SURFACE AIR TEMPERATURE VARIABILITY OVER TURKEY AND ITS CONNECTION TO LARGE-SCALE UPPER AIR CIRCULATION VIA MULTIVARIATE TECHNIQUES

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1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 25: (2005) Published online in Wiley InterScience ( DOI:.02/joc.1133 SURFACE AIR TEMPERATURE VARIABILITY OVER TURKEY AND ITS CONNECTION TO LARGE-SCALE UPPER AIR CIRCULATION VIA MULTIVARIATE TECHNIQUES HASAN TATLI, a, *H.NÜZHET DALFES b and Ş. SIBEL MENTEŞ a a Istanbul Technical University, Meteorology Department, Maslak 34469, Istanbul, Turkey b Istanbul Technical University, Eurasia Institute of Earth Sciences, Maslak 34469, Istanbul, Turkey Received 19 January 2004 Revised 25 October 2004 Accepted 25 October 2004 ABSTRACT The problem of statistical linkages between large-scale and local-scale processes is investigated through noise reduction by singular spectrum analysis (SSA) and spatial principal component analysis in order to construct appropriate statistical models for estimating the local-scale climate variables from large-scale climate processes. This paper presents an approach for downscaling monthly temperature series over Turkey by upper air circulations derived from the National Centers for Environmental Prediction National Center for Atmospheric Research Reanalysis data sets (500 hpa geopotential heights and hpa thicknesses). The proposed approach consists of three stages. First, the available data sets are separated into deterministic, statistical components and random components by SSA. Second, the deterministic components are saved and the random components are eliminated by spatial principal component analysis. Subsequently, the statistical components are combined with the deterministic components constituting a noise-free data set. Furthermore, so-called Sampson correlation patterns are determined between the noise-free large-scale and the local-scale variables for interpreting the large-scale process impacts on local-scale features. Third, the significant redundancy variates based on canonical correlation analysis are extracted in order to identify the statistical downscaling model for temperature series of 62 stations in Turkey. The results show that the interpretation of the local-scale processes with the noise-free data sets is more significant than with the raw data sets. Copyright 2005 Royal Meteorological Society. KEY WORDS: canonical correlation analysis; downscaling; monthly temperature; redundancy analysis; Sampson correlation; singular spectrum analysis; Turkey 1. INTRODUCTION On average, general circulation models (GCMs) are powerful tools for analysing large-scale climate features by integrating a variety of fluid-dynamical, chemical and biological equations that are derived from physical laws for atmospheric motions, but the outcomes of GCMs generally indicate a statistical sense. However, on local scales or scales near the surface, the outputs of GCMs may not be able to estimate the nature of climate. Since the free troposphere is spatially and temporally more homogeneous than the Earth s surface, the logic of downscaling from large-scale processes of the free troposphere is understandable (Kim et al., 1984; Wilks, 1989; Karl et al., 1990; Wigley et al., 1990; Giorgi and Mearns, 1991; Zorita et al., 1992; von Storch et al., 1993; Cubasch et al., 1996; Hewitson and Crane, 1996; Rummukainen, 1997; Schubert and Henderson-Sellers, 1997; McGregor, 1997; Kidson and Thompson, 1998; Solman and Nunez, 1999; Murphy, 1999, 2000; Landman and Tennant, 2000; Tatlı et al., 2004). Unfortunately, there are serious problems with GCMs, related to the fundamental properties and the very nature of the climate system. These errors in the estimation of, for example, snow and sea-ice cover by GCMs * Correspondence to: Hasan Tatli, Istanbul Technical University, Aeronautics and Astronautics Faculty, Meteorology Department, Maslak, 34469, Istanbul, Turkey; tatli@itu.edu.tr Copyright 2005 Royal Meteorological Society

