Spatial variability of precipitation in Spain. Nicola Cortesi, José Carlos Gonzalez- Hidalgo, Michele Brunetti & Martín de Luis

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1 Spatial variability of precipitation in Spain Nicola Cortesi, José Carlos Gonzalez- Hidalgo, Michele Brunetti & Martín de Luis Regional Environmental Change ISSN Reg Environ Change DOI /s

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3 Reg Environ Change DOI /s ORIGINAL ARTICLE Spatial variability of precipitation in Spain Nicola Cortesi José Carlos Gonzalez-Hidalgo Michele Brunetti Martín de Luis Received: 31 January 2012 / Accepted: 31 December 2012 Ó Springer-Verlag Berlin Heidelberg 2013 Abstract The spatial variability of annual and seasonal precipitation in the conterminous land of Spain has been evaluated by using correlation decay distance analysis (CDD). The CDD analysis essentially explores how the correlation between neighbouring stations varies according to distance. We analysed CDD independently for the decades , , , , and using only those stations with no missing values for each decade. To this end, 972, 1,174, 1,242, 773 and 695 complete series were used for each decade, respectively. In particular, for each station and decade, we calculated the threshold distance at which the common variance between target (i) and neighbour series is higher than 50 % (r 2 = 0.5) to evaluate whether current density of the climate data set captures the spatial variability of precipitation within the study area. Results indicate that, at an annual scale, neighbouring stations with 50 % of common variance are restricted on average to about 105 km, but this distance can vary from 28 to 251 km within the study area. The lowest variability is located to the SW and in winter, while the higher spatial variability is found to the north, in the Cantabrian area, and to the east, in the Mediterranean and Pyrenees, during summer. Our results suggest that current density of climate stations (those operating in 2005) N. Cortesi J. C. Gonzalez-Hidalgo (&) M. de Luis Department of Geography, University of Zaragoza, Zaragoza, Spain jcgh@unizar.es J. C. Gonzalez-Hidalgo M. de Luis Instituto Universitario de Ciencias Ambientales, Universidad de Zaragoza, Zaragoza, Spain M. Brunetti ISAC-CNR, Bologna, Italy is good enough to study precipitation variability at an annual scale for winter, spring and autumn, but not enough for summer. Keywords Precipitation Correlation decay distance Spatial variability Spain Introduction Water is the most relevant factor that constrains the development of natural systems and society in Mediterranean climate areas. It explains the interest of the last IPCC report (AR4) on precipitation analyses at regional and subregional scales in this area, where predictions from models suggest a decrease in precipitation at the end of the twentyfirst century (Christensen et al. 2007). However, due to the well-documented variability of precipitation around the Mediterranean basin, there is a high degree of uncertainty about present and future behaviour of precipitation (Lionello et al. 2006; Norrant and Douguedroit 2005). Spatial variability affects climate analyses, particularly interpolation, grid construction, model validation and quality control (Hofstra and New 2009; Caesar et al. 2006; New et al. 2000; Osborn and Hulme 1997). As a consequence, detailed sub-regional analyses are needed to capture as much as possible of such variability (Lana and Burgueno 2000; Huntington 2006; Trenberth et al. 2007). Among other approaches, the spatial variability of different climate variables has been evaluated by correlation decay distance (CDD), also called correlation length scale (CLS) or decorrelation length. The CDD analysis essentially explores how the correlation between neighbouring stations varies according to distance. Numerous analyses of CDD at different spatial and temporal domains have shown

