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  • View in gallery

    Schematic of the centered composite analysis.

  • View in gallery

    Composites, (a) centered and (b) uncentered, expressed in t values [Eq. (1)] of filtered OLR (shading) and ERA-40 u200 (contours) for MJO events over the Indian Ocean with lags indicated on the right in days. Composites are based on a selection of dates from filtered OLR for 1981–2000. Contour intervals are ±2, 2.6, 3.3, 4.5, and 6.5, and the magnitude at the t = 2.6 contour is approximately 2 m s−1. The centers of the crosses are the mean position of the OLR minima used to define the composites, and the arms of the crosses define the east–west and north–south distance of one standard deviation from the mean location of the center of all of the elements contributing to the composites.

  • View in gallery

    Same as in Fig. 2, but for composites of filtered OLR (shading) and ERA-40 u1000 (contours) for MJO events over the western Pacific Ocean.

  • View in gallery

    Same as in Fig. 2, but for centered composites of unfiltered ERA-40 surface pressure (shading) and OLR (contours) for MJO events over the (a) Indian Ocean and (b) western Pacific Ocean. The magnitude at the t = 2.6 contour is approximately 1 hPa.

  • View in gallery

    Same as in Fig. 2, but for centered composites of unfiltered NCEP–NCAR surface pressure (shading) and OLR (contours) for MJO events over the (a) Indian Ocean and (b) western Pacific Ocean.

  • View in gallery

    Same as in Fig. 2, but for centered composites of unfiltered ERA-40 u1000 (shading) and u200 (contours) for MJO events over the(a) Indian Ocean and (b) western Pacific Ocean. The magnitude at the t = 2.6 contour is approximately 0.4 m s−1 for 1000 hPa and 0.2 m s−1 for 200 hPa.

  • View in gallery

    Same as in Fig. 2, but for centered composites of MJO filtered ERA-40 ∇ · V1000 (shading) and q850 (contours) for MJO events over the (a) Indian Ocean and (b) western Pacific Ocean.

  • View in gallery

    Meridional means (10°S–10°N) of centered composites of unfiltered OLR, surface pressure, u1000, and u200 for MJO convective centers over (a), (b) the Indian Ocean and (c), (d) the western Pacific for lags of (b), (d) zero and (a), (c) −10 days. All units are in standard deviations of the respective quantity.

  • View in gallery

    Same as in Fig. 8, but for unfiltered OLR, Ts, q850, LH, and SSR.

  • View in gallery

    Same as in Fig. 2, but for centered composites of unfiltered ERA-40 surface pressure for MJO events over the Maritime Continent.

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Centered Composite Analysis of Variations Associated with the Madden–Julian Oscillation

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  • 1 Atmospheric Science Program, University of California, Davis, Davis, California
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Abstract

Centered composite analysis is described and applied to gain a better understanding of the initial phases of the Madden–Julian oscillation (MJO). Centered composite analysis identifies the dates and central locations of key events. The elements of the composite means are centered on these central locations before averages are calculated. In this way much of the spatial fuzziness, which is inherent in traditional composite analysis, is removed. The results for the MJO, based on MJO-filtered outgoing longwave radiation for the reference data and 40-yr ECMWF Re-Analysis (ERA-40) and NCEP–NCAR reanalysis products for the composites, show highly significant composites of unfiltered data for not only zero lag, but also lags back to 20 days before the target events. These composites identify propagating patterns of surface pressure, upper- and lower-troposphere zonal winds, surface temperature, and 850-hPa specific humidity associated with MJO convective events in the Indian Ocean. The propagation characteristics of important features, especially surface pressure, differ substantially for MJO convective anomalies centered over the Indian or western Pacific Oceans. This suggests that distinctly different mechanisms may be dominant in these two regions, and that many earlier analyses may be mixing properties of the two.

Corresponding author address: Bryan C. Weare, Atmospheric Science Program, Dept. of Land, Air and Water Resources, University of California, Davis, 1 Shields Ave., Davis, CA 95616. Email: bcweare@ucdavis.edu

Abstract

Centered composite analysis is described and applied to gain a better understanding of the initial phases of the Madden–Julian oscillation (MJO). Centered composite analysis identifies the dates and central locations of key events. The elements of the composite means are centered on these central locations before averages are calculated. In this way much of the spatial fuzziness, which is inherent in traditional composite analysis, is removed. The results for the MJO, based on MJO-filtered outgoing longwave radiation for the reference data and 40-yr ECMWF Re-Analysis (ERA-40) and NCEP–NCAR reanalysis products for the composites, show highly significant composites of unfiltered data for not only zero lag, but also lags back to 20 days before the target events. These composites identify propagating patterns of surface pressure, upper- and lower-troposphere zonal winds, surface temperature, and 850-hPa specific humidity associated with MJO convective events in the Indian Ocean. The propagation characteristics of important features, especially surface pressure, differ substantially for MJO convective anomalies centered over the Indian or western Pacific Oceans. This suggests that distinctly different mechanisms may be dominant in these two regions, and that many earlier analyses may be mixing properties of the two.

