CLASSIFICATION OF DAILY RAINFALL PATTERNS IN A MEDITERRANEAN AREA WITH EXTREME INTENSITY LEVELS: THE VALENCIA REGION

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1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 22: (2002) Published online in Wiley InterScience ( DOI: /joc.747 CLASSIFICATION OF DAILY RAINFALL PATTERNS IN A MEDITERRANEAN AREA WITH EXTREME INTENSITY LEVELS: THE VALENCIA REGION D. PEÑARROCHA, M. J. ESTRELA* and M. MILLÁN Fundación CEAM, Parque Tecnológico, C/ Charles Darwin 14, Paterna (Valencia), Spain Received 26 January 2001 Revised 19 October 2001 Accepted 28 October 2001 ABSTRACT The objective of this paper is to identify the spatial distribution patterns of heavy rainfall in the Valencia region, Spain. Rainfall in this area reaches one of the highest intensity levels in the Mediterranean, with daily precipitation values above 800 mm. Although high intensities characterize the region s precipitation, there is a zone situated in the south of the Gulf of Valencia that registers exceptionally high daily precipitation intensities. Our spatial analysis is based on two different perspectives and methods. In the first, we studied the most important torrential rain events in the period and obtained a classification based on the geographical distribution of the daily precipitation maxima. In the second, we applied statistical techniques to classify the distribution patterns of torrential rain by using principal components analysis and cluster analysis. This analysis was conducted for the period. The results of both methodologies are similar and reflect the main characteristics and sub-types of the spatial distribution of the daily precipitation patterns. These spatial patterns are directly linked to the action of topographic factors in atmospheric situations of humid easterly flows. Copyright 2002 Royal Meteorological Society. KEY WORDS: western Mediterranean; Spain; heavy precipitation; spatial distribution patterns; principal components analysis; cluster analysis; daily precipitation 1. INTRODUCTION The Valencia region, located in the east of the Iberian Peninsula (Figure 1), is similar to many other Mediterranean areas in its highly variable and irregular rainfall regime. The annual rainfall distribution consists of a very dry period in summer and a wet season in autumn and winter. Precipitation can vary substantially from year to year; periods of severe drought can be followed by torrential rain episodes that, in only 24 h, can yield precipitation amounts that exceed average annual rainfall. The spatial distribution of the average annual rainfall in this region is also very complex. Within a relatively small area, average precipitation values vary between 250 mm in the arid zones of the south and 880 mm in the relatively wet zones of the north and in the areas surrounding the Gulf of Valencia. (Peñarrocha, 1994). This distribution is directly related to the mountainous and partitioned orography of the region. Torrential rainfall is one of the most interesting climatic features of the Valencia region, since it represents one of the main potential causes of natural hazards in the area. The economic losses and damage caused by this phenomenon are extensive and frequent, and they are mostly due to floods in the alluvial plains of the principal rivers of the region the Turia, the Júcar and the Segura and to flash-flooding in usually dry watercourses, typical of a Mediterranean semi-arid climate. Precipitation in the Valencia region tends to be concentrated in a relatively low number of days, with a large share of the total precipitation generated in a few rainfall episodes. The characteristics of the atmospheric * Correspondence to: M. J. Estrela, Fundación CEAM, Parque Tecnológico, C/Charles Darwin 14, Paterna (Valencia), Spain; Estrela@ceam.es Deceased February Copyright 2002 Royal Meteorological Society

2 678 D. PEÑARROCHA, M. J. ESTRELA AND M. MILLÁN Figure 1. Location of the Valencia region in Europe; orography conditions that give rise to torrential precipitation in the region have been studied from several different perspectives. The crucial factor is the presence of easterly flows accompanied by upper troughs or depressions. Armengot (1994, 2000), Estrela et al. (2000), and Peñarrocha et al. (1999) describe the synoptic situations that produce torrential precipitation in the area. Doswell et al. (1998), from a meteorological perspective, stress dynamical factors and diagnostic methodologies that could be useful in predicting torrential rainfall.

