Three Dimensional Analysis of HALOE CH4:Implications of Stratosphere-Mesosphere Dynamics
P. K. Patra1 and M. S. Santhanam2
1Frontier Research System for Global Change, Yokohama 236 0001, Japan2IBM-Research, India Research Laboratory, New Delhi 110 016, India
Manuscript submitted toAnnales Geophysics
Manuscript version: 3 May 2002
Offset requests to:P. K. Patra
Send proofs to:P. K. Patra
Abstract
Measurements of methane (CH4) is being made in the stratosphere and mesosphere by
HALOE/UARS since November 1991 on irregularly located space and time coordinates.
These data are used to generate the seasonal distributions of CH4 mixing ratio on a three
dimensional regularly spaced grid. We have shown that the results from this analysis are
comparable with the seasonal latitude-pressure distributions data from UARP. Thus we
are able to reproduce all the major features observed so far in the latitude-pressure distri-
bution of such minor constituents quite satisfactorily. In addition the longitude-pressure
distributions of CH4 reveals the seasonal variation in the wave activity in the stratosphere.
The Principal Component Analysis (PCA) has been performed on the 3D mixing ratio
anomalies of CH4. It is quantitatively shown that the most dominant PCAs on pressure
surfaces capture variabilities in CH4 caused by the quasi-biennial oscillation in the mid-
dle stratosphere, the annual and semiannual oscillations in the lower-middle mesosphere,
and mixture of both in the upper mesosphere. The 3rd dominant PCA brings out the
variations associated with the seasonal oscillations in the middle-upper stratosphere and
mesosphere, and QBO in the lower stratosphere. The longitude-pressure crosssections
are used to analyse the QBO-annual cycle interaction and influence of isentropic mixing
and mean meridional circulation in determining the tracer distribution in the stratosphere.
Correspondence to: P. K. Patra
1
1 Introduction
Studies on the variability of various atmospheric trace gas concentrations have provided a deep in-
sight into the dynamics, radiation, and chemistry of the Earth’s atmosphere in a number of ways
(Dobson, 1956; Brewer, 1949; Andrew et al., 1987). Many of these efforts primarily started with the
measurements and later followed by the numerical modelling. While the in situ measurements of-
fer excellent precision, the global observations based on the satellite remote sensing techniques have
provided a great deal of understanding on the stratospheric processes based on SAMS CH4 and N2O
(Jones and Pyle, 1984), temporal and spatial extent of the ozone hole from the Total Ozone Map-
ping Spectrometer (WMO, 1998), the effect of pollutant transport into a rather clean tropospheric
environment (Fishman et al., 1991), to name a few. Since the Upper Atmosphere Research Satellite
(UARS) carried many instruments on board for the measurements of several atmospheric parameters,
there have been significant advancement in our understanding of the chemistry and dynamics of the
stratosphere, mesosphere and ionosphere [see an overview by Dessler et al. (1998)].
Studies based on the latitude-height distributions of trace gases have been made with the help of
satellite observations as well as by using the numerical models (Baldwin et al., 2001). Recently,
longterm global coverage of various trace species from the HALOE have been used to understand the
effect of quasi-biennial oscillation (QBO), annual and semiannual oscillations on tracer transport with
the help of latitude-height distributions (Randel et al., 1998; Dunkerton, 2001). However, the distri-
butions in longitude-pressure plane and constant pressure layers still remain relatively unexplored,
and thus the relative contribution of the dynamical oscillations in describing the trace gas concentra-
tion anomalies at different altitude levels are not known quantitatively. For such studies, it would be
desirable to work with a four dimensional regularly gridded data set of the trace species as in the case
of meteorology (Barnes, 1964; Wilks, 1995). The data set can also be used as a testing ground for our
overall understanding of the atmospheric processes.
Due to space-time irregularity, the satellite measurements are subjected to rigorous analysis prior
to their use on a regularly spaced grids and time series analysis. The focus of this article is to under-
stand the manifestations of dynamics on the distributions of methane, trace gases in general, in the
stratosphere and mesosphere, with an emphasis on longitude-pressure and longitude-latitude cross-
sections. Section 2 describes the details of the data analysis to produce the methane mixing ratio
on a regularly spaced grids and its further processing using principal component analysis (PCA; also
known as empirical orthogonal functions, EOFs). Section 3 focuses on the results and discussion
2
on CH4 distribution and its observed variability, and results from the PCA/EOF analysis on different
spatial cross sections and time. Section 4 highlights the major findings from this work.
2 Data and Analysis
The HALogen Occultation Experiment (HALOE) is making continuous measurements of various
atmospheric constituents such as ozone, water vapour, methane, hydrogen halides, nitrogen oxides
etc. from the Upper Atmosphere Research Satellite since its launch in September 1991 (Russell et
al., 1993). These observations have also undergone multiple quality check evaluations and it has been
recognised that the observations consist of a variety of information about our planetary atmosphere
(Park et al., 1996; Dessler et al., 1998; Randel et al., 1998; Gray and Russell, 1999; Dunkerton, 2001;
Patra et al., 2002).
