The Madden–Julian oscillation (MJO) is the main controller of the weather in
the tropics on intraseasonal timescales, and recent research provides
evidence that the quasi-biennial oscillation (QBO) influences the MJO
interannual variability. However, the physical mechanisms behind this
interaction are not completely understood. Recent studies on the normal-mode
structure of the MJO indicate the contribution of global-scale Kelvin and
Rossby waves. In this study we test whether these MJO-related normal modes are
affected by the QBO and stratospheric ozone. The partial directed coherence
method was used and enabled us to probe the direction and frequency of the
interactions. It was found that equatorial stratospheric ozone and
stratospheric zonal winds are connected with the MJO at periods of 1–2 months
and 1.5–2.5 years. We explore the role of normal-mode interactions behind the
stratosphere–troposphere coupling by performing a linear regression between
the MJO–QBO indices and the amplitudes of the normal modes of the atmosphere
obtained by projections on a normal-mode basis using ERA-Interim reanalysis
data. The MJO is dominated by symmetric Rossby modes but is also influenced by
Kelvin and asymmetric Rossby modes. The QBO is mostly explained by westward-propagating inertio-gravity waves and asymmetric Rossby waves. We explore the
previous results by identifying interactions between those modes and between
the modes and the ozone concentration. In particular, westward inertio-gravity
waves, associated with the QBO, influence the MJO on interannual
timescales. MJO-related modes, such as Kelvin waves and Rossby waves
with a symmetric wind structure with respect to the Equator, are shown to have
significantly different dynamics during MJO events depending on the phase of
the QBO.
Introduction
The Madden–Julian oscillation (MJO) and the quasi-biennial oscillation (QBO)
are two of the main elements of atmospheric low-frequency variability in
the tropics. The MJO acts on intraseasonal timescales on the troposphere and
impacts tropical monsoons, with global impacts . The
QBO manifests in the tropical stratosphere as a reversal of the zonal winds
with descending cycles with a mean period of 28 months, also with important
impacts on the global circulation of the atmosphere . Both
are important players for the Earth system's weather and climate. Causal relationships between such processes and the physical
mechanisms behind their interaction are active research topics .
The stratosphere can act as a mediator between solar forcing and the climate
variability of the troposphere. It is conjectured that stratospheric influence
on the troposphere exists via the so-called top-down mechanism
. According to this hypothesis, stratospheric ozone absorbs
ultraviolet (UV) solar radiation, releasing heat. This heat then generates
temperature and wind perturbations in the stratosphere that might induce
a tropospheric response through downward energy transport. However, the details of
the physical mechanisms through which stratospheric signals could propagate
down to the troposphere are not completely understood.
Stratospheric control of tropospheric phenomena in middle to high latitudes was
addressed in several papers. For instance, highlight the
polar vortex as an important example of such control. Another example is that
of stratospheric impacts on tropospheric upper-level jets and storm tracks as
seen in . showed that the MJO is sensitive
to the QBO phase in the annual timescale, concluding that including QBO
information improves the MJO predictability . attribute differences between the QBO–MJO
interaction and the QBO phase to differences in the static stability of the
upper troposphere–lower stratosphere, leading to changes in the excitation of
MJO-related disturbances. associated the increased
predictability and intensity of the MJO during the boreal winter and QBO
easterly phase with differences in the vertical structure of the MJO,
depending on the QBO phase. The problem of MJO–QBO connection, however, is still
not well-understood from the perspective of the underlying physical mechanism,
nor is it well-represented in numerical models, as pointed out recently in
.
The study of QBO effects on the MJO has gained a lot of interest in the last few
years, since new evidence pointed out this connection . Since
then several articles have explored both the physical mechanisms behind this
interaction and the consequences for weather and climate. One of the main
factors that plays a role in the QBO–MJO connection is the difference in the
static stability in the tropopause region depending on the phase of the QBO
. suggest that negative temperature
anomalies in the tropopause region during the easterly QBO phase act to
destabilize the upper troposphere in phase with MJO-associated convection,
thus reinforcing the MJO event. Alternative mechanisms that could contribute
to this stratosphere–troposphere connection include the downward reflection of
planetary waves and effects on tropospheric Rossby waveguides
and teleconnection patterns . Here we investigate a different
class of mechanism, namely the role of wave interaction. Nonlinear wave
interaction is believed to have a role in the initiation of an MJO event
though the interaction between the tropics and extratropics (see Sect. 6.4;
). This interaction takes place through the coupling
between equatorially confined modes, which are baroclinic Rossby waves, and
non-confined modes, which are barotropic Rossby waves. Inspired by this type of
mechanism, we investigate whether the interaction between QBO-related modes
and MJO-related modes could have a role in the MJO–QBO connection.
