SPATIAL AND TEMPORAL VARIABILITY OF THE DAILY RAINFALL REGIME IN CATALONIA (NORTHEASTERN SPAIN),

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1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 24: (2004) Published online in Wiley InterScience ( DOI: /joc.1020 SPATIAL AND TEMPORAL VARIABILITY OF THE DAILY RAINFALL REGIME IN CATALONIA (NORTHEASTERN SPAIN), X. LANA, a, *M.D.MARTÍNEZ, b C. SERRA a and A. BURGUEÑO c a Departament de Física i Enginyeria Nuclear, ETSEIB, Universitat Politècnica de Catalunya, Av. Diagonal 647, Barcelona, Spain b Departament de Física Aplicada, ETSAB, Universitat Politècnica de Catalunya, Av. Diagonal 649, Barcelona, Spain c Departament d Astronomia i Meteorologia, Facultat de Física, Universitat de Barcelona, Av. Diagonal 647, Barcelona, Spain Received 28 July 2003 Revised 22 December 2003 Accepted 17 January 2004 ABSTRACT Spatial and temporal patterns in the daily rainfall regime of Catalonia (northeastern Spain) recorded for the period are analysed from several points of view, including the irregularity of the time series in terms of entropy, the Mann Kendall test for time trends, a principal component analysis (PCA), an average linkage (AL) clustering algorithm and, finally, a power spectrum analysis, which includes a comparison of white-noise and Markovian red-noise hypotheses. The analyses are based on three monthly variables derived from the amounts recorded on a daily basis: the average daily rainfall and the standard deviation of the daily rainfall for each month, together with the corresponding coefficient of variation. The joint spatial temporal variability is manifested by the irregularity index, which is characterized by relevant values in all cases and gradients from the north (Pyrenees and Pre-Pyrenees mountain ranges) to the south (Ebro Valley) and to the Mediterranean coast. The interpretation of the factor scores derived from the PCA and of the clusters obtained from the AL algorithm also describes the complex spatial distribution of the daily rainfall regime, given that the effects of atmospheric circulation patterns on rainfall regimes are conditioned by the complex orography of Catalonia and its proximity to the Mediterranean Sea. The factor loadings associated with the PCA also suggest a distinction between hot, cold and mild seasons. Finally, it is worth noting that monthly series are usually accompanied by white background noise and, in a few cases, signs of Markovian behaviour and some significant periodicities, which are generally of less than 10 months and which change from one cluster to another. Copyright 2004 Royal Meteorological Society. KEY WORDS: northeastern Spain; spatial and temporal irregularity; Mann Kendall test; clustering algorithms; power spectrum analysis; daily rainfall intensity 1. INTRODUCTION Catalonia is characterized by a varied orography and its proximity to the Mediterranean Sea. In the north, the Pyrenees and Pre-Pyrenees mountain ranges boast the highest altitudes of the country. The rest of the area is configured by the Central Basin (inland areas of the country), the Transversal range (northeast of the country) and the Littoral and Pre-Littoral mountain ranges (parallel to the Mediterranean coast). Figure 1 depicts these main orographic features, including the end part of the Ebro Valley and the Ebro Delta. As a result of this relatively complex orography, the daily amounts recorded by different rain gauges can differ remarkably depending on the kind of atmospheric circulation pattern that generates the rain episode and the location of the recording stations. For instance, under the effects of easterly advections, gauges on the coast will record higher amounts of rain than gauges on the western face of the Transversal, Littoral and Pre-Littoral ranges, given that these gauges are sheltered by these mountains; whereas gauges in the Central Basin are not usually as affected by these easterly advections. Consequently, in addition to the characteristic time irregularity of * Correspondence to: X. Lana, Departament de Física i Enginyeria Nuclear, ETSEIB, Universitat Politècnica de Catalunya, Av. Diagonal 647, Barcelona, Spain; francisco.javier.lana@upc.es Copyright 2004 Royal Meteorological Society

2 614 X. LANA ET AL. m Western Pyrenees Central Basin Ebro Valley 50 km F R A N C E Eastern Pyrenees Pre-Littoral Chain Littoral Chain Transversal Chain MEDITERRANEAN SEA N Ebro delta Figure 1. Main orographic features of Catalonia and indication of its location in the Iberian Peninsula the Mediterranean climate, a striking spatial variability should be observed. This property has been clearly shown through different processes of spatial clustering in terms of daily and monthly totals by Periago et al. (1991), Fernández-Mills et al. (1994) and Serra et al. (1996, 1998), who considered both geographic and atmospheric patterns in the interpretation of the results. Other aspects that affect the precipitation regime, such as the extreme daily precipitation (Lana et al., 1995) and the time interval between consecutive wet and dry episodes (Lana and Burgueño 1998a,b,c), have also been studied for the same geographic area. A wider geographical scale that includes the Catalan territory has been adopted by different workers in their research on the annual, seasonal and monthly rainfall regime of the Iberian Peninsula, by means of principal component (PC) techniques (Fernández-Mills, 1995; Esteban-Parra et al., 1998; Rodríguez-Puebla et al., 1998; Serrano et al., 1999; García et al., 2002) and of the Spanish Mediterranean area (Romero et al., 1998, 1999a,b,c; Sumner et al., 2001). In all the aforementioned cases, daily data were used to obtain monthly, seasonal and annual amounts, which constituted the database for these studies. Interest now centres on a more detailed analysis of the daily pluviometric regime in Catalonia, which should be the starting point for determining how this regime is influenced by the main orographic features and by atmospheric circulation patterns. Consequently, a denser network of rain gauges and a new definition of pluviometric variables, which differ from annual, seasonal and monthly amounts, and are computed from daily amounts that are equal to or exceed a threshold level of 0.1 mm, are necessary. The averaged daily amount (ADR) for each month and rain gauge, the first variable considered, is obviously necessary if we are interested in the daily pluviometric regime. The second variable, the standard deviation (SDR) of the daily amount for each month and rain gauge, could be associated with a very common feature in Mediterranean territories, i.e. a significant variability in the daily totals. The third variable, the coefficient of variation (CV) summarizes the previous two variables. Given the characteristics of the three variables chosen, the monthly scale is the average length of time taken to obtain statistically representative values of ADR, SDR and CV. These variables are intended to characterize, at the same time, the mean daily rainfall intensity and the scatter of the daily amounts. Additionally, it is worth noting that they contribute with different points of view to our knowledge of the pluviometric regime, when compared with variables associated with, for example, monthly totals. According to the current literature, they represent a new way of analysing the spatial and temporal organization of rain fields, as they in fact