2.1 Source of CH4 vertical profiles
In this work, we have used the complete sets of measured vertical profiles of CH4 during both sunrise
and sunset (SPF formatted Level 2 data). The profiles of CH4 are measured in the altitude range of
the tropopause (∼ 16 km in the tropics and 10 km around the midlatitude) and mesopause (∼ 90 km).
The maximum latitudinal coverage is from 800S to 800N over the course of one year, and minimum
latitudinal coverage in the same period is up to about 500 on either side of the equator. The measure-
ments of CH4 profiles are available since October 1991 to present; the data until November 2000 is
used in this work. We take advantage of this long time series and near global data on atmospheric
methane to study its temporal, vertical, latitudinal and longitudinal distributions.
2.2 Three dimensional analysis
For atmospheric (meteorological as well as chemical) parameters, it is convenient to use the data when
produced on a regularly spaced grids for studying any atmospheric phenomena on a fixed coordinate
system. More importantly, with the advent of scientific computing, three dimensional chemistry-
transport models are gaining popularity and four dimensional data assimilation schemes have started
providing us the advantage of ingesting past atmospheric observations into the numerical models for
better simulation/forecast products (Swinbank and O’Neill, 1994). Therefore, it is extremely useful
to generate the three dimensional distribution of CH4 or any other dynamically and chemically active
trace atmospheric constituents based on their irregularly spaced observations from all possible sources
3
over a long time period. Such databases do exist for many meteorological fields and are downloadable
from the Internet (http://www.cdc.noaa.gov/PublicData/ for details).
To generate four dimensional data (including time) for CH4 mixing ratio we followed a procedure
that consists of three steps: 1) interpolation of vertical profiles on to the predetermined pressure levels,
2) creating the data sets segregated in to four seasons, namely December-January-February (DJF),
March-April-May (MAM), June-July-August (JJA) and September-October-November (SON), and
3) performing Barnes analysis (Barnes, 1964) on the observed data at a particular pressure level
which results in data distributed on equidistant longitude-latitude grids (hereinafter this database is
referred to as the analysis data).
Figure 1 shows the typical measurements of CH4 from the HALOE for the period from September
01, 1993 to September 29, 1993 as observed over different locations (symbols) at arbitrary pressure
levels ranging from about 150 mb to 0.03 mb (i.e. ≈ 14 to 73 km altitude in the tropics). Each
observed vertical profile is then used to interpolate the values of CH4 on 19 predetermined pressure
levels using standard techniques. The selected pressure levels in ascending order (descending altitude)
are 0.03, 0.05, 0.07, 0.1, 0.2, 0.3, 0.5, 0.7, 1.0, 2.0, 3.0, 5.0, 7.0, 10.0, 20.0, 30.0, 50.0, 70.0, and
100.0 mb. The levels chosen in the stratosphere are those for which the meteorological analysis is
also available. The interpolated profiles are also shown in Fig. 1 (dashed lines) for comparison. The
fractional error encountered at this step are typically much less than 3%. The precision of this vertical
interpolation is also evident from the diagram. The validity of this interpolation has also been checked
with HALOE temperature profiles.
The interpolated vertical profiles are then grouped into four seasons mentioned above. The main
purpose of such seasonal grouping is to increase the number of sampling points neighbouring any
defined spatial grid. We have defined a horizontal mesh of resolution 10 degrees in longitude (i.e. 36
points around the globe) and 5 degrees in latitude in the range from 500S to 500N (i.e. 21 points). The
higher latitudes beyond 50 degrees have not been considered due to lack of sufficient measurements in
some of the seasons. The Barnes objective analysis scheme is employed on every pressure level for all
the seasons in a year separately. The Barnes’ scheme performs multiple scans using a weighted linear
sum of the observations with a defined radius of influence around each grid point. The weighting
functions are calculated based on the data density which is again a function of the distance between
the observation point and the grid point within the radius of influence (Barnes, 1964). This analysis
procedure generates a four dimensional data set of 36 (longitude) × 21 (latitude) × 19 (pressure level)
4
× 36 (seasons; ranging from DJF of 1991-92 to SON of 2000).
2.3 Empirical orthogonal functions (EOFs)
The EOF technique is widely applied in meteorology to obtain the dominant and independent modes
of oscillation/circulation patterns present in any atmospheric parameter such as geopotential height,
sea level pressure, winds etc. (Wilks, 1995), and often performed on a pressure surface and regular
grid point data. Using the four-dimensional analysis of CH4 observations, obtained as outlined above,
we construct the EOFs for the horizontal distributions of CH4. This analysis is commonly carried out
on a correlation matrix formed by using the fluctuations in any data about their sample means. In this
work, the time series data are for 9 years in four seasons. For each season, the averages are calculated
separately and so are the fluctuations/anomalies. This method of averaging and calculation of CH4
anomaly are chosen for the following reasons. It can be assumed that the radiation budget (by ne-
glecting the 11 year solar cycle variation) and chemical behaviour of the stratosphere and mesosphere
remain constant for any given season over a decade. It is, therefore, obvious that the CH4 anomalies
are due to the differences in dynamics varying with time rather than to the changes in radiation or
chemistry.