Recent studies have given a normal-mode description of the MJO
. These studies concluded that the MJO can be
described as global-scale baroclinic Rossby and Kelvin waves. The same
approach was used to study the conditions that led to the 2016 QBO disruption
. In this context a natural question arises: what is the
role of these normal modes in the MJO interaction with the stratosphere? In
particular, how do these modes interact with QBO-related modes?
In this article, we study the interactions between the stratosphere and the
tropical troposphere, with particular emphasis on the MJO. A time series
analysis causality method, partial directed coherence (PDC)
, was used. We determine whether equatorial ozone,
equatorial stratospheric zonal winds, and tropospheric fields interact and how
this interaction occurs, including information on directional interaction. Our
analysis is based on daily data for stratospheric zonal wind, ozone
concentration, and the unfiltered (on the intraseasonal timescale) MJO index
from 1979 to 2015. We obtained the stratospheric zonal wind and ozone
concentration from ERA-Interim reanalysis data from the
European Centre for Medium-Range Weather Forecasts. Zonal wind at
the 30 hPa level was averaged in an equatorial belt from -15 to
15∘ latitude for all longitudes, which is a reasonable choice to
represent the QBO . Ozone data were averaged from -20 to
20∘ in latitude and integrated over all levels from 100 to
0.1hPa. MJO data were obtained from the daily MJO index RMM
. The MJO index is presented in a polar coordinate diagram
with two time series: amplitude and phase. The amplitude of the MJO index is
defined as the sum of the squares of the first two empirical orthogonal
functions (EOFs) of combined pressure fields at 200 and 850hPa
and outgoing longwave radiation data in the tropics (RMM1 and RMM2). An
equivalent way to represent the MJO index (a complex number) is to use two
real variables that correspond to the two first components. In order to use
minimal mathematical operations with the original EOF time series we choose
the last representation.
To resolve the spectrum of the different timescales, timescale separation
was applied to the data. We split the data into a fast timescale (periods
shorter than 1 year) and a slow timescale (periods greater than 1 year). This was done by performing a resampling procedure on the data with a
10 d rate for the fast timescale. A 6-month window was applied for
the slow timescale.
The causality between the QBO, tropical stratospheric ozone, and the MJO was
studied using the PDC method. PDC roughly corresponds to a frequency domain
counterpart of the Granger causality test , with the
additional advantage of providing information on the specific frequencies at
which the causality occurs.
We search for normal modes that might contribute to the interactions between
stratospheric and tropospheric phenomena by performing a linear regression
with the MJO indices and stratospheric zonal winds. We then perform the PDC
analysis with the time series for the energies associated with each of the
Hough modes responsible for the MJO dynamics (as in ) and
the stratospheric zonal wind. The results indicate that the interaction of
internal westward gravity waves, which are responsible for the QBO as well as Kelvin and
Rossby waves associated with the MJO, partially explains the stratospheric
influences on the MJO.
MethodsGranger causality
The concept of causality is a central question in science. One possible
definition of causality related to the predictability of two or more distinct
processes was introduced in and is currently known as
Granger causality in the literature. The main advantage is the ability to
pinpoint the direction of interaction, unlike other measures such as
coherence, correlation, partial coherence, and partial correlation. The
following definition is specific to trivariate time series but is readily
generalizable to an arbitrary number of time series.
Consider a vector-valued signal X(t)=[X1(t),X2(t),X3(t)]⊤, where the superscript ⊤ indicates the transpose of a
vector and X(t) is assumed to have a vector autoregressive
representation of order p (hereafter referred as VAR(p)):
X1(t)X2(t)X3(t)=∑k=1pa11(k)a12(k)a13(k)a21(k)a22(k)a23(k)a31(k)a32(k)a33(k)X1(t-k)X2(t-k)X3(t-k)1+ϵ1(t)ϵ2(t)ϵ3(t),
where aij(k) represents the VAR(p) coefficients representing the kth lagged
influence of the jth component of the signal on the ith component and t
denotes the time variable. The innovation processes (the random component)
ϵi(t) have a zero mean and covariance matrix C=[σij] such that Cov(ϵi(t),ϵj(s))=0 for t≠s
and for all i,j∈{1,2,3}.
It is enough to say that Xj(t) Granger causes Xi(t) for i≠j if
aij(k)≠0 with statistical significance for some lag k=1,…,p. Thus, the absence of Granger causality from X1(t) to X2(t)
implies that X1(t) does not help to predict X2(t) once the past of
X2(t) and X3(t) is considered.
In practice, given a trivariate time series X(t) of length n, we
estimate the VAR(p) model from the data and test for aij(k)
nullity. More precisely, the idea is to verify the null hypothesis,
H0:aij(k)=0,k=1,…,p,
against
H1:k∈{1,⋯,p} such that aij(k)≠0.
