Authors:
Shreyasi Debnath,Mourani Sinha,DOI NO:
https://doi.org/10.26782/jmcms.2022.04.00003Keywords:
Rotated empirical orthogonal functions,Principal components,Data analysis,Significant wave height,Bay of Bengal,Abstract
Given any space-time field, Empirical orthogonal function (EOF) analysis finds a set of orthogonal spatial patterns along with a set of associated uncorrelated time series or principal components (PCs). Spatial orthogonality and temporal uncorrelation of EOFs and PCs respectively impose limits on the physical interpretability of EOF patterns. This is because physical processes are not independent, and therefore physical modes are expected in general to be non-orthogonal. Rotated empirical orthogonal functions (REOF) were introduced to generate general localized structures by compromising some of the EOF properties such as orthogonality. EOF and REOF analysis are carried out for the significant wave height (SWH) data for the Bay of Bengal (BOB) region for the period 1958 to 2001. Separate experiments were conducted for all the months together and also for July and December representing the southwest and northeast monsoon periods. The first eigenmodes account for 84%, 68%, and 59% of the total variability for the above three cases respectively. The REOF proved to be more effective than EOF for the above region.Refference:
I. Craddock, J. M., 1973: Problems and prospects for eigenvector analysis in meteorology. The statistician, 22, 133-145.
II. Crommelin, D. T., and A. J. Majda, 2004: Strategies for model reduction: Comparing different optimal bases. J. Atmos. Sci., 61, 2206–2217.
III. Farrell, B. F., and P. J. Ioannou, 1996: Generalized stability theory. Part I: Autonomous operators. J. Atmos. Sci., 53, 2025–2040.
IV. Hannachi, A., I. Joliffe, and D. Stephenson, 2007: Empirical orthogonal functions and related techniques in atmospheric science: Areview. Int. J. Climatol., 27, 1119–1152, doi:10.1002/joc.1499.
V. Hotelling, H., 1933: Analysis of a complex of statistical variables into principal components. J. Educ. Psych,, 24, 417-520.
VI. Jolliffe, I. T., 2002: Principal Component Analysis. Springer-Verlag, 2nd Edition, New York.
VII. Kleeman, R., 2008: Stochastic theories for the irregularity of ENSO. Philos. Trans. Roy. Soc., 366A, 2509–2524, doi:10.1098/rsta.2008.0048.
VIII. Kutzbach, J. E., 1967: Empirical eigenvectors of sea-level pressure, surface temperature and precipitation complexes over North America. J. Appl.Meteor., 6, 791-802.
IX. Lo`eve, M., 1978: Probability theory, Vol II, 4’th ed., Springer-Verlag, 413pp.
X. Lorenz, E. N., 1956: Empirical orthogonal functions and statistical weather prediction. Technical report, Statistical Forecast Project Report 1, Dept. of Meteor., MIT, 1956. 49pp.
XI. Monahan, A. H., and A. Dai, 2004: The spatial and temporal structure of ENSO nonlinearity. J. Climate, 17, 3026–3036.
XII. North, G. R., T. L., Bell, R. F. Cahalan, and F. J. Moeng, 1982: Sampling errors in the estimation of empirical orthogonal functions. Mon.Weather Rev., 110, 699-706.
XIII. North, G. R., 1984: Empirical orthogonal functions and normal modes. J. Atmos. Sci., 41, 879–887.
XIV. Penland, C., 1996: A stochastic model of Indo-Pacific sea surface temperature anomalies. Physica D, 98, 534–558.
XV. von Storch, H., and F. W. Zwiers, 1999: Statistical Analysis in Climate research, Cambridge University Press, Cambridge.
XVI. Weare, B. C., and J. S. Nasstrom, 1982: Examples of extended empirical orthogonal function analysis. Mon. Weath. Rev., 110, 481-485.
XVII. Wilks, D. S., 1995: Statistical Methods in the Atmospheric Sciences. Academic Press, San Diego.