The correlation matrix for the CH4 fluctuation time series n is formed from the following equation
S =1
nZ ZT (1)
where, the Z is data matrix of order 36 × 14364 (i.e. 9 · 4 time points × 36 · 21 · 19 space points) and
ZT is its matrix transpose, and the resultant correlation matrix (S) is square matrix of order 14364. The
real symmetric matrix S is numerically diagonolised using the standard LAPACK (LAPACK, 1999)
routines to determine the eigenvalues and eigenvectors. The eigenvectors of S, given by E, depict
the spatial distribution of relative variabilities (arbitrary unit) whereas the eigenvalues defines the
percentage of total variability associated with the particular eigenvector (also called as eigenmode).
The temporal picture is obtained from the kth principal component (PC), given by,
PCi,k =
m∑
j=1
zj,i ek,j i = 1, ..., n (2)
where zi,j and ej,k represents the components of the data matrix Z and eigenvector E, respectively. The
value of m depends on spatial crosssection to be studies; e.g., 756 for horizontal pressure surfaces,
684 for longitude-pressure crosssections etc.
5
2.4 Time-series analysis
Methane abundance in the atmosphere is increasing ever since the industrial revolution has started,
and there could also be gradual change in CH4 concentration due to changes in instrumental efficiency
over time. While forming Z, it is therefore possible that some of the dominant signals in the data,
relating to the atmospheric dynamics, may get deteriorated. To avoid any such difficulty and to
strengthen our assumption of interannually static radiation and chemistry of the atmosphere, the time
series data on CH4 at every grid point is fitted to a straight line (see Figure 2) and subsequently the
time series has been detrended. The detrended CH4 values are calculated as CH4 (new) = CH4 (old) -
slope × time (in year, starting 1992). This results in the more recent values being elevated for negative
slope and the reverse in the case of positive slope. In general, the slopes of the fitted straight line for
the lower stratosphere are positive which is in compliance with the increasing tropospheric loading
of CH4 into the stratosphere. However, the trend reverses in the upper stratosphere and the slope is
negative. This could be caused by the changing chemistry of our atmosphere due to the increase of
water vapour and halogen compounds (Randel et al., 1999), i.e. higher production of hydroxyl and
halogen radicals in the upper stratosphere in 1990s. This is one of the important outcomes from such
four dimensional data analysis (Patra et al., 2002).
3 Results and Discussion
The 4D data set has been used to show, firstly, the well established features in CH4 distributions in
latitude-pressure crosssections and then to illustrate the longitude-pressure crosssections. However,
it could be mentioned here that the horizontal distributions of CH4 on longitude-latitude planes at
different atmospheric pressure levels (not shown here) clearly depict the temporal variations in the
location of tropical upwelling region. The location of upwelling can seen as high CH4 values in the
summer hemisphere with decreasing concentrations on either latitude sides and its movement with
season is greater across the equator as the height increases.
3.1 Latitude-Pressure distributions
The latitude-pressure vertical cross-sections of CH4 distributions over a constant longitude of 700E
are shown in Figure 3. The gradual decrease in CH4 mixing ratio with both height and latitude oc-
curs primarily due to the reaction with O1D and OH in the stratosphere and caused by photolytic
6
destruction in the mesosphere. These plots clearly bear the signatures of the known meridional trans-
port, active in the stratosphere. Firstly, the surfaces of constant CH4 concentration is pushed upward
in the tropics and sharply slopes downward in the extratropics as a result of the known overturning
circulation across the isentropes, characterised by upwelling in the tropics and downwelling in the ex-
tratropics, on a meridional plane. The isentropic surfaces (surface of constant potential temperature)
can be assumed parallel to the pressure surface for all practical purposes. Secondly, the longitudinally
asymmetric wave induced dispersion along the isentropes; the planetary wave breaking cause rapid
mixing, particularly in the extratropics of the winter hemisphere. As a result the constant mixing
ratio surfaces tend to flatten in the southern hemisphere (SH) during JJA and SON. It should also be
mentioned that our analysis data could reproduce the double peak structure (or ”rabbit ears”) dur-
ing westerly phases of the quasi-biennial oscillation (QBO) in the upper stratosphere (Randel et al.,
1998). A comparison of the latitude-pressure distributions of CH4 from this analysis and the UARS
Reference Atmosphere Project (URAP) data (Remedios et al., 1998) shows that the profiles are in
excellent agreement. The standard deviations of the differences between this analysis and the URAP
data have been found to be 0.0779 (at 100 mb), 0.0538 (at 7 mb), and 0.0156 ppmv (at 0.3 mb) with
typical averages of about 1.5758, 0.9636, and 0.2264 ppmv, respectively.
