Statistical downscaling model based on canonical correlation analysis for winter extreme precipitation events in the Emilia-Romagna region

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1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 28: (2008) Published online 18 July 2007 in Wiley InterScience ( Statistical downscaling model based on canonical correlation analysis for winter extreme precipitation events in the Emilia-Romagna region A. Busuioc, a R. Tomozeiu b * and C. Cacciamani b a National Meteorological Administration of Bucharest, Romania b ARPA-SIM, Bologna, Italy ABSTRACT: Optimum statistical downscaling models for three winter precipitation indices in the Emilia-Romagna region, especially related to extreme events, were investigated. For this purpose, the indices referring to the number of events exceeding the long-term 90 percentile of rainy days, simple daily intensity and maximum number of consecutive dry days were calculated as spatial averages over homogeneous sub-regions identified by the cluster analysis. The statistical downscaling model (SDM) based on the canonical correlation analysis (CCA) was used as downscaling procedure. The CCA was also used to understand the large-/regional-scale mechanisms controlling precipitation variability across the analysed area, especially with respect to extreme events. The dynamic (mean sea-level pressure-slp) and thermodynamic (potential instability-δq and specific humidity-sh) variables were considered as predictors (either individually or together). The large-scale SLP can be considered a good predictor for all sub-regions in the dry index case and for two sub-regions in the case of the other two indices, showing the importance of dynamical forcing in these cases. Potential instability is the best predictor for the highest mountain region in the case of heavy rainfall frequency, when it can be considered as a single predictor. The combination of dynamic and thermodynamic predictors improves the SDM s skill for all sub-regions in the dry index case and for some sub-regions in the simple daily intensity index case. The selected SDMs are stable in time only in terms of correlation coefficient for all sub-regions for which they are skilful and only for some sub-regions in terms of explained variance. The reasons are linked to the changes in the atmospheric circulation patterns influencing the local rainfall variability in Emilia-Romagna as well as the differences in temporal variability over some sub-regions and sub-intervals. It was concluded that the average skill over an ensemble of the most skilful and stable SDMs for each region/sub-interval gives more consistent results. Copyright 2007 Royal Meteorological Society KEY WORDS extreme events; cluster analysis; canonical correlation analysis; statistical downscaling Received 15 June 2005; Revised 7 February 2007; Accepted 17 March Introduction The extreme climate events have a high impact on the environment and human activities. This is one main reason for paying great attention to the study of changes in frequency, intensity or magnitude of such events in the past and for estimating whether they will occur more frequently in the future. Coupled atmosphere ocean global climate models (AOGCMs) are the primary tool for simulating the global climate system and providing reliable projections of climate change in the future perturbed climate under various greenhouse gas emission scenarios. Because of their still coarse horizontal resolutions, against the needs of the impact studies, two main approaches have been developed to obtain high-resolution climate change scenarios: dynamical downscaling given by the regional * Correspondence to: R. Tomozeiu, ARPA - Servizio Meteorologico Regionale 40122, Viale Silvani 6, Bologna, Italia. rtomozeiu@arpa.emr.it climate models (e.g. Giorgi et al., 2001) and statistical downscaling models (SDMs). Both techniques have strengths and weaknesses. The conclusion from the most recent studies achieved in the statistical and regional dynamical downscaling of extremes (STARDEX) project ( that both statistical and dynamical downscaling techniques are comparable for simulating current climate (Schmidli et al., 2006; Haylock et al., 2006) is in agreement with the IPCC TAR (IPCC, 2001). Generally, the extreme events are defined as statistical indices by processing daily time series, being mostly calculated on a seasonal scale (see STARDEX project). This fact leads to the possibility of using two ways to downscale these indices: a direct technique in which the seasonal indices are directly downscaled and an indirect one in which daily time series are firstly generated and then the seasonal extreme indices are calculated from these. Comparing the merits of the two techniques, as well as the merits of about 20 SDMs, Goodess et al. Copyright 2007 Royal Meteorological Society

2 450 A. BUSUIOC ET AL. (2006) concluded that it is difficult to define the best method. The performance of SDMs varies by index, season and station, the last one prevailing. A major recommendation resulting from the STARDEX project is to use a range of better statistical downscaling methods for elaborating scenarios on extremes, as it was recommended to use the ensembles of GCMs/RCMs in order to reflect a wider range of uncertainties. This technique is also approached in this paper but only for ensembles based on the same method using various predictors (see Section 3 for details). Many different types of statistical downscaling models are available, which can be grouped into two basic models: linear and non-linear. Linear models refer to simple/multiple regressions (Johansson and Chen, 2003; Hanssen-Bauer et al., 2003; Matulla et al., 2003; Huth, 2004), models based on canonical correlation analysis (CCA) (von Storch et al., 1993; Busuioc et al., 2001, 2006; Benestad, 2002; Chen and Chen, 2003; Huth, 2004; Xoplaky et al., 2004) or singular-value decompositions (e.g. Huth, 2002; Widmann et al., 2003). Nonlinear models employ the weather classification/analogue method (Zorita and von Storch, 1999; Palutikof et al., 