The authors analyze atmospheric Mixed Rossby Gravity waves over the central tropical Pacific Ocean. They identify the waves in a straightforward way by filtering meridional wind data near the equator for 2-6 days and for wavenumbers 5-6 followed by EOF analysis. They confirm the already well-known development of the waves by lateral forcing of middle latitude Rossby waves, and by analysis of data following a range of time lags and vertical moisture fluxes, they show the wave phase planes propagating downward as they move westward over the Pacific Ocean. The waves ultimately disturb the lower troposphere farther west, where they can develop tropical depressions. The vertical propagation is shown in greater detail in this manuscript than in previous works, but the connections to the extratropics are not new (the authors have cited well the relevant previous works). I found the work interesting, and I think the ultimate conclusions are robust to my concerns. However, I think the details could be substantially improved by responding to two major comments: 

1. The zonal spatial filtering to wavenumbers 5-6 is very restrictive. Although the results appear to provide clear and robust connections to real signals over the Central Pacific Ocean, the Gibbs phenomenon would extended the filtered signal substantially east and west of the central point. In the real world, the MRG wave signals have a broad spectral footprint, with a peak in the power spectrum extending over planetary to small synoptic scales. Many previous works have shown substantial variance at the target band the authors are using. Yet individual disturbances have their zonal scales evolve across their lifetimes. For example, a disturbance moving westward across the Dateline near wavenumber 4 or 5 might arrive over the west Pacific, slowing down as it moves, ultimately projecting more strongly to narrower wavelengths, better characterized by wavenumbers 6 or 7. Figure 1 suggests that the authors' data are overfiltered, thus masking the scale change evident in previous works as the waves move westward. See Figure 12 of Kiladis et al. (2009) for an example. Although the central results of the authors over the middle of the Pacific basin conform well to previous works, Figure 1 does not allow for the disturbance to evolve in its zonal scale, because the wavenumber is over prescribed. It is unclear how this issue will impact the timing and other characteristics of the downward propagation of the disturbance that they diagnose. The authors should broaden their wavenumber filter and repeat their analysis to assess the extent of the difference associated with the narrower scales that are evidently important as the disturbances move to the West Pacific. The filtering is likely not the only way the algorithm constrains results zonally. Even using a broader wavenumber filter, the EOF analysis will constrain the results to a particular range of zonal scales, but it will allow the zonal widths of the anomalies to vary geographically. Data filtered for a broad band along the MRG spectral peak ultimately expresses in several EOF pairs, each higher EOF pair explaining progressively smaller zonal scales. This means that one pair of EOFs is not sufficient to describe the whole population of waves. There is nothing wrong with the authors emphasizing a particular range of these scales through selecting a single pair of EOFs, but they should acknowledge that MRG energy also occurs at longer and narrower wavelengths than those that they show here. EOFs based on data filtered for a broader band of wavenumbers will still have leading modes concentrate at wavenumbers 4, 5, or 6 over the central Pacific, but the individual modes will associate with signals at narrower scales as the disturbances move westward. 

2. The MRG wave exhibits eastward group velocity, not westward. The manuscript appears to state that the group velocity is westward. The wavenumber filtering and the EOF analysis selects for wave scale in a particularly narrow way, which will mask the development of the group velocity in their results. If the authors filtered for a broader wavenumber band, a pair of EOFs would still select for a particular narrow range of wavenumbers (even though the patterns would allow the same disturbance to be characterized by different wavelengths in different regions). In that case, analysis of multiple pairs of EOFs of MRG filtered data retained together would reveal the group velocity as the interference pattern that emerges from including wave signals propagating at different phase speeds over a range of zonal wavenumbers. 

This is an interesting study of the statistical structure and behavior of tropospheric mixed

Rossby-gravity waves over the eastern equatorial Pacific during northern winter. Using

EOF analysis, the authors have obtained some nice results related to the extratropical

forcing of MRG waves within the westerly duct, however I think that the zonal

wavenumber 5-6 filtering they used is unnecessarily narrow, and that this has the

potential to distort the actual scales of MRG waves compared to what has been shown in

past studies (see comments below). In addition, the descriptions of the methodology used

are incomplete, and while I was finally able to back out what they are actually using in

their approach, this should be made more obvious to the reader at the outset in Section

3.1. In addition, a lot of relevant literature has not been cited, and I think the authors need

to compare their results to those from these past studies. I recommend revisions of

this manuscript while taking into account the comments by line number below:

25: The term “WMRG” has also been used to identify westward propagating MRGs by

Yang et al. starting in 2003, to distinguish from the eastward propagating EIGs of

Matsuno’s n=0 meridional mode. MRG-E has also been used to describe the eastward

propagating side by Knippertz et al. (2022), for example. If you are going to use MRGW

instead of simply MRG then I think it would be important to make this point in order to

avoid confusion.

29: I think it’s important to distinguish convectively coupled MRGs in the troposphere

from the free MRGs in the stratosphere. The early studies focused on MRGs in the

stratosphere, and these have decidedly different scales from those in the stratosphere (e.g.

Wheeler et al. 2000 their Fig. 12, Yang references below, Kiladis et al. 2016).

