Observed Structure of Convectively Coupled Waves as a Function of Equivalent Depth: Kelvin Waves and the Madden Julian Oscillation


a. Regression at Various Equivalent Depths Along Kelvin Dispersion Curves



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Results


a. Regression at Various Equivalent Depths Along Kelvin Dispersion Curves

Figure 2 shows regressed geopotential height anomalies (contours) and zonal wind anomalies (shading, with westerly anomalies in red) for panels a-e, equivalent depths of 90, 25, 12, 8, and 5m (respectively) for zonal wave number 4 Kelvin waves. These data are plotted against regressed total geopotential height instead of pressure to facilitate measurement of the vertical tilts of the regressed anomalies. Thus, the plotted geopotential height anomalies represent the displacement of isobars at a given height from their climatological positions. The results show patterns that tilt toward the west with height between the surface of the earth and roughly 10,000m, with tilt reversing toward the east above (consistent with Kelvin wave composites by Kiladis et al. 2009 and references therein). Each panel shows eastward flow in the ridges and westward flow in the troughs above 104m, but structures vary with equivalent depth below that level. At the equivalent depth of 90m (panel a), westerly wind anomalies are collocated with positive geopotential height anomalies near the center of the composite. Comparison of all panels shows that the westerly wind anomalies near the centers of the composites are nearly an order of magnitude stronger at h=5m (panel e) than at h=90m, but the as equivalent depth decreases, the geopotential trough in the easterlies on the east side of the domain extends westward until at h=5m it encompasses nearly all of the westerly anomalies near the center of the composite below 10,000m. The differences between the composites for large and small equivalent depths occur smoothly across the equivalent depths plotted here. The regressed geopotential height anomalies do not vanish at some equivalent depth, as would occur if the MJO and Kelvin band signals include two distinct modes characterized by opposite pressure wind relationships. The vertical cross sections for the other wave numbers are similar to those for k=4.

Figure 3 shows the horizontal maps of the regressed geopotential height and winds for wave number 4 at 900 hPa along the Kelvin wave dispersion curves for the same equivalent depths as in Fig. 2. Regressed OLR anomalies are shaded, with active convection suggested in blue, and regressed geopotential height anomalies are contoured with positive anomalies in red. At h=90m, westerly wind anomalies are collocated with positive geopotential height anomalies and slightly negative OLR anomalies. Easterly wind anomalies occur in the trough, consistent with the shallow water model Kelvin wave. With increasing equivalent depth, the negative OLR anomalies strengthen in the vicinity of the equatorial westerly wind anomalies. At the same time, locally positive geopotential height anomalies shift westward from the active convection toward the suppressed convection. Trough anomalies shift westward from east of the negative OLR anomalies at h=90m (panel e) through the convective region by h=5m. The increased amplitude of the OLR anomalies with decreasing equivalent depth suggests that lower equivalent depths are associated with higher rainfall rates. TRMM 3B42 rain rate data available since 1999 confirm this observation (not shown). The structure of the OLR and geopotential height anomalies also changes with equivalent depth. The negative OLR anomaly at h=90m nearly forms an ellipse centered on the equator, but at smaller equivalent depths, the negative OLR and geopotential anomalies distort increasingly westward with distance form the equator, forming boomerang patterns across the equator. Regression maps for other wave numbers show similar structures (not shown). Thus, both long and short Kelvin waves become more like the MJO with increasing precipitation rates. This statement also holds true for Kelvin waves of wave number 6 and 8 (not shown). Although the h=5m result at wave number 6 has a period of about 11 days, well outside of the traditional MJO band of the wave number frequency domain, the associated regression maps still show pronounced westward shifting of the geopotential height anomalies relative to the OLR anomalies, along with pronounced westward distortion with latitude. In other words, signals along the Kelvin wave dispersion curve at h=5m and wave number 6 are associated with structures similar to those of the MJO, but with smaller zonal scale. Within the traditional MJO band, structures observed along the dispersion curve for the h=5m Kelvin wave at zonal wave number 2 also shows similar traits. That signal propagates at about 7ms-1 and has a period of about 30 days.

b. Regressed MJO Structure

For comparison with Fig. 3, Fig. 4a shows a horizontal map of geopotential height anomalies and zonal wind regressed against MJO-filtered OLR anomalies at 900 hPa. These results show a geopotential trough collocated with easterly wind anomalies on the eastern side of the domain. That trough also extends westward across much of the region of low-level westerly winds collocated with the negative OLR anomaly. That geopotential trough and the negative OLR anomalies form a triangle pattern with one side perpendicular to and bisected by equator on the west and the two other legs meeting to the east on the equator. This pattern is consistent with distortion of the OLR and geopotential height anomalies westward with distance form the equator at low equivalent depths in Fig. 3d and e. Figure 4b shows the corresponding vertical cross section of regressed geopotential height anomaly and zonal wind anomaly on the equator, for comparison with Fig. 2. The result compares well with Fig. 2d and 2e.