3.2 Longitude-Pressure distributions
The longitude-pressure distributions of CH4 or any other chemical species of similar lifetimes in
the stratosphere (e.g. nitrous oxide, chlorofluorocarbons etc.) have not been studied in great detail,
primarily due to the lack of proper database. This section shows that the longitude-pressure cross-
sections also contain substantial amount of information on the waves in the stratosphere. Figure 4
shows the longitude-pressure vertical cross-sections of CH4 mixing ratio in all the four seasons and
over a fixed latitude of 400N. It is evident from the panels that the winter (DJF), fall (SON), and spring
(MAM) are more vulnerable to the waves wherein the amplitude in the oscillating isopleths are quite
larger than those in the summer (JJA). The phase of maximum upward displacement corresponds to
easterly in the winter whereas in summer it corresponds to westerly (see Figure 4). Amplitude of the
wavelike features also decreases towards the equator and increases polewards (not shown here). In this
discussion, it is assumed that the upward displacement of the CH4 isopleths have been caused by the
vertically propagating planetary waves. The cross-section over 400S also exhibits similar seasonality
in the wave activity with a maximum in the winter months (JJA) and minimum in the summer months
7
(DJF). It should also be pointed out that there is no apparent difference in observed wave activity with
seasons over the equator (at around 00 latitude).
However, these results are not free from artifacts of the observational set up as we are analyzing
seasons for single years. Therefore, it is likely that the wave-like structure is due, in part, to the
combining of sets of profiles from more than one sweep into the seasonal result. For example, a given
latitude will have about 14 occultations from a single sweep. The max/min structure of the JJA plot in
the mesosphere has about that frequency and could be caused by combining scans from two discrete
time periods within that season. In further discussion of the relation of CH4 mixing ratio fluctuations
with the atmospheric waves, we keep in mind the above drawback arising from the method adapted
for observation and the analysis.
3.3 PCAs and atmospheric oscillations
We have performed the principal component analysis on CH4 mixing ratio anomalies in 3D space.
Since the latitude-pressure crosssections of PCA and SVD analyses have been discussed in the pre-
vious studies (Randel et al., 1998; Dunkerton, 2001), we analyse the other two crosssections, namely
the horizontal crosssections on constant pressure surface and longitude-pressure crosssections at fixed
latitudes, in this study.
3.3.1 On horizontal surfaces
Figures 5, 6, and 7 show the principal components (PCs) for the anomalies of CH4 and zonal winds
on a number of pressure surfaces. The anomalies for the whole horizontal domain (i.e. 500S to 500N
latitude, and 00 to 3500 longitude) at a particular pressure surface is used in the PCA calculation.
The zonal winds are taken from the NCEP/NCAR reanalysis data and are available only up to 10
mb (Kalnay et al., 1996). The PC of zonal wind anomalies is obtained to examine how the first
few dominant principal components behave in the light of the known dynamical oscillations in the
stratosphere and also to better visualise the problem at hand with CH4 mixing ratio anomalies.
The first principal component (PC-1) of zonal wind anomaly (see Figure 5a) shows that QBO is
the dominant feature in the stratosphere. The Fourier analysis of PC-1 exhibits a perfect match in
frequency (27 month period) with the QBO index (Marquardt and Naujokat, 1997), leaving the other
frequencies at very low energy in the frequency spectrum (see Table 1). The Fourier analysis of the
PCA time series are done using IMSL routine. However, a shift in phase is evident with the increase in
8
altitude; i.e. the peaks formed by the PC-1 at 10 mb (∼ 31 km) and 20 mb (∼ 24 km) are preceded by
9 and 3 months from the peaks formed by PC-1 at 50 mb (∼ 21 km), respectively. This is in excellent
agreement with the overall downward propagation rate of the easterly and westerly wind regimes (≈ 1
km month−1). Similarly the PC-2 and PC-3 are mostly indicative of the dominant frequencies varying
from 7.7 to 15.4 months (see Table 1B), indicating that the annual oscillation (AO) plays second most
dominant role in the dynamics of lower-middle stratosphere. However, dominance of one frequency
over the others are not very clear in these PCAs.
