Time-scale and extent at which large-scale circulation modes determine the wind and solar potential in the Iberian Peninsula

The SP and WP series analyzed here were derived from primary data of surface short-wave downward radiation (SWD) and wind speed (WS) obtained from a hindcast regional climate simulation performed with the mesoscale model MM5 (Grell et al 1994) driven by the ECMWF ERA40 reanalysis (Uppala et al 2005) and analysis data. This simulation covers the whole Iberian Peninsula with a 10-km resolution homogeneous grid and spans the period 1959–2007 with hourly resolution, and has demonstrated skill for reproducing accurately the spatial and temporal variability of meteorological variables such as wind speed and direction, precipitation and maximum and minimum daily temperature, at least at the monthly time-scale (Jerez et al 2013b). Unfortunately, we could not validate similarly the accuracy of the simulated surface solar radiation due to the lack of observations at our disposal.

Following the set of rules proposed by Ruiz-Arias et al (2012), the series of SWD and WS were transformed into series of SP (considering only the photovoltaic technology as it is the most widely used) and WP respectively (equations (1) and (2)). In equation (1), G_STC refers to the incoming surface short-wave radiation at standard test conditions (which is 1000 W m⁻²) and P_R is the performance ratio accounting for system losses (typically 0.75). For the transformation of WS into WP (equation (2)), we considered the cut-in, cut-off and rated speeds (S_I,S_O and S_R respectively) specified for the GAMESA (www.gamesa.es) wind turbine model G87 (i.e. S_I = 4 m s⁻¹,S_O = 25 m s⁻¹ and S_R = 12 m s⁻¹), one of the most used in Iberia. The vertical layer of the simulation being closest to its tower height (87 m) corresponds to an altitude of about 100 m. Given that the relationship between WS and WP expressed in equation (2) is not linear, it is particularly valuable the hourly resolution of the WS data used here (at coarser time-scales, e.g. monthly, equation (2) may not be valid).

$$\begin{eqnarray} \mathrm{SP}&=&\frac{\mathrm{SWD}}{{G}_{\mathrm{STC}}}{P}_{\mathrm{R}} \end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray} \text{WP}&=&\left \{ \begin{array}{@{}ll@{}} \displaystyle 0&\displaystyle \tqs \text{if WS }\lt {S}_{\mathrm{I}} \\ \displaystyle \frac{{\mathrm{WS}}^{3}-{S}_{\mathrm{I}}^{3}}{{S}_{\mathrm{R}}^{3}-{S}_{\mathrm{I}}^{3}}&\displaystyle \tqs \text{if }{S}_{\mathrm{I}}\leqslant \text{WS}\lt {S}_{\mathrm{R}} \\ \displaystyle 1&\displaystyle \tqs \text{if }{S}_{\mathrm{R}}\leqslant \text{WS}\lt {S}_{\mathrm{O}}\\ \displaystyle 0&\displaystyle \tqs \text{if WS}\geq {S}_{\mathrm{O}}. \end{array}\right . \end{eqnarray} \tag{ 2 }$$

Note that SP and WP, as they are considered here, are normalized (dimensionless) values representing the power generation potential (sometimes simply referred to as potential). The power generation would be the product of these values of SP or WP and the installed capacity power that we have for each resource. Hence, SP and WP range between 0 (no generation potential) and 1 (the power generation would equal the installed power capacity).

The values of the NAO, EA and SCAND indices for the whole simulated period were retrieved from the Climate Prediction Center (CPC) of the NOAA (www.cpc.ncep.noaa.gov) at the finest temporal resolution available for each: daily for the NAO index and monthly for EA and SCAND.

Temporal correlation (r), computed through the Pearson coefficient, is used to measure the strength and linearity of the relationship between the large-scale circulation indices and the renewable power generation potential series.

