Using bias-correction to improve future projections of offshore wind energy resource: A case study on the Iberian Peninsula

Applied Energy 262 (2020) 114562

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Using bias-correction to improve future projections of offshore wind energy resource: A case study on the Iberian Peninsula

T

⁎

X. Costoyaa,b, , A. Rochab, D. Carvalhoc,d a

CRETUS Institute, Group of Nonlinear Physics, Department of Particle Physics, University of Santiago de Compostela, Santiago de Compostela, Spain CESAM, Physics Department, University of Aveiro, Portugal c Global Modeling and Assimilation Office (GMAO), NASA Goddard Space Flight Center, Greenbelt, MD, USA d Goddard Earth Sciences Technology and Research (GESTAR), Universities Space Research Association (USRA), Columbia, MD, USA b

H I GH L IG H T S

speed from the Coordinated Regional Climate Downscalling project was corrected. • Wind based on quantile mapping and correction in the frequency domain were used. • Methods combination of bias correction methods reduces wind power density (WPD) error. • The reduction was found for future in most of the western Iberian Peninsula. • AA WPD • WPD increase is projected for summer and a decrease in autumn and spring.

A R T I C LE I N FO

A B S T R A C T

Keywords: Bias correction Frequency dependent bias correction Offshore wind energy West Iberia

The reduction of the error in climate model’s meteorological variables representation is a key challenge to improve the reliability of future climate projections. It has special importance when analyzing wind power density (WPD) because this variable is proportional to the wind speed cubed. The first aim of this study is to determine whether bias correction improved WPD future projections from the Coordinated Regional Climate Downscalling project. With this purpose, two bias correction techniques have been applied over wind speed climatic projections. The first one was based on quantile mapping approach, while the second one was based on the correction in the frequency domain. It was found that the combination of bias correction techniques reduced biases both in terms of temporal variability and in the distribution of wind series. Regarding the sensitivity of WPD to bias correction techniques, it was detected that not corrected simulations tended to overestimate offshore wind energy in the area selected as case study, the Iberian Peninsula. Thus, a WPD reduction higher than 200 W m−2 at an annual scale for the end of the 21st century was observed in most of the Western Iberia coastal areas when comparing the median WPD from not corrected and corrected simulations. A WPD reduction was observed for near, mid and far future by means of corrected projections, except for the northwestern corner of the Iberian Peninsula. At seasonal scale, an increase of about 20% was projected in summer, while a WPD decrease was observed in spring and, especially in autumn (20%).

1. Introduction Climate projections produced by Global Climate Models (GCMs) have received significant attention in the last decade [1]. GCMs simulate the complex interactions between atmosphere, ocean, land surface and sea ice. Thus, these numerical models have become a useful tool to progress in the understanding of the physical processes that condition climate system, and, therefore, climate change. Under the assumption of considering different greenhouse gases emissions and concentrations ⁎

for the future, it is possible to estimate how climate variables will change. On the global scale, the most ambitious project regarding climate projections is the phase 5 of the Coupled Model Intercomparison Project (CMIP5) [2], which considers three different gas emission scenarios, called Representative Concentration Pathways (RCPs) [3]. More recently, it was launched the Coordinated Regional Climate Downscaling Experiment (CORDEX) by the World Climate Research Program (WRCP), which uses as forcing the state-of-the-art GCMs from CMIP5 to provide climate projections for different regions worldwide through

Corresponding author. E-mail address: [email protected] (X. Costoya).

https://doi.org/10.1016/j.apenergy.2020.114562 Received 11 October 2019; Received in revised form 13 January 2020; Accepted 25 January 2020 0306-2619/ © 2020 Elsevier Ltd. All rights reserved.

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dynamical downscaling with a wide range of Regional Climate Models (RCMs). Thus, CORDEX is supposed to provide a significant improvement in the representation of regional climates given its increased spatial resolution. Although many improvements have been implemented in the last generation of climate models [4,5], some uncertainties and biases still remain in the simulation of the frequency and intensity of climate variables. This fact is mainly caused by limited computational resources, uncertainties in model parameterization, simplified assumption during model construction, insufficient spatial resolution to resolve some climate processes and misunderstanding of the way the climate reacts [6]. To deal with these biases, different statistical techniques, encompassed under the broad term of bias correction or bias adjustment, were implemented. Overall, bias correction of climate projections is based on the comparison between observed and GCM-simulated variables. Thus, it is possible to establish a statistical relationship, called transfer function, between both sources of data and apply it to the variable for a future period. The simplest bias correction techniques applied in the correction of future climate projections consist of adding the difference between the modelled and observed variable for a common period to the projected value (unbiasing method, e.g: [7]) or adding the difference between the current modeled climate and the future projection to an observed baseline (delta method, e.g: [8]). A more sophisticated bias correction technique widely used in future climate analysis is quantile mapping (QM), which is based on correcting the shape of the entire variable distribution by establishing statistical relationships between cumulative density functions from the observed and simulated variable [9,10]. A basic assumption of the traditional QM approach [11] is that the distribution for the future period will remain similar to the common period between observations and modelled data. However, due to climatic nonstationarity, it could be important to preserve changes in the distribution in the future corrected projections in a context of climate change [12]. With this aim, other QM based techniques has been developed [13,6]. A detailed discussion with different approaches based on QM can be found in Pierce et al., [14]. In addition, these authors also develop an innovative method to reduce frequency-dependent climate model biases, called frequency dependent bias correction (FDBC). This method showed a reduction in the error model’s representation of the spectrum of variability when applied to precipitation data [14]. Bias correction techniques have been applied to model outputs from CMIP5 project to different regions worldwide. Most of these studies analyzed temperature or precipitation variables (e.g: [15,16]). Although in a smaller quantity, bias correction techniques using a QM approach were also applied to carry out analysis of temperature and precipitation data from the CORDEX project (e.g: [17,18]). However, bias correction for climate projections regarding other variables, such as wind speed, was less commonly applied. This fact is related to the lack of consistent daily gridded datasets of observations for wind speed [19,20]. In fact, only a few studies have applied bias correction to wind speed climate projections and most of them for specific locations using station-based observational data to compare with simulations [21,22]. Previous analysis comparing simulated wind speed with observations agree that the representation of winds for coastal regions and areas with complex topography remains a modelling challenge [23,20]. Mesoscale models show higher inaccuracies in coastal areas caused by thermal gradients due to land-sea temperature differences, discontinuity between land and sea roughness and due to local topography, which plays an important role in defining coastal winds [23]. These errors in coastal areas, in conjunction with the fact that wind power is proportional to wind speed cubed that amplifies errors when wind power output is calculated, make bias correction techniques an important step to reduce errors and improve offshore wind power resource projections. However, as stated earlier, there is a lack of published literature focusing on the analysis of future offshore wind energy resource by means of bias corrected projections over a wide region. As far as we know, the