Figure 5 also suggests that the QBO is not the governing factor in controlling the CH4 anomalies
in the lower stratosphere (at 50 mb, panel b), although at this altitude QBO dominates in zonal wind
anomaly. The Fourier analysis exhibits a broad peak in the energy spectrum, corresponding to a time
period of about 27-36 month (see Table 1A) which is not free from ambiguity. This suggests that
the CH4 distribution in the lower stratosphere is mainly controlled from the bottom (troposphere-
stratosphere exchange) than from the top (QBO influences). However, as expected it dominates in the
middle stratosphere (at 20 mb and 3 mb, panels b and c). The PC-1 captures about 26% and 37% of
the total anomaly in CH4 mixing ratio at 20 mb and 7 mb, respectively (see Table 1A for details). It
should also be mentioned that the phase of PC-1 at 20 mb lags PC-1 at 7 mb by about 6-9 months,
comparable to that has been seen in the zonal winds. The QBO like features in the PC-1 distributions
diminishes on either side of the middle stratosphere. The results from Fourier analysis for the time
series of these PCs are tabulated in Table 1A. It is discernible that the periods of about 22-27 months
(≈ the QBO period) are dominating in the region of 20 mb to 3 mb, whereas periods in the range of 8.3
to 10.8 months dominate the region between 1 mb to 0.5 mb. This periodicity compares favourably
with the time period of the semiannual oscillations (SAO) of about 6 months, and that of AO with
a period of 12 months (see Figure 5d,e and Table 1A for further details). Better agreement would
possibly be reached if time resolution of the data is higher. The layers in the mesosphere (at pressure
levels 0.5 mb, 0.2 mb, and 0.07 mb) are dominated by both the periodicities with QBO periodicity
being the dominant one. This feature is probably arising due to the lower stratosphere coupling with
the mesosphere through QBO (Abraham et al., 1997). It can also be seen from the Figure 5e that the
oscillation is out of phase by 1800 with that of the zonal wind QBO index.
In PC-2 the annual oscillations (AO) and semiannual oscillations (SAO) appear to dominate the
upper stratosphere and mesosphere (see Fig. 6). If we proceed further down to PCA number 3 (Fig. 7),
it shows a few more characteristics in the CH4 mixing ratio anomalies. Firstly, the QBO effect on trace
9
constituent distribution like CH4 comes out at lower stratospheric height. The PC-3 at 50 mb (Figure
7b) now shows very good match with the QBO periodicity of about 27 months (Table 1A). Secondly,
the effect of seasonal oscillation (SO) on CH4 concentrations start appearing in the middle-upper
stratosphere as well as in the middle stratosphere zonal wind anomalies (Figure 7). The percentages
of anomalies captured by the PCAs at each pressure level in the stratosphere and mesosphere are given
in Table 1. Though a very different approach to study the influence of dynamics on tracer distribution
has been employed here, the height regions of dominating dynamical oscillations on CH4 anomaly
distribution are generally in agreement with those suggested in Baldwin et al. (2001). We also believe
that this approach is more direct to study the effect of dynamical oscillations at different heights
compared to the previous studies those use the latitude-pressure crosssections of tracer distributions
(Randel et al., 1998; Dunkerton, 2001). Since projections of tracer anomalies on the derived EOF
structures are likely to decipher time variations of constituent anomalies integrated over latitude and
pressure (section 2.3; see also Randel et al. (1999)).
3.3.2 Longitude-pressure crosssections
Figure 8 shows the spatial structure of EOF-1 on the longitude-pressure surfaces at 100 latitude in
both hemispheres. The EOF-1 captures about 40% of total variability in CH4 anomalies, and clearly
identify the regimes of stratospheric transport mechanisms, e.g. the isentropic mixing and advection
due to mean meridional circulation, that vary with altitude. The three altitude ranges are in fairly
good agreement with the layers suggested by Gray and Russell (1999). They suggested that in the
layer below about 50 mb (potential temperature, Θ = 500 K) isentropic mixing plays the dominant
role. In the middle layers, between Θ = 500 K and 750 K (≈ 50 mb to 15 mb height), transport
by the mean meridional circulation is most important in determining the tracer distribution in the
subtropical latitudes. In upper stratosphere, though isentropic mixing becomes more influential on
tracer distribution, both mixing and advection have currently inseparable contributions (Gray and
Russell, 1999). From the longitude-pressure crosssections of EOF-1 at 100 latitude, it is apparent that
different layers are indeed identifiable. In the lower stratosphere (below 50 mb) and upper stratosphere
(above 7 mb) eigenmodes are generally anticorrelated with that in the middle. The distribution in the
lower stratosphere show many fine structures, which could have been generated by propagation of
tropospheric disturbances to the stratosphere. As the altitude increases, the values tends to alter sign,
suggesting that the mean meridional circulation is taking over the isentropic mixing. However, above
10
about 12 mb height the situation changes and that continues till the top of the stratosphere, which
probably indicate increasing influence of isentropic mixing process in stratospheric tracer distribution.
It should be mentioned here that such structures in EOFs distribution is observed in the tropical
stratosphere and starts fizzling out beyond 300 on both sides of the equator. The altitude of middle and
upper layers also slightly changes with latitude, shifts upward as the latitude increases. This finding is
consitent with the observed slopes in CH4 distributions during NH winter and spring in the subtropics
(see Fig. 4). It is seen that the CH4 mixing ratio isolines of sharp latitudinal gradient are located
about 200N in the height range of 50-10 mb, while at higher latitudes near 300N those are found
at higher heights (range: 10-2 mb). The overall asymmetry in northern and southern hemisphere
EOF distributions is more prominent with the increase in latitude. In addition, it has been noticed
that the longitude-pressure crosssections of EOF distributions with lesser significance are much more
complicated, and thus is not included in the discussion.
