Lawrence C. Gloeckler and Paul E. Roundy Department of Atmospheric and Environmental Sciences
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Transcript of A Sample AMS Latex File - Albany · Web viewAlthough the MJO clearly modulates Kelvin wave...
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Observed Structure of Convectively Coupled Waves as a Function of Equivalent Depth:
Kelvin Waves and the Madden Julian Oscillation
Paul E. Roundy1
University at AlbanyState University of New York
1 Corresponding author address: Paul Roundy, Department of Atmospheric and Environmental Sciences, 1400 Washington Ave., Albany, NY, 12222.E-mail: [email protected]
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Abstract
The view that convectively coupled Kelvin waves and the Madden Julian oscillation are
distinct modes is tested by regressing data from the Climate Forecast System Reanalysis
against satellite outgoing longwave radiation data filtered for particular zonal wave
numbers and frequencies by wavelet analysis. Results confirm that nearly dry Kelvin
waves have horizontal structures consistent with their equatorial beta plane shallow water
theory counterparts, with westerly winds collocated with the lower tropospheric ridge,
while the MJO and signals along Kelvin wave dispersion curves at low shallow water
model equivalent depths are characterized by geopotential troughs extending westward
from the region of lower tropospheric easterly wind anomalies through the region of
lower tropospheric westerly winds collocated with deep convection. Results show that as
equivalent depth decreases from that of the dry waves (concomitant with intensification
of the associated convection), the ridge in the westerlies and the trough in the easterlies
shift westward. The analysis therefore demonstrates a continuous field of intermediate
structures between the two extremes, suggesting that Kelvin waves and the MJO are not
dynamically distinct modes. Instead, signals consistent with Kelvin waves become more
consistent with the MJO as the associated convection intensifies. This result depends
little on zonal scale. Further analysis also shows how activity in synoptic scale Kelvin
waves characterized by particular phase speeds evolves with the planetary scale MJO.
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1. Introduction
The tropical atmosphere organizes moist deep convection over a broad range of spatial
and temporal scales. The Maddan-Julian oscillation (MJO) dominates variability in
convection on intraseasonal timescales of roughly 30-100 days (Madden and Julian 1994;
Zhang 2005). Rainfall associated with the local active convective phase of the MJO
(hereafter, active MJO) is in turn organized into smaller scale wave modes and mesoscale
convective systems. Convectively coupled Kelvin waves are widely recognized as a
leading signal among the population of modes that comprise the sub scale anatomy of the
MJO. These waves produce the highest amplitude signals in outgoing longwave radiation
(OLR) data near the equator (Wheeler and Kiladis 1999 (hereafter WK99); Straub and
Kiladis 2002; Roundy 2008). MacRitchie and Roundy (2012) showed that roughly 62%
of rainfall that occurs in the negative OLR anomalies of the MJO between 10N and 10S
over the Indo-Pacific warm pool regions occurs within the negative OLR anomalies of
the Kelvin wave band (after excluding those negative anomalies that do not enclose
signals less than -0.75 standard deviation). That result represents nearly twice the average
rainfall rate per unit area outside of the Kelvin waves but still within the active MJO.
MacRitchie and Roundy also showed that potential vorticity (PV) accumulates in the
lower to middle troposphere in wakes along and behind the Kelvin wave convection on
its poleward sides, and that this PV remains in the environment for longer than the period
of the Kelvin waves. The enhanced PV spreads pole ward behind the waves, and it
becomes part of the rotational structure of the MJO itself. Another portion of the
rotational response to convection coupled to Kelvin waves propagates eastward with the
waves, yielding low-level cyclones poleward of the equatorial convection (Roundy
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2008). The response to deep convection moving eastward with convectively coupled
Kelvin waves makes them similar in many respects to the geographically larger MJO. On
the other hand, these patterns distinguish observed convectively coupled Kelvin waves
from theoretical Kelvin waves of Matsuno (1966) and Lindzen (1967), which do not
include meridional circulation. Nevertheless, many authors acknowledge that Kelvin
wave dynamics dominate their evolution because of their dispersion characteristics and
because of the relationship between wind and pressure observed in the lower stratosphere
away from the deep convection, which consistently shows westerly wind in the ridge and
easterly wind in the trough, with little meridional circulation. Although the MJO clearly
modulates Kelvin wave activity, amplitudes, and propagation speeds (Straub and Kiladis
2003; Roundy 2008), these waves occur independent of the MJO.
