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Joint Spatio-temporal Modes of Wind and Sea Surface Parameters Parameters
Variability in the North Indian Ocean during 1993-2005
Thaned Rojsiraphisala, Balaji Rajagopalanb,c , and Lakshmi Kanthac
a Department of Mathematic, Faculty of Science, Burapha University, Thailandb Department of Civil, Environmental, and Architectural Engineering, University of
Colorado, Boulder, Colorado, USAc Co-operative Institute for Research in Environmental Sciences, versity of Colorado,
Boulder, Colorado, USAd c Department of Aerospace Engineering Sciences, University of Colorado, Boulder,
Colorado, USA
Submitted to
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XXXX Journal of Geophysical Research
2008
Corresponding author:
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Thaned Rojsiraphisal
Department of Mathematics, Faculty of Science, Burapha University
169 Long-Hard Bangsaen Road, T. Saensook, A. Muang, Chonburi 20131, Thailand
Tel: (66)-89-174-6747 Email: thaned@buu.ac.th
Abstract
Sea surface height (SSH) and sea surface temperature (SST) in the North Indian
Ocean are mostly affected by reversing the monsoon. Their variability and dynamics are of
interest to population live surround the Oceansurrounding population. In this study we use a
set of data generated from a data-assimilative model to examine coherent spatio-temporal
modes of winds and surface parameters via Multiple Taper Method with Singular Value
Decomposition (MTM-SVD). Our analysis shows significant variability at annual and semi-
annual, while only joint variability of winds and SSH is significant at an inter-annual mode
(2-3 yr timescale) which is related to ENSO mode and its pattern exhibits a situation of
“dipole” mode. The winds seem to be the driver of variability in SSH and SST at the annual
cycle, semi-annual and interannual frequency bands. Furthermore, the forcing patterns in the
winds are consistent with the large scale monsoon, especially the Indian summer monsoon
feature in the basin. Other dominant patterns of joint variability give us insight information at
specific frequency. Time series of zonal wind stress (WSX) and SSH at the inter-annual mode
are investigated. Results reveal that strong WSX variability in the area of South Sir Lanka are
strongly affected the SSH variability in the east of Indian Ocean with WSX leading SSH by
1-2 weeks.
Keyword: MTM-SVD, joint spatiotemporal variability, ENSO
1. Introduction
North Indian Ocean (NIO hereafter) is the least explored among the Oceans in the
world. It is forced by seasonally reversing monsoons, which play an important role in its
variability. In particular, the mMonsoonal winds in the NIO NIO greatly influence the
variability ofaffect many lives living surround the Indian Ocean. Sea surface height (SSH)
and sea surface temperature (SST) which have an impact on the regional rainfall and
consequently, the socio-economic well being of large population in the surrounding regions
variability in the NIO are mostly influence by the Asiatic monsoon and vary from place to
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place. Thus, bBetter understanding of of these the nature of this variability leads to well
preparation for people live around the Indian Ocean rim whose agriculture and fishery are
their principal works.is critical for improved resources planning and management.
Relationships between monsoon and SSH as well as SST are studied in this paper.
The relationship of ENSO-monsoon during 1997-98 created climate and oceanic
anomalies (Saji et al., 1999; Webster et al., 1999). SST anomaly affected from ENSO line
condition yields SSH anomalies piling up along the South Asia coast. Sea level rises up and
retards the outflow of estuaries resulting flood in the deltaic area especially in Bangladesh
and India (University of Colorado at boulder, 2001; Singh, 2002).
The SST anomaly is also an important key to climate change. One of the strong SST
variations shows an out-of-phase SST in the tropic in the Indian Ocean, called Indian dipole
Ocean (Saji et al., 1999; Webster et al., 1999; Yu and Rienecker 1999 and 2000) or the Indian
Ocean zonal mode (IOZM). Situation of warm SST anomaly in the Indian Ocean, usually in
order of 0.5oC, leads too strong monsoon (Hastenrath, 1987; Harzallah and Sadourny, 1997;
Clark et al., 2000). Not only the monsoon affects the South Asia area but also the East
African. A few studies confirmed that the SST variation in the Indian Ocean is a major
contribution to the East African precipitation variation (Mutai et al., 1998; Goddard and
Graham, 1999; Clark et al., 2003).
In the past few decades, several mathematical and statistical techniques have been
developed and used to identify variability from signal data. Techniques such as Singular
Value Decomposition (SVD) (Wallace et al., 1992; Bretheron et al., 1992) related orthogonal
multivariate spatiotemporal decompositions (Bretherton et al., 1992), Spectral Analysis
(Emery and Thomson, 1998), Principal Oscillation Patterns (von Storch and Zwiers, 2003),
Principal Component Analysis (PCA) (Preisendorfer, 1988; Jolliffe 2002), Wavelet Spectrum
(WS) Analysis (Torrence and Compo, 1998) as well as Multiple-Taper Method-Singular
Value Decomposition (MTM-SVD) (Mann and Park, 1994) have been applied in the analysis
of atmospheric and oceanic data. Some methods only limit to identify either frequency
domain or spatial domain. Some methods can only identify standing mode without
information of dynamics and some methods can only identify localized variation.
