Objective Regionalisation of R. Asokan1 and N. Sivagnanam2 1Regional Meteorological Centre, Chennai Tamil Nadu, a Southern State of 2(Retd.), Department of Geography India based on Principal University of Madras, Chennai Component Analysis E-mail: [email protected] ABSTRACT The daily rainfall of 29 districts of Tamil Nadu during northeast monsoon is used for principal component analysis. Out of 29 districts, 22 districts are grouped into five homogenous Sub-regions which are having stronger relationship with five Varimax rotated principal components and the 7 districts are found with weak / moderate relations to any of the Principal components. Tamil Nadu is regionalised in to five Sub-regions based on strong relationship with first 5 PCs; Sub- region 1 comprises of districts Cuddalore, Perambalur, Pudukottai, Thanjavur, Thiruvarur and Nagapattinam. The Interior districts Madurai, Sivaganga, Virudhunagar and Dindugul make sub- region II. The districts Dharmapuri, Salem, Namakkal, Karur, Erode, Nilgiris and Coimbatore make Sub-region III and the districts Chennai, Kanchipuram, Vellore and Thiruvallur form Sub- region IV. The group of districts Tirunelveli, Thoothukudi and Kanyakumari make Sub-region V. Keywords: Principal component analysis, sub-regions, northeast monsoon, climate variables. 1. Introduction Wales based on the daily rainfall data. Barring (1987) Tamil Nadu is one of the southernmost states applied common factor analysis for the of India The proximity of sea influences the climate regionalisation of daily rainfall of Kenya. White et al of eastern and southern part of Tamil Nadu whereas (1991) made use of cluster analysis and different hilly orography and distance from the sea play an rotation algorithms to monthly Pennsylvanian pre- important role over rest of the State. The topography cipitation data while Bonell and Sumner (1992) used and proximity to sea influences the rainfall cluster analysis and obliquely rotated Principal Com- distribution of Tamil Nadu and the state provides ponent Analysis (PCA) for the daily precipitation in an interesting area for studies of spatial variability Wales. Fovell and Fovell (1993) identified the cli- of rainfall. As per convention followed by India matic zones and sub zones of the conterminous Meteorological Department at Chennai, Tamil Nadu United States from monthly temperatures and pre- is divided into four sub regions mainly based on cipitation after clustering the orthogonally rotated their proximity to coast and their geographical principal components. Also objective regionalisation location for the purpose of regional level forecasting was done by Sumner et al (1993) for Mallorea, of weather over Tamil Nadu (Fig.1). They are Periago et al (1991) for Catalonia and Romero et al namely, (1) North Coastal Tamil Nadu (NCTN), (2) (1999) for whole of Spain. Therefore, arriving an South Coastal Tamil Nadu (SCTN), (3) North objective regional division shall be more meaning- Interior Tamil Nadu (NITN) and (4) South Interior ful and can be explained with reasoning. Further Tamil Nadu (SITN). It may be noted that objective such objective analysis will facilitate forecasting in regionalisation concept is not a factor for the a more meaningful way. classification of the administrative districts. Identifying basic rainfall regions of Tamil Nadu Objective regionalisation based on different cli- objectively, therefore, may explain the sub regional mate variables like temperature and rainfall is the characteristics of the distribution. In other words, basis for dividing the large areas into many sub re- the identification of the 29 districts of Tamil Nadu gions. This regionalisation can be obtained by us- into fewer objective rainfall regions can serve for ing different methods, ranging from elementary link- practical administrative purposes. This type of age analysis to more complex multivariate statisti- regionalisation has potential use in providing a cal techniques like factor analysis, cluster analy- regional short, medium and long range forecasting sis, corresponding analysis, etc. Sumner and Bonell of rainfall during NEM season. (1990) used linkage analysis regionalisation of 113 region into fairly homogeneous areas is required, the rotated PCs will almost inevitably do it better than unrotated PCs (Jolliffe, 1987). Since the loadings of various PCs depend upon the number of PCs retained for rotation, several criteria based on dominant variance rule are suggested by various authors for deciding how many PCs to be retained. Kaiser criterion (Kaiser, 1958), Scree test (Cattle, 1996) & Log-Eigen value (LEV) diagram (Craddock et al, 1969), Preisendorfer's rule 'N' are generally used as methods to decide the number PCs to be retained for rotation. Kaiser criterion says that the factors with Eigen values having greater than one are to be retained for rotation. Figure 2(a) is