c. The Association Between Synoptic Kelvin Wave Activity and the MJO

Straub and Kiladis (2003) evaluated the evolution of signals in the broader Kelvin wave band with the northern hemisphere summer MJO. The present work expands on their analysis by demonstrating how that evolution depends on the phase speeds of the Kelvin waves in a generalized MJO without explicit assessment of seasonality. Figure 5 shows regressed activity in Kelvin waves at zonal wave numbers 3-8 (shading) along with regressed MJO-filtered OLR. Panels (a)-(e) represent results for equivalent depths of 90, 25, 12, 8, and 5m, respectively. Enhanced convection in the MJO band is indicated by blue contours. Fast Kelvin waves (~30ms-1) at 90m equivalent depths (Fig. 5a) are characterized by lower amplitude signals in OLR anomalies than all other equivalent depths (consistent with the expectation that such Kelvin waves should be nearly dry). Figure 5a suggests that prior to onset of convection in the MJO band over the Indian basin (hereafter called “MJO initiation” for simplicity), fast Kelvin waves are prevalent over the Atlantic basin and Africa, but quiet over the Pacific basin. This activity extends eastward early in the lifetime of the negative OLR anomaly in the MJO band over the Indian basin. This activity then declines to below average over the Indian basin after lag = +5 days. Activity in these fast Kelvin waves then grows over the Pacific Ocean to the east of the active MJO. Kelvin waves characterized by h=25m also show enhanced activity in OLR anomalies over the Atlantic basin and Africa prior to MJO initiation, but substantially more than for h=90m. After lag = 0, enhanced activity occurs at the eastern edge of the negative OLR anomalies in the MJO band, a little farther west than for h=90m. At h=12m, similar to at h=90m and h=25m, activity begins over the Atlantic basin and Africa prior to MJO initiation, but the level of activity becomes much stronger over the Indian basin within the active MJO and then extends only slightly eastward from the negative OLR anomaly of the MJO after lag = +5 days. Although signal at h=8m and h=5m is also suggested over the Atlantic basin and Africa leading up to the active MJO, most of the signal in these bands concentrates within the negative OLR anomaly of the MJO over both the Indian and western Pacific basins. These slow Kelvin wave signals are more consistent with the slow eastward-moving supercloud clusters of the active convective phase of the MJO noted by Nakazawa (1988) than are the faster Kelvin waves. Figure 5a confirms the previous result of Kikuchi and Takayabu (2003) that dry Kelvin waves radiate eastward from the active convective phase of the MJO over the western Pacific basin, but Fig. 5 b-d also shows that a substantial convectively coupled Kelvin wave signal at h=12m and h=25m (about 11 and 16 ms-1 respectively) also occurs over the Pacific basin east of the active MJO. The slowest Kelvin waves at wave numbers 3-8 are largely confined to the active convective phase of the MJO over the Indo Pacific warm pool. Although the local amplitudes of OLR anomalies at h=8m and 5m are substantially higher than for OLR anomalies at 25m, the isolation of these low h signals largely within active convective phases of the MJO over the warm pool reduces their net contribution to the OLR spectrum, leading to the more global signals near 25m standing out in the OLR spectrum. These results are especially interesting in the context of Figs. 2 and 3, which suggest that these synoptic scale Kelvin waves themselves have spatial structures similar to those of the planetary scale MJO.
  1. Conclusions


A wave number frequency wavelet analysis of OLR anomaly data and simple linear regression reveal how the structures associated with signals along the dispersion curves of Kelvin waves change with equivalent depth. Results suggest that the phase relationship between geopoential height and wind anomalies for signals along Kelvin wave dispersion curves adjusts continuously westward with decreasing equivalent depth from patterns consistent with Kelvin waves of equatorial beta plane shallow water theory (which have westerly wind anomalies in the geopotential ridge) to patterns that look more like the MJO (with westerly wind anomalies extending westward through the geopotential trough). If there were two distinct modes present with opposite pressure wind relationships overlapping in the spectrum, with one mode dominant at low frequencies and the other dominant at higher frequencies, then at some frequency in between the two, the geopotential signals would wash out of the regression while regressed wind and OLR signals would remain. Instead, the regression analysis reveals a continuous shift of the phase between zonal wind and pressure signals. High wave number Kelvin waves whose signals are far in the spectrum from the MJO band follow similar patterns at low equivalent depths. These results thus do not support the perspective that the MJO and Kelvin waves are distinct modes like the present consensus suggests. This continuous evolution instead supports the perspective that more intense convection modifies the convectively coupled Kelvin wave to take on characteristics more consistent with the MJO. In that sense, the low wave number portion of the disturbance traditionally labeled as the MJO might be a planetary scale Kelvin wave modified by the influence of intense convection. Analysis of the power spectrum by Roundy (2012) further confirms that no separation between the Kelvin and MJO spectral peaks occurs over the low-level westerly wind zones over the warm pool. Thus in those regions, MJO signals cannot be distinguished from a continuum of disturbances that begin at high frequencies in association with dry Kelvin waves.

