Monthly Modes of Variation of Precipitation over the Iberian Peninsula

Antonio Serrano Departamento de Física, Facultad de Ciencias, Universidad de Extremadura, Badajoz, Spain

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JoséAgustín García Departamento de Física, Facultad de Ciencias, Universidad de Extremadura, Badajoz, Spain

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Vidal Luis Mateos Departamento de Física, Facultad de Ciencias, Universidad de Extremadura, Badajoz, Spain

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María Luisa Cancillo Departamento de Física, Facultad de Ciencias, Universidad de Extremadura, Badajoz, Spain

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Juan Garrido Departamento de Física, Facultad de Ciencias, Universidad de Extremadura, Badajoz, Spain

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Abstract

An attempt is made to find the main monthly modes of variation of precipitation over the Iberian Peninsula. The modes of variation of precipitation were derived from principal component analysis. The dataset used consists of records of monthly precipitation from 40 meteorological stations over 74 yr (1919–92). The stations are spatially representative of most of the Iberian Peninsula. To take into account the seasonality of precipitation over the Iberian Peninsula, one analysis was performed separately for each calendar month. The modes of variation resulting from the different analyses were compared and clustered in groups according to their loading patterns. Seven main patterns were found to be of importance during various months of the year. These seven patterns explained more than 75% of the variance of the precipitation field from December to April. However, less than 20% of the total variance is explained for July and August. It is concluded that, depending on the month or season of interest, different modes of variation should be considered in order to achieve a better description of the monthly precipitation field.

Corresponding author address: Antonio Serrano, Departamento de Física, Facultad de Ciencias, Universidad de Extremadura, Avda. de Elvas, s/n, 06071 Badajoz, Spain.

Email: asp@unex.es

Abstract

An attempt is made to find the main monthly modes of variation of precipitation over the Iberian Peninsula. The modes of variation of precipitation were derived from principal component analysis. The dataset used consists of records of monthly precipitation from 40 meteorological stations over 74 yr (1919–92). The stations are spatially representative of most of the Iberian Peninsula. To take into account the seasonality of precipitation over the Iberian Peninsula, one analysis was performed separately for each calendar month. The modes of variation resulting from the different analyses were compared and clustered in groups according to their loading patterns. Seven main patterns were found to be of importance during various months of the year. These seven patterns explained more than 75% of the variance of the precipitation field from December to April. However, less than 20% of the total variance is explained for July and August. It is concluded that, depending on the month or season of interest, different modes of variation should be considered in order to achieve a better description of the monthly precipitation field.

Corresponding author address: Antonio Serrano, Departamento de Física, Facultad de Ciencias, Universidad de Extremadura, Avda. de Elvas, s/n, 06071 Badajoz, Spain.

Email: asp@unex.es

1. Introduction

Precipitation has a large impact on society, making it an important variable to study. It is directly related to water resources for human consumption, agriculture, and other purposes. Its intrinsic interest is even greater in the case of the Iberian Peninsula due to its large intraannual and interannual variability and to the frequent lack of water resources in this area.

As far as its study is concerned, precipitation is a very complicated variable. Its description involves a large range of temporal and spatial scales. This is especially true in the case of the Iberian Peninsula because of its sharp orographic relief, which strengthens some precipitation-generating mechanisms. The prevailing west–east orientation of the main mountain chains of the peninsula (Fig. 1) also plays an important role in the spatial distribution of precipitation. Whereas air masses moving along parallels find scarcely any obstacle, air masses moving southward or northward strike transversal mountain chains, which, under certain conditions of instability and high moisture content, causes precipitation on the windward side of the mountains.

The precipitation over the peninsula is also determined by its midlatitude location (36°–44°N, 10°W–3°E), which implies a certain synoptic circulation and an influence of the seas, which surround the peninsula. These seas are the sources of moisture for many of the air masses that produce rainfall over the peninsula.

The precipitation over the peninsula has a strong seasonal character (Garrido and García 1992). This seasonality involves not only the amount of precipitation, but also its nature (frontal or convective) and, therefore, its spatial and temporal scales. During autumn, winter, and spring, precipitation is mainly related to baroclinic synoptic-scale perturbations generated near the polar jet stream and moving eastward from the Atlantic Ocean. In contrast, the sparce summer rainfall in most parts of the peninsula depends especially on local factors and is mainly caused by convective storms associated with ground heating, high moisture content, and upper instability. This seasonal dependency makes the analysis of each calendar month separately highly interesting.

The present paper not only attempts to identify and characterize the main modes of variation of monthly precipitation over the Iberian Peninsula, but also to assess their evolution throughout the year. This evolution will be studied by analyzing the 12 calendar months separately.

Principal component analysis (PCA) is a method that has been extensively used to characterize the variability of many meteorological variables in very different countries. There have been a number of studies aimed at obtaining the modes of variation of precipitation for Spain only (Fernández 1995) or for the whole Iberian Peninsula (Zorita et al. 1992; J. Garrido et al. 1997, personal communication; Rodríguez-Puebla et al. 1998). These studies yield a unique set of modes of variation regardless of the different months or seasons.

The present study takes into consideration the convenience of allowing different descriptions for the different calendar months in order to improve the characterization and the understanding of the precipitation regimes of the Iberian Peninsula. Similar articles that analyze separately each calendar month are those by Grimmer (1962) and Barnston and Livezey (1987). Grimmer studies monthly temperatures in Europe and obtains a set of patterns specific to each calendar month. Barnston and Livezey perform separate analyses of each calendar month in order to assess the seasonality and persistence of the atmospheric circulation patterns.

2. Data

Total monthly precipitation series of 40 meteorological stations dispersed over the Iberian Peninsula were selected for this study. The dataset was intended to spatially and temporally represent the monthly precipitation field over the Iberian Peninsula. To be included in this study, series were required to have long successive records of data and to be nearly regularly distributed over the peninsula. These requirements permit reliable climatic conclusions to be drawn.

The precipitation records have been previously tested for quality (Garrido et al. 1996; Mateos et al. 1996). Nevertheless, shifts in the series and extremely high data that might have been anomalous were detected and verified. This quality control was based on the inspection of the accumulative deviation series (Buishand 1982).

Thirty-five monthly precipitation series belong to the Instituto Nacional de Meteorología de España, four series belong to the Instituto Nacional de Meteorologia e Geofísica de Portugal, and one to the Real Instituto y Observatorio de la Armada Española. The location of the series from the Real Instituto y Observatorio de la Armada Española is San Fernando (Cádiz) and extends over more than 100 yr.