3 HEAVY PRECIPITATION PATTERNS IN VALENCIA 679 Also interesting are the studies of Romero et al. (1998) on the mesoscale environment, Riosalido et al. (1998) on convective systems in the western Mediterranean, and Ramis et al. (1995) on simulation of torrential rain episodes in Catalonia. The important role of sea-surface temperature is analysed in Millán et al. (1995) and Pastor et al. (2000), and the latter also present the first numerical simulations of torrential events in the Valencia region. The objective of the present work is to identify the spatial distribution patterns of torrential rainfall in the Valencia region. The analysis is based on two different perspectives and methods. In the first, we studied the most important torrential rain events and obtained a classification based on the distribution of the daily precipitation maxima. In the second, we applied statistical techniques to classify the torrential rainfall distribution patterns by using principal components analysis (PCA) and cluster analysis (CA). The results section of this paper offers a comparative analysis of the classifications obtained with both methods. 2. PRECIPITATION DATA The precipitation data used in this work are from the network of meteorological observatories operated by the Instituto Nacional de Meteorología (INM). The database includes daily records (7 AM 7 AM) from 497 observatories in the Valencia region and bordering areas for the period The classification based on daily precipitation maxima used the period. Data were not available at all observatories over this time period; it is common for observatories to stop working temporarily or permanently, and new observatories are put into operation. An average of 250 stations are available for the daily precipitation study. The data coverage was sufficiently dense and considered to be ample enough to study the spatial distribution at the regional scale. Only one area in the north was insufficiently covered, since the station network in this zone is less dense than in the rest of the region. A shorter time period ( ) was used for the PCA and cluster analysis. A rigorous spatial analysis requires the use of complete series of daily data within a delimited period. We did not consider it appropriate to make any kind of extrapolation from the daily precipitation values for the purpose of completing data series gaps. Given this, we aimed to find a sufficient number of available observation points scattered throughout the whole study area and to base our spatial analysis on a period of time that was climatologically significant in terms of torrential rainfall events. A period of 10 years was considered enough for this purpose. Although a longer period would be more adequate, the availability of complete data has limited the length of the study period. Analysis of the chronological series of available daily data showed the most suitable period to be , because it offered the greatest number of observatories with complete data series (a total of 83), attaining a data set absolutely free of missing values. The spatial coverage was deemed sufficient to determine the main distribution patterns in the area under study. 3. SPATIAL DISTRIBUTION OF TORRENTIAL RAINFALL EVENTS: A CLIMATOLOGICAL AND GEOGRAPHICAL APPROACH Figure 2 shows a map of daily absolute maximum values. It includes data from the observatories that offered complete data series of 10 years or more within the study period ( ). A maximum value of 222 mm was reached in the north, whereas a local maximum of 316 mm was registered in the south. The wet central nucleus includes several zones above 300 mm, with local maxima of 790 and 817 mm. This latter area shows extraordinary intensity levels; it is, in fact, one of the main focuses of extreme precipitation events in the western Mediterranean. A review of the literature on intense precipitation events in the western Mediterranean found daily registers above 800 mm only in the area of Liguria (Guigo, 1973, cited in Pérez Cueva and Armengot (1983)), where more than 900 mm was recorded in Bolzaneta, near Genoa, and in southern France, with 840 mm recorded in La Llau, in the eastern Pyrenees (Jacq, 1994). In the Valencia region, 817 mm was recorded on 3 November 1987 in Oliva, on the southern coast of the Gulf of Valencia. But this is not an isolated case: 878 mm was registered nearby, in Javea, on 2 October Within the period, there were 19 instances where daily totals exceeded 350 mm and 57 above 250 mm.

4 680 D. PEÑARROCHA, M. J. ESTRELA AND M. MILLÁN Figure 2. Map of absolute daily maximum precipitation values From the above, it can be seen that the spatial distribution of heavy rainfall is not homogeneous throughout the region and that the most important feature is the existence of an area of exceptionally high rainfall intensities on the southern shore of the Gulf of Valencia. This area shows the highest 24 h intensity of the whole Iberian Peninsula (Elias Castillo and Ruiz Beltrán, 1979), with daily maximum precipitation totals exceeding 300 mm having a return period of 30 years. The northern and southern extremities of the region are also areas with relatively high values: a daily total of 175 mm has a return period of 30 years. For the period, Martín Vide (1994) presents a more in-depth study on the distribution of the daily maximum precipitation occurrences.