2002), neural networks/self-organizing maps (e.g. Trigo and Palutikof, 2001; Cavazos et al., 2002; Hewitson and Crane, 2002) and weather generators/stochastic models (e.g.huth et al., 2001; Palutikof et al., 2002; Busuioc and von Storch, 2003; Katz et al., 2003; Wilby et al., 2003; Buishand et al., 2004). These methods are generally used for downscaling the extreme indices as well, being applied in the two ways presented above. Each statistical downscaling technique has advantages and disadvantages (Wilby et al., 2004). In general, conclusions from comparing different statistical downscaling techniques (Buishand et al., 2004; Huth, 2004; Diaz-Nieto and Wilby, 2005; Goodess et al., 2006) depend on regions and criteria of comparison. Regarding the extremes, Haylock et al. (2006) found that the statistical downscaling models based on non-linear artificial neural networks are the best at modelling the inter-annual variability of heavy precipitation indices but underestimate extremes. Generally, the non-linear models are applied for daily data, and they are more appropriate to study extreme events (e.g. Huth et al., 2001; Busuioc and von Storch, 2003). Nevertheless, some indices describing extreme events, such as frequency of exceeding a threshold, are successfully modelled by linear models (e.g. Beckmann and Buishand, 2002; Wang et al., 2004). Such models were also used in this study. In this paper, a direct method based on CCA was used to develop statistical downscaling models for regional precipitation indices (especially referring to extreme events) across the Emilia-Romagna region, situated in northern Italy. It is supposed that the local random weather fluctuation leading to isolated high amplitude extreme events is reduced by calculating the regional rainfall indices. This was the main reason for using them here as predictands. Among other linear SDMs, those based on CCA lead to a physical interpretation of the mechanism controlling regional climate variability (e.g. von Storch et al., 1993; Heyen et al., 1996; Busuioc et al., 2001; Tomozeiu et al., 2006) by selecting pairs of optimally correlated patterns between predictands and predictors. The large-scale dynamical forcing represented by mean sea-level pressure (SLP) and the regional-scale thermodynamic forcing represented by specific humidity (SH) and potential instability (δq) were used as predictors. The strong influence of these predictor variables on the regional climate considered in this study, and especially on the thunderstorm activity, was presented in previous papers (Cacciamani et al., 1994,1995). All these studies found spatial circulation patterns controlling the climatology of precipitation in the Po Valley located within Emilia-Romagna through composite maps. In this work, the large-scale circulation patterns were objectively selected through the CCA method. A similar method was used by Xoplaky et al. (2004) to find the connection between precipitation variability over the wet season across the entire Mediterranean basin and the large-scale circulation. In the present study, the time series associated with selected CCA patterns were then used to build a statistical model estimating regional anomalies of extreme precipitation events from large-scale predictor anomalies. This is a first step in creating regional climate change scenarios for extreme precipitation events across the analysed area and another goal of the paper. More details are presented in Section 2. The results are summarized in Section 3 and the conclusions of this study are presented in Section Data and methods 2.1. Data The time series of the observed daily winter precipitation at 41 weather stations covering the Emilia-Romagna region over the period were used to create the predictands in this study. Figure 1 shows the map of Italy with the position of the studied area Emilia-Romagna. The location of stations, including the orographic characteristics of the region, is also presented. The dynamic (mean SLP) and thermodynamic (δq and SH) variables provided by the NCEP reanalysis data set (Kalnay et al., 1996) were considered as predictors to build the statistical downscaling models. The SLP area covers the Atlantic European domain between 35 W 35 E and 30 N 60 N, while the δq/sh covers a smaller area from northern and central Italy between 42.5 N 47.5 N and 7.5 E 12.5 E. The Emilia-Romagna region, lying in northern Italy, in the Po River Valley, is surrounded by the Apennines to the south and the Adriatic Sea to the east. The climate of this region is characterized by a high spatial variability due to both mountain and sea influence. Cacciamani et al. (1994) have shown that maximum precipitation amounts during the cold season are recorded in the Apennines chain and precipitation decreases from north-east to the plain.

3 STATISTICAL DOWNSCALING MODEL BASED ON CANONICAL 451 Figure 1. Map of Italy indicating the position of Emilia-Romagna. The stations (marked by circle) used in this study and the orography of Emilia-Romagna are also presented (shaded area) Methods of analysis Three indices providing a complex description of rainfall in the analysed area were computed from the daily precipitation time series. These indices, studied in the STARDEX project, were mainly focused on extreme rainfall events: the number of events exceeding the long-term 90 percentile of rainy days abbreviated frpp90, simple daily intensity (rain per rainy day) abbreviated sdi and maximum number of consecutive dry days abbreviated dry. The 90th percentile has been calculated only for those days with precipitation above 1 mm (rainy days) and at least 10 rainy days in the season, otherwise the percentile value appears as missing. All indices were calculated for every winter and for each station with less than 20% of data missing. A hierarchical cluster analysis has been applied to the station index time series (DJF) in order to reduce local random weather fluctuations at single stations. This fact makes the identification of particular large-scale circulation patterns strongly connected with the occurrence of winter