Therefore, we can say that the jth component of the time series causes the
ith component in the sense of Granger if the past of the jth component
helps to predict the future of the ith component. We have used the
MATLAB Toolbox (free) implementation of the VAR(p) and Granger
causality estimator implementations from , available at
http://www.lcs.poli.usp.br/~baccala/pdc (last access: 12 January 2020).
Partial directed coherence
Partial directed coherence (PDC) is an extension of the concept of Granger
causality to the frequency domain as a measure of information flow. Thus,
PDC incorporates advantages of the Granger causality and of the classical
coherence methods with the additional advantage that it can be generalized to
more than two time series, enabling us to explicitly pinpoint the directed
information flow from mere indirect interactions . PDC has been successfully applied in complex
systems for neuroscience and economics
. PDC was also used to detect the causality between the El
Niño–Southern Oscillation and monsoons, as well as in the sea–air
interaction in the South Atlantic Convergence Zone .
Again, consider a trivariate time series X(t)=[X1(t),X2(t),X3(t)]⊤ with a VAR(p) representation defined in Eq. (); let
A¯kl(ν)=δkl-∑s=1pakl(s)e-i2πνs,
where δkl is the Kronecker delta symbol, i2=-1,
ν the Fourier frequency (Hz), and s the time (s). Here we use
the more general PDC definition, the information–partial directed coherence
(iPDC), which is closely related to information theory. It has
been shown that iPDC corresponds to the information flow (in
Shannon's sense) between different signals . Therefore, the
information flow, iPDC, from Xj(t) to Xi(t) in a specific
frequency, ν, is given by
iPDCi←j(ν):=ιπij(ν)=A¯ij(ν)/σija¯jH(ν)C-1a¯j(ν),
where a¯j(ν) is the jth column of the matrix with
coefficients A¯kl(ν), and a¯jH(ν)
denotes its Hermitian transpose.
Note that there is a duality between the Granger causality and PDC, as
demonstrated in . Therefore, the nullity of
ιπij(ν) corresponds to the absence of connection (similarly
to the aforementioned Granger causality condition), which, in the PDC case,
also has a rigorous and well-defined statistical criterion for the null
hypothesis test . Confidence intervals for the PDC analysis
are explicitly calculated as the statistics of the PDC coefficients,
ιπij(ν), are asymptotically Gaussian (at the limit of a large
number of data points). For a proof of this theorem and more information on
confidence intervals for PDC, see and
. To estimate the iPDC from the data, the
first step is to obtain the vector autoregressive model, which is estimated
through the Hannan–Quinn criterion in this paper, and substitute the estimated
coefficients in Eq. (3). The implemented test statistics are described in
, and we used the computations of iPDC
generated from AsympPDC package version 3.0 MATLAB Toolbox, which is freely
available as mentioned before. A detailed example showing how to interpret the
PDC plots is given in the Supplement (see Fig. S1).
The partial directed coherence and Granger causality quantities
are linear measures, and a natural question is whether these methods are able
to capture the interaction between signals that arise from nonlinear
problems. There are several publications addressing this question such as
the possible nonlinear extension of this technique and the introduction of other techniques that are intrinsically
nonlinear in nature based on time-lagged embedding, such as
, or based on the concept of Markov partitions, such as
. give an example in which
Granger-based techniques perform poorly. Here we argue that although PDC does
not capture all kinds of nonlinear coupling between timescales, especially
with more intermittent and/or non-Gaussian behavior, it certainly captures certain
kinds of nonlinear interactions. As shown in , there is
an equivalence between the concepts of a mutual information rate that would
account for all information flow between two or more signals and PDC in the
case of Gaussian processes. In the general non-Gaussian case bounds are given
for the difference of the mutual information rate estimated by PDC and the
actual mutual information rate, meaning that even if the signals are nonlinear
and non-Gaussian PDC is still able to capture part of the information flow
between the signals.
The main advantage of PDC and Granger causality is that they are theoretically
related to the mutual information rate (MIR) between signals
. Information–theoretic quantities are usually costly to
estimate directly from time series since they rely on the estimation of
multi-dimensional probability distributions. As shown in Takahashi et al.