2 332 H. TATLI, H. N. DALFES AND Ş. S. MENTEŞ have an order of often close to 0% with respect to observed values (Dobrovolski, 2000). The important technical problems of GCMs are investigated by Houghton et al. (1996). Three statistical downscaling approaches are available in the literature: (1) model output statistics (predictors come from GCM outputs); (2) perfect prognosis (predictors come from large-scale free atmospheric observations, or reanalysis data sets); (3) downscaling with surface variables (predictors come from large-scale surface observations; Rummukainen, 1997). A multivariate regression based on redundancy analysis (RA) is developed for interpreting the Turkish temperature series (Gower, 1975; Tyler, 1982). The monthly temperatures have dominant periodic components preventing a true statistical analysis, for instance, in trend and in stochastic components. Hence, Fourier analysis (Richardson, 1981) may not be applied directly, since the Fourier method requires the assumption of stationarity in the process. Thus, singular spectrum analysis (SSA) is performed to decompose the variables into deterministic and mixed statistical random components (Vautard et al., 1992; Elsner and Tsonis, 1996). After determining the cycle and trend of deterministic components, principal component analysis (PCA; Kidson, 1975; North, 1984; Preisendorfer, 1998) is performed on the residuals to extract the statistical and noise components. Later, the deterministic and statistical components are combined to a new data set, which is called noise free. Furthermore, the Sampson (1984) correlation ratio is used to determine the relationships between the largescale predictors and local-scale predictands in order to recognize the predictors and predictands in the sense of a prediction model. Although canonical correlation analysis (CCA; Glahn 1968; Mardia et al., 1979; Van de Geer, 1984; TenBerge, 1988; Jackson, 1991; Chen and Chang, 1994; Chen et al., 1994) is widely employed in the climatology literature, CCA cannot recognize the predictor and the predictand variables as in the case of the Sampson correlation ratio (Jackson, 1991). Thus, in this paper, the canonical correlation variates are only required while extracting redundancy variaties (RVs). In the final stage, a so-called multivariate regression model is identified between the significant RVs of large-scale processes and the RVs of monthly temperature series. A number of applications regarding the statistical analysis of Turkish temperature series have already been published, (e.g. Jones, 1995; Kadıoǧlu 1997; Tayanç et al., 1997; Kömüşçü, 1998; Türkeş et al., 1995, 2002). This paper includes the following aspects: in Section 2 the temperature climate of Turkey is briefly discussed. The methodology is given in Section 3. Section 4 contains an application of the proposed approach to a downscaling of monthly temperature series (maximum, minimum and mean temperatures) of 62 stations in Turkey from large-scale upper air circulations. In Section 5, some comments and conclusions are given. 2. A Brief Description of the Temperature Climate of Turkey Turkey is in a region which is often described as having a warm and moderate climate (Erinç, 1984). The highest maximum temperature is observed in the southeast of the country, particularly in summer months. The temperature decreases gradually towards the northwest and northeast, yet this decrease is less strong during summer due to the continental effects of the inner regions. At low altitudes, the coastal regions are warmer than the inner regions, which are separated from the former by high mountains. On average, the Mediterranean coast has the highest temperature, followed by the Aegean, the eastern part of the Black Sea region and the Marmara coasts. In eastern Anatolia, owing to continental effects and high altitudes, there is a widespread temperature decrease. The extension of the continental and the topographic effects are important in determining the distribution of temperature variability. The most interesting thermal characteristic of Turkey is the rise of temperature in all the regions due to continental effects and, thereby, a decrease in regional contrasts during summer. The resulting temperature field has a negative gradient towards the northwest. Central Anatolia becomes very hot during the summer, and its temperature contrast with the coastal areas decreases. Roughly speaking, from a macro-climate point of view, Turkey represents a more homogeneous region during summer. During winter, continental influence, altitude and, of course, the latitude are determining factors for the minimum temperature. The main difference between summer and winter is that during winter the regional

3 TEMPERATURE AND ATMOSPHERIC CIRCULATION RELATIONSHIPS 333 temperature contrasts are very strong, implying that there is negative temperature gradient from the coasts towards the interior. In the interior, the continental effects are pretty much the same and there are no huge temperature differences from region to region, but still there is a gradual temperature decrease towards the east within the Anatolian Plateau. There is a negative temperature gradient towards the west in the Thrace region. This means mostly closed isotherms over Turkey, with positive temperature anomalies towards the coasts and negative temperature anomalies observed towards the interior. The highest temperatures during winter are observed along the Mediterranean coast, which is influenced by subtropical air masses. In the Aegean and eastern part of the Black Sea region the temperature does not fall very much due to marine effects (also due to the foehn winds in the case of the eastern part of the Black Sea region). Southerly winds are generally common in the central part and move towards the convergence field in the eastern Black Sea. The lowest temperature values are observed in the northeastern Anatolian Plateau. Yearly temperatures are more equable at the coasts (especially along the eastern Black Sea coast due to the additional effects of the foehn winds). The yearly temperature contrast increases towards the interior. The transitions from the cold to the warm period are more abrupt in the interior than in the coastal areas. The daily temperature has a similar character, with a small contrast at the coasts and a high contrast in the interior. In particular, in the high plateaus of Anatolia, during winter there is a strong daily contrast when frontal activities are common, but also in the transitional seasons of spring and autumn. In Turkey, the monthly extreme temperature averages are quite different from the monthly averages. This is mainly due to continental effects. The above-mentioned difference increases towards the interior of the country and becomes very large in eastern Anatolia. During summer, the differences between the monthly mean temperature series and those of the extremes are greatest in the coastal areas. The extreme temperatures have maxima in the southeastern region of Anatolia during summer. The average maxima are smallest in the Black Sea region. In central Anatolia it is common for the monthly mean temperature to fall below zero in January. In winter, these values are usually well below zero towards eastern Anatolia, while moderate values are observed in the coastal areas. 3. DATA AND METHODS An example of perfect prognosis (PP) based on a regression technique which is a downscaling method (von Storch, 1995) is outlined in the following. Assume that X and Y are the predictors and predictands respectively. Mathematically, the downscaling process may be defined as Y(t) = F [X(t)] + e(t) (1) where F is an operator to be determined and e(t) indicates the multivariate error term. To perform a successful large-scale analysis (Rummukainen, 1997), noise-free predictors must come from a sufficiently large-scale region that can explain global circulation features of the climate. Therefore, the large-scale National Centers for Environmental Prediction National Center for Atmospheric Research (NCEP NCAR) reanalysis data sets (Kalnay et al., 1996) are considered as large-scale predictors between the ranges of 50 E and N, since this area is large enough to represent the large-scale processes that affect the monthly temperature series over Turkey. The first step in downscaling is to determine the appropriate predictors. There are many statistical methods according to the scientific literature, of which two such possibilities are CCA and stepwise regression (Noguer, 1994; von Storch and Zwiers, 1999). Here, however, the Sampson (1984) correlation ratio is used to recognize the predictors and predictands (e.g. Tatlı et al., 2004). This is defined as R S = Tr(C YX C 1 XX C XY) Tr(C YY ) (2)