Corresponding author address: Bryan C. Weare, Atmospheric Science Program, Dept. of Land, Air and Water Resources, University of California, Davis, 1 Shields Ave., Davis, CA 95616. Email: bcweare@ucdavis.edu

1. Introduction

The Madden–Julian oscillation (MJO) was first identified by Madden and Julian (1972, 1994) as an eastward-propagating anomaly in the tropical winds and surface pressure with a period of around 45 days. The anomalous circulation is identified by a surface low pressure region with upward motion associated with deep convection and adjacent surface high pressure regions of suppressed convection. Many of these features are observed to propagate eastward along the equator at speeds of a few meters per second. Since its discovery, the MJO has evoked a great deal of interest in part because of its potential use as a forecast tool for such diverse situations as the timing of Indian monsoon depressions (Yasunari 1981), the frequency and intensity of hurricanes in the Caribbean (Maloney and Hartmann 2000), and the occurrence of intense winter rains in California (Jones 2000).

The initiation, growth, and propagation of the MJO have been investigated using multiple techniques including sophisticated statistical analyses of observations (e.g., Hendon and Salby 1994), and diagnostics from the results of simple models (e.g., Wang and Xie 1997) and global climate models (e.g., Hendon 2000). A large number of papers (e.g., Hendon and Salby 1994; Maloney and Hartmann 1998) have found that once an MJO is established over the Indian Ocean most of its features propagate eastward as a slow-moving Kelvin–Rossby wave complex with a first baroclinic mode structure. However, a number of fundamental questions remain concerning the initiation and periodicity of MJO events. One initiation theory, the circumnavigating wave hypothesis, suggests that convection in the Indian Ocean is stimulated by the remnants of an earlier MJO after propagating around the globe. These models often invoke frictional wave conditional instability of the second kind (CISK; e.g., Wang and Rui 1990; Salby et al. 1994) to stimulate the observed eastward propagation. However, researchers have often found it difficult to observe organized remnants of earlier MJO events over Africa. In addition, this theory cannot explain how MJO events start long after any earlier event has disappeared. Another hypothesis (Kemball-Cook and Weare 2001; Maloney and Hartmann 1998) suggests that initiation occurs over the Indian Ocean through an internal recharge in low-level moisture and moist static energy. This leads to convective instability that is released when low-level convergence induces convection. Although this hypothesis has been partially confirmed by observations, detailed moisture and energy budgets in the data-sparse regions of the tropical oceans are difficult to accurately attain. Thus, it has been difficult to elucidate the exact physical processes that lead to the buildup of instability. An additional initiation mechanism involves a rectification of higher-frequency middle-latitude perturbations into low-frequency low-latitude anomalies (Hsu et al. 1990). Unfortunately, there has been very little observational evidence that such a mechanism works on a regular basis.

A number of analytical/statistical techniques have been used to analyze observations relating MJO convective events to such diverse variables as precipitation (e.g., Bantzer and Wallace 1996), upper-level winds (e.g., Hartmann and Gross 1988), low-level moisture divergence (e.g., Jones and Weare 1996), and sea surface temperature (e.g., Hendon and Glick 1997). For instance, many authors have used composite analysis (Von Storch and Zwiers 1999) to discern important space–time interactions. In such an analysis, a time series is first defined that is thought to describe an important aspect of the MJO phenomenon. This time series may be chosen ad hoc or may be the result of an initial empirical orthogonal function (EOF) analysis of a relevant data field. Then, key dates in this time series are established, for instance, when the convection at a specific location exceeds some threshold. Finally, any variable can then be averaged together for times corresponding to those key dates and, most importantly, for days that either precede or follow the key dates. The significance of important features is often established by standard Student’s t tests, using the variability within members of a given composite. A primary drawback of this technique is that individual elements of the means tend to move around within the domain. This leads to smeared results, whose t statistics may not be significant at the 95% level.

Another commonly used methodology to infer the space–time structure of a complex phenomenon like the MJO is the development of so-called teleconnection maps. In this method a primary time series is also defined in some manner. The time coefficients are then used as an index time series to calculate lag correlations or regression coefficients with a variety of other fields. Statistical significance is established using traditional tests for correlations (Von Storch and Zwiers 1999). One of the criticisms of this methodology is that the significances of the resulting correlations or regression coefficients are sometimes low and difficult to establish because the data are often highly autocorrelated in time. Other statistical techniques have included EOF (e.g., Wheeler and Hendon 2004) and singular value decomposition (e.g., Weare 2003) analyses.

