quality in observed wind
power generation.

Figure 3: Comparison of statistical parameters for simulations with ERA5 and
MERRA-2 reanalyses for all analysed regions. Non-overlapping notches indicate
a difference in the medians statistically significant at the 95% level.

###  4.2 Bias correction with GWA

In order to adjust the mean bias of the wind speeds taken from reanalysis
data, we use the Global Wind Atlas. Due to the higher spatial resolution
compared to the reanalysis data sets, we expect an improvement in particular
in RMSE and MBE. The effect of bias-correction on correlations depends on the
non-linear relationship between wind speeds and wind power as shifting wind
speeds by a constant factor does not imply a proportional shift in wind power
output. Hence, bias correction may impact correlations, too. In most cases,
however, this impact is small and not significant (see 4). In New Zealand,
correlations are slightly increased with GWA2 and in South Africa using any of
the GWAs, however these increases are not significant (Figure 11).

The RMSEs are decreased slightly by GWA2 in comparison to simulations without
bias correction, but the median does not differ significantly. The simulation
with GWA3, however, implies a significant increase of the median of the
distribution of RMSEs, compared to GWA2 as well as compared to the simulation
without mean bias correction. On a regional level, however, the significant
difference in medians of GWA3 to the other simulations is only found in the
USA, as well as between simulations with GWA2 and GWA3 in New Zealand (see
Figure 11), i.e. the overall results are mainly driven by the US and New
Zealand.
If measured by MBEs, a similar conclusion can be drawn: GWA2 reduces the
median of the error and shifts it closer to 0. Even though this is not
significant for the overall regions, a significant shift towards 0 is seen in
all countries besides New Zealand. The GWA3, in contrast, leads to a large
increase in the MBE. This applies also in New Zealand and South Africa, while
for Brazil GWA2 is less recommended.
To sum up, in most of the investigated regions, the GWA2 may be used to
increase correlations (New Zealand, South Africa), decrease the RMSE (all
countries) and shift the MBE closer to 0 or to a small positive value (all
except Brazil). From our results, GWA3 is not recommended for bias correction
as it increases the errors (RMSEs as well as MBEs for three out of four
countries, see Figure 4).
A similar analysis was conducted by applying the GWA to MERRA-2 based wind
power simulation. The results can be found in section A.5. For MERRA-2, using
the GWA for bias-correction has ambiguous impacts on results and we therefore
do not fully recommend using it as a mean for bias-correction.

Figure 4: Comparison of statistical parameters for simulations with ERA5 and
different versions of the GWA for all analysed regions. Non-overlapping
notches indicate difference in medians statistically significant at the 95%
significance level.

###  4.3 Impact of spatial and temporal aggregation

In this section we assess the impact of spatial and temporal aggregation on
the quality of wind power simulations. The impact on the correlation cannot be
analytically derived: while an aggregation of two time-series of capacity
factors will lower the variance of the combined time-series compared to the
maximum of the variance of the original time-series, the change in co-variance
of the combined time-series compared to the single locations cannot be
analytically derived, as it depends on the co-variances of wind patterns at
the two locations (see Appendix A.1).
Therefore, we assess here empirically, how aggregation impacts time-series
quality. For this analysis, the wind power simulations with ERA5 data and bias
correction with GWA2 on Brazil and New Zealand (the only countries in which
wind park level data are available)) are used, as this combination showed
decent simulation quality for all regions. Figure 5 shows the resulting
simulation quality indicators. Overall, a tendency that at larger system size,
the simulation quality as measured by correlations and RMSEs decrease can be
observed. In particular, the largest system (Brazil) has a significantly lower
median than the smaller systems in terms of RMSE, although single negative
outliers can reach the simulation quality of the largest systems. For
particular countries, this is difficult to assess, since there is a lack of
variety of different system sizes. Nevertheless, in the USA and Brazil
simulation quality increases as can be observed in Figure 17.

With regard to spatial relations, we also assess how geography might impact
the accuracy of simulation. We therefore consult the correlations of the best
simulation (ERA5 with GWA2 mean bias correction) in Brazil and New Zealand
(where validation data on wind park level are available). Figure 16 indicates
that in Brazil southern wind parks have higher correlation, whereas in New
Zealand the highest correlations are found in proximity to the coast.

