Rainfall uncertainty in the Mediterranean: Intraseasonal rainfall distribution

Abstract

The rainfall distribution within the rainy season has crucial implications on a variety of disciplines. According to one approach of analyzing the intraseasonal rainfall distribution, it is essential to examine the date of different accumulated percentage (DAP hereafter), as presented in Paz and Kutiel (Isr J Earth Sci 52:47–63, 2003). The present study identifies various intraseasonal temporal distributions of rainfall, in 41 stations within the Mediterranean basin. Furthermore, classifications of these distributions according to their time, yield, and length are presented. The accumulated percentage was calculated for each Julian day for every available year in all stations. A correlation matrix between every possible pair of years, in each station, was calculated, and a cluster analysis (average linkage method) was performed. Finally, the averages of the entire dataset and the average of every cluster were compared in order to classify the clusters by using three parameters: timing represented by DAP_{(25%, 50%, 75%)} annual rainfall total and the rainy season length (RSL). Between 2 and 5 different types of clusters, with various probabilities, were defined for every station. Out of 132 overall clusters, which were found in 41 stations, the most frequent type (cluster 1) was the median in all three parameters. There were 16 clusters identified as short in their RSL, and 18 were identified as having a long classification. There were 19 dry clusters, and only eight were identified as wet. As for the parameter of timing, 39 clusters were classified as early and 38 as late. One conclusion of this study was that the probability of a dry year is higher than a wet one, and likewise, the probability of a long year is higher than of a short one.

1 Introduction

The rainfall distribution within the year is one of the basic characteristics of the rainfall regime in a certain location. It has crucial implications on a variety of disciplines, regardless of the rainfall total (TOTAL hereafter). The temporal rainfall accumulation varies from year to year. Therefore, the same exact TOTAL in two different years, but with different temporal distributions, will have a different effect on the hydrological budget of the area. For example, if in a station, characterized by a Mediterranean climate, the same TOTAL in 1 year fell in December–January–February and in another in February–March–April with exactly the same daily distribution, the impacts on a variety of systems, such as water resources, ecosystems, regional agriculture management, and economic and social development, may be completely different due to the different PET rates, antecedent soil moisture, etc. in the different months.

Studies of rainfall variability have tended to focus on inter-annual time scales, while the intraseasonal scale has been relatively unexplored. Most of the researchers try to find consistency patterns in order to improve the predictabilities or to identify changes in climate (e.g., Maheras 1988; García-Oliva et al. 1991; Türkeş 1996; Romero et al. 1998; Rodriguez-Puebla et al. 1998; Lázaro et al. 2001; Rodrigo 2002; Tomozeiu et al. 2002; Norrant and Douguédroit 2005).

Everywhere in the world a few months tend to be wetter than others, even in regions where there are no defined wet or dry seasons, and rainfall is rather evenly distributed throughout the year, as in northwestern Europe, for example (Logue 1984), all the more so in a Mediterranean climate, where the wet and dry seasons are very distinguishable. Ramos (2001) characterized the Mediterranean climate as a complex pattern of seasonal variability, with large and unpredictable rainfall fluctuations from 1 year to the other. The variation in the mean annual rainfall did not follow a consistent trend in northeastern Spain, where dry, normal, and wet years have not been regularly distributed over time. However, during the most recent decades, less annual variability (from 1 year to the other) has been observed. The number of years with normal rainfall TOTAL has increased, but rainfall has been more irregularly distributed throughout the year.

According to one approach of analyzing the intraseasonal rainfall distribution, it is essential to examine the date of different accumulated percentage (DAP hereafter), as presented in Paz and Kutiel (2003). These are dates in which any percentile of the TOTAL was accumulated. For instance, DAP_(25%) is the date when the first quartile of the annual rainfall was accumulated. Similarly, the DAP_(50%) is the mid-season date or the date in which half of the annual rainfall was accumulated and so on.

On a given date in a certain year, for example, 75% of the TOTAL could accumulate, while in another year, only less than 25% of the TOTAL was accumulated at that date. In this example, the first year represents an early rainy season, whereas the second represents a late one. Furthermore, the same accumulated percentage (AP) may be reached at a variety of dates, spreading over several months (Paz and Kutiel 2003). Thus, the rainy season can be characterized according to these dates; for example, seasons are characterized according to abundant early season, abundant late season, and so on.