The current paper describes and applies an extension of composite analysis, which is designed to better elucidate the complex spatial and temporal relations inherent in the MJO and other geophysical phenomena. This extension, which will be called centered composite analysis, identifies not only the dates, but also the central locations, of key events. The elements of composite means are centered on these central locations before averages are calculated. In this way much of the spatial fuzziness, which is inherent in traditional composite analysis and tends to reduce the significance of the composites, is removed. The expectation is that the greater significance obtained using the centered composites will enable one to usefully analyze unfiltered observations rather than the filtered data commonly used in MJO diagnostic studies. Analyzing unfiltered data is important because it is possible that the filtering process, which uses data over a broad time swath, is producing artificial temporal autocorrelations that are not present in the raw data. The next section further explains centered composites and the subsequent sections apply this method to better understand MJO initiation.

2. Methods and data

a. Centered composite analysis

To describe the calculation of centered composite analysis a specific example will be used. In this case, the key times and locations will be determined from MJO-filtered outgoing longwave radiation (OLR), which effectively monitors changes in convection associated with the MJO. The composite dataset will be daily surface pressure departures from long-term daily means. In step a (see Fig. 1) the filtered OLR data for a broad search region are scanned over a smaller target region (say 5° latitude by 10° longitude) for a strong minimum. For each date meeting this criterion the center of this minimum is located, and the vector distance to a fixed central location is calculated in step b. In step c the whole map of the surface pressure data is translated the vector distance calculated in step b. This process is repeated for each date of a significant OLR negative anomaly. In step d the surface pressure data for all of these centered maps are averaged together. To define the significance of the calculated means, Student’s t tests are used. Last, in step e the composite surface pressure maps are translated back to the mean position of the OLR minima in order to facilitate interpretation of the composites.

b. ERA-40 data

Forty-year European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40; Simmons and Gibson 2000) observations are the result of the assimilation of traditional observations and satellite data, including the Television Infrared Observation Satellite (TIROS) Operational Vertical Sounder (TOVS), Special Sensor Microwave Imager, European Remote Sensing Satellite, Advanced TOVS, and cloud motion winds, into a start-of-the-art forecast model. The result is a set of gridded data fields that agree well with observations and are dynamically and energetically self-consistent. In this case, a three-dimensional variational technique is applied using the T159L60 version of the European Centre forecast model. The current analysis uses 1200 UTC daily values of surface pressure, 200- and 1000-hPa winds, 1000-hPa divergence · V1000, 850-hPa specific humidity q850, surface temperature Ts, net surface solar radiation (SSR), and surface latent heat flux (LH; positive for heat exiting the ocean). These data are on a 2.5° × 2.5° grid for the region between 45°S and 45°N and are sampled every 5 days for 1981–2000.

c. NCEP–NCAR reanalysis data

A set of observations similar to that obtained from the ERA-40 has been derived from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis (Kalnay et al. 1996) for the same 1981–2000 period. The NCEP–NCAR reanalysis fields are on a 2.5° × 2.5° grid at 17 vertical levels. As with ERA-40, sparsely spaced rawinsonde low-level wind and humidity are supplemented by extensive satellite data and other data such as the Tropical Atmosphere–Ocean array (Hayes et al., 1991) moored buoy surface data, which help to better define the near-surface humidity and flows. One important difference between NCEP–NCAR reanalysis and ERA-40 is that the former does not use Microwave Sounding Unit observations, which are thought to be important in reproducing tropical precipitation fields. Newman et al. (2000) show significant differences between the NCEP–NCAR and an earlier version of the ECMWF (Gibson et al. 1997) reanalysis divergence fields over the western equatorial Pacific Ocean. Other important differences are likely to exist between the ERA-40 and NCEP–NCAR reanalyses in the data-sparse Tropics studied here.

d. Interpolated OLR

Daily OLR data, which are on the same 2.5° × 2.5° grid as the reanalysis data, are used to define the locations of extensive organization and suppression of convection associated with the MJO. These data have been carefully calibrated and adjusted in order to reduce the influence of the different satellite platforms and instruments used to gather them (Lucas et al. 2001; also see http://www.cdc.noaa.gov/cdc/data.interp_OLR.html). The relatively few missing data have been interpolated using the method described by Liebmann and Smith (1996). To identify the MJO these data are filtered at each point using a high-quality 150-point Lanczos filter (Duchon 1979) that captures most of the 20–100-day periodicities. The filtered data are then sampled every 5 days for a total of 1430 time points. No spatial filtering, such as the strong wavenumber truncations used by Hendon and Salby (1994), has been applied. In a few cases the Lanczos filter and 5-day sampling were also applied to reanalysis fields.