Figure 5: Impact of spatial resolution (system size 1: wind parks (system size
parameter (ssp) $<$ 5), system size 2: states of Brazil and New Zealand (5
$\leq$ ssp $<$ 25), system size 3: Brazil (ssp $\leq$ 25)) on simulation
quality in Brazil and New Zealand. Non-overlapping notches indicate a
statistical difference in the median at the 95% significance level.

When assessing the impact of temporal resolution on simulation quality, for
the US some locations had to be excluded, as they do not provide hourly time
resolution. Therefore, there only the regions of Texas and the Bonneville
Power Administration were included. In all other countries, all locations are
available at hourly resolution. The medians of correlation significantly
increase from hourly to daily as well as daily to monthly correlations (Figure
6. While the increase from daily to monthly correlation is at around 5 %
points, daily correlations are around 15 % points higher than hourly ones.
This is observed in all individual countries, however only Brazil shows
significant changes in median correlation for both temporal aggregation steps
(Figure 18).
The RMSE can be reduced by temporal aggregation, from hourly to daily by about
12 % points, and from daily to monthly by around 10 % points on average. In
all countries except Brazil, the decrease in correlation is significant
(Figure 18).

Figure 6: Impact of temporal resolution on simulation quality. Non-overlapping
notches indicate a statistical difference in the median at the 95%
significance level.

To sum up, simulation quality tends to increase rather strongly when
aggregating temporally. Spatial aggregation is somehow ambiguous, but when
comparing very low to very high resolutions, the effect can also be detected.

##  5 Discussion

In this work we compare the capabilities of the two reanalyses MERRA-2 and
ERA5 as data sources for wind power simulation in several countries around the
world and analyse the suitability of the Global Wind Atlas to increase the
quality of the simulated time series. With a few exceptions, ERA5 performs
better, with respect to the chosen quality measures and the selected samples,
than MERRA-2. The better performance may be partly due to a higher spatial
resolution of the input data set, but also due to using a more recent climate
model based on a large amount of observed data [62]. The capability of
representing wind conditions especially in complex terrain should therefore be
improved [29]. This result is not supported by Lileó et al. [63] who claim
that an increase in spatial resolution does not necessarily result in higher
correlations between reanalyses and local wind measurements in a similar
assessment for wind speeds. Our results coincide with findings of Olauson
[29], who studied the performance of these two reanalysis data sets for wind
power simulation in four European countries and a region in the USA, as well
as Jourdier [34] who compared MERRA-2, ERA5, two high-resolution models and
the New European Wind Atlas for the purpose of wind power simulation in
France. Olauson found hourly correlations of over 0.94 for all regions
investigated (except the BPA with MERRA-2, where it is at 0.75), which is
higher than the correlations identified in our study. For most locations, we
find correlations above 0.7, only in South Africa they are around 0.6 (ERA5)
or even below (MERRA-2). This coincides with the correlations fround by
Olauson for individual wind parks in Sweden, which are above 0.5 (MERRA-2) and
0.8 (ERA5). While Olauson finds an increase in correlation by ERA5 compared to
MERRA-2 by less than 1 % point in three of the examined regions (i.e. Germany,
Denmark and France), in our study correlations of ERA5 are up to 10 % points
higher, with a higher increase in some exceptional cases. This is in the range
of the increase in correlation reported by Jourdier [34] in France and sub
regions, with correlation being 0.15 higher for ERA5 compared to MERRA-2.
However, in our analysis in some cases there is also a lower correlation with
ERA5 based simulations compared to MERRA-2, especially in New Zealand. An
interesting result is that in [29] the highest increase in correlation by
nearly 20 % points is seen in the BPA in the USA, which agrees with the
results of the present study.