precipitation extremes easier. Two clustering methods have been applied in order to check the robustness of results: complete linkage and Ward s methods (Wilks, 1995). The number of clusters has been determined by analysing the plotted distances between merged clusters as a function of the analysis step. When a similar cluster has been merged early in the process, these distances are small, and they increase relatively slowly, step by step. The point where distances between merged clusters jump significantly represents the point where the clustering process is stopped, just before these distances become large. In our case, the clusters provided by both methods are similar. Therefore, in the following we present the results provided by Ward s method. This method aims at minimizing the sum of squares of any two (hypothetical) clusters that can be formed at each step. Ward s method is regarded as being very efficient. However, it tends to create small-size clusters. Through the cluster analysis, four or five homogeneous sub-regions were identified for each precipitation index and spatial indices associated with these sub-regions were computed as spatial average of the station index time series covering the respective areas. In order to show the advantages and disadvantages of using spatial precipitation indices instead of using station indices, as an example, for the Z5-frpp90 index, both cases were analysed. Figure 2(a), (b), (c) shows the homogeneous subregions identified for the three precipitation indices. Using the cluster analysis, four areas were identified for the simple daily intensity (abbreviation Z4-sdi) and maximum number of consecutive dry days (abbreviation Z4-dry), while for the number of events exceeding the long-term 90th percentile five areas (abbreviation Z5-frpp90) were revealed. Generally, the subregions identified through the cluster analysis (mountain, coastal area, plain Po-Valley and sub-mountain) correspond to the main climate types characterizing Emilia- Romagna (Cacciamani et al., 1994; Quadrelli et al., 2001; Tomozeiu et al., 2002). The statistical downscaling model used in this study is based on the CCA and is similar to that presented by von Storch et al. (1993), Heyen et al. (1996), Busuioc et al. (1999, 2001, 2006). CCA finds the optimum linear combination of two multidimensional vectors (predictands and predictors) and selects pairs of patterns of spatial- and temporal-dependent variables so as their

4 452 A. BUSUIOC ET AL. (a) follows: δq = Q e500 Q e850 where Q eh is the equivalent potential temperature at level h, derived from (b) (c) Figure 2. Sub-regions for the extreme rainfall indices: (a) Z5-frpp90, (b) Z4-dry, (c) Z4-sdi. coefficient time series are optimally correlated (Barnett and Preisendorfer, 1987). Therefore, by construction, the CCA allows a physical interpretation of the mechanism controlling regional climate variability, this being the main reason why we selected this method for the present analysis. Before CCA, the predictors and predictands are projected onto their empirical orthogonal functions (EOFs) to eliminate unwanted noise (small-scale features) and to reduce the dimension of the data space. The input data in EOF analysis are the anomalies of spatial indices, calculated as deviations from the longterm mean. Those EOFs explaining most of the total observed variance are retained for CCA. A subset of CCA pairs is then used in a multivariate linear model (SDM) to estimate the predictand anomalies from the predictor anomalies. Large-scale SLP and regional moisture parameters (SH and δq index) were considered as predictors and the three regional indices presented above were used as predictands. A specific humidity index was calculated as average over the levels of 1000, 950, 850 and 700 mb. The potential instability index was computed using the procedure presented by Cacciamani et al. (1995) as LR S Q e = Qe C p T L = (J/kg) C p = dry air specific heat at constant pressure = 1004 J/(deg kg) R S = specific humidity (kg/kg) T = temperature at level h ( K), Q = potential temperature at level h ( K) The SDM was built separately for each predictor field as well as for various combinations of them. The anomalies used in combined predictors were standardized by dividing by their standard deviation. In this case, the EOF analysis is applied to the vector containing the combination of standardized predictor anomalies. The optimum SDM for each rainfall index is selected so that the skill of the model, expressed as correlation coefficient between observed and reconstructed values for the independent data set, should be maximum. An alternative measure of the skill (EV) is the variance (var) explained by the reconstructed values (Y ) as a fraction from total variance of observed values (Y ), as follows: EV = 1 (var(y Y )/var(y )) It should be noted that the model s skill is strongly dependent on the number of EOFs used in CCA and the number of CCA pairs used in SDM. An optimum SDM, as presented above, was selected from a hierarchy of SDMs considering various combinations of numbers of EOFs and CCA patterns for each predictor data set, following the technique presented by Busuioc et al. (1999). Evaluating SDM s skill is a crucial element of any downscaling application. One simple way to avoid the artificial skill effect is to divide the available data set into learning and validation data sets; the model is fitted to the learning data and tested on the independent data included in the validation subset (von Storch and Zwiers, 1999; Busuioc et al., 2001; Trigo and Palutikof, 2001; Hanssen-Bauer et al., 2003; Wilby et al., 2004; Goodess et al., 2006; Tomozeiu et al., 2006). This technique allows testing SDM s performance for various climate regimes. It has also been used in this study. A disadvantage of this method is that it is based on the availability of long-enough data sets. To analyse SDM s stability over the calibration/validation periods, the whole interval of was divided into two sub-intervals, namely and , which were alternatively considered as fitting and validation intervals.