5 HEAVY PRECIPITATION PATTERNS IN VALENCIA 681 In all three areas, enhancement of rainfall totals can be attributed to topographic factors, such as orographic convergence and ascent, and optimal exposure to wet easterly fluxes (Figure 1), conditioned by: (1) the eastern extreme of the Pre-Betico system; (2) the region s northern mountains with a SSW to NNE alignment; and (3) the eastern extreme of the Betico system, the Carrascoy Sierra Spatial distribution classification of the daily precipitation maxima We analysed all of the severe rainfall episodes registered during the period, using 125 mm/day as the intensity threshold. After scrutinizing all the daily data series from the meteorological observatories in the Valencia region and bordering areas (497 observatories), we obtained 899 registers above the threshold, grouped into 168 days. As a second step, we selected events in which the 125 mm threshold had been exceeded at six or more observatories (i.e. in more than 2% of all those operational) during the same 24 h period. The purpose of this was to discard excessively local precipitation episodes and be able to base our spatial pattern classification on the most important torrential rainfall events. Within the period, 26 precipitation events fulfilled the above-mentioned selection criteria (Table I). Those events were concentrated in the autumn months (19), although some occurred in winter (four) and in spring (three). Table I. Heavy rainfall events Event Rainfall distribution Daily maximum pattern a (date) (mm) 4 9 October 1971 a.1 (6 X) November 1972 a.1 (28 XI) March 1973 a.1 (22 III) December 1973 a.1 (29 XII) December 1975 a.2 (5 XII) October 1977 a.2 (25 X) January 1980 a.2 (13 I) October 1982 a.2 (20 X) November 1983 a.1 (6 XI) November 1984 a.2 (10 XI) February 1985 c (21 II) September 1985 b (26 IX) October 1985 a.1 (28 X) November 1985 a.1 (15 XI) September 6 October 1986 a.1 (29 IX) November 1986 a.1 (17 XI) November 1987 a.2 (4 XI) September 2 October 1988 a.1 (30 IX) November 1988 b (11 XI) March 1989 a.1 (18 III) September 1989 c (4 IX) October 1991 a.1 (4 X) April 5 May 1992 a.1 (3 V) January 8 February 1993 a.2 (1 II) October 1993 a.1 (26 X) October 1994 b (10 X) a a.1. Coastal focuses in the Gulf of Valencia. a.2. Large focuses in the Gulf of Valencia. b. Focuses in the northern half of the region. c. Focuses in the southern area of the region.

6 682 D. PEÑARROCHA, M. J. ESTRELA AND M. MILLÁN The maps of the severe rainfall episodes (Figures 3 7) showed different distribution patterns that were related to the same topographical factors pointed out in the analysis of the spatial distribution of the 24 h absolute maximum values. Storms tend to concentrate their maxima in certain areas and show particular morphologies. Thus, in spite of the spatial irregularity of the daily rainfall distribution, several patterns could be defined. Figure 3. Daily precipitation. Maxima centred in the littoral of the southern part of the Gulf of Valencia

7 HEAVY PRECIPITATION PATTERNS IN VALENCIA 683 Figure 4. Daily precipitation. Maxima centred in the littoral of the southern part of the Gulf of Valencia Generally, there is a well marked 24 h maximum that stands out clearly from the precipitation of the rest of the event. This is due to the fact that a great percentage of the precipitation is usually concentrated in the space of a few hours. Besides this temporal concentration, there is also a marked feature of spatial concentration. Heavy rainfall tends to present a focus shaped pattern, as a result of the formation of convective systems bearing intense rainfall, and their interaction with topographic factors. We have used a classification method

8 684 D. PEÑARROCHA, M. J. ESTRELA AND M. MILLÁN Figure 5. Daily precipitation. Large focuses in the southern part of the Gulf of Valencia based on the geographical location of the 24 h maximum precipitation focus for each event. Based on this information, we determined three types or patterns of torrential-rain distribution in the Valencia region: (a) precipitation maxima centred in the Gulf of Valencia (a.1) coastal focuses (Figures 3 and 4) (a.2) large focuses (Figure 5);