4 334 H. TATLI, H. N. DALFES AND Ş. S. MENTEŞ where C XY, C XX and C YY indicate multivariate cross-covariance and covariance matrices and Tr denotes the trace of the related matrices. The Sampson correlation R S [0, 1] represents the correlation between two matrices and it is not particularly symmetric, whereas the Pearson moment correlation is symmetric representing the correlation between two vectors. In this study, the contour map based on noise-free data sets between the set of time series of gridded data and the multiple time series of observations is termed the Sampson correlation pattern R S. The statistical significance level of R S is tested by the alpha level of statistics. Before constructing a downscaling model, a statistical preprocessing is required in order to determine the significant large-scale variables in a compressed manner (such as principal components (PCs) or independent components (Tatlı et al., 2004)). If we plot the time series of the monthly temperature series of 62 stations shown in Table I, and, for instance, of 500 hpa geopotential heights and of hpa geopotential thicknesses, then the irregular noise components emerge. Fourier analysis (Richardson, 1981) is one possible way of removing such noise in the data sets, but Fourier analysis assumes a stationarity constraint in the process. SSA is another possible way based on eigenvalue techniques without satisfying stationarity constraints. The SSA approach or temporal PCA is well known in climate studies (e.g. Ghil and Vautard, 1991; Vautard et al., 1992; Green et al., 1993; Elsner and Tsonis, 1994, 1996; Schlesinger and Ramankutty, 1994; Allen and Smith, 1996). Table I. The selected meteorological stations in Turkey Station name ( E) ( N) Station name ( E) ( N) ZONGULDAK AFYON İNEBOLU KAYSERİ SİNOP MALATYA SAMSUN ELAZIǦ GİRESUN SİİRT TRABZON İZMIR RİZE AYDIN ARTVİN BURDUR EDIRNE ISPARTA TEKİRDAǦ KONYA KİREÇBURNU NIǦDE GÖZTEPE GAZİANTEP KOCAELİ ŞANLIURFA BOLU MARDİN KASTAMONU DİYARBAKIR MERZİFON BODRUM ÇORUM MUǦLA SİVAS FETHİYE ERZİNCAN ANAMUR ERZURUM MERSİN AǦRI ADANA BANDIRMA İSKENDERUN BURSA LULEBURGAZ BİLECIK ŞİLE YOZGAT FLORYA BALIKESİR KUTAHYA VAN DÖRTYOL DİKİLİ ISLAHİYE AKHİSAR ANTAKYA MANİSA ESKİŞEHİR UŞAK ANKARA

5 TEMPERATURE AND ATMOSPHERIC CIRCULATION RELATIONSHIPS 335 Moreover, for analysis of non-stationary and non-linear univariate time series there are alternative methods, such as the empirical mode decomposition of Huang (Huang et al., 1998) and wavelet analysis (Torrence and Compo, 1998), which have been applied successfully in atmospheric and climate studies (e.g. Wu et al., 1999; Wang et al., 2000; Ouergli, 2002; Coughlin, 2003; Duffy, 2004). The large-scale predictors come from grids of the window between N and 50 E of NCAR NCEP reanalysis data with a total number of 442 time series. Owing to the huge volume size of the predictors, any model structure will be so complex and the parsimonious properties of the model may disappear. Furthermore, the noise may also affect the model parameters while constructing an economical downscaling model. In other words, the model tries to estimate predictable components, but it may estimate the non-predictable components due to the noise. To solve this problem, both SSA and PCA approaches are proposed to remove these non-predictable components; thereafter, a true redundancy analysis (RA) based on CCA may be applied. To illustrate the method, let x(t) be a univariate time series that can be decomposed into three components: x(t) = x d (t) + x s (t) + x e (t) (3) where x d (t) is the deterministic component (trend and/or periodic cycles) being predictable by mathematical models (e.g. GCMs), x s (t) represents the statistical component that can be estimated by statistical models (e.g. regression, autoregressive (AR), AR moving average), and x e (t) indicates the noise component that is not predictable by either the mathematical or the statistical models. However, a problem might arise if the process is constituted by the product of the deterministic and statistical components in addition to the noise component: x(t) = x d (t) x s (t) + x e (t) (4) The constraint of our approach is based on the assumption of Equation (3); the analysis of Equation (4) is beyond the scope of this study. Figure 1. Flow chart of the model components in the proposed downscaling approach