The impact of the various modes on SP and WP is quantified through composites showing the difference (Δ) in their mean values between the positive (>0.5) and negative (< − 0.5) phases of the NAO, EA and SCAND indices (as in Jerez et al 2013b). These differences are given as percentage with respect to the climatology of the assessed magnitude (e.g. equation (3)). Note that the value of Δ would increase with higher thresholds in the definition of the positive and negative phases of the indices (since we would be considering more extreme cases). However, this would reduce the number of events averaged in each case and thus higher values of Δ would be required for achieving statistical significance. The subjective threshold of 0.5 was chosen by pondering both issues.

$$\begin{eqnarray} &&\Delta =\frac{\vert \bar {X}(t\in {\text{NAO}}^{+})-\bar {X}(t\in {\text{NAO}}^{-})\vert }{\bar {X}(\forall t)}\times 1 0 0. \end{eqnarray} \tag{ 3 }$$

In order to investigate the extent at which NAO plus EA plus SCAND are able to explain the temporal evolution of the SP and WP series, we use a multi-linear regression model (MLRM) including the three large-scale circulation indices as predictors (equation (4)), hence taking into account their joint influence. First, in order to obtain the values of the coefficients C₀,C_N,C_E and C_S, we calibrate the MLRM by fitting the original SP and WP time-series to equation (4) using the minimum mean square error method. Second, we use these values to reproduce, with equation (4), the SP and WP series according to the variations of NAO, EA and SCAND. The accuracy of these modeled series is then evaluated by comparison with the original ones. To this end, we use two scores: the temporal correlation (r) between the original and the modeled series, and the standard deviation ratio (std_r) defined as the ratio between the standard deviation of the modeled series and the standard deviation of the original series.

$$\begin{eqnarray} X(t)&=&{C}_{0}+{C}_{\mathrm{N}}\text{NAO}(t)+{C}_{\mathrm{E}}\text{EA}(t)\nonumber\\ &&+~{C}_{\mathrm{S}}\text{SCAND}(t). \end{eqnarray} \tag{ 4 }$$

The availability of daily records of NAO makes it possible to assess its influence on SP and WP at a wide range of time-scales. We have computed the temporal correlation between the NAO index and SP/WP using daily, weekly, monthly, seasonally and yearly averaged series (figures 1(a) and (b)). Similarly, the correlation between EA/SCAND and the resources was computed at time-scales ranging from monthly to yearly (figures 1(c)–(f)). In this analysis we have considered either all the records in the series or only those corresponding to the different seasons or months. This approach allows to identify both the time-scale and season of the year with maximum influence of each mode on the resources. This analysis was done for each grid-point of the domain, but we opted to present here spatially averaged series of SP and WP for simplicity. These series were obtained by averaging spatially over those land grid points showing significant correlation values between the resources and the climatic indices. We have indicated in figure 1 if the fraction of grid points averaged in each case exceeds 30% or 50% of the total number of land grid points of the Iberian Peninsula.

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Significant correlations are obtained at every time-scale for both SP and WP series and NAO, often over more than 50% of the Iberian Peninsula area. Worth mentioning, Jerez et al (2013b) showed indeed significant correlation between the NAO index and measured series of solar and wind power generation in Spain at the yearly time-scale (these public data are not available at finer time-scales with sufficient length). However, according to figure 1, the strength of the correlations is maximum at the monthly time-scale for the months of the winter half of the year (within the range 0.5–0.7, with positive values for SP while negative for WP) in comparison to larger (seasonal, yearly) and smaller (daily or weekly) time-scales. The greatest influence of NAO in winter may reflect the fact that local processes, such as land–atmosphere interactions, gain relevance in summer (Jerez et al 2012) and can mask to some extent the influence of the large-scale circulation. However, both EA and SCAND not only show similarly high and widespread correlations with the monthly series of SP and WP in the winter months (although with opposite sign than the correlations with NAO in each case), but also in some months of the summer half of the year (figures 1(c)–(f)). For example, SP and SCAND show maximum correlation in June and WP and EA in April.

Noteworthy, the strength and even the sign of the correlation between modes and resources differ from one season to another. This explains that, although high correlations still appear at the seasonal time-scale for some seasons (mainly winter, i.e. for the DJF-averaged series), they are less appreciable at the annual time-scale.