4 N. Cortesi et al. that these spatial relationships between stations can vary at different latitudes, and between climate variables (Longley 1974; Dai et al. 1997; Jones et al. 1997; New et al. 2000; Caesar et al. 2006; Ha et al. 2007; Hofstra and New 2009). Osborn and Hulme (1997) and Hofstra and New (2009) reported lower CDD in the Mediterranean area compared to North West Europe, suggesting a SE-NW increasing pattern in CDD. Sub-regional analyses in Italy (Brunetti et al. 2006) and in the Alps (Auer et al. 2005) corroborated these findings. The Iberian Peninsula (IP) is a critical area for analysing the spatial variability of precipitation because of its marginal position in the Mediterranean basin (between the Atlantic Ocean and Mediterranean sea), the latitudinal gradient from north to south (c. 1,000 km), and the orography that differentiates the littoral and inland areas, as the mountain ranges are very close to the coastland plains, except in the west, and affect the patterns of rainfall (Rodriguez-Puebla et al. 1998; Sotillo et al. 2003; Martin- Vide 2004; Gonzalez-Hidalgo et al. 2011). However, to our knowledge, no research has been done in the Iberian Peninsula into the spatial variability of precipitation by means of CDD with high spatial detail so far. In this paper, we present an analysis of spatial correlation decay distance at an annual and seasonal scale in the conterminous land of Spain (IP). The aim of the paper is to quantify and discuss, at sub-regional level, the spatial variability of precipitation in the study area to identify the optimal threshold distance between neighbouring stations in support of several climate and climate-impact studies, such as reference series for quality control and homogeneity analyses, to reconstruct precipitation series from neighbours stations, and to estimate the optimal weighting distance function in grid and data interpolation, and many other tasks. Data and methods Original data source was the monthly precipitation data available from the Spanish Meteorological Office archives (AEMet). These archives store information from more than 9,000 climate stations. Original database (only stations with more than 10 years of data) was quality controlled and suspicious data were discarded and inhomogeneous series corrected in González-Hidalgo et al. (2011). The final data set consists of 6,821 original, homogeneous series without suspicious data. However, this data set was not useful for our purposes, due to different lengths, gaps and missing data still affecting the series; in fact, no series are complete for the whole study area during the whole period , and only 192 series are available with more of 99 % of data (please remember that these series were previously quality controlled and some original data may have been discarded; see González-Hidalgo et al. 2011). To avoid this problem, CDD values were calculated on a decade basis to exploit the availability of data as far as possible. Thus, we analysed CDD independently for the decades , , , and using only those stations with no missing values for each decade. To this end, 972, 1,174, 1,242, 773 and 695 complete series were used for each decade, respectively (Fig. 1). For each decade, CDD analysis was performed at a seasonal and annual scale following the common aggregation for winter (December January February), spring (March April May), summer (June July August) and autumn (September October November; de Luis et al. 2010). A correlation matrix was calculated for each decade at an annual and seasonal scale using monthly anomalies data (ratio between data and mean value for decade) to prevent the annual cycle from playing a dominant role in the CDD estimation; thus, no assumption about distribution was needed. For each station, decade and season, the common variance r 2 (using the squared of Pearson coefficient of correlation, r) was calculated between all neighbouring precipitation series. Following this, we modelled the relation between r 2 and distance according to the following Eq. (1): Log rij 2 ¼ b p ffiffiffiffiffi d ij ð1þ being rij 2 the common variance between target (i) and neighbouring series (j), and d ij the distance between them. Ordinary least squared approach was applied. The model was forced to be equal to 1 for d ij = 0, and the equation was estimated for each location, taking into account only the surrounding stations within a distance of 50 km, with a minimum of 5 stations required. In many previous researches, the selected correlation threshold between stations for reference series was [see classical examples in Alexandersson (1986), and Peterson and Easterling (1994), between many other], but also lower values around 0.4 were selected (Mitchell and Jones 2005) determining it by using the (r = 1/e = 0.37). Lower values than 0.7 or 0.8 also are usually selected for gridding (see, for example, Hofstra and New 2009; Ramos-Calzado et al. 2008). In this paper, we chose r 2 = 0.5 (i.e., Pearson correlation r *0.7), following previous research (Brunetti et al. 2006; Auer et al. 2005), in order to have a 50 % of explained variance, a more intuitive quantity for practical and at the same time a more restricted threshold considering that the high spatial variability characterizes the Iberian precipitation (at daily and monthly scale).

5 Spatial variability of precipitation in Spain Fig. 1 Iberian Peninsula elevation and distribution of complete available meteorological stations (without missing values) for each of the five decades analysed According these assumption, using Eq. (1), we calculated the threshold distance at which the common variance between target (i) and neighbouring series is higher than 50 % (r 2 = 0.5). If the estimated threshold distance was greater than 50 km, the radius was increased by 10 km until the threshold distance was lower than the radius itself (see an example in Fig. 2). In this way, all distance threshold values are not extrapolated, because they always fall within their maximum radius. As mentioned above, the seasonal and annual CDD values were interpolated using the Ordinary Kriging with a spherical variogram that relies on 15 neighbouring stations over conterminous land in Spain (Vicente and Saz 2002; Ninyerola et al. 2007) and finally converted on a regular 10 km grid for each decade. Next, the raster maps for the 5 decades were averaged to obtain the mean maps for the period for each season and for the year. Finally, we evaluated whether the current density of the climate database used is sufficiently high to capture spatial variability of precipitation within the study area. This was done by counting for each pixel the number of stations operating in the 2005 network (3,036 stations in total) within a radius equal to the CDD value of the pixel itself (at an annual and seasonal time scale). Fig. 2 Regression curves for two different stations within the same decade and season. Neighbour series used in the regression are showed with blue triangles (first location) and red circles (second location). Horizontal dotted line indicates a common correlation Pearson coefficient r of 0.7 (i.e., variance of 50 % between couples of stations). Distance threshold values are calculated at each intersection with the regression curves: blue station has a threshold distance of 81 km, red station of 405 km (colour figure online)