(2010), PDC is a Gaussian approximation of the MIR. This means that if the
time series are stationary and Gaussian, PDC provides an exact estimate for
the MIR; when the time series are not Gaussian (possibly due to underlying
nonlinearities) the PDC will capture part but not all of the information flow
between the time series. There are many “causality” estimation methods in
the literature, all of them with some advantages and drawbacks. Among the
several causality detection methods the convergent cross-mapping (CCM) method
is proposed as a method that is capable of capturing couplings in
highly nonlinear settings since it relies on phase-space embedding
procedures. However, it comes with a few drawbacks that would require
more in-depth investigation before we could apply it in the present setting,
namely the following. (1) CCM is a bivariate measure. Granger causality and PDC are
genuinely multivariate measures. (2) CCM may lead to wrong or misleading
results when moderate to high levels of noise are present (see
). Granger causality and PDC are designed to work for
signals with stochasticity. (3) CCM does not have an automated way to decide
the optimal lag between time series. Granger causality and PDC are based on an
autoregressive process in which order estimation is well-studied. (4) There
are no theoretical guarantees for the statistical properties of CCM. Both PDC
and Granger causality are very well-studied measures for which there are
thousands of articles demonstrating their application, and we understand their statistical
properties well .
On the right are the time series resampled at a 10 d rate of the first
component of the MJO index (a, d), ozone spatially averaged in the
equatorial region (b, e), and equatorial stratospheric wind (c, f). On the
left is the same with band with a resampling rate of 6 months.
Finally, although PDC is a stochastic linear method, it correctly reconstructs
the topology of networks of nonlinear oscillators; see
. Moreover, it has been successfully and extensively
used to infer information flow in highly nonlinear time series data in
neuroscience . The fact that PDC can detect nonlinear
interactions is not difficult to understand, given that linear regression can also
reveal nonlinear interaction unless the nonlinearity is highly nonmonotonic.
PDC statistics
The PDC is a function of the coefficients of a vector autoregressive
model. Given that the coefficients are asymptotically jointly normally
distributed, we can use the delta method to analytically obtain
the asymptotic statistics for PDC. After an algebraic computation
we can show that PDC at frequency lambda is distributed asymptotically (under
the null hypothesis of zero PDC) as the weighted sum of two chi-square variables with
1 DOF (degree of freedom) (). Therefore, we can
use the asymptotic distribution to calculate the p value. More specifically,
let ιπ^ij(ν) be the estimator of
ιπij(ν) for a time series of length n. We have the
following convergence in distribution:
na¯jH(ν)C-1a¯j(ν)(|ιπ^ij(ν)|2-|ιπij(ν)|2)→dl1Y1+l2Y2,
where Y1 and Y2 are independent χ12-distributed random variables,
and l1 and l2 are weights that can be estimated from the data. For
details of the derivation, we refer to . The significance
level used in the article for PDC is the frequency-wise value as it is the
standard for frequency domain analysis given the high correlation between the
point estimates for neighboring frequencies .
Normal-mode decomposition
Based on the methodology of ,
introduced software to project atmospheric fields from reanalysis
onto the normal modes of the hydrostatic primitive equations on the
sphere. For a vector-valued function X=[u,v,h]⊤,
u(λ,ϕ,z) is the zonal velocity field, v(λ,ϕ,z) is
the meridional velocity field, and h(λ,ϕ,z) is the modified
geopotential height. A separation of variables is then performed, and the state
vector X is represented as a series of horizontal and vertical
structure functions, which in discrete form is
X(λ,ϕ,z)=∑m=1MSmXm(λ,ϕ)Gm(z),
where Xm is the horizontal structure vector function, Gm is the
vertical structure function, and Sm is a square matrix defined as
Sm=gDm000gDm000Dm,
where g is Earth's gravity and Dm the equivalent depth of the mth
vertical mode. The horizontal fields Xm, on the other hand,
are expanded in Hough harmonics as
Xm(λ,ϕ)=∑n=1N∑k=-KKχm,n,kHm,n,k(λ,ϕ),
where Hm,n,k represents the eigenfunctions of the Laplace tidal equation
considering zonal periodicity and regularity at the poles as boundary
conditions . The expansion coefficients
χm,n,k are obtained as
χm,n,k=12π∫02π∫-11Xm(λ,ϕ)⋅Hm,n,k(λ,ϕ)*dμdλ,
with μ=sin(ϕ), and the superscript * indicates the complex
conjugate. Details of the procedures for obtaining the amplitudes
χm,n,k from the data are described in . The MODES
software then provides the amplitudes χm,n,k given input timescales
of reanalysis data. proposed a procedure to decompose the
MJO into the contributions of each normal mode by performing a linear
regression between the MJO time series and the mode–amplitude time series:
Rm,n,k=1N-110×∑t=1Nχm,n,k(t)-Eχm,n,k(t)Y(t)-E[Y(t)]VarY(t),
where χm,n,k(t) is the Hough expansion
coefficient (Eq. ) for a time instant t, Y(t)
is the MJO index time series, and E[Y(t)] and Var[Y(t)] are the
respective expectation and variance.