Unlike other univariate or multivariate, MTM-SVD is a powerful multivariate tool to
simultaneously detect an oscillatory signal in both spatial and temporal data that can be used
to identify frequencies where an unusual concentration of narrowband variance occurs. It can
also be used to reconstruct the time history and spatial pattern associated with a frequency of
interest (Mann and Park, 1999). Mann et al. (1996) applied the MTM-SVD to investigate
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decadal climate variation in the Northern America. Tourre et al. (1999) identified joint
variability between SST and sea level pressure with MTM-SVD. Rajagopalan et al. (1998)
and Mann and Park (1999) used the MTM-SVD to show how reliable the method was by
testing through a synthetic data set with colored noise added and applied the method to
climate data.
In this study we intend to investigate joint variability and its dynamics of wind and
two surface parameters; SSH and SST using MTM-SVD. The paper is organized as follows.
Data description used in this study is first discussed and follows by brief detail of the MTM-
SVD on joint variability. Results of MTM-SVD analysis is presented next. Discussions of the
results conclude the paper.
2. Data
Because Wind and surface parameters are derived from satellite observations and
hence, have coarse resolution and sometimes contain missing values. Thus, to have data on a
finer scale and devoid of missing values, we used SSH, SST and wind data are available from
satellite observations with coarse resolution and sometimes contains missing values. To get
evenly data, we use data obtained from an assimilation numerical ocean model applying
applied to the NIO on a hindcast mode for the period during 1993-2005 (Rojsiraphisal,
2007). The numerical ocean model used used in this study is the University of Colorado
version Princeton Ocean Model (CUPOM) , which baseds on a primitive equation model
using topographically conformal coordinate in the vertical and orthogonal curvilinear
coordinates in the horizontal. The SSH is calculated explicitly using the split-mode technique.
More Ddetails of the basic features of CUPOM can be found in Kantha and Clayson (2000)
and Mellor (1996).
The NIO hindcast model has 1/4o resolution in the horizontal and 38 sigma levels in the
vertical, with the levels closely spaced in the upper 300 m. The model is forced by 6-hourly
ECMWF winds with Smith (1980) formulation for the drag coefficient CD to convert the
ECMWF 10-meter wind speed to wind stress at the surface:
It assimilates altimetric sea surface height anomalies and weekly composite MCSST
using a simple optimal interpolation-based assimilation technique. The model and the
assimilation methodology based on conversion of SSH anomalies into pseudo-BT anomalies
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for adjusting the model temperature field via optimal interpolation, have been described in
great detail in Lopez and Kantha (2000a and b). Details of CUPOM applied to the NIO along
with validation of model’s results can be found in Kantha et al. (2008) and Rojsiraphisal
(2007). The SSH is calculated explicitly using the split-mode technique.
This coupled assimilation resulted in a continuous space-time data of wind and all the
surface parameters (i.e., SST, SSH) for the 1993-2005 period. Weekly values are computed
from this data for use in this research. To keep the data size reasonable and maintain all the
spatial information data at every 1.5o ×1.5o degree resolution north of 10o S in the Indian
Ocean is used in the analysis. In all the data consists of 13-years (1993 to 2005) of weekly
and monthly SSH (N = 676 weeks assuming 52 weeks a year) covering 10o S-26o N, 39o -
120o E; total of 888 locations (M = 888 grid points) in the spatial domain (Figure 1).
3. Investigation Tool – Frequency Domain Multi Taper Method-Singular Value
Decomposition (MTM-SVD) Approach
Robust diagnosis of the key low-frequency modes of large-scale climate entails
capturing the coherent space-time variations across multiple climate state variables.
Traditional time-domain decomposition approaches for univariate and multivariate
data provide useful details on the broad-scale patterns of variability. However, these
approaches lack the ability to isolate narrow-band frequency domain structure (Mann
and Park, 1994; 1996). Detailed methodology development and examples of the
MTM-SVD methodology can be found in Thomson (1982); Mann and Park (1994,
1996); Lees and Park (1995). The method relies on the assumption that climate modes
are narrow band and evolve in a noise background that varies smoothly across the
frequencies. Subsequently, spectral domain equivalents of each grid point are
computed based on the multi-taper spectral analysis (Thomson, 1982; Park et al.,
1987).