The locations of the selected stations are shown in Fig. 2. One sees that these 40 meteorological stations are almost regularly distributed over the peninsula, except in the northwest where the series available lack the proper temporal continuity in order to be included in this study.

The common continuous period of time of the 40 series extends from 1919 to 1992. Since the minimum period required for this type of study is 30 yr (Jansá 1969), the analyzed period (74 yr) permits one to establish very reasonable climatic conclusions.

Some precipitation series suffer from missing data, although these were not common in any of the series. Missing data formed less than 3% of the total number of data. Since the type of analysis to be done demands complete records, missing data were replaced by the monthly precipitation mean for the corresponding calendar month. The mean was obtained as the arithmetic average of the rest of the data for the same calendar month. This approach is fairly common in multivariate methods, and has produced satisfactory results (Beale and Little 1975). Also, this method for completing series does not modify the seasonality of the original series.

Table 1 lists the names and geographical parameters of the selected meteorological stations.

The mean and the standard deviation of the monthly total precipitation series for the calendar months for the common period 1919–92 are shown in Figs. 3 and 4. The two variables show similar contour patterns, that is, the higher the mean, the higher the standard deviation. Both variables show a strong annual cycle. In summer, the precipitation is very low except in the northern part of the peninsula. During the cold months, the mean precipitation and its standard deviation reach the highest values in northern Portugal, Galicia, the Cantabrian coast, and central Andalusia. Precipitation is very low in Levante except during September and October, when the standard deviation is also extremely high. The high values reached by the standard deviation are especially notable. At several stations the standard deviation is as high as the mean monthly precipitation. The Iberian Peninsula exhibits an extreme variability with periods of great amounts of rainfall and others that remain practically dry.

3. Principal component analysis

a. Mathematical method

PCA is a widely known statistical technique that has been used very often in meteorology and climatology. It was first introduced by Pearson (1901), and Hotelling developed its mathematical basis in 1933.

PCA attempts to synthesize in a small number of new uncorrelated variables most of the total variation of a large number of highly intercorrelated variables. This reduction in dimensionality can lead to a more tractable understanding and interpretation of the data. The new uncorrelated variables are called principal components (PCs) and consist of linear combinations of the original variables. The coefficients of the linear combinations are called loadings and they represent the weight of the original variables in the PCs.

The PCs represent the modes of variation of the field described by the original set of variables. The PCs are numbered according to the variance that they explain. The first PC is the linear combination with the maximum possible variance, the second PC is the linear combination with the maximum possible variance that is uncorrelated with the first PC, and so on with the subsequent PCs.

Several full mathematical descriptions of PCA are detailed in the literature (Jolliffe 1986; Preisendorfer 1988; Sneyers et al. 1989).

Due to its great versatility, PCA has been applied in many studies with very different goals. It has been widely used to identify the coherent modes of variation of several fields. Of particular interest are the PCA studies that deal with precipitation (Dyer 1975; Ogallo 1980; Maheras 1988; Whetton 1988; Ogallo 1989).

In this study a PCA was applied to the monthly precipitation dataset in order to identify the individual modes of variation of the precipitation field over the Iberian Peninsula.

b. Mode

There are six possible modes for the previously mentioned analysis: the so-called O, P, Q, R, S, and T (Richman 1986). The modes differ according to which parameter is chosen as variable, which as individual case, and which as fixed entity. In the case that the meteorological parameter (in this study, precipitation) has been fixed, there are two options: the S and T modes.

The T-mode is the result of choosing the individual temporal observations as the variables, and the stations as the cases of those variables. When rotated, T-mode identifies subgroups of observations with similar spatial patterns. Fernández Mills (1995) performed a T-mode PCA for the monthly precipitation over Spain.

The S-mode PCA considers the stations as the variables and the temporal observations as the cases. The S-mode compares the series and identifies those stations in which precipitation varies similarly. It can be used for regionalization.

The present study performs an S-mode PCA since it fulfills the main objective of this analysis, and also because it is the natural process to use to obtain a correlation matrix of maximum rank when the number of observations (74 yr) is higher than the number of stations (40 stations).

c. Month-to-month analysis

To take into account the seasonality shown by precipitation over the Iberian Peninsula (Garrido and García 1992), 12 PCAs were performed, one for each month of the year. The separate monthly analyses permit one to detect characteristics that could remain hidden in an annual study. The evolution of the individual modes of variation will be assessed by comparing the PCs that result from the different analyses.

We separated months instead of seasons since no precipitation seasons could be defined a priori for all the stations. Moreover, the monthly temporal scale can provide more detailed results and is more suitable for further applications in the field of teleconnection and forecasting.

Each data series for the monthly analyses consists of 74 values, that is one per year. The serial correlation of the series was tested by means of the nonparametric test of Wald and Wolfowitz (1943). All the monthly series showed no persistence at a confidence level of 95%. The long temporal interval used (1 yr) guarantees statistical independence between data. Therefore, any variation between one temporal data point and the next is completely caused by the natural variability of the precipitation.

Twelve (one for each calendar month) 74 × 40 data matrices were constructed from the 40 variables (stations) and 74 cases (temporal observations).

d. Dispersion matrix

Another decision to be taken is the election of the dispersion matrix for the analysis. Different similarity measurements can be employed. The most usual are cross-product (Molteni et al. 1983), covariance (Kutzbach 1967;Craddock and Flood 1969), and correlation (Jolliffe 1990). A suitable similarity measure and its corresponding dispersion matrix must be chosen according to the characteristics and objectives of the study to be performed.

Some authors prefer the covariance matrix since it considers the actual magnitudes of the variations and preserves the metric. The covariance matrix gives greater weights to those stations with larger initial variation. The correlation matrix, however, uses standardized variables, giving all stations equal weight. In studies dealing with regionalization, the use of standardized variables can be very useful in order to avoid high-variance variables dominating the first few PCs (Jolliffe 1990).

In this present study, the correlation matrix was used in order to achieve a complete description of the precipitation field by considering every station in spite of its possible low variance. Thus, 12 40 × 40 correlation matrices were constructed from the original dataset.