6 336 H. TATLI, H. N. DALFES AND Ş. S. MENTEŞ Table II. Explained variances of the temporal PCs of maximum temperature at some sites of Turkey Cycles Temporal PC (eigenvector) Explained variance (%) Mersin Antalya Adana Gaziantep Şanlıurfa Muǧla Periodic Non-Periodic The most significant aspects of SSA are described in the following. SSA consists of the diagonalization of the lagged autocovariance (or autocorrelation) matrix; like in PCA, the eigenvectors represent patterns of temporal behaviour and the PCs are significant embedding dimensions (or characteristic series). When two eigenvalues of the lagged autocovariance (or autocorrelation) matrix are nearly equal and their corresponding eigenvectors are phase shifted 90 they represent an oscillation. If there is a trend, then the first eigenvalue, the biggest, represents the trend, and the following nearly equal eigenvalue pairs represent periodic cycles. In this study, the reconstruction of the univariate time series is considered as a low-pass filter. After SSA, the residuals are decomposed via PCA and then the subsequent step is the reconstruction of data series with significant PCs. Consequently, the resulting time series are now noise free according to the applied methods. After determining the noise-free data sets the downscaling model based on redundancy analysis can be calibrated. Hotelling (1936) proposed CCA as a model to relate two sets of variables. He derived linear combinations of the X variables (in this study the large-scale variables) and linear combinations of the Y variables (in this study the local-scale variables) that were maximally correlated, subject to the constraint that each variate derived was uncorrelated with other variates. Denote one vector of X by x and one vector of Y by y; CCA can reduce linear components of x and y, t i and u i,: t i = w T i x, u i = v T i y (5) choosing w i and v i such as to maximize the correlation between t i and u i subject to the constraints w T i C XXw j = 0, v T i C YYv j = 0 i = j (6) and w T i C XXw i = 1, v T i C YYv i = 1 (7) where C XX and C YY denote the covariance matrices. Canonical correlation vectors (or weights) w i and v i can be obtained by an orthogonal decomposition procedure of the related matrices, where w i and v i are the eigenvectors of C 1 XX C XYC 1 YY C YX and C 1 YY C YXC 1 XX C XY respectively. The square roots of the eigenvalues of these two matrices are equal and represent canonical correlation coefficients between the pairs of t i and u i. CCA has a property of biorthogonality satisfying the diagonalizability of C XY : W T C XY V = D (8)

7 TEMPERATURE AND ATMOSPHERIC CIRCULATION RELATIONSHIPS Figure 2. R S (Sampson correlation) pattern of monthly 500 hpa geopotential heights with monthly maximum temperature series in Turkey during the period of : winter; spring; summer; autumn where D is the diagonal matrix representing the square of the canonical correlation coefficients. However, a CCA approach is symmetrical and cannot recognize which of the components is the predictor and predictand, i.e.: V T C YX W = D (9) Furthermore, the structure matrices for X and Y can be defined as the correlation matrices between variables and canonical correlation variates: C XX W, C YY V, for X for Y } where the maps of C XX W and C YY V denote canonical correlation patterns (structure matrices). CCA finds variates that are correlated, but it is not so practical in the prediction frame since they do not explain enough covariance. A statistical prediction model must satisfy asymmetric features, such as to predict ()

8 338 H. TATLI, H. N. DALFES AND Ş. S. MENTEŞ Figure 3. R S pattern of monthly hpa geopotential thicknesses with monthly maximum temperature series in Turkey during the period of : winter; spring; summer; autumn local-scale processes from large-scale processes (downscaling), and may not be invertible to predict largescale features from local-scale features (upscaling), particularly in climate processes. Van den Wollenberg (1977) devised a linear model of RA as an alternative CCA that avoids this problem. The weights for RVs w i are determined by solution of the following equation: [C XY C YX b i C XX ]w i = 0 (11) where b i is the covariance explained by the ith variate pair. In the RA technique, the RVs for X and Y can be obtained as in the following (Tyler, 1982): v i = b 1/2 i C YX w i (12) The same redundancy vectors can also be obtained by using singular value decomposition (SVD): C 1/2 XX C XY = HEV T } W = C 1/2 XX H (13)

9 TEMPERATURE AND ATMOSPHERIC CIRCULATION RELATIONSHIPS Figure 4. R S pattern of monthly 500 hpa geopotential heights with monthly minimum temperature series in Turkey during the period of : winter; spring; summer; autumn where H is the left-side eigenvector matrix of C 1/2 XX C XY, W is the matrix of variates for the X variables, V is the matrix of the variates for the Y variables, and E is the diagonal matrix whose elements are square roots of b i. Once the redundancy vectors are obtained, the regression equation is obtained as in the following: Y = XWW T C XY (14) Equation (14) is our final model for downscaling of monthly temperature series. However, obtaining RVs from asymmetric matrices is not a preferred way; Tyler (1982) proposed another method for RA from symmetric matrices. First, the orthonormal eigenvectors of C YX C 1 XX C XY, U and the corresponding matrix of R roots are obtained, and then RVs can be written as W = C 1 XX C XYUR 1/2 (15) where Y and X represent noise-free local-scale predictands and large-scale predictors respectively. The flow chart that describes the components of the proposed downscaling model is shown in Figure 1.

10 340 H. TATLI, H. N. DALFES AND Ş. S. MENTEŞ Figure 5. R S pattern of monthly hpa geopotential thicknesses with monthly minimum temperature series in Turkey during the period of : winter; spring; summer; autumn 4. RESULTS The predictands are monthly maximum, mean and minimum temperature series of 62 stations in Turkey (Table I) during the period 1951 to Since data sets of temperature time series have dominant periodic cycles, these components can easily be estimated by any linear prediction model. On the other hand, these periodic components may hide the non-seasonal components, which are called non-periodic and trend components (linear or non-linear) in the stochastic literature (Richardson, 1981; Bras and Rodriguez-Iturbe, 1993; Box et al., 1994; Hipel and Mcleod, 1994; von Storch and Zwiers, 1999). However, the variability of climate may usually be in the non-seasonal components, which may show non-stationary characteristics. Hence, SSA is applied to both large-scale predictors and local-scale predictands before preprocessing the data sets by spatial PCA in order to extract the predictable components. The variances explained by the temporal PCs of maximum temperatures at some locations in Turkey after SSA are shown in Table II as examples of the indicators used to diagnose the components. In the SSA procedure, if the length of a univariate time series is N then the lag-window is generally selected between N/3 and N/4 (Elsner and Tsonis, 1996). Accordingly, in this study the lag-window selected is N/4.