9 HEAVY PRECIPITATION PATTERNS IN VALENCIA 685 Figure 6. Daily precipitation. Maxima centred in the northern area (b) precipitation maxima centred in the northern half of the region (Figure 6); (c) precipitation maxima centred in the southern area of the region (Figure 7). The cartographic distribution of daily precipitation was achieved by constructing grids of 54 columns and 100 rows. The precipitation values of each point on the grid are inversely proportional to the square

10 686 D. PEÑARROCHA, M. J. ESTRELA AND M. MILLÁN Figure 7. Daily precipitation. Maxima centred in the south of the region of the distance between the point and the set of precipitation data observed. This type of interpolation method preserves the magnitudes of the centres of highest rainfall intensities observed (although with a slight moderation) and does not alter their exact location. These two facets were of top priority when representing the marked spatial variation in the daily precipitation values and their tendency to be concentrated in spatially restricted areas. In some cases, nevertheless, in areas with insufficient station density, the cartography showed

11 HEAVY PRECIPITATION PATTERNS IN VALENCIA 687 an excessive representation of small negative or positive focuses around the observation points. This is the bull s-eye effect (Surfer 7, 1999), which is typical of this method of interpolation, and is sometimes too evident (Figures 6(b) and 7(c)) and causes an unsatisfactory representation of the precipitation field. On the other hand, in areas with many observation points, the above interpolation method was ideal for the representation of the focuses of highest rainfall intensities. The solution to this problem could be to decrease the grid density, but this would result in a loss of data resolution in cases of good observation point density. Alternatively, other interpolation methods could be used, such as increasing the power of the distance in the calculation function of the grid values, but then there would be a tendency to represent maximum focuses with too large surfaces. Thus, although we recognize this as a debatable point, these latter considerations convinced us to retain our original methodology. The cartography of daily precipitation (Figures 3 7) presented attains a good representation of the maximum precipitation focuses and of the general distribution of the precipitation field. A totally realistic representation of the daily precipitation could only be possible with a very dense observation network, which is practically impossible from an operational point of view. The heavy rain distribution patterns which we determined here by means of direct cartographic analysis (a more subjective classification) agree with the types established by means of statistical classification criteria (cluster method) both in this paper and in the study by Romero et al. (1999a), whose methodology we followed Precipitation maxima centred in the southern part of the Gulf of Valencia. This is the distribution pattern that occurred most frequently and was associated with the highest precipitation totals. Of the 26 events, 21 were of this type. Two sub-types could be differentiated within the distribution. The first type, which was more frequent (14 events), had higher rainfall totals near the coast. The second showed more extensive heavy precipitation focuses and affected more interior areas of the Gulf of Valencia; in spite of being less frequent (seven events), it was associated with the torrential rain episodes that produced the 24 h absolute precipitation maxima. These latter registers were the highest recorded in the Iberian Peninsula and among the most extreme in the Mediterranean. The orography in this area is extremely well exposed to humid easterly flows due to the confluence of mountain chains in the littoral and pre-littoral zones (Pre-Betico mountains with a WSW ENE direction and the southeast extreme of the Iberian System with an SSE NNW direction). The shape of the fluvial valleys reinforces the confluence and ascent of humid air, associated with convection and precipitation Intense rainfall centred in the coastal area: Intense precipitation events along the coast tend to be centred in the same area, i.e. in the eastern extreme of the Pre-Betico mountains. Ten of the events showed this pattern (Figure 3(a) (c)). The maxima for the four remaining cases were found slightly to the north but were also associated with mountain systems very near the coast or in the narrow littoral plains windward of the humid easterly flows (Figure 4(b) and (c)). Figure 4(b) shows the coexistence of two heavy rain focuses: the more important one corresponds to this type, whereas the other is situated in the far north of the region. Although not common, the coexistence of several intense precipitation focuses in a 24 h period is possible, as are rain events that are very extensive and relatively unfocused (Figure 7(c)). In that case, orographic reinforcement is due to barrier and convergence effects of the surface flow on the coastal mountain barriers, presenting reduced areas of intense precipitation adapted to a coastal disposition delimited by mountain barriers. The morphology of the short fluvial valleys in the area, with their origins in mountains located near the sea and oriented towards easterly fluxes, triggers or enhances the action of convective systems that cause intense rainfall Intense rainfall in the southern part of the Gulf of Valencia. Large focuses: These focuses are very similar to the sub-type described in Section The principal distinctive feature is that the precipitation focuses are more extensive, they are associated with the most important events, and they affect zones situated further inland. Among the cases studied, the 24 h absolute maximum of 817 mm was registered during the storm of November 1987 (Figure 5(c)). For this event the totals for two precipitation days were mapped, since the storm maximum was reached during the night of 3 4 November, with the result that the total was

