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

(prabir@jamstec.go.jp)

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

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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

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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

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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)

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× 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.

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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

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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

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(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

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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

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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

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1996.

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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.