Therefore, the optimum approach to characterize the impact of these large-scale circulation modes on SP and WP consists on analyzing it at the monthly time-scale and, given the differences among the various months along the year, for each month separately. In other words, these modes appear to play a major role on the interannual variations of the monthly mean values of SP and WP, particularly during the winter half of the year, thus representing a major low-frequency (within the context of this analysis) driving factor for both of them.

Following such approach, we have focused on the October-to-March months in the following sections. The choice of these winter months responds to three reasons: (1) brevity, (2) they showed the highest signals in many cases (see squares in figure 1), and (3) although, contrary to the wind resource, the solar resource is maximum in summer (the wind maxima peaks in winter), both resources present the highest interannual variability in winter (not shown), when thus a better understanding of the underlying causes becomes more relevant.

The correlation patterns between the various indices and SP (WP) at the monthly time-scale for each winter month individually are depicted in figure 2 (3) (first-to-third columns, in colors). This analysis further shows noticeable differences both in the magnitude and the spatial distribution of the correlations from one month to another, highlighting that in some places/months these correlations are up to 0.8.

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In order to quantify the variations in SP and WP associated to phase changes of the various modes, we computed the difference in the mean values of SP and WP between their positive and negative phases in each month (the number of events averaged in each case is specified in table 1). This difference is provided in percentage with respect to the mean climatology of each resource by contours in the first three columns of figures 2 and 3.

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Regarding SP (figure 2), the signature of NAO is appreciable and statistically significant in every month, although the most significant signals appear in December, February and March. The role of the EA pattern is also very relevant throughout the considered winter months (particularly in November, December and February) although being irrelevant in October. Likewise, the impact of the SCAND mode is quite noticeable in all months with the exceptions of December and March. In general, the strongest signals appear concentrated in western and central sectors, prevailing in the southwestern those associated to NAO and in the northwestern those associated to EA. The impact of SCAND evolves spatially from the northwest in the last months of the year to the southeast in January and February. Variations in mean SP associated to changes in the phase of the indices range from 10% of its climatology to over 30%, although these later are restricted to small areas and observed only for a few months. These signals are attributed to changes in cloudiness, in turn associated to changes in the synoptic flow. Westerly and northwesterly flows advect humid air from the ocean into the Iberian Peninsula, thus promoting the formation of clouds, enhancing precipitation and diminishing the solar radiation that reaches the surface. On the contrary, land-to-ocean flows and the more anticyclonic conditions during some phases of the considered modes have associated clearer skies in terms of clouds and thus enhanced surface downward short-wave solar radiation (Trigo et al 2002, Trigo 2006, Jerez et al 2013b).

Variations in WP (figure 3) reach frequently 30%, mounting up to values higher than 40% in several months associated to phase changes of both NAO and SCAND. As in the case of the solar resource, there are months with feeble signatures from EA and SCAND, while significant signals associated to the NAO phase appear in every month. In this sense, these patterns are similar to those obtained for the solar resource, although depicting different spatial distributions. In particular, the composites for the WP suggest an important role of the orographic factor, with lower values often associated with high mountain ranges and strengthened signals appearing in general within the river valleys. This has been attributed to the fact that in the high lands the wind does not blow through well-defined preferred directions, in contrast to the anisotropy derived from the orographic channeling within the valleys. Hence, as the primary impact of the large-scale circulation patterns on the wind field is on the wind direction, it translates into different wind speeds mainly where changes in the wind direction affect it, i.e. inside the orographic channels (Jerez et al 2013b).

Worth mentioning, the sign of the impact of the various circulation modes on either SP or WP is opposite. While positive NAO phases and negative EA and SCAND phases generally promote SP, the opposite phases of each index enhance WP. This suggests that months expected to be poor (good) in solar production would compensate with increased (decreased) wind production, at least to the extent at which these resources are determined by the aforementioned large-scale patterns.