Although several authors during the 1980s and 1990s suggested that the MJO
itself might be a modified moist Kelvin mode (e.g., Lau and Peng 1987; Wang 1988; Cho
et al. 1994), the idea has since fallen out of favor for several reasons. First, the
relationship between zonal wind and pressure anomalies in the MJO appears to be
reversed or dramatically offset from that of Kelvin waves, with westerly wind anomalies
frequently appearing in the pressure trough collocated with the deep convection (e.g.,
Madden and Julian 1994; Zhang 2005). Second, a spectral peak associated with
convectively coupled Kelvin waves appears to be distinct from that of the MJO (Kiladis
et al. 2009), suggesting that the two have phase speed distributions that might not
overlap. Third, zonal wave number frequency spectra of OLR data suggest that the
spectral peak of the MJO extends across a broader range of wave numbers at a given
frequency than does the spectral peak associated with the Kelvin waves, giving the
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impression of a flat dispersion relationship, even though most of that signature can be
explained by geographical variation in MJO propagation rather than true dispersion. This
perspective is supported by composite MJO events plotted in the longitude-time lag
domain (such as by Hendon and Salby 1994), which show structures favoring wave
number 2 over the warm pool (consistent with opposite signed anomalies of convection
over the Indian and western Pacific basins) and a half wave number 1 across the western
hemisphere. Such half wave number 1 signals project more onto wave number 1 than any
other wave number, as shown by a simple application of the Fourier transform in space
and time to a perfect eastward-propagating wave number 1 sine wave that is set to zero in
one hemisphere and left alone in the other (a synthetic half wave number 1 pattern). Such
geographical variations in MJO propagation must project onto different portions of the
spectrum. Seasonal variations in MJO propagation must also project onto different
portions of the spectrum. A global wave number-frequency spectrum analysis
conglomerates all of these varying signals together, such that a spectral peak aligned in a
particular pattern does not necessarily imply wave dispersion.
A more careful look at each of these characteristics casts some doubt on the
assertion that the MJO and Kelvin waves are distinct. First, the algorithm of WK99
would artificially enhance the extent of the spectral gap between the MJO and Kelvin
peaks. WK99 normalized their OLR spectra by dividing by a smoothed background
spectrum. This background spectrum was obtained by smoothing the original spectrum
by an arbitrary number of repeated applications of a 1-2-1 filter in frequency and in wave
number. This approach conserves the total power in the spectrum but redistributes power
in the MJO peak into its surrounding neighborhood, including the region of the spectral
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gap. This artificial increase in background power would reduce the normalized power
there, making the MJO and Kelvin peaks appear better separated. For reference, Fig. 1
shows a wave number frequency spectrum of OLR calculated in a similar manner. The
more objective spectrum analysis of Hendon and Wheeler (2007) confirms the presence
of a local minimum in power in the spectrum, but not as pronounced as suggested by
WK99.
Recently, Roundy (2012) integrated wavelet power in the zonal wave number
frequency domain over geographical regions where the 100-day low pass filtered 850 hPa
zonal winds are easterly or westerly. He found that the gap in the global OLR spectrum
derives entirely from regions of easterly low-level background flow. The spectrum
integrated over regions low-level westerly winds has power decline smoothly from the
maximum in the MJO band, with no evident spectral gap. Thus the source of the spectral
gap is not over warm pool zones where MJO convective signals attain their greatest
amplitude. The lowest rate of decline of power occurs along Kelvin wave dispersion
solutions between equivalent depths of 5 and 8m. This result suggests that Kelvin waves
also propagate eastward more slowly over the warm pool than over trade wind zones.
Signals in trade wind zones dominate the global spectrum because these zones occur over
more of the global tropics for more of the time than do signals in warm pool westerly
wind zones, even though the individual events over the warm pool zones average higher
in amplitude.