The purposes of the present study are:

• 1. To identify various intraseasonal temporal distributions of rainfall in different stations within the Mediterranean basin.

• 2. To characterize each temporal distribution in every station, identified in 1, their yield, and length.

2 Study area and data

The study area is located in the Mediterranean basin, between longitudes 10° W and 40° E and latitudes 30° and 46°N, excluding the North African coasts (Fig. 1). Forty-one rain stations were selected to represent the various rainfall regimes within the study area, not all having a typical Mediterranean climate.

Fig. 1

The location of rain stations and the study area

Daily rainfall data within the period of 1931 and 2006 were obtained from the European Climate Assessment & Dataset. A dataset of at least 36 years was used for each station (Table 1). The selection of stations was based on the availability of the entire datasets without missing data (with very few exceptions, see Table 1), and therefore, no further process of completing data was necessary. Data was tested for homogeneity and was proven to be homogenous.

Table 1 Main characteristics of rain stations

3 Methodology

The data were analyzed by a specially designed statistical model, entitled rainfall uncertainty evaluation model (RUEM). The RUEM was developed by the authors at the Laboratory of Climatology in the Department of Geography and Environmental Studies, University of Haifa. Description and more details can be found in the following website: http://geo.haifa.ac.il/~geoweb/RUEM%204.pdf.

Figure 2 presents a schematic flow chart illustrating the various steps in the process of rainfall data analysis:

• 1. Starting analysis date (SAD) determines the date on which the analyses start in each station as defined and detailed by Reiser and Kutiel (2008) and listed in Table 1.

• 2. The daily rainfall threshold (DRT) in each station was determined to exclude the lowest rain days that contribute altogether 4% of the annual rainfall. Table 1 presents the DRT (mm) for each station as suggested by Reiser and Kutiel (2009a).

• 3. The determination of the rainy season beginning and ending dates filters out sporadic rain events at the beginning and/or the end of the rainy season, regardless of their amount. These parameters were calculated separately for each year according to the distribution of the AP and in turn determined the rainy season length (RSL; Reiser and Kutiel 2009a).

Fig. 2

A schematic flow chart representing the various steps needed for the analysis of the rainfall regime

These steps have already been done and reported in details in the two abovementioned studies.

The methodology used in the present study is demonstrated on data from the station of Madrid as an example. The selection of Madrid does not imply anything regarding its representation of the Mediterranean climate.

3.1 Cluster analysis

The APs were calculated for each Julian day, thus creating an annual course for every available year in all stations. A matrix was established, in which each column represents an annual course in a different year and each row a different Julian day. A correlation matrix between every possible pair of years in each station was calculated, and a CA (average linkage method) was performed. This methodology has been used previously mainly for clustering stations with similar characteristics into coherent regions (e.g. Tennant and Hewitson 2002). In the present study, however, it is used for merging different annual course in each station into groups of years according to similarities in their temporal course of AP.

The distance from one step to the following in the CA were calculated and averaged. The distance indicates the coherence within the grouped years in each cluster and the inconsistency between one cluster and the others. Years with very similar annual courses, and hence highly correlated, were clustered first at a very short distance (the vertical axis in Fig. 3a). As the differences between years or clusters increased, they were clustered at longer distances. The distance sums the squared differences of each of the variables in question, also known as the squared Euclidian distance. All distances are standardized, i.e., transformed to variables with mean = 0 and variance = 1. Once the distance between one step and the next one was higher than twice the average distance, the process was stopped and the obtained clusters were retained.

Fig. 3

The clustering dendrogram (case number 1 = 1948, 2 = 1949 and so on) (a) and the distribution of the difference between one step to another (b) in Madrid

The dendrogram in Fig. 3a illustrates an example of the clustering process in Madrid. One can see that the first clustering steps occurred at short distances. The differences between one step and the next tended to increase as the process advanced. As long as the difference between one step and the following is short, it means that adding years to a cluster, or joining clusters, do not reduce considerably the coherence. When this difference is large, it means that the added years/clusters reduced considerably this coherence. The aim is to stop the clustering process at the shortest distance in order to ensure the highest coherence on the one hand and detect the main clusters in order to characterize the main temporal rainfall distributions patterns on the other hand.