e. e. Experimental setup

The 20–100-day filtered OLR observations are used to determine the key dates and locations of MJO convective events in the centered composite analysis. An event is identified if the filtered OLR averaged over a 7.5° latitude by 12.5° longitude region has a value less than −50 W m−2. Other methods, such as EOF indices, are possible for determining the key dates and times. Experiments using different size averaging regions and different thresholds show that the results are quite insensitive to these choices. The regions of interest for the convective events were the tropical Indian Ocean (20°S–20°N, 30°–90°E) and the western Pacific Ocean (20°S–20°N, 120°E–180°). Because of the reduction of data required by the filtering, the time period of the analysis was approximately 15 March 1981 through 15 October 2000. For the Indian Ocean this identification process identified 189 MJO convective events out of a total of 1430 possible pentad samples. For the western Pacific Ocean there were 152 events included in the composites. For both basins the means of the centers of MJO activity were within 4° latitude of the equator. The standard deviations of the positions of the centers from those means were less than 10° of latitude and 20° of longitude. Nearly 60% of the chosen pentads fell within the Northern Hemisphere winter defined by October through March.

The primary centered composite means are composed of unfiltered departures of the ERA-40 data from the 19-yr pentad means derived from the period 15 March 1981 through 14 March 2000. Also utilized were unfiltered departures of the Climate Diagnostics Center (CDC) OLR observations and the NCEP–NCAR reanalysis products for the same period. Use of unfiltered data in these composites, which is not common in MJO studies, assures that no artificial lag/lead relationships are introduced in the results through the substantial time averaging inherent in all filtering schemes. A few of the composites to be discussed were composed of 20–100-day filtered observations. The statistical assessment as to whether a composite mean at each point is different from zero is determined by the Student’s t test (Von Storch and Zwiers 1999) such that
i1520-0442-19-9-1834-e1
where N is the number of samples in the composite mean, and X and σX are the mean and standard deviations of the variable X, respectively. Absolute values of t greater than 2, 2.4, and 3.3 are judged to be statistically different than zero at approximately the 95%, 97.5%, and 99.5% significance levels. To relate composites of different variables with different units the results are plotted in terms of the t statistic values.

3. Results

To compare this methodology with previously published results analyses were first made using filtered CDC OLR and ERA-40 200- and 1000-hPa zonal winds as the target data. Two sets of composite analyses were completed. In the first, the centered composite analysis methodology, described above, was carried out. In the second, mean maps of the filtered OLR and 200-hPa zonal winds u200, without the centering steps, were calculated. This latter method, which will be called the “uncentered” analysis, corresponds to traditional composites. Sample centered and uncentered composites of filtered OLR and u200 for times in which convection occurs in the Indian Ocean are illustrated in Fig. 2. The maps at the different lags correspond to the composites for 0, 5, 10, 15, and 20 days before the filtered OLR minima. In Fig. 2a the centers of the large crosses near the equator identify the mean positions of the OLR minima, which define the mean locations of the centered maps, and the north–south and east–west spreads identify one standard deviation from the mean positions. The results for lags 10 and 0 days may be compared with the composites in Figs. 1 and 2 of Hendon and Salby (1994; hereafter HS). These authors defined MJO events by using filtered OLR centered at 0°, 84°E. Their filtering was a bandpass identifying eastward periods of 35–95 days and zonal wavenumbers 1–3. Their results are displayed for target fields, which have been similarly filtered.

The most prominent features of the shaded OLR in Fig. 2a are near the equator and clearly propagate slowly eastward in the centered and the HS analyses. The uncentered composites in Fig. 2b show comparable minima that have smaller magnitudes and are much less significant than the corresponding values for the centered analysis. Furthermore, the uncentered analysis very poorly shows the propagation of OLR minima for times earlier than about 10 days before the targeted events. For lags of 0, 5, and 10 days the locations of the centers of the negative anomalies are very similar in both analyses. The locations of the dominant positive anomalies are not easily followed in the uncentered analysis. The results for the centered, uncentered, and HS analyses of filtered u200 show eastward propagation near the equator of both westerly and easterly wind anomalies. Again, the centered composites generally have much larger magnitudes and are more significant than the uncentered results. This is especially evident for the 5- and 10-day lags for which large easterly anomalies are evident in the Western Hemisphere in the centered, but not the uncentered analysis. At zero lag there is an indication, especially in the centered result, of the meridional structure exhibited in Fig. 2 of HS. Overall, the centered analysis shows more distinct features with much greater statistical significance than the uncentered analysis, while preserving the locations and approximate speeds evident using the more traditional methodology.