6 N. Cortesi et al. Results The mean value of CDD presents large spatial variability, both at annual and seasonal scales, over the Iberian Peninsula. The most striking overall results can be summarized as follows (see composite maps in Fig. 3). At an annual scale, CDD varies from 28 to 251 km in the study area, with an overall mean value of 105 km. These values greatly vary across a SW-NE gradient. Thus, in SW Iberian Peninsula, annual precipitation shows a lower spatial variability, with CDD being higher than 200 km. On the other hand, the highest spatial variability in precipitation is observed in the northern and Mediterranean coastland areas, and in some inland mountain regions, with CDD lower than 50 km (Fig. 3a). In general terms, the gradual variation from SW-NE is a clear exemplification of anisotropy, which is higher in the surrounding areas of mountain chain. The winter season has a CDD pattern similar to the annual one, but with stronger spatial gradients, and CDD values range from less than 30 km in northern and southeastern coastland areas to more than 400 km in a very large southwestern area (Fig. 3b). The overall mean CDD value is 162 km. Also, spring and autumn present a CDD pattern similar to the annual one, with overall mean CDD of 105 km (ranging from 24 to 264 km) and 120 km (ranging from 28 to 291 km), respectively (Fig. 3c, e). It is interesting to highlight the lower CDD values in inland mountain areas in spring (Fig. 3c). Summer differs from the other seasons and presents the highest spatial variability of precipitation over the whole study area. The highest variability in summer (i.e., lower CDD) is found in NE and eastern coastal areas, where stations closer than 20 km have less than 50 % of common variance, while the lower summer variability is again observed in SW, but also in this area, summer CDD values are very low (i.e., high spatial variability) if we compare with the other seasons (CDD being always lower than 140 km; Fig. 3d). To evaluate how representative the present precipitation station database is, we calculated, for each pixel, the number of AEMet stations operating in 2005 within a distance equal to its CDD value. The results are shown in Fig. 4. At an annual scale (Fig. 4a), on average, 181 individual stations are available within CDD. However, this number greatly varies in space from the SW (where more than 500 stations are closer than CDD) to the Pyrenees (where available stations decrease to less than 20). During winter, spring and autumn, the 5 % of study area with the lowest number of stations available within CDD always includes at least 62 stations (Fig. 4b, c, e), while in summer, this Annual (a) Winter (b) Spring (c) Summer (d) Autumn (e) Fig. 3 Averaged threshold distance values (CDD) at which the common variance between target and neighbouring series is higher than 50 % for at an annual and seasonal time scale. In text a year, b winter, c spring, d summer, e autumn

7 Spatial variability of precipitation in Spain Fig. 4 Spatial density of the station operating in year The value in each pixel is equal to the number of stations existing in 2005 whose distance from the pixel is equal or inferior to the CDD value drops to 5 stations, as the spatial variability of precipitation increases, particularly in the southeastern region and for large area of Pyrenees (Fig. 4d). In summer, there are also some areas (\1 % of study area) with no stations within CDD. Discussion Precipitation in the IP is a variable characterized by strong spatial and temporal variability (see Romero et al. 1998; Martin-Vide 2004; Morata et al. 2006; Valero et al. 2009; de Luis et al. 2010; González-Hidalgo et al. 2011, among many others). Nevertheless, precipitation variability in the IP has rarely been quantified in detail at a sub-regional scale, because of the lack of observations at an adequately high spatial density. The recently developed MOPREDAS database has helped to solve this problem by allowing such variability to be explored (González-Hidalgo et al. 2011). CDD is a comprehensive quantity in the study of precipitation variability both at regional and sub-regional scales. In a global analyses, Dai et al. (1997) have found that CDD averaged by zones for annual precipitation were lower in the northern hemisphere than the southern and varied between 200 km from latitude 0 30 N to 400 km in the temperate band N, while Mitchell and Jones (2005) suggested that stations for gathering precipitation data should not be further apart than 400 km. At a regional scale, Brunetti et al. (2006) reported for Italy that, on average, it is difficult to have more than 50 % of common variance in precipitation for pairs of stations more than 100 km apart, and Auer et al. (2005) present similar results for Alpine regions. These values are consistent with those obtained here for the IP, where, for annual precipitation, the mean CDD value is about 150 km. However, this distance varies greatly across the IP, and CDD considerably lower than 100 km can be observed in the Mediterranean fringe, to the north in the Cantabrian coastland and to the northeast in the Ebro Valley and Pyrenees. These values suggest higher spatial variability of precipitation in the study area. We also observed a large seasonal difference in the spatial variability of precipitation patterns. Winter represents the season where, in general, spatial variability of precipitation is lower and distance thresholds for 95 % of the territory vary between 21 and 424 km. On the contrary, spatial variability of precipitation is much higher in summer, when distance thresholds for 95 % of the territory vary between 7 and 98 km. Similar results were observed at a global scale by Osborn and Hulme (1997) and New