3 CATALONIAN RAINFALL REGIME VARIABILITY 615 describe the monthly average of the daily intensity. Therefore, these three variables should be able to show which areas of Catalonia experience intense rainfall and signs of time variability. In this way, applications aimed at civil engineering, the prevention of soil erosion and the management of water resources could be more effectively targeted. As a detailed description of daily rainfall that indicates its average value, scatter and relative variation is required in order to understand its effects, different statistical strategies were applied to show its spatial and temporal behaviour. A first insight into the complexity of the daily rainfall regime is proposed by quantifying the irregularity of the monthly series of the three aforementioned variables. This pattern is evaluated by means of an index that is closely related to the entropy of the series, which permits a straightforward interpretation of the temporal irregularity in terms of the average deviation between two consecutive elements in a series. Maps of this index offer a clear picture of how the temporal irregularity of the daily regime is spatially distributed throughout Catalonia. The statistical significance of the time trends that affect the three variables, derived by means of the Mann Kendall statistical test, is evaluated for every rain gauge and, at the same time, a model based on the binomial distribution allows us to quantify the statistical significance of an overall trend for Catalonia as a whole. Another approach to the complex spatial distribution of the daily rainfall regime is to characterize each rain gauge by means of 24 variables, consisting of the ADR and SDR for every month of the year. The interpretation of the PC derived from a PC analysis (PCA) of the 24 variables, in terms of their factor scores (FSCs) and factor loadings (FLs), reveals the spatial variability of the rainfall regime and suggests a seasonal behaviour. In addition, the average linkage (AL) clustering algorithm allows the rain gauges to be grouped in terms of FSCs. Moreover, the complexity of the spatial features is enhanced by the results of this clustering process. The sequential Mann Kendall test, which enables abrupt changes in a series to be detected, is applied to representative gauges, each of them belonging to one of the clusters deduced from the PCA and AL algorithms. The power spectra analysis is limited to the same representative gauges. The spectral contents of the power spectra are compared with those that are based on white-noise and Markovian red-noise behaviours. In this way, the red- or white-noise spectral background and statistically significant periodicities are deduced for the gauge that represents each region. The statistical relevance of spectral contents and cross-correlation lag-zero coefficients are also analysed with the aim of establishing possible links between different areas of Catalonia. The analysis of the white-noise and red-noise behaviours is complemented by mapping the first-lag correlation coefficients obtained for the rain gauges and a revision of their main spatial features. 2. DATABASE Daily amounts (from 1950 to 2000) that were equal to or exceeded 0.1 mm were compiled from 75 rain gauges that belong to the Instituto Nacional de Meteorología (Spanish Ministry of the Environment). The geographic distribution of the gauges in this pluviometric network is depicted in Figure 2. This shows that the density of gauges is relatively homogeneous, except in certain areas of the Pyrenees where orography makes access difficult and in a small area of the Central Basin. Prior to undertaking the proposed set of analyses, an assessment of data quality and of the homogeneity and continuity of the records was necessary. The homogeneity of the pluviometric series was analysed by means of the Von Neumann ratio test (Mitchell et al., 1966), which is applied to the residuals of monthly amounts in the way described by Lana et al. (2001) for a similar pluviometric network. Figure 3 shows four examples for gauges 6, 16, 23 and 49, whose location is shown in Figure 2, and which were selected to represent the whole set of rain gauges because of their increasing distance from the Mediterranean Sea. Squares represent the evolution of the Von Neumann ratio, which should tend asymptotically to 2.0 with increasing length of the recordingperiod, and the 95% confidence bands are indicated. The empirical points of these bands indicate episodes of inhomogeneity, but these are not confirmed by the Von Neumann ratios computed for the whole recording period, because they never differ significantly from 2.0. The lack of homogeneity at the beginning of the recording period for gauges 6, 16 and 49 may be attributed to the computational procedure, which tends to give poor representative values for small quantities of data. In fact, the rest of the Von Neumann ratios for an increasing number of data are always

