EMPIRICAL ORTHOGONAL FUNCTION ANALYSIS FOR CLIMATE VARIABILITY OVER THE INDONESIA-PACIFIC REGION

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1 EMPIRICAL ORTHOGONAL FUNCTION ANALYSIS FOR CLIMATE VARIABILITY OVER THE INDONESIA-PACIFIC REGION Orbita Roswintiarti 1, Betty Sariwulan 1 and Nur Febrianti 1 1 Natural Resources and Environmental Monitoring Division Indonesian National Institute of Aeronautics and Space (LAPAN) Jl. LAPAN No. 70, Pekayon Pasar Rebo, Jakarta Telp./Fax Abstract An Empirical Orthogonal Function analysis has been performed on monthly mean Outgoing Longwave Radiation anomaly for the greater part of Indonesia-Pacific region (30 S 30 N; 80 E 80 W) during the period In this paper, the first three Empirical Orthogonal Function modes are presented. A mode is defined spatially in terms of an empirical orthogonal function, which describes the degree of coherence of variation. The principal component s corresponding coefficients depict the evolution of the mode in time. The results show the most important non-seasonal convective variation over the Indonesia-Pacific region (the first mode) is governed by the west-east overturning Walker circulation. The spatial and temporal patterns of this mode are identified by the El Niño/Southern Oscillation phenomenon. Other two modes are discussed. 1. INTRODUCTION The climate of Indonesia is determined by the temporal and spatial distribution of the Inter- Tropical Convergence Zone (ITCZ) and South Pacific Convergence Zone (SPCZ). ITCZ is a zone of low-pressure near the equator where two easterly trade winds originating from the Northern and Southern hemispheres converge. This zone of enhanced convection, cloudiness, and rainfall constitutes the rising branch of the meridional Hadley circulation. SPCZ is a band of abundant cloudiness extends southeastward the Indonesian convection center. One of the most striking characteristics of the ITCZ and SPCZ is its variability on a wide range of temporal scales. On the interannual time scales, the ITCZ and SPCZ over Indonesia is dominated by the El Niño/Southern Oscillation (ENSO). The El Niño is associated with the anomalous warm sea surface temperature (SST) in the easterncentral tropical Pacific Ocean. The Southern Oscillation is referred to the strength of the Walker circulation over the Pacific region, i. e., to the difference in surface pressure between the southeastern tropical Pacific and the Indonesian- Australian regions. Ropelewski and Halpert (1987) demonstrated that 80% of the ENSO events from 1879 to 1982 were accompanied by below normal rainfall in Indonesia between June and November. Moreover, Ropelewski and Halpert (1989) found that 90% of La Niña events were associated with abnormally wet season over Indonesia between July and December. Table 1 shows the El Niño and La Niña (the anomalous cold SST in the eastern-central tropical Pacific Ocean) events from 1951 to 2000 identified using SST anomalies in the Nino 3.4 region (5 N-5 S; W) and 0.4 C threshold (Trenberth 1997). MBA - 33