Equatorial beta plane theories suggest that Kelvin waves are non dispersive
except at the shortest wavelengths (e.g., Roundy and Janiga 2012), but variation in
coupling between the waves and deep convection apparently results in a large range of
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phase speeds across the full population of events (Roundy 2008). Although many of these
Kelvin waves propagate eastward at 15-17 ms-1 around much of the globe, or roughly
twice the phase speed of the MJO, Roundy (2008 and 2012) showed that they tend to
propagate more slowly over the warm pool zones. He also showed that synoptic scale
Kelvin waves propagate eastward even more slowly as they move through the local
active convective phase of the MJO. The same Kelvin wave disturbance can
circumnavigate the entire globe, with its phase speed changing continuously with the
amplitude of the associated convective signal. This observed variation in phase speeds
leaves open the possibility that long Kelvin waves and the MJO may have overlapping
dynamics because their phase speed distributions might overlap. These results
demonstrate that the spectral characteristics of the MJO and the Kelvin waves are not as
distinguishable as previously thought.
The relationship between zonal wind and pressure remains a factor whereby
Kelvin waves and the MJO might be distinguishable. Since the pressure wind relationship
differs between dry Kelvin waves and the observed MJO, and since the observed
distribution of frequencies associated with Kelvin waves are higher than the comparable
distribution for the MJO, the pressure wind relationship associated with eastward-moving
signals in OLR data must vary with frequency. If the prevailing view that Kelvin waves
and the MJO are distinct modes is correct, the presence of both modes would yield a
particular pattern of transition in frequency between the spatial patterns associated with
Kelvin waves and those associated with the MJO. At low wave number, the spectral
peaks of Kelvin waves and the MJO are proximate to each other. Since the spectral
characteristics of both the MJO and Kelvin waves vary substantially from event to event,
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proximity of the two peaks suggests that there must be overlap between the spectra of the
two phenomena. If the MJO and Kelvin waves represent distinct modes in which the
pressure-wind relationship is not a function of frequency (consistent with the prevailing
view), then at some point in spectrum between the peaks of the two modes, both signals
would be present and explain roughly the same amount of variance in geopotential height
anomalies. Both modes would have low-level westerly wind anomalies collocated with
negative OLR anomalies, but the associated geopotential height anomalies are strongly
offset or opposite. Thus, active convective anomalies at that frequency would be
associated with negative geopotential height anomalies with one mode and positive with
the other mode. Statistical analysis to extract the average coherent pattern associated with
the active convection at that frequency without distinguishing between the modes would
thus yield significant lower tropospheric westerly wind anomalies associated with active
convection but no significant geopotential anomalies because the two opposite signals
would wash each other out. If, however, only one dominant coherent mode exists, with
structure modulated by the intensity of the associated rainfall, then the phase relationship
between wind and geopotential might shift as a continuous function of frequency, with no
geopotential amplitude minimum associated with signals at frequencies between the two
extremes.
Statistical analysis of observations and reanalysis data might shed light on the
nature of the transition of spatial structures as a function of frequency between the
spectral peaks that we associate with Kelvin waves and the MJO. Recently, Roundy and
Janiga (2012) applied zonal wave number-frequency wavelet analysis and simple linear
regression to assess the structure of convectively coupled mixed Rossby gravity (MRG)
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waves characterized by specific zonal wave numbers and frequencies. They applied
wavelet analysis at a particular zonal wave number and a specified frequency to generate
a time index of the corresponding signals. Regression of fields of data against that index
reveals the space-time structures of the patterns corresponding to those signals. By
choosing frequencies consistent with a selected equivalent depth at several different
individual wave numbers, they showed how MRG wave structures vary with wave
number along particular shallow water model dispersion curves. A similar analysis of
signals proximate to the Kelvin wave peak in the OLR spectrum might suggest how
Kelvin wave structures change with equivalent depth (h), or how structures of coherent
disturbances change between the Kelvin and MJO spectral peaks. The purpose of this
work is to apply this technique to better understand what observations suggest about the
extent to which the MJO and long convectively coupled Kelvin waves can be considered
independent phenomena and to enhance our understanding of interactions between short
Kelvin waves and the MJO.
2. Data
Daily-interpolated outgoing longwave radiation (OLR) data on a 2.5-degree grid are
applied as proxy for moist deep convection (Liebmann and Smith 1995). These OLR data
have been updated every few months since 1995 following the original algorithm. Daily
mean zonal and meridional wind, temperature, and geopotential height data are obtained
from the Climate Forecast System Reanalysis (Saha et al. 2010). The mean and first four
harmonics of the seasonal cycle are subtracted from the OLR, wind, and geopotential
height data to generate anomalies. All data are analyzed for the period January 1, 1979
through December 2009.
