Ana Mª Palomares
CIEMAT-DER.
Avda. Complutense, 22; 28040- Madrid, Spain.
e-mail: ana.palomares@ciemat.es
There is a great interest in the development of offshore wind energy in Spain, especially in the Strait of
Gibraltar, one of the places with more potential and possibilities for the installation of future offshore plants.
For this purpose, it is necessary to make an improvement in the wind power forecasting in this place, due to the high level of investments that this kind of installations requires.
Although there are many different prediction models with acceptable results for onshore places, it is necessary new research for offshore wind applications, especially in places like the Strait of Gibraltar, where the topography plays a relevant role in the local wind behaviour. The difficulties in this case are greater than in other open areas, like the ones in the North coasts of Europe, moreover if we take into account that in the Strait case there are not data series of measurements at the sea, but we only can use the data from the coastal stations, buoys and those coming from short ship campaigns.
This paper shows the results of the application of a statistical downscaling technique (Tarifa model) for local wind surface forecasting at the Strait of Gibraltar. The method consists of a Perfect Prognosis model applied to ECMWF reanalysis data and fitted to wind data recorded at the State Meteorological Agency
(AEMET) meteorological station in Tarifa, throughout a 3-years period. The statistical model validation has been carried out comparing local wind observations with the results from the downscaling equations applied to the operational ECMWF model predictions for an independent one year period.
KEYWORDS: Statistical downscaling, Perfect Prognosis, Strait of Gibraltar, offshore wind forecasting
Due to the high level of the Wind Energy development and exploitation in Spain, to its geographic characteristics and to the fact that there are some places that have reached the top of their wind power installation capacity, there is a special interest in the Offshore Wind
Energy research.
The Strait of Gibraltar is a privileged place for the wind energy development and there are quite a few onshore wind farms near the coast that make good use of the wind power at the surroundings. Nevertheless, this wind power is even greater just in the Strait, which is a real gateway for the winds coming either from the
Atlantic or the Mediterranean seas.
It is well known that there are important differences between the wind behaviour onshore and offshore, mainly because of the differences in the surface roughness, atmospheric stability and wind-wave interactions, besides the breeze cycles that are usual near the coast. There are interesting studies about these influences on the offshore wind, most of them placed in open areas [8], but the Strait of Gibraltar has a very particular wind regime because of the topography influence, and not all the conclusions made for other offshore places can be applied here.
But the main target today is to get a high level of reliability in the wind power forecasting, so that the difficulties of the penetration in the grid can be solved.
Current NWP global operational models, as the
ECMWF model, have not a spatial resolution enough to provide accurate wind predictions, especially in complex terrain and in places where changes in stability or extreme weather conditions play an important role. That is why it is necessary to develop downscaling methods that can take into account these effects, ignored in the large scale models.

An exhaustive review of the state of the art in wind energy can be found in [2].
There are two ways of downscaling: the dynamical and the statistical approaches. The dynamical methods deal with the application of very high resolution limited area numerical models (LAMs) nested in a global NWP model output. Such a high spatial resolution allows essentially a better representation of topography, which greatly affects the low-level winds.
The statistical methods are applied to fit NWP model output to local observations. They can be either strictly empirical or semi-empirical. The first ones include artificial neural networks
(ANN) or Kalman filter techniques, and the second ones are based on statistical multivariate regressions between the local-scale independent variable to be predicted –wind in this case- and the most significant atmospheric variables calculated by the NWP model for the site of interest. The last method can use either predicted or analysed atmospheric fields as input data. In the first case, the technique is called Model Output Statistics (MOS) and in the second one, it is known as Perfect Prognosis
(P.P.), because it mostly avoids the predictability related errors of the NWP models
[1 and 3].
In this work a statistical semi-empirical (P.P.) downscaling model is developed and applied to output atmospheric fields from the ECMWF global NWP model for reproducing local-scale wind in the Strait of Gibraltar.
The most relevant wind characteristics at the
Strait of Gibraltar are:
The surface wind is always influenced by the synoptic situation at the surface level, and not so much by the higher levels, because of the usual atmospheric stability in this place.
This influence is modified by the Strait topography, so that the only possible direction is W-E, giving place sometimes to isobaric winds and other times to transisobaric winds, that flow directly towards the lower pressures.
Therefore, this influence is very different to the normal one in other places, but it is qualitatively known
[6].
The wind suffers a high acceleration as passing through the channel, especially when it is coming from the east, because of the narrowest entrance, giving place to very high speeds.
The only two possible sectors (E and
W), determine two kind of winds with very different characteristics, as if they belonged to different places.
The W winds can come from the NW-
W-SW sectors, but the E winds only blow from the E sector.
The easterly winds are usually higher than the westerly winds, and have more persistence.
The W winds are more variable than the E winds.
The W winds show a daily cycle but the E winds don’t [5]. But even in the first case, this cycle is not directly related to a breeze regime, which is masked by the acceleration effect through the Strait.
The “calms” (winds with horizontal component lower than 1 m/s) are not frequent, and they only appear instantaneously when the wind changes from W to E and vice versa.
One of the reasons because the ECMWF global model [4] does not give good enough wind predictions at the Strait is the model resolution.
Fig. 1. Comparison of 2x2 km (left) and 50 x 50 km (right) resolution topographies of the Strait of Gibraltar region .