2 Table 1. The El Niño and La Niña events identified using SST anomalies in the Nino 3.4 region and exceeding ± 0.4 C threshold El Niño events Begin End Duration (months) La Niña events Begin End Duration (months) Aug 1951 Feb Mar 1950 Feb Mar 1953 Nov Jun 1954 Mar Apr 1957 Jan May 1956 Nov Jun 1963 Feb May 1964 Jan May 1965 Jun Jul 1970 Jan Sep 1968 Mar Jun 1973 Jun Apr 1972 Mar Sep 1974 Apr Aug 1976 Mar Sep 1984 Jun Jul 1977 Jan May 1988 Jun Oct 1979 Apr Sep 1995 Mar Apr 1982 Jul Jun 1998 Jun Aug 1986 Feb Sep 2000 Feb Mar 1991 Jul Feb 1993 Sep Jun 1994 Mar Apr 1997 May On the annual time scales, the ITCZ over Indonesia is dominated by the Asian-Australian (AA) monsoon that implies a complete reversal of wind regimes in the course of the year. The Northeast monsoon, which dominates the general circulation from November to February, is characterized by northeasterly trade winds over the western Pacific and Southeast Asia from about 20 N to the equator. Proceeding southward across the equator, the low-level flow turns to westerly winds which extend between 10 S and 20 S across Java, northern Australia, and the southwest Pacific. Heavy rainfall and associated heat release of condensation exist between 5 S and 15 S extending from the Indian Ocean to the western Pacific Ocean. The Southwest monsoon, which prevails from June to September, is a continuation of the southwesterly winds from southern Indian Ocean to Asia. During the southwest monsoon, the primary region of heating is situated over the Tibetan Plateau and cooling region over the Southern Indian Ocean. Following the onset of the monsoon, there is an intense low-level jet along the east coast of Africa and over the Arabian Sea (the Somali Jet). Significant fluxes of moisture from the ocean surface to the atmosphere occur over these regions, which fuel the deep convection rains over India and neighboring countries. Heavy precipitation also occurs over southern and central China. However, its moisture source appears to be primarily from the equatorial regions of Indonesia. The Empirical Orthogonal Function (EOF) analysis enables fields of highly correlated data to be represented adequately by a small number of orthogonal functions and corresponding orthogonal time coefficients. The purpose of this study is to employ the EOF analysis to define a number of variables which account for much of the spatial and temporal non-seasonal variability of climate over the Indonesia Pacific region. 2. DATA AND METHOD The data sets used for this analysis are monthly OLR, i. e. the longwave radiation observed at the top of the atmosphere. The OLR data set is one of the most widely data used as a proxy for tropical convection (Waliser et al. 1993; Vincent et al. 1998). In the tropics, OLR is governed primarily by cloud top temperatures, so that low OLR values are related to high cloud tops or deep convection and thus to the ITCZ/SPCZ. The OLR has been routinely obtained from the µm window on operational National Oceanic and Atmospheric Admistration (NOAA) polarorbiting satellites since 1974 (Gruber and Winston 1978). New algorithms were developed in MBA - 34

3 subsequent years to improve the accuracy of the OLR (Gruber and Kruger 1984). The OLR data set is available globally at a 2.5 x 2.5 resolution from the Climate Prediction Center-National Oceanic and Atmospheric Administration (CPC-NOAA). The period used in this analysis spans from January 1982 to December 2003 (264 months). The global monthly OLR data are then cropped to the greater part of Indonesia region from 30 S to 30 N and between 80 E 80 W (a 25 x 81 matrix). Generally, the OLR values 240 Wm -2 refer as deep convection and OLR values > 240 Wm -2 as clear-sky conditions in the sense of monthly mean. The long-term monthly mean OLR derived from the entire record investigation is first calculated to identify the climatological conditions. Roswintiarti (2005) analyzed the relationship between the tropical OLR value and rain rate obtained from the Global Precipitation Climatology Project (GPCP) dataset during the period. The linear relationship is given as: Rr = x OLR (1) Here Rr is the rain rate (mm/day) and OLR is the monthly OLR value (W/m 2 ). Secondly, the EOF is performed for the monthly OLR anomaly. In EOF, the covariance matrix is constructed from the data field and diagonalized to obtain eigenvectors and corresponding eigenvalues. The elements of this covariance matrix must be formed from the deviations or anomalies from the mean values of the data. Each eigenvector describes a mode of spatial pattern and the associated a series of time coefficients (PC) that define the evolution of the spatial mode. As the eigenvectors are orthogonal in space, the associated PCs are also orthogonal in time. A fraction of the total variance given by particular eigenvector is proportional to its corresponding eigenvalue. Furthermore, the eigenvalues are arranged in decreasing order according to the percentage of variance associated with them. The eigenvectors that account for large fractions of the variance are, in general, considered to be physically meaningful. The remaining modes that account for very small fractions of the variance are considered statistically and presumably physically non-significant (noise). Since the modes are orthogonal, any two modes may be regarded as uncorrelated. Complete descriptions and applications of the EOF method can be found in, for example, Kutzbach (1967) and Peixoto and Oort (1992). The outline of the computational steps is given below: Given a matrix data F MxN, whose elements f mn are denoted by anomaly values. Here m=1, 2,..M is a grid point or station position counter and n=1, 2, N is a time counter. The eigenvectors and eigenvalues are calculated from the characteristic equation of the covariance matrix R given by: ( I ) E = 0 R λ (2) where E = [e 1, e 2, e M ] is the eigenvector data set, λ = [λ 1, λ 2, λ M ] is the eigenvalue data set, I is the unit matrix of order M, and R is given as: R 1 N T = FF (3) with F T is the transpose matrix of F. This, any observation vector f n can be expressed as a linear combination of the M eigenvector e m : n M f = C m= 1 mn e m (4) Here C mn are the components of the projection of f n on e m. The coefficients C mn are the elements of MxN matric C such that: T C = E F (5) For the computations of EOF, the OLR anomaly dataset is arranged into a rectangular matrix, where the rows represent grid points and the columns months. In this analysis, there is a 2025 x 264 matrix. MBA - 35