Only for the USA we estimated RMSEs comparable to the results in [29], with
values between 2.35 % and 9.1 % for ERA5, and 2.82 % and 18.4 % for MERRA-2.
In the other regions (Brazil, New Zealand, South Africa), the RMSE is higher,
with about 75 % of the locations showing RMSEs above 10 %. Reasons for these
differences may be explained on the one hand by different data quality of
validation data, on the other hand by a better fit of the data for the regions
of the USA and Europe compared to other world regions (South America, Africa
or Oceania). Regarding the comparison of the two reanalyses, Olauson found
that for ERA5, the RMSE was between 20 % and 50 % lower than for MERRA-2
(except in Denmark where there was hardly any impact). In absolute terms, this
means a decrease of up to 0.02 (except for BPA with over 0.09), while we found
that in some locations the RMSE was up to 0.2 lower for ERA5 than for MERRA-2.
In other, but fewer locations, particularly in New Zealand, however, the RMSE
was up to 0.2 higher with ERA5 compared to MERRA-2 based simulations.

The GWA does not improve simulation quality consistently for all locations.
While GWA2 showed a potential to decrease RMSEs, GWA3 rather increases them.
Considering the MBEs, the results are ambiguous. GWA3 often increased errors
and performed worse than GWA2. Despite an analysis showing that ERA5 performs
better than ERA-Interim [64], this cannot be confirmed for GWA3 and GWA2,
respectively, which are based on these two different reanalysis data sets. So
far, no other study using the GWA3 has been conducted, but results from
analyses of the previous version showed that applying the GWA for downscaling
MERRA reanalysis wind speeds (EMHIRES dataset [65]) has no unambiguously
positive effect on the simulation quality when compared to TSO time series.
Despite the claim of the authors that the simulation based on MERRA data
underestimates the variability compared to the GWA-downscaled dataset
(EMHIRES) and that downscaling improves results, their statistical results
indicate that neither correlations increase (13 of 24 countries investigated
have higher correlation with EMHIRES than with MERRA), nor RMSE (9 countries)
or biases (7 countries) decrease consistently [35]. This fits well to the
results of our current study, where the results of different countries or
regions vary in terms of whether the GWA improves the quality of wind power
simulation time series or not. Another study which uses the GWA and MERRA-2
for wind power simulation in Brazil finds that bias correction in general
improves results [66].

A further subject we investigated are the implications of spatial and temporal
aggregation on the measures applied for quality assessment. The expectation
was that the higher the level of spatial or temporal aggregation, the lower
the error, since compensating effects of negative and positive bias could
reduce errors. For temporal aggregation this could be confirmed by the
analysed data. This is also confirmed by Staffell and Pfenninger who compute
higher correlations for eight European countries on a monthly than on an
hourly basis [21] . For spatial aggregation, however, we could not
consistently confirm such an effect. This matches the results of an analysis
conducted in Europe, using MERRA and MERRA-2 reanalysis data. Monthly
correlations on country level were lower than correlations on European level
only in some of the 13 studied countries (9 for MERRA and 7 for MERRA-2).
Also, the median of correlations per country was above the correlations of
aggregated data [21]. In contrast to this Olauson [29] finds higher
correlations, as well as lower RMSEs and errors in Sweden compared to 1051
individual wind turbines when simulating wind power with MERRA-2 and ERA5.
Limitations of this study were data availability and data quality. For future
research, also validation in other countries is desirable. Moreover, better
quality data for simulation could highly increase the validity of the results.
Nevertheless, we feel confident that our results hold when comparing different
simulations, despite some of the validation timeseries being of lesser
quality.

##  6 Conclusions

In this paper we assessed how different reanalysis data sets for wind power
simulation in different regions of the world, as well as means for global bias
correction of reanalysis wind speeds, affect simulation quality. We
additionally looked into the implications of spatial and temporal aggregation
on quality measures.

Our main conclusions are (1) that ERA5 performs better than MERRA-2 in all
regions and for all different indicators, with ERA5 showing approximately 0.05
higher correlations than MERRA-2 and 0.05 lower RMSEs in most regions. (2) No
version of the GWA consistently improves simulation quality. GWA2 may be used,
however improvements over the use of no bias correction may be minor and in
some cases, simulation results may even deteriorate. We discourage the use of
GWA3. (3) Temporal aggregation increases quality indicators due to
compensating effects, with an increase of about 0.2 in correlation and about
0.1 to 0.2 lower RMSEs in most regions when aggregating from hourly to monthly
time series. (4) For spatial aggregation, a much more limited effect was
found: only when comparing very low and very high spatial aggregations, an
increase in quality was observed.