Here we applied the MTM-SVD approach tTo study the individual and joint
variability of joint spatiotemporal modes of variability of wind and sea surface parameters in
the NIO region., we apply MTM-SVD on spatial time series of wind field, SSH, as well ass
SST. The spatial time series of each parameter is standardized by removing the long-time
mean at each grid point and normalized by dividing the long-term standard deviations by
weekly (or monthly) basis so that the variability has a unit variance and also the weekly
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(seasonal) cycle is removed. This normalization eliminates the disparity in the units between
the variables. The details of the technique can be found in the aforementioned references but
below we provide a brief description of the method abstracted from the references for the
benefit of the readers. allows us to compare joint-variability between variables, which have
different units. This can also isolate signal that may be cancel in coarse spatial averaging
patterns such dipoles, quadruple patterns (Mann and Park, 1996) and also insures that the
spatially coherent information is preserved. Since the detail of MTM-SVD on single
parameter has been discussed in great detail in Mann and Park (1999), thus we only briefly
discuss process of MTM-SVD on joint variability as follow.
Consider a standardized of spatiotemporal time series at site m-th of
and , where N is the length of the
time series, and are numbers of sites of first and second variables, respectively.
The first term of are time series of the first variable, and the next are time
series of the second variable. The standardized is calculated from ,
where prime notation represents the anomalies data and is the standard deviation at site
m-th. Note that the location of each variable need not be at the same site but both
spatiotemporal time series must have same length in temporal space. Then we apply multiple-
taper transform to the time series and obtain “eigenspectra” at each frequency as
(1) ,
where Δt is the sampling interval and is the k-th member in an orthogonal sequence
of K data tapers (also called Slepian tapers), The set of K tapered eigenspectra
have energy peaks within a narrow frequency bandwidth of , where f is a given
frequency and is the Rayleigh frequency (the minimum resolvable frequency
range for the time series). Note that the number of tapers K represents a compromise between
the variance and frequency resolution of the Fourier transforms (Mann and park, 1996). Also,
note that the Slepian tapers can considered as a sequence of weighting function, an example
of the first three Slepain tapers can be found in Mann and Park (1999).
With the set of eigenspectra, we can form a matrix
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(2)
where each row is calculated from a different grid point time series. Each column uses a
different data taper from equation (1) and represents specific weighting at each grid point.
Note that each row is computed from a different series (grid point), and each column
corresponds to using a different taper. Subsequently, a complex singular value
decomposition (CSVD)is performed through,
Because the MTM alone cannot consistently reveal all significant
information in frequency domain; therefore, a better approach with cooperation
between MTM and SVD (Rajagopalan et al., 1998; Mann and Park, 1999).
Thus, we perform the complex singular value decomposition
(CSVD) onto matrix and obtain
, where is complex spatial pattern and is spectral domain containing information of
both variables (i.e., the first M components contain information of the first variable and the
next components contain information of the second variable). These eigenvectors
can be inverted to obtain the smoothly varying envelope of the kth mode of variability
at frequency f (Mann and Park, 1996). The localized fractional variance (LFV)
provides a measure of the distribution of variance by frequency, and above a select
confidence level threshold (e.g., 90%, 95%), represents a dominant narrow band
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mode. The confidence levels are computed based on the locally white noise
assumption, and are constant outside the secular band. Mann and Park (1996)
describe a bootstrap method used to obtain the confidence bands for this study. In
general, the computed principal eigen-spectrum (described above) yields a number of
narrowband peaks. The MTM-SVD technique has been effectively applied to the
analysis of global SSTs and SLPs (Mann and Park, 1994 and 1996), identification of
dominant modes of variability in the Atlantic basin (Tourre et al., 1999), and also for
forecasting (Rajagopalan et al., 1998).
The LFV spectrum was used to identify significant frequencies, and temporal
and spatial reconstructions were carried out to understand the joint variability of the
climate fields in the NIO region.
4. Analysis
In this study, In this study we apply MTM-SVD to surface parameters wind fields generated
from CUPOM. we used the choice With choices ofof bandwidth parameter p = 2 and K = 3
tapers, which provide enough spectral degrees of freedom for signal-noise decomposition,
and allow reasonably good frequency resolution as well as stability of spectral estimates
according to Mann and Park, (1994) and ; Mann and Lees, (1996). The monthly data allows
for a maximum frequency of f = 6 cycle yr-1 (2 months period) to be resolved efficiently.
as well as the stability of spectral estimates Mann and Park, (1999). To make the MTM-SVD
analysis covering the NIO feasible, the weekly and monthly means of model results have
been computed and only data at every 1.5 degree north of 10oS have been selected. We will
now consider 13-years weekly and monthly SSH from 1993 to 2005 (N = 676 weeks
assuming 52 weeks a year) in the NIO with 1.5o×1.5o resolution covering 10oS-26oN, 39o-
120oE; total of 888 locations (M = 888 grid points) in the spatial domain (Figure 1). To ensure
statistical reliability, 1000 independent bootstrap realizations were performed on the fields
that were kept spatially intact, but the original data were randomly permuted into a new
random sequences data of the same length. This allows at least f = 6 cycle yr-1 (about 2
months) to be resolved efficiently.