The MLRM (equation (4)) was calibrated using the monthly mean series of SP and WP for each winter month individually. The patterns of temporal correlation between the MLRM-modeled series and the original series for both renewable resources are provided in the last column of figures 2 and 3. The results show high correlations (often above 0.8) over most of the Iberian Peninsula for all considered months. The improvement achieved with the MLRM approach in comparison with considering each index individually is noticeable: the strong signals covering almost the entire Iberian Peninsula for most subplots in the last column of figures 2 and 3 stand above those related to each individual mode depicted in the first-to-third columns. Hence, these results prove that the three predictors/indices considered (NAO, EA and SCAND) are not redundant and that, when considered jointly, they are capable of explaining a large fraction of the variability of both renewable resources at this time-scale.

This last result further suggests that NAO, EA and SCAND could be considered for improving the medium-range forecasts of monthly means (i.e. months ahead, given our climatological framework) of the solar and wind potential, as it was similarly stated regarding the usefulness of the NAO for the wind resource in the UK by Brayshaw et al (2011). However, for this purpose it would be desirable that the October-to-March series obtained from merging the individual month series modeled so far, capture well the month-to-month variations of the resources.

We assessed this latter obtaining that the agreement between the original and the modeled October-to-March monthly series of SP and WP (constructed by merging the series modeled for the individual months) is such that r achieves an extremely high value for the SP series (0.96) and a smaller but still significant value in the case of the WP series (0.64) (figures 4(a) and (b)). However, these values are inflated by the inclusion of the seasonal cycle of the series (not removed so far), which is particularly appreciable in the case of the solar resource (figure 4(a)). Thus, we compared the series after removing the annual cycle (figures 4(c) and (d)) obtaining correlation values of 0.67 (0.55) and standard deviation ratios of roughly 0.6 (0.5) for the SP (WP) series. These lower r and std_r values still support the potential of the MLRM for reproducing the temporal variability of the monthly anomalies of the October-to-March series of both SP and WP up to a point.

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4.3.1. Comparison with simpler approaches.

4.3.2. Predictive potential.

Finally, in order to deepen on the predictive/reproductive potential of the optimum MLRM-based method identified above, we have validated the model using more stringent conditions: different periods for calibration and validation (Wilks 2006). First, we simply used the MLRM calibrated for the period 1959–1989 (for each month separately) to reproduce the SP and WP October-to-March monthly anomaly series of the remaining period 1990–2007. The validation of these modeled series through comparison with the original ones is summarized in figures 5(a) and (d). Second, we adopted the more elaborated leave-one-out approach. For each year within our study period, we reconstructed the October-to-March series of monthly anomalies with the MLRM calibrated using the whole period but excluding that specific year (after removing the records of the corresponding year, the MLRM was calibrated for each month separately as well). Figures 5(b) and (e) provides the means of the values of r and std_r obtained for each single year in this manner, and figures 5(c) and (f) depicts the standard deviation of these sets of r and std_r values. For SP, in both panels (a) (that illustrates the predictive potential of the MLRM with an example) and (b) (that characterizes it statistically) of figure 5, r ranges between 0.6 and 0.7 over wide areas of the western half of the Iberian Peninsula, where the std_r is also well sustained above 0.5 (0.6 in panel (b)). For WP, the results are generally more modest than those for SP, with the highest values of both r and std_r more constrained to western river basins areas, although still reaching values around 0.5–0.6 for r and 0.5 for std_r there (figures 5(d) and (e)). These values agree with those showed in figures 4(c) and (d) and therefore prove that NAO, EA and SCAND can be considered as a set of useful predictors in the time-scale and season assessed here. On the other hand, these patterns (whose spatial distributions resemble to a large extent those obtained in figures 2 and 3) allow to identify the areas with the highest SP and WP predictability based on the large-scale modes. Moreover, figure 5(c) and (f) highlights that the predictability in these areas remains more constant along the study period than in the areas showing lower averaged values of both r and std_r in figures 5(b), (e). This results from the fact that the spread in r and std_r throughout the entire period analyzed is lowest where indeed r and std_r reach the highest values.

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