Figure 3 shows another example of both the centered and uncentered analyses of filtered data. In this case, the compositing used the OLR minima in the western Pacific Ocean to determine key dates and locations with filtered OLR and filtered ERA-40 1000-hPa zonal wind u1000 as the target fields. These can be compared with Figs. 2–4 of HS. Again, the centered and uncentered analyses show eastward propagation of both the filtered OLR and u1000 fields comparable to that of HS. Also, again the centered OLR composites have larger magnitudes and greater significance. However, the magnitudes of the centered u1000 are not clearly larger in the centered analysis. One difference between the two analyses is that the patterns in both fields in the centered analysis are slightly to the east of the comparable patterns in the uncentered. Nevertheless, these two analyses suggest about the same speed of propagation of both fields, approximating those of HS.

The primary motivation for the centered composites is to provide a compositing methodology that gives more significant means, and thus can be applied to unfiltered, rather than filtered data. Figure 4 shows the MJO-centered composite mean unfiltered ERA-40 surface pressure and unfiltered CDC OLR separately for MJO anomalies in the Indian Ocean and western Pacific regions for various lags. Again, the crosses near the equator identify the mean position and spread of the positions of the OLR minima. The most prominent features in Fig. 4a for zero lag are the broad minima in surface pressure in the region of and east of the center of MJO activity, coupled with the equally prominent positive pressure anomalies to the west of the MJO centers. As expected, the zero lag unfiltered OLR departures are strongly negative in the region of the filtered anomaly centers. The zero lag map for MJO convective events centered in the western Pacific (Fig. 4b) has a very similar morphology. However, there is a large difference in the progression of the surface pressure and OLR anomalies from 20 days before the MJO event for the Indian and western Pacific Ocean regions. For the Indian Ocean there is a clear eastward propagation of the low pressure and negative OLR regions starting for the pressure in the Atlantic sector at day −20. This propagation of the pressure field is comparable to the progression in this region shown in Sperber (2003), who illustrates a lag versus longitude diagram of filtered surface pressure relative to variations near the equator and 130°E.

For the western Pacific events there is little or no progression of the surface pressure lows; there only appears to be a gradual reduction in pressure in the general region of the future MJO convection. The Sperber results also suggest an important shift in propagation properties near 150°E. The pattern of change of OLR in the western Pacific shows little propagation and seems close to a simple reversal of OLR anomaly from positive to negative as time progresses from day −20 to day 0. Kikuchi and Takayabu (2003) also note a strong shift of propagation properties of filtered OLR between the Indian and Pacific Ocean basins. Differences in the character of the high pressure anomalies also exist between the Indian and western Pacific MJO centers. For the Indian Ocean convection there is a strong high pressure pattern near the location of the future MJO convection at days −15 and −20. There are no such patterns for those periods for the western Pacific MJO anomalies. These results strongly point to fundamental differences between how MJO convective events initially develop over the Indian Ocean and then strengthen over the western Pacific Ocean.

Since the ERA-40 and NCEP–NCAR reanalyses are known to have important differences in the Tropics, the analysis in Fig. 4 was repeated using NCEP–NCAR data. Figure 5 shows the MJO center composited mean unfiltered NCEP–NCAR surface pressure and unfiltered CDC OLR as in Fig. 4. The general patterns are very similar to the composites of the ERA-40 surface pressure. In particular there is an eastward propagation of low pressure from day −15 to day 0 associated with the Indian Ocean MJO events and primarily a stationary deepening of low pressure associated with the western Pacific events. Thus, both reanalyses illustrate distinctly different patterns of variation of surface pressure associated with MJO convective events over the Indian and western Pacific Oceans.

The centered composites of unfiltered ERA-40 1000- and 200-hPa zonal winds are shown in Fig. 6. The u200 result in Fig. 6a may be compared with the result for filtered data in Fig. 2a; that for u1000 in Fig. 6b is comparable to the filtered result in Fig. 3a. At the time of the convective events (zero lag) in both the Indian and western Pacific Oceans low-level (upper level) westerly (easterly) anomalies exist to the west and easterly (westerly) anomalies exist to the east of the convective centers. Eastward propagation of low-level easterly and upper-level westerly anomalies is clearly evident for Indian Ocean convective events. Initiation of Indian Ocean MJO convective events is associated with persistent surface easterlies and upper-level westerlies over the Indian Ocean and eastern Africa. For western Pacific events there appears to be clear eastward propagation of both upper- and lower-atmosphere anomalies starting with day -10. However, propagation of low-level anomalies from earlier times is not clear in the unfiltered data. This is in contrast with the filtered results illustrated in Fig. 3a in which clear propagation is seen starting 20 days before the convective events.