The timeseries of first PCs in the latitude range of 500S-500N are shown in Fig. 9. The zonal wind
variations at 50 mb over Singapore is also shown in panel (a) for better comparison and verification of
phase lag/lead of QBO signals in the CH4 on longitude-pressure planes. The PC-1 over equator and
200N show good matches in periodicity with the QBO index, and QBO signal amplitude becomes
smaller when the latitudes beyond 300N are studied. The most surprising finding lie in the phase
and periodicity of PC-1 at 100N - the CH4 QBO phase was apparently lagging behind by about 6
months during first two zonal winds QBO cycles, and that during last two zonal winds QBO cycle is
found to lag by about 12 months (acquired a net phase lag of 6 months) (see Figs. 9a,b for details).
This is probably a manifestation of QBO-annual cycle interaction, by which the subbiennial period
is stretched towards 24 months and subsequently the QBO period is contracted (Dunkerton, 2001).
However, it is not conclusive at this moment why the PC-1 at 200N is tending to return to QBO cycle.
The timeseries in the southern hemisphere (Fig. 9c) do not show very clean QBO cycles, nonetheless
it is present, suggesting that the propagation of tropical QBO signal into the southern hemisphere
extratropics is rather weak.
A test for statistical significance of the principal component analysis suggests that only first three
PCA components contain most of the information available in the anomaly data used in this study.
We employed the Rule-N test by forming 756 matrices of order 756 (see Wilks, 1995 for details of
the implementation). Each element of the matrix is a normally distributed pseudo-random number
with zero mean and unit variance. All the 756 randomly generated correlation matrices are used to
11
estimate average eigenvalue distribution which sets the cutoff for the most significant eigenvalues of
the correlation matrix formed with the actual anomalies. The details of the statistical test is beyond
the scope of this article.
4 Conclusions
Three dimensional analysis of the CH4 observations from the HALOE/UARS has been made. The
analysed data is utilised to study the variabilities in CH4 distributions with respect to time, and all the
three spatial cross-sections. The time-series analysis suggests an increase in troposphere to strato-
sphere loading of atmospheric CH4, and enhanced rate of photolytic destruction with increase in
altitude and latitude. Using our analysed data we could reproduce all the known behaviour of the
stratospheric and mesospheric transport mechanisms in the meridional cross-section. Additional in-
formation have been obtained from the longitudinal-pressure cross-sections in connection with zon-
ally symmetric/asymmetric wave propagation and breaking, in relation to the easterly and westerly
phases of the QBO. The EOF analysis have been performed on the 3D CH4 anomalies, and PC and
Fourier analysis are carried out on various spatial crosssections, i.e. longitude-latitude planes of con-
stant pressure and longitude-pressure planes of constant latitude. In contrast to the previous works,
our results help us in understanding the relative contributions of various stratospheric and mesospheric
oscillations, such as QBO, AO, and SAO, in modulating the CH4 concentrations at different layers of
the atmosphere. The longitude-pressure crosssections of EOFs over various latitude help to identify
the layers under the influence of isentropic mixing and advection due to mean meridional circulation.
The corresponding most dominant principal components indicate the interaction of QBO and annual
cycles in the northern hemisphere tropics.
Acknowledgements. We are grateful to the HALOE team members for making methane data available on the
Internet, and Ellis Remsberg for helpful comments on an initial draft of this manuscript and educating us
on technicalities of HALOE measurements. We also thank Abhinanda Sarkar for useful discussions. NCEP
Reanalysis data is provided by the NOAA-CIRES Climate Diagnostics Center, Boulder, Colorado.
12
References
Abraham, S., S.K. Dhaka, K.D. Praveen, N. Nath, O.P. Nagpal, and K.L. Baluja, Lower stratosphere coupling
with the mesosphere through QBO, J. Atmos. Solal-Terr. Phys., 59, 1885-1889, 1997.
Andrew, D.G., J.R. Holton, and C.B. Leovy, Middle Atmosphere Dynamics, Academic Press, Orlando, 1987.
Baldwin, M.P. et al., The quasi-biennial oscillation, Rev. Geophys., 39, 179-229, 2001.
Barnes, S.L., A technique for maximizing details in numerical weather map analysis, J. Appl. Meteor., 3, 396-
409, 1964.
Brewer, A.W., Evidence for a world circulation provided by measurements of helium and water vapor distribu-
tion in the stratosphere, Quart. J. Roy. Meteorol. Soc., 75, 351-360, 1949.
Dessler, A.E., M.D. Burrage, J.-U. Grooss, J.R. Holton, J.L. Lean, S.T. Massie, M.R. Schoeberl, A.R. Douglass,
and C.H. Jackman, Rev. Geophys., 36, 183-210, 1998.
Dobson, G.M.G., Origin and distribution of polyatomic molecules in the atmosphere, Proc. Roy. Soc. Lond. A,
236, 187-199, 1956.