8 N. Cortesi et al. et al. (2000), who detected a lower spatial variability in winter while summer precipitation was higher. The same seasonal pattern was observed at a regional scale by Longley (1974) on the Canadian Prairies; in Korea by Ha et al. (2007), who found values of CDD of 100 km for January and 50 km for July; in Florida by Baigorria et al. (2007), who suggested differences in CDD with higher values (600 km) in winter precipitation months and lower distances during summer (200 km), etc. Thus, a weaker relationship between pairs of stations seems to be more typical in summer than winter, which was also noticed by Caesar et al. (2006) and Alexander et al. (2006) in other global analyses suggesting that the scale of precipitationcausing disturbances is larger in winter (frontal systems) than in summer. In general terms, spatial variability of precipitation in the IP is lower in the southwest and during winter season, and three reasons could be argued for this. It is well known that spatial distribution of precipitation in winter in the IP is mostly caused by frontal systems that enter from the Atlantic Ocean, associated with a positive phase of NAO (see Paredes et al. 2006). This fact and the spatial distribution of relief with no barriers to the west give rise to a more regular winter spatial distribution of precipitation in these areas than to the east and north (however, see below) and more regular than during the other seasons; in fact, the western and southwestern areas of the IP have a winter seasonal rainfall regime (de Luis et al. 2010). On the other hand, the spatial variability of precipitation is higher to the east and north, where spring and autumn are the main precipitation seasons (de Luis et al. 2010). Thus, the Cantabrian coastland in the north and Mediterranean fringe and the Pyrenees mountains in the east are affected by more local atmospheric patterns such as WeMOI (Martin-Vide and Lopez-Bustins 2006), in which the effect of mountain chains along the coast can cause high spatial variability in. The greatest spatial differences can be observed in transition areas where are located the main mountain chains (compare Figs. 1a and 3a e), a clear demonstration of anisotropy originated by mountain barriers (not analysed in this paper). Within the framework of recommendations made by AR4 on sub-regional analysis, our results can be successfully applied to defining the minimum station density in databases required for references series (quality control and reconstruction), grid construction and model validation, and to describe the spatial and temporal variability of precipitation in Mediterranean climates. The reference series constitutes a key point in climate research (Begert et al. 2005), and in order to create them, there must be a compromise between a minimum number of neighbouring stations, to prevent inhomogeneity entering the reference series, and a maximum distance threshold, to ensure that only genuine correlation with distant stations is included (Mitchell and Jones 2005; Auer et al. 2005; Brunetti et al. 2006). However, no clear consensus has been achieved abut such topics (see different opinion in Rhoades and Salinger 1993; Peterson and Easterling 1994; Keiser and Griffiths 1997; González-Hidalgo et al. 2011, between many others). Further analyses on such topic would be useful for continuous advance on precipitation spatial variability knowledge in Iberian Peninsula. Conclusions We have detected high spatial variations of precipitation CDD in the IP. At an annual scale, neighbouring stations with 50 % of common variance are restricted on average to about 105 km, but this distance can vary from 28 to 251 km within the study area. The lowest variability (i.e., higher distance) is located in the SW and in winter, probably linked to higher influence of large-scale precipitation processes (such as NAO). On the other hand, the highest spatial variability (lower distance) is found to the north, in the Cantabrian area, and to the east in the Mediterranean and Pyrenees, particularly during summer. A reasonable explanation is that these areas are not under NAO influences, and more local atmospheric patterns could be acting together with mountain barriers parallel to the coast. If we take these distances as the threshold for representing spatial variability of precipitation in the study area, then current available station density is good enough to precipitation analyses (references series, grids, interpolation, model validation, etc.) at an annual scale for winter, spring and autumn, but not enough for summer. Acknowledgments The authors acknowledge the financial support given by Gobierno de España, and FEDER Research Project CGL C02-01, CGL C02-01, and Gobierno Regional de Aragón DGA, Grupo de Investigación Consolidado Clima, Agua, Cambio Global y Sistemas Naturales (BOA 69, ). Nicola Cortesi is FPI-PhD student supported by Ministerio de Cultura (Spanish Goverment). References Alexander L, Zhang X, Peterson T et al (2006) Global observed changes in daily climate extremes of temperature and precipitation. J Geophys Res 111:DO5109 Alexandersson H (1986) A homogeneity test applied to precipitation data. 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