Low-level divergence · V1000 and moisture q850 patterns are key features of the frictional wave CISK (e.g., Salby et al. 1994) and recharge (e.g., Kemball-Cook and Weare 2001) hypotheses of MJO development. Centered composites of the MJO-filtered ERA-40 values of these two parameters are shown in Fig. 7. The comparable maps of unfiltered surface divergence (not shown) have almost no regions that are statistically different from zero at the 95% level. The filtered · V1000 shows a region of convergence near the convective center at days 0 and −5 and divergence at days −15 and −20. However, unlike suggestions by the frictional wave CISK hypothesis and some earlier observational studies (e.g., Hendon and Salby 1994; Sperber 2003), the filtered divergence features do not appear to propagate to the east for convective features centered either over the Indian or western Pacific Ocean. There is also no evidence that surface convergence extends to the east of the active convection. Figure 6 also shows that near the centers of MJO convection the lower layer of the atmosphere is moistening from day −20 to day 0. For moisture there is also a strong suggestion of a slow eastward propagation associated with convection in both ocean basins.

Figure 8 summarizes the relationships between the dynamical variables (surface pressure, u1000, and u200) at lags 0 and 10 days in terms of their zonal means between 10°S and 10°N for MJO convective anomalies in both the Indian and western Pacific Oceans. At zero lag the relationships between the variables in the Indian and western Pacific Oceans are quite similar. In both cases an anomalous low is slightly east of the region of convection as indicated by the OLR minimum. This low is accompanied by surface easterlies and upper-level westerlies starting slightly east of the region of maximum convection. Perhaps the largest difference between the two regions at zero lag is the more pronounced dipole nature of most of the variables in the western Pacific. At the 10-day lag differences in the dynamical variables in the two ocean basins are much more pronounced. Most dramatically the surface pressure anomalies east of the convective center are positive for the Indian Ocean and negative or neutral for the western Pacific Ocean. This is despite the fact that as for zero lag the surface (upper level) winds are easterly (westerly) to the east of the convection in both regions. Thus, it is clear that the evolution of convective centers in the Indian and western Pacific Oceans differ remarkably.

Additional analyses have been designed to shed light on possible physical mechanisms associated with the development of MJO convective events. These include centered composites of unfiltered surface temperature Ts, q850, net SSR, and LH. The Ts anomaly patterns for zero lag (not shown) are similar to the unfiltered surface temperature regression patterns in Sperber (2003, his Fig. 6) in that the primary positive features are east of the convective centers. Figure 9 shows plots comparable to those in Fig. 8 for these “thermodynamic” variables (Ts, q850, SSR, and LH). In both regions at zero lag the OLR minimum is accompanied by a maximum in q850 near the convective center and a maximum of Ts just to the east of the center. The results for a lag of 10 days (and other lags not shown) in the Indian Ocean suggest an eastward propagation of Ts, but not of q850. On the other hand, over the western Pacific the results suggest propagation of q850, but not of Ts. There is, however, a strong indication of a fixed location surface warming near the future convective center.

As expected at zero lag the SSR is a minimum near the convective centers. The LH is a minimum slightly to the east and a maximum slightly to the west of the center. The magnitudes of these heating departures are about 10 W m−2 (not shown). The zero lag LH anomaly patterns are shifted slightly west of those of the unfiltered NCEP–NCAR LH regression patterns shown in Sperber (2003). The Sperber zero lag NCEP–NCAR SSR pattern is quite different from that found in the centered composite maps (not shown). In the centered case there is a clear east–west dipole, whereas Sperber shows a maximum (minimum) south (north) of the equator and the main convective zone. The primary differences at zero lag between events over the Indian and western Pacific Oceans are that the variations in the western Pacific exhibit a more pronounced dipole structure than those in the Indian Ocean region. At a lag of 10 days the LH in both basins has a maximum to the east of the developing convective center. SSR also has a maximum to the east of the convection at a lag of 10 days over the Indian Ocean, but not over the western Pacific Ocean. These same differences are evident at all lags between 5 and 20 days (not shown). This suggests that heating and moistening processes play complex roles in the development of convection over the western Pacific, and especially over the Indian Ocean.

4. Discussion

Centered composite analysis has been described and applied to gain a better understanding of the initial phases of the MJO. Centered composite analysis identifies mean maps centered on the main features of a reference dataset, which generally have greater statistical significance than those derived from traditional composite analysis. Unlike in most of the earlier studies this allows for statistically significant composite means of unfiltered, rather than filtered, data.