PDC between tropical stratospheric ozone and stratospheric zonal wind (SZW) as well as the RMM MJO index at the fast (>20d) timescale; frequencies are given are given in cycles per year. Panels in the main diagonal show the power spectral density of each time series. Off-diagonal panels indicate the PDC values between the time series. For each panel, the x axis represents the frequency and y axis the value of the PDC. Red lines represent the PDC values that were statistically significant.
From the time series of the amplitudes of the normal-mode functions we compute
the energy within a group of modes, consisting of the sum of the squares of
their amplitudes weighted by their equivalent depths Dm:
E(t)=12∑m=M0M‾gDm∑k=0K‾∑n=N0N‾([Xkmn](t)[Xkmn]*(t)),
where M‾=43,K‾=32, and N‾ are wavenumber
truncations. Throughout the text we select different N to represent
different modes (e.g., Kelvin, Rossby, westward inertio-gravity).
Statistical analysis: QBO–MJO–ozone interaction
Time series of the stratospheric zonal wind at 30 Mb, the equatorial ozone
concentration in the stratosphere, and the RMM index are presented in
Fig. . The autoregressive fitting of the time series was found
to be well-represented by passing the Portmanteau test
. The PDC analysis for the fast (interannual) timescale, shown in
Fig. , indicates that there is a statistically significant
interaction between the stratospheric mean zonal wind and the MJO and between
tropical stratospheric ozone and the MJO; the results here are presented only for
RMM1 (RMM2 yields similar results). Concerning the influence of the
stratospheric variables on the MJO, tropical stratospheric ozone is shown to
have a significant causality (in the Granger sense) on the MJO indices,
influencing RMM1 during periods of around 1 month, which corresponds to the
higher-frequency range of an MJO cycle. The periods when ozone influences RMM1
and RMM2 show, by the definition of Granger causality, that information on
ozone should improve the MJO predictability.
PDC analysis between the MJO and stratospheric zonal wind (SZW) at the slow (>1-year periods) timescale. Results indicate significant interaction on annual–biennial timescales. Figure conventions are the same as in Fig. .
In order to investigate the interaction between the stratospheric variables
and the MJO index we performed a 6-month resampling procedure. Results are
presented in Fig. . Ozone is found to significantly influence
the MJO, as can be seen in Fig. 2, on the annual timescale for RMM2, possibly
due to the annual cycle, and on the timescale of 1.6–2.1 years, possibly
associated with the QBO. Both RMM indices are found to be significantly
affected at frequencies with a peak at 11 years, which is a strong indication
of the effect of the solar cycle on the MJO through ozone, which could
explain the solar-cycle-related monsoon variability ; see
also for evidence of the impact of solar variability on
the MJO. Interactions that are significant are found from ozone to the MJO in
a period ranging from 1 to 2 years, possibly as a combination of the effects
of the annual cycle and the QBO, corroborating recent results in the
literature .
Modal decomposition and wave interactions
Several studies point to the role of the interaction of waves with
different vertical structures in the dynamics of the MJO. For instance,
studied the interaction of barotropic and baroclinic Rossby
waves in the interaction of the tropics and extratropics since barotropic
waves are not equatorially confined as baroclinic ones are.
further explored this mechanism in the initiation of the MJO. A similar
mechanism could in principle play a role in stratospheric–tropospheric
interactions, with modes with dominant energy in the stratosphere interacting
with modes that have more energy in the troposphere. We therefore aim to
test such a hypothesis.
We initially perform a linear regression analysis between the time series
associated with the MJO indices and the stratospheric zonal wind
representative of the QBO, aiming to find which normal modes best represent
such oscillations. This analysis was introduced by in a
normal-mode decomposition of the MJO. showed that the
dominant modes in the decomposition are the symmetric Rossby mode (with the
largest contribution coming from the Rossby mode with meridional index 1,
denoted by RSSY1) and Kelvin waves (KWs). Both Kelvin and Rossby modes
have a larger regression coefficient for the vertical mode indices 5–9, which
have a first baroclinic structure in the troposphere. We performed a similar
analysis with the daily time series of equatorial zonal wind at 30 hPa,
which is dominated by the QBO. We find that the dominant modes in our
regression analysis are westward-propagating gravity waves (WIGs) and the first
asymmetric Rossby modes (meridional index 2, denoted by RWASY1); we refer to
for details on the normal-mode decomposition of the
QBO.
We search for interactions between the MJO and QBO normal modes. In order to do
so, we calculate the time series of the energy associated with each of the
modes (i.e., a weighted sum of the square of the absolute value of each of the
modes). We begin by describing the interaction between modes associated with
the MJO and the QBO as well as tropical stratospheric ozone forcing on sub-annual
timescales. Due to the large number of variables we split the analysis into
three sets, each containing all the “stratospheric variables” against one of
the variables associated with the MJO. Since the most important interactions
between QBO modes and MJO modes are through the QBO-related WIG waves, we
restrict the analysis to these modes.