The straight horizontal line in Fig. 3b represents twice the average difference (10.04). Step 49 occurred at a difference of 25.22 from step 48, and therefore, the process was stopped at step 48. At this step cluster 2 was created by the union of a cluster containing 7 years (1954, 1985, 1981, etc.) and a cluster build up of 5 years (1958, 1995, 1962, etc., see Fig. 3a). This step occurred at a total distance of 49.2, and the analysis retained five clusters.

At this stopping step, 52 years out of 56 (92.9%) were grouped into five different clusters: cluster 1 grouped 25 years (44.6%), cluster 2 grouped 12 years (21.4%), cluster 3 grouped 6 years (10.7%) and clusters 4 and 5 grouped 5 and 4 years (8.9% and 7.1%, respectively). The remaining 4 years (1970, 1972, 1974, and 1980; 7.1%) were not clustered at this step.

To complete the analysis process, two conditions were set:

• 1. A cluster was defined only when it comprised of at least 2 years and not less than 5% of all years.

• 2. For each station, a minimum of two clusters and no more than five clusters were retained. This condition was made in order to assure that there would be enough information to characterize the variety of the temporal distributions of the AP in each station on the one hand. On the other hand, it was meant not to present too many clusters with very small differences between them and that were hardly identifiable one from the other.

The clusters are numbered according to their probabilities. The probability of a cluster is defined as the number of years included in that cluster divided by the total number of analyzed years. Cluster 1 was defined to be the cluster, which grouped the largest number of years, while cluster 5 the smallest number.

The clusters were obtained only on the basis of the annual distribution of the AP. Their characterization was defined on the basis of three parameters: their accumulation rate represented by DAPs (25%, 50%, and 75%), their TOTAL, and RSL.

3.2 Characterization of the cluster

3.2.1 Characterization according to the DAPs

The average timing of DAP_(25%), DAP_(50%), and DAP_(75%) of the entire dataset and their standard deviations were calculated. Correspondingly, the average annual AP courses of the years in each cluster were calculated.

A cluster was characterized as late when at least two out of the three of the above DAPs occurred at a certain date, which was at least 0.5σ later than the average date of the relevant DAP.

Similarly, a cluster was characterized as early when at least two out of the three of the above DAPs occurred at a certain date, which was at least 0.5σ earlier than the average date of the relevant DAP.

A cluster was characterized as median in two cases:

• 1. When at least two out of the three above DAPs occurred within the average date ± 0.5σ of the entire dataset

• 2. When each DAP was classified differently in each of the three percentiles (e.g. DAP_(25%) = early, DAP_(50%) = median, DAP_(75%) = late).

The selection of a deviation ≥|0.5σ| was done in order to differentiate between clusters that behave similarly to the normal distribution, from clusters differing significantly from this distribution. Increasing this threshold to, e.g. ≥|1.0σ| would cause that the majority of clusters would be regarded as median, and only the very extreme cases would remain out of this classification. On the other hand, reducing this threshold, say to ≥|0.25σ| would cause that most clusters would be classified as extreme and would differ from the normal. Therefore, ±0.5σ seems to be a reasonable selection.

Figure 4 presents the five clustered annual AP distributions in the case study of Madrid. The time scale represented by the horizontal axis is longer than a year. However, the shadow represents the period from the SAD (July 1st in Madrid) until SAD + 364 (June 30th of the following year), which is the analyzed year in Madrid (Reiser and Kutiel 2008). The average DAP_(25%) ± 0.5σ of the entire dataset, representing the median period for AP_(25%), is between October 24th and November 24th. Similarly, the average period for ±0.5σ AP_(50%) is between December 20th and January 29^th, and for AP_(75%), the period is between March 11th and April 15th. It can be seen that all three DAPs (25%, 50%, and 75%) of cluster 1 fall within these average periods ±0.5σ of each DAP, and therefore, cluster 1 was characterized as median. The same information is illustrated in Fig. 5a.