The results of our analysis 888The resulting time series aggregated per wind
park will be made available after submission in an online repository can be
used as basis for future wind power simulation efforts and are the foundation
for a new global dynamic wind atlas. Access to this global dynamic wind atlas
is enabled by making our code openly available [49]. The tool is able to
generate wind power generation timeseries for all locations worldwide for use
in energy system models or for studying the variability of wind power
generation. Furthermore, our results allow estimating the magnitude of error
that has to be expected when relying on reanalysis data for wind power
simulation. These conclusions are important for energy system modellers when
designing highly renewable energy systems.

##  7 Acknowledgements

This project has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No. 758149).

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##  Appendix A Appendix

###  A.1 Aggregation of time series

We have time series $X$ and $Y$ and measure their similarity using the
correlation. We want to see if aggregation of time series has an impact on
correlation.

Let be $X_{1}$ and $Y_{1}$ time series e.g. in region $1$ and $X_{2}$ and
$Y_{2}$ time series in another region $2$. Given correlations
$corr\left(X_{1},Y_{1}\right)$ and $corr\left(X_{2},Y_{2}\right)$ we are
interested in $corr\left(X,Y\right)$ for the aggregated time series $X:=a\cdot
X_{1}+b\cdot X_{2}$ and $Y:=a\cdot Y_{1}+b\cdot Y_{2}$ for some $a,b>0$ with
$a+b=1$.

Note: we are not interested in negative correlations, so when we say “increase
of correlation” we mean that
$\left|corr\left(X_{1},Y_{1}\right)\right|<\left|corr\left(X,Y\right)\right|$.

Let’s first show that correlation can increase by aggregation:

######  Example 1.

Let $Z$ be some arbitrary random variable with $\mathbb{V}Z\neq 0$. Further
assume that $X_{1}$ and $Y_{1}$ are independent. If we set $X_{2}:=-X_{1}+Z$,
$Y_{2}:=-Y_{1}+Z$ and $a:=\frac{1}{2}$ and $b:=\frac{1}{2}$, then we get
$X=\frac{1}{2}Z$ and $Y=\frac{1}{2}Z$. Therefore $corr(X_{1},Y_{1})=0$ but
$corr\left(X,Y\right)=1$. If we choose $Z$ with
$\mathbb{V}Z\ll\mathbb{V}X_{1}$ and $\mathbb{V}Z\ll\mathbb{V}X_{2}$, also
$corr(X_{2},Y_{2})$ is almost $0$.

⬇

import numpy as np

N = 1000

noise = np.random.normal(size=N, scale=0.1)

x1 = np.random.normal(size=N)

x2 = -x1 + noise

y1 = np.random.normal(size=N)

y2 = -y1 + noise

a = b = 0.5

def corr(x, y):

return np.corrcoef(x, y)[0, 1]

print(”x1 and y1 are not correlated:”, corr(x1, y1))

print(”x2 and y2 are not correlated:”, corr(x1, y1))

print(”x and y are strongly correlated:”,

corr(a * x1 + b * x2, a * y1 + b * y2))

# weirdly this is violated:

# min(var(x1), var(x2)) <= var(ax1+bx2) <= max(var(x1), var(x2))

print(”var(x1): ”, np.var(x1))

print(”var(x2): ”, np.var(x2))

print(”var(a*x1 + b*x2): ”, np.var(a * x1 + b * x2))

Output:

⬇

x1 and y1 are not correlated: -0.003968605464354068

x2 and y2 are not correlated: -0.003968605464354068

x and y are strongly correlated: 1.0

var(x1): 1.0845349544321836

var(x2): 1.0952631334805492

var(a*x1 + b*x2): 0.00228463494772665

Algorithm 1 Numerical example for Example 1.

Now we show that correlation of the aggregated random variables can vanish
even for high correlation of $X_{i}$ amd $Y_{i}$, $i=1,2$.

######  Example 2.

Now choose $Z$ to be a random variable with $0<\mathbb{V}Z\ll\mathbb{V}X_{i}$
for $i=1,2$. Further let $X_{1}$ be some arbitrary random variable with
$\mathbb{V}X_{1}\neq 0$ and independent to $Z$.