PDC analysis of the interaction of Kelvin, asymmetric Rossby, and westward gravity modes with ozone at the fast timescale (periods given in days). Significant interactions (red curve) between the MJO and ozone as well as QBO-related modes are found on intraseasonal, semi-annual, and annual timescales. Panels in the main diagonal show the power spectral density of each time series. Off-diagonal panels indicate the PDC values between the time series; PDC direction is from the time series indicated in the column to the one indicated in the row. For each panel, the x axis represents the frequency and y axis the value of the PDC. Red lines represent the PDC values that were statistically significant.
PDC analysis of the interaction of symmetric Rossby n=1, asymmetric Rossby n=1, and westward gravity modes with ozone at the fast timescale (periods given in days). Again, significant interactions (red curve) between the MJO and ozone as well as QBO-related modes is found on intraseasonal, semi-annual, and annual timescales. Figure conventions are the same as in Fig. .
In Fig. we present the PDC analysis of the interaction of
Kelvin waves vs. westward inertio-gravity waves vs. stratospheric ozone
vs. asymmetric Rossby waves. The first three variables are associated with
stratospheric phenomena and the last one is associated with the MJO. We observe
that the ozone forcing acts directly on the MJO-related Kelvin waves, most
notably on intraseasonal timescales, with a peak around 50d. The
influence of ozone on this mode is also relevant on a semi-annual and annual
timescale, both associated with the annual cycle. WIG waves are found to
influence the Kelvin waves on the timescale of 30 d, while asymmetric
Rossby waves are found to influence the Kelvin waves on timescales from
around 50 d to semi-annual and annual timescales. We find a
feedback from Kelvin waves to the stratospheric-related variables on
intraseasonal, semi-annual, and annual timescales.
Finally, we perform a PDC analysis of the interaction between symmetric
Rossby waves (the dominant mode in the MJO decomposition), asymmetric Rossby
waves, WIG waves, and stratospheric ozone on the fast timescale. The
corresponding PDC plot is presented in Fig. . The influence of
stratospheric ozone on symmetric Rossby waves has peaks at 40, 60 d,
and on a semi-annual timescale. The influence of the modes associated with the
stratospheric zonal wind on the MJO-related Rossby mode seems to be
significant throughout the entire intraseasonal timescale range, most notably
around 30–40 d, as well as on semi-annual and annual
timescales. Similarly to the previous cases, the feedback of the MJO-related
mode to the stratospheric-related variables takes place on intraseasonal,
semi-annual, and annual timescales.
PDC analysis of the interaction of ozone modes and Kelvin waves (KWs) at the slow timescale (periods given in years). The results show that KWs influence ozone on the annual timescale, while ozone influences KWs on decadal timescales. Figure conventions are the same as in Fig. .
PDC analysis of the interaction of Kelvin modes (KWs) and westward gravity modes (WIGs) at the slow timescale (periods given in years). The results show a strong influence of the WIG mode on KWs on biennial and decadal timescales. Figure conventions are the same as in Fig. .
PDC analysis of the interaction of symmetric Rossby modes (meridional index 1, denoted by RWSY1) and westward gravity modes (WIG1) at the slow timescale (periods given in years). Important interactions are found on annual to interannual timescales. Figure conventions are the same as in Fig. .
We proceed by analyzing the PDC between the modes associated with
stratospheric zonal wind and stratospheric ozone vs. MJO-related modes on slow
timescales (annual–decadal timescales). Most importantly, we search for
stratospheric influences on the MJO on decadal and biennial timescales. The
analysis of the interaction between Kelvin waves, associated with the MJO and
tropical stratospheric ozone is presented in Fig. . It shows
that there is a significant causality from ozone to Kelvin waves on a decadal
timescale. Given that both spectra have a peak on the decadal timescale we
can say that ozone, which is directly influenced by solar variability,
has a peak directly associated with the solar cycle, and the peak on the Kelvin
wave spectrum is at least partially explained by the influence of ozone on
it. Kelvin waves, on the other hand, influence ozone on annual timescales,
probably due to the annual cycle. The analysis of the interaction between
gravity waves associated with the stratospheric zonal wind and the MJO-related
Kelvin waves is presented in Fig. . We found an important
influence of the westward inertio-gravity waves on the Kelvin waves on
biennial timescales and on decadal timescales. The first one is clearly
associated with the biennial peak on the inertio-gravity wave spectrum, which
is a product of the quasi-biennial oscillation and might be associated with the
results of and subsequent articles on the relationship between
the QBO and the MJO. The PDC peak on the decadal timescale is possibly
associated with the solar cycle, and the gravity modes are forced by the ozone
(Fig. ). Since we do not find spectral peaks in this range, we
suspect that this is related to the nearest peak, which is annual. A strong
causality is also found on a decadal timescale, again probably due to the
solar cycle. The influence of WIG modes on the MJO-related Rossby modes is
presented in Fig. , showing an influence of WIG modes on Rossby
modes on annual and biennial timescales.
PDC analysis of the interaction of westward gravity modes and ozone at the slow timescale (periods given in years). Important interactions are found on annual–biennial timescales and on the decadal timescale. Figure conventions are the same as in Fig. .
Evolution of MJO normal modes
Previous studies point to different MJO behavior depending on the phase
of the QBO (east or west) ; it is therefore important to
examine how and if these differences manifest in the MJO-related normal
modes. In order to do so, we follow the methodology used in
to study the Northern Hemisphere extratropical response of the MJO using normal-mode decomposition. We construct composites representing velocity and pressure
fields associated with MJO normal modes for each phase of the MJO. In order to
exclude periods without MJO events we include in our analysis only days on
which (RMM12+RMM22>1). We then divide the MJO events into eight
phases depending on the phase of the MJO
ϕ=arctg(RMM2/RMM1) for which QBO (positive or negative)
state and for which MJO phase (i=1,2,…,8) we calculated the mean
velocity and pressure fields associated with rotational (ROT) and Kelvin modes at 200 Mb.
Reconstruction at 200 Mb of the velocity and geopotential height fields associated with ROT modes with (positive stratospheric zonal wind) SZW30+.
Reconstruction at 200 Mb of the velocity and geopotential height fields associated with ROT modes with (negative stratospheric zonal wind) SZW30-.
Difference between the velocity and geopotential height fields associated with ROT modes with SZW30+ and SZW30-. The hatched region corresponds to a significant difference of the geopotential height values under the 5 % confidence level.
Figures and respectively display the
composites associated with the reconstructions of velocity and geopotential
height fields associated with ROT modes for each of the eight MJO phases with
positive (SZW30+) and negative
(SZW30-) stratospheric zonal wind at 30 mb. In order to compare the two composites we compute the difference
between SZW30+ and SZW30- of each field for each MJO phase. This is
displayed in Fig. . We notice that for phases 1–3 the
difference (of the geopotential height fields represented by the hatched
region) is statistically significant for almost the entire domain. For phase 4
the fields are more similar, with small regions of significant difference
associated with Rossby double vortices. Between phases 5 and 8 the areas with
significant difference become larger again.
Reconstruction at 200 Mb of the velocity and geopotential height fields associated with Kelvin modes with SZW30-.
Reconstruction at 200 Mb of the velocity and geopotential height fields associated with Kelvin modes with SZW30-.
Difference between the velocity and geopotential height fields associated with Kelvin modes with SZW30+ and SZW30-. The hatched region corresponds to a significant difference of the geopotential height values under the 5 % confidence level.
Figures and respectively display the
composites associated with the reconstructions of velocity and geopotential
height fields associated with the Kelvin mode for each of the eight MJO phases
with positive (SZW30+) and negative
(SZW30-) stratospheric zonal wind at 30 mb. In order to compare the two composites we compute the difference
between SZW30+ and SZW30- of each field for each MJO phase. This is displayed
in Fig. . We notice that for phases 1–3 the difference (of
the geopotential height fields represented by the hatched region) is
statistically significant for almost the entire domain. Unlike in the case of
ROT modes, for the Kelvin modes the distribution of statistically significant
difference is more even throughout an MJO cycle, with a larger area in phase 2
and more similar fields in phase 4. It is possible to notice a propagation
pattern with a negative geopotential height anomaly beginning in phase 4 and
ending in phase 7.
Final remarks
The PDC results show strong coupling between tropical ozone, stratospheric
zonal wind, and the MJO. Most notable are the effects of tropical stratospheric
winds and ozone influencing the MJO on both intra-annual and interannual
timescales. The PDC analysis shows that tropical stratospheric ozone
influences the MJO in periods of 30–60 d and 1.5–2.5 years. The
first period agrees with the MJO period range, suggesting that stratospheric
ozone may play a role in the MJO dynamics. The second roughly agrees with the
QBO period, and the third suggests a solar cycle influence on the
MJO. Stratospheric zonal winds also influence the MJO during periods that fall
into the QBO period range, in agreement with the recent results of
, who showed that there is interannual variability in the
MJO amplitude that depends on the QBO phase. Marshall (2016) also shows that
the QBO explains up to 40% of the MJO interannual variability in
the boreal winter (see also ).
By the definition of Granger causality, one signal causes a second signal if
the information from the first helps to predict the future of the other after
taking into account the past of the second signal. In this sense, we confirm
the results of the recent studies cited above. We also show that tropical
stratospheric ozone improves MJO predictability on interannual and
decadal timescales. The periods of interaction suggest that the QBO might be
an important process in troposphere–stratosphere coupling through the MJO. This
conclusion agrees with numerical studies such as that of ,
stressing the importance of a realistic QBO in coupled
troposphere–stratosphere models. We note that ozone influences the MJO on
intraseasonal timescales, raising the possibility of tropical stratospheric
ozone fluctuations contributing to the initiation of the MJO cycle. On the
decadal timescale, ozone and the QBO are modulated by solar activity, and ozone
was shown to have important impacts on the MJO on this timescale. There is
strong evidence in the literature for a solar cycle impact on the Asian
monsoons from both instrumental observations and paleoclimatic
reconstructions, with the rainfall rate on the Indian subcontinent increasing
by up to 20% during the solar maximum . Since
monsoons are linked to the MJO, especially in the Indian region where the MJO
signal is strongest, it would be natural to hypothesize that the MJO is a
mediator between solar variability and monsoons.
It was also found that the MJO can affect stratospheric ozone, a possible
mechanism for this being the impact of deep convection on the tropopause
height . Another interesting question is whether the
relationship between the MJO and the QBO is affected by the recent anomalous
behavior of the QBO .
As for physical mechanisms that could link stratospheric heating driven by
solar UV forcing and tropical convection, tropopause changes
caused by ozone absorption are possible candidates. suggested
a polar latitude mechanism associated with changes in wave momentum flux due
to ozone depletion associated with the ozone hole. Although this mechanism was
proposed for high latitudes, it would be interesting to investigate whether it
can be extended to the tropics and to ozone changes due to annual and
solar cycles. Recently, suggested that changes in the
waveguides of planetary waves in the stratosphere, caused by solar forcing
changes in the mean flow of the stratosphere, might cause downward planetary
wave reflection under conditions of high solar activity.
We performed a linear regression analysis of the MJO index and stratospheric
zonal winds against the time series of the amplitudes of the Hough modes. We
confirm that the MJO is explained mainly by the first symmetric Rossby mode
(meridional index 1) and Kelvin modes, in agreement with
. The stratospheric zonal wind variability is explained
mainly by the WIG modes and the first asymmetric Rossby modes (meridional
index 2). We analyzed the interaction among those variables and tropical
stratospheric ozone. The exchange of energy between the modes and their
interaction with the ozone forcing explain the previous results. We highlight
the strong influence of ozone on the MJO-related modes on
intraseasonal timescale and on decadal timescales, the last one possibly being
a result of the solar cycle. We found the influences of the gravity modes
on the MJO-related modes to be the most relevant on biannual
timescales. This at least partially explains the work of and subsequent articles on the QBO–MJO relation.
A composite analysis of the velocity and geopotential height of the Kelvin and
Rossby modes associated with the MJO reveals the differences in the
characteristics of these modes during MJO events when the winds are positive
at 30 Mb and when they are negative. For the Rossby modes, differences
(Fig. ) are shown to be more significant during the initial
(1–3) and final (7–8) phases of an MJO cycle, and the spatial pattern is that
expected of the rotational component of the MJO with a double vortex
pattern. The differences reveal a stronger rotational component of the MJO
when the zonal winds at 30 Mb are positive. For Kelvin modes, significant
differences are found throughout the whole MJO cycle, and the composite for the
difference between the fields from both QBO phases follows a propagation
pattern that seems to evolve eastward with a similar speed as a typical MJO event
(5 ms-1). This
suggests that the QBO effect on the Kelvin mode is more uniform throughout a
QBO cycle, and in the Rossby modes this effect takes place in the initial and
final phases of the MJO.
Data availability
The time series for the amplitudes of the selected normal modes studied here is provided under the following DOI: 10.5281/zenodo.4437766.
The supplement related to this article is available online at: https://doi.org/10.5194/esd-12-83-2021-supplement.
Author contributions
BR proposed the study, wrote the paper, and did the statistical analysis. DYT and LM worked on the PDC analysis. AST performed the normal-mode decomposition analysis, and PLdSD helped with the discussion and the interpretation of the analysis.
Competing interests
The authors declare that they have no conflict of interest.
Financial support
This research was supported by the FAPESP-PACMEDY project (grant nos. 2015/50686-1 and 2017/23417-5), CAPES IAG/USP PROEX (grant no. 0531/2017), and the Meteorology Graduate Program at IAG-USP (CAPES finance code 001).
Review statement
This paper was edited by Ben Kravitz and reviewed by Christian Franzke and two anonymous referees.
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