Fig. 4

Five courses of the AP according to the cluster analysis results in Madrid

Fig. 5

The average DAP_{(25%, 50%, 75%)} ±0.5σ of the entire dataset and the DAP_{(25%, 50%, 75%)} of every cluster (a), the average TOTAL ±0.5σ for the entire dataset and the clusters' average TOTAL (b), the average RSL ±0.5σ for the entire dataset and the clusters' averages RSL (c), and a schematic illustration for the definitions of the five clusters, according to the average TOTAL, RSL, and DAP (d) in Madrid

The annual course of cluster 2 demonstrates a slower accumulation rate at the beginning of the season (up to 40%). DAP_(25%) was reached only on December 16th, much later than the average ±0.5σ and therefore was characterized as late. However, in the second half of the season [between DAP_(50%) and DAP_(75%)], the accumulation rate increased. DAP_(50%) was obtained within the median period, on January 17th, and DAP_(75%) on March 12th. Thus, cluster 2 was characterized as median despite its slow accumulation rate at the beginning of the year.

In cluster 3, the accumulation was fast in the first quarter of the season, when the DAP_(25%) was obtained as early as October 10th. Further on, the accumulation rate decreased, and both DAP_(50%) and DAP_(75%) were late. Thus, this cluster was characterized as late.

Finally, at least two out of the three DAPs, in both clusters 4 and 5, were earlier than the median period of the entire dataset, and thus, the characterizations for both clusters were early.

3.2.2 Characterization according to the TOTAL

The averages TOTAL of the entire dataset and the standard deviations were calculated. The TOTAL for every cluster was averaged and compared to the average TOTAL of the whole series in order to define the clusters as follows:

A cluster was characterized as wet when the average TOTAL was at least 0.5σ above the average TOTAL of the entire dataset.

Similarly, a cluster was characterized as dry, when the average TOTAL was at least 0.5σ below the average TOTAL of the entire dataset.

A cluster was characterized as median, when the average TOTAL was within the average ±0.5σ TOTAL of the entire dataset.

3.2.3 Characterization according to the RSL

Similarly, the averaged RSL of the entire dataset and the standard deviations were calculated, and the average RSL of every cluster was compared to it and the characterizations are as follows:

A cluster was characterized as long when the average RSL was at least 0.5σ longer than the average RSL of the entire dataset.

Similarly, a cluster was characterized as short when the average RSL was at least 0.5σ shorter than the average length of the entire dataset.

A cluster was characterized as Median when the average RSL was the average ± 0.5σ length of the entire dataset.

In the case study of Madrid, the averages TOTAL ±0.5σ and the averages RSL ±0.5σ for the entire dataset are illustrated in Fig. 5b and c, respectively. The averages TOTAL and RSL of all clusters are also presented. As can be seen, the TOTAL range is between 371.9 and 482.1 mm, and the RSL range is between 251 and 283 days. The departure of cluster 1 in both the TOTAL and the RSL are within these ranges (449.5 mm and 278 days, respectively). Therefore, cluster 1 is classified as median for these parameters.

Cluster 2 is classified as median in the TOTAL with 413.7 mm and short in the RSL with 246 days. Cluster 3 has a dry classification with only 336.7 mm on average, and the classification for the RSL is median (with 281 days). In cluster 4, the TOTAL is 489.1 mm, and it is classified as wet. However, the RSL is 269 and thus classified as median. Finally, cluster 5 is classified as dry for the TOTAL (345.7 mm) and short with only 245 days.

In the final analysis process, all three characteristics (the DAPs, the TOTAL, and the RSL) were combined in each cluster. Figure 5d presents a three-dimensional schematic illustration of this combination for the five clusters found in the case study. It can be seen that Madrid demonstrates five different types of annual rainfall courses:

• 1. Cluster 1 (blue) represents a Median course in all three parameters with the highest probability of more than twice in 5 years.

• 2. Cluster 2 (red) represents a median course in its DAPs and TOTAL and a short feature in its RSL, with a probability of once every 5 years.

• 3. Cluster 3 (green) represents a dry and late course, with a median length and with a probability of once every 9 years.

• 4. Cluster 4 (orange) represents a wet and early course, with median length and a probability of once in 11 years.

• 5. Cluster 5 (brown) represents a dry, early and short course with a probability of once in 14 years.