4 616 X. LANA ET AL FRANCE MEDITERRANEAN SEA N Figure 2. Network of 75 rain gauges belonging to the Instituto Nacional de Meteorología (Spanish Ministry of the Environment) within the 95% confidence bands up to the end of the series, and the final value is close to 2.0. Nevertheless, a transient lack of homogeneity may be assigned to the pluviometric records for which the Von Neumann test parameter falls outside the confidence band. An example is gauge 6, for the period 1974 to 1980, given that the Von Neumann test parameter lies slightly outside the 95% confidence band for this period. In spite of this, the overall Von Neumann parameter falls within the 95% confidence band centred on 2.0, as in the case of gauge 6. In addition, the effects of inhomogeneity at a few individual stations are minimized overall if these stations represent a small fraction of the whole set of rain gauges (New et al., 2001). The database could be expanded to include 51 years from 1950 to 2000, but in practice there are some records that lack daily data even after An example of this is gauge 49, for which the recording period begins in 1955, as shown in Figure 3. Although amounts for months in which recordings were not taken could be roughly evaluated by assuming monthly average values, it is more hazardous to estimate daily amounts that were not recorded. Consequently, the decision was taken not to replace missing data with estimations. Obviously, gauges with a short recording period were not included in the set of 75 rain gauges; 85% of the selected rain gauges have an effective recording period of at least 31 years and the rest of them exhibit total recording periods of slightly less than 31 years. A more debatable issue is the continuity of the records and how data have to be treated when isolated periods with missing data are detected. The results derived from the PCA and AL algorithms are not significantly affected by this absence of data, since they analyse 24 monthly average ADRs and SDRs for the 12 months in a year, from January to December, and for every rain gauge. For instance, a gauge with one or two January months without data represents a small fraction of the whole number of January months and, consequently, this lack of data should not noticeably affect the ADR and SDR values for that month. Months without data must also be discarded prior to the computation of the temporal irregularity indices; this disadvantage, however, becomes practically irrelevant if these months make up a relatively low fraction of the entire recording period. For the same reason, the incidence of a lack of data on autocorrelation and cross-correlation coefficients should not be significant. However, if the monthly series are not complete, the power spectra from these series are not directly available. Thus, the Fourier transform is applied to the

5 CATALONIAN RAINFALL REGIME VARIABILITY Von Neumann Ratio Von Neumann Ratio Years Years Von Neumann Ratio Von Neumann Ratio Years Years Figure 3. Von Neumann ratio test applied to residuals of monthly amounts for several gauges of the pluviometric network correlation function and, as a consequence, relatively reasonable estimations of empirical power spectra are achieved. The biggest problem with missing data appears when the single Mann Kendall and the Mann Kendall sequential tests are applied. It should be pointed out that the statistical parameter of both tests is based on the computation of a data rank, which may be incorrectly evaluated if there is a lack of data, leading to the erroneous computation of the statistical significance. This fact may be relevant when the significance of a time trend is being evaluated, especially when the miscomputed significance is close to 95%, a limit that is usually used to accept or reject the null hypothesis. This shortcoming may affect some of the time trends evaluated for monthly ADR, SDR and CV series, because all the pluviometric records available are analysed and temporal continuity is not always assured. The effects of missing data on the Mann Kendall sequential test are less relevant, given that it is only applied to selected rain gauges that show data continuity.

6 618 X. LANA ET AL Main spatial features 3. DATA TREATMENT A preliminary overview of the spatial distribution of the daily rainfall regime is achieved by assigning ADR, SDR and CV for the whole recording period to every gauge. The spatial distribution of these three variables is depicted in Figure 4, which shows ADRs ranging from 6 to 22 mm/day and two strong gradients, with ADRs varying from 14 to 22 mm/day, close to the Transversal mountain range and to the Ebro Delta. Similar patterns are detected for SDRs, with the same two strong gradients (14 to 22 mm/day) and the same overall range (from 6 to 22 mm/day). Besides these gradients, an overall tendency for the SDRs to increase from west to east is observed. Patterns of ADRs and SDRs are very different from a geographical point of view to those of CVs. On the one hand, there are three nuclei of very remarkable CVs that exceed 180% in the Ebro Valley and in two relatively small areas of the Mediterranean coast. On the other hand, there is not a clear evolution of CVs from west to east or from north to south, but the highest CVs are achieved close to the Mediterranean coast. In short, a confirmation of the complex spatial distribution of the daily rainfall intensity is obtained from these maps. More detailed analyses of spatial and temporal variability are discussed in the subsequent sections in terms of monthly ADRs, SDRs and CVs Temporal irregularity index The irregular behaviour of a climatic variable may be quantified in several ways. One of these is the sequential variability introduced for the case of 1 min rainfall in storms (Conrad and Pollack, 1962; Huff, 1970). In the case of very different time scales, as with monthly amounts, Walsh and Lawler (1981) proposed a seasonal rainfall index, similar to the one previously used by Ayoade (1970). In our case, we accept a concept similar to entropy (Martín-Vide, 1984, 1987; Burgueño, 1989, 1993). This has previously been employed to characterize the annual pluviometric irregularities of the Spanish Mediterranean coast (Lana and Burgueño, 2000a) and the irregularities of several annual pluviometric indices introduced by Lana et al. (2003b) in their analysis of the daily rainfall regime at the Fabra Observatory in Barcelona (northeastern Spain). The definition of the temporal irregularity index applied takes into account the quotients between time-consecutive values X i of the monthly ADRs, SDRs and CVs as follows: S = 1 N 1 N 1 ( ) log Xi+1 (1) i=1 X i Here, N is the number of months. Consecutive monthly elements that are very similar imply a value of S very close to zero, but very different ones lead to a high value for S. Thus, this parameter may be interpreted as a measure of the disorder of the time series, i.e. of its entropy. A shortcoming in the application is that it is possible that there will be months without rainfall due to dry periods (null ADR and SDR and undefined CV), lack of daily data (undefined ADRs, SDRs and CVs) or just one rainy day in a month (null SDRs and CVs). The possibility of a month with no rainfall must not be ruled out for northeastern Spain, especially in summer, and months with just one rainy day are also relatively common for certain seasons and areas. In all cases, these monthly values cannot be used for the computation of Equation (1), and the number of terms available for a good estimation of the irregularity diminishes. Additionally, as previously discussed, when a gauge was not operative for a certain number of days in a month, instead of substituting the null or missing monthly data by the corresponding mean monthly value, all cases that display these kinds of singularity were removed in the computation of S with the aim of avoiding the addition of false irregularities. In contrast, the S index may be subject to several uncertainties due to the contributions lost in Equation (1). Nevertheless, given that the number N of consecutive months of the recording period is generally large, these uncertainties must be small. Additionally, uncertainties derived from null monthly ADRs can be ignored by defining S as an irregularity index for months with at least a day of 0.1 mm rainfall, which is generally the threshold level to define a rainy day.