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3. Methods
a. Space-time Wavelet Decomposition
Signals in atmospheric convection obtained from the regions of the zonal wave
number frequency domain near equatorial beta plane shallow water model solution
dispersion curves at h=25m are associated with spatial patterns similar in many respects
to those obtained from shallow water theory (Matsuno 1966; Lindzen 1967; WK99). For
reference, Fig. 1 shows dispersion lines of shallow water model Kelvin wave solutions at
h=8 and 90m superimposed on a normalized OLR spectrum. All subsequent
observational analyses of Kelvin wave signals in this study are reported for points in the
OLR spectrum along the Kelvin dispersion curves with h ranging from 5 to 90m. It is
important to point out that other signals and noise occur along the dispersion curves of
the shallow water model Kelvin wave solutions. Extratropical waves advected eastward
by westerly winds project substantially onto similar regions of the spectrum as Kelvin
waves. Such signals tend to be small over the warm pool zones and large in regions of
upper tropospheric westerly winds such as the eastern Pacific and Atlantic basins. In spite
of other signals, the OLR spectral peaks between the dispersion curves of Kelvin wave
solutions of h=5 and 90m include those of convectively coupled Kelvin waves (centered
on roughly 25m, but ranging from roughly 8 to 90m), and the MJO, which extends
roughly from wave numbers 0-9 eastward and periods of roughly 30-100 days. Keep in
mind, however, that these spectral peaks are not distinct when the spectrum is integrated
only over the low-level westerly wind zones of the warm pool (Roundy 2012). The
Kelvin wave dispersion curves intersect with the traditionally defined MJO spectral peak
at low wave number (Wheeler and Kiladis 1999).
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Most previous observational analyses of Kelvin wave signals conglomerate structures
of a broad range of wavenumbers and frequencies through filtering in the wave number
frequency domain across broad bands (e.g., Wheeler et al. 2000; Roundy and Frank
2004). Interpretation of the results is complicated because the vertical and meridional
structures of the observed waves might vary with wavenumber and frequency. This
project applies zonal wave number-frequency wavelet analysis to extract signals from
OLR data at specified wave numbers and frequencies, following Roundy and Janiga
(2012). When combined with regression or composite analysis, this more specific
approach diagnoses how spatial structures change with frequency at a given wave
number. A detailed description of space-time wavelet analysis is beyond the scope of this
paper, but Kikuchi and Wang (2010) and Wong (2009) offer overviews of the technique.
The space-time wavelet transform is the wavelet transform in longitude of the wavelet
transform in time of the OLR anomalies. This analysis applies the Morlet wavelet
Ψ (s )= 1√ (πB )
exp (iσs )exp (−(s2 )B ), (1)
where s represents x or t for the spatial or temporal transforms, respectively, and
represents angular frequency or wavenumber k. B, the bandwidth parameter, was
assigned a value of 4( ν2π )
−3/2
for the temporal transform and 1.5( k2π )
−3/2
for the temporal
transform. Conclusions are not sensitive to these arbitrarily assigned values of B, but
much larger values reduce the amplitude contrast in time of signals and enhance a ringing
effect, and substantially smaller values do not sufficiently resolve large-scale or low
frequency waves. The transform is obtained by taking the time-centered dot product of
the wavelet and all daily consecutive overlapping time series segments at each grid point
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around the globe, then applying a similar transform in longitude to the result by the same
approach. The transform for a selected wave number and frequency is calculated for
every day and at every longitude grid point in the 7.5S to 7.5N averaged OLR anomaly
data from 1975 to 2009. Averaging OLR over 7.5S to 7.5N increases the likelihood that
the dominant coherent signals are Kelvin waves because this average acts as a filter for
cross equatorial symmetry, and proximity to the equator reduces the net contribution of
extratropical waves.