Dunkerton, T.J., Quasi-biennial and subiennial variations of stratospheric trace constituents derived from
HALOE observations, J. Atmos. Sci., 58, 7-25, 2001.
Fishman, J., K. Fakhruzzaman, B. Cros, and D. Nganga, Identification of widespread pollution in the Southern
Hemisphere deduced from satellite analyses, Science, 252, 1693-1696, 1991.
Gray, L.J., and J.M. Russell, Interannual variability of trace gases in the subtropical winter stratosphere, J.
Atmos. Sci., 56, 977-993, 1999.
Jones, R.L. and J.A. Pyle, Observations of CH4 and N2O by the Nimbus 7 SAMS: a comparison with in situ
data and two-dimensional numerical model calculations, J. Geophys. Res., 89, 5263-5279, 1984.
LAPACK Users Guide, E. Anderson et al., SIAM Press, Philedelphia, 1999. (see also
http://www.netlib.org/lapack).
Kalnay, E. et al., The NCEP/NCAR 40-Year Reanalysis Project, Bull. American Meteorol. Soc., 77, 437-472,
1996.
Marquardt, C., and B. Naujokat, An update of the equatorial QBO and its variability. 1st SPARC Gen. Assemb.,
Melbourne Australia, WMO/TD-No. 814, Vol. 1, 87-90, 1997.
Park, J. H. , J. M. Russell III, L. L. Gordley, S. R. Drayson, D. Chris Benner, J. McInerney, M. R. Gunson, G. G.
Toon, B. Sen, J.-F. Blavier, C. R. Webster, E. C. Zipf, P. Erdman U. Schmidt, and C. Schiller: Validation of
Halogen Occultation Experiment CH4 Measurements from the UARS, J. Geophys. Res., 101, 10,183-10,203,
1996.
Patra, P.K., S. Maksyutov, and M.S. Santhanam, Derived trends of CH4 in the stratosphere from HALOE
measurements, in Proc. Non-CO2 Greenhouse Gases: Scientific Understanding, control and implementation,
13
Allenpress, Netherlands, 2002 (in press).
Randel, W. J., F. Wu, J. M. Russell III, A. Roche, and J. W. Waters, Seasonal Cycles and QBO Variations in
Stratospheric CH4 and H2O Observed in UARS HALOE Data, J. Atmos. Sci., 55, 163-185, 1998.
Randel, W. J., F. Wu, J. M. Russell III, and J. W. Waters, Space-time patterns of trends in stratospheric con-
stituents derived from UARS measurements, J. Geophys. Res., 104, 3711-3727, 1999.
Remedios, J. J., A. E. Roche, and J. M. Russell III: A Strategy for the Development of Climatologies for Tracer
Species: Proposed New Reference Models for Methane and Nitrous Oxide, Adv. Space Res., 21, 1425-1434,
1998.
Russell, J. M. III, L. L. Gordley, J. H. Park, S. R. Drayson, D. H. Hesketh, R. J. Cicerone, A. F. Tuck, J.
E. Frederick, J. E. Harries, and P. J. Crutzen: The Halogen Occultation Experiment, J. Geophys. Res., 98,
10,777-10,797, 1993.
Swinbank, R., and A. O’Neill, A stratosphere-troposphere data assimilation system, Mon. Wea. Rev., 122, 686-
702, 1994.
Wilks, D.S., Statistical Methods in the Atmospheric Sciences, Academic Press, San Diego, California, 1995.
World Meteorological Organisation (WMO), Scientific assessment of ozone depletion: 1998, Rep. 44, Global
Ozone Res. and Monit. Proj, Geneva, 1999.
14
Figure Captions
Fig. 1. Typical HALOE measured vertical distributions (shown by the symbols) and the interpolated profiles
(dashed lines) of CH4 depicting that the accuracy of the interpolated data used in this study are as good as the
satellite observations.
Fig. 2. Trends in the CH4 measurements at two representative space locations (a) for (700E, 00N) at 20 mb
pressure, and (b) for (100W, 50N) at 3 mb pressure (solid line). Slope from a straight line fit (dotted line) is
used to detrend the data and the resulting time-series is shown by the dashed line. This procedure is repeated
for each longitude, latitude and pressure level analysis data.
Fig. 3. Latitude-Pressure distributions of CH4 (ppmv) in four seasons: December-January-February (DJF),
March-April-May (MAM), June-July-August (JJA), and September-October-November (SON).
Fig. 4. Longitude-Pressure distributions for CH4 (in ppmv) at 400N latitude belt, shows the effect of the
seasonal differences in wave activities in the stratosphere.