Once in 14 years, on the average, the annual course does not fit in any of the above five clusters.

This methodological process was applied on all stations.

The spatial distribution of the stations according to their intraseasonal accumulated course was found using the same methodology of CA as detailed above. For this purpose, the annual course of cluster 1, which is the most frequent cluster in all stations, was analyzed and mapped.

4 Results and discussion

Table 2, summarizes the number of clusters as a result of the clustering process and the percentage of the clustered and non-clustered years in all stations. Stations are sorted first according to the number of clusters in an ascending order, then according to the probability of cluster 1 in a descending order. In 11 stations, the available years were grouped into two clusters, in 15 stations into three clusters, in ten stations into four clusters, and in the remaining five stations, five clusters were found. In all stations on average, 93.6% of the years were grouped into clusters (two to five). In Valencia, 98.5% of the years (67 out of 68 years) were clustered, whereas the lowest percentage of years was grouped in Jerusalem with only 87% (47 out of 54 years). Therefore, it seems that the limitation of having at least two clusters and not more than 5 is justified.

Table 2 The number of clusters, percentage of clustered, and non clustered years and the probability of every cluster in all stations

Stations with a high clustered percentage of years grouped into only two or three clusters indicate a relatively predictable accumulation courses. Hence, it is possible to assume that, for example, the uncertainty related with the intraseasonal distribution in Bucurest (96.0% of the years clustered in only two clusters) is lower than in Ljubljana (87.5% in five clusters). Another way of expressing the uncertainty related to accumulation rates can be derived from the percentage of years grouped into cluster 1 (highest probability). The highest percentage of years grouped in cluster 1 was found in Bucurest (89.3%); hence, only 10.7% of the years have a different distribution, while in Brindisi, only 33.3% of the years were clustered in cluster 1, meaning that two thirds of the years had different distributions.

The clustered annual distributions in all stations are presented in Fig. 6. The shadow represents a year period from the SAD in each station (Table 1) until SAD + 364. Generally, it can be observed that the AP courses have three different shapes:

• 1. Accumulation rates having straight oblique lines are found mainly in stations from the northern part of the study area, e.g., Zagreb, Sarajevo, Merignac, Beograd, and Ljubljana. This shape is formed when precipitation occurs throughout the entire year, and therefore, the accumulation rate is constant all year long.

• 2. An “S” shape accumulation rate is found mainly in the southern Mediterranean basin, e.g., Jerusalem, Larnaca, Heraklion, Rodos, and Muğla. This shape is formed when, at the beginning of the year, the accumulation rate is very slow; at some point, it increases during the mid year, and at the end of the year, it slows down again. Most of these stations demonstrate two distinguishable seasons: a dry period during the summer months, mainly between May and September, and a concentrated rainy period during the rest of the year.

• 3. Crossed courses (occur in clusters 3, 4, or 5), which indicate inconsistent intraseasonal rates and timing. For example, a season starts slow and late, and at its end, it accumulates faster and ends early, or vice versa (e.g., Niš, Alexandroúpoli, Salamanca, Lisboa, Brindisi, and Barcelona).

Fig. 6

The clustered annual courses in all stations

Figure 7 presents the median periods and the DAP_{(25%, 50%, 75%)} of every cluster. The objective of this illustration is to point out the differences in the AP timing. However, since, for example, DAP_(25%) accumulates as early as May in some stations while in others this occurs around November, the comparison between the stations can only be within each group of stations having the same SAD, as presented in Reiser and Kutiel (2008). The stations' order is therefore based on their SAD and according to the >number of clusters in an ascending order. All DAPs of all clusters 1 were within the median period, and so these clusters were classified as median in all stations. The largest departures were identified in three stations located in the eastern coast of the Iberian Peninsula. Departures of clusters 2 and 3 in Barcelona (81 days) and Tortosa (66 days), respectively, from the median period of DAP_(25%) (Fig. 5a) and in cluster 3, in Valencia, a 105-day departure from the median period of DAP_(75%) (Fig. 5c).