5 STATISTICAL DOWNSCALING MODEL BASED ON CANONICAL 453 The alternative way of cross validation (e.g. von Storch and Zwiers, 1999; Huth, 2002; Xoplaky et al., 2004) allows using the complete interval of the available data set for validation. However, some cautions are necessary in order to ensure that the information used to fit the model in each cross-validation step is completely independent of the information withheld for validation data, which is more difficult than it sounds, especially when the validation subsets are small (e.g. size 1), as they often are (for details see von Storch and Zwiers, 1999). The time series in almost all statistical techniques are assumed to be independent and identically distributed (von Storch and Zwiers, 1999). This is not usually the case with climatological time series, which often exhibit a trend on decadal or longer time scales. This problem is solved by removing the linear trend before building the statistical model (e.g. Barnett and Preisendorfer, 1987); such a technique is also used in this study. The SDM is built using de-trended data from the fitting interval and is then applied to predictor s anomalies from the validation interval. Model s skill for the validation interval is calculated after removing the linear trend from observed and reconstructed data in order to avoid an artificial enhancement of the correlation (von Storch and Zwiers, 1999). The SDMs are considered skilful when the correlation coefficients are statistically significant, reaching at least 10% of the confidence level. 3. Results As discussed in Section 2.2, the SDM performance depends on the number of EOFs/CCAs selected to build the model. In a previous paper (Busuioc et al., 1999), the combination of EOFs and CCAs was selected so as to maximize the correlation coefficient between the spatial averages of observed and reconstructed anomalies. Obviously, the SDM selected in this way for the entire country (corresponding to an optimum EOFs/CCAs combination) does not imply a high skill for all stations. Busuioc et al. (2006) proposed an alternative technique to optimize the SDM skill as follows. Firstly, an SDM hierarchy is obtained by using several combinations of EOFs/CCAs for various predictors. Secondly, the SDM of highest performance is selected separately for each station rather than considering the overall performance for the entire set of stations. A similar technique, repeated for each sub-interval and various predictors (SLP alone, SH alone, δq alone and SLP combined with SH or δq), is used in this study. Therefore, for each predictand, an SDM ensemble composed of SDMs with maximum skill for each sub-region and each sub-interval was selected. The results on the SDM skill for various predictors are discussed in Section 3.1. In order to understand the reasons leading to the results presented in Section 3.1, the mechanisms controlling the variability of regional rainfall indices in Emilia-Romagna are presented in Section SDM s skill for various predictors SLP predictor Regarding the SLP predictor, the EOF/CCA combinations leading to the most skilful SDMs for all regional rainfall indices (Z5-frpp90, Z4-dry, Z4-sdi) are presented in Table I (see more details below). The SDM skill (expressed as correlation coefficient and explained variance) corresponding to these EOF/CCA combinations was computed for each of the two sub-intervals ( and ) considered as validation intervals. Therefore, the first value from columns 4 to 8 in Table I refers to the SDM skill (correlation coefficient/explained variance) calculated for the first subinterval ( ) as an independent data set (validation interval), with SDM fitted over the second subinterval, (fitting interval). For the second value, the situation is reversed. SDM skills for each sub-region significant at the 5% level are marked in bold face and those significant at the 10% level are marked in italic. Only the positive values of variance and correlation coefficients are shown. More combinations of SLP predictors are given only for the Z5-frpp90 index. The average skill derived over an ensemble of stable SDMs with highest skill for each sub-region/sub-interval is also shown, together with the numbers of ensemble members (in brackets) and predictors for which the SDM ensemble was considered. Analysing the results displayed in Table I shows that the best results were obtained for the Z4-dry index. In this case, regarding the correlation coefficient, the SDM skill is stable for all sub-regions, while in terms of explained variance the SDM skill is stable only for sub-region 2 (small mountain area in south-east Emilia- Romagna). For the other regions, the most skilful results were obtained with SDM fitted over the first interval (the second value from columns 4 to 7). Comparing the patterns of the first two CCA pairs derived for the two sub-intervals, it was found that they are similar (as presented below). This result leads to the idea that the SDM skill should be similar over the two subintervals. In order to find the reason for this result, the characteristics of temporal variability of regional index anomalies were analysed. Figure 3 presents the observed and reconstructed anomalies of extreme precipitation indices derived from the most skilful combination of predictors. As could be noted for sub-region 2, the very large dry-index anomalies (peaks) are almost uniformly distributed over the entire period analysed (Figure 3(b), left), meaning that temporal variability over the two sub-intervals is almost similar. For other sub-regions, the situation is different. As an example, for sub-region 1 (Figure 3(b), right), two isolated peaks are recorded only in the period (corresponding to years 1989 and 1993), affecting the SDM calibration over this period (Wilks, 1995) and leading to negative explained variance (e.g. error variance is greater than observed variance). They induce an overestimated linear trend. However, it can be noted that the observed trend is quite