12 688 D. PEÑARROCHA, M. J. ESTRELA AND M. MILLÁN divided between those two days. The maximum values mapped were 860 mm ( mm) and 830 mm ( mm). The October 1982 storm was also catastrophic (Figure 5(b)); it caused the Tous Dam to rupture. The daily maximum registered for this event was 632 mm. In this case, there is a clear orographic factor due to the confluence of the humid flow channelled by river valleys and larger topographical obstacles leeward of the first mountain barrier. Furthermore, these are situations that produce overflows in the main rivers of this area (the Júcar River and its tributaries, the Magro and the Albaida) generating important floods in the alluvial plain of Jucar River, a densely populated zone. Logically, some cases appeared which were considered to be transitional between the two distribution pattern sub-types centred in the south of the Gulf of Valencia (Figure 4(a)) Precipitation maxima centred in the northern area. This is an area affected by torrential precipitation events, though they are less frequent and intense than those in the southern part of the Gulf of Valencia, and the absolute maximum values of the precipitation are lower. This type of spatial distribution is determined by the interaction of easterly fluxes with orographic factors (Iberian System with SSW NNE direction). Various sub-types could also be distinguished in this distribution pattern, though less clearly than in the previous area since the total number of cases was smaller. Moreover, the observatory coverage is not good in the northern part of the region. For this reason, it is quite probable that in some cases both the frequencies and the absolute maximum values were underestimated. One type showed maximum values at the northern end of the region (Figure 6(a)). Other types included events with maximum values located in fluvial valleys oriented SE NW (Figure 6(b)), as well as episodes on the narrow coastal plain close to Castellón (Figure 6(c)) Precipitation maxima centred in the southern area. Maximum rainfall values were also obtained in the extreme south of the Valencia region. This is an area characterized by severe arid conditions and low average annual precipitation (below 300 mm in the driest zones). Nonetheless, it is affected by important torrential rain events, although they occur less frequently than the other two torrential zones in the region. Daily precipitation values exceeding 200 mm have been recorded here. Only two of the events in our study had their daily maximum centred in this area. These two cases (Figures 7(b) and 7(c)) wererelated to the local orographic conditions (the eastern extremity of the Betico mountain chain, with an SSW NNE orientation). The third case presented (Figure 7(a)), located slightly to the north, was an example of torrential rains enhanced by the mountains near the city of Alicante. It can be considered a sub-type distribution pattern of the events centred in the south of the Valencia region, which occasionally cause serious damage to that provincial capital. The figures show that the maxima centred in the south of the region always occur when there is intense precipitation in the south of the Gulf of Valencia, at least within the 25 year period analysed. This is because both distribution patterns are produced under the same type of atmospheric situation and synoptic conditions. Nevertheless, with a relatively low frequency, during these events convective systems develop in this southern area, producing extreme precipitation too. The occasional yield of great amounts of rainfall in this area is a result of mesoscale factors (advection and convergence of humidity), probably related to sea-surface temperature distribution, a key factor in the transference of energy and water to trigger the processes of deep convection and heavy rainfall Classification of the spatial distribution of torrential rain by means of PCA and CA After obtaining a wide selection of cases of heavy rainfall and establishing a descriptive classification based on the localization and morphology of the focuses of intense rainfall, we have applied an objective methodology of spatial analysis to the same data in order to test these techniques and verify the level of agreement between the patterns determined by both methodologies. PCA techniques are a useful data analysis tool because they are designed to achieve a reduction of data and its dimensionality, retaining their fundamental modes of variance. In contrast, with other multivariate statistical techniques, designed to explain the variation in a set of dependent variables, the entire data set is considered simultaneously with each variable relating to every other variable. PCA is designed so that