Then set $X_{2}:=-X_{1}+Z$, $Y_{1}:=3\cdot X_{1}$ and $Y_{2}:=-X_{1}$. This
yields $X=\frac{1}{2}X_{1}-\frac{1}{2}X_{1}+\frac{1}{2}Z$ and $Y=X_{1}$. Since
$X_{1}$ and $Z$ was chosen to be independent, we have
$corr\left(X,Y\right)=0$, but $corr\left(X_{1},Y_{1}\right)=1$ and
$corr\left(X_{2},Y_{2}\right)$ is very close to $1$ because $Z$ was chosen to
be small noise.

###  A.2 Validation of USWTDB with IRENA

We validate the data in the USWTDB [50] with installed capacities as provided
by the International Renewable Energy Agency (IRENA) [58]. Figure 7 shows the
ratio of capacities in the USWTDB to IRENA capacities. After the year 2010,
this ratio is close to 1, but before 2010 capacities do differ quite
significantly. This indicates that there are large capacities missing in the
USWTDB in earlier years.

Figure 7: Installed capacities in the US wind turbine data base [50] compared
to IRENA [58]

###  A.3 Additional data sources South Africa wind parks

For the wind park data set in South Africa, part of the information was
missing and therefore needed to be complemented by additional sources. Some
data points were not available at all and data was selected according to
turbine specific available data. The turbine type is known, therefore from
turbine specification data sheets missing information can be derived. In case
there are several possibilities, e.g. hub height in a range, instead of only
one number, a value in the medium range is picked. The data that needed to be
added are listed in Table 4.

Table 4: Additional data gathered for complementing the South African wind
park data set

Windpark Data quality issue Correction Source Dorper wrong height Set to 80 m
(derived from existing turbine type) Nordex N100/2500 [67] Excelsior missing
height Set to 100 m (derived from existing turbine type) Goldwind GW121/2500
[68] Gibson Bay missing height Set to 100 m (derived from existing turbine
type) Nordex N117/3000 [69] Longyuan once height, once diameter missing
complement with each other Karusa missing height and diameter use height from
project homepage https://www.windbase.eu/projects/wind-farm-karusa-en-
soetwater.aspx Soetwater missing height use height from project homepage
https://www.windbase.eu/projects/wind-farm-karusa-en-soetwater.aspx
Tsitsikamma missing height set to 112 m (derived from existing turbine type)
ref Wesley-Ciskey missing height, diameter and capacity assume 126 m diameter
and 137 m height for V126 3.45MW https://www.afrik21.africa/en/south-africa-
vestas-to-build-wesley-ciskei-wind-farm-for-edf/ Nxuba missing height,
diameter and capacity assume Acciona AW123-3MW with 125 m diameter and 120 m
height https://www.aced.co.za/nxuba-wind-farm Oyster Bay missing height and
diameter assume Vestas V117-3.45 with 117 m diameter and 91.5 m height
https://www.aa.com.tr/en/energy/news-from-companies/vestas-awarded-148-mw-
wind-project-in-south-africa/22153 Klawer Wind Farm missing height, diameter
and capacity assume information from project plan
http://www.energy.gov.za/files/esources/kyoto
/2011/06-06-2011%20-%20Klawer%20PDD.pdf Hopefield Community Wind Farm missing
height, diameter and capacity assume same as Hopefield Wind Farm Golden Valley
missing height, diameter and capacity assume GW121/2500 with 121 m diameter,
120 m height and 2500 kW capacity https://www.windpowermonthly.com/article
/1488858/long-delayed-south-african-wind-farms-reach-financial-close Garob
missing height and diameter assume AW125/3150 with 125 m diameter and 120 m
height https://www.afrik21.africa/en/south-africa-enel-begins-garob-wind-farm-
construction-140-mw/ Copperton missing height and diameter assume AW125/3150
with 125 m diameter and 120 m height https://www.evwind.es/2018/09/13/nordex-
acciona-awarded-big-ticket-wind-energy-contracts-in-south-africa/64501

###  A.4 Difference in simulation quality MERRA-2 vs. ERA5

Figure 8 displays the change in the indicators correlation, RMSE and MBE when
applying ERA5 instead of MERRA-2 for wind power simulation. In the USA, Brazil
and New Zealand the correlation is up to 10 % points higher with ERA5 than
with MERRA-2, for the USA there are even some outliers with an increase in
correlation of up to 80 % points. Only in New Zealand correlations with ERA5
based simulations are lower. The RMSE is lower with ERA5 compared with MERRA-2
except in New Zealand where simulations with ERA5 result in RMSEs up to 20 %
points higher than with MERRA-2. The difference in MBEs is more consistent in
the different regions, in the range of 10 to 20 % points lower for ERA5.

