Observational estimates of Kelvin wave momentum fluxes in the tropical lower stratosphere remain challenging. Here we extend a method based on linear wave theory to estimate daily time series of these momentum fluxes from high-resolution radiosonde data. Daily time series are produced for sounding sites operated by the US Department of Energy (DOE) and from the recent Dynamics of the Madden-Julian Oscillation (DYNAMO) field campaign. Our momentum flux estimates are found to be robust to different data sources and processing and in quantitative agreement with estimates from prior studies. Testing the sensitivity to vertical resolution, our estimated momentum fluxes are found to be most sensitive to vertical resolution greater than 1 km, largely due to overestimation of the vertical wavelength. Climatological analysis is performed over a selected 11-year span of data from DOE Atmospheric Radiation Measurement (ARM) radiosonde sites. Analyses of this 11-year span of data reveal the expected seasonal cycle of momentum flux maxima in boreal winter and minima in boreal summer, and variability associated with the quasi-biennial oscillation of maxima during easterly phase and minima during westerly phase. Comparison between periods with active convection that is either strongly or weakly associated with the Madden–Julian Oscillation (MJO) suggests that the MJO provides a nontrivial increase in the lowermost stratospheric momentum fluxes.

Atmospheric equatorial Kelvin waves represent a tropical eastward-propagating
wave disturbance generated primarily by convection. As tropical convection is
nearly ubiquitous, particularly near to the Intertropical Convergence Zone,
Kelvin waves are regular phenomena. These equatorially trapped waves have
zero meridional wind perturbations and are a consequence of the equatorial
beta-effect

Due to this upward flux of westerly momentum, Kelvin waves are known to
influence the downward progression of stratospheric westerlies that occur
during the roughly 28-month cycle of winds known as the quasi-biennial
oscillation (QBO). There are established connections between the QBO and
midwinter polar stratospheric variability

Phasing of the QBO is initiated in the upper stratosphere by gravity waves of
opposite propagation direction to that of the winds

A missing component from our understanding of the interaction between Kelvin
waves and the QBO is a precise measure of the actual vertical transport of
zonal momentum. This transport quantity is most typically written as the eddy
momentum flux

Observational shortcomings such as these do not prevent estimation of the
Kelvin wave momentum fluxes, however.

Yet there remain places where our understanding and estimation may be
improved. For instance, few climatological analyses of Kelvin wave momentum
fluxes have been performed. While satellite and reanalysis studies have long
data records over which to analyze, the vertical resolution of both data
sources is greater than a kilometer in the lower stratosphere. It is not
clear how sensitive momentum flux calculations are to vertical resolution,
particularly for lower-stratospheric Kelvin waves with vertical wavelengths
on the order of 2–4 km.

Here we extend previous methods using radiosonde data to analyze climatologies, variabilities, and vertical resolution dependences of Kelvin wave momentum fluxes. We make use of both quality-controlled, high-resolution data from a recent field campaign and raw, high-resolution data from long-term radiosonde stations. We apply an algorithm for producing continuous, daily time series of momentum flux estimates. By varying the vertical stepping of input data to the algorithm, we determine the role of vertical resolution on estimations of the fluxes. Because we utilize a relatively long-term dataset, we are able to analyze the intraseasonal and interannual variability of these time series of momentum fluxes, demonstrating that our methodology reproduces expected qualitative structures. From our estimates of the flux, we find evidence that convection associated with the MJO increases momentum flux variability in the lower stratosphere.

Section

The radiosonde data we use come from two sources. The first source contains
short-term but high-resolution data from the Dynamics of the Madden-Julian
Oscillation (DYNAMO) field campaign

The second radiosonde source contains lower temporal resolution but longer
spanning data from two US Department of Energy Atmospheric Radiation
Measurement (ARM) program sounding sites: Manus Island and Nauru
(0.5

Data from the European Centre for Medium-Range Weather Forecasting (ECMWF)
Interim Reanalysis (ERAi) are also used

Outgoing longwave radiation (OLR) data are from a long-term record of daily,
1

For analyzing the MJO, we use the OLR MJO Index (OMI)

To grid the radiosonde data, raw data are linearly interpolated in height and cubic spline interpolated in time. To constrain the interpolation, we require that each output data point has at least three input data points within the span from 3 days prior to 3 days following, and at least three input data points within the span from 500 m above to 500 m below. Note that this interpolation does not fill all gaps, allowing for missing data to remain. The results are not significantly different for other orders of interpolation, nor for moderate changes in the time range or spatial range in which data points must exist in order to interpolate to a specified output point. This does not hold if the time range or spatial range is too small – shorter than 1 day or less than 100 m, respectively – in which case few output points will be produced.

We range the output temporal resolution from 6 to 48 h, and the output vertical resolution from 100 to 2000 m. These ranges are used to study resolution effects on the calculated momentum fluxes. For our standard analysis, we use temporal resolution of 24 h and vertical resolution of 250 m. While daily data are standard for the field, motivation for why we use vertical stepping of 250 m is given in the next section.