33: MGWs => MRGWs

33: Kiladis et al. 2009 did not document lateral forcing but mentioned previous studies

that did. More recent examples include Yang and Hoskins (2016), Yang et al. (2018),

Kiladis et al. (2016) and Suhas et al. (2020). Suggest citing these here for completeness,

as these will also become relevant below.

89: Examples of different methods employed are discussed in detail in Knippertz et al.

(2022).

90: as was done in Kiladis et al. 2016.

Based on what is stated on line 107 it appears that you are using a correlation matrix and

not a covariance matrix for the EOF analysis. This should be stated here.

91: not evident in this statement is the important point that EOF analysis of propagating

disturbances will generally yield two EOFs in spatial and temporal quadrature, which is

why you can use the combined PC1 and PC2 as an activity index.

95: what is the basis for the spatial and temporal filtering? 2-6 days can be justified in the

troposphere, but using only zonal wavenumbers 5 and 6 is very restrictive. In 1982

Hayashi had limited knowledge of the spatial scales of MRGs, which we now know are

localized wavepackets that are comprised of a number of zonal wavenumbers in both the

troposphere and stratosphere. While spectra of meridional wind at 200 hPa do have

power concentrated on wavenumbers 5, the power is broad band and extends especially

to lower wavenumbers (Randel 1992). Indices based on antisymmetric OLR (Kiladis et

al. 2009, 2016) or dynamical based indices (Yang et al. 2003; Knippertz et al. 2022)

generally include wavenumber 1-4 components as well, and the structures of MRGs

obtained in these studies are generally broader in scale than what is obtained here. I think

you need to reconsider your filtering by including a broader zonal wavenumber range,

while testing the sensitivity of your results to these choices. It seems to me that including

wavenumbers 1-4 initially would be a good test. In the 2-6 day period range, it is

probably not necessary to only include westward propagating wavenumbers, but I suggest

testing that approach as well. In other seasons such as northern summer, this broader

band filter would also include tropical depression (TD-type) disturbances that MRGs

often morph into, but that should not be an issue during DJF.

98: “MRGW”

99: was the meridional wind area weighted by cos latitude? This will not make a

difference at the latitudes used but still should be done. Justification for the domain used

should also be given.

101: should point out that PC1 would lead PC2 for a westward propagating disturbance.

102: what is the lagged correlation between PC1 and PC2? I don’t doubt it’s quite large,

but knowing that would further justify using the combined first two EOFs as an index.

107: Suggest pointing out that the standard deviation of PC1 will be equal to one when

using a correlation matrix (or standardized input). I assume you are compositing on local

temporal maxima in PC1? It is stated in the figure caption that the winds are band passed

filtered but is that also true of humidity and OLR? More information on the compositing

technique is needed here.

110: The patterns compare favorably with those obtained by Wheeler et al. (2000) and

Kiladis et al. (2009, 2016) using OLR or brightness temperature as a basis, including the

diagonal tilt of the OLR signals, although the circulation gyres are somewhat smaller

scale, likely due to the wavenumber filtering used here.

124: not sure I see the quadrature relationship referenced in the text in Fig. 3. It seems

more that divergence is out of phase in the vertical without much longitudinal

displacement between moist and dry regions, also reflected in the locations of the OLR

anomalies.

138: I can see from the scale that these really are lag correlations (not lagged regressions)

for OLR, but how are you scaling the wind field using correlations? What does a vector

length of “1” mean, a perfect correlation with both u and v? Much more detail is needed

here. Also, are “anomalies” 2-6 day band pass filtered fields?

144: Kiladis et al. 2009 does not show midlatitude coupling with MRGs but Kiladis et al.

2016 does.

147: In what sense does the omega equation hold? Looks like negative OLR does occur

ahead of troughs, as expected.

148: 10 m/s is quite a bit slower than the 15-25 m/s reported in past studies. This may be

because of the restriction to wavenumber 5-6, which in itself would yield a slower phase

speed just based on the dynamics of the MRGs.

150: I guess you are talking about the weak OLR anomalies off the west coast of South

America in Fig. 3c? This is not a particularly strong signal.

176: “eastward group velocity”

181: I think what you mean to say is that the group velocity causes an MRG to form over

the Atlantic which then has the characteristic antisymmetric specific humidity field

associated with it.

215: I think you need to refer to Fig. 7 here. I don’t understand why you are using PC2

for Fig. 7, since that can’t be directly compared with the circulation Fig. 6c, for instance.

Is there justification for this?

219: A comparable statistical 200 hPa sequence for MRG activity further west during

DJF is also shown in Kiladis et al. 2016, their Fig. 16.

226: Can’t say that I see the humidity and OLR signals over southern Mexico referred to,

if you are talking about either Fig. 6 or 7.

234: Once again, are these anomalies 2-6 day filtered? They should be identified as such.

244: You mean it’s a standing wave?

305: Please see Yang and Hoskins (2017) for a discussion of the eastward tilt in height of

MRGs within the westerly duct during Dec.-Feb.

Signed,

George Kiladis

References:

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Yang, N. Zagar, J. Dias, A. H. Fink, J. Methven, A. Schlueter, F. Sielmann, and M. C.

Wheeler, 2022: The intricacies of identifying equatorial waves. Quart. J. Roy. Met. Soc.,

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