Hotelling normalization for the loadings was used (Hotelling 1933). This transformation means postmultiplying the loadings of each PC by the square root of its corresponding variance. When using correlation matrices, this normalization gives the loadings the meaning of the correlation between the PCs and the original variables.

e. Number of PCs to be retained

Another important aspect of PCA is the number of PCs to be retained. The PCs selected are intended to adequately represent the original dataset variation without loss of significant information, depending on the future use to be made of the PCs.

In the present study, the loading spatial patterns of the PCs will be analyzed from a physical point of view. Since this analysis focuses on the description and interpretation of the sources of variation, the fact that the number of PCs retained remains reasonably low becomes a significant criterion. Several objective and subjective criteria for the election of the cutoff value have been described in the literature (Jolliffe 1986; Preisendorfer 1988). These criteria are called selection rules. The following ones were tried out in this study: cumulative percentage of total variation, Kaiser’s rule (Kaiser 1960), Scree graph (Cattell 1966), log-eigenvalue (or LEV) diagram (Craddock and Flood 1969), and rule N (Preisendorfer and Barnett 1977). Four cumulative total variation percentages (75%, 80%, 85%, 90%) were considered. Following Jolliffe’s suggestion (Jolliffe 1972) for Kaiser’s rule, in addition to the usual threshold of 1.0, a weaker threshold of 0.7 was also tried out in order to allow for sampling variation. Results of the different selection rules for each calendar month are listed in Table 2.

Except for the graphical criteria (Scree graph and LEV diagram) and rule N, the number of PCs that should be retained according to the selection rules reaches a maximum during the summer and a minimum during the winter. This fact is more than likely related to the increasing importance of local factors during the warm months, thereby increasing the intrinsic dimensionality of the problem during this period of the year.

The rule N suggests retaining very few PCs (Table 2). This result is in agreement with experiments that show that rule N tends to slightly underestimate the number of PCs to be retained (Preisendorfer et al. 1981).

The North et al. test (1982) was also applied in order to account for the sampling error of the eigenvalues. This test recommends retaining complete multiplets and not only a part of them. However, in the present study no multiplets could be isolated near the truncation points. In several cases, well-limited multiplets comprised only the first two or three eigenvalues. After these well-defined multiplets, and probably due to the small number of cases (74 yr), the error bars overlap continuously, and it was impossible to find a truncation point that verifies the criterion.

Some authors recommend overfactoring (Jeffers 1967; Richman 1981) since usually the consequences are slight. However, retaining insufficient PCs could mask some modes of variation (Stone 1989).

Following these recommendations, from all the above selection rules, we chose Kaiser’s rule with 1.0 as threshold in this study. When using the correlation matrix, only those PCs with variance greater than or equal to 1.0 should be retained according to Kaiser’s rule. This criterion is quite in line with the PCA perspective, since the set of PCs retained explains as much information as possible with that fixed total number of PCs. Since some of the later PCs were difficult to interpret physically, the lower threshold was unsuitable, as it would have meant the retention of physically ambiguous PCs.

The number of PCs retained according to the chosen selection rule (Kaiser’s rule with 1.0 as threshold) and the percentage of total variance that is explained by them for each calendar month are listed in Table 3. Following Kaiser’s rule, a total of 89 PCs were retained from the original 480 variables (40 series × 12 months). These 89 PCs explain 77.5% of the total variance of the set of the original 480 variables. The high percentages (from 74% to 80%) of total variance explained for each calendar month shows the reliability of the set of PCs selected in representing the variation of the original data. The great reduction in dimensionality achieved for each calendar month indicates the success of PCA in this study.

f. Rotation of principal components

One of the most important aspects of PCA is the possibility of rotation of the PCs (Richman 1986). This mathematical transformation consists in the replacement of the PCs retained by the same number of derived variables, called rotated principal components (RPCs), differently aligned from the first. Rotation does not affect the total amount of variance explained by the PC set. The RPCs are obtained as linear transformations of the unrotated PCs. The linear transformations are typically required to fulfill some criterion of simplicity.

The main advantage of RPCs is their easier physical interpretation since they are designed to remove ambiguities from the original PCs. Thus, RPCs allow a better identification of individual modes of variation.

There are different opinions regarding the value of rotation (Richman 1986, 1987; Jolliffe 1987), and no universal rule can be given independently of the objectives of each study.

The domain shape dependence of unrotated PCs is a major obstacle to attaining regionalization. This problem was studied by Buell (1975, 1979). He predicted an almost fixed sequence of maxima and minima in the loading patterns for any study with a square or rectangular domain. Buell concluded that topographies of unrotated PC loadings are primarily fixed by the shape of the domain rather than by the data. In this present study, the loading patterns for unrotated PCs roughly showed the sequence predicted by Buell, as is seen in Fig. 5 for the case of January.

Following the conclusions of a number of articles (Richman 1986; White et al. 1991) regarding the advisability of choosing rotation for studies requiring a physical interpretation of the resultant PCs, a rotation of PCs was performed in this study.

Varimax rotation (Kaiser 1958) was chosen as the rotation method since it is widely accepted as being the most accurate orthogonal rotation method and has virtually been the only orthogonal rotation used in climatology studies (Richman 1986; White et al. 1991). Varimax rotation was performed for each of the 12 PCAs (one for each calendar month).

Loading maps for Varimax rotated PCs for January are shown in Fig. 6. Each rotated PC shows relatively high loadings confined to certain regions and loadings close to zero elsewhere. The gain in interpretability reached by means of rotation can be confirmed by comparing loading maps for unrotated PCs (Fig. 5) with those for Varimax rotated PCs (Fig. 6).

Following Richman’s suggestion (Richman and Lamb 1985), the Varimax rotated PCs were compared with oblique rotated PCs in order to confirm that the constraint of orthogonality inherent in Varimax rotation does not result in misleading patterns. The Direct Oblimin (Jennrich and Sampson 1966) and Promax (Hendrickson and White 1964) oblique rotations were applied. Promax k = 2 was used since Richman (1986) showed that it is more accurate than the widely used Promax k = 4. Differences between Varimax, Direct Oblimin, and Promax sets of rotated PCs were very small, as is shown in Figs. 6–8 for the case of January. However, they were notably different from the unrotated results (Fig. 5). These results prove that the resultant modes of variation are independent of the rotation method used.

The matrices of PC intercorrelations for the Direct Oblimin rotated January PCs (Table 4) and for the Promax rotated January PCs (Table 5) were computed in order to assess the orthogonality of the rotated PCs. RPC1 and RPC2 show the highest intercorrelation, which is lower for Promax rotation than for Direct Oblimin rotation. Most values do not exceed 0.4.