6 454 A. BUSUIOC ET AL. Table I. Skill of the statistical downscaling model for winter precipitation indices across Emilia-Romagna over two sub-intervals ( first value, second value) considered as an independent data set using several predictors. Significant correlation coefficients at levels 5 and 10% are in bold and italic, respectively. Only the positive values of variance and correlation coefficients are shown, while stands for values that are not shown. The average skill (shaded) derived over an ensemble of stable SDMs with highest skill for each sub-region/sub-interval is also shown, together with the numbers of ensemble members (in brackets) and predictors for which the SDM ensemble was considered. Predictand Predictor No. of EOFs Skill (correlation 100/explained variance 100) (predictor+ predictand), CCAs Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 Z5-frpp90 SLP 5 + 4, 4 55/30, 33/ 49/21, 37/ 7/, 19/ 11/, 43/ 13/, 36/ 4 + 4, 4 23/3, 27/ 14/0, 36/ 8/, 19/ 6/, 46/6 17/, 41/ 5 + 2, 2 39/15, 37/ 52/25, 33/ 19/, 17/ 15/, 34/ 31/9, 45/ δq 3 + 3, 2 64/40, 53/18 32/8, 15/ 3 + 3, 3 47/21, 66/33 13/2, 24/- SLP + δq 5 + 4, 4 59/31, 40/ 50/24, 34/ Ensemble average (no. of members = 2), δq 60/33, 61/28 36/6, 21/ Ensemble average(no. of members = 3), δq, 60/41, 57/16 52/15, 28/ SLP + δq Z4-dry SLP 6 + 2, 2 53/, 67/42 52/16, 67/43 53/, 59/34 50/, 62/36 SLP + SH 5 + 2, 2 54/, 72/48 56/25, 71/47 55/, 67/42 53/, 69/45 SLP + Q 5 + 3, 1 66/2, 71/46 62/37, 67/38 62/, 60/36 64/6, 59/35 Ensemble average (no. of members = 2), SLP + SH, 61/, 71/47 60/33, 69/43 59/, 64/40 60/, 65/40 SLP+Q Z4-sdi SLP 5 + 2, 2 42/6, 55/30 30/, 41/7, 45/13 SLP + SH 6 + 2, 1, 37/5 46/10, 47/22 38/, 48/23, 31/2 SLP + δq 5 + 2, 1, 37/1 45/20, 46/21 38 /, 33/9 47/18, 29/2 Ensemble average (no. of members = 3), SLP, 47/17, 53/27 37/, 27/7 49/24, 37/8 SLP + SH, SLP+Q

7 STATISTICAL DOWNSCALING MODEL BASED ON CANONICAL 455 Figure 3. Observed and reconstructed anomalies of the regional extreme precipitation indices in Emilia-Romagna, obtained from the most skilful combination of predictors: (a) Z5-frpp90, (b) Z4-dry, (c) Z4-sdi. For each index, an example of high SDM skill region (left column) and of low skill region (right column) is shown. The reconstructed values are presented for the two sub-intervals ( and ) considered as independent data sets (e.g. the index anomalies for one sub-interval are derived with the SDM fitted over the other sub-interval for de-trended data). well reproduced by reconstructed Z4-dry anomalies (even some large anomalies) for the stable SDM (Figure 3(b), left). Normally, these peaks, similar to outlying points, should be excluded from the analysis (von Storch and Zwiers, 1999), but if the problem is solved for one index it is not sure that it will also be solved for the others. For instance, when years 1989 and 1993 were excluded from the analysis performed for the second interval and SDM was fitted for the rest of the 18 years, the SDM skill over the first interval, considered as validation interval, was significantly improved (especially in terms of explained variance) only for sub-region 1: explained variance 31% against negative values for the previous case and correlation coefficient 0.55 against For the other sub-regions, a lower SDM skill was recorded. When the SDM developed in this study is applied to climate change scenarios, the problem of isolated peaks could be seriously taken into consideration for the fitting interval. Building SDMs over longer periods could partially solve this problem. For other indices, the SLP predictor leads to skilful SDMs only for some sub-regions. Thus, for the Z5- frpp90 index, a skilful and stable SDM (in terms of correlation coefficient) was obtained only for the two mountain sub-regions (zones 1 and 2 Table I), while as far as the explained variance is concerned only the model

8 456 A. BUSUIOC ET AL. fitted over the second sub-interval is skilful for these two sub-regions. The best EOF/CCA combination consists of the first five SLP EOFs and first four Z5-frpp90 used in CCA and first four CCAs used to construct SDM, hereinafter referred to as the (5 + 4, 4) combination. For sub-regions 4 and 5, a skilful SDM (in terms of correlation coefficient) was found only with a model fitted over the first sub-interval for the (4 + 4, 4) and (5 + 2, 2) combinations, respectively. For sub-region 3, no skilful SDM was found (Table I). In the case of the Z4-sdi index, the most skilful SDM was obtained for sub-regions 2 and 4usingthe(5+ 2, 2) combination. However, explained variance was low, excepting for sub-region 2 (second sub-interval). To show the advantage of using regional indices instead of individual station indices, for instance, the corresponding SDM for the frpp90 index at 41 meteorological stations over the sub-interval was also carried out. The SDM skill at each station for two EOF/CCA combinations, namely (4 + 5, 4) and (6 + 10, 6), is presented in Figure 4(a) and (b) respectively. As it can be noticed, the areas of significant skill for the two SDM versions are different. For other EOFs/CCAs combinations (not shown), another spatial distribution of significant SDM skill was obtained. Therefore, on station level, it was more difficult to draw a clear conclusion about the most skillful SDM, as it was a case of clear conclusions from regional indices. This result shows the advantage of using regional indices against individual station indices. The disadvantage is that the information that some impact studies require is not available on station scale. This drawback could be avoided by carrying out separate SDMs for stations corresponding to each subregion Humidity predictors In order to improve the statistical model s performance, δq and SH have been added as predictors. These predictors have been tested separately (results are presented in this section) or combined with SLP (results can be seen in the following section). The results are included in Table I. As can be noticed, a significant improvement of the SDM skill over both sub-intervals was found only for the highest mountain area of the Z5-frpp90 index (sub-region 1) using δq as predictor. The combination (3 + 3, 2) gives the highest SDM skill for the first sub-interval and the combination (3 + 3, 3) gives the highest SDM skill for the second sub-interval. Therefore, an ensemble composed of the two SDM versions has been considered, and an ensemble mean of the reconstructed anomalies has been calculated over the two subintervals. The corresponding skill for this ensemble mean is improved, especially in