This work also demonstrates how synoptic scale Kelvin waves characterized by particular phase speeds (or equivalent depths) vary with the MJO. Kelvin wave activity at all phase speeds tends to be enhanced over the Atlantic basin and Africa prior to development of deep convection in the MJO band over the Indian basin. Fast Kelvin waves are also prevalent well to the east of MJO convection when that convection is located over the western Pacific basin. The slowest Kelvin waves characterized by equivalent depths of less than 12m are strongest within the active convective phase of the MJO over the Indian basin, consistent with the assessment of the associated supercloud clusters by Nakazawa (1988) and slow Kelvin waves by Roundy (2008). These slow synoptic scale Kelvin waves themselves have vertical and horizontal structures similar to those of the planetary scale MJO.


Acknowledgments.


Funding was provided by the National Science Foundation Grant# 1128779 to Paul Roundy. The NOAA PSD provided OLR data, and the NOAA CPC provided CFS reanalysis data.

References

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List of Figures

Figure 1. Shallow water model dispersion curves for various equatorial wave modes plotted on a spectrum of OLR anomalies. The spectrum was normalized by dividing by a smoothed background spectrum.

Figure 2. Longitude-height cross sections of regressed zonal wind anomalies (shading, ms-1) and geopotential height anomalies (contours, negative in blue, with an interval of 0.25m) for signals along the Kelvin wave dispersion curves at zonal wave number 4. Panels a-e represent results for equivalent depths of 90, 25, 12, 8, and 5m, respectively. The vertical axis is labeled in terms of regressed total geopotential height to facilitate measurement of vertical tilts. Positive longitude is represented as degrees east of the base points.

Figure 3. Horizontal maps of regressed OLR anomalies (shading, Wm-2), geopotential height anomalies (positive in red, contour interval 0.15m), and wind anomalies at 900 hPa for signals along the Kelvin wave dispersion solutions for zonal wave number 4. Panels correspond to equivalent depths of 90, 25, 12, 8, and 5m, corresponding to the same panels of Fig. 2.

Figure 4. a. Anomalies of 900 hPa wind (vectors), OLR (shading, with negative in blue), and geopotential height (with negative anomalies in blue) regressed against OLR anomalies filtered in the wave number frequency domain for the MJO. b. Vertical cross section of zonal wind (shading) and geopotential height anomalies (contours, with negative in blue) on the equator, plotted against regressed total geopotential height.

Figure 5. Shading shows the result of regressing absolute value of OLR anomalies along the Kelvin wave dispersion curves for zonal wave numbers 3-8 against MJO-filtered OLR anomalies at 80°E (Wm-2). The local mean is subtracted at each grid point. The shading thus provides a measure of how Kelvin wave activity at particular equivalent depths varies with the local phase of the MJO. Red (blue) shading thus represents anomalously active (suppressed) mean OLR anomaly amplitude at the equivalent depth noted in the panel title. Contours represent regressed MJO-filtered OLR anomalies, with negative in blue (the interval is 5Wm-2 with the zero contour omitted). Panels a through e show results for signals along Kelvin wave dispersion solutions at equivalent depths of 90, 25, 12, 8, and 5m (respectively).


Figure 1. Shallow water model dispersion curves for various equatorial wave modes plotted on a spectrum of OLR anomalies. The spectrum was normalized by dividing by a smoothed background spectrum. The MJO band is outlined in a rectangle, and wave number 4 is marked with a vertical dashed line. Equivalent depths of 5, 12, and 25m are marked along that line in addition to the plotted dispersion curves.


Figure 2. Longitude-height cross sections of regressed zonal wind anomalies (shading, ms-1) and geopotential height anomalies (contours, negative in blue, with an interval of 0.25m) for signals along the Kelvin wave dispersion curves at zonal wave number 4. Panels a-e represent results for equivalent depths of 90, 25, 12, 8, and 5m, respectively. The vertical axis is labeled in terms of regressed total geopotential height to facilitate measurement of vertical tilts. Positive longitude is represented as degrees east of the base points.



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