11 TEMPERATURE AND ATMOSPHERIC CIRCULATION RELATIONSHIPS Figure 6. R S pattern of monthly 500 hpa geopotential heights with monthly mean temperature series in Turkey during the period of : winter; spring; summer; autumn In order to obtain the noise-free spatial modes of climatic variability, the deterministic components (periodic cycles and trend) are subtracted from the raw data series and then the spatial PCs are selected for these residuals of the data sets, with the model fit assessment being based on the maximum likelihood method under a χ 2 distribution with a 95% confidence level with the degrees of freedom equal to 1/2 (p q) 2 (p + q) (Jöreskog and Sörbom, 1989). Here, p and q represent the entire PCs and the significant PCs respectively. Both the NCAR NCEP reanalysis data sets and the observations are divided into four seasons in order to study the relationships between the temperature series and large-scale processes. To test the performance of the proposed model, the first 360 months (30 years) are used for the model calibration and the other 216 months (18 years) are used for model validation. The relationships between monthly near-surface air temperature series in Turkey and upper air circulations (500 hpa geopotential heights and hpa geopotential thicknesses) are shown in Figures 2 7 as R S (Sampson correlation patterns) in the seasonal-scale months for four seasons. As depicted in these figures, based on the 99% (R S > 3) significance level of correlations between maximum temperatures and 500 hpa geopotential heights, the area that includes the southern and western parts of Turkey is at appreciable levels in summer and spring.

12 342 H. TATLI, H. N. DALFES AND Ş. S. MENTEŞ Figure 7. R S pattern of monthly hpa geopotential thicknesses with monthly mean temperature series in Turkey during the period of : winter; spring; summer; autumn Since, at the beginning of spring, Turkey is under the influence of warm subtropical air systems, 500 hpa geopotential heights are transformed into ridges over the corresponding locations. This leads to an increase in maximum temperatures. On the other hand, while the 500 hpa high centre extends its influence over Europe, further effects on maximum temperatures arise. Displacement of the Azores high centre over Europe leads northerly flows being further east in the summer. As a result of this mechanism, the maximum temperature decreases, especially in the regions of western and northern Turkey. During winter, subtropical air masses just affect the southern parts of the country. The second effect is seen from central and northern Europe. In this season, the Iceland low pressure and Siberian high pressure systems start to affect northern and eastern Europe (due to dynamical and thermal reasons), since both systems have cold characteristics leading to a decrease of 500 hpa geopotential heights. The northerly flows have effects on decreasing maximum temperatures in Turkey (especially in northern parts). The effect of the Icelandic low is mentioned through its connection with the North Atlantic oscillation during winter (Türkeş and Erlat, 2003). The effects of large-scale upper air circulations on maximum, minimum and average temperatures show similar patterns during the winter season. On the other hand, those effects mostly resemble the R S

13 TEMPERATURE AND ATMOSPHERIC CIRCULATION RELATIONSHIPS 343 Var = 57.84% Var = 38.98% Var = 60.22% Var = 37.34% (e) Var = 51.5% (f) Var = 23.41% (g) Var = 20.67% Figure 8. The varimax rotated PC patterns of the downscaling model outputs and the actual maximum temperature: and show the first two PC patterns of noise-free data; and show the first two PC patterns of model outputs; (e), (f) and (g) show the first three PC patterns of actual raw data. The third PC patterns of both noise-free and model-output data are not significant, in contrast to the third PC pattern of raw data (the patterns represent correlation coefficients between individual station s temperature series and rotated PCs. These patterns are generally called loadings). The period of the extracted PCs is the validation period of the suggested model (18 years data) correlation patterns for maximum and average temperatures, whereas the minimum temperature series show very different patterns in other seasons (summer, autumn and spring). In autumn, the areas influenced by subtropical air masses that are effective during summer are shifted towards southern and southeastern parts of Turkey. According to the 500 hpa geopotential heights, another area of influence linked to the Azores high affects western Europe, encompassing Italy and France. There are strong correlations between hpa thicknesses and average-maximum temperatures. The thicknesses have positive effects on increasing the Turkish average-maximum temperatures, starting in spring and continuing in summer. In this season, the movement of the tropical (monsoon) low to higher latitudes over the eastern and southeastern parts of Turkey (including the eastern and central Black Sea parts of Turkey) has important effects for those regions. The warm features of this air mass lead to increased thicknesses and ridges at the 500 hpa level.