terms of stability over the two sub-intervals. For the other two indices, no improvement in SDM skill was found when only δq wasusedaspredictor. It could be concluded that, for the mountain area, the instability factor is much more important than surface Figure 4. SDM s skill (expressed as correlation coefficient between observed and reconstructed anomalies) calculated for the frpp90 index at the 41 stations, considering various combinations of SLP/frpp90 EOFs in CCA and several numbers of CCAs retained in the downscaling model: 4 + 5, 4 (a) and , 6 (b). atmospheric circulation only for the frequency of heavy rainfall. For other sub-regions and indices, the dynamical factor is dominant in the winter season. The reason could be that thermodynamic factors are likely to be determined to a great extent by large-scale circulation Combined predictors Considering the combined vector of standardized SLP and δq/sh fields (Table I) as predictor, an improvement in SDM performance is obtained for all sub-regions and both sub-intervals (Z4-dry), while in the Z4-sdi case it is obtained only for one of the two sub-intervals and across the same sub-regions for which SDM is skilful using SLP predictor (Table I). The combination between SLP and SH is the best predictor for the Z4-dry index (second sub-interval) using the combination (5 + 2, 2) and for Z4- sdi (first subinterval, sub-region 4) using the combination (6 + 2, 1). The combination between SLP and δq is the best predictor for the first sub-interval (Z4-dry) using the (5 + 3, 1) combination and first sub-interval (Z4-sdi, sub-region 2) using (5 + 2, 1) combination. This result shows that thermodynamic (humidity/stability) factors add some information related to SLP only for consecutive number of dry days index. For the Z5-frpp90 index, thermodynamic (humidity/stability) factors do not bring significant additional information. This conclusion is in agreement with that obtained by analysing the CCA pairs derived from using the combined vector of standardized SLP and δq anomalies as predictor (see Section 3.2 for details). However, the combined predictors are preferable since they could capture the climate change signal for

9 STATISTICAL DOWNSCALING MODEL BASED ON CANONICAL 457 rainfall indices better. Therefore, the SLP + Q could also be considered as a good and quite stable predictor for the two mountain sub-regions (1, 2) of the Z5-frpp90 index (Table I). The results presented above reveal that, as far as the considered indices of extreme precipitation are concerned, only the consecutive number of dry days index ( dry index) presents high skill for all sub-regions. This is in agreement with the results obtained for other European regions using the same predictor but various SDMs, including those based on CCA (Goodess et al., 2006), e.g. the most skilful SDMs were obtained for dry persistence index and only across some regions for other indices. Figure 3 presents, as an example, the observed and reconstructed anomalies for two subregions of each regional index: one for the highest SDM skill and one for low SDM skill, excepting for Z4- dry, where the SDM is skilful and stable for all subregions in terms of correlation coefficient but unstable in terms of explained variance. The reconstructed values are presented for the best predictor. As it can be seen, the SDM, built on the best predictor, reproduces the observed anomalies very well, even the largest ones, in the case of extreme precipitation frequency (Z4-frpp90) and dry persistence (Z4-dry), but in the case of indices referring to rainfall intensity (Z4-sdi), extreme values are not so well reproduced. The linear trend, not shown in Figure 3 (decrease for Z5-fr90 and increase for Z4-dry), is well reproduced by the skilful SDM. If the SDM ensemble composed of SDM versions of highest skill for each sub-region, obtained from the approximately stable SDMs (e.g. stable as regards at least one criterion: correlation coefficient or explained variance), is considered, the ensemble average s skill (shaded in Table I) could be considered as an optimized SDM skill for the respective sub-regions Mechanisms controlling the variability of regional rainfall indices in Emilia-Romagna SLP predictor In order to understand the reasons leading to the results presented above, the mechanisms controlling the variability of analysed indices (given by the most important CCA patterns) and corresponding changes over the two sub-intervals are analysed in this section. As expected, the atmospheric circulation mechanisms controlling variability of the three rainfall indices are generally similar from one index to another, since all of them refer to the same climate variable (e.g. rainfall). It was found that, generally, the combination of the first five to six SLP EOFs and first two EOFs for all regional indices gives the best results, meaning that the corresponding CCA pairs reveal the main physical mechanisms controlling regional rainfall variability across Emilia-Romagna. But, for the Z5-frpp90 index, which presents a higher spatial variability, CCA patterns that resulted from another EOF combination are also important, as presented above (Section 3.1.1). Some dissimilarities regarding the extension/position of the SLP pattern nucleus and importance hierarchy of SLP patterns (given by the canonical correlation coefficient and explained variance of CCA patterns) can be noticed. For some indices, similar dissimilarities were also found when the CCA was performed over the two sub-intervals. Table II shows these differences with respect to canonical correlation coefficient and explained variance for the first two CCA patterns computed for the two sub-intervals: and To simplify the presentation, these mechanisms are explained in detail for both sub-intervals for the Z4-dry index for which the most skilful model was found and for one of the most important EOF combinations for the Z5-frpp90 index (Table I). Figure 5(a) and (b) shows the first two CCA pairs using the first six SLP EOFs and first two Z4-dry EOFs in Table II. Correlation coefficient ( 100) and explained variance ( 100) of predictor (var1) and predictands (var2) of the first two CCA pairs for the three precipitation indices. The values are presented for the two sub-intervals: (first value) and (second value). Predictor No. of EOFs CCA1 CCA2 r var1 var2 r var1 var2 Z5-frpp90 SLP 5, 2 63, 72 25, 18 55, 37 58, 64 15, 18 34, 44 4, 4 74, 77 23, 19 16, 32 57, 65 11, 34 45, 18 5,4 78, 78 15, 16 10, 39 72, 75 20, 30 34, 18 δq 3, 3 78, 81 69, 66 27, 21 46, 34 26, 8 42, 25 SLP + δq 5, 4 82, 81 13, 23 18, 27 71, 76 28, 14 28, 37 Z4-dry SLP 6, 2 80, 76 27, 21 93, 93 35, 55 27, 17 5, 4 SLP + SH 5, 2 81, 76 29, 31 93, 94 41, 49 16, 14 4, 3 Z4-sdi SLP 5, 2 70, 60 21, 28 57, 57 62, 52 12, 11 33, 35 SLP + SH 6, 2 67, 65 21, 16 48, 57 59, 56 9, 15 42, 34 SLP + δq 5, 2 67, 66 22, 13 43, 53 54, 52 9, 21 47, 39