Fig. 1. Area under scope and bathymetry. Numbers mark the location of buoys. Green line represents 200 m isobath.

analysis carried out by Moemken et al. [20] was the only study in which bias correction is applied over wind speed CORDEX data in order to analyze a vast area. These authors only applied the bias correction approach developed by Michelangeli et al., [24] using data from ERAInterim as observations. The main aim of this study is primarily to assess if bias correction techniques, including correction in the frequency domain [14], can improve the accuracy of wind speed series from CORDEX project. As far as we know, the present study is the first attempt in which a combination of bias correction techniques is used to obtain more reliable offshore wind energy estimations for the future in a wide area, not only at specific locations. As a case of study, this test will be carried in the Iberian Peninsula Atlantic Coast (Fig. 1) because it presents attractive conditions for a significant offshore wind energy development in the future. However, it is important to keep in mind that this methodology was designed to allow its application in any coast of the world. 1.1. Area under scope The sensitivity analysis on how bias correction affects future offshore wind energy resource was carried out in the western area of the Iberian Peninsula, which comprises the Portuguese coast and a part of the Atlantic coast of Spain (Fig. 1). Although Iberian countries have been among the leading European ones in onshore cumulative wind power capacity [25], offshore wind energy have not yet been developed in this area. The main drawback of this region is its narrow continental shelf that reduces the available area to install offshore wind farms based on fixed wind turbines (Fig. 1). At this point it is necessary to consider the technical progress in developing floating wind structures (e.g: [26]). In fact, a floating offshore wind turbine prototype has been deployed for five years 5 km off the coast in the NW of Portugal. After this test, it is planned the installation of the first floating wind farm west of the Iberian Peninsula [27]. Previous studies have already analyzed the economic feasibility of different offshore platforms, including floating wind turbines, in the northwest of the Iberian Peninsula [28,29], as well as, the legal restrictions in conjunction with the analysis of the 2

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wind power density [30,31]. Pacheco et al. [32] also analyzed the potential for offshore wind exploitation using floating wind structures in the Sagres area (SW Portugal). Therefore, this area has received much attention in recent years in order to ensure the viability of the newest offshore wind platforms, which gives an idea of the suitability of this area to offshore wind energy exploitation. Different studies have been carried out focused only in the offshore wind energy resource of the western area of the Iberian Peninsula due to its attractive wind resource. Salvação and Soares [33] analyzed energy density by means of simulations carried out with WRF model. They observed annual wind energy densities between ~400 W m−2 and ~1000 W m−2 at 10 m above sea level (a.s.l.), with the highest values occurring in the winter. Previously, different studies had already quantified wind energy resource using wind data from different wind data sources (ASCAT and OSCAT scatterometers [34], QuikSCAT [35], reanalysis databases [36], CCMP [37], Blended Sea Winds [34], ocean wind vectors [36] or high-resolution WRF model simulations [38,39]. According to these studies, the highest wind energy density is located off the northwestern corner of the Iberian Peninsula, with high values also around Cape Roca and Cape St. Vincent. These authors reported values between 300 and 700 W m−2 in the west Iberian Peninsula at a height of 10 m. Besides the offshore wind energetic resource, the impact of climate change on offshore wind power generation has been a subject of research in the recent past. Soares et al. [40] used a multi-model of RCMs under the framework of the CORDEX project (scenarios RCP 4.5 and RCP 8.5) to project future changes in offshore wind power. These authors projected a 2.5% to 10% yearly reduction over the entire western Iberian coast for the period 2071–2100, except for the Iberian northwestern area, where no change was expected due to the increase projected in summer. However, Santos et al. [41] also analyzed variations in wind energy density using data from several RCMs from the CORDEX project and they found a slight increase in most of the western Iberian coast in the near future (2019–2045) under RCP 8.5. They also noticed an increase for the far future (2073–2099) in areas with high yearly mean values [34], such as northwestern Iberian coast, Cap Roca or Cape St. Vincent. Therefore, previous analysis show uncertainties with respect to the sign and magnitude of the changes in wind energy projections in the western Iberian coast. The present study aims also to fills a gap in the present knowledge related to offshore wind energy in the western Atlantic coast of the Iberian Peninsula by applying bias correction techniques to offshore wind energy projections, thus reducing these uncertainties. Therefore, the main aim of the present study is to evaluate whether bias correction improves CORDEX simulations by quantifying different errors, before and after of applying bias correction techniques. In addition, differences between corrected and not corrected CORDEX wind data will be also analyzed. This methodology will be applied to a case study on the west coast of the Iberian Peninsula due to its suitability for future offshore wind energy development.

Table 1 Regional climate simulations from CORDEX (http://www.cordex.org/) project used in this study. Historical & RCP8.5 Experiments