The results for the MJO, based on MJO-filtered OLR for the reference data and ERA-40 reanalysis products for the composites, show highly significant composites for a variety of unfiltered data for not only zero lag, but also lags back to 20 days before the target events. Most of the displayed analyses here have been repeated using the NCEP–NCAR reanalyses as the target dataset, and the results are very similar to those shown as illustrated for surface pressure in Fig. 5. In addition the analyses have been repeated using different compositing threshold criteria. In one set of experiments the averaging region of the filtered OLR primary field was reduced to a 2.5° latitude by 7.5° longitude region. The results (not shown) are qualitatively very comparable to those illustrated. In two other experiments the composites were based upon thresholds of −40 and −60 W m−2, rather than the −50 W m−2 as in the illustrated results. In these cases the number of elements of the composites increased and decreased, respectively, by about 10%. However, these centered composites, especially for zero lag, are very similar to those illustrated.

The centered composites identify propagating and standing patterns of surface pressure, upper- and lower-troposphere zonal winds, surface temperature, and 850-hPa specific humidity for MJO convective events over the Indian and western Pacific Oceans. However, many of the propagation characteristics of important features differ substantially for MJO convective anomalies centered over the two basins. This is especially true for surface pressure derived from either the ERA-40 or NCEP–NCAR reanalyses. However, recognizable differences are evident in all of the variables analyzed here. This suggests that distinctly different mechanisms may be dominant in these two regions. These differences are not evident in most of the earlier analyses.

There are several possible reasons for the differences from prior studies. First, many of those earlier analyses used a reference dataset, which focuses on convection centered over the Maritime Continent. The composites from these analyses would tend to give a mixture of properties from events over the Indian and western Pacific Oceans. In particular, the choice of the Maritime Continent for the reference location might exaggerate the propagation characteristics of the MJO because features would tend to cluster either to the east over the Indian Ocean or to the west over the western Pacific. This was tested by carrying out centered analyses for target OLR anomalies between 70° and 140°E. The results for unfiltered ERA-40 surface pressure are shown in Fig. 10. Comparing this figure with the results in Fig. 4, one sees that the zero lag pattern is a mixture of the properties of the Indian and western Pacific centered composites. Thus the location of the broad region of the negative pressure anomalies is similar to that of the western Pacific composite, but the location of the broad positive anomaly is between that in the western Pacific and Indian composites. At a lag of 10 days in Fig. 10 the negative anomaly is spread over the Indian Ocean and far western Pacific. This does not correspond well to the results for the Indian or western Pacific composites. Overall, the results in Fig. 10 appear to be a combination of those in Figs. 4a and 4b. Thus, many earlier composite and regression analyses of MJO may have seriously mixed the very different properties of the two regions, thus suggesting relations that are applicable to neither.

Another reason for the differences between the current results and earlier studies may be that most of those studies used filtered target data. Since filters usually sample data over several MJO events, the filtering process itself may be building lag/lead relationships into the results. This could be especially true when there are large standing oscillations as has been found for the MJO (Salby and Hendon 1994). Most of the present analyses have been repeated using filtered, rather than unfiltered, data from both the ERA-40 and NCEP–NCAR analyses. Overall, as previously discussed with reference to Figs. 2, 3 and 6, the filtered means tend to show more distinct propagation than the unfiltered ones. However, the statistical significance of these lagged features may disappear if one carefully accounted for the fact that the filtered data are much more highly autocorrelated in time than the unfiltered data (Kikuchi and Takayabu 2003). Nevertheless, more robust propagation may still exist using filtered data. It is an open question as to whether this is because the filtering effectively excludes irrelevant information or because it subtly introduces artificial autocorrelations.

A final reason that the current results may differ from earlier studies is that the centering methodology may itself be introducing some unexpected bias. For instance, if the region from which the composites are drawn was very large, then it is possible that the results could be due to the mixing of fundamentally different phenomena. The qualitative similarities between the centered and uncentered results in Figs. 2 and 3 suggest that this is not a major concern for the domains in the current study. This is in part because the two search regions were carefully chosen to be relatively homogeneous without major topographic barriers, and to be close to the equator so as not to mix features associated with tropical and middle-latitude dynamics.

As a further test, the analyses in Figs. 4a, 6a and 7a were repeated using a smaller Indian Ocean search region covering only 30°–60°E, rather than 30°–90°E. This smaller region was chosen to test whether a possible mixing of the MJO initiation and growth regions was influencing the composites. The results (not shown) are qualitatively very similar to the original figures. However, the modified maps show slightly less significance overall because the number of elements of the composites of the modified analysis is smaller than for the original. This illustrates a general characteristic of all compositing techniques. Narrowing the selection criteria reduces the number of samples and often the statistical significance of the results. As centered composite analysis is more generally applied, a better understanding of all of the possible biases of its results as well as those of regular composite analysis will undoubtedly be obtained.