7 CATALONIAN RAINFALL REGIME VARIABILITY ADR (mm/day) SDR (mm/day) CV (%) Figure 4. ADRs, SDRs and CVs evaluated by considering the whole recording period of every rain gauge A debatable issue is how to define a threshold level for the temporal irregularity beyond which a series can be considered irregular in time. An attempt was made by Walsh and Lawler (1981), who introduced a set of empirical classes for their seasonal index that ranged from 0 (all months with equal rainfall) to 1.83 (all the annual rainfall concentrated in a month). In our case, certain classes were also introduced, although averaged deviations between two consecutive elements of a series had to be represented. Let us assume the possibility that consecutive values of a time series are related by ( X i+1 = X i 1 ± µ ) (2) 100

8 620 X. LANA ET AL. where µ, expressed as a percentage, is the excess or shortage of X i+1 with respect to X i. By introducing this behaviour of the series in Equation (1), deducing the measure of irregularity is straightforward and can be expressed as S = 1 log (1 + µ ) 1 + log (1 µ ) (3) where we assume that one half of the elements in the series represents a shortage of µ with respect to the preceding element and that the other half represents an excess of µ. Equation (3) behaves linearly for a wide range of µ, up to 50%. Nevertheless, for µ>50% it grows logarithmically. This percentage might be considered to be the limit between low and moderate irregularity (<50%) and high and very high irregularity ( 50%). As real series do not behave exactly as Equation (3) imposes, an irregularity quantified by this equation could only be interpreted as a series of elements that have an average shortage and excess percentage with respect to the preceding elements. Figure 5 depicts the spatial evolution of the irregularity index S on a monthly scale, which, especially for the ADR and SDR cases, shows a clear growth of the irregularity from the north (Pyrenees) to the south (Central Basin and Ebro Valley) and a less marked increase from the western Pyrenees to the Mediterranean coast. In terms of the average excess or shortage µ, the first variable (ADR) is characterized by percentages that range from 38% (S = 0.4) to 80% (S = 1.1). The second variable (SDR) exhibits the highest irregularities, with percentages that range from 60% (S = 0.7) to 86% (S = 1.3). The case of CV is characterized by the most moderate irregularities, with percentages that range from 29% (S = 0.3) to 60% (S = 0.7), again with a slight tendency of the irregularity to increase from north to south. Nevertheless, the increase from the west (Central Basin) to the east (Mediterranean coast) is not as evident, in spite of two nuclei of relatively high irregularities on the central and northern Mediterranean coasts. In short, it is striking that the highest temporal irregularity is detected only in certain nuclei located on the Mediterranean coast and not all along it Analysis of time trends Significant time trends that affect the monthly ADR, SDR and CV series are investigated by means of linear regression and the Mann Kendall statistical test (Sneyers, 1990). For every element X i (i = 1,...,N) of monthly ADR, SDR or CV series, the number n i of preceding elements X j accomplishing X j <X i is computed. The statistical parameter is then defined as t = N n i (4) i=1 and, assuming that t has an asymptotically normal distribution, the mean and variance of t are t = var(t) = N(N 1) 4 N(N 1)(2N + 5) 72 (5) (6) Subsequently, t is standardized, obtaining the statistic u(t) ={t t }/var(t) 1/2, and the associated probability α is determined according to α = P { u > u(t) } (7) where the normal distribution for u is assumed. Once a level of confidence α 0 is defined (usually 5%), the null hypothesis (absence of a time trend) must be rejected in favour of the existence of a time trend if α<α 0.