Figure 8: Differences (ERA5 - MERRA-2) in statistical parameters for
simulations with MERRA-2 and ERA5 (MERRA-2 - ERA5)

###  A.5 Applying GWA to MERRA-2 simulated wind power time series

Here, we show the impacts of applying GWA to MERRA-2 data. As for ERA5, in
most cases the impact of the GWA on correlations is negligible, as can be seen
in Figure 9. In New Zealand the correlation is slightly increased with GWA2
and decreased with GWA3, but the changes are not significant. The RMSE
decreases with GWA2 in all regions but New Zealand (the decrease is only
significant in the USA), while GWA3 shows a tendency to increase the RMSE
(with significantly increased RMSE in the USA and New Zealand) except in
Brazil where it has a significantly decreasing effect. In Brazil the best fit
according to MBEs is observed using GWA 3 which decreases the MBE leading to a
lower error. As with ERA5, using GWA2 decreases MBEs leading to an
underestimation on average. In the USA, the smallest mean bias is achieved
with GWA2 which reduces the MBE, while GWA3 increases the MBE and thus the
error. In New Zealand, using no bias correction with GWA leads to a small
error and a good fit. If GWA2 is applied, overestimation of around 10 %
capacity factor is achieved, while GWA3 increases the overestimation to more
than 20 % capacity factor. For New Zealand it is therefore not recommended to
apply GWA for mean bias correction. In South Africa simulations overestimate
observed power generation by around 5 % capacity factor, which is increased
slightly but insignificantly by GWA3, while GWA2 decreases the error to nearly
-10 % capacity factor. The best fit is therefore achieved without GWA. All
other changes in MBE are significant.
To sum up, the results of mean bias correction with GWA using MERRA-2
reanalysis data is ambiguous. While the RMSE is decreased except for New
Zealand with GWA2, GWA3 usually increases the RMSE, but on the other hand
performs better than GWA2 in terms of MBE in Brazil and South Africa. From
these results, neither GWA2 nor GWA3 can be fully recommended for bias
correction of MERRA-2 data as simulation quality is not consistently
increased.

Figure 9: Comparison of statistical parameters for simulations with MERRA-2
and different versions of the GWA

###  A.6 Country-specific results

This section presents results as in section 4, but per country. This allows to
compare specifics in different countries compared to the overall picture.

####  A.6.1 Impact of the choice of reanalysis dataset on simulation quality

Figure 10 shows the three indicators measuring simulation quality (i.e.
correlation, RMSE and MBE) in the four different countries for the two
reanalysis datasets. ERA5 has, on average, higher correlations than MERRA-2.
The median differs, however, only for South Africa significantly. For the
RMSE, ERA5 is significantly better than MERRA-2 in the USA and Brazil. In New
Zealand and South Africa, however, no significant difference in the median of
RMSEs is found. The MBEs are closer to 0 in the USA and Brazil with ERA5,
however MERRA-2 performs better in New Zealand. In South Africa the MBEs
indicate a similar error for both data sets, but ERA5 underestimates while
MERRA-2 overestimates. All differences in the MBE are significant.
Overall, it can be concluded that ERA5 performs better than MERRA-2 in terms
of higher correlations but lower errors, with the exception of New Zealand
(Figure 10). However, in many cases the differences in the median between the
two datasets are insignificant (95% confidence interval), in particular for
the correlations.

Figure 10: Comparison of statistical parameters for simulations with ERA5 and
MERRA-2 reanalyses for each of the four countries analysed individually. Non-
overlapping notches indicate a difference in the medians statistically
significant at the 95% level.