To estimate the Kelvin wave momentum fluxes, we follow the technique
described in

Although this scale height is too long for the
lower stratosphere, it is the value used in the literature

Following

For stratification, this slowly varying assumption is true above the
tropopause inversion layer

The values of

The zonal means of both zonal wind and temperature are approximated by their
time mean over each window. Such an approximation is reasonable in the
stratosphere. We have compared our estimates of the zonal mean fields to
those calculated from ERAi and found that the fields do not qualitatively
differ. From our approximations of

Vertical wavenumbers

This method of estimating the vertical wavenumber was applied to the Nauru99
data that

With

This sign selection for

An additional constraint we could apply is that the meridional wind
perturbations

With all inputs known for Eq. (

An example of the Kelvin wave momentum flux calculation for Gan
Island over the 40-day window between 21 December 2011 and 29 January 2012.

An example of our method of calculation is shown in Fig.

Figure

Figure

We test the dependence of the calculated momentum flux amplitudes on the
resolution of input data by independently varying the vertical and temporal
resolutions of the imposed interpolation. These tests are performed for a
reference level of 18 km. We carry out the following tests at levels above
18 km and find that the results qualitatively hold. At higher levels, a number
of complicating effects may come into play. First, coexistence of strong
easterlies and relatively short vertical wavelengths occurs frequently above
20 km. As these two conditions tend to result in horizontal wavelengths
shorter than 500 km, such regions violate the assumptions that allow the
derivation and application of Eqs. (

Figure

There is a strong linear relationship between the vertical resolution and the
percent differences of the calculated momentum fluxes, with a mean increase
of

We also study the impact of holding individual input parameters constant at
the 250 m resolution values. The inputs considered here are stratification

In contrast, for constant vertical wavelength (dashed), the calculated fluxes
increase to 900 m resolution and then decrease for still larger vertical
stepping. This suggests that a large portion of the dependence of momentum
fluxes on vertical resolution greater than 1000 m results from changes in the
vertical wavelength. Figure

Time series of 5–20-day Kelvin wave momentum fluxes (shading) for
Gan Island

Performing analytic experiments with Eqs. (

A similar analysis for changing temporal resolution finds that the overall variations from changes in time stepping are much smaller than those from vertical resolution (not shown). For time steps between 0.25 and 2 days, the mean flux is at most 5 % different from the value for 24 h resolution.

Figure

A noteworthy difference between the two is that the amplitudes at Gan Island
are roughly 2–3 times larger than those at Manus Island. While this is
certainly the case for the month of January, it is perhaps more obvious for
the period between mid-October and mid-November. This amplitude difference
arises in part because our method estimates the momentum fluxes from a point
source of data. While Gan Island is located in a region of the Indian Ocean
that is relatively far removed from other land surfaces, Manus island is
located just to the east of the Maritime Continent. The Maritime Continent is
known to diminish both Kelvin waves

Figures

Time series of momentum fluxes from the Manus ARM site. Plotted
fields are as in Fig.

Time series of momentum fluxes from the Manus ARM site, continued. The span here covers 1 July 2008 through 31 December 2013.

In the time series, there are broad regions of data in the center of the
easterlies in which the theoretical assumptions are violated (gray shading;
see discussion in Sect.

Climatology of momentum flux and related fields from the Manus ARM
sounding site.

We find that our estimated momentum flux amplitudes qualitatively agree with
those estimated by

Calculated momentum fluxes for the Manus ARM site are remarkably similar to
those from the Manus DYNAMO data, when the resolution between the two
datasets is the same (cf. Fig.

One interpretation of the above results that arises when comparing
simultaneous calculations of momentum fluxes at different sounding sites (see
Figs.

Our calculated momentum fluxes largely represent local contributions to the
zonal mean. However, stratospheric Kelvin waves are known to strongly project
onto planetary scales

The annual cycle of momentum fluxes and of input fields to the calculation
of Eq. (

Composite momentum flux in shading and composite zonal mean zonal
winds in gray contours, both as functions of QBO

Figure

We next analyze the typical momentum fluxes associated with the QBO. We
determine phases of the QBO based on an index of the phasing between zonal
mean zonal wind at 30 hPa (

Average residence time and standard errors, in units of days, for
each bin of QBO

Figure

The composite momentum flux fields are also shown in Fig.

Percent of days in each QBO phase bin that fall between December and March. The total number of days in each bin is given along the top abscissa.

A natural step in this line of study is to analyze the relation between
tropical convection and our estimated Kelvin wave momentum fluxes. However,
tying a certain stratospheric Kelvin wave packet to a specific tropospheric
deep convection event is not necessarily straightforward. While Kelvin waves
are predominantly generated by convection, not all tropical convection will
generate Kelvin waves. When Kelvin waves are forced, their upward propagation
will be strongly affected – and often inhibited – by changes in background
winds and static stability near the tropical tropopause

Rather than relying on advanced techniques to thoroughly quantify the effects of tropical deep convection on stratospheric Kelvin waves, here we show a cursory analysis of this relationship through use of compositing (superposed epoch analysis). Compositing relies on an appropriate definition of an event start date in order to filter out noise in the data, leaving the desired signal. Fundamentally, this method shows the lead–lag relationship between two fields: in our case between a measure of deep convective activity and stratospheric Kelvin waves.