9 CATALONIAN RAINFALL REGIME VARIABILITY S (ADR), monthly scale S (SDR), monthly scale S (CV), monthly scale Figure 5. Spatial distribution of the temporal irregularity index for the monthly series of ADR, SDR and CV Null monthly ADRs and SDRs do not present computational problems. It is only undefined monthly CVs, which are a consequence of null ADRs, that must be ignored in the computation of the statistic t. Consequently, these undefined CVs have a similar incidence on the significance level given by Equation (7) as discussed before with respect to the effects of missing data. Figure 6 depicts the distribution of statistically significant (solid symbols) and non-significant (open symbols) trends. According to the legend, the symbol size is proportional to the magnitudes of the time trends. The first pattern worthy of note is that significant trends are not concentrated but, rather, are dispersed throughout Catalonia. Secondly, negative significant trends are dominant with respect to positive trends for monthly ADRs and SDRs. Nevertheless, the inverse situation is detected for monthly CVs. Thirdly, several very outstanding negative and positive trends, which imply changes of ±20% in a decade with respect to the averaged values for the series,

10 622 X. LANA ET AL. Average daily rainfall (ADR) Standard deviation (SDR) Trends (%/dec) >20 10 to 20 0 to 10 n.s (95%) -10 to 0-20 to -10 < -20 Trends (%/dec) >6 3 to 6 0 to 3 n.s (95%) -3 to 0-6 to -3 < -6 Coeficient of Variation (CV) Trends (%/dec) >10 5 to 10 0 to 5 n.s (95%) -5 to 0-10 to -5 < -10 Figure 6. Time trends for the series of monthly ADR, SDR and CV of the 75 rain gauges. Trends are depicted as percentage deviation per decade with respect to averaged values are observed for monthly ADRs. The most negative trends basically correspond to locations in western Catalonia (Central Basin), where the ADRs are the lowest in the whole territory. The variation range is attenuated in the case of the SDR (±6% in a decade) and increases slightly (±10% in a decade) for monthly CVs. An overall time trend on a regional scale for all Catalonia is difficult to ascertain from a visual inspection of Figure 6 because there are a remarkable number of rain gauges with non-significant time trends. Whereas for monthly ADRs the northeastern corner is characterized by several positive trends and the rest of the territory by negative trends, almost all significant trends are negative for monthly SDRs. Monthly CVs are characterized by the combination of positive and negative significant trends. In spite of this relatively complex pattern, the statistical significance of overall positive or negative trends can be quantified. Firstly, the null hypothesis is introduced as the absence of a global time trend. This hypothesis would imply that half of the rain gauges are affected by positive trends and the other half by negative trends. In terms of the binomial

11 CATALONIAN RAINFALL REGIME VARIABILITY 623 distribution: P(x M) = M x=0 m x!(m x)! px q m x M m (8) is the probability of having x number of positive trends below or equal to M with probability p and of m x negative trends with probability q for m rain gauges. Secondly, in terms of the null hypothesis (p = q = 0.5) P(x M) = M x=0 m! x!(m x)! (1/2)m (9) Equation (9) is the probability of defining the confidence level for a possible overalltrend. Values of P(x M) greater than 95% will determine whether an overall positive or negative trend can be considered for the whole set of rain gauges with a possible error of as much as 5%. According to this formulation, when all the rain gauges are considered, overall trends for monthly ADRs, SDRs and CVs for Catalonia must be discarded given that the probabilities found in Equation (9) are very close to zero. If only significant positive and negative cases are considered, then the conclusions are quite different. Firstly, 39 gauges with significant monthly ADR trends (34 negative and five positive) suggest a negative overall trend with a probability of 99.9%. Secondly, 13 negative and two positive significant trends are detected for monthly SDRs. Thus, an overall negative trend is very likely in this case. Thirdly, an overall positive trend can be deduced for monthly CVs with a probability of 98.9%, because 25 out of 37 significant cases correspond to positive trends Principal component analysis PCA (Jolliffe, 1986; Preisendorfer, 1988) is applied to 75 rain gauges by characterizing all of them by means of 24 variables, which consist of 12 monthly average ADRs and 12 SDRs, from January to December. The corresponding 12 CVs were not considered, given that they do not add a larger spatial coherency to the clusters derived. As discussed before, only a lack of data could slightly affect the monthly ADRs and SDRs used to characterize every rain gauge. According to the PCA algorithm, after a varimax rotation to facilitate the interpretation of the results, the 24 original variables can be replaced by four PCs that explain 82.3% of the data variance. Retained PCs fulfil two criteria. On the one hand, PCs associated with eigenvalues of less than 1.0 explain less data variance than the original variables and thus are not considered. On the other hand, PCs associated with degenerate eigenvalues, due to sampling errors (North et al., 1982), are also discarded. Table I shows the FLs that establish the linkages between the PCs and the original variables. The values in Table I suggest that PC1 is closely associated with cold months, from November to March. The possible linkages of PC2 to the original variables are not as clear because several FLs have relevant values, but this PC can be considered as mainly linked to the hottest months, due to significantly higher FLs in July and August. PC3 does not depict a clear association with a set of months, but relevant FLs are detected for April, May and June. Consequently, PC3 could be associated with the spring season. Finally, PC4 shows a preference for several autumn months, with significantly high FLs for September and October. Figure 7 shows the spatial distribution of the FSCs for the four PCs. FSC-1, which explains 27.3% of the data variance, is characterized by high values in northeastern Catalonia, including the eastern Pyrenees, and an almost homogeneous distribution for the rest of the areas, except for a small negative nucleus in the Central Basin and a positive nucleus close to the Ebro Valley. The evolution of the FSC-2 (21.8% data variance) is characterized by increasing values from the southwest (Central Basin) to the north (Pre-Pyrenees and Pyrenees). This relatively simple pattern is complicated by a strong gradient close to the Ebro Delta on the southern Mediterranean coast and a small nucleus of maximum values in the northeastern area. Patterns of FSC-3 (18.9% data variance) are even more complicated. A large part of the territory is linked to positive values; dispersed nuclei show maximum values. Moreover, a great variety of FSC values within the Central Basin and throughout the area of the Pyrenees are observed, and the northern and central Mediterranean coast are characterized by values that are significantly smaller than those of the southern coast and the Ebro