Fig. 5. First Principal Components (PC-1) obtained from the EOF analysis for the horizontal distributions
of CH4 and zonal wind: (a) shows PC-1 for the zonal winds at 50 mb (dashed line) and 10 mb (continuous
line); (b) shows PC-1 for CH4 distributions at 50 mb (dashed line) and 20 mb (continuous line); (c) PC-1 for
CH4 mixing ratio at 7 mb (dashed line) and 3 mb (continuous line); (d) PC-1 for CH4 concentration at 1 mb
(dashed line) and 0.5 mb (continuous line); (e) PC-1 for CH4 mixing ratio at 0.2 mb (dashed line) and 0.07 mb
(continuous line).
Fig. 6. Same as Figure 5, but for PC-2.
Fig. 7. Same as Figure 5, but for PC-3.
Fig. 8. Longitude-pressure crosssections of most dominant 3D EOFs of CH4 anomalies over 100 latitude.
Fig. 9. The most dominant principal component of CH4 anomalies on longitude-pressure surfaces of constant
latitudes: a) is for the equator and QBO index in terms of 30 mb zonal winds observed at Singapore (Marquardt
and Naujokat, 1997), b) and c) are the PCAs constructed with EOFs-1 at various latitutes of northern and
southern hemisphere, respectively.
Figures
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6Methane (ppm)
0.1
1
10
100
Pres
sure
(mb)
31.1N, 62.8E0.3N, 100.5W20.1S, 110.2E40.0S, 58.7E60.3S, 23.1E68.7S, 3.9E
Fig. 1. Typical HALOE mea-
sured vertical distributions
(shown by the symbols) and the
interpolated profiles (dashed
lines) of CH4 depicting that the
accuracy of the interpolated data
used in this study are as good as
the satellite observations.
1992 1993 1994 1995 1996 1997 1998 1999 2000
Calander Year
1.4
1.45
1.5
1.55
1.6
CH4
[ppm
]
0.6
0.7
0.8
0.9
1
1.1
CH4
[ppm
]
Detrended dataLinear fitHALOE data
Fig. 2. Trends in the CH4 mea-
surements at two representative
space locations (a) for (700E,
00N) at 20 mb pressure, and (b)
for (100W, 50N) at 3 mb pres-
sure (solid line). Slope from a
straight line fit (dotted line) is
used to detrend the data and the
resulting time-series is shown by
the dashed line. This procedure
is repeated for each longitude,
latitude and pressure level anal-
ysis data.
Fig. 3. Latitude-Pressure distributions of CH4 (ppmv) in four seasons: December-January-February (DJF),
March-April-May (MAM), June-July-August (JJA), and September-October-November (SON).
Fig. 4. Longitude-Pressure distributions for CH4 (in ppmv) at 400N latitude belt, shows the effect of the
seasonal differences in wave activities in the stratosphere.
1992 1993 1994 1995 1996 1997 1998 1999 2000Calander Year
−200−100
0100200
−1012
−2−1012
Prin
cipa
l Com
pone
nt #
1 −2−101
−1−0.5
00.5
11.5
A
B
C
D
E
Fig. 5. First Principal Components (PC-1) obtained from the EOF analysis for the horizontal distributions
of CH4 and zonal wind: (a) shows PC-1 for the zonal winds at 50 mb (dashed line) and 10 mb (continuous
line); (b) shows PC-1 for CH4 distributions at 50 mb (dashed line) and 20 mb (continuous line); (c) PC-1 for
CH4 mixing ratio at 7 mb (dashed line) and 3 mb (continuous line); (d) PC-1 for CH4 concentration at 1 mb
(dashed line) and 0.5 mb (continuous line); (e) PC-1 for CH4 mixing ratio at 0.2 mb (dashed line) and 0.07 mb
(continuous line).
1992 1993 1994 1995 1996 1997 1998 1999 2000Calander Year
−100−50
050
100
−1−0.5
00.5
1−2−1012
Prin
cipa
l Com
pone
nt #
2 −1−0.5
00.5
1−0.5
00.5
1
A
B
C
D
E
Fig. 6. Same as Figure 5, but for
PC-2.
1992 1993 1994 1995 1996 1997 1998 1999 2000Calander Year
−100−50
050
100−1
−0.50
0.51
−1012
Prin
cipa
l Com
pone
nt #
3
−1−0.5
00.5
−0.5−0.25
00.250.5
A
B
C
D
E
Fig. 7. Same as Figure 5, but for
PC-3.
Fig. 8. Longitude-pressure crosssections of most dominant 3D EOFs of CH4 anomalies over 100 latitude.
1992 1993 1994 1995 1996 1997 1998 1999 2000
−2
−1
0
1
2
50 S40 S30 S20 S10 S
−2
−1
0
1
2
10 N20 N30 N40 N50 N
−4
−2
0
2
4QBO IndexEquator
a
b
c
Fig. 9. The most dominant principal component of CH4 anomalies on longitude-pressure surfaces of constant
latitudes: a) is for the equator and QBO index in terms of 30 mb zonal winds observed at Singapore (Marquardt
and Naujokat, 1997), b) and c) are the PCAs constructed with EOFs-1 at various latitutes of northern and
southern hemisphere, respectively.