14 344 H. TATLI, H. N. DALFES AND Ş. S. MENTEŞ Var = 51.87% Var = 45.14% Var = 51.51% Var = 46.31% Var = 49.82% (e) Var = 45.75% (f) Figure 9. The varimax rotated principal components of the downscaling model outputs and the actual minimum temperature: and show the first two PCs of noise-free data; and show the first two PCs of model outputs; (e) and (f) show the first two PCs of actual raw data. The third PCs of the noise-free, model-output, and actual raw data are not significant In autumn, tropical air masses shift to the south as a result of cooling land areas. In summer, the significant correlations are observed over northwestern parts of Europe. Those areas and the influence of the Azores high centre s area overlap. As may be seen in Figures 2 7, the discussion of the R S patterns for maximum and average temperatures is also valid for minimum temperature series during winter. However, in summer and the transition seasons the locations of significant correlations are different, since the large-scale circulation features of winter are more effective than the other three seasons. In other words, Turkey is under the influence of large-scale systems in winter; hence, similar correlation patterns are expected for all three temperature types. Minimum temperature patterns, in addition to large-scale features, are also affected by so-called local topographical conditions. In

15 TEMPERATURE AND ATMOSPHERIC CIRCULATION RELATIONSHIPS 345 Var = 51.4% Var = 47.7% Var = 51.92% (e) Var = 52.46% Var = 46.84% Var = 46.87% (f) Figure. The varimax rotated PCs of the downscaling model outputs and the actual mean temperature: and show the first two PCs of noise-free data; and show the first two PCs of model outputs; (e) and (f) show the first two PCs of actual raw data. The third PCs of the noise-free, model-output, and actual raw data are not significant spring, summer and autumn, the significant correlations are observed in the eastern and northeastern parts of the country Downscaling results To show to spatial performance of the model, the significant varimax rotated (Kaiser, 1959) PCs of both the downscaled and the observed monthly temperature series are shown in Figures 8 to demonstrate which parts of the country s temperature fields can be estimated from the large-scale upper air circulation by the

16 346 H. TATLI, H. N. DALFES AND Ş. S. MENTEŞ Training Part Training Part Training Part Training Part Training Part 24 Training Part (e) (f) Training Part (g) Figure 11. The frequency scatter plots of minimum temperatures of observations and model outputs during the calibration period of the proposed model. The observations are series that are not filtered by SSA. The ellipses indicate the 95% confidence interval; the data outside the ellipses are the unpredictable part of the data by the proposed model: Göztepe (Istanbul); Ankara; Diyarbakır; Izmir; (e) Adana; (f) Adana; (g) Erzurum

17 TEMPERATURE AND ATMOSPHERIC CIRCULATION RELATIONSHIPS 347 proposed downscaling approach. As may be seen in these figures, without the noise-reduction procedure the number of significant PCs is increased only for the maximum temperature series. However, the third PC of the maximum temperature series cannot be connected with the large-scale processes; therefore, noisefree data sets may be seen as more appropriate for downscaling purposes. As seen in these figures, the temperature variability over Turkey is represented by two PC patterns. One indicates coastal regions and the other represents inland regions. The similar patterns are also extracted from the proposed downscaling model. In order to show the proposed model s performance, seven stations minimum temperature series are selected according to Tatlı et al. (2004). The other temperature series (maximum and mean) generally follow general circulation patterns, but minimum temperature series can also show local-scale characteristics. The downscaled versus observed minimum temperature series are given in Figure 11, which shows the 95% confidence intervals of the frequency scatter plots of the proposed model outputs and observed series during the calibration step. Figure 12 shows the validation part of the model outputs versus observations. 5. CONCLUSIONS In this study, the problem of statistical linkages between the monthly near-surface temperature series over Turkey and the large-scale upper air circulations from NCAR NCEP reanalysis data sets are investigated by a particular downscaling approach based on multivariate redundancy and Sampson correlation analysis during the period The noise-reduction techniques of SSA and PCA are employed in order to filter the data mentioned as deterministic (trend and/or cycles) and statistical components. The approach suggested shows that the effects of the large-scale upper air circulations on monthly maximum, minimum and mean temperature series show similar patterns in winter. These effects resemble the Sampson correlation patterns for monthly maximum and mean temperatures, whereas the minimum temperature series show very different patterns in the other seasons (summer, autumn and spring). In the autumn, the areas influenced by subtropical air masses which are effective in summer form a belt towards southern and southeastern regions of Turkey. The Sampson correlation patterns indicate that the correlations between maximum temperatures and 500 hpa geopotential heights in the area covering the southern and western parts of Turkey are at a significant level in summer and spring. Since Turkey is under the influence of warm subtropical air masses in early spring, the ridge in the geopotential height field leads to an increase in temperatures. On the other hand, the 500 hpa high centres extend towards Europe and, therefore, their signatures are termed in the variability of the temperature fields. In summer, displacement of the Azores high centre over Europe generates a northerly flow and leads to a decrease in temperature, especially in the regions of western and northern Turkey. The Sampson correlation patterns between the hpa thickness and the temperature series show that the thickness increases Turkish temperature starting in the spring and continuing in summer. In this season, the movement of the subtropical air system (monsoon low) to high latitudes over eastern and southeastern parts of Turkey (includes the eastern and central Black Sea region of Turkey) has important effects. The warm features of this air system lead to increased thicknesses and create ridges at the 500 hpa level. Additional effects of thickness anomalies are observed for the Caucasus and Caspian, where cold advection invades the topographic depression between the Balkans highlands and the Caucasus, and even across the Anatolian upland and the Balkans, this cold air being derived mainly from Russian and Balkan sources. The methods applied in this study are selected according to the large-scale and local-scale climate variability and asymmetric relationships. Data assimilation or upscaling is indeed a processing of convolution between large-scale and local-scale variables. The problem of reconstructing the local-scale variables is, on the other hand, an inverse problem. In more general terms, the deconvolution problem is to reconstruct the inputs (local scale) of a climate system (represented by a GCM) from its outputs (large scale). However, the interactions of large-scale and local-scale climate features make the separation of the processes highly nonlinear to a great extent. In the majority of downscaling studies it is assumed that it is possible to identify the local-scale variables by means of suitable analysis of free tropospheric variables, for instance the 500 hpa geopotential heights and hpa geopotential thicknesses which are also used in this study. These variables can be simulated as perfectly by GCMs.