Fig. 7

The average DAP_(25%) ± 0.5σ of the entire dataset and the DAP_(25%) of every cluster (a). The average DAP_(50%) ± 0.5σ of the entire dataset and the DAP_(50%) of every cluster (b) and the average DAP_(75%) ± 0.5σ of the entire dataset and the DAP_(75%) of every cluster in all stations (c). Stations are presented according to their SAD as recommended in Reiser and Kutiel (2008)

Figure 8 illustrates the average TOTAL ± 0.5σ range for the entire dataset and the averages RSL ± 0.5σ in all stations. In addition, the average TOTAL and average RSL of every cluster are presented. The stations are sorted according to the TOTAL in an ascending order, where Larnaca is the driest and Genoa the wettest. One noticeable fact is that there is no correlation between the TOTAL and the RSL. Hence, a station can be dry, and its rainy season will not necessarily be short and vice versa. Furthermore, it can be noticed in Fig. 8a that the departures from the average TOTAL are mostly drier than the average range.

Fig. 8

The averages TOTAL ± 0.5σ for the entire dataset and the clusters' average TOTAL (a) and the average RSL ±0.5σ for the entire dataset and the clusters' average RSL (b). Stations are sorted according to the average TOTAL in an ascending order

The combined definitions of the three parameters (DAPs, TOTAL, and RSL) in all stations are presented in Fig. 9. Stations are sorted according to Table 2 and then according to the number of classifications, since in eight stations, there were two clusters characterized with the same classification in an ascending order. In these cases, the differences between the two types of seasons could not be described accurately by using only the parameters, which describe the timing, quantity, and length. The differences that caused the separation of the relevant years into two clusters in the clustering process were evident in the rate of the annual course as demonstrated in Fig. 6. One example for such a case can be seen in Ankara, where clusters 1 and 2 were both defined as median for all three parameters. The clustered annual courses as presented in Fig. 6 indicate that cluster 1 has a more moderate and constant accumulation, while the course in cluster 2 accumulates in a slower rate at the beginning of the season (up to 25%) and in a faster rate at the second half of the season. In general, most of these cases are crossed courses.

Fig. 9

A schematic illustration for the definitions of the clusters according to the average TOTAL, RSL, and DAP in all stations. Stations are sorted according to the number of classifications and Table 2

According to Fig. 9, all clusters 1 (blue) in all stations are identical and were classified as Median for all three parameters, DAPs, TOTAL, and RSL. Other similarities in the classification types that were found:

• 1. In Bucurest, Zagreb, Calarasi, and Larisa, clusters 2 are median for the TOTAL and for the RSL and late for the DAPs.

• 2. In Dar el Beida and Argostoli, clusters 2 are median for the TOTAL, long for the RSL, and median again for the DAPs.

• 3. In Turnu Magurele and Marseille, three identical clusters were found. Clusters 2 were median for the TOTAL, short, and late; clusters 3 were median in both TOTAL and RSL and Early DAPs.

• 4. In Merignac and Tirana, three identical clusters were found; yet, their probabilities were different, as can be seen in Table 2. Whereas in Merignac, the probability of a median TOTAL, median RSL, and early DAPs distribution was only 8.5% (Cluster 3), it stands on 22.0% in Tirana (cluster 2). On the other hand, the probabilities for a late distribution (TOTAL and RSL are both median) was almost similar, with 13.6% in Merignac (Cluster 2) and 14.6% in Tirana (Cluster 3).

• 5. In Beograd, Genoa, and Jerusalem, three identical clusters were found, though the probabilities were different as can be seen in Table 2. In Beograd, the probability for a median TOTAL, median RSL, and early DAPs classification was 22.9% (Cluster 2), while only 10.0% for a dry and median RSL and late DAPs (cluster 3). In Genoa and Jerusalem, on the other hand, the probability for median TOTAL, median RSL, and early DAPs (cluster 3) was only 10.6% and 7.4%, respectively, whereas for a dry and median RSL and late DAPs (cluster 2), the probability was 29.8% and 33.3%, respectively (Table 2).

• 6. Three identical clusters were found in Valencia, Tortosa, and Blagnac. The probability for a median cluster (cluster 1) was the highest in Valencia (among these three stations), with 80.9%, and the smallest was in Blagnac (74.6%). In Valencia and Blagnac, the probability for a median TOTAL, median RSL, and late DAPs type was similar (10.3% and 10.2%, respectively); yet, in Tortosa, it was only 6.7%. Finally, the probability for a median TOTAL, short RSL, and early DAPs type was the smallest in Valencia (7.4%) and the highest in Tortosa (13.3%).