13 HEAVY PRECIPITATION PATTERNS IN VALENCIA 689 the synthetic variables produced maximize the explanation of the variation in the entire data set and are selected in such a way as to measure spread along a latent direction in the attribute data space (Griffith and Amrhein, 1997: ). In this way, it is possible to obtain a simplified description of the data variation, representing it as a reduced number of linear orthogonal combinations. The mathematical theory of PCA and factor analysis can be consulted in detail in Griffith and Amrhein (1997) and Hair et al. (1995). PCA has been widely used in climatology, meteorology and other scientific fields that use large data sets. Of a total of six PCA modes, two are most commonly applied in climatological data analysis, depending upon which parameters are used as variables in the construction of the correlation matrix subjected to analysis (cross-product or covariance matrices can be used too). In the S-mode analysis (spatial), locations, characterized by their temporal series, are the elements to be correlated in the matrix. Alternatively, in a T-mode analysis (temporal), a series of temporal elements is correlated, each element being characterized by a group of observed values; frequently, as in our study, these values are spatially referenced. Each principal component has a score for each place and represents an orthogonal pattern in the spatial domain (Molteni et al., 1983). Molteni et al. (1983), Pandzic (1988), and Mallants and Feyen (1990) are examples of the large body of precipitation spatial analyses that use principal components methodology. In those studies, though the power of this method as a data reductor is evident, its difficulty and its deficiencies as an interpretational tool can be detected. Although rotation of principal components reduces these deficiencies, this kind of method gives results that, from the spatial point of view, scarcely reflect real distribution patterns and which are too influenced by the orthogonality of the linear combinations inherent in this mathematical method. It is evident that not only spatial, but also temporal and other climatic and meteorological patterns, rarely correspond to orthogonal models. Attempts have been made to solve this problem by oblique rotation techniques. Richman (1981), in his study about meteorological maps typing, noticed that unrotated components did not represent the input data patterns, but oblique rotation of components achieved the best depiction of the meteorological maps. The application of CA to the components loadings, however, has been used to avoid the orthogonal constraint and improve the interpretational problems of the patterns depicted by the principal components scores. This method, as a first step, uses the ability of PCA to obtain a simplified analysis of the data variance, and then, in a second step, groups data in clusters with similar components loadings. This technique has not only been used in spatial analyses: Stone (1989) applied these methods to the study of weather types; Green et al. (1993) used this method to determine seasonal periods; and Romero et al. (1999b) used them to study the types of atmospheric circulation that produce precipitation in the Spanish Mediterranean area. Spatial studies that employ PCA and CA methods to examine precipitation in Spanish Mediterranean regions are those of Sumner and Guijarro (1993) and Romero et al. (1999c). In our spatial analysis of torrential rainfall in the Valencia region, we apply the methodology developed by Sumner et al. (1995) and Romero et al. (1999a) for their spatial analyses of the daily precipitation in Mallorca and in the Spanish Mediterranean regions respectively. Daily data series from 83 observatories for the period have been used in this objective classification of spatial patterns of daily intense rainfall in the Valencia region. Precipitation was considered to be torrential when one or more stations registered 50 mm or more during a 24 h period. Using this criterion, we obtained 223 days with torrential precipitation. Tests using a threshold of 125 mm were done, in an attempt to use the same selection criterion used in the daily maximum cartographic classification (Section 3.1). Nevertheless, we considered our database at this threshold to be inadequate for the application of a cluster aggregation methodology, since only 35 cases were registered within our 10 year study period. Therefore, using the 223 day database we subjected the T -mode correlation matrix to PCA. This matrix consists of the correlations between the selected days, calculated from the variables set that characterizes them, which in this case are the precipitation values registered at the 83 selected observatories. This calculation and the subsequent CA were made using the STATISTICA computer program (Statistica Utility, 1994). The first 12 principal components (unrotated) were retained for the subsequent CA. They explained 60.2% of the total variation in the data (Table II). The scree diagram in Figure 8 shows a gently sloped curve after this point, with eigenvalues explaining less than 2% of the total variance. So, although this selection has