4 Table 2. Percentages of variance explained by the first 10 EOF s Var (%) Mode Month January February March April May June July August September October November December RESULTS AND DISCUSSION Figure 1 illustrates the long-tem monthly means of OLR over Indonesia-Pacific region for the sample months of January, April, July and October representing boreal winter, spring, summer, and fall. The mean position of the ITCZ and SPCZ reaches its farthest south position at most longitudes in January and February. The heaviest rainfall (smaller OLR) is located along the equator and in regions just to the south. In contrast, the lightest rainfall (highest OLR) is located along India to the eastern Pacific Ocean (between 10 N and 25 N) and Australia. As heating from the sun increases in the northern hemisphere during the months of April and May, the ITCZ and SPCZ begin moving northward. In June and July, the ITCZ and SPCZ reach its northernmost position. During these months, the ITCZ over the Pacific Ocean is characterized by a narrow cloud band located between 5 N and 10 N. During September and October, the ITCZ and SPCZ areas of heavy rainfall begin to move southward towards the equator, a process that will continue as the boreal fall progresses. The percentages of variance of the non-seasonal OLR anomaly modes explained by the first ten EOF s are given in Tabel 1. Figures 2-4 show the respective first three EOF of the spatial patterns (eigen vectors) and plots of corresponding time coefficients (principal components) for January, April, July and October. In viewing these figures it should be noted that, the actual anomaly value at each grid point is the product between eigenvector for that grid and the value of principal component for that month. The first EOF (EOF-1), explaining 39.1% (January), 27.4% (April), 21.3% (July), and 35.3% (October), clearly corresponds to the mode of variation characteristic of ENSO with 4 6 year periodicity (Fig. 2). From the principal component patterns, the years corresponding with ENSO are 1982/83, 1987, 1991,92, 1997/98, while with La Niña are 1984/85, 1988/89, 1998/2001. In these figures, convection anomalies over Indonesia and the central Pacific act as the opposite western and eastern Southern Oscillation dipoles in the interannual variability. Enhanced convection (negative OLR anomaly) over Indonesia is associated with suppressed convection (positive OLR anomaly) over the central Pacific and vice versa. These features are strongest during the boreal winter. During the boreal spring, the western dipole over Indonesia becomes weaker whereas a narrow band along northern equatorial Pacific Ocean is more prominent. The eastern dipole over Pacific is more to he east in this time. During the boreal summer, the narrow band along the northern Pacific Ocean splits into two in-phase dipole centered over Indonesia and (20 N, 160 E). On the other hand, the eastern dipole of the central Pacific extends to the eastern Pacific. During the boreal fall, the east-west dipole features become distinguished again. The second EOF (EOF-2), explaining 11.9% (January), 20.0% (April), 15.0% (July), and 9.2% (October), still portrays the west-east patterns in MBA - 36

