İstanbul İçin Klimatolojik Mevsimlerin Belirlenmesi

Abstract

Mevsimlerin bilinen iki tanımlama şekli vardır: 1. Astronomik tanımlama. 2. Bir yılı üçer aylık peryotiara bölen meteorolojik tanımlama. Bunlar karşılaştırıldığında kış en soğuk üç ayı, yaz en sıcak üç ayı, ilkbahar ve sonbahar bu mevsimler arasındaki geçiş peryotlannı temsil etmektedir. Klimatolojik paternler hiç bir standart mevsim tanımlamasının belirlediği peryotiara uymaz. Bu çalışmada da gözlenen sıcaklık değerleri kullanılarak İstanbul için klimatolojik mevsimler saptanıp, bu mevsimlerin meteorolojik ve astronomik olarak tanımlanan mevsimlere uyup uymadığı belirlenmiştir. Bu amaçla Kandilli Rasathane' si Meteoroloji Laboratuvar'ımn 1912-1993 yıllarına ait sıcaklık verilerine grafik, ana bileşen ve kümeleme analizi uygulanmıştır. Günlük ve aylık sıcaklık ortalamaları bir takvim yılı içersinde gözönüne alman ( eski veri olarak adlandırdığımız) veri grubu ve bir yıllık veri oluşturulmasında günlük ve aylık sıcaklık ortalamaları bir yıl önceki aralık ayından başlatılan (yeni veri olarak adlandırdığımız) veri grubu olarak analize tabi tutulmuştur. Günlük ortalama sıcaklıkların grafiksel analizi sonucunda 6 Mart-30 Mayıs, ilkbahar; 30 Mayıs-29 Eylül yaz; 29 Eylül-3 Ocak, sonbahar; 3 Ocak-6 Mart, kış olarak belirlenmiştir. Günlük ve aylık ortalama sıcaklık verilerinin ana bileşen çözümleme analizi mevsimleri belirlemede olumlu sonuç vermemiştir. Yeni veri grubuna ait veriden elde edilen sonuçlara göre, İstanbul için şubat, mart, nisan,mayıs ve haziran aylan ilkbaharı; temmuz ve ağustos aylan yazı; eylül ve ekim aylan sonbaharı; kasım, aralık ve ocak aylan kışı temsil etmektedir. Sonuç olarak grafik ve kümeleme analizlerinden İstanbul için belirlenen klimatolojik mevsimlerin meteorolojik ve astronomik mevsimlere uymadığı görülmüştür.