12 624 X. LANA ET AL. Table I. FLs for the four PCs that substitute the 24 original variables. Bold type identifies FLs with values that are equal to or exceed 0.6 PC1 PC2 PC3 PC4 January ADR SDR February ADR SDR March ADR SDR April ADR SDR May ADR SDR June ADR SDR July ADR SDR August ADR SDR September ADR SDR October ADR SDR November ADR SDR December ADR SDR Delta. Finally, patterns of FSC-4 (14.3% of data variance) change absolutely with respect to the other three FSCs. Other than in a small area, there is a gradient from the Mediterranean coast to inner Catalonia and the lowest (negative) values are achieved in the western corner of the Pyrenees, in areas with high relief towards the north. The highest FSCs are concentrated on the coastal fringe, especially in the northern and southern extremes. An interpretation of these FSC values in terms of atmospheric circulation patterns must also take into account the linkages of hot, cold and mild months with different empirically determined topographic influences and rainfall regimes in Catalonia. The easiest interpretation corresponds to FSC-4. Its FLs are strongly linked to autumn months and especially to the SDR, when easterly advection can generate abundant, but also irregular, daily amounts in places close to the coast and to the Littoral and Pre-Littoral mountain ranges. Thus, FSC-4 values would largely reflect the irregular daily amounts recorded in autumn under the effects of easterly advection. The effects of these advections are mitigated in inland areas of Catalonia, due to the sheltering effect of different mountain ranges, an extreme case being the western Pyrenees corner. In this zone, located on the north face of the Pyrenees, rain gauges are sheltered from the effects of easterly advections by this mountain range. The spatial pattern observed for FSC-1 again suggests that it is related to easterly advections, in this case with a northerly component and the most active nuclei in the northeastern corner of the territory. Once more, the FSC values would mostly be due to the irregularity of amounts generated by Mediterranean advections during the colder months, in agreement with the fact that, month by month, the relevant factor loadings of the SDRs are systematically higher than those of the ADRs. Thus, gauges facing the west of the Transversal range would be sheltered by it. In contrast, gauges facing the east and close to the Transversal or Littoral and Pre-Littoral ranges should record higher daily intensities. The effects of these advections would be mitigated from the eastern to the western Pyrenees. Moreover, the minimum detected in the Central

13 CATALONIAN RAINFALL REGIME VARIABILITY FSC FSC FSC FSC-4 Figure 7. Factor scores for the four rotated PCs derived from the PCA algorithm applied to the 24 variables (monthly ADR and SDR) Basin should also be in agreement with the explanation proposed. Another possibility might be the diversion of northwesterly to northerly airflows around the eastern end of the Pyrenees. It is empirically known that advections from the north do not usually produce significant precipitation on the southern face of the Pyrenees or in northeastern Catalonia; therefore, this circulation pattern hardly ever contributes to positive factor scores for FSC-1. With respect to FSC-2, assuming that it is closely related to the hottest months (July and August) as shown in Table I, its patterns should be interpreted in terms of spatially unconnected convective phenomena, which constitute the main contribution to daily rainfall in the hot season. The relevance of other circulation patterns, such as cold fronts from the Atlantic, should be discarded. Consequently, the FSC-2 map would separate areas of more copious convective episodes (Pyrenees, Pre-Pyrenees and part of the Mediterranean coast) from areas with less daily intensity, such as the Central Basin.