10 458 A. BUSUIOC ET AL. (a) (b) Figure 5. (a) Patterns of the first two CCA pairs for winter SLP (right) and the Z4-dry index (left), using the first six SLP EOFs and the first two Z4-dry EOFs in CCA, over the interval Canonical correlation coefficient (r) between the time series associated with the patterns of the two parameters as well as corresponding explained variance are shown. (b) The same as in Figure 5(a) but for the interval CCA for the sub-intervals and respectively. It can be seen that the two CCA pairs are similar over the two sub-intervals, except for the differences in magnitude of Z4-dry anomalies of the first CCA pair. The patterns of the first CCA pair are similar to those of the first EOF for both parameters (not shown), except for smaller SLP explained variance for the second sub-interval, which means that Z4-dry variability in the Emilia-Romagna region is mainly controlled by the large-scale SLP variability. A slight dissimilarity in Z4-dry patterns of the second CCA pair is related to the anomaly sign s spatial distribution, but this pattern explains only 5% of total observed variance. The atmospheric circulation mechanism given by the first CCA pair is very reasonable from the physical point of view: an anti-cyclonic/cyclonic structure, extended Europe-wide and centred over United Kingdom for the first sub-interval and over central Europe for the second sub-interval (explaining 27 and 21% of total SLP observed variance, respectively), is maximum correlated with longer/shorter dry periods across the entire Emilia-Romagna region (explaining most of Z4-dry variance 93%). The highest anomalies are recorded in the sub-region close to the Adriatic Sea (zone 4) and the

11 STATISTICAL DOWNSCALING MODEL BASED ON CANONICAL 459 lowest in the highest mountain area (sub-region 1). Index variability is high for all sub-regions and quite homogeneous in terms of magnitude over the first sub-interval and very high for sub-regions 1, 3 and 4 over the second sub-interval. The variability of sub-region 2 is similar over the two sub-intervals. The very large anomalies for the three sub-regions are induced by very long dry periods in only 2 years within (not shown) over the interval , as against those recorded across sub-region 2 on the one hand and against the first subinterval on the other (Figure 3(b) and comments on SDM skill above). For sub-region 2, the large anomalies are quite uniformly distributed over the two sub-intervals. The CCA2 pattern associates a cyclonic/anti-cyclonic structure centred over the Atlantic Ocean with a dipolar Z5-dry pattern, the spatial structure depending on the position of SLP pattern s zero line. The results presented above explain the high skill of the SDM based on the first two CCA pairs and its stability with regard to correlation coefficient for all sub-regions, but, in terms of explained variance, only for sub-region 2. In the case of the Z5-frpp90 index, the mechanisms given by the CCA based on the first five SLP EOFs and first four Z5-frpp90 EOFs for the two sub-intervals are presented in Figure 6(a) and (b) respectively. The SDM built using the time series associated with the first four CCA pairs shows the highest skill for subregions 1 and 2 over the sub-interval , which is used as validation interval. For the first sub-interval, the first two CCA pairs show strong and close correlations (a) (b) Figure 6. (a) The same as in Figure 5(a) but for the first five SLP EOFs and first four Z5-frpp90 EOFs used in CCA. (b) The same as in Figure 5(b) but for the first five SLP EOFs and first four Z5-frpp90 EOFs used in CCA.

12 460 A. BUSUIOC ET AL. Figure 6. (Continued). (0.78 and 0.72) but the second CCA pair explains a higher variance for both parameters (20% for SLP and 34% for Z5-frpp90), giving the most important mechanism that controls Z5-frpp90 variability. This pair associates an extended cyclonic/anti-cyclonic structure centred over central Europe with more/less frequent extreme precipitation over Emilia-Romagna, the highest anomalies being recorded for the mountain areas (subregions 1 and 2). This mechanism seems to be reasonable from the physical point of view: the cyclonic structure induces a south-westerly flow across the Italian peninsula, which is associated with more frequent heavy rainfall events over the entire region, but with higher values for the Northern Apennine (sub-regions 1 and 2), which are most affected by this circulation type. This result explains the highest skill for these two regions when the SDM is validated over this interval. The mechanism is similar to that given by the second CCA pair derived for the second sub-interval (CCA2 Figure 6(b)) but the SLP pattern (explaining higher variance 30% and higher correlation 0.75) is less extended with nucleus shifted to east, inducing weaker south-westerly flow over Italy. In this case, the Z5-frpp90 CCA pattern is similar to the corresponding one over the first sub-interval (CCA2 Figure 6(a)) but the local index anomalies are lower and explained variance is much lower (18% compared to 34%). This could explain the lower SDM skill over the second validation interval. The second important mechanism controlling Z5- frpp90 variability over the first sub-interval is that given by the third CCA pair (CCA3 Figure 6(a)), showing a lower correlation coefficient (0.56, still significant)

