1. IntroductionWinter storms are responsible for more than 50% of the total economic loss in central Europe, due to natural hazards [1,2] and a single extreme storm event can cause economic losses exceeding 10 billion euros. A rise in storm-related monetary losses for Europe in the course of the 20th century has been observed by Barredo [3], explained principally by changes in economic and demographic conditions, with much of the recent infrastructure in various parts of the world increasingly constructed in zones at risk from severe weather [2]. Therefore, the knowledge of atmospheric circulation patterns, particularly the one dealing with atmospheric patterns conducive to risky meteorological situations related to extreme wind events, is especially important for wind energy applications [4-6]. Forecasters, energy producers and grid operators have different views on what extremes related to wind generation are. Extreme events have been categorized taken into account damages and economic loss
[7,8]. Extremes have been also identified as their occurrence probabilities [9]; they have been analyzed from the spatial-temporal characteristics of prediction errors [10], or taking into account their probabilistic forecasts by statistical scenarios [11,12], by ensemble predictions [13]. The final analysis can be used for nowcasting wind power over the whole area, and for data assimilation purposes (in order to update and improve wind power predictions) for better understanding the, or for issuing “global” warnings related to expected accuracy of weather and wind power forecasts over the area considered.
In determining temporal-spatial distribution changes of wind and other climatological elements, it is necessary to take into account the atmospheric circulation variability. The Western European climate steps are necessary on the available knowledge of natural variability in regional scales and its relationship to large-scale circulation [14- 20]. The relative location of different pressure centers over the North Atlantic area influence different air masses with distinct physical characteristics over Iberia to produce a wide range of differentiated regional climates, playing the topography a leading role. In fact, at local scales the development of cloud systems or the enhancement of wind speed over different areas can be especially affected due to the topography [21-23]; at largescale domains, topography can generate o redirected synoptic and mesoscale flows [24]. The present study is firstly focused on showing relationships between wind and large-scale atmospheric fields over an Atlantic area, with special emphasis on results involving extreme situations. These connections are attained by using different methods and procedures, such us cumulative probability curves and composite maps. Composites have already been used by the authors in several studies in order to analyse different fields, obtaining relationships between them, so that maximum and minimum intensity phases of a field can be related to the other one [16,18,19].
On the other hand, the improvement of meteorological forecasts of wind by means of dynamic modelling has been progressing by means of limited area models or ensemble prediction systems in several research projects (ANEMOS, ANEMOS.plus). However, this methodology bears high computational costs. In order to overcome this problem, the analog method for predicting time series can be used [25]. With this method, local prediction models are obtained finding in a set of historic data similar situations to a particular situation [26-28]. This technique has been implemented for both climatic anomaly predictions [29,30] and short-range prediction [31], revealing as an alternative to other more complex models with high computational cost. In the framework of the European Project SafeWind, the authors have been developing several works based on multivariate methodologies for obtaining atmospheric situations analog to a situation associated with extreme winds [32]. One of the final purposes of this European Project is to develop a statistical downscaling model (ANPAF: ANalog PAttern Finder) for diagnosing large-scale atmospheric circulation patterns and subsequently estimating extreme wind probabilities. In the present paper, from an atmospheric circulation pattern set obtained by multivariate methodology [18,19,33,34] applied to a large-scale atmospheric circulation field, estimations of wind fields, particularly extreme winds, are obtained by means of the analogs methodology.
The study is organized as follows. In Section 2, data used in the study are described. In Section 3, the connections between wind speeds and large-scale atmospheric patterns are shown, presenting the relationships between large-scale atmospheric patterns and wind speed patterns statistically obtained. Moreover, the interactions between observational winds and large-scale atmospheric circulation statistical modes are provided and analyzed. Section 4 is devoted to analyze the analog results for both the large-scale atmospheric field and the Spanish mean wind speed and wind gust, in terms of some deterministic and probabilistic tools. The main conclusions are drawn in Section 5.
2. DataIn order to analyze the relationships between wind speeds and large-scale atmospheric fields and to extract information about extreme situations it is very important to select the appropriate datasets. In this work, in order to characterize the atmospheric circulation, 1000 hPa daily geopotential heights at 12:00 UTC (Z1000) for 36 winters from 1971 to 2007 covering from 51.5˚W to 15.5˚E and 20˚ to 60˚N have been used. Z1000 data are a product of the ERA40 Reanalysis [35]. Concerning the wind speed, firstly daily mean wind speed (MWS) data for 21 stations distributed over Spain (Figure 1) during the winter (D-J-F) season from 1970 to 2002 have been considered. These wind data come from in-situ measurements of the station network of the Spanish Meteorological Service (Agencia Estatal de Meteorología, AEMET). In order to analyze the relationships between wind speeds and large-scale atmospheric fields and to extract information about extreme situations it is very important to select the appropriate datasets. In this work, in order to characterize the atmospheric circulation, 1000 hPa daily geopotential heights at 12:00 UTC (Z1000) for 36 winters from 1971 to 2007 covering from 51.5˚W to 15.5˚E and 20˚ to 60˚N have been used. Z1000 data are a product of the ERA40 Reanalysis [35]. Concerning the wind speed, firstly daily mean wind speed (MWS) data for 21 stations distributed over Spain (Figure 1) during the winter (D-J-F) season from 1970 to 2002 have been considered. These wind data come from in-situ measurements of the station network of the Spanish Meteorological Service (Agencia Estatal de Meteorología, AEMET).
On the other hand, some techniques for estimating and forecasting wind speeds are reviewed, with special emphasis in extreme winds. To do this wind speed and wind gust estimations in Spain, with special emphasis in extreme values, are obtained using the analog methodology applied to the Z1000 data base. To do this, a additional data set is considered, the daily wind gust (WGU) data over Spain. The WGU data used in this paper consist of 73 time series of daily gusts in Spain (Figure 1). Taking into account the observational data quality and the methodology employed in this contribution, in this part of study described in Section 4, the three datasets finally cover the common period from 1971 to 2002.
3. Extreme Wind Speeds-Large Scale Atmospheric Patterns Connections3.1. Large-Scale Atmospheric Patterns—Wind Speed Statistical Mode RelationshipsA Principal Component Analysis (PCA) is applied to the MWS and Z1000 fields in order to know its general behaviour and to extract the most significant patterns from the original data [36]. However beyond mere data compression, a PCA is a very useful tool for exploring large multivariate data sets because of its potential for yielding substantial insights into both the spatial and temporal variations of the analysed fields. This methodology applied to spatial data enables patterns to be identified that can be attributed to specific physical processes by statistical assessment. The new uncorrelated variables are called principal components (PCs) and consist of linear combinations of the original variables derived from the diagonalization of the covariance/correlation matrix. The coefficients of the linear combinations represent the weight of the original variables in the PCs and they are named loadings or PC patterns. The PCs indicate modes of variation of the original field and are numbered according with their related variance. Thus, the first PC is the linear combination with the maximum possible variance; the second one is the linear combination with the maximum possible variance which is uncorrelated with the first PC and so on. The projection of the original series onto each eigenvector gives as result the time-dependence coefficient named scores or PC time series. In our case, the PCA was applied to the correlation matrices of both data sets, the MWS and Z1000 fields, being a set of eigenvalues and eigenvectors produced for each data set. Generally, the most important (the first ones) eigenvectors tend to describe regions with largest fluctuations. Thus, most relevant information from the data can be represented using fewer numbers of the principal components and a much smaller data set. Five leading modes for both datasets have been selected (not all shown). They account for more than 66% and 77% of the total variability for MWS and Z1000, respectively.
For reasons of brevity only the first mode is shown. In Figure 2(a), the eigenvector or spatial pattern of the retained MWS PCs is shown which helps highlighting diverse areas of different wind behaviour over Spain. The leading wind PC pattern (Figure 2(a)) accounts for the most important percentage of variance in the original data (37.9%). In Figure 2(a) the spatial pattern shows homogeneous wind behaviour in inner Iberia, and also underlines the area to the North Iberian Plateau with high correlation values. This conduct in the wind field could be related to the predominant westerly circulation regime (Poniente) in the Iberian Peninsula. The time variability of the spatial pattern above described is depicted showing the evolution of its PC time series obtained by applying the PCA over the MWS data in wintertime (Figure 2(b)). Significant trends are not found after applying a Mann-Kendall test and a spectral analysis of the PC time series. As stated previously, the first spatial pattern of Figure 2a showed homogeneous wind pattern over Iberia, underlying areas corresponding to the North Iberian Plateau. This behaviour can also be represented in the corresponding time series (Figure 2(b)) with mostly positive and high score values over the selected period (1970-2002).
However, the derived modes are statistically obtained. To analyze the extreme situations is needed to find connections between wind speed and the atmospheric field.
Thus, to examine the real atmospheric circulation features associated with the winter wind speed patterns a set of positive and negative composite plots (of Z1000 and MWS) was constructed from the dates associated with 5 and 95 percentiles of the scores of the time series obtained of the PCA (Figure 2(c)). The composite maps represent configurations of the variable which are comparable to observations. Composites are defined here as the averaged ensemble of sets of maps of the large-scale atmospheric variable and the wind speeds [37]. Physical distinctive features in the composite plots are achieved through obtaining additional information to the statistical meaning of the derived spatial modes. Here, the anomaly composites of large-scale atmospheric variables have been built for those weather configurations associated with the highest and lowest PC scores of the wind speed. This way, the composites represent the atmospheric state associated with particular extreme wind characteristics. Positive (negative) composites are constructed directly from a number of configurations with high (low) scores of the PC time series because they indicate situations in which the corresponding PC mode is dominant in its positive (negative) phase. The selected number of configurations represents 5% of the total number of cases in the dataset.
Figure 3 shows the anomaly composites for Z1000 displaying the positive and negative composite plots conditioned by the 5% highest and lowest PC scores of the MWS. Subsequently, mean maps of Z1000 anomalies are drawn up from these days, and highlight the mean atmospheric state conditioned by predominant oscillation of the selected wind speed PC mode. Additionally, maps of MWS, also corresponding to those days, are picked up to illustrate the behaviour of the wind speed field over Spain in such atmospheric situations. Thus, the Z1000 anomaly composites associated to the first wind speed PC (Figures 3(a) and (b) first positive and negative composites) highlight two different mean atmospheric situations associated with the wind behaviour. Thus, in the first positive anomaly composite (Figure 3(a)), a strong gradient of Z1000 is observed over the Iberian Peninsula, underlying strong winds over Iberia as it can be noted in Figure 3(c) with wind speeds exceeding 8 m∙s−1 (30 km∙h−1) in daily average. In contrast to this atmospheric situation, the first negative composite (Figure 3(b)) displays high anomaly pressure over Iberia with little gradient over it and a nucleus over northern France. This situation is indicative of low wind speed