14 626 X. LANA ET AL. The case of FSC-3, according to Table I, is closely linked to mild months (the spring season), when frontal passages from the west and the northwest, and sometimes easterly advections, generate the daily rainfall episodes. Both ADRs and SDRs, with moderate values, have FLs with very balanced weights in the generation of the FSC-3, in agreement with the superposition of atmospheric circulation patterns that is characteristic of spring. April and May depict slightly higher FLs for the ADRs, but June is characterized by the opposite case: FLs related to SDRs are slightly higher than those linked to ADRs. In agreement with all these facts, most of the Central Basin achieves the highest FSCs, due to the effects of westerly frontal passages, whereas low FSCs are predominantly observed towards the Mediterranean coast, which is relatively sheltered by the Littoral and Pre-Littoral ranges and by the northern face of the western Pyrenees. A single exception is the southern corner, which can be affected by westerly advections in the Ebro Valley. A significant issue is the absence of relevant positive FSCs in the first four retained PCs for the northwestern corner of Catalonia. This sector is characterized by low values of rainfall intensity and by a regular rainfall regime (small SDRs) due to the influence of Atlantic advections. Given that these circulation patterns affect a small area of Catalonia and show a low percentage of data variance in the PCA procedure, it may be assumed that positive FSCs for the northwestern corner of Catalonia should be detected for PCs that explain a low percentageof data variance (eigenvalueslessthan 1.0) and arelinked to westerly and northwesterly advections The clustering process The clustering process is achieved by applying the AL procedure (Kalkstein et al., 1987). Each rain gauge is characterized by its four FSCs instead of by the original 24 variables. The AL algorithm is based on a hierarchical procedure, in which two clusters are fused for every iteration, going from the most disperse configuration, in which every gauge generates a singular cluster, up to all the gauges forming a unique cluster. Two clusters separated by the minimum Euclidean distance are put together for every chosen fusion, and the similarity index is defined as L ij = W i N i + W j N j + D 2 ij (10) which increases for every fusion. D ij is the Euclidean distance between the centroids of clusters j and i; W i and W j are the within-group sum of squares, and N i and N j are the number of elements (gauges) in clusters i and j. Thus, the optimal configuration of clusters will be defined as that which is previous to a sharp increase in L ij. Figure 8 depicts the evolution of the similarity index with the number of merged clusters and Figure 9 shows the spatial distribution of clusters. According to the evolution of the similarity index, 20 clusters might be an optimal regionalization of the 75 gauges. Nevertheless, the number of clusters is excessive if one considers the number of PCs that replace the 24 original variables and the excessive partition of the pluviometric network. The other possibility, 15 clusters, is also discarded for similar reasons. Finally, a partition of 12 clusters is accepted, six of them being singulars (just one gauge). Thus, the network of 75 gauges is divided into six rather homogeneous areas and six singular recording points. Attempts with a lesser number of clusters generate very remarkable increases in L ij and, at the same time, singularities are not incorporated by the other clusters. A good example might be the configuration of seven clusters, associated with an evident break in the similarity index if a lower number of clusters is attempted. In spite of the fact that this clustering might be a good solution to the problem, a close look at the composition of the groups reveals that a big cluster is built by all the rain gauges except for the aforementioned six singularities (gauges), which remain isolated. This configuration is obviously unacceptable because it would produce useless results, comprising a set of singular points and a large cluster of the remaining gauges. Figure 9 shows the final retained configuration of clusters, including singular cases. In this figure, one can observe the relatively complex distribution, partially imposed by the orography and the proximity of the sea. Cluster 2 can be roughly assigned to the Central Basin and it is partially coincident with high loadings for FSC-3. Clusters 3 and 5 represent territories that correspond to the northern and southern Mediterranean coast respectively, and cluster 1 merges a part of the Pyrenees area, the eastern part of the Central Basin and a small part of the central Mediterranean coast. Besides these more extended clusters, clusters 7 and

15 CATALONIAN RAINFALL REGIME VARIABILITY 627 SIMILARITY INDEX NUMBER OF CLUSTERS Figure 8. Evolution of the similarity index of the AL algorithm for the last 30 fusions FRANCE MEDITERRANEAN SEA N Figure 9. Spatial distribution of clusters obtained after the application of the AL clustering algorithm 11 represent the eastern Pyrenees and areas on the eastern face of the Transversal range; finally, six singularities (clusters 4, 6, 8, 9, 10 and 12) are distributed throughout Catalonia. A close revision of series belonging to these singular gauges seems to suggests that clusters 6 and 10 should be discarded because their singularity could be caused by the low quality of the records. Nevertheless, singular clusters

16 628 X. LANA ET AL. 4, 8, 9 and 12 exhibit data of good quality and they must be accepted as representative of very local effects. From a general point of view, two blocks can be roughly distinguished after a close look at Figure 9. The first is constituted by clusters 1 and 2 together and several singularities, and it includes the western Pyrenees and Pre-Pyrenees, central Catalonia and the Ebro Valley. The second is constituted by a narrow fringe close to the Mediterranean coast and northeastern Catalonia, from the northern Mediterranean coast to the eastern Pyrenees and the Transversal range. This second block is constituted by clusters 3, 4, 5, 7 and 11 and several other singularities. Table II summarizes average ADRs, SDRs and CVs, the average number of rainy days per year (NRD) and their coefficient of variation (CVN) for 12 gauges, taking as the database the whole recording period. These gauges, to which the sequential Mann Kendall test and the spectral analysis will be applied later, have been chosen to represent each cluster derived from the PCA and AL procedure. Every singular cluster is represented by its singular gauge and every non-singular cluster is represented by a rain gauge without a significant lack of homogeneity and without missing data. Additionally, the ADRs and SDRs of every chosen gauge must be similar to the average values for each cluster. The average and standard deviation for each cluster are also included within parentheses in Table II. According to Table II, the variation range of all pluviometric variables is wide, with ADRs ranging from 5.9 to 19.6 mm/day, SDRs from 8.2 to 21.3 mm/day and CVs from to 208.8%. Besides all these features, which suggest spatial irregularity, the least irregular variable is NRD, which changes remarkably from one cluster to another, but exhibits very moderate coefficients of variation (regular behaviour over time) for all clusters considered. NRD ranges from 32 to 134, but the corresponding CVNs achieve very moderate percentages that never exceed 31%. The variety of daily pluviometric regimes is then manifested by the combination of high or low numbers of rainy days with remarkably different sets of ADRs, SDRs and CVs Mann Kendall sequential test Given that the spectral analyses will be applied to monthly series of ADR, SDR and CV of gauges that represent the different regional clusters derived from the PCA and AL algorithms, it is convenient to have Table II. Pluviometric variables of the 12 gauges that represent clusters derived from the PCA and AL procedures. NRD and CVN designate the average number of rainy days in a year and the coefficient of variation. Averaged values and standard deviation for every non-singular cluster are also included within parentheses Cluster Gauge ADR (mm/day) SDR (mm/day) CV (%) NRD (days/year) CVN (%) (9.8 ± 1.4) (12.3 ± 1.6) (126.9 ± 11.2) (76) (31.5) (7.8 ± 1.0) (11.1 ± 1.4) (142.5 ± 16.7) (71) (31.5) (8.8 ± 1.0) (13.9 ± 1.1) (159.8 ± 14.1) (81) (29.9) (10.3 ± 1.5) (15.1 ± 1.7) (146.8 ± 9.2) (56) (29.9) (12.4 ± 1.9) (16.8 ± 1.3) (136.8 ± 11.9) (101) (29.1) (10.9 ± 0.5) (14.9 ± 0.4) (136.5 ± 4.0) (82) (21.2)