In this study, daily and monthly temperature data from Kandilli Observatory Meteorology Laboratory for 1912-1993 years have been analyzed to determine seasonal periods, using graphical, principal components and cluster analysis. The concept of dividing the year into four seasons is reexamined to appraise critically the relative merit of two commonly used definitions of the seasons. 1. The astronomical definition 2. The Meteorological breakdown into four three- month periods. These are compared with the definition of winter as the coldest seasons, summer as the warmest season and spring and autumn as the transition seasons. The astronomical seasons define winter as period from the winter solstice (22 December an average) to the vernal equinox (21 March). Spring ends at the summer solstice (22 June). Summer continues until the autumnal equinox (23 September) and autumn completes the cycle, ending an the winter solstice. Note that the astronomical seasons vary length from 89 to 93 days. In meteorology, the most widely used breakdown into seasons is simply the subdivision into four three-month periods. Winter is December, January and February, the three coldest months; spring is March, April and May; summer is the three warmest months; June, July and August and autumn is September, October and November. However, climatological patterns do not necessarily have temporal patterns coinciding with the standard definitions of seasons. In litis study, we have used observational data on surface temperature over the Istanbul, are used to determine what the seasons should be. First, graphical method was applied daily temperature data. This analysis gave different seasons than meteorological seasons. Secondly, principal components analysis was applied monthly and daily long-term temperature data. The technique of using principal components has been around a long time (Hotelling, 1933), but modern computers have made routine the formerly burdensome calculations. Since 1980, the principal component analysis has been widely used in meteorological and climatological investigations for different purposes. The original application of principal components analysis was in the field of educational testing. Principal components and factor analysis are also used extensively in psychological applications in an attempt to discover underlying structure. There are six possible modes of principal component analysis, depending upon which parameters are used as variables, individuals, or fixed entities. These six modes have been denoted as 0, P, Q, R, S, and T by Catell (1952). In this study, R-mode principle components analysis was applied daily and monthly temperature data for Istanbul. Temporal principal components analysis was applied separately to monthly long-term wind, temperature, and precipitation data for Southern California by Green (1993). The objective of principal component analysis is to find a linear transformation of a set of variables into a small number of variables may extract maximum information from the original variables. The sum of the variances of all principal components is equal to the sum of variance of the original variables. The technique can be summarized as a method of transforming the original variables into new, uncorrelated variables. If there are p linear functions of p random variables in a data set these variables, although related to each other, may not all contain the same amount of information, and in fact some variables may be completely redundant. Obviously, this will result in a loss of information and waste of resources analyzing the data. Thus we should select only variables that will truly discriminate one variable from another, while those least discriminatory should be discarded. Often this is not an easy task. However, this task is simplified if the transformations are made in such a way that these p linear functions become uncorelated. Or, if the original variables are normally distributed these p linear functions become independent. In this case we could discard the variables from study functions reflecting less variability and consider only these functions that have higher variances. These p uncorrelated linear functions are called principal components (Srivastava et al., 1983). Suppose that we have observations represented by a vector X consisting of p random variables, simultaneously observed p times. A first attempt in order simplify the situation one may inquire whether it is possible to find new variables. For the linear transformation, Where Tp^is the transformation matrix. We must thus have, Var(Y) = Y1RT (2) Where R is the correlation matrix and Var (Y) is a diagonal matrix, the values of which are the variances the components. The column vectors tj and the corresponding A,- of the principal diagonal of Var (Y) are the corresponding eigenvector and eigenvalue of the correlation matrix R. We have: (R-A,I)tj = 0 (3) Where I is the unit matrix, ki,..., Xp are the eigenvalues. If the components are identified according to the magnitude of the eigenvalues (variances), we may say mat the first component, yi, has the largest possible variance of any linear function; the second, y2, has the largest variance subject to being, uncorrelated with the first; third has the largest variance of linear functions which are uncorrelated with the first and second and so on down to the smallest eigenvalue, which corresponds to the linear combination with the smallest variance (Kendall, 1975). XI As Jolliffe (1986) said, a major advantage for using correlation matrices, rather than covariance matrices in order to define principal component is that the results of analyses for different sets of random variables are more directly comparable than for analyses based on covariance matrices. There are several methods available in order to decide how many principal components are to be retained. Such as the screen test, log-eigenvalue graph, Monte Carlo test and eigenvalue-one method. Throughout this work, the eigenvalue-one method has been adopted. In the eigenvalue-one method only the variances or eigenvalues which are greater than unity are retained since the rest of the principal components. Would in this case possess variances which are smaller than the variance of at least one of the eigenvalues which are retained. The two fundamental issues centering around principal components are, first, the issue of whether or not there is a need to rotate principal component: and second, if rotation is favored, the selection of the most appropriate rotation method. In a detailed review, Daultry (1976) argued that rotation was inappropriate because it eliminates both the properties of maximum variance (orthogonal rotation) and orthogonality. Despite these objections, there has been a resurgence in interest in the application of rotated principal components analysis. Richman (1986), for example, comprehensively argued for rotation, whereby after they had been extracted each principal component should, as far as possible, have high associations with some original axes, and low associations with others. Of the several methods of rotation available (e.g. Richman, 1986) the two used most commonly in climatology are the varimax (orthogonal) and oblimin (oblique) rotations. Of these two rotations, varimax appears to have been used most frequently; for example, by Steiner (1965), McBoyle (1971,1972), Perry (1972), Preston-Whyte (1974), Atwoki (1975), Barring (1987), Ogallo (1989), Whetton (1989), although not always in the same mode. Few have used only oblimin (for example, Richman, 1981), but some have published the results of comparative studies using non-rotated and varimax-oblimin (Dyer, 1975) and varimax-oblimin (Ogallo, 1980; Stone, 1989; Eklundh and Pilesjo, 1990). In this study, principle components are linearly transformed using the varimax method. The main principle of the varimax orthogonal rotation is to maximize the variance of the squared loadings, so that the simplest pattern is described while explaining the maximum amount of variance. Hence the rotation of the principal components using the varimax method increases the discrimination among the loadings and makes easier to interpret the results (Horel, 1981). In this study, varimax orthogonal rotation was applied to principal components. After that, in this study cluster analysis of temperature data in Istanbul are described. Cluster analysis was developed to group similar data on the basis of several measurements. An example would be to find areas with similar climates on the basis of yearly rainfall and temperatures patterns. Cluster analysis assumes the researcher has little knowledge of the group structure. In hierarchical cluster analysis one presumes no knowledge of the grouping structure. Non-hierarchical methods such as McQueen's K-means require the researcher to specify the number of clusters to be Xll mode and seed points upon which to build clusters. Several important points must be considered when using cluster analysis. First, the data units must be selected. Clustering should be done using only one dimension at a time because interactive effects are very difficult to interpret in practice. Yearly data for several areas can be used to group similar years or similar areas. A second issue is the need carefully select the variables to be included. Naturally, as in all statistical analyses, the number of data units must be much larger than the number of variables included. It is also important that the data be standardized within each variable. The researcher must decide on a measure of association between the data unit. In clustering procedures for grouping similar variables, Pearson correlation may be used, but Pearson correlation does not work well in clustering data units. Rather, in clustering similar data units a distance measure should be used, frequently Euclidean distance. The Euclidean distance (dy) between two units i and j, each having m (k=l,..., m) variables with values x is calculated. m dij=[Z(xik-xJl£)2]I/2 (4) k=l Another important decision for the researcher is the selection of the researcher is the selection of which clustering technique to use. Several are available, and each has certain advantages and limitations. First of all, there are hierarchical techniques successively combine or divide clusters of data units. The first methodology is called agglomerative; the second is called divisive. Some of the most popular clustering techniques are agglomerative hierarchical. Several agglomerative hierarchical techniques have been developed. Each can be used to detect different types of clusters, and again each has certain advantages and limitations. The most popular techniques are single linkage, complete linkage, average linkage and Ward's minimum variance. In this study, we have used single linkage method. Analysis were performed using daily and monthly temperature data for long years. The results gave seasonal periods of uneven length. Rather than each season being the conventional three months long, seasons ranged from one to six months for 1913-1993 periods (new data) and from two to five months for 1912-1993 periods (old data). The temperature analyses gave short summer, winter and spring periods and long autumn for old data. This analyses gave short summer, winter and autumn periods and long spring for new data. Finally, these analyses gave different seasons than meteorological seasons. As the same, cluster analysis was applied to monthly long-term wind, temperature, and precipitation data for Southern California by Green (1993). The temperature and wind analyses gave same seasons for California. Table 1 contains climatological seasons for Istanbul and meteorological seasons. XIII Table 1. Climatological seasons for Istanbul and meteorological seasons.