5 which the east varies in the opposite sense of the west with a period of approximately 4 6 years. Moreover, this mode is also influenced by the annual variation (Fig.3). The time series corresponding with ENSO are 1983, 1987, 1991/92, and During the boreal winter, the west-east convective dipole is clearly occurred over the central and eastern Pacific Ocean. During the boreal spring, the west-east convective dipole is more to the west, i. e over Indonesia and central Pacific. During the boreal summer, the east dipole moves towards the Philippines. During the boreal fall, the east dipole over the western Pacific Ocean splits into two in-phase dipole with north-south oriented. The third EOF (EOF-3), explaining 7.1% (January), 7.0% (April), 8.0% (July), and 7.2% (October), closely associates with the zonal variation with periodicity of 2 3 years (Fig. 4). The time series has a period of approximately 3 years. Comparing with the other two modes, this mode has much smaller amplitudes. During the boreal winter, the convective variability mostly occur over Indonesia with the strongest variation is located over the Java Sea near East Nusa Tenggara. During the boreal spring, the north-south dipole clearly occurs over the central Pacific Ocean. During the boreal summer, the north-south dipoles take place over the northern-equatorial and southern-equatorial Indian Ocean and over the Pacific Ocean centered at (25 N, 170 E) and (10 N, 180 E). During the boreal fall, the notorious in-phase patterns are seen over western Pacific Ocean north of Papua island. 4. CONCLUSION The EOF analysis, in principle, is a data reduction technique. The reduction of data is achieved by finding a set of empirical orthogonal eigenvectors (spatial patterns) and the corresponding principal components (temporal patterns) which account for an adequate total variance of the original data. The EOF analysis is performed to obtain the modes of variability. We have shown the EOF analysis used to identify the modes of non-seasonal climate variability over the Indonesia-Pacific region. The spatial and temporal patterns of the first mode, which displays the most important mode of convective variation over the Indonesia-Pacific region, correspond with the ENSO event of the west-east overturning Walker circulation. Suppressed convection over Indonesia is associated with enhanced convection over the central Pacific during ENSO events and vice versa during La Niña event. These features are weakest in boreal spring and summer and strongest in fall and winter. The second mode of EOF still portrays the west-east variation of the Walker circulation at smaller amplitudes with influences from the annual variation. The third mode of EOF closely links with the zonal variability. REFERENCES Gruber, A. and J. S. Winston, Earthatmosphere radiative heating based on NOAA scanning radiometer measurements. Bull. Am. Meteorol. Soc., 59, Gruber, A., and A. F. Krueger, The status of the NOAA outgoing longwave radiation data set. Bull. Am. Meteorol. Soc., 65, Kutzbach, J. E., Empirical eigenvectors of sea level pressure, surface temperature and precipitation complexes over North America. J. Appl. Meteor., 6, Peixoto, J. P., and A. H. Oort, 1992: Physics of Climate. American Institute of Physics- NY, Ropelewski, C. F., and M. S. Halpert, Global and regional scale precipitation patterns associated with the El Niño/Southern Oscillation. Mon. Wea. Rev., 115, Ropelewski, C. F., and M. S. Halpert, Precipitation patterns associated with the high index phase of the Southern Oscillation. J. Climate, 2, Roswintiarti, O., 2005 (Ed.). Laporan Pemantauan Cuaca dan Iklim di Indonesia Tahun 2004 (Transl. Year 2004 Weather and Climate Monitoring Report). Pusat Pengembangan Pemanfaatan dan Teknologi Penginderaan Jauh, 2005 (unpublished). Trenberth, K. E., The definition of El Niño. Bull. Amer. Meteor. Soc., 78, Vincent, D.G., A. Fink, J. M. Scrage, and P. Speth, 1988: High- and low-frequency MBA - 37

6 intraseasonal variance of OLR on annual and ENSO time scale. J. Climate, 11, Waliser, D. E., and C. Gautier, A satellitederived climatology of the ITCZ. J. Climate, 6, MBA - 38

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