18 348 H. TATLI, H. N. DALFES AND Ş. S. MENTEŞ 22 Validation Part Validation Part Validation Part Validation Part Validation Part 28 Validation Part (e) (f) Validation Part (g) Figure 12. The frequency scatter plots of minimum temperatures of observations and model outputs during the validation period of the proposed model. The observations are series that are not filtered by SSA. The ellipses indicate the 95% confidence level; the data outside the ellipses are the unpredictable part of the data by the proposed model. The entire data of the validation period is 216 months (18 years). As seen in Figures 11 and 12, the outliers of both the calibration (identification) and the validation data show parallel features. The lowest minimum temperatures are not perfectly estimated by the identified model during either the calibration or validation period according to 95% significance level: Göztepe (Istanbul); Ankara; Diyarbakır; Izmir; (e) Adana; (f) Adana; (g) Erzurum

19 TEMPERATURE AND ATMOSPHERIC CIRCULATION RELATIONSHIPS 349 On the other hand, the uncertainties may be decreased by the Bayesian philosophy of using prior information at the local scale before calibration of a downscaling model. A study of the second approach may be found in Tatlı et al. (2004) for Turkish precipitation series. For further case studies over Turkey, the designs of proposed models both in this study and in Tatlı et al. (2004) may be bridged by nested models in order to extract climate impacts with physical-based model approaches. Additionally, during the parameterization of nested models, the results of the proposed analyses methods may be supportive in explaining the linkages between local-scale and large-scale climate variability and atmospheric disturbances. The proposed model ability to downscale local-scale climate features from a nested model for Turkey is still one of the open questions in these studies. ACKNOWLEDGEMENTS We wish to thank the anonymous reviewers for their very useful and constructive comments and suggestions. REFERENCES Allen MR, Smith LA Monte Carlo SSA: detecting irregular oscillations in the presence of coloured noise. Journal of Climate 9: Box GEP, Jenkins GM, Reinsel GC Time Series Analysis: Forecasting and Control, 3d edn. Prentice Hall. Bras RL, Rodriguez-Iturbe I Random Functions and Hydrology. Dover Publications. Chen JM, Chang CP A technique for analyzing optimal relationships among multiple sets of data fields. Part II: reliability case study. Monthly Weather Review 122: Chen JM, Chang CP, Harr P A technique for analyzing optimal relationships among multiple sets of data fields. Part I: the method. Monthly Weather Review 122: Coughlin KT Stratospheric and troposheric signals extracted using empirical mode decomposition. PhD thesis, Applied Mathematics, University of Washington, USA. Cubasch U, von Storch H, Waszkewitz J, Zorita E Estimates of climate change in southern Europe using different downscaling techniques. Max Planck Institute für Meteorologie, report no Dobrovolski SG Stochastic Climate Theory: Models and Applications. Springer: Berlin. Duffy DD The application of Hilbert Huang transforms to meteorological datasets. Journal of Atmospheric and Oceanic Technology 21: Elsner JB, Tsonis AA Low-frequency oscillation. Nature 372: Elsner JB, Tsonis AA Singular Spectrum Analysis: A New Tool in Time Series Analysis. Plenum Press: New York. Erinç S Climatology and Its Methods. Marine Science, Institute of Geography, Istanbul University Press: Istanbul, Turkey (in Turkish). Ghil M, Vautard R Interdecadal oscillations and the warming trend in global temperature time series. Nature 350: Giorgi F, Mearns LO Approaches to the simulation of regional climate change: a review. Reviews of Geophysics 29: Glahn HR Canonical correlation and its relationship to discriminant analysis and multiple regression. Journal of the Atmospheric Sciences 25: Gower JC Generalized procrustes analysis. Psychometrika 40: Green MC, Floccini RG, Myrup LO Use of temporal principal components analysis to determine seasonal periods. Journal of Applied Meteorology 32: Hewitson BC, Crane RG Climate downscaling: techniques and application. Climate Research 7: Hipel KW, Mcleod AI Developments in Water Sciences: Time Series Modelling of WaterResources and Environmental Systems. Elsevier. Hotelling H Relations between two sets of variates. Biometrika 28: Houghton JT, Meira Filho LG, Callender BA, Harris N, Kattenbarg A, Maskell K (eds) Climate Change The Science of Climate Change. Cambridge University Press: Cambridge. Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen NC, Tung CC, Liu HH The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences 454: Jackson JE A User s Guide to Principal Components. John Wiley. Jones PD Maximum and minimum temperature trends in Ireland, Italy, Thailand, and Turkey. Atmospheric Research 37: Jöreskog KG, Sörbom D LISREL-7: A Guide to the Program and Applications, 2nd edn. SPSS Publications: Chicago. Kadıoǧlu M Trends in surface air temperature data over Turkey. International Journal of Climatology 17: Kaiser HF Computer program for varimax rotation in factor analysis. Educational and Psychological Measurement 19: Kalnay E, Kanamitsu M, Kistler R, Collins W, Deaven D, Gandin L, Iredell M, Saha S, White G, Woolen J, Zhu Y, Chelliah M, Ebisuzaki W, Higgins W, Janowiak J, Mo KC, Ropelewski C, Wang J, Leetmaa A, Reynolds R, Jenne R, Joseph D The NCEP/NCAR reanalysis 40-year project. Bulletin of the American Meteorological Society 77: Karl TR, Wang WC, Schlesinger ME, Knight RW, Portman D A method of relating general circulation model simulated climate to the observed local climate. Part I. Seasonal statistics. Journal of Climate 3: Kidson JW Eigenvector analysis of monthly mean surface data. Monthly Weather Review 3: Kidson JW, Thompson CS Comparison of statistical and model-based downscaling techniques for estimating local climate variations. Journal of Climate 11:

20 350 H. TATLI, H. N. DALFES AND Ş. S. MENTEŞ Kim JW, Chang JT, Baker NL, Wilks DS, Gates WL The statistical problem of climate inversion. Determination of the relationship between local and large-scale climate. Monthly Weather Review 112: Komüşçü AU An analysis of the fluctuations in the long-term annual mean air temperature data of Turkey. International Journal of Climatology 18: Landman WA, Tennant WJ Statistical downscaling of monthly forecast. International Journal of Climatology 20: Mardia KV, Kent JT, Bibby JM Multivariate Analysis. Academic Press: New York. McGregor JL Regional climate modelling. Meteorology and Atmospheric Physics 63: Murphy JM An evaluation of statistical and dynamical techniques for downscaling local climate. Journal of Climate 12: Murphy JM Predictions of climate change over Europe using statistical and dynamical downscaling techniques. International Journal of Climatology 20: Noguer M Using statistical techniques to deduce local climate distribution. Meteorology Applications 1: North G Empirical orthogonal functions and normal modes. Journal of Atmospheric Science 41: Ouergli A Hilbert transform from wavelet analysis to extract the envelope of an atmospheric mode: examples. Journal of Atmospheric and Oceanic Technology 19: Preisendorfer RW Principal Component Analysis in Meteorology and Oceanography. Elsevier. Richardson CW Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resources Research 17: Rummukainen M Methods for statistical downscaling of GCM simulation. SWECLIM (Swedish Regional Climate Modelling Programme), Reports Meteorology and Climatology, no. 80. Sampson AR A multivariate correlation ratio. Statistics and Probability Letters 2: Schlesinger ME, Ramankutty N An oscillation in the global climate systems of period years. Nature 367: Schubert A, Henderson-Sellers A A statistical model to downscale local daily temperature extremes from synoptic scale atmospheric circulation patterns in the Australian region. Climate Dynamics 13: Solman SA, Nunez MN Local estimates of global change: a statistical downscaling approach. International Journal of Climatology 19: Tatlı H, Dalfes HN, Menteş ŞS A statistical downscaling method for monthly total precipitation over Turkey. International Journal of Climatology 24: Tayanç M, Karaca M, Yenigun O Annual and seasonal air temperature trend patterns of climate change and urbanization effects in relation to air pollutants in Turkey. Journal of Geophysical Research Atmosphere 2: TenBerge JMF Generalized approaches to the Maxbet problem and Maxdiff problem, with applications to canonical correlations. Psychometrika 53: Torrence C, Compo GP A practical guide to wavelet analysis. Bulletin of American Meteorology Society 79: Türkeş M, Erlat E Precipitation changes and variability in Turkey linked to the North Atlantic oscillation during the period International Journal of Climatology 23: Türkeş M, Sümer UM, Kılıç G Variations and trends in annual mean air temperatures in Turkey with respect to climatic variability. International Journal of Climatology 15: Türkeş M, Sümer UM, Demir I Re-evaluation of trends and changes in mean, maximum and minimum temperatures of Turkey for the period International Journal of Climatology 22: Tyler DE On the optimality of the simultaneous redundancy transformations. Psychometrika 47: Van de Geer Linear relations among k sets of variables. Psychometrika 49: Van den Wollenberg Redundancy analysis. Psychometrika 42: Vautard R, Yiou P, Ghil M Singular spectrum analysis: a toolkit for short, noisy and chaotic series. Physica D 58: Von Storch H Inconsistencies at the interface of climate impact studies and global climate research. Meteorologie Zeitschrift 4: Von Storch H, Zwiers FW Statistical Analysis in Climate Research. Springer/Cambridge University Press: Cambridge, UK. Von Storch H, Zorita E, Cubash U Downscaling of global climate change estimates to regional scales: an application to Iberian rainfall in wintertime. Journal of Climate 6: Wang J, Chern CS, Liu AK The wavelet empirical orthogonal function and its application to the analysis of internal tides. Journal of Atmospheric and Oceanic Technology 17: Wigley TML, Jones PD, Briffa KR, Smith G Obtaining sub-grid scale information from coarse-resolution general circulation model output. Journal of Geophysical Research 95: Wilks DS Statistical specification of local surface weather elements from large-scale information. Theoretical and Applied Climatology 40: Wu ML, Schubert S, Huang NE The development of the south Asian summer monsoon and the intraseasonal oscillation. Journal of Climate 12: Zorita E, Kharin V, von Storch H The atmospheric circulation and sea surface temperature in the North Atlantic area in winter: their interaction and relevance for Iberain precipitation. Journal of Climate 5: