27-day Solar Cycle in MLS Temperature: A Synthesis of Statistical
Approach
King-Fai Li1, Mao-Chang Liang2,3, Charles D. Camp4, Yuk L. Yung1
1
Division of Geological and Planetary Sciences, California Institute of Technology,
Pasadena, California, USA.
2
Research Center for Environmental Changes, Academia Sinica, Taipei, Taiwan.
3
Graduate Institute of Astronomy, National Central University, Jhongli City, Taiwan.
4
California Polytechnic State University, San Luis Obispo, California, USA.
Abstract
We report a 27-day solar cycle in the stratospheric temperature observed by the
Microwave Limb Sounder/Aura (MLS). The Monte-Carlo Empirical Mode
Decomposition (MCEMD) was employed to filter out the seasonal cycles and
irrelevant periodicities in the time series. The meridional spatial pattern and the
temporal variation of the temperature response were studied by composite mean
difference (CMD) approach. A statistically significant spatial response of the 27-day
solar cycle was obtained for the first time. An increased temperature of 0.13 – 0.42 K
during the 27-day solar maximum relative to the 27-day solar minimum was observed
in the tropical stratosphere and lower mesosphere, where the solar heating due to
ozone absorption is dominant. In the mesosphere, a decreased temperature of -0.7 K
was observed at the equator, companioned by a strong temperature increase (> 1.26 K)
at high latitudes. There was a general agreement in the stratosphere compared to the
previous study from the ERA-40 reanalysis data. We also compared the observation
with simulations from chemistry climate models and found good agreement, except
that the temperature decrease in the equatorial mesosphere was not simulated in the
models. No statistically significant global phase lag against solar forcing was found.
1. Introduction
Whether the solar cycle has important impacts on the current climate remains as one
of the most controversial issues in the community [Camp and Tung, 2007a; Foukal et
al., 2008; Tung and Camp, 2008]. Nonetheless, it is sometimes used to test the climate
sensitivity of general circulation models [see, e.g. [Hansen et al., 2007]]. Since most
of the solar cycle variations occur in the shortwave region (~120 – 300 nm) [Khosravi
et al., 2002; Williams et al., 2001], any solar-cycle effects on climate are expected to
be observable in the middle atmosphere via solar heating due to stratospheric ozone
absorption. Take the 11-year solar cycle as an example. The variation in total solar
irradiance is only ~ 0.08% [Lean, 2000]. Therefore it is extremely hard to either
measure or simulate the solar cycle effects in climate models. Furthermore, other
difficulties often arise from the fact that atmospheric processes such as the El Niño
Southern-Oscillation, the quasi-biennial oscillation and even volcanic effects, may
interact with or contaminate the 11-year solar cycle [Camp and Tung, 2007b; Kodera
et al., 2008; Soukharev and Labitzke, 2001; Tung and Camp, 2008].
In this Letter, we examine the 27-day solar cycle in the stratospheric temperatures
observed by the Microwave Limb Sounder (MLS) onboard the National Aeronautics
and Space Administration (NASA) Earth Observing System (EOS) Aura mission
during 2004 – 2008. With this relatively short periodicity, only that allows more
cycles to pin down the standard error of measurement, but interactions with other
atmospheric processes will also be avoided automatically. The same study was
pioneered by [Hood, 1984], who analyzed the zonal averages of both ozone and
temperature measured by NIMBUS 7 SBUV and SAMS. In a subsequent paper,
[Hood and Cantrell, 1988] concluded that near 1 mb, the temperature sensitivity of
SAMS is 0.06 ± 0.01% per 1% change in 205 nm solar flux, with a phase lag of 6
days. The vertical dependences of these parameters are rather strong, with the phase
lag being as much as 14 days in the middle stratosphere (~ 10 mb). Early attempts
using photochemical models as well as photochemical-dynamics interactive models
underestimated both of these quantities [Brasseur et al., 1987; Hood and Jirikowic,
1991]. Later,[Hood and Zhou, 1998] studied the ozone and temperature products
measured by MLS aboard NASA's Upper Atmosphere Research Satellite (UARS), the
prototype of EOS MLS, and again found that near 1 mb, the solar cycle sensitivity is
0.08 ± 0.01% per 1% change in 200-205 nm solar flux; but the phase lag was not well
constraint. A number of efforts tried to simulate these observations with
chemistry-climate models [Austin et al., 2007; Brasseur, 1993; Chen et al., 1997;
Rozanov et al., 2006; Williams et al., 2001]. Most of them show considerable success
but [Rozanov et al., 2006], who ran the Germany SOCOL model, pointed out that the
temperature responses may not be robust against ensemble averages. Nonetheless
these works altogether underscore the importance of the coupling between dynamics
and chemistry for a successful simulation of these tiny effects. Thus, further
characterizations of temperature variability due to solar variations in the rotational
time scales are desired.
With substantial improvements over the previous generation, EOS MLS data should
provide the most accurate data of stratosphere temperature suitable for our purpose.
[Ruzmaikin et al., 2007] has already used the EOS MLS version 1.51 products for
studying the 27-day cycle in ozone and temperature. One difficulty of analyzing
periodicities of time scales shorter than the others in the data is the way of filtering.
For example, [Hood, 1984] and subsequent work used running averages to remove
day-to-day fluctuations as well as periods long than 36 days. The cut-off frequencies
of these kinds are, to some extent, defined artificially, and such filtering works best
only for linear processes. [Ruzmaikin et al., 2007] employed a new filtering tool, the
Empirical Mode Decomposition (EMD), which does not require pre-defined cut-off
frequencies or quantities alike, and this method works well for non-linear data sets
[Huang and Wu, 2008]. They applied the EMD filter at each point in space, leaving
only the 4-th intrinsic mode function (IMF) which contains mainly the 27-day cycle in
the data. By putting together all the time series, they were able to create the
height-temporal and latitudinal-temporal distributions of the 27-day mode. As a result,
they found a polar amplification in both ozone and temperature in the winter
hemisphere, which cannot be explained by any photochemical models.
We have two goals in this work. First, we append to [Ruzmaikin et al., 2007] the
recently released EOS MLS version 2.2 product to provide further evidence of the
27-day variability in temperature in the upper atmosphere. We refine their results with
the noise-assisted or the Monte-Carlo Empirical Mode Decomposition (MCEMD)
[Wu and Huang, 2004], where the statistical significance of the IMFs can be tested.
Second, we go one step further to expand the filtered data into a linear combination of
spatial and temporal functions by a recent technique, which is a spatial filter called the
Composite-Mean-Difference (CMD) [Camp and Tung, 2007a], and examine the
latitudinal-height pattern of the 27-day solar cycle response in temperature. This is the
first observational spatial picture for the temperature response. This will also allow an
easy comparison with model simulations.
In Section 2, we briefly describe the MLS data set to be employed in this work. In
Section 3, we describe in detail the two tools, MCEMD and CMD, to be employed for
extraction of the 27-day solar cycle signal in the data. The extracted spatial pattern of
temperature response is compared to previous simulations in Section 4.
2. Data
The EOS MLS uses the microwave limb sounding techniques to measure atmospheric
quantities in troposphere, stratosphere and mesosphere [Waters et al., 2006]. It is
onboard NASA Aura satellite, launched on July 15, 2004 into a sun-synchronous polar
orbit at altitude 705 km with inclination of 98º, period 98.8 minutes and 1:45 P.M.
ascending (north-going) equator-crossing time. The overall mission is designed for a
5-year lifetime. The upper limit of the degradation rate of the EOS MLS instrument is
expected to be ~0.003 % per year, similar to the previous generation the UARS MLS
instrument. The retrieved temperature studied in this work is measured by the isotopic
spectral lines of O2 at 118 GHz and 239 GHz.
The MLS version 2.2 products were released to the public in June 2008, where the
retrieval precision and vertical resolution have been improved over version 1.51
products. The temperature product spans from 316 mb to 0.001 mb. Typical precision
range from 0.6 K in the lower stratosphere to 2.5K in the mesosphere, typical vertical
resolution is ~ 4 – 6 km in 316 – 1 mb and ~ 10 km in 1 – 0.001 mb [Livesey et al.,
2007]. The data used in this work spans from August 8, 2004 – October 25, 2008. We
follow the data selection recommendations suggested in [Schwartz et al., 2008]: Only
data points whose convergence < 1.2, status being an even number not equal to 32 and
quality > 0.6 are included. We further apply a data quality control by throwing data
points that are five standard deviations away from the daily average. Due to
occasionally missing or rejected data at extreme levels and high latitudes, we will
focus only between 100 – 0.01 mb and 82º S – 82º N. The accepted data is then
averaged daily and zonally into latitudinal strips of 4º wide, giving a total of 1066
time series. Figure 1 shows the average temperature over the whole time span in gray
scales, with the average precision plotted in contour lines.
The daily solar ultraviolet flux to be used is measured by the Solar Stellar Irradiance
Comparison Experiment (SOLSTICE) onboard the Solar Radiation and Climate
Experiment (SORCE) [Rottman, 2006], downloadable from
http://lasp.colorado.edu/sorce/index.htm. The wavelength ranges between 115 – 300
nm with resolution 1 nm. The major short-term periodicities in the 205-nm solar flux
include 27-day and 13.5-day solar cycles (not shown).
3. Analysis
All time series are dominated by daily thermal fluctuations, seasonal cycles and
secular drifts. To extract the 27-day solar cycle, it is necessary to filter out all these
irrelevant components. There are two classes of noises: spatial and temporal. It is hard
to find a single filter that would properly get rid of these two classes of noises. Here
we introduce a synthesis of two relatively recent statistical techniques for isolating the
desired signal.
3.1 Empirical Mode Decomposition
A common way of filtering is the windowing through the Fourier fast transform (FFT).
One seeks the peak near the desired frequencies in the power spectrum, multiplies a
windowing function (or kernel) such that powers away from the peak are suppressed
to near zero, and backward-transforms the windowed spectrum. This algorithm is
simple and easy to use. However, it possesses a number of weaknesses. First, it is
well-known that due to the finite time span of a real measurement, the uncertainty of
the raw spectrum so estimated is theoretically 100% at all frequencies [Press et al.,
1992]. Second, the windowing function filters the desired frequency component by
brute force. A noisy component may potentially be regarded as a false peak, although
the red-noise spectral estimation is usually employed for preventive measure [Ghil et
al., 2002]. Finally, the physical processes imprinted in the time series are assumed to
be linear, which is not always true in the real world. Other common filtering methods
including running averaging and ARMA models also assume the linearity of the
processes.
A relative new and intuitive nonlinear method, the Empirical Mode Decomposition
(EMD), has been developed and used extensively for signal filtering [Huang and Wu,
2008]. This method does not impose any assumptions on the time series, and the
intrinsic mode functions (IMFs) are determined empirically by the sifting process.
Moreover, the time series needs not to be uniformly sampled, in contrast to other
conventional methods like FFT. The noise-assisted Monte-Carlo EMD (MCEMD)
[Wu and Huang, 2004] allows one to determine the significance level of an IMF
against white noises. A test against red noises is also feasible [Coughlin and Tung,
2004] but requires a large number of Monte-Carlo simulations, which makes it
computationally uneconomical for analysis of global data such as this work. In the
following discussions, all significance levels of IMFs are tested against white noises.
In principle, as a dyadic filter, at most log2N of IMFs plus one mode of residual can be
obtained, where N is the number of daily measurements. However, not all of the IMFs
are physically meaningful. Their significance levels can be tested through defining the
normalized mean energy Enorm (sum of squares of amplitudes) and mean period 
(time span divided by number of maxima or minima) [Wu and Huang, 2004]. Figure 1
shows their correlation for the 1066 time series. Assuming that the first IMF (mainly
daily fluctuations) is close to a white noise spectrum, its Enorm is always normalized
to 0.5636. The 95% and 99% confidence levels are readily estimated (solid and
dash-dotted lines respectively). It is clear that MCEMD is statistically an effective
dyadic filter, where the third and fourth IMFs are dominated by ~ 13-day and ~
27-day cycles respectively.
We emphasize here that, albeit its period being close to 27 days, it is inappropriate to
take the fourth IMF as the only mode that contains the 27-cycle solar cycle. It is
because mode mixing may occur during the Monte-Carlo simulations, where two
IMFs with two different dominant periods might mix into each other. Indeed,
examination of the FFT spectra reveals that the third model contains a tiny component
of a 27-day cycle. We also point out that the effect of mode mixing could deteriorate
the basic assumptions of EMD: An IMF is defined as a time series in which there
must exist one zero crossing between a maximum and its neighboring minimum. This
is violated in some cases of MCEMD. We found that only when the standard
deviation of the Monte-Carlo simulations is considered would the definition of an
IMF be statistically satisfied. Hence, EMD or MCEMD is strictly a statistical tool
rather than determinative. Therefore, we add up the third and fourth IMFs as the
filtered time series to preserve all possible 27-day cycle signals.
3.2 Composite Mean Difference
The EMD filter has been described in the previous subsection. It is a powerful filter in
the time domain; it works point-by-point individually in space, neglecting any
correlation among different locations. To better isolate the desired signal from the data,
we proceed to the next step where we try to apply a spatial filter to separate the spatial
and temporal dependences of the 27-day cycle signal.
Given a global data set, one seeks a linear decomposition such that the spatial and
temporal dependences are separated:
n
D  t , x    Tk  t  X k  x   R  t , x     t , x  ,
(1)
k 1
where R  t , x  is some residual term and   t , x  is the noise component whose
expectation values over x and t are zero. For example, the Principal Component
Analysis aims to find a complete set of orthogonal basis functions from the covariance
matrix with rank n, in which case   t , x  are the singular components and
R  t , x   0 . However, unless the underlying physical processes are independent and
orthogonal, they are usually coupled into the principal modes, which make the
physical interpretation difficult. Another way of isolating a signal is to employ a
discrimination analysis, yet at an expense of an a priori knowledge about the process,
which is the major weakness of the method.
Here we describe an intuitive discrimination analysis, the composite mean difference
(CMD), where k can only be 1 [Labitzke, 2001]. This method has been used to extract
the 11-year solar forcing over the annual surface air temperature [Camp and Tung,
2007a]. Following their procedure, we, using the solar flux at 205 nm as the training
set, partition the time axis into 27-day solar maximum and minimum groups and
calculate the temporal mean (area-weighted) meridional pattern of the stratospheric
temperature within each group. As for the MLS data, we used MCEMD filtering to
extract the 27-day solar cycle. Investigations show that the fourth mode, designated as
f 205 hereafter, is a pure 27-day cycle and mode-mixing effects with other modes are
minimal. Thus this mode will be used as the desired training set. The 27-day solar
cycle is defined as maximum if f 205  0.01 Wm 2  m 1 and minimum if
f 205  0.01 Wm 2  m 1 .
The spatial function X  x  , where x   , p  ,  being the latitude and p being the
pressure coordinate, is defined as the difference between the two mean patterns. Thus
X  x  characterizes the perturbative changes due to the 27-day variation in the solar
flux. The evolution of the temperature changes is described by the score T  t  , which
is defined as the projection of X  x  onto D  t , x  :
T t  
where the inner product
D t, x  X  x 
X x X x
,
(2)
is the summation over all x:
f  x  g  x    f  xm  g  xm  .
(3)
m
By construction, X  x  must be orthogonal to R  t , x  , i.e.
X  x  R  t , x   0 for
all time t. The residual term R  t , x  contains all physical components independent
of the 27-day solar cycle, which can be nonzero.
X  x  and T  t  are unique up to a multiplication constant. In [Camp and Tung,
2007a], the global surface mean of X  x  has been normalized to unity, so that solar
response in temperature is completely embedded in T  t  . However, since the
atmosphere is stratified, it is difficult to define a global mean in height. Instead, we
define the standard deviation of T  t  always normalized to unity. The signatures of
physical processes at different pressure altitudes are then contained in the spatial
pattern X  x  .
In reality, the difference between two means is seldom exactly zero. The significance
of X  x  may be tested by Student’s t-test [[Press et al., 1992] , chapter 14-2]. Thus,
at each location x   , p  , let    x  and    x  be the standard deviations for
27-day maximum and minimum groups respectively. Define the t-statistics as
t
X
(4)
 2 N    2 N  
12
with the degree of freedom


  2  2 



 N N 
2

N
  
2
N 1
2

2
N

2
.
(5)
N 1
where N  are the effective number of elements, defined as the sum of the
area-weights, in the respective groups. The confidence level is then derived from
P  1 I

 t 2
 1 
 , ,
 2 2
(6)
I x  a, b  being the incomplete beta function.
It has been shown that the CMD pattern serves effectively as a spatial filter for
extraction of the desired temporal signal [Camp and Tung, 2007a]. However, there is a
downside of it. Obviously, CMD works best only when the temporal behavior is
globally coherent. Any non-zero relative phase differences, say, between different
pressure levels or latitudes will not be recognized, which may be important for
studying the dynamics. Instead of performing a point-by-point study of the phase lags
in space, we study the global phase lags by shifting the group indices as a whole.
4. Discussions
Figure 3 (upper panel) shows the spatial pattern of X  , p  as a function of latitude
 (80º N – 80º S, with a resolution 4º) and pressure p (100 – 0.01 mb, with 26
levels) at zero phase lag. The solid and dash-dotted lines are the boundaries of the
95% and 99% confidence levels, respectively, calculated from Eq. (6). There is a
significant (> 95%) positive component (~ 0.14 – 0.42 K) in stratosphere (30 – 1 mb)
and lower mesosphere (1 – 0.2 mb) over deep tropics (   20 ), showing a
temperature increase in the 27-day solar maximum group relative to the 27-day solar
minimum group, except for a small region near 1 mb. This component extends
towards 1 mb and 30º N, and 0.1 mb and 45º S, with maxima 0.56 K and 0.7 K,
respectively. This proximity is primarily heated by ozone absorption in the shortwave
region, where the average heating rate is ~ 10 K/day [Mertens et al., 1999]. There is a
negative component (-0.96 K) in the northern stratosphere (65º N) near 2 mb, which
extends down to the lower stratosphere. A similar negative component (-1.12 K)
seems to be present in the southern stratosphere (80º S) but is barely significant. We
note that the polar response in the northern hemisphere occurs at lower latitude than
that in the southern hemisphere.
The spatial pattern in the stratosphere is consistent with the one found by [Crooks and
Gray, 2005], who analyzed the European Centre for Medium-Range Weather
Forecasts 40-year reanalysis (ERA-40) data set. In their Figure 2, they found a pattern
of increased temperature due to the 11-year solar cycle between 8 – 0.6 mb (or 35 –
48 km) over the tropics, overlapping well with the region found in Figure 3 of this
work. Their pattern peaks at the equator near 2 mb with an amplitude of 1.75 K. This
agrees with the value obtained in Figure 3 (0.42 K) if we take into account the 27-day
solar cycle forcing in shortwave being about one-fourth of that of the 11-year solar
cycle forcing. They also found a large negative component (peak value -2.75 K) at 55º
N in the stratosphere near 2 mb, but which was not supported by previous satellite
analysis [Hood, 2004]. Compared to [Crooks and Gray, 2005], the statistics in Figure
3 of this work is much more significant because of the short period (~ 27 days) of
interest compared to the time span of the data set (~ 4 years), which reduces the
standard errors substantially. This also highlights the amazing power of the
state-of-the-art satellite measurements with high precision and accuracy as well as
high spatial and temporal resolution.
Several efforts have been attempted to simulate the 11-year solar cycle effects on
temperature in the upper atmosphere. Provided that the solar cycle forcing acts only
perturbatively on the current climate, we assume that the solar responses to the 27-day
and the 11-year solar cycles should be close, which allow us to compare our analysis
with the modeling work. [Marsh et al., 2007] employed the NCAR Whole
Atmosphere Community Climate Model, version 3 (WACCM3), in which the
dynamics and chemistry are coupled and the solar cycle is parameterized using the
f10.7-cm radio flux. They examined the solar cycle effects on temperature as well as
the major chemical constituents, including water vapor and ozone, from surface up to
5×10-6 mb. Their simulated solar cycle response in temperature is ~2 times smaller
than [Crooks and Gray, 2005] yet the pattern of maximal responses is quite similar.
Recently, [Austin et al., 2008] conducted a comprehensive survey of the solar cycle
responses from 11 coupled chemistry climate models (including WACCM3), which
may or may not have solar cycle forcing implemented. The mean solar cycle response
of 9 simulations from 7 different models in the solar-cycle group shows positive-only
responses between 100 – 0.3 mb, with a peak of 0.5 K uniformly extended from 3 mb
upwards to 0.3 mb in the tropics and mid-latitudes (~ 60º N/S), which is still smaller
than [Crooks and Gray, 2005]. However, the mean uncertainty is as high as 0.3 K
throughout the whole atmosphere, showing that the solar response is rather
model-dependent.
In the mesosphere shown in Figure 3, there is a robust region of increased temperature
in the northern mesosphere, peaked at 50º N at ~ 0.1 mb with amplitude of 1.26 K. A
similar peak (1.68 K) can be found in the southern mesosphere at 80º S at ~ 0.01 mb.
The locations of these positive components agree well with WACCM3 simulation, but
the amplitude would be a factor of 3 greater than the model even if the ratio of the
11-year/27-day solar forcing is considered. There is also a significant negative
component in the tropical region between 0.1 – 0.01 mb and 30 º N - 30º S, with a
peak amplitude -0.7 K near 0.03 mb at the equator. This negative component is not
reproduced in the model, yet its position coincides with the region (~ 0.1 mb) where
the model response is insignificant.
[Camp and Tung, 2007a] suggested an innovative method by making use of the
composite-mean-difference as a spatial filter to extract the time evolution of the
surface air temperature, where they successfully obtained a solar response with high
statistical significance. We obtain the normalized scores T  t  of the projected
27-day solar cycle response in the temperature data from Eq. (2) (Figure 3, the lower
panel). It has a correlation coefficient of 0.30 ± 0.05 ( 2 ) with the 205-nm solar flux.
The error bar is calculated by bootstrap [Efron, 1979]. That is, the score-solar flux
pairs are resampled with replacement, and the correlation coefficient of each sample is
calculated. The distribution of the correlation coefficients are approximately normally
distributed around 0.30 with standard deviation   0.025 . The power spectrum of
the scores has a very broad peak of ~ 30 days, extending from periods 10 days up to
100 days, implying strong couplings of the radiative forcings with the underlying
atmospheric dynamical processes (Figure 4). The Solar Cycle 23, began declining in
2003, has almost reached its minimum in 2008. The 27-day solar cycle imprinted in
f 205 shows a coherent decrease in amplitude as time progresses. However, the
amplitude of T  t  does not follow this trend.
A strong polar amplification that scales with the seasonal cycles at the poles was
observed by [Ruzmaikin et al., 2007]. We briefly examine this in MLS data by
dividing the data into summer and winter. It is found (not shown) that in the summer
poles, the temperature response is positive (  0.7 K) in both stratosphere and
mesosphere. It is completely different in the winter poles, where the temperature
response is negative ( T  0.6 K) in the stratosphere and it is positive in the
mesosphere (  1.2 K). The magnitude of the response is clearly stronger in the winter
poles. However, due to the reduced number of observations, the statistical significance
of these results is not as good as the global picture. Further investigations with longer
time span are required to confirm any sign of polar amplifications.
[Hood, 1984] and other authors [e.g. [Austin et al., 2007] and references therein]
found phase lags between the temperature response and the solar forcing. We here
examine the global phase lag by shifting the group indices in time (Figure 5). When
the phase lag increases from zero, a sharp increase in the correlation coefficient occurs
at lag-4 and reaches the peak value (0.35 ± 0.04) at lag-6. However, it is not
statistically distinct from lag-0 if the uncertainty is also considered. Figure 6 shows
the spatial pattern of CMD corresponding to lag-6. We notice that the expected
response in the tropical stratosphere is completely absent. The overall statistical
significance has also degraded. Moreover, the range of temperature response drops by
a factor of 2 (from -1.12 – 1.68 at lag-0 to -0.56 – 0.96). Thus it is evident that the
correlation coefficient alone does not suffice to determine statistical significance; both
the spatial significance and the correlation with the group indices are important.
5. Summary
With the combined approach using EMD and CMD as temporal and spatial filtering
respectively, we examined the 27-day solar cycle in the middle atmospheric
temperature observed by MLS, assuming that the middle atmosphere is in radiative
equilibrium. The solar flux at 205 nm has been used as the forcing index. From the
spatial pattern of CMD, the solar heating due to ozone absorption is clearly seen in the
tropical stratosphere and lower mesosphere, with increased temperature ranged
between 0.12 – 0.48 K. This spatial pattern is shown to be consistent with the ERA-40
reanalysis data. Furthermore, the sites of increased temperatures generally agree with
simulations in chemistry-climate models but the observed negative responses are not
seen from the models.
However this approach has to assume that the signal being studied must be globally
coherent. Any phase differences between different positions cannot be recognized,
which may be important for studying the nonlinear atmospheric dynamics. Instead, we
examined the global phase difference between the 27-day solar cycle signal and the
forcing index. No statistically significant global phase difference was found.
The GPS radio occultation instruments onboard the Constellation Observing System
for Meteorology, Ionosphere and Climate (COSMIC), which measures the refractive
index of the atmosphere, also provides the retrieval of temperature in the stratosphere
[[Schreiner et al., 2007], and references therein]. In a companion paper, we will
describe another evidence of the 27-day solar cycle in stratospheric temperature from
the COSMIC satellite mission [Liang, 2009].
Acknowledgement
We thank Norden Huang for introducing the standard deviations of IMFs as a measure
of statistical significance. We also thank Dr. Run-Lie Shia and Prof. K.-K. Tung for
reading the manuscript. The work is supported by NASA grant XXX.
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Figure 1. Temporal mean (gray scales) and precision (contour lines) of the EOS MLS
data during August 8, 2004 – October 25, 2008. Both are in unit Kelvins.
Figure 2. Mean energy (normalized) and period of the intrinsic mode functions. The
light and dark gray scales are used to guide the separations of neighboring modes. The
95% (solid) and 99% (dash-dotted) confidence levels are shown. Below these levels
implies that the modes cannot be distinguished from a white-noise decomposition [Wu
and Huang, 2004].
Figure 3. Upper: Composite-mean-difference (CMD) pattern at lag 0. The 95% (solid)
and 99% (dash-dotted) confidence levels show that the differences are of statistical
significance. Lower: The solar flux at 205 nm observed from SOLSTICE/SORCE
(thick gray) and the projected scores of the CMD pattern (red). The standard deviation
of the scores is normalized to unity. The cross-correlation coefficient of this pair is
0.30 ± 0.05.
Figure 4. Power spectrum of the projected scores. The 95% (solid) and 99%
(dash-dotted) confidence levels are derived from lag-1 autocorrelated spectrum [Ghil
et al., 2002].
Figure 5. Correlation coefficients as a function of phase lag. The bars are the
corresponding uncertainty estimated by resampling the score-solar flux pairs with
replacement; see text.
Figure 6. Same as Figure 4 except for the CMD pattern at lag 6. The cross-correlation
coefficient of the score and the solar flux is 0.35 ± 0.04; see Figure 5.