In the figure 1, the quasi-real topography of the
Strait (2x2 km) is compared to the topography used by the ECMWF model (approximately
50x50 km, although the current forecasts have double resolution using interpolation methods).
It is easy to understand the impossibility of reproducing the flow across the Strait (there is not even a channel!). In fact, this global model sometimes predicts strong meridian component winds, which are not actually observed at the
Strait.
Today, there are several physical models with high resolution that give acceptable wind forecasts, but they still fail in the Strait more than in other areas, because it is very difficult to reproduce the dynamics in this place.
There are other pure statistical models that only uses the data series, that perform well in occasions, but they fail when predicting the sudden changes from W to E and vice versa.
That is why it has been tried a method that takes into account the qualitative knowledge already achieved from previous studies.
After having analysed very carefully the wind regime at the Strait [4 and 5] (see section 1) it has been concluded that there is a strong relation between the low-level meteorological patterns (represented by significant atmospheric variable fields) and the surface wind across the
Strait. This fact suggested using a tool that could take into account this relation. Therefore the Perfect Prognosis (P.P.) technique, above mentioned, was chosen.
This method uses multivariate regression analysis in order to get an equation that shows this relation between the surface wind speed
(dependent variable) and other atmospheric independent variables V i
(predictors) derived from the operational ECMWF model reanalysis:
WIND SPEED= C
0
+ C
1
V
1
+ C
2
V
2
+ C
3
V
3
+ ...
C n
V n
Thus, the objective is finding the best predictors
(explaining most of the observed variance) and the corresponding coefficients C i
of the multiple regression equation. In this case, a backward stepwise method was used.
As there are not measurements at the sea by now, the empirical wind speed data used in this work have been collected from the AEMET meteorological station in Tarifa (Spain), placed very near the coast (fig.2) during the 1995-97 years.
The independent variables used come from the
ECMWF reanalysis (ERA data) for the same period. They can be either individual atmospheric variables at diverse p-levels or appropriate combinations of them, taking into account the previous knowledge about the qualitative relation between these variables and the resultant local-scale wind.
The ERA data used correspond to different nodes of a 0.5
 x 0.5

lat-lon grid mesh in the vicinity of Tarifa station, as figure 2 shows.
Fig. 2. Map of the Strait of Gibraltar showing the nodes of the ECMWF model grid mesh, used to develop the statistical model. The location of the Tarifa meteorological station corresponds to the 642 node .
The atmospheric ERA considered variables were:

At surface: Mean sea level pressure (p)

At the 1000, 925, 850, 700 and 500 hPa levels: Temperature (T), geopotential, humidity (q), horizontal wind components
(u,v), vertical wind (w), horizontal vorticity
(vor) and divergence (div)
Both the ERA data and observed wind at the
Tarifa Station correspond to 00, 06, 12, 18 h
(UTC) for every day.
From the previous knowledge of the atmospheric dynamic in this place and of the different influence of the Strait topography at its west and east sides (see section 1), a total of 18 nodes have been considered, as it can be observed in the figure 2. It can be seen that most of the selected nodes are at the east side because of the most channelling effect across the Strait at this side.
After some previous analysis based on individual regressions between the observed local wind speed and the different possible atmospheric variables, those who showed greater correlation coefficients, were chosen as independent variables, taking into account the multi-colineality effects and avoiding lineal dependent variables.
Thus, a total of 41 meteorological variables in the nodes and levels before mentioned were eventually selected.

Because of the peculiarities of the wind regime at the Strait (see section 1), it is clear that the relationship between local wind and meteorological pattern at the Strait of Gibraltar cannot be reduced to a general case. Instead, two main groups of situations were considered: easterly and westerly winds. Furthermore, within these two populations it has been necessary to distinguish some other sub-groups in order to get the best possible results. Some tests were made by using sub-groups based on the different hours of the day and on the seasons.
Finally it was chosen a sub-division based on the seasons (for each of the two main groups of easterlies and westerlies) and considering separately “calms” (winds with horizontal component lower than 1 m/s). The main reason for that was that this classification is the most representative of the reality because, for instance, the easterly winds do not show any kind of diurnal variations but all winds show characteristic seasonal variations.
Thus, 10 sub-groups or cases were considered: four corresponding to the seasons for the easterly winds, four to the seasons for the westerly winds and two for the easterlies and westerlies “calms” (v< 1 m/s).
There is a final multiple regression equation for each one of the ten considered cases. For example, the equation corresponding to the
“spring easterlies” is:
WIND SPEED = 5.50
– 0.40
U1000MB – 2.80
GRADPSUP + 4.10
GT311000 - 7.60
GT411000 + 4.00
GT51000 + 0.20
INTPOTAR
+ 0.41
DTAR1000 – 0.62
D6431000+ 0.61
VTAR1000 – 0.66 V6431000 where

U1000MB = horizontal wind component at
1000hPa level

GRADPSUP = horizontal mean sea level pressure gradient between the two sides of the Strait (east and west)

GT311000, GT411000 AND GT511000= horizontal temperature gradients between different nodes placed at the east side of the
Strait and the node at the west side

INTPOTAR = potential temperature difference between 1000 and 925 hPa at the node nearest to Tarifa

DTAR1000 = divergence at 1000 hPa level in Tarifa node

D6431000 = divergence at 1000 hPa level in a node at the east side of the Strait

VTAR1000 = vorticity at 1000 hPa level in
Tarifa node

V6431000 = vorticity at 1000 hPa level in a node at the east side of the Strait
As it can be seen in this example, these equations not only can be used for wind predictions but also, important conclusions about actual physical or dynamical atmospheric phenomena influences on the observed surface wind can also be derived from them, giving place to new suggestions for improving the model. Table 1 shows the number of samples, the multiple determination coefficient corrected by the freedom degrees (R 2 ) and the standard error of estimates for each one of the considered cases.
EASTERLIES WESTERLIES Calms
Sp Su Au Wi Sp Su Au Wi E W
N. of samples
518 434 465 278 411 454 442 565 173 214
Adjusted R 2 .72 .74 .72 .79 .62 .54 .54 .67 .50 .35
Standard error of estimates
2.41 2.17 2.04 2.21 2.26 2.40 2.38 2.43 2.40 2.18
Table 1: Statistical regression results, including the number of samples, the adjusted R 2 and the standard error of estimates values for each one of the ten considered cases .
The multiple determination coefficient corrected by the freedom degrees (R 2 ) gives a measure of the percentage of variance explained by the equation. It is greater for the easterly than for the westerly cases, reaching the maximum value for the winter easterlies (0.79) and the minimum for the summer westerlies (0.54). The cases of “ calms ” show the worst results, but these groups represent only a 6% of the total data and they do not persist. The better results for the easterlies were expected, because of the greater time variability of the westerlies.
The standard errors of estimates are very similar for all the cases and goes from 2.04 m/s
( autumn easterlies ) to 2.43 ( winter westerlies).
Figure 3 shows the scatter-plot of predicted values vs. observed values for the case of spring easterlies .
A residual analysis for all the considered cases was also performed to be sure that all the error terms hypothesis are fulfilled.

r d v . O r d lu ( e s e e d n ia le S in )
6
2 e r s n
% o
4 8 r d te w s e (
Fig. 3. Predicted wind speed using the regression equation versus observed values (in
Tarifa Station) for the Spring Easterlies case during the 1995-97 years.
In order to validate the regression Perfect
Prognostic model (Tarifa), the ECMWF model forecasting daily data at 24h, 36h and 48h horizons for the whole 1997 year were considered. The regression equations obtained from the P.P. technique were applied to forecasts and the wind estimations were compared to the observed values at the Tarifa station through comparisons of their means
(sample contrast test), standard deviations and probability distributions.
In every case, these comparisons show that these samples (observations and estimations) are statistically equal, except for the “ calms” cases.
Table 2 shows the correlation coefficients between the observed and predicted winds for each one of the considered cases. It can be seen that these coefficients are quite high and also that the highest values correspond to the easterly cases. It is also observed that the results for the
24h, 36h and 48h horizon predictions are quite similar, which means that the prediction quality does not decrease significantly within the 24 to
48 hours prediction range.
E E E E W W W W E
Spring Summer Autumn Winter Spring Summer Autumn Winter calms
W calms
24h 0.74 0.79 0.88 0.89 0.68 0.52 0.83 0.76 -0.24 -0.20
36h 0.76 0.78 0.83 0.83 0.71 0.68 0.71 0.74 -0.17 -0.08
48h 0.75 0.75 0.73 0.86 0.63 0.42 0.58 0.67 -0.05 -0.22
Table 2: Correlation coefficients between the observed and the prediction values after applying the statistical downscaling to the
ECMWF model predictions for the 24h, 36h and
48h horizons during 1997 .
Table 3 shows the mean square errors of wind predictions from the ECMWF model before and after the statistical downscaling method was applied. These have been calculated for different speed intervals and for the three horizon predictions (24h, 36h and 48h). The number of data corresponding to each case is also included. It can be seen that the ECMWF model wind speed prediction errors are much higher than the statistical model ones. Besides, for example, ECMWF model does not predict speeds higher than 15 m/s. This is a result which reflects that the coarse resolution ECMWF global model can not reproduce the channelling effect through the Strait, but the statistical model does.
It is also seen that errors do not increase with the horizon forecasting (from 24h to 48h).
Horizon SPEED INTERVALS
1-5 m/s
/U1000/>1
5-10 m/s 10-15 m/s > 15 m/s TOTAL
CALMS
/U1000/<1
24h
36h
48h
Mean square error (m/s)
Number of samples
Mean square error (m/s)
Number of samples
Mean square error (m/s)
Number of samples
1.99
20
2.32
60
2.55
19
3.00
136
3.44
114
3.20
141
2.79
103
3.27
89
3.99
97
3.28
55
4.14
50
3.47
56
2.94
314
3.25
313
3.39
313
4.25
40
3.66
40
3.50
39
Horizon SPEED INTERVALS
1-5 m/s
/U1000/>1
5-10 m/s 10-15 m/s > 15 m/s TOTAL
CALMS
/U1000/<1
24h
36h
Mean square error (m/s)
Number of samples
Mean square error (m/s)
Number of samples
7.07
200
5.73
223
8.36
101
8.34
81
7.16
13
6.54
9
--
0
--
0
7.53
314
6.51
313
4.77
40
2.97
40
48h
Mean square error (m/s)
Number of samples
6.65
205
8.18
100
7.14
8
--
0
7.19
313
5.14
39
Table 3: Number of samples and mean square errors corresponding to different speed intervals and forecasting horizons for the statistical regression model (up) and the
ECMWF model (down) during 1997.
The first model has been lightly modified after carrying out different residual and outliers analysis, and testing new variables and periods, decreasing the model errors.
Besides, the MM5 model has been applied to compare the forecasts with the statistical model ones, giving the first one (MM5), high errors than the second one (P.P. model) [7].
Now, there is a new project whose main objective is to forecast just over the sea, in order to be useful for offshore applications. Although there are not measurements at the sea available by now, different analysis and recorded data coming from short ship campaigns and buoys, will be used, until an offshore meteorological mast can be installed.
Nevertheless, from the previous knowledge acquired through the different studies of the wind characteristics in this place, it can be deduced that the model developed for Tarifa

(Tarifa model), could be also applied to the sea area, because of the influence of the Strait that affects all the area. But it is very important to evaluate the particular place for the installation of an offshore plant, especially if it is thought to be placed at the west side of the Strait, where the winds could vary from one point to another, because of the wider entrance through this side.
Wind speed values deduced from the ECMWF operational forecasting model do not reproduce properly the actual wind field across the Strait of Gibraltar, making necessary to implement a downscaling method.
The statistical model (Tarifa) based on multiregression analysis, is an adequate downscaling model which reduces errors greatly. The quality of prediction does not significantly decrease with the forecasting horizon (from 24h to 48 h).
The best results correspond to the easterly winds while the worst correspond to the “ calms ”.
It is presumable to think that this model is valid for the whole Strait of Gibraltar influence zone, because the wind flow characteristics are directly related to a topographical effect, but it requires new research, since the final objective is the offshore wind power prediction.
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