Selecting an event in tropical convection is not straightforward since it is
a nearly ubiquitous feature there. However, tropical deep convection is not
spatially and temporally stochastic but instead routinely organizes into
large-scale patterns, most notably the MJO

Here we define an event as any continuous span of days during which outgoing
longwave radiation (OLR) indicative of deep convection covers more than
66 % of the upstream area for a given sounding site. We use 200 W m

Composite momentum flux anomaly for events where OLR is less than
200 W m

Using these event identification criteria, we find 88 events for the Manus
sounding site. The composite Kelvin wave momentum flux anomaly and zonal wind
are shown in Fig.

The relatively small amplitudes of the anomalies and low linear correlations
indicate that spatially dense signals in OLR are not the primary factor
preceding positive anomalies of momentum flux in the stratosphere. For
instance, this composite analysis does not account for the background wind
state or changes in stratification, and is only for a single radiosonde site
that may miss some or all of the momentum flux signal generated by the local
convection. Yet, the 95 % significant signal shown here is in line with
expectations from theory: organized convection leads to generation of Kelvin
waves. These results are also in line with those from

As noted earlier, such patterns of organized convection in the Tropics are
often associated with the convectively active phases of the MJO – phases 3–6
from

Figure

As in Fig.

A second feature of Fig.

Our method of compositing with this 11-year record of data is ultimately not sufficient to make definitive arguments about the impact of the MJO on lowermost stratospheric Kelvin wave momentum flux. Nevertheless, the above findings do suggest that the MJO is associated with anomalous increases in the flux, in at least the lowermost stratosphere.

We expand on prior methods for using high-resolution radiosonde observations
to estimate upward fluxes of zonal momentum by Kelvin waves. Our methodology,
in contrast to previous studies that used non-overlapping windows of data,
makes use of short-time Fourier transform to generate daily time series of
momentum fluxes that are useful for detailed analyses of intraseasonal and
interannual variability. Unlike prior work using similar methods, we make use
of relatively long-term sources of high-vertical resolution radiosonde data
provided by the DOE ARM program to enable analysis of such variability. The
qualitative nature of our derived time series is found to agree well with
previous results – e.g., they show amplification during both JFM and QBO
easterly phases – and they qualitatively match prior estimates

Dependence of our results on vertical and temporal resolution is determined
by reprocessing raw radiosonde data across different resolutions and
comparing spatially and temporally overlapping points from our momentum flux
calculation. Temporal resolution does not strongly affect the flux amplitudes
for the tested time steps. In contrast, there is an approximately linear
increase in the calculated flux amplitudes with increased vertical step,
particularly beyond 500 m resolution (Fig.

Sensitivity to vertical stepping larger than 500 m highlights the need for continued collection of high-vertical-resolution observations in the tropical stratosphere. Both satellite observations and reanalysis reconstructions have much larger (order 1 km and larger) vertical stepping at these altitudes, so estimations derived from these sources alone may not fully capture the vertical structure. Perhaps more problematic is that the effect of coarse vertical resolution is not equal in westerlies and easterlies. Estimates will be too large in easterlies when the flux is large but will be relatively larger in westerlies when the flux should be small. Advances in remote sensing and computing capabilities will allow for smaller vertical stepping in both these platforms, helping to alleviate this sensitivity. However, there will still be a significant role for routine, high-resolution radiosonde data in constraining satellite observations and in nudging data assimilation procedures for reanalyses.

By comparing calculated fluxes from highly processed radiosonde data during
the DYNAMO field campaign to calculated fluxes from synchronous raw
radiosonde data at identical and nearby sounding stations, we find that our
method is well suited for application to these raw data, of which there is a
considerably longer data record. Kelvin wave momentum fluxes are then
calculated from an 11-year span (2003–2013) of quality radiosonde
observations from this data record. The annual mean cycle of momentum fluxes
shows a JFM maximum and a minimum 6 months later for July through September
(Fig.

A composite analysis of events featuring broad deep convection shows that
momentum fluxes are significantly increased by 30 days following the onset.
Though the signal is only significant up to

Such studies should continue technique developments and data analyses that are necessary to further constrain the tropical stratospheric momentum flux budget. Techniques could be developed to incorporate simultaneous soundings from multiple sites into a single calculation of momentum fluxes. The results derived here come from two radiosonde sites, but many additional sites with long data records are available. A careful reprocessing of these radiosonde data may allow for extending the data record with already available data.

Continued collection of high-quality radiosonde observations that probe the
tropical stratosphere will also be vital for increasing the number of
observed annual and QBO cycles. In addition to the role radiosondes have in
forecasting

Level 4 DYNAMO data for Manus and Gan are
available from the data archive at NCAR/EOL (

The authors declare that they have no conflict of interest.

The authors would like to acknowledge Paul Ciesielski for his help in
obtaining the L4 DYNAMO data and the raw radiosonde data. The analysis of
Sect.