Given the similarity in results between the rotated solutions, and in order to retain components that are uncorrelated with each other, the simpler orthogonal Varimax rotation was chosen.

4. Common patterns

a. Common and singular patterns

Once significant PCs have been retained and subsequently rotated, the loading patterns for different months are compared with each other. The idea behind this comparison is that, if PCs are linked to circulation conditions and these conditions vary slowly throughout the year, then the main patterns must remain relevant for various months, and, therefore, be found in various analyses.

This idea is confirmed by the visual inspection of loading maps for different calendar months. In Fig. 9, loading maps for the fourth RPCs of January and February are shown side by side. Taking into account their great similarity, it can be concluded that they represent the same precipitation mode of variation, which is of importance in, at least, these 2 months.

The spatial patterns that are common for two or more months are called common patterns. On the contrary, those patterns that are unique and appear only for 1 month are called singular patterns. This classification separates the modes of variation depending on the temporal scale of their main causes. While a common pattern can be interpreted in terms of general atmospheric circulation conditions varying slowly throughout the year, a singular pattern is markedly influenced by local features, which explains its nonpersistent nature.

Loading maps for all 89 RPCs were plotted. Among the 89 loading maps assumed to be meaningful, there might be recognized a number of marked spatial structures that are found repeated in the analyses of different calendar months.

b. Cluster analysis

To compare all 89 RPCs with each other, and to extract the common spatial rainfall patterns, an agglomerative hierarchical cluster analysis was performed. Initially, in this method, each element, namely each RPC, is considered to be a separate cluster. Subsequently, the two most similar clusters are joined into a single cluster. This joining process continues stepwise until only one cluster remains. This last cluster contains all the RPCs. This type of cluster analysis is completely established by the definition of the similarity measure between two elements (that is to say, between two RPCs) and the similarity measure between two clusters.

Most cluster analyses of PCs use the PC time series. However, we propose an innovative approach, which consists in using the congruence coefficient proposed by Harman (1976) as the similarity measure between pairs of spatial loading patterns. The congruent coefficient gAB betweeen two PCs A and B is defined as follows:
i1520-0442-12-9-2894-e1
where ai and bi refer to the station loadings of the PCs A and B, respectively.

It has been shown that this congruence coefficient is more reliable than the correlation coefficient for spatial pattern comparison (Richman and Lamb 1985). The form of the congruence coefficient is similar to a correlation coefficient, but with loadings instead of deviations from their mean. The mean of a PC loading vector is important when one physically interprets the pattern, so that using a coefficient that preserves the mean is highly desirable.

In this present study, average linkage was chosen as the method for combining clusters since it overcomes many of the drawbacks suffered by other widely used hierarchical clustering techniques such as single linkage, complete linkage, centroid technique, and Ward’s technique (Stooksbury and Michaels 1991). Moreover, average linkage has been proved to give the most realistic results in climatological research (Kalkstein et al. 1987). This method computes the average similarity between two clusters as the arithmetical mean of pairwise similarities of all possible combinations with one RPC from each of the two clusters.

Initially, several average similarity thresholds were tested in order to extract meaningful clusters. However, the inspection of the fusion tree showed that the homogeneity of the distinct clusters was very different. This fact suggested the advisability of using not a single threshold for all clusters, but a different threshold for each of them. The use of the same rigid threshold for all clusters becomes unsuitable because, while a high threshold does not account for the logical variation due to noise in clusters that include summer RPCs, a loose one jeopardizes interesting differences in better defined clusters.

To use a cluster-adapted threshold, clusters were first delimited by an average threshold of 0.82. Subsequently, each resultant cluster was analyzed and the threshold, if needed, relaxed or strengthened depending on the homogeneity and the interpretability of the differences between RPCs. The relaxing or strengthening of the threshold allows the inclusion of interpretability of differences between RCPs as a factor in the identification of meaningful clusters. This is very interesting information that cannot be formulated in mathematical terms, but which greatly improves the classification with regard to its physical meaning.

As a result of the cluster analysis, seven strong clusters were found. Each cluster consists of those RPCs that are similar enough to be said to represent the same mode of variation of precipitation. These are the RPCs that we call common. The singular patterns correspond to those RPCs that remain ungrouped in the clustering process because of being dissimilar to every other RPC.

Each cluster is considered to be a representative mode of variation of monthly precipitation in the Iberian Peninsula. The clusters are labeled in agreement with the area with the highest loadings:

  • Atlantic pattern (ATL)

  • interior pattern (INT)

  • south pattern (SOU)

  • Galicia and northern Portugal pattern (POR)

  • Catalonia pattern (CAT)

  • Levante pattern (LEV)

  • Cantabrian pattern (CAN)

Most clusters are well defined since their thresholds are all high (Table 6). The threshold of the POR pattern is relatively low (0.72). The reason is that this pattern is characteristic of warm months, when low precipitation values complicate pattern discovery. Nevertheless, the loading maps of RPCs belonging to this cluster show a reasonable similarity under visual inspection.

Fifty-seven of the total 89 meaningful RPCs belong to the common patterns. None of the 32 singular RPCs showed any similarity to any of the seven large clusters or to any of the other singular RPCs. The 89 RPCs explained 77.5% of the total original variance; 60.6% corresponds to common patterns, and 16.9% to singular patterns.

The variance explained by both common and singular patterns together remains quite constant throughout the year (Fig. 10). However, the variances explained by only common and by only singular patterns vary remarkably (Fig. 10). The variance explained by common patterns is very high (about 70%) during cold months, decreases as summer approaches, reaching a quite sharp minimum with values of less than 20% during July and August. It begins to increase in September and reaches the 70% value again in October. June and September are transition months with medium variances (47.6% and 58.5% of the total variance explained, respectively). The evolution throughout the year of the variance explained by singular patterns is almost the opposite of the variance explained by common patterns. The variance that is explained by singular patterns reaches a sharp maximum value in August (59.5%) and its minimum value during cold months (less than 10%).

During the cold months, common patterns account for a high proportion of the total variance of the standardized variables set. However, most of those patterns are not so evident in summer, when, in most parts of the Iberian Peninsula, rainfall is mainly caused by local convective storms. Precipitation is then mainly influenced by extremely local factors, leading to singular spatial patterns dissimilar to each other.