Evaluation Experiment

GCM

RCM

INSTITUTE

RCM

INSTITUTE

CNRM-CM5 CNRM-CM5 EC-EARTH IPSL-CM5A-MR IPSL-CM5A-MR MPI-ESM-LR MPI-ESM-LR

CCLM4-8-17 RCA4 RACMO22E RCA4 WRF331F CCLM4-8-17 REMO2009

CLMcom SMHI KNMI SMHI INERIS CLMcom MPI-CSC

CCLM4-8-17 RCA4 RACMO22E WRF331F REMO2009 RegCM4-2 HIRHAM5

CLMcom SMHI KNMI INERIS MPI-CSC DHMZ DMI

important to mention that 2005 and 2008 are the last year with available data for Historical and Evaluation CORDEX experiments, respectively. Three future periods were considered to analyze the projected wind variations after bias correction: near future (2025–2040), mid future (2055–2070) and far future (2085–2100). A multi-model ensemble was created for Evaluation, Historical and RCP8.5 simulations since previous studies have demonstrated that it minimizes the individual model biases [42,5]. The first step to create the multi-model was interpolating wind speed values to a common grid with the same spatial resolution of RCMs (0.11° × 0.11°). Future projections, not forecasts, were taken considering the most pessimistic (although perhaps the most realistic at the present moment) future greenhouse gases emission rates, the scenario RCP 8.5, which represents that greenhouse gas emissions will lead to 8.5 W m−2 radiative forcing and that this increase will continue after 2100 (more information regarding climate scenarios can be found in [43]. 2.1.2. CCMP ocean surface winds analyses The Cross-Calibrated Multi-Platform (CCMP) Ocean Surface Wind Vector Analyses [44] was the database used to carry out the bias correction of CORDEX data. It is a dataset that provides a consistent, gapfree long-term time-series of ocean surface winds from July 1987 through December 2017. It combines data from in situ wind measurements and satellite winds derived from different microwave radiometers (SSM/I, SSMIS, AMSR, TMI, WindSat and GMI) and microwave scatterometers (QuikScat and SeaWinds). The observed winds are combined with first guess fields from the ERA-Interim reanalysis using a Variational Analysis Method, resulting in a gridded, high-resolution (0.25° × 0.25°), 6-hourly wind analysis dataset [45]. All wind data is referenced to a height of 10 m above sea level. Data from the CCMP V2.0 version was retrieved from the Remote Sensing Systems server (http://data.remss.com/ccmp/) over the period 1990–2008. This period was selected because there is some missing data over the years 1988–1989 in CCMP database, whilst 2008 is the last year with data available for CORDEX evaluation experiment. Therefore, the common period without gaps with CORDEX project was selected. The choice of this dataset to carry out the bias correction of CORDEX data was based on the analysis of previous studies [36,34] that compared different offshore wind datasets with buoys measurements for the Iberian Peninsula Atlantic coast in order to assess which product was the most accurate. Carvalho et al. [36] compared ten datasets and they found that CCMP was the one with the best performance in terms of wind speed biases, which is the variable analyzed in the present study. In addition, when analyzing other statistics, such as wind direction or Weibull parameters, they also concluded that CCMP clearly stands out since it showed winds closest to the measurements. Carvalho et al. [34] compared CCMP with wind products derived from the newest generation scatterometers (ASCAT and OSCAT), concluding that CCMP represents the best alternative to analyze offshore wind data, especially when gridded data, higher spatial resolution or higher temporal sampling is needed, which is the case of the present study. Therefore,

2. Data and methodology 2.1. Data 2.1.1. CORDEX data Daily 10 m wind speed data were obtained from simulations carried out within the framework of the CORDEX project (http://www.cordex. org/). Data from three different experiments (evaluation, historical and RCP8.5 future scenario) were retrieved from the German Climate Computing Center node (https://esgf-data.dkrz.de/search/cordexdkrz/). These daily data have a spatial resolution of 0.11° × 0.11° latitude and longitude. Evaluation, historical data and future projections were retrieved from seven Regional Climate Models (RCMs) (Table 1). Historical data was retrieved over the period 1990–2005, whilst evaluation data was retrieved from 1990 to 2008. At this point it is 3

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Table 2 Location, period considered in this analysis, depth and distance to coast of buoys provided by Puertos del Estado (http://www.puertos.es/). Number

Buoy

Latitude (°N)

Longitude (°E)

Period

Depth (m)

Distance Coast (km)

1 2 3 4 5

Cape Peñas Estaca de Bares Sisargas Cape Silleiro Gulf of Cádiz

43.75 44.12 43.50 42.12 36.48

353.84 352.31 350.8 350.57 353.04

1998–2018 1997–2018 1998–2018 2003–2018 2003–2018

615 1800 386 600 450

~20 ~32 ~30 ~40 ~55

QM procedure in which the value for each quantile of the observed dataset (CCMP) is assigned to the same quantile of the modelled dataset (CORDEX simulations) in order to correct the whole cumulative distribution. After that, to carry out the adjustment a weighting factor that depends on model error is added ( g ). This factor was calculated as the fraction between the average value for the whole series of CCMP dataset and the whole series of CORDEX historical data. Finally, the average difference between historical and future simulations of CORDEX was also considered. The difference is calculated for each quantile as CORDEX for the future period less CORDEX for the historical period and, then, all these difference values are averaged for the ¯) whole period (15 years) with the aim of obtaining a unique value (Δ that accounts for the intrinsic climate change signal of CORDEX data. Detailed information about this BC method can be found in Amengual et al. [22]. These authors successfully tested it for different atmospheric variables at a specific location in Mallorca Island. In addition, this BC method has been used also for analyzing, for example, heat waves projections in Europe [22] or precipitation in France [49]. In addition to BC of historical and future wind speed projections from CORDEX project, a method to reduce frequency-dependent climate model biases [14] was also implemented. The frequency dependent bias correction (FDBC) is based in the calculation of a “spectral correction factor” using observed and future modelled data assuming that model errors in the historical period are also present in the future simulations. In brief, to carry out this calculation it is necessary to transform model time series to frequency space using the Fourier transform. Then, the spectral power is calculated for historical data and future projections and the ratio of the observed to model spectral power at 100 logarithmically space frequency bins is computed. This ratio is termed the spectral correction factor. After its calculation, each spectral component is multiplied by the corresponding spectral correction and, finally, the corrected spectral is passed from frequency to temporal space by means of the inverse Fourier transform. Detailed information about each step of FDBC can be found in Pierce et al. [14]. Fig. 2 shows a diagram with the aim of summarizing the approach followed to carry out the correction of CORDEX projections. Daily CORDEX data from all model simulations were re-gridded to a common grid of 0.25° × 0.25° of horizontal spatial resolution. Considering that CORDEX data has a daily temporal resolution, wind

considering these previous studies, it was found that CCMP is the option that best fit the purpose of the present work. 2.1.3. Buoy data Hourly wind data were obtained from five buoys deployed by Puertos del Estado (http://www.puertos.es/). These buoys sample at a height of 3 m a.s.l. and their coordinates can be seen in Table 2 (white points in Fig. 1). All the available data up to 2008, which is the last year with available data for the Evaluation experiment in CORDEX project, was retrieved for each buoy. 2.2. Methods 2.2.1. Bias correction and frequency dependent bias correction The basic assumption of bias correction is to establish a statistical relationship (called transfer function) between model outputs and observations. A QM approach (also called Distribution Mapping or Quantile-Quantile method) was chosen to carry out bias correction [9]. From here onwards, we will refer to the bias correction process by means of QM as ‘BC’. QM, which has been widely used for correcting biases in simulated meteorological variables (e.g: [46,47]), adjusts the cumulative distribution of modelled data to the cumulative distribution of observed data using a transfer function. Thus, historical CORDEX data can be corrected according to the following expression [13,6]:

x m − adjust = Fo−1 [Fm (x m)]

(1)

F0−1

where is the inverse of the cumulative density function of historical observed wind speed; Fm is the cumulative density function for historical modelled data; Xm is the wind speed modeled value and x m − adjust is the historical modelled bias corrected value. Following Eq. (1), the wind speed projected for future periods can be also corrected by changing the projected value to the observed value at the quantile that the model value falls in the model’s historical distribution [14]. This approach assumes that the future distribution will remain similar to that in the reference period. However, in a context of climate change, this approach is not valid since the probabilistic structure of climatic variables changes over time [12,48]. For this reason, different quantilebased mapping methods have been developed in order to deal with climatic non-stationarity. In the present analysis, the method applied by Amengual et al. [22] was considered suitable for our purposes, because its calibration amends mean, variability and shape errors in the CDFs of the simulated climatic variables. In brief, their calibration methodology can be calculated quantile to quantile as follows:

¯ + f Δ'i x f − adjust = oi + g Δ

(2)

where oi is the observed (CCMP database) wind speed value for quantile ¯ represents the average difference between both modelled (historical i; Δ and future) distributions, while Δ'i is the quantile difference (future ¯ ); g represents the ratio minus historical) less the average difference (Δ between the mean wind speed value of the observed series and the modelled historical series; f is the ratio of the interquartile ranges of the observed and simulated historical series. According to this method, future wind speed projections are rescaled for each pixel quantile by quantile on the basis of the observed CDF. Therefore, this first step accounts for the classical approach of a

Fig. 2. Diagram showing the approach followed to correct CORDEX projections using wind speed series from CCMP dataset. 4

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following:

speed from 6-hourly CCMP data and wind speed from buoys (3-hourly data) was also daily averaged to allow BC. To carry out the comparison between CORDEX data and in-situ wind speed from buoys the nearest pixel to each buoy from CORDEX data is selected.

⎡1 NRMSE = ⎢ N ⎣

1 ρ WH3 2 a

(3)

where ρa is the air density (1.225 kg m−3 at 288.15 K and 1000 hPa) and WH is the wind speed at the hub height. To carry out WPD estimation a height of 120 m was selected, which is the typical hub height of offshore wind turbines. WPD is the metric most widely used in offshore wind energy resource assessment analysis since it allows distinguishing the areas with a higher resource and thereby facilitate comparison among different zones. It is necessary to extrapolate wind speed data to different heights since speed from buoys was measured at 3 m and modelled wind speed is referred to a height of 10 m a.s.l. The most accurate methods to extrapolate wind data are those that consider the atmospheric stability, such as Monin-Obukhov theory [50] or the Liu and Tang method [51]. However, the buoys used in this study do not collect some variables required to apply these methods, such as heat flux or friction velocity. Therefore, a logarithmic wind profile method, which considers a neutrally stratified atmosphere, was selected to carry out wind extrapolation. This approach allows a good compromise between availability and low cost for data [52]. It was applied following the expression applied in previous studies [53,54].

( ) ln ( ) ln

WH = Wns

H z0

Hns z0

⎦

i=1

100 ⎞ .⎛ ¯ sim. W ¯ obs )1/2 ⎠ ⎝ (W ⎜

⎟

(5)

where N is the number of pairs of simulation/observed records; Wsim and Wobs represents the simulated wind speed and observed (CCMP) ¯ obs is the average of the ¯ sim and W wind speed, respectively, whilst W whole wind speed series for simulated and observed variable, respectively. For each CORDEX Evaluation model (7 models were used as depicted in Table 1) a corresponding NRMSE was computed. The results presented in Table 3 and Fig. 4 consist of the average NRMSE of the 7 models. While the results presented in Table 3 show the average NRMSE of the 7 models of CORDEX Evaluation experiment when compared with the buoy winds, Fig. 4 shows a spatial map of the average NRMSE when compared with the independent CCMP data. Next, the distributions of corrected and not corrected CORDEX data were compared with the distributions of the independent verification datasets: buoy measurements and CCMP data not used in the bias correction. Since the wind speed distributions, and not the wind speed temporal variability, are of concern here, wind speed data from the CORDEX Historical experiment was used instead of the Evaluation experiment. Data from the models shown in Table 1 were combined into a multi-model ensemble. To assess differences in the wind speed distributions between CORDEX and reference datasets (buoy and independent CCMP), three statistic metrics were used: Overlap percentages (OP), difference in wind speed median and difference in Weibull peak. OP allows to quantify the percentage of overlapping between the measured and modeled probability distribution functions (PDFs). Each metric was calculated individually for each RCM and, then, following the multi-model approach were averaged to obtain a single value. This procedure is similar to that applied by Perkins et al. [57], which has been adapted in previous studies that also compared wind speed data series (e.g: [58]). This method is based on the following expression:

2.2.2. Wind energy calculation and wind extrapolation Wind power density (WPD) was calculated following the expression:

WPD =

1/2

N

∑ (〈Wisim 〉 − 〈Wiobs 〉)2⎤⎥

(4)

where Hns is the height at which near-surface winds are measured (3 m for buoys and 10 m for CORDEX simulations); H is the selected height to extrapolate winds; Wns is the wind speed measured at Hns; WH is the wind speed at the desired measurement height H and z0 is the roughness length. A value of 1.52 × 10−4 was selected for the ocean roughness length following Peixoto and Oort [55].

n

OP =

∑ minimum (Zm, Z0 )

∗ 100

1

(6)

where n is the number of bins used to calculate PDFs, which were 26 in the present analysis; Zm and Z0 are the frequency of values in a given bin from the model and buoy, respectively. Therefore, OP equal to 100% means that model reproduces perfectly in situ data. The percentage of difference in wind speed median (DM) is calculated as following

2.2.3. Validation of BC and FDBC methods The main aim of the present study is to assess whether BC and FDBC are effective in improving the accuracy of CORDEX wind speed data. With this purpose, two tests were used to evaluate and quantify the impact of BC and FDBC on CORDEX wind data. A diagram of the validation process including both tests can be seen in Fig. 3. First, a comparison was carried out to evaluate the impact of BC and FDBC CORDEX representation of the wind temporal variability. For this, wind speed time series of the CORDEX Evaluation experiment from the models showed in Table 1 were used. This experiment uses ERAInterim reanalysis, which means that it integrates the wind temporal variability. Thus, CORDEX evaluation allows comparing errors such as RMSE that accounts for biases related to temporal variability. The NRMSE was used to quantify the errors of corrected and not corrected CORDEX wind speed time series relative to two different and independent wind speed verification datasets: buoy observations and CCMP data. The use of independent wind speed observations (independent in the sense that they were not used as reference for BC and FDBC) allows assessing whether BC and FDBC improves CORDEX future wind speed projections. For this, the common period of wind data availability from buoys and CORDEX and a CCMP 6-years period not used to perform BC and FDBC were used as validation datasets. Therefore, those days with missing data from buoys were not considered to carry out the validation process. NRMSE (%) is calculated based on Gualtieri and Secci [56] as

DM = 100 ×

MEDsim −MEDobs MEDref

(7)

where MEDsim and MEDobs accounts for the median of the simulated and observed wind speed, respectively, while MEDref is calculated as the average between measured and simulated medians. Median instead of mean was selected because it is more robust when using an ensemble of different models because it is less sensitive to outliers. The percentage of difference in the maximum value of the Weibull distribution, which is the most widely used method to characterize wind speed [59], is calculated following the same expression as Eq. (7) but considering the wind value at which the maximum value of frequency occurs, that is, the modal value. Therefore, complementary statistics that consider differences in median values but also differences in the PDFs and Weibull distribution were used to carry out the comparison. It should be highlighted that other complementary indicators that weight on other areas of the probability distribution, such as the analysis of tail errors (e.g: [60]), are other possibility to carry out the validation process. The results presented in Table 4 show the differences between the CORDEX and buoy wind speed distributions, while Fig. 5 shows a spatial map of these differences using as reference the independent CCMP data. For this, data for 10 years were randomly sampled over the period 1990–2005. Then, BC and FDBC were applied 5

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Fig. 3. Diagram showing the two tests applied in the validation process.

using equations (1) and (2), respectively. Finally, validation was conducted by comparing corrected wind speed data over the remaining 6 years not selected for calibration. To ensure robustness of this evaluation and to minimize the dependence of the selected calibration period, the cross validation process was repeated 20 times following a similar approach to that applied by Miao et al., [6]. After the validation of BC and FDBC methods, the sensitivity of CORDEX data to these processes was analyzed by comparing corrected and not corrected WPD projections. In addition, the difference between historical CORDEX WPD and future CORDEX WPD projections was calculated with the aim of knowing how will change the offshore wind energy resource along the 21st century. These calculations were done

Table 3 NRMSE of the comparison between corrected CORDEX data (Evaluation experiment) and buoy wind measurements over the common historical period.

Peñas Sisargas Bares Silleiro Cádiz Average

NC

Only BC

Only FDBC

BC + FDBC

46.13 35.91 36.06 37.86 48.85 40.96

42.52 34.75 36.25 36.36 40.64 38.10

43.78 35.51 36.35 36.70 43.08 39.08

37.71 33.76 33.99 34.45 36.87 35.36

Fig. 4. NRMSE of the comparison between (a) not corrected and (b) BC + FDBC CORDEX data (Evaluation experiment) and independent CCMP wind speed data for the whole area under scope over the historical period. (c) Percentage of difference by applying BC + FDBC calculated as NRMSE NC less NRMSE BC + FDBC. Results showed in these figures are based on the cross-validation procedure. 6

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improve after BC. Overall, comparison metrics for each buoy also improve after BC, with the exception of Peñas buoy, which is the closest to the coast. This fact, in conjunction with the proximity of a mountain range with complex orography, conditions the terrain-induced wind flows at this buoy [23]. The combination of BC and FDBC did not improve the statistics so clearly as occurred with the NRMSE (Table 3) when compared to only BC. Although an improvement was obtained in the percentage of Weibull Peak difference, a slightly lower Overlapping percentage (from 90 to 89.4) was seen. A cross validation was also done to analyze the percentage of improvement in the wind speed distributions in the whole area under scope (Fig. 5). In terms of percentage difference in wind speed median, overlapping and the Weibull peak difference, the percentage of improvement was higher if compared to NRMSE. Thus, values higher than 75% over most of the area under scope were reached for median difference and Weibull peak difference. A lower improvement was obtained in the overlapping percentage (< 20%). In this case, the highest progress was obtained along the areas closest to the coastline, especially along the Portuguese coast. A higher improvement was obtained through the cross validation process (Figs. 4 and 5) compared with the validation with buoys (Tables 3 and 4). It should be considered the fact that in the cross validation process CCMP was used both for BC + FDBC and as reference dataset.

Table 4 Differences between the wind speed distributions of not corrected (NC), bias corrected (BC) and BC plus frequency dependent bias correction (FDBC) CORDEX data (Historical experiment) and buoy wind measurements over the common historical period. NC

BC

FDBC

BC + FDBC

PEÑAS

Overlapping W Median Dif. (%) Peak Dif. (%)

88.74 6.22 7.26

84.59 6.49 9.92

87.18 7.38 7.26

85.23 7.57 8.57

SISARGAS

Overlapping W Median Dif. (%) Peak Dif. (%)

90.98 9.40 9.24

92.78 1.05 5.35

89.72 9.95 8.85

92.83 1.30 4.64

BARES

Overlapping W Median Dif. (%) Peak Dif. (%)

89.38 5.48 6.73

91.93 2.52 13.25

88.58 6.36 6.51

91.16 2.77 12.01

SILLEIRO

Overlapping W Median Dif. (%) Peak Dif. (%)

85.76 18.82 19.98

91.19 3.99 10.02

83.06 20.81 19.89

88.26 5.17 6.03

CÁDIZ

Overlapping W Median Dif. (%) Peak Dif. (%)

76.83 23.10 21.28

89.61 4.38 15.23

76.21 23.35 21.10

89.40 3.24 13.89

AVERAGE

Overlapping W Median Dif. (%) Peak Dif. (%)

86.34 12.60 12.90

90.02 3.69 10.75

84.95 13.57 12.72

89.38 4.01 9.03

3.2. Sensitivity of WPD future projections to BC + FDBC following the same expression showed in (7). To know the statistical significance of the differences the Mann-Whitney (or Wilcoxon rank sum) non-parametric test was used. This test was selected because both wind speed and power are, generally, not normally distributed functions [61]. The Mann-Whitney test checks the null hypothesis that two data samples belong to continuous distributions with equal medians, against the alternative that they do not. A 1% significance level was considered at each grid point.

As previously mentioned, small variations in mean wind speed result in higher changes in the wind power density (WPD, W m−2). To quantify the changes provoked by applying BC and FDBC in terms of offshore wind energy resource, WPD was calculated for the multi-model ensemble of RCMs for the end of the 21st century. Fig. 6a shows the multi-model ensemble median of the not corrected CORDEX data, while Fig. 6b shows the same information for the BC + FDBC corrected CORDEX. Values higher than 600 W m−2 (median of annual averages) were observed in the northwestern area when RCMs were not corrected. WPD values higher than 350 W m−2 were detected in most of the coastal area, while around the coastal areas of Cape Roca and Cape St. Vincent WPD can surpass 450 W m−2. However, the median of the BC + FDBC corrected multi-model ensemble CORDEX shows WPD values considerably lower. In this case, the highest WPD is of around 500 W m−2 and values lower than 300 W m−2 are seen for the whole Portuguese coast. Fig. 6c represents the difference of the WPD medians between the corrected and not corrected CORDEX ensembles shown in Fig. 6a and b, that is, it shows the variation in terms of wind energy resource after applying BC + FDBC. It is important to mention that negative values mean a lower WPD of the corrected RCMs. A reduction in WPD was observed in the whole area under scope after applying BC + FDBC. This WPD reduction was higher than 150 W m−2 in most of coastal areas, being less intense in farther from the coast. In order to take advantage of the FDBC, the same analysis showed in Fig. 6 was done for each season (Fig. 7). In seasonal terms, it can be observed the same pattern showed at annual scale, that is, lower WPD when the multi-model ensemble of RCMs is corrected (Fig. 7, last column). The highest difference was found in winter (December-February) (Fig. 7, first row), especially in the northern half of the area under scope. It is important to highlight that winter is the season with the highest WPD value in the western Iberian Peninsula (Fig. 7a; b). During summer (June-August) (Fig. 7, third row) it was also observed an important difference after the application of BC + FDBC, especially at coastal areas where a reduction higher than 200 W m−2 was detected for most of the Portuguese coast. The lowest difference was observed in autumn (September-November), while in spring (March-May) an important reduction (> 200 W m−2) is seen mainly around Cape Roca after applying BC + FDBC. The influence of BC + FDBC methods over the climate change signal was quantified both at an annual scale (Fig. 8) and at a seasonal

3. Results 3.1. Validation of BC and FDBC The ability of BC and FDBC methods to improve CORDEX wind data time variability was analyzed by comparing corrected and not corrected (NC) CORDEX data with wind speed time series from five buoys (Table 2). To carry out this comparison, the closest pixel to each buoy was selected and the NRMSE was calculated for each model. After that, a mean NRMSE value for each buoy and CORDEX dataset (corrected and not corrected) was obtained by averaging the error values from the seven models of CORDEX Evaluation experiment (Table 1). Table 3 shows that the lowest NRMSE in all buoys was obtained when BC and FDBC are applied together (first BC and then FDBC). However, both methods are able to reduce the NRMSE when applied separately. In this case, lower NRMSE values were obtained by using only BC. Once the results of BC and FDBC were compared with an independent dataset, a cross validation was also done to analyze the percentage of NRMSE improvement in the whole area under scope (Fig. 4). To carry out this calibration, the steps described in Section 2 were followed. The percentage of improvement in these figures was calculated considering the difference between corrected and not corrected data at each pixel and comparing this difference with the not corrected value. A slight reduction of NRMSE was detected in the whole area after BC + FDBC. Higher differences in terms of NRMSE was detected along the western area of the Iberian Peninsula and in the southern area of Portugal with values higher than 5%. Table 4 shows the comparison of BC + FDBC CORDEX Historical wind speed data with wind speed from buoys in terms of differences in the wind speed distributions (overlapping, percentage difference in the wind speed median and the Weibull peak). In average, all statistics 7

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Fig. 5. Percentage of wind speed overlapping (first column), difference in median (second column) and difference in mean Weibull Peak (third column) between not corrected (NC) (first row) and BC + FDBC by means of CCMP data (second row). The last row shows the percentage of improvement reach by using BC + FDBC. Results showed in these figures are based on the cross-validation procedure.

historical and future. According to the evaluation carried out in Section 3.1, it is important to highlight that although differences with NC data and BC + FDBC data are shown in this section, the future variations calculated by means of BC + FDBC CORDEX data are expected to approximate better future projections since BC + FDBC CORDEX data are

scale (Fig. 9). For this purpose, WPD differences were calculated in two ways. On the one hand, variations were calculated as the difference between historical NC CORDEX ensemble median and future projection NC CORDEX ensemble median. On the other hand, the same difference was calculated but using BC + FDBC CORDEX data for both periods, 8

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Fig. 6. Annual multi-model ensemble median of wind power (W m−2) (a) not corrected (NC) and (b) after BC + FDBC at 120 m over the period 2085–2100. (c) WPD difference between BC + FDBC (a) and not corrected WPD (b). Difference was calculated as: BC + FDBC WPD less NC WPD.

4. Discussion and conclusion

closer to the reference wind data (buoy and independent CCMP). The percentage of change in terms of median WPD calculated with NC CORDEX ensemble (Fig. 8, first row) and BC + FDBC CORDEX ensemble (Fig. 8, second row) were calculated for the three future periods. A similar pattern was obtained in both cases since, overall, a significant WPD reduction was found in the whole area under scope for the three future periods. This WPD reduction is higher for the far future, reaching maximum values of −15%. However, null changes and even a WPD increase were detected for the mid and far futures in the coastal area of the northwestern corner of the Iberian Peninsula, whilst a slight decrease was observed for the near future in this zone. Some differences can be seen between NC and BC + FDBC. Overall, the projected WPD reduction is lower for the three future periods when BC + FDBC is applied. This fact is clearly reflected in the northwestern corner of the Iberian Peninsula, where the area with a positive percentage of change is higher in BC + FDBC projections, or around the coastal areas of Cape Roca and Cape St. Vincent, where reductions lower than 3% were detected even in the far future. Regarding the seasonal differences (Fig. 9), the WPD percentage of change was calculated also with NC (Fig. 9a–d) and BC + FDBC (Fig. 9e–h) CORDEX ensembles for the end of the 21st century. In general, both NC and BC + FDBC future projections showed similarities. WPD changes are not homogenous along the year since important differences can be observed depending on the season. A WPD decrease was projected in autumn, winter and spring. However, a significant increase was projected in summer for the end of the 21st century. When analyzing only the median WPD percentage of change for the BC + FDBC future projections, which are closer to reality, it can be seen that the most important WPD reduction was found during autumn (Fig. 9h), with the exception of the southern area. However, an important WPD increase was observed in the coastal area of the northern half of the Iberian Peninsula (> 20%) during summer (Fig. 9g). Regarding winter (Fig. 9e), a slight WPD was projected in the northern part, while a reduction was found for the rest of the area under scope. This is the season that showed the most different WPD change when compared with NC projections since in this case a WPD reduction was detected in the whole area under scope (Fig. 9a). Finally, a WPD reduction was projected in most of the area under scope in spring (Fig. 9f) by means of BC + FDBC CORDEX data.

Future variations in wind speed should be considered in order to ensure the future viability of offshore wind farms in a context of climate change [62,63]. Considering that wind energy output is proportional to the cube of wind speed, biases in wind speed are severely amplified in energy terms. Therefore, it is crucial to reduce the biases of wind power future projections carried out by GCMs or RCMs. With this aim, the present study has tested a BC method that preserves the climatic nonstationarity [22] in combination with the FDBC method developed by Pierce et al. [14]. It has been shown that the ability of CORDEX RCMs in representing wind speed improved when BC (quantile mapping method) and FDBC were applied using wind speed data from CCMP for calibration. Thus, different statistics such as overlapping percentage, percentage difference in wind speed median or percentage difference in Weibull peak indicated a reduction of the error when corrected wind speed series are compared with in-situ wind speed data from buoys (Table 4). In addition, the lowest NRMSE was obtained when BC and FDBC methods were combined (Table 3). Apart from the comparison with buoy data, a cross-validation process using independent CCMP wind data showed the robustness of the BC process since the error of the different statistics was clearly reduced (Fig. 5). The sensitivity of WPD projections to the bias correction method was analyzed by calculating the difference between WPD median from BC + FDBC and from NC CORDEX ensembles at an annual scale (Fig. 6). A reduction of WPD when BC + FDBC is applied was detected in the whole area under scope. Maxima difference values higher than 200 W m−2 were observed in most of the coastal area western of Portugal and in the northwestern corner of the Iberian Peninsula. Accordingly, a first conclusion is that CORDEX RCMs tend to overestimate WPD in this area. This conclusion was corroborated by calculating the difference between wind speed median for the multi-model CORDEX ensemble and CCMP dataset at 10 m for the historical period (1990–2005) (See Appendix A, Fig. A1). To put the differences showed in Fig. 6 into context, it should be mentioned that according to the wind power classification developed by the National Renewable Energy Laboratory [64]the wind resource can be considered fair for WPD higher than 300 W m−2 and good if 400 W m−2 is reached as annual average at 50 m. Therefore, these large differences highlighted the importance of considering bias correction when wind energy production is projected for future periods. 9

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Fig. 7. Seasonal multi-model ensemble median of wind power (W m−2) (first column) not corrected and (second column) BC + FDBC at 120 m over the period 2085–2100 for winter (DJF), spring (MAM), summer (JJA) and autumn (SON). (Third column) WPD difference between BC + FDBC and not corrected WPD. Difference was calculated as: BC + FDBC WPD less NC WPD.

10

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Fig. 8. Map of percentage of change of annual WPD (%) medians for future periods relative to the historical period (1990–2005) under the RCP8.5 scenario, considering the NC CORDEX ensemble (first row) and BC + FDBC CORDEX ensemble (second row). Changes were calculated for the three future periods namely, near future (2025–2040) (first column), mid future (2055–2070) (second column) and far future (2085–2100) (third column). Black dots represent the grid points with a Mann-Whitney statistical significance level of 1%.

and south of Portugal (Fig. 6b). Overall, this WPD spatial pattern is in good agreement with previous analysis that have shown past WPD using an ensemble of CORDEX RCMs [40] or numerical models such as WRF [34,33]. The spatial pattern of the median BC + FDBC WPD projections at seasonal scale are also in good agreement with the analysis carried out by Salvaçao and Soares [33] for the past. Fig. 8 showed an overall WPD decrease along the 21st century, with the exception of the northwestern coastal area, where no change or even a WPD increase was detected for the end of the 21st century. Previous studies that analyzed future wind patterns in the Iberian Peninsula [65,66] suggested a weakening of the westerly wind due to the strength of the Azores High and its displacement to the northeastward over the 21st century. This fact could explain the overall annual pattern described in the present study. Projected wind speed variations for the future were not homogenous along the year (Fig. 9). Thus, an important WPD increase was projected for summer (Fig. 9g), while a decreasing pattern was found in autumn (Fig. 9h) and spring (Fig. 9f) Regarding winter, an increase in the northern part and a decreasing in the rest of the area under scope was

The sensitivity of the climate change signal to the BC + FDBC methods in terms of WPD was also evaluated (Fig. 8). Overall, BC + FDBC CORDEX ensemble showed a lower WPD reduction for the three future periods in the whole area under scope. In addition, it can be seen that the area where a WPD increase or null changes were projected in the northwestern corner of the Iberian Peninsula is higher when using BC + FDBC CORDEX data. Despite these changes, BC + FDBC methods maintain most of the intrinsic climate change signal from CORDEX models, which was one of the reasons why the BC method developed by Amengual et al. [22] was selected to carry out the present study. Once the sensitivity of CORDEX models to BC + FDBC was discussed, and, taking into account that BC + FDBC corrected winds are expected to have lower errors when compared with NC ones, the previous analysis will be discussed only considering the BC + FDBC WPD future projections. Regarding the median BC + FDBC WPD future projections, the highest annual median densities (> 600 W m−2) at 120 m for the far future were obtained in the northwestern corner of the area, whilst the lowest WPDs were observed in the coastal areas west 11

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Fig. 9. Seasonal projected future changes in WPD medians for CORDEX under the RCP8.5 scenario for the far future (2085–2100) relative to the historical period (1990–2005) by means of NC CORDEX data (a-d) and BC + FDBC CORDEX data (e-h). Differences were calculated considering historical CORDEX (NC and BC + FDBC) and future projections (NC and BC + FDBC) from Black dots represent the grid points with a Mann-Whitney statistical significance level of 1%.

output decrease in winter and an increase in summer, although with lower percentages of change when compared with the present analysis. Tobin et al., [69], who also projected variations in wind energy outputs for Europe, observed a reduction for the whole oceanic area western Iberia. Therefore, previous analyses that calculated WPD projections at annual and seasonal scales in the western Iberian showed differences with the present analysis. These differences are in part a consequence of the application of BC + FDBC, which according to the comparison with independent observations are expected to be more reliable. The present manuscript is an example of bias-correction methodology that correct wind speed model bias with high efficiency. It has been shown that better results can be obtained through the combination of different bias correction techniques. In this analysis, the different recommendations regarding bias corrections techniques specified, for example, by the IPCC [70] and other studies that have made a critical review of bias correction techniques (e.g: [71,72]) have been applied. Although these recommendations were followed, it is important to bear in mind that bias correction of any climatic variable do not correct the inaccuracies from climate models derived from misrepresenting fundamental physical processes. These errors are unlikely to be solved soon, thus the bias adjustment process developed in the present analyses provides an effective technique that can be already used to compensate these inaccuracies. Therefore, the bias correction process described in the present manuscript can solve in a short period of time the necessity of more accurate offshore wind energy projections, which can be of high value for practitioners in the decision-making process when new offshore wind farms are projected.

observed (Fig. 9e). It is important to consider that summer is the season with the lowest mean WPD values in the western Iberia. Therefore, variations in this season will condition the stability of the offshore energy resource throughout the year. A stable wind power generation benefits the gathering and conversion of wind energy, while unstable wind power density is worst for the conversion of wind energy [67,68]. When calculating future projections of any climatic variable, it is important to consider that results can change depending on the future scenario, models selected to create the ensemble, the future and the past period considered to do the projection. Therefore, these aspects are important when future projections are compared among different studies. Previous studies that analyzed projections in the western Iberian by means of CORDEX data [41,40] found, in general, a WPD decrease for the end of the 21st century at annual scale, which is in accordance with the present analysis. At seasonal scale, Soares et al., [40] also observed a WPD increase for summer, although less intense, and the highest WPD decrease for autumn. However, these authors projected a higher decrease during winter and a less one for spring. More differences were observed with the analysis carried out by Santos et al., [41], especially for autumn since these authors found a WPD increase in most areas of the western Iberia for this season, while the highest decrease was projected during this season in the present analysis (Fig. 9h). Moemken et al., [20] analyzed changes in wind energy output by means of EURO-CORDEX data at the end of the 21st century but all over Europe. They also found an overall decrease in the western Iberia, with the exception of the northwestern corner were they detected null changes. In seasonal terms, these authors observed a wind energy 12

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– A future WPD reduction was projected by correcting regional multimodel ensemble under the most unfavorable climate change scenario for the near future (2025–2040), mid future (2055–2070) and far future (2085–2100) when compared to the historical period (1990–2005) in the western Iberia, with the exception of the northwestern corner of the Iberian Peninsula where null changes and even a slight increase were found. – For the end of the 21st century, it was found that WPD changes with respect to historical period are not homogenous along the year. Thus, a WPD increase was projected for summer in the whole area under scope, whilst a reduction was detected for spring and, especially, for autumn. Regarding winter, a WPD increase was projected in the northern area, whereas a reduction was detected for the rest of the area under scope.

5. Concluding remarks Future projections of wind energy resource are crucial in order to know how climate change will affect wind energy production and, therefore, to ensure the viability of wind farms. To assess future wind energy resource reliable future climate projections are necessary. With the aim of improving wind speed future projections, two bias correction techniques, one based on a quantile mapping approach and the another based on the correction in the frequency domain, were tested in the offshore area west of the Iberian Peninsula, which has attractive conditions for the future development of this renewable resource. Wind speed data from CCMP dataset was selected as reference to carry out bias correction. Bias correction methods were applied to a multi-model ensemble from the Coordinated Regional Climate Downscalling project. The main finding of the present study is that the highest reduction of the errors in wind speed future climate projections, both in terms of temporal variability and in terms of the distributions, was achieved when quantile mapping was applied followed by correction in the frequency domain. As far as we know, this is the first study that applied a combination of bias correction techniques, including frequency domain, in order to improve the offshore wind energy projections. The improvement both in the temporal variability and the distribution of wind series proved that this methodology is a valid tool to obtain more reliable offshore wind energy projections. In addition, the approach of using CCMP database to carry out bias correction allow using this methodology in any coastal area of the world. Regarding the case study, the main findings of the present study can be summarized as follows:

CRediT authorship contribution statement X. Costoya: Conceptualization, Methodology, Software, Writing original draft, Writing - review & editing, Visualization, Formal analysis, Funding acquisition. A. Rocha: Writing - review & editing, Resources, Formal analysis, Data curation. D. Carvalho: Conceptualization, Methodology, Supervision, Investigation. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

– Regional models from the Coordinated Regional Climate Downscalling project tended to overestimate WPD future projections in the west Iberian. Thus, lower WPD values were detected when bias correction was applied compared to the not corrected projections for the end of the 21st century, especially during winter and summer. – Bias correction barely modified the climate change signal intrinsic to regional models at annual scale. However, higher variations were detected at seasonal scale.

Acknowledgments X. Costoya was supported by the Portuguese Science Foundation (FCT) through a postdoctoral grant (SFRH/BPD/118142/2016) and the Spanish Government through a Juan de la Cierva Postdoctoral Fellowship (FJCI-2017-32577). Thanks are due for the financial support to CESAM (UID/AMB/50017/2019), to FCT/MEC through national funds, and the co-funding by the FEDER, within the PT2020 Partnership Agreement and Compete 2020.

Appendix A See Fig. A1.

Fig. A1. Annual multi-model ensemble median of wind power (W m−2) by means of (a) CORDEX and (b) CCMP at 10 m over the period 1990–2005. (c) Wind speed median difference between CORDEX and CCMP wind speed over the period 1990–2005. Difference was calculated as: CORDEX less CCMP. 13

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