14 690 D. PEÑARROCHA, M. J. ESTRELA AND M. MILLÁN Table II. Variance accounted for by the first 12 components (see Figure 8) Principal component Eigenvalue Variance explained (%) Cumulative variance (%) Figure 8. Scree plot diagram (see Table II) a subjective component, the rest of the principal components calculated have not been used for the cluster aggregation. These principal components, reflect variations of low frequency or spatial scale that are not important for our purpose. They account for a considerable amount of variance (39.8%). This means that the degree of spatial irregularity is extremely high in a data set extracted with the threshold used. In fact, in the test made with a 125 mm threshold, the first ten principal components explained 78.2% of the variance, but this data set gathered only 35 cases of intense precipitation. We have preferred to use a larger sample (223 cases), retaining the more significant principal components. A CA was undertaken by grouping the days with similar principal component loadings on the 12 components, thus obtaining a division into groups of similar spatial distribution. For the final solution, we selected a division into six clusters using the k-means method. This number of groups is sufficient in order to

15 HEAVY PRECIPITATION PATTERNS IN VALENCIA 691 obtain a good explanation and description of the real spatial patterns of torrential daily rainfall in the Valencia region. The use of a larger number of clusters resulted in sub-types of more detailed spatial distribution, but which were still directly related to the six patterns presented. The precipitation distribution for each cluster shows the average precipitation calculated for the days included in each cluster Torrential rains in the southern part of the Gulf of Valencia. (a) Cluster 1. This cluster groups the cases of maximum precipitation located at the eastern end of the Betico Mountains, over the southern coastal zone of the Gulf of Valencia. It shows exactly the same features as the type determined by means of the previous classification method, characterized by very localized areas of high precipitation (Figure 9(a)). (b) Cluster 2. This distribution is very similar to that of cluster 1, although it shows more extensive precipitation focuses affecting interior zones near the southern side of the Gulf of Valencia. Again, this spatial pattern is identical to a type determined by means of the previous classification method (Figure 9(b)) Torrential rains in the northern half of the Valencia region. (a) Cluster 3. Although the distribution pattern of this cluster affects the northern half of the region, it shows a more littoral character and its maxima are located in a more central position; thus it groups cases that affect the littoral of the Gulf of Valencia although in a more northerly position than those mentioned above as well as cases whose maxima are located in SE NW-oriented valleys situated in the centre and north of the region (Figure 9(c)). (b) Cluster 4. This groups the cases of precipitation displaced to the far north, in an almost marginal position, probably associated with events affecting the neighbouring region of Catalonia and the northern third of the Valencia region (Figure 9(d)). (c) Cluster 5. This groups the precipitation events that affect the northern half of the region in a more widespread way, with the most important rains affecting the mountainous areas oriented NNE SSW (Figure 9(e)) Torrential rains in the interior of the Valencia region. Cluster 6. This is the only distribution type that cannot be directly related to the spatial distribution patterns established in the classification based on daily maxima location. This cluster groups the intense precipitation events in the interior of the region s central sector (Figure 9(f)). 4. RESULTS: COMPARATIVE ANALYSIS OF THE CLASSIFICATIONS The spatial distribution patterns established by the cluster classification confirmed most of the characteristics revealed in the classification based on the localization of the daily precipitation maxima. Both methods subdivide the torrential rains centred in the southern part of the Gulf of Valencia, the area with highest rainfall intensities, into two large spatial distribution groups: one characterized by torrential rain focuses of limited area and a coastal location, and the other showing larger focuses, extending to inland areas. Nevertheless, cluster 3 includes both the focuses on the coast of the Gulf of Valencia (those showing maxima in its most northern sector) and the focuses affecting the central-northern part of the region. In other words, cluster 3 combines transitional cases between two large groups determined by the classification based on daily maxima localization. Unfortunately, the north south distinction used on the cartographic classification is excessively simplistic. This cluster groups together the maximum coastal focuses near the north south latitudinal border and events with maxima focused in the centre north of the region. The classification based on daily maxima localization grouped this latter pattern in the Northern-half category. Another important difference between the classifications obtained via cluster analysis and via daily maxima location is the lack of a spatial pattern characterized by the presence of torrential rain focuses in the south of the region. This is logical, considering that this is a semi-arid zone with a very low frequency of torrential rain, although high precipitation values are occasionally registered. Detailed analysis of the clusters shows that most of the high precipitation focuses in the south are grouped in cluster 2, together with the focuses in