Centered composite analysis is likely to be a useful diagnostic tool for any phenomenon that has relatively well defined centers of action. In addition to the MJO, such phenomena include the El Niño–Southern Oscillation (ENSO; Barnett et al. 1991) and, perhaps, such things as the Pacific decadal oscillation (Zhang et al. 1997) and the North Atlantic Oscillation (e.g., Hurrell 1995). The primary requirement for such analyses is to define a variable that allows one to identify not only the times of strong occurrences of a phenomenon, but also the approximate location of an important feature associated with a key time.

Acknowledgments

ERA-40 data were provided by the European Centre for Medium-Range Weather Forecasts from their Web site at http://data.ecmwf.int/data/d/era40_daily/. NCEP–NCAR reanalysis data were provided by the NOAA–CIRES Climate Diagnostics Center, Boulder, Colorado, from their Web site at http://www.cdc.noaa.gov. Interpolated OLR data were also provided by NOAA–CIRES from the same Web site. This work was supported by NSF Grant ATM-0212685.

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Fig. 1.
Fig. 1.

Schematic of the centered composite analysis.

Citation: Journal of Climate 19, 9; 10.1175/JCLI3703.1

Fig. 2.
Fig. 2.

Composites, (a) centered and (b) uncentered, expressed in t values [Eq. (1)] of filtered OLR (shading) and ERA-40 u200 (contours) for MJO events over the Indian Ocean with lags indicated on the right in days. Composites are based on a selection of dates from filtered OLR for 1981–2000. Contour intervals are ±2, 2.6, 3.3, 4.5, and 6.5, and the magnitude at the t = 2.6 contour is approximately 2 m s−1. The centers of the crosses are the mean position of the OLR minima used to define the composites, and the arms of the crosses define the east–west and north–south distance of one standard deviation from the mean location of the center of all of the elements contributing to the composites.

Citation: Journal of Climate 19, 9; 10.1175/JCLI3703.1

Fig. 3.
Fig. 3.

Same as in Fig. 2, but for composites of filtered OLR (shading) and ERA-40 u1000 (contours) for MJO events over the western Pacific Ocean.

Citation: Journal of Climate 19, 9; 10.1175/JCLI3703.1

Fig. 4.
Fig. 4.

Same as in Fig. 2, but for centered composites of unfiltered ERA-40 surface pressure (shading) and OLR (contours) for MJO events over the (a) Indian Ocean and (b) western Pacific Ocean. The magnitude at the t = 2.6 contour is approximately 1 hPa.

Citation: Journal of Climate 19, 9; 10.1175/JCLI3703.1

Fig. 5.
Fig. 5.

Same as in Fig. 2, but for centered composites of unfiltered NCEP–NCAR surface pressure (shading) and OLR (contours) for MJO events over the (a) Indian Ocean and (b) western Pacific Ocean.

Citation: Journal of Climate 19, 9; 10.1175/JCLI3703.1

Fig. 6.
Fig. 6.

Same as in Fig. 2, but for centered composites of unfiltered ERA-40 u1000 (shading) and u200 (contours) for MJO events over the(a) Indian Ocean and (b) western Pacific Ocean. The magnitude at the t = 2.6 contour is approximately 0.4 m s−1 for 1000 hPa and 0.2 m s−1 for 200 hPa.

Citation: Journal of Climate 19, 9; 10.1175/JCLI3703.1

Fig. 7.
Fig. 7.

Same as in Fig. 2, but for centered composites of MJO filtered ERA-40 ∇ · V1000 (shading) and q850 (contours) for MJO events over the (a) Indian Ocean and (b) western Pacific Ocean.

Citation: Journal of Climate 19, 9; 10.1175/JCLI3703.1

Fig. 8.
Fig. 8.

Meridional means (10°S–10°N) of centered composites of unfiltered OLR, surface pressure, u1000, and u200 for MJO convective centers over (a), (b) the Indian Ocean and (c), (d) the western Pacific for lags of (b), (d) zero and (a), (c) −10 days. All units are in standard deviations of the respective quantity.

Citation: Journal of Climate 19, 9; 10.1175/JCLI3703.1

Fig. 9.
Fig. 9.

Same as in Fig. 8, but for unfiltered OLR, Ts, q850, LH, and SSR.

Citation: Journal of Climate 19, 9; 10.1175/JCLI3703.1

Fig. 10.
Fig. 10.

Same as in Fig. 2, but for centered composites of unfiltered ERA-40 surface pressure for MJO events over the Maritime Continent.

Citation: Journal of Climate 19, 9; 10.1175/JCLI3703.1

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