13 STATISTICAL DOWNSCALING MODEL BASED ON CANONICAL 461 but explaining a highest fraction of Z5-frpp90 variance (36%). The SLP pattern shows a dipole SLP structure with southwest-northeast gradient, which induces a southeasterly/north-westerly flow across northern Italy, and it is associated with more/less frequent heavy precipitation over this area, highest anomalies being recorded across sub-region 4 (close to the Adriatic Sea) followed by Po valley (sub-region 5), a reasonable mechanism from the physical point of view. A similar mechanism can be revealed over the second sub-interval given by the first CCA pair (CCA1, Figure 6(b)) with the highest correlation coefficient (0.78) but with shifted pattern (southeastnorthwest gradient). The Z5-frpp90 anomalies are lower compared to the first sub-interval (CCA3 Figure 6(a), left). This result could explain the highest SDM skill for sub-region 4 over the second validation sub-interval. The first CCA (Figure 6(a)) pair shows a highest correlation coefficient (0.78) but lower explained variance for both parameters (15% for SLP and 10% for Z5-frpp90). This mechanism is also reasonable from the physical point of view: the SLP pattern (showing three nuclei) associates a cyclonic/anti-cyclonic structure centred over eastern Europe, which induces a north-easterly/southwesterly circulation (bringing cold and dry continental air mass or warm and moist Mediterranean air mass over Emilia-Romagna) with a decrease/increase in extreme precipitation frequency, the most affected being subregion 1 (the highest mountain area). This CCA pair is not stable over the two sub-intervals (e.g. it has no correspondent over the second sub-interval; compare Figure 6(a) and (b)). Similarly, the third CCA pair derived over the second sub-interval has no correspondent over the first sub-interval. These differences in the CCA patterns over the two sub-intervals could be explained by different physical mechanisms controlling regional climate variability on various time scales, which cannot be captured over shorter intervals. This is an example to underline how sensitive is the variability of extreme rainfall frequency across this complex region to the intensity and position of a circulation pattern and why it is so difficult to find a single optimum model for all sub-regions. Therefore, the variability of extreme precipitation frequency for each sub-region/group of sub-regions is controlled by different circulation patterns. This result is also in agreement with that presented in previous studies by Caccia-mani et al. (1994), Quadrelli et al. (2001) and Tomozeiu et al. (2002). As presented in Section 3.1.1, in order to show the advantage of using regional indices instead of individual station indices, the CCA applied for 41 weather stations instead of regional indices for frpp90 index over the interval was also carried out (not shown). It was found that the SLP patterns are mainly similar to those presented in Figure 6(a) and the mechanisms controlling local variability are similar Humidity predictors Considering the results presented in Section 3.1.2, a significant improvement in the SDM skill was obtained for sub-region 1 of the Z5-frpp90 index by using only δq as predictor. It was found that the first three EOFs for both parameters make the optimum EOF combination. We have to note that the positive δq anomalies show stability situations that correspond to the surface anti-cyclonic structure (as presented below), while the negative anomalies show the reverse situation. As an example, only the Figure 7. The patterns of the first two CCA pairs of winter instability index δq (right) and the Z5-frpp90 index (left) in Emilia-Romagna over the interval The first three EOFs for both parameters were used in CCA. Canonical correlation coefficient (r) between the time series associated with the patterns of the two parameters as well as corresponding explained variance are shown.

14 462 A. BUSUIOC ET AL. first two CCA pairs are presented in Figure 7. The first CCA pair (correlation coefficient of 0.78) associates a stability/instability situation region-wide (explaining 69% of total observed variance), absolute anomalies decreasing from north to south, with negative/positive anomalies for extreme precipitation frequency across Emilia-Romagna (explaining 27% of total observed variance). The highest values are recorded in the mountain area, especially for sub-region 1, where the highest mountains are located, which is reasonable from the physical point of view: a higher instability in the atmosphere, between 850 and 500 mb, as instability index was defined in Section 2, mainly affects the higher-altitude stations, where higher precipitation amounts are recorded and, therefore, heavy precipitation is more frequent here. This result explains the considerable improvement in SDM skill for this subregion. The second CCA pair shows a similar mechanism but the absolute δq anomalies increase from north to south and from west to east. The higher stability in the eastern part of northern Italy is associated with negative heavy rainfall frequency in this area. The canonical correlation coefficient, quite low for the second CCA pairs (0.46), could explain the unskilful SDM for sub-regions 3, 4 and 5 that show high variability in this CCA pair. Since explained variance is highest for the index pattern, the SDM based on the first two CCA pairs gives a high and stable skill for sub-region 1 (highest for the first sub-interval). Using the first three CCAs to construct the SDM, the highest skill is obtained for the second sub-interval Combined predictors In order to explain why the combination between SLP and δq does not lead to a significant improvement in SDM skill for the Z5-frpp90 index, the first two CCA pairs of standardized anomalies of combined SLP and δq field and Z5-frpp90 were analysed (Figure 8). The first five EOFs for predictor and first four EOFs for predictand were retained for the CCA. It can be seen that the two pairs show a similar mechanism to those obtained when SLP and δq only are used as predictors. Therefore, the SLP and δq patterns are similar to those presented in the first two CCA pairs from Figure 6 and Figure 8 respectively. 4. Conclusions In this paper, SDMs for three winter precipitation indices in the Emilia-Romagna region were developed using various predictors. These models are based on CCA that (a) (b) (c) Figure 8. The first two CCA pairs of the SLP (a) instability index δq (b) and the Z5-frpp90 index (c) as derived from the CCA between combined vector of SLP δq and the Z5 frpp90 index.