16 692 D. PEÑARROCHA, M. J. ESTRELA AND M. MILLÁN the south of the Gulf of Valencia. The coexistence of both distribution patterns can be more clearly seen in the analysis made for the daily maxima location classification. Lastly, the cluster 6 spatial pattern does not appear in the classification via daily maxima location due to the fact that the cluster classification uses a lower selection threshold for determining days of torrential rain Figure 9. Precipitation maps: (a) Clusters 1; (b) Clusters 2; (c) Clusters 3; (d) Clusters 4; (e) Clusters 5; (f) Clusters 6

17 HEAVY PRECIPITATION PATTERNS IN VALENCIA 693 Figure 9. (Continued) (50 mm). In this way, days with very different atmospheric circulation characteristics enter into the analysis. In the classification according to daily maxima, the major rainstorms are always seen to be produced under one general type of atmospheric circulation: humid easterly flows. Within the set of days classified by cluster methodology, one can detect other types of atmospheric circulation with very different spatial precipitation

18 694 D. PEÑARROCHA, M. J. ESTRELA AND M. MILLÁN patterns: convective storms during the warm months and, less frequently, Atlantic frontal systems driven by westerly flows that occasionally produce precipitation above the 50 mm threshold. These kinds of atmospheric situation frequently show distribution patterns similar to that of cluster CONCLUSIONS The primary objective of this work was to determine the spatial distribution patterns of torrential rainfall in the Valencia region. Nevertheless, given that many methods of analysis are available and that some are more subjective than others, a secondary objective of this work was to use various methods and compare the results to see if important differences could be detected. Thus, we obtained classifications by using the mapped distribution of daily maxima during torrential precipitation events as well as by using PCA and CA. Several conclusions can be made. (a) The first is that both methods agree that three types of distribution pattern of torrential rainfall exist in the Valencia region. (b) The area under study (Valencia region) showed extraordinarily high intensity levels; it is, in fact, one of the areas of extreme daily rainfall in the Mediterranean. In the study period, daily precipitation values above 800 mm were reached. To our knowledge, only some locations in northern Italy as well as the eastern Pyrenees showed similar totals. The maximum recorded was 817 mm in Oliva (3 November 1987). Furthermore, this was not an isolated case: 878 mm was recorded in Javea on 2 October During the period there were 19 occurrences above 350 mm, and 57 registers above 250 mm. (c) Inside the study area, a zone situated in the south of the Gulf of Valencia registered exceptionally high daily precipitation totals. (d) Three daily precipitation distribution types or patterns were determined on the basis of a daily maxima precipitation classification: (a) precipitation maxima centred in the south of the Gulf of Valencia (a.1) coastal focuses (a.2) large focuses; (b) precipitation maxima centred on the northern half of the region; (c) Precipitation maxima centred in the south of the region. (e) Not only did the above areas show the highest rainfall totals, but they were also the areas where intense precipitation was most frequently centred. This is due to topographical factors, such as optimum exposure to humid easterly flows and orographic ascent: the extreme eastern part of the Pre-Betico system; mountain chains in the north of the Valencia Region with an SSW NNE orientation; the extreme eastern part of the Betico, the Carrascoy Sierra. (f) The cluster classification for the spatial distribution of daily intense precipitation in the Valencia region showed analogous results, but with some differences. The precipitation focuses centred in the extreme south of the region were not clearly differentiated because of their low frequency; as a result, they became hidden within the clusters corresponding to torrential rains centred in the coastal area of the south of the Gulf of Valence. The coexistence of both distribution patterns is real and can be clearly seen in the analysis of the most important torrential rain events that occurred during the period. Owing to the use of a lower torrential rain threshold (50 mm), a new spatial pattern appeared over the region s interior. In most cases, this pattern was related to precipitation caused by convective storms or humid westerly flows of Atlantic origin. (g) The spatial analysis methodology involving a T-mode PCA followed by a CA of the days with similar principal component loadings proved to be valuable in the detection of real spatial distribution patterns of precipitation, even in small spatial areas of complex orography.

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