17 CATALONIAN RAINFALL REGIME VARIABILITY 629 a more detailed description of trends and heterogeneities that may affect these specific data. Sharp changes in the series can be detected by means of the Mann Kendall sequential test (Sneyers, 1963, 1975; Goossens and Berger, 1986). In this case, according to the formulation introduced for the Mann Kendall test, a set of parameters u j (t) (j = 1,...,N) is computed for an increasing number of monthly ADRs, SDRs and CVs. Similarly, another set of similar parameters u j (t) is determined for an increasing number of elements of the retrograde series. The first set of parameters, designated C1, provides an initial indication of when a relevant change in the series occurs. In fact, with this single interpretation of curve C1, it is certain that change affects the series before the confidence level is exceeded. A more accurate interpretation is provided by the joint representation of curves C1 and C2 (the second set of parameters obtained for the retrograde series). If curves C1 and C2 cross at a point that lies within the confidence band given by ±α 0, then we can consider that either a significant heterogeneity or the beginning of a trend has been detected in the series. Figure 10 depicts an example of the monthly ADR, SDR and CV for gauge number 5, which represents cluster 4. The monthly ADR of this gauge is affected for the whole recording period by a negative trend of 1.89 mm/day over a decade, with a statistical certainty of 99%. Curve C1 suggests that a change occurred in the series prior to 1980, when curve C1 exceeds the ±1.96 band corresponding to α 0 = 5%. The point at which it crosses curve C2, within the ±1.96 band, marks the beginning of a significant alteration in the series in or around This fact is also corroborated by the mean value of monthly ADRs, which changes from 17.9 mm/day for the period to 12.2 mm/day for The case of monthly SDRs is characterized by 0.07 mm/day in over a decade, a trend that cannot be considered statistically significant, and a crossing point within the ±1.96 band in 1953, close to the beginning of the monthly series. Given that the normalization factors defined by Equations (5) and (6) are computed assuming that N is a large number, this crossing point at the beginning of the series might be doubtful. This possibility is reinforced by the fact that the mean values of monthly SDRs from 1950 to 1955 and from 1955 to 2000 are very similar: 7.1 mm/day and 6.9 mm/day respectively. This possible change in the series might, therefore, be considered unlikely. Finally, the monthly CVs have a positive time trend of 6.4% over a decade, with a statistical certainty of 99%. The Mann Kendall sequential test suggests a change in the series occurring in or around 1984, which is corroborated by the mean values of the monthly CVs, which change from 40.7% ( ) to 55.2% ( ). For gauges that represent clusters derived from the PCA and AL algorithms, Table III summarizes the years for which abrupt changes in the series or the beginning of time trends are detected according to the sequential test. The influence of missing data is minor in this case, as gauges have been chosen according to their recording continuity. Moreover, null ADRs and SDRs do not imply computational problems, and only the effects of the very few undefined CVs are very similar to those effects that derive from missing data. Only those cases that have crossing points within the ±1.96 band and show significant trends are considered. The first remarkable feature is the lack of statistically significant crossing points in the SDR series for all the gauges that represent the clusters. Secondly, the gauges for clusters 1, 4, 5, 8, 9, 11 and 12 show several abrupt changes, but only those linked to clusters 4, 5 and 9 are affected by a change in both ADR and CV. Additionally, the years in which these changes are detected do not coincide for the ADR and CV series and they vary over a long period from 1965 to Consequently, these features should be attributed to modifications in the settings of the rain gauges or the replacement of instrumentation, among other variations, and not to an overall change in the climate of Catalonia. The most striking discontinuities appear for the ADRs that represent cluster 9, which vary from 31.9 to 18.3 mm/day over a decade, and the CVs of clusters 5 and 9, which show increments of 36% and 24% respectively Spectral analyses, autocorrelation and cross-correlation Analyses based on power spectra and correlations are considered for the monthly ADR, SDR and CV series, but only for the rain gauges that represent the 12 clusters to which the Mann Kendall sequential test has been applied. In all cases, power spectra are obtained by applying the discrete Fourier transform (DFT) to the autocorrelation functions derived from the monthly series, taking a Hamming window as the smoothing function. Details concerning autocorrelation and DFT computations, as well as the removal of a possible shift