5. Interpretation of common patterns

In the present study, the temporal interval between data (1 month) is considerably longer than the temporal scale of precipitation generating mechanisms (from a few hours for highly convective precipitation to several days for precipitation associated with frontal systems). This fact makes it difficult to interpret the modes of variation, which one can only do looking for the traces that a certain precipitation event might leave in the total monthly precipitation records. Therefore, we here attempt to identify broad regions in which precipitation varies, at a monthly scale, in a coherent way.

Table 7 shows the rank and percentage of total variance explained by common patterns for each calendar month. Most patterns, except POR and CAN, disappear in the warm months. During these months no coherent regions of precipitation can be defined in most parts of the Iberian Peninsula even at such a broad temporal scale as the monthly scale. This is mainly due to two causes: on the one hand, the extremely local character of precipitation during the warm season and, on the other hand, the decrease of signal-to-noise ratio due to the lack of rainfall in most parts of the Iberian Peninsula.

Table 7 is symmetric with respect to the middle of the year. This confirms our previous idea of interpreting the common patterns in terms of the north–south oscillation of the general atmospheric circulation structures throughout the year.

a. Atlantic pattern: ATL

Figure 11 represents the loading maps that correspond to the ATL for different calendar months.

In the first classification with the threshold 0.82, this cluster was joined to the cluster corresponding to the INT into a single large cluster. The visual inspection of the fusion tree showed the existence of two very similar highly homogeneous subclusters. The reason for considering these two clusters separately is that, despite their great numerical similarity, their precipitation mechanisms are different. The main difference is for the Atlantic coastal stations, where loadings are very high for the ATL (Fig. 11) and very low for the INT pattern (section 5b, Fig. 13).

ATL is the spatially broadest pattern. It is characterized by high loadings on the Atlantic coast and in the Meseta. This area is open to air masses that come from the Atlantic Ocean since there is no mountain chain oriented in the north–south direction that could limit their action (Fig. 1). The main valleys are oriented in the west–east direction due to the slight slope of the Meseta toward the west.

Most synoptic situations that contribute to the ATL consist of a center of low pressure located to the north or northeast of the Iberian Peninsula (Fig. 12). This situation produces a strong westerly flow that drives the humid atlantic air mass to the Peninsula causing major precipitation on the Atlantic coast and the Meseta. The moisture source of this humid flow is the Atlantic Ocean.

The aforementioned lows usually bear associated fronts. These frontal systems enter the Iberian Peninsula moving eastward and are responsible for great amounts of precipitation on the Atlantic coast and in the interior.

The existence of a front is not completely necessary, since precipitation can occur without a well-defined front if there is a strong zonal flow. In this case precipitation is enhanced by the presence of upper instability.

The precipitations described by ATL pattern are the most extensive and common during the cold months. The ATL pattern is found to be important from November to March (Table 7), when it accounts for a very high percentage of total variance, ranging from 26.2% in December to 42.8% in February.

Figure 11 shows the evolution of the ATL throughout the year. Despite mode 1 of March corresponding to the ATL, the loading maxima have begun to move to the interior of the Peninsula, which is a first sign of the transition to the INT.

During the cold months the general circulation conditions allow the fronts to cross the Iberian Peninsula. However, from April to October the northward displacement of all structures of the atmospheric general circulation (the Polar Front among them) makes most frontal systems move along higher latitudes, leaving the Iberian Peninsula out of their range of influence. This is the reason why this pattern is not found from April to October.

b. Interior pattern: INT

The loading maps that correspond to the INT are shown in Fig. 13. High loadings of INT pattern are located in the interior part of the Iberian Peninsula, decreasing toward the coast. It is a widely extended pattern. The loading maxima are located in the Submeseta Norte (Fig. 1). However, their exact location moves from 1 month to the next due to the convective nature of the precipitation events that cause this pattern.

From April to November the precipitation events associated to frontal systems described by the ATL are rare. During these months, precipitation in the interior is mainly caused by convective storms. These convective storms are activated by instability conditions such as a thermal low, an upper trough, etc. (Fig. 14). The successful development of these convective storms is enhanced by ground heating, high moisture, and sharp orography.

The INT represents the very important precipitation of April, May, September, and October in the Duero Valley (Capel Molina 1981). This pattern is characteristic of the transition months between cold and warm seasons. During these months it explains high percentages of total variance, ranging from 10.7% in October to 16.3% in April (Table 7). As do most patterns, it vanishes during June, July, and August.

c. South pattern: SOU

The loading maps that correspond to the SOU are shown in Fig. 15.

The SOU has its highest loadings in the southern part of the Iberian Peninsula (Fig. 15). Stations having the highest correlations tend to be close to the Andalusian coast and loadings decrease slowly to the north. The loading maxima are located sometimes in the Andalusian Atlantic coast and sometimes on the Andalusian Mediterranean coast. The Strait of Gibraltar contributes greatly to this heterogeneity. Despite this, and taking into account the nature of the month to month variability, it is not possible to distinguish different subclusters and it has to be considered as a single cluster. The congruence coefficient threshold for the cluster was 0.82 (Table 6), which indicates a somewhat variable pattern.

Precipitation represented by this pattern is mainly caused by low pressure centers located around the Cape of San Vicente, the Gulf of Cádiz, or the Strait of Gibraltar, and moving eastward (Fig. 16). The annual precipitation in the southern peninsula depends greatly on the frequency of these synoptic situations. The low produces a southerly flow that drives the Atlantic humid and warm air mass into the Iberian Peninsula.

The SOU vanishes only in July and August. During the other months it explains very high percentages of total variance (near 20% in 6 of the 10 months when this pattern is found) as is seen in Table 7.

d. Galicia and Northern Portugal pattern: POR

The loading maps corresponding to the POR are shown in Fig. 17.

The highest loadings for the POR are located in the Galicia region and the northern two-thirds of Portugal. The maxima occur near the Atlantic coast and they decrease toward the east. This is the least homogeneous cluster, with a congruence coefficient of 0.72 (Table 6). One reason for this low congruence is the high noise-to-signal ratio during the warm months when this pattern is found. However, the loading maps show a moderate similarity (Fig. 17), which permits one to consider it as a meaningful pattern.

Most synoptic situations that contribute to the POR consist of a center of low pressure located near the British Isles, and there is usually an associated front (Fig. 18). Since the low is far from the Iberian Peninsula, only the tail end of the front reaches the Peninsula. The tail end of the front is very weak and causes precipitation only in Galicia and northern Portugal.