####  A.6.2 Bias correction with GWA

Regarding correlations, the changes are minor, only in New Zealand there is a
shift up to higher correlations with GWA2, in South Africa with both GWAs, but
in none of these regions significantly.
The RMSE decreases with GWA2 in all regions, while the GWA3 shows a tendency
to increase the RMSE. Only in Brazil the impact of the GWA3 is minor. While no
version of the GWA increases or decreases the RMSE significantly, in the USA
and New Zealand the simulation with GWA3 has a significantly higher RMSE than
with GWA2. In the USA, the GWA2 however reduces the spread of RMSEs from
between approximately 0.05 and 0.15 (IQR: 0.05) to 0.04 and 0.21 (IQR: 0.1)
without GWA.
Regarding the MBEs, in Brazil the best fit is observed without using bias
correction. With GWA2, MBEs are decreased, indicating an underestimation,
while GWA3 results in an increase of MBEs. As no downtime, wake effect or
other losses are taken into account in the wind power simulation model, an
overestimation as with GWA3 seems more appropriate. In the USA, using no bias
correction at all results in the best fit to observed wind power generation as
measured by the MBE. GWA2 slightly increases the error, and GWA3 does so even
more. In this case, GWA2 might be used to shift the MBE more to a positive
range, to take account of possible losses. In New Zealand, observed wind power
generation is underestimated by around 10 to 20 % of the capacity factor
without bias correction. If GWA2 is applied, generation is overestimated by up
to 7 %, while GWA3 increases the overestimation to around 15 to 20 %. For New
Zealand it is therefore also recommendable to apply bias correction with the
GWA2.
In South Africa, simulations underestimate observed power generation by circa
10 % capacity factor, which is decreased to less than 5 % by GWA2, while GWA3
increases the error to nearly 10 % capacity factor. In all studied regions,
the median of MBEs differ significantly. Furthermore, in all regions the
spread of MBEs is decreased when using bias correction, with the interquartile
range (IQR) reducing by about 50% except in Brazil.

Figure 11: Comparison of statistical parameters for simulations with ERA5 and
different versions of the GWA. Non-overlapping notches indicate difference in
medians statistically significant at the 95% significance level.

####  A.6.3 Wind speed correction factors

Figures 12-15 show the calculated correction factors for Brazil, New Zealand,
the USA and South Africa for different combinations of reanalysis and GWA
datasets. A common pattern in all countries and for all datasets is that
correction factors are higher in mountainous regions. Regarding the applied
datasets, however, there are differences. While in New Zealand the highest
correction factors are resulting form bias correction of ERA5 with any of the
GWA, in the USA and South Africa this is only the case with GWA3. In the USA
the correction factors with GWA2 applied to ERA5 are only about half compared
to the correction factors with GWA3. In Brazil, on the other hand, the
correction factors are highest with GWA2, irrespective of the reanalysis
dataset they are applied on. This indicates, that either reanalysis data, or
GWA, or both indicate different wind patterns depending on the region they are
applied to.

Figure 12: Correction factors with GWA2 and GWA3 for MERRA-2 and ERA5
reanalyses in Brazil (the map is powerlaw-normalised) Figure 13: Correction
factors with GWA2 and GWA3 for MERRA-2 and ERA5 reanalyses in New Zealand
Figure 14: Correction factors with GWA2 and GWA3 for MERRA-2 and ERA5
reanalyses in South Africa Figure 15: Correction factors with GWA2 and GWA3
for MERRA-2 and ERA5 reanalyses in USA (the map is powerlaw-normalised)

####  A.6.4 Relation of geography and correlations of simulated and observed
wind power generation time series

Figure 16 shows the hourly correlations between ERA5 simulation with GWA2 bias
correction and observed wind power generation time series. In Brazil higher
correlations are observed in the South, and lower at the coast of the North-
East. The lowest correlations are in the north west of Ceará. In New Zealand a
difference is seen between coastal and inland wind parks: At the coast
correlations are higher.