b. Linear Regression Models
Simple linear regression is frequently applied to diagnose structures that are coherent
with filtered signals (e.g., Hendon and Salby 1994; Wheeler et al. 2000). In this analysis,
the space-time wavelet transform at a selected longitude, wave number, and frequency,
becomes a base index time series for regression models at each grid point over a range of
longitudes and pressure levels. Either the real or imaginary parts of the transform work
for this index. The imaginary part produces convenient zonal phasing in the regression
maps, but the conclusions are the same regardless of this choice. Base longitudes are at
each 2.5 grid point from 60E to 90E. This focus on the Indian basin reduces the
contribution of extratropical features that are much more pronounced over the western
hemisphere. Calculating regression models at each base point, then averaging over all of
them reduces local disconformities, yielding conclusions less sensitive to geography. The
time series from each of those points serve as predictors in regression models at each grid
point across a broad geographical domain to diagnose the associated structures. One grid
of regression models is calculated for each base point time series. To illustrate, the
algorithm models the variable Y at the grid point S as
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Ys Px As , (2)
where Px is a matrix whose first column is a list of ones and second column is the base
index at the longitude grid point x. As is a vector of regression coefficients at the grid
point S. After solving for As at each grid point by matrix inversion, (2) is then applied as a
scalar equation to diagnose wave structure by substituting a single value for the second
column of
Px that is representative of a crest of a wave located at the base longitude (its
value is set here at +1 standard deviation). These regression models are applied to create
‘composite’ anomalies of OLR, u and v winds, and geopotential height. Results are
calculated for the region 180 to the east and west of each base longitude, and then the set
of results from all base points are averaged, following Roundy and MacRitchie (2012).
The statistical significance of the difference from zero of the result at each point on the
map is assessed based on the correlation coefficient (e.g., Wilks 2011), and I analyze and
discuss only those regressed signals that are deemed to be significantly different from
zero at the 90% level. This significance test is completed for each individual regression
map before averaging over results from each base point, so that the number of degrees of
freedom is not inflated by inclusion of the same wave events at multiple grid points.
Since the regression is accomplished in the time domain, some signal from wave numbers
other than the target wave number can appear in results if they tend to occur together in a
particular pattern (Wheeler et al. 2000). Such regression results will be most reliable
close to the centers of the composites because spreading will occur due to the episodic
nature of convection and variations in the background state. Amplitudes of regressed
anomalies following this approach are much smaller than those of other authors who have
regressed signals against OLR data filtered for the broader Kelvin band of Wheeler and
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Kiladis (1999) because the full band includes much more variance than is retained at just
one wave number and frequency.
The above approach diagnoses the spatial structures associated with signals along
the dispersion curves of shallow water model Kelvin wave solutions at particular
equivalent depths. For reference, we also calculate a composite MJO following a similar
approach, by replacing the base index time series with MJO band pass filtered OLR
anomalies averaged from 10N to 10S. The MJO band signal is averaged over a broader
latitude band than are Kelvin signals in this work in order to capture the signals of some
MJO events that have OLR anomalies shifted farther into one hemisphere. The MJO band
is defined as wave numbers 0-9 eastward and periods of 30-100 days. The value of −1
standard deviation in the base index is then substituted to generate a map. Base points for
the MJO composite are selected from 70E to 110E in order to reduce contamination of
the western portion of the regression maps by Africa. Kelvin band signals at higher wave
numbers did not require such an eastward shift because the wavelengths assessed for
them yielded less contamination from Africa.
A variation on the above regression approach is also applied here to diagnose how
signals along the Kelvin wave dispersion curves at particular equivalent depths vary with
the phase of the MJO. An index of OLR anomaly data filtered for the wave number
frequency band of the MJO at 80E is assigned as P in equation (2) and applied to predict
Y, which is assigned to be the absolute value of the sum of the real and imaginary parts of
the wavelet transform at a selected wave number and frequency at a time lag. Averaging
regression maps over multiple base points is not applied for this analysis since the
associated geographical signals is the target outcome. The value of −1 standard deviation
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is then substituted for the second column of P at each grid point and time lag. After
discarding the time local mean of the result, it shows how the timing of changes in
activity in Kelvin waves characterized by particular phase speeds varies with the MJO.
4. 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
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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
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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
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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
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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.
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5. 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
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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.
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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.
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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).
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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.
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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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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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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.
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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.
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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.
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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 80E (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).
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