This mode of variation is related to the same precipitation mechanisms that explain the ATL. The difference is that the Atlantic frontal systems that reach the Iberian Peninsula during the warm months are very debilitated and, therefore, cause precipitation only in the area near the coast.

The POR pattern is characteristic of warm months, since it appears in April and vanishes in November. It is related to differences that arise between Atlantic coast and interior stations during the warm months. Tables 8 and 9 show the intercorrelation coefficient between two typical Atlantic coast stations (Coimbra and Oporto) and two typical interior stations (Palencia and Valladolid) for the months of January and May. In January, the correlation between coastal and interior stations is very high, reaching values higher than 0.8. However, in May, the correlation between coastal and interior stations declines to values of about 0.4. In spite of the increase in local precipitation, the intercorrelation between the two coastal stations is around 0.8 and the intercorrelation between the two interior stations is about 0.7. The differences in behavior are due to the increasing importance of the local factors during warm months. From November to March synoptic conditions prevail over local factors and almost solely determine whether it rains or not. This situation was well described by the ATL. However, in April, ground heating and orography become important factors, and synoptic conditions are no longer the only factors to be considered. The increasing importance of local factors causes the coherent region described by the ATL pattern to split into two parts: an interior region represented by the INT pattern and a coastal region represented by the POR.

Unlike most patterns, the POR does not vanish during July and August. The reason is that precipitation in the area with high loadings is not as infrequent in summer as in the rest of the Iberian Peninsula. Rainfall in this area ranges from 90 mm to 120 mm during the summer (Font Tullot 1983).

The POR explains percentages of total variance that range from 5.7% in September to 9.8% in April (Table 7).

e. Catalonia pattern: CAT

The loading maps that correspond to the CAT are shown in Fig. 19.

The coherent precipitation region represented by the CAT fundamentally corresponds to the Catalonia region, which is located to the northeast of the Iberian Peninsula. The loading maxima are located near the coast and the loadings decrease toward the southwest.

The Mediterranean Sea, the Pyrenees, and the Sistema Ibérico (Fig. 1) give this region a marked climatological identity regarding monthly precipitation behavior.

Most synoptic situations that contribute to the CAT consist of a center of high pressure over the Atlantic Ocean or a center of low pressure over Algeria, or both (Fig. 20). Those structures cause an easterly flow, which is first forced to ascend over the Cordilleras Catalanas and subsequently channeled between the Pyrenees and the Sistema Ibérico (Fig. 1). This is a flow with high moisture content since it comes from the Mediterranean Sea, which is a closed warm sea with high evaporation rates. These factors, and the existence of upper instability cause most of the precipitation over the Catalonia region.

The CAT pattern explains about 10% of the total variance of the precipitation field. As do most patterns, it vanishes in June, July, and August (Table 7).

f. Levante pattern: LEV

The LEV identifies the eastern Iberian Peninsula as one precipitation coherent region (Fig. 21). High loadings are located near the Mediterranean coast and sharply decrease toward the interior.

Most synoptic situations that contribute to the LEV consist of a center of low pressure to the south of the Iberian Peninsula (Fig. 22). This situation causes a strong easterly flow that strikes the coast and is forced to ascend (orographic forcing). The flow can be enhanced by the existence of a center of high pressure to the north of the Peninsula. It has a very high moisture content due to the high evaporation rate over the Mediterranean Sea. The situations described are responsible for most of the precipitation over the Levante region.

This pattern is quite well defined in the months when it is found. During these months it explains about 10% of the total variance of the precipitation field (Table 7). As do ATL, INT, SOU, and CAT, it vanishes during July and August.

g. Cantabrian pattern: CAN

The loading maps that correspond to the CAN are shown in Fig. 23. The coherent region defined by this mode of variation consists of the entire Cantabrian coast. High loadings are located near the coast and decrease sharply southward due to the presence of the Cordillera Cantábrica (Fig. 1). This mountain chain sharply limits the extent of the coherent precipitation region.

The CAN is spatially well defined and hardly changes from one month to the next (Fig. 23). The cluster showed a high stability in the fusion tree with respect to a large range of thresholds.

Typical precipitations on the Cantabrian coast are associated with northerly flows. Most synoptic situations that cause precipitation in this area consist of a center of high pressure to the northwest of the Iberian Peninsula, around 50°N (Fig. 24). It is also necessary to have an upper zonal flow or an upper trough causing instability. Under these conditions the Cordillera Cantábrica forces the air mass coming from the Cantabrian Sea to ascend (orographic forcing), producing great amounts of precipitation on the windward side (northern slopes). The air mass reaches the leeward side (southern slopes) dry and hot because of the so-called föhn effect.

This pattern is the only one that appears in every calendar month without exception. The relatively high precipitation during summer on the Cantabrian coast (more than 120 mm during the summer trimester (Font Tullot 1983), which is quite high in comparison with the rest of the Iberian Peninsula) and in northern Portugal and Galicia, makes it possible to identify the CAN and POR patterns even during the warm months.

6. Stability of the patterns

An obvious proof of stability of the patterns is the finding of the same pattern in independent adjacent monthly analyses.

To address the stability of the patterns regarding the rotation method, the regionalization was performed also with the Promax and Direct Oblimin results. The same seven common patterns were found, showing the independence with respect to the rotation method.

The regionalization was also performed with the PCs retained by the Kaiser rule with threshold of 0.7, that is, with more PCs retained. The same seven common patterns were obtained. This confirms that the patterns are not affected by retaining a higher number of PCs.

To address the stability of the regions, the period of 74 yr was divided into subperiods. Dividing into two equal halves was found to yield singular correlation matrices. Therefore the 45-yr subperiods 1919–63 and 1948–92 were used. These subperiods are not completely independent but have 16 years in common. In both regionalizations, the ATL, SUR, CAT, LEV, and CAN were obtained. However, INT and POR were not found. This is probably due to the small number of observations in each subperiod (45 yr), which leads to a decrease in stability compared to the analysis of the total period (Gray 1981). The INT and POR were characteristic of the warm months and, therefore, more affected by noise and more unstable.

7. Summary and conclusions

This study aimed at obtaining the main modes of variation of the monthly precipitation field over the Iberian Peninsula. The patterns were found by means of performing an S-PCA for each calendar month separately. The PCA technique was confirmed as being suitable for the present study since it allowed a marked reduction in dimensionality even for the noisiest months, when only 10 PCs explained 70% of the original total variance.

The PCs were rotated since, while unrotated PCs suffered from domain-shape-dependence and were not physically interpretable, rotation led to meaningful patterns that are in agreement with certain frequent synoptic situations. Three different rotations (Varimax, Direct Oblimin, and Promax) of the PCs were performed and compared for the January case. They all led to analogous meaningful patterns that were, however, very different from the unrotated patterns. Since the results showed no significant differences, the simpler orthogonal Varimax rotation was chosen.

The rotated PCs obtained in the different month analyses were compared and classified by means of a cluster analysis in order to find those main modes of variation that are of importance not only for one but for several calendar months. The result was that 57 of 89 PCs were classified into seven main patterns, which were called common patterns. The method used to classify the PCs was a hierarchical cluster analysis with the Harman congruence coefficient as measure of similarity between loading patterns. This innovative approach profits from the suitability of the congruence coefficient for spatial pattern comparison. It has shown itself to be suitable for the identification of similar PCs and can be a useful alternative to the visual inspection, correlation, and other methods used until now.

The seven common patterns that were found—ATL, INT, SOU, POR, CAT, LEV, and CAN—account for 60.6% of the variance of the monthly precipitation field. They can be explained in terms of geographical factors and large-scale synoptic fields. It must be noted that all patterns except POR and CAN vanish in summer. This is due to the decreasing signal-to-noise ratio and to the increasing influence of local factors during the warm months.

The separate study of the calendar months led to very interesting results that have remained masked in previous studies. The main result was that some modes of variation are characteristic of certain calendar months, but vanish during the others. For instance, the ATL pattern is found only from November to March, and splits into two different patterns, INT and POR, from April to October. This division is probably related to the different large-scale circulation conditions, the increasing importance of local factors, and the more convective character of precipitation events during the warm months. These factors lead to a different behavior in summer between the coastal and interior stations in summer, which, however, behave similarly from November to March.

The patterns obtained, and the associated calendar months when each of them is reliable, constitute a useful basis to describe the monthly precipitation field over the Iberian Peninsula.

Acknowledgments

Thanks are due to the Instituto Nacional de Meteorología de España, to the Instituto Nacional de Meteorologia e Geofísica de Portugal, and to the Real Instituto y Observatorio de la Armada Española en San Fernando (Cádiz) for kindly providing the data. This study was supported by the Spanish CICYT under Project CLI96-1871-C04-03 and by the Junta de Extremadura-Fondo Social Europeo under Project PRI97C139.

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Fig. 1.
Fig. 1.

The Iberian Peninsula orography.

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 2.
Fig. 2.

Location of the selected meteorological stations.

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 3.
Fig. 3.

Mean of the monthly total precipitation (mm) for the calendar months.

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 4.
Fig. 4.

Standard deviation of the monthly total precipitation (mm) for the calendar months.

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 5.
Fig. 5.

Loading maps for unrotated PCs for Jan.

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 6.
Fig. 6.

Loading maps for Varimax rotated PCs for Jan.

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 7.
Fig. 7.

Loading maps for Direct Oblimin rotated PCs for Jan.

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 8.
Fig. 8.

Loading maps for Promax rotated PCs for Jan.

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 9.
Fig. 9.

Loading maps for the fourth Varimax rotated PCs of (a) Jan and (b) Feb (right).

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 10.
Fig. 10.

Percentages of total variance explained by common patterns, singular patterns, and both common and singular patterns together for each month of the year.

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 11.
Fig. 11.

ATL in Jan (mode 1), Feb (mode 1), Mar (mode 1), Nov (mode 1), and Dec (mode 1).

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 12.
Fig. 12.

Synoptic situation that contributes to the ATL pattern.

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 13.
Fig. 13.

INT in Apr (mode 2), May (mode 2), Sep (mode 2), and Oct (mode 3).

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 14.
Fig. 14.

Synoptic situation that contributes to the INT.

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 15.
Fig. 15.

SOU in Jan (mode 2), Feb (mode 2), Mar (mode 4), Apr (mode 1), May (mode 1), Jun (mode 1), Sep (mode 5), Oct (mode 1), Nov (mode 2), and Dec (mode 2).

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 16.
Fig. 16.

Synoptic situation that contributes to the SOU.

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 17.
Fig. 17.

POR in Apr (mode 5), May (mode 6), Jun (mode 5), Jul (mode 4), Aug (mode 7), Sep (mode 7), and Oct (mode 6).

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 18.
Fig. 18.

Synoptic situation that contributes to the POR.

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 19.
Fig. 19.

CAT in Jan (mode 3), Feb (mode 5), Mar (mode 2), Apr (mode 4), May (mode 4), Sep (mode 4), Oct (mode 7), Nov (mode 3), and Dec (mode 3).

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 20.
Fig. 20.

Synoptic situation that contributes to the CAT.

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 21.
Fig. 21.

LEV in Jan (mode 5), Feb (mode 3), Mar (mode 3), Apr (mode 3), May (mode 3), Jun (mode 2), Sep (mode 3), Oct (mode 4), Nov (mode 5), and Dec (mode 5).

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 22.
Fig. 22.

Synoptic situation that contributes to the LEV pattern.

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 23.
Fig. 23.

CAN in Jan (mode 4), Feb (mode 4), Mar (mode 5), Apr (mode 6), May (mode 5), Jun (mode 3), Jul (mode 5), Aug (mode 3), Sep (mode 6), Oct (mode 5), Nov (mode 4), and Dec (mode 4).

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Fig. 24.
Fig. 24.

Synoptic situation that contributes to the CAN.

Citation: Journal of Climate 12, 9; 10.1175/1520-0442(1999)012<2894:MMOVOP>2.0.CO;2

Table 1.

Number, name, altitude, latitude, and longitude of the selected meteorological stations.

Table 1.
Table 2.

Number of PCs to be retained according to several selection rules for each month of the year. Var ≡ variance.

Table 2.
Table 3.

Number of PCs to be retained according to the chosen selection rule (Kaiser’s rule with 1.0 as threshold) and percentage of total variance explained by those PCs for each month of the year.

Table 3.
Table 4.

Matrix of Direct Oblimin rotated PCs intercorrelations for Jan.

Table 4.
Table 5.

Matrix of Promax rotated PCs intercorrelations for Jan.

Table 5.
Table 6.

Pattern names and thresholds used to define clusters.

Table 6.
Table 7.

Rank and percentage of total variance explained (parenthetically) by PCs which are associated to common patterns.