Table 3 summarizes all classifications in all stations. As aforementioned, all clusters 1 presented a median character of the three parameters. Clusters 2 had more variability in three classifications with 13 features. Most clusters (34 out of 41) had a median TOTAL character, 16 of them were late and ten were early.

Table 3 Characteristics of all clusters in all stations

Out of a total of 132 clusters found in all 41 stations, 99 were median in their RSL, 16 were short, and 17 had a long classification. There were 19 dry courses and only eight wet, while most of the clusters had a Median rainfall quantities (105). The intraseasonal distribution, represented by three DAPs, had a relatively even distribution in the various types. Forty clusters classified as early, 38 as late, and 54 had a course median.

There are 149 years (in all stations together) out of a total of 2,303 analyzed years (6.5%), which were not clustered. The non-clustered years from all stations were classified as well, using the same method, and the results are presented in Table 4. Most of these years were late (92 out of 149), almost half of the cases had a dry character (70 years) and 65 were short. These extreme years will be further studied.

Table 4 Characteristics of all non-clustered years in all stations

There were four types of courses, which did not appear in any of the clusters or non-clustered years (marked with a gray shadow in Table 4). All four types are median in their timing and:

• 1. Wet and short

• 2. Wet and median (in length)

• 3. Dry and short

• 4. Dry and long.

Only two cases were classified as dry with median RSL and DAPs: cluster 4 in Alexandroúpoli and one non-clustered year, 1972, in Beograd.

The spatial distribution of the stations according to their annual course of cluster 1 is presented in Fig. 10. Figure 11 presents the average annual courses of cluster 1 in the four regions. Each line represents the average course of all stations in the relevant region. The horizontal axis relates to a year period, from the SAD until SAD + 364.

Fig. 10

Spatial distribution of the annual courses of custer 1

Fig. 11

The averaged AP annual courses in the four regions presented in Fig. 10

The study area was divided into four regions:

• Region I in the Southeastern Mediterranean, comprising five stations. It presents an “S” shape distribution with a long dry period of approximately 3 months in the beginning of the year and about two additional dry months at its end, leaving a very intense rainy season, comprising of about 6–7 months.

• Region II in the central basin is comprised of 13 stations. These stations have also an “S” shape distribution, though less severe than in region I. This means that the rainy season is longer, and the dry period ends earlier and starts later at the end of the rainy season.

• Region III in the Northern part of the basin is comprised of 19 stations. This region presents an oblique line, which means that precipitation occurs throughout the entire year with no real definable dry or wet periods.

• Region IV is comprised of three stations: Barcelona, Tortosa, and Ankara. In this region, like in region III, rainfall occurs throughout the year but at a slower rate for the first half of the rainy season and a faster one in the second half.

Bucurest is the only station that was not clustered in any region.

5 Conclusions

The main conclusions of the present study can be summarized as follows.

The use of CA, as a tool for identifying the temporal (rather than spatial) behavior of the rainfall along the year, was proven to be satisfactory. It enables to detect and group various years into clusters with similar accumulation courses.

When applied to the Mediterranean basin, stations were characterized by two to five different types of seasons with various probabilities. Furthermore, each cluster in each station was characterized also by its TOTAL and its RSL. The main findings are:

• 1. The most frequent type (cluster 1) was median in all three parameters, in all stations with probabilities ranging from 33.3% to 89.3%.

• 2. The probability for a year to be dry is higher than wet. Likewise, the probability of a year to be long is higher than to be short.

• 3. The highest probability for non-clustered years is to be characterized as dry, short, and late (14.8%, 22 years out of 149). These years were excluded from the representations and are considered as extreme events. A further analysis of these years is necessary in order to provide more information about extreme rainfall variability.

• 4. A spatial distribution of the most frequent AP courses reveals that, in the northern part of the Mediterranean basin, there is a constant accumulation rate throughout the entire year, whereas the southern part is characterized by an intense accumulation rate and a long dry period.