Figure 16: Correlations between simulated wind power generation based on ERA5
reanalysis with GWA2 bias correction with observed wind power generation in
Brazilian and New Zealand wind parks

####  A.6.5 Impact of spatial and temporal aggregation

For the USA, a slight tendency of higher correlations as well as lower errors
(lower RMSEs, MBEs closer to 0) can be observed, when system size is
increased. However, only for larger system sizes, medians of the distributions
differ significantly. In Brazil, a similar trend is visible, except for the
third-largest group (10, 20], in which simulation quality drops. This can be
attributed to the state of Bahia, where the GWA skews the wind speeds and
therefore leads to a higher over-estimation. In New Zealand and South Africa
results are ambiguous, i.e. no relation between system size and simulation
quality can be identified.

Figure 17: Impact of spatial resolution (absolute system size, i.e. number of
occupied reanalysis grid cells) on simulation quality per country. Non-
overlapping notches indicate a statistical difference in the median at the 95%
significance level.

Figure 18 shows a strong correlation between temporal resolution and
simulation quality: as expected, the error is decreased and the correlations
are increased going from hourly to monthly temporal resolution. An exception
is the USA, where the monthly correlations are not higher than daily or hourly
correlations. This may be a result of correlations being high for any temporal
resolution in the USA ($>$ 0.85). Also, the RMSEs are the lowest (0.05 monthly
to 0.11 hourly) compared to the other countries. Lowest average correlations
are observed in South Africa, with hourly and daily correlations of around
0.6, which is increased to 0.75 to 0.85 by monthly aggregation. In New Zealand
two very low outliers in the hourly and daily correlations are visible, which
are located at The Wind Farm 3. Only in Brazil the increase by temporal
aggregation in the median of the distribution of correlations is significant,
while Brazil is the only region where the RMSE does not change significantly
due to temporal aggregation. The MBE is not consulted, since it is the same on
average for each of the levels of temporal resolution (Figures 17 and 18).

Figure 18: Impact of temporal resolution on simulation quality per country.
Non-overlapping notches indicate a statistical difference in the median at the
95% significance level.

###  A.7 Time series quality assessment for USA

As described in section 2.5, generation data in the USA were selected by
visual assessment of the time series. For this purpose, the monthly time
series were plotted and screened for obvious errors, such as several months of
(nearly) constant wind power generation, or observed generation fluctuating
between a limited amount of levels without showing typical seasonal pattern.

While the monthly generation of the USA (Figure 19) exhibits no obvious data
quality issues, three regions are removed, since their production is constant
at two nearly constant levels for the first years (Figure 20): New England
(NewEng), East South Central (ESC) and Pacific Non-Continental (PacNon)
regions.
Seven of the states were discarded for further use, due to their unsatisfying
data quality (Figure 21): Arkansas (AK), Connecticut (CT), Delaware (DE),
Illinois (IL), North Carolina (NC), South Dakota (SD) and Tennessee (TN). In
nine states only a part of the time series was used, while the the remainder
was discarded due to unusual patterns such as fluctuating generation between
plateaus or unusually high or low generation instead of seasonal patterns:
Massachusetts (MA), Nebraska (NE), New Jersey (NJ), Ohio (OH), Rhode Island
(RI), Vermont (VT) and Wisconsin (WI).

Figure 19: Simulated and observed monthly wind power generation in the USA
Figure 20: Simulated and observed monthly wind power generation in ten regions
of the USA (a)  Figure 21: Simulated and observed monthly wind power
generation in the states of USA. The validation period is shaded yellow. If
the time-series was not used at all, this period has 0 length. (a)  Figure 22:
Simulated and observed monthly wind power generation in the states of USA. In
states where only part of the time series is used, the validation period is
shaded yellow (a)  Figure 23: Simulated and observed monthly wind power
generation in the states of USA. In states where only part of the time series
is used, the validation period is shaded yellow

Apart from several regions with bad quality time series, it was also perceived
that the observations in the years before 2010 fit the simulations worse than
the past ten years. Therefore, the time series before 2010 were discarded and
the results compared to the analysis based on the entire time series. As
Figure 24 shows, correlations can be increased and RMSEs decreased when
considering the shorter period only.

Figure 24: Correlations (left) and RMSEs (right) of simulated vs. observed
wind power generation in the USA and its states and regions, comparing time
series for the entire period (2000-2019) to only the past ten years
(2010-2019)