the Scree plot and 2(b) is LEV diagram. The goal here is to identify the break in slope or a cut off in the difference between successive PCs in the plot. The method of Preisendorfer's rule N (Preisendorfer et al (1981), Wilks (1995)) identifies the largest number of principal components to be involved on the basis of resampling tests involving the distribution of Eigen values of randomly generated dispersion matrices. The first method suggests 5 PCs for rotation but other three methods suggest 4 PCs for rotation. Here in this study, the first 5 PCs are retained for rotation as per Kaiser's criterion. Generally Varimax (orthogonal) (Richman, 1986, Fig.1 29 districts and four sub-regions of Tamil Nadu. 1987), Quartimax (orthogonal), Equamax (orthogonal) and Oblimin (oblique) (Richman, 1981) rotation methods are used for rotation of PCs. Here 2. Data and Methodology in this study, Varimax rotation IS used to find out The daily rainfall data of 173 rain gauge stations most interpretable simple structure of PC loadings. of Tamil Nadu during the main rainy season namely northeast monsoon season (1st October to 31st December) for the period from 1965 to 1996 is used. The rain gauge stations are spatially well distributed in the state and there is no spatial bias in the data set. Based on this data, the daily rainfall data of the 29 districts of Tamil Nadu during northeast monsoon season for the period of 31 years (1965 to 1996) is constructed. The daily rainfall series is a complete time series. Here S- mode Principal component analysis (PCA) is carried out taking 29 districts as Fig.2(a) Scree diagram. variables and 2852 days rainfall as cases to provide an objective pluviometric regionalisation of Tamil Nadu. Since the casual mechanisms of precipitation are fuzzy and overlapping, the regionalisation based on unrotated PCs will have overlapping areas. For this reason, assuming the rotation can produce simple structures (as in Gong and Richman, 1995), rotation of PCs has been attempted. The rotation of components wants to simplify the interpretation of the derived variables and to optimise by a criterion to obtain a 'simple structure'. If the division of a Fig.2(b) Log- Eigen value (LEV) diagram. 114 3. Results and Discussion accounted for by each component, add the sum of 3.1 Variance explained by Principal the squared factor loadings for that component and Components divide by the number of variables. Here the first 10 Table 1 shows the Eigen values and the principal components are sufficient for explaining corresponding variance explained by each PC with 85% of total variance while first 14 and 20 principal the cumulative percentage of total variance. The components are needed to explain 90% and 95% component loadings are the correlation coefficients of total variances respectively. The first five PCs between the variables and components analogous explained about 73% of total variance. In this study to Pearson's correlation coefficient 'r'. The squared first five components are chosen for interpretation component loadings are the percentage of variance and further analysis, as it is often customary to in that variable explained by the component. To get restrict the choice of Eigen values higher than or the percentage of variance in all the variables equal to 1.0 only. TABLE 1 Variance and cumulative variance explained by first 10 PCs based on 2852X29 matrix. PC Numbers Eigen value Cumulative Variance (%) Cumulative % of Eigen value Total variance. 01 12.43 12.43 42.88 42.88 02 3.21 14.24 11.07 53.95 03 2.59 18.23 8.93 62.95 04 2.17 20.40 7.51 70.39 05 1.00 21.40 3.46 73.85 06 0.73 22.13 2.52 76.36 07 0.72 22.85 2.47 78.83 08 0.65 23.50 2.26 81.09 09 0.56 24.06 1.94 83.03 10 0.50 24.56 1.73 84.77 Fig.3a Fig.3b 115 3.2 Unrotated Principal Components. The factor loadings of first 5 PCs are shown in Fig.3. The raw or unrotated component I (variance explained 43%) has positive loadings in all districts. This means that all districts are positively correlated with PC I. This PC indicates that first source of (c) variance in the data is associated with the overall magnitude of rainfall events in the region as a whole. In the table, factor loadings greater than 0.7 are found in central coastal districts along with Dindugul and in some north interior districts. PC II (variance explained 11%) has positive loadings of more than 0.3 in south TN and negative loading of less than - 0.3 in north coastal and neighbouring north interior districts. PC III (variance explained about 9%) has positive loadings (more than 0.3) in central coastal districts and in south coastal districts. Negative loadings (less than -0.3) are found over northwest Tamil Nadu. PC IV (variance explained is about 8%) has positive loadings of more than 0.3 in Cauvary basin region and adjoining districts while northeast Tamil Nadu have negative loading of less than -0.3.