Table 7.
Table 8.

Intercorrelation between several coastal and interior stations in Jan.

Table 8.
Table 9.

Intercorrelation between several coastal and interior stations in May.

Table 9.
Save
  • Barnston, A. G., and R. E. Livezey, 1987: Classification seasonality and persistence of low-frequency atmospheric circulation patterns. Mon. Wea. Rev.,115, 1083–1126.

  • Beale, E. M. L., and R. J. A. Little, 1975: Missing values in multivariate analysis. J. Roy. Statist. Soc. B,37, 129–145.

  • Buell, C. E., 1975: The topography of empirical orthogonal functions. Preprints, Fourth Conf. on Probability and Statistics in Atmospheric Sciences, Tallahassee, FL, Amer. Meteor. Soc., 188–193.

  • ——, 1979: On the physical interpretation of empirical orthogonal functions. Preprints, Sixth Conf. on Probability and Statistics in Atmospheric Sciences, Banff, AB, Canada, Amer. Meteor. Soc., 112–117.

  • Buishand, T. A., 1982: Some methods for testing the homogeneity of rainfall records. J. Hydrol.,58, 11–27.

  • Capel Molina, J. J., 1981: Los Climas de España. Oikos-Tau, 429 pp.

  • Cattell, R. B., 1966: The scree test for the number of factors. J. Multi. Behav. Res.,1, 245–276.

  • Craddock, J. M., and C. R. Flood, 1969: Eigenvectors for representing the 500 mb geopotential surface over the Northern Hemisphere. Quart. J. Roy. Meteor. Soc.,95, 576–593.

  • Dyer, T. G. J., 1975: The assignment of rainfall stations into homogeneous groups: An application of principal component analysis. Quart. J. Roy. Meteor. Soc.,101, 1005–1013.

  • Fernández Mills, G., 1995: Principal component analysis of precipitation and rainfall regionalization in Spain. Theor. Appl. Climatol.,50, 169–183.

  • Font Tullot, I., 1983: Climatología de España y Portugal. Servicio de Publicaciones del Instituto Nacional de Meteorología, Madrid, 296 pp.

  • Garrido, J., and J. A. García, 1992: Periodic signals in Spanish monthly precipitation data. Theor. Appl. Climatol.,45, 97–106.

  • ——, ——, and V. L. Mateos, 1996: Homogeneidad y variabilidad natural de series largas de precipitación. Anales de Física,92, 19–31.

  • Gray, B. M., 1981: On the stability of temperature eigenvector patterns. J. Climatol.,1, 273–281.

  • Grimmer, M., 1962: The space-filtering of monthly surface anomaly data in terms of pattern, using empirical orthogonal functions. Quart. J. Roy. Meteor. Soc.,89, 395–408.

  • Harman, H. H., 1976: Modern Factor Analysis. The University of Chicago Press, 487 pp.

  • Hendrickson, A. E., and P. O. White, 1964: Promax: A quick method to oblique simple structure. Brit. J. Stat. Psych.,17, 65–70.

  • Hotelling, H., 1933: Analysis of a complex of statistical variables into principal components. J. Educ. Psychol.,24, 417–441, 498–520.

  • Jansá Guardiola, J. M., 1969: Curso de Climatología. Sección de Publicaciones del Instituto Nacional de Meteorología Madrid, 445 pp.

  • Jeffers, I. N. R., 1967: Two case studies in the application of principal component analysis. Appl. Stat.,16, 225–236.

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  • Fig. 1.

    The Iberian Peninsula orography.

  • Fig. 2.

    Location of the selected meteorological stations.

  • Fig. 3.

    Mean of the monthly total precipitation (mm) for the calendar months.

  • Fig. 4.

    Standard deviation of the monthly total precipitation (mm) for the calendar months.

  • Fig. 5.

    Loading maps for unrotated PCs for Jan.

  • Fig. 6.

    Loading maps for Varimax rotated PCs for Jan.

  • Fig. 7.

    Loading maps for Direct Oblimin rotated PCs for Jan.

  • Fig. 8.

    Loading maps for Promax rotated PCs for Jan.

  • Fig. 9.

    Loading maps for the fourth Varimax rotated PCs of (a) Jan and (b) Feb (right).

  • Fig. 10.

    Percentages of total variance explained by common patterns, singular patterns, and both common and singular patterns together for each month of the year.

  • Fig. 11.

    ATL in Jan (mode 1), Feb (mode 1), Mar (mode 1), Nov (mode 1), and Dec (mode 1).

  • Fig. 12.

    Synoptic situation that contributes to the ATL pattern.

  • Fig. 13.

    INT in Apr (mode 2), May (mode 2), Sep (mode 2), and Oct (mode 3).

  • Fig. 14.

    Synoptic situation that contributes to the INT.

  • Fig. 15.

    SOU in Jan (mode 2), Feb (mode 2), Mar (mode 4), Apr (mode 1), May (mode 1), Jun (mode 1), Sep (mode 5), Oct (mode 1), Nov (mode 2), and Dec (mode 2).

  • Fig. 16.

    Synoptic situation that contributes to the SOU.

  • Fig. 17.

    POR in Apr (mode 5), May (mode 6), Jun (mode 5), Jul (mode 4), Aug (mode 7), Sep (mode 7), and Oct (mode 6).

  • Fig. 18.

    Synoptic situation that contributes to the POR.

  • Fig. 19.

    CAT in Jan (mode 3), Feb (mode 5), Mar (mode 2), Apr (mode 4), May (mode 4), Sep (mode 4), Oct (mode 7), Nov (mode 3), and Dec (mode 3).

  • Fig. 20.

    Synoptic situation that contributes to the CAT.

  • Fig. 21.

    LEV in Jan (mode 5), Feb (mode 3), Mar (mode 3), Apr (mode 3), May (mode 3), Jun (mode 2), Sep (mode 3), Oct (mode 4), Nov (mode 5), and Dec (mode 5).

  • Fig. 22.

    Synoptic situation that contributes to the LEV pattern.

  • Fig. 23.

    CAN in Jan (mode 4), Feb (mode 4), Mar (mode 5), Apr (mode 6), May (mode 5), Jun (mode 3), Jul (mode 5), Aug (mode 3), Sep (mode 6), Oct (mode 5), Nov (mode 4), and Dec (mode 4).

  • Fig. 24.

    Synoptic situation that contributes to the CAN.

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