Principal components of monsoon rainfall

Abstract

Monsoon rainfall over India during the 120-day period from the beginning of June to the end of September exhibits interesting oscillations over the country. According to an analysis by Subbramayya (1968), there is a negative correlation in rainfall between the north-eastern and west-central parts of India. But his analysis does not indicate how much of the total variance of rainfall is explained by different rainfall patterns. We examined this aspect by expressing rainfall as a linear combination of orthogonal functions. This technique was suggested by Lorenz (1956). It was later used by Kutzbach (1967) and Weare (1977) to evaluate the principal components of sea-level pressure over the northern hemisphere, and sea surface temperature over the Atlantic Ocean.Let P be a n x m matrix of monsoon rainfall over m stations and a series of n years. The elements (p,) of P represent departures of rainfall from their mean values for the sth station and the rth year. We used the data of 70 evenly distributed stations for a period of 60 years ). As P represents the time and space variability of rainfall, we put P = QF (1) Where the matrices Q and F represent, respectively, the time and space variation of rainfall. The elements of P are m = qrk(l) x&(X,y)(2) k== I As F is an orthonQrma1 matrixWhere F' is the transpose of F and Z is the identity matrix.To determine F and Q from P we define a matrixWhere D is a diagonal matrix. The columns of F are now the eigenvectors of S, while the elements of D are the eigenvalues of S. Each element of Q represents the amplitude of eigenvector, and every element of D is a measure of the percentage variance explained by the corresponding eigenvector. F and D were determined from S by Jacobi's method (Greenstadt, 1960). This is an iterative process which utilizes successive rotations of each element of S. It was observed that the process converged sufficiently after about 2500 iterations. A tolerance of was used before stopping further iterations.Figs. 1 -4 depict the first four principal components of P. A total of 15 components were examined. This accounted for 72% of the total variance of monsoon rain, but the first four components by themselves were able to explain 47 % of the variance. The contributions by components beyond the 15th were negligibly small. The amplitudes of each component are shown at the bottom of each figure.The opposition between northeast and western India appears to be the dominant feature of monsoon rain. This explained 26.9% of the total variance. We also observed that positive and negative amplitudes were evenly distributed over the last 60 years, with a tendency for more rapid oscillations in the two decades following 1950, but oo40-2826/80/030296-03$02.50/0 0 1980 Munksgaard, Copenhagen Tellus 32 (1980), 3

Classification of summer monsoon rainfall patterns over India

“…The fourth EOF (VE= 6.6 per cent) shows positive loadings over the northern and southern parts and negative loadings over the western and eastern parts. These EOFs compare well with the EOFs published by Bedi and Bindra (1980) and Prasad and Singh (1988). A major problem with EOF analysis is that the unrotated EOFs have a tendency to always produce a predictable sequence of patterns (Buell, 1979).…”

“…Empirical orthogonal functions of seasonal monsoon rainfall over India have been determined by several workers (e.g. Bedi and Bindra, 1980;Prasad and Singh, 1988). However, we have computed them from the same data of 114 years.…”

Regionalization of Rainfall Using RCDA Cluster Ensemble Algorithm in India

“…Spatial correlation analysis has been utilized for identification of homogeneous regions [5]. The concept of empirical orthogonal function analysis has been used for computation of regionalization [6]. The principal component analysis (PCA) and cluster analysis has been utilized for identification of the regions [7,8].…”

Spatial variability of daily rainfall over Orissa, India, during the southwest summer monsoon season

“…Studies on spatial variability of monsoon rainfall over India using EOF/PCA include those of Bedi and Bindra (1980) on seasonal (June-September) monsoon rainfall of 70 stations during 1911-70; of Hastenrath and Rosen (1983) on annual total rainfall of 31 meteorological subdivisions of contiguous India during 1900-72, as estimated by the India Meteorological Department (IMD); of Rasmusson and Carpenter (1983) on seasonal area-weighted monsoon rainfall of 31 meteorological subdivisions calculated from 31 representative stations during 1875-1979of Shukla (1987) on seasonal monsoon rainfall of 31 meteorological subdivisions during 1901-70 of Prasad and Singh (1988) on area-weighted seasonal moonsoon rainfall of 31 subdivisions during 1901-80; and of Gregory (1989) on area-weighted seasonal rainfall of 29 meteorological subdivisions during 1871-1985 as calculated from rainfall over 306 stations representing 306 districts of contiguous India (Parthasarathy et al, 1987). Applications of EOF/PCA in the medium-range scale have been made by Gadgil and Iyengar (1980), Kripalani et al (1991) and Majumdar (1998).…”