In this section we will isolate the dominant frequencies of each individual surface
parameters; SSH and SST then we will discuss its individual dynamic. Later, we will analyze
spatiotemporal variability jointly between a pair of zonal and meridional wind stresses and
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SSH and SST. This allows us to obtain insight information of possible dynamical processes
governing such signals.
LFV of Single parametersResults
The MTM-SVD method is applied to the fields individually and also jointly. First we
present results from the individual analysis of SSH and SST and then jointly between winds
and SSH and winds and SST.
4.1.1 LFV of SSHSea Surface Heights
The LFV spectrum of SSH based on the analysis of monthly data is shown in We can
get information in frequency mode from fractional variance explained by kth mode within a
given narrow-frequency band, which is called “Local Fractional Variance” (LFV). In this
study we apply the MTM-SVD method with choices of bandwidth parameter
p = 2 and K = 3 tapers, which provide enough spectral degrees of freedom for signal-
noise decomposition, and allow reasonably good frequency resolution according to Mann and
Park, (1994); Mann and Lees, (1996) as well as the stability of spectral estimates Mann and
Park, (1999). The first (principal) mode in LFV contains important information that explains
the most variability. Thus, we use the first mode for all analysis hereafter. For better
understand of dynamic of joint spatio-temporal variability, we first analyze the variability of
individual variable; SSH, SST.
Figure 2a (blue). shows the LFV spectra associated with principal mode (k = 1) and
the confidence limits (99%, 95%, 90%, and 50%) for weekly SSH (green curve) of the NIO
along with those from monthly (blue curve) SSH time series. The dominant frequencies can
be seen in,fractional variance spectrum based on 13-years monthly data yields significant
variance peaks on inter-annual signals of 1.6-4 years period band (f ~ 0.3-0.6 cycle yr-1), on
annual cycle (f ~ 1.0 cycle yr-1), on semi-annual cycle (f ~ 2.0 cycle yr-1), and on seasonal
cycle (f ~ 4.0 cycle yr-1). All these peaks appear to breach the 99% confidence level, with
highest spectrum on the annual signal except the peak at about f ~ 4.75 cycle yr1 which is
slightly above 99% limit.. The LFV spectrum from the weekly data (green curve in the
figure) is similar to the the one from monthly data.
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Comparing LFV from different SSH data, all peaks observed from weekly SSH
spectra are also detected from the monthly time series (N = 156 months). However, the
monthly spectra (blue curve) are relative low in spectrum than those produced from weekly
data, with a large gap at higher frequency (f > 3.0 cycle yr-1) and that the peak of monthly
spectra centered at about f ~ 4.75 cycle yr-1 are not significant (hardly reach 90% confident
level). Another noticeable difference in these two different data can be found at low
frequency (f = 0.25-0.75 cycle yr-1) while the weekly spectra are separated into two
significant peaks instead of one continuous peak as seen in monthly data. From these results,
it suggests that both data sets do not show significantly dissimilar results; i.e., both signals
can detect important variations varying from seasonal to inter-annual robustness. Thus, we
can use either data set to study the variability of the NIO. In this case, we choose weekly data
set which contains higher spectrum at each frequency.
Sea Surface Temperature4.1.2 LFV of SST
Next we analyze LFV of SST with weekly and monthly time series. The LFV
spectrums of SST (Figure 2b3—Plan to omit) reveals two significant cycles frequencies
(>99% confidence limit) at annual and semi-annual modes periods (f = 1.0 and 2.0 cycle yr-1)
in both weekly and monthly data. The LFVs of weekly data are slightly higher in variation
than those of monthly data at high frequency. We also notice the otherThe frequencies in the
interannual bands two peaks at f = 0.25-0.4 and 3.0 cycle yr-1 are barely significant at 90%
confidence level – this a difference from the SSH results. A linear trend is evident between f
= 0 and 0.75. cycle yr-1 , this reddening of the spectrum and a secular trend is consistent with
prior results in the Indian Ocean (xxxx).
emerging but both of them are not robust (slightly above 90% confidence limit). This
implies that there is no significant change of SST neither at inter-annual nor intra-seasonal
mode.
Joint Wind and SSH VariabilityJointed parameters on Wind and SSH
We have investigated results of single parameter via the LFV. We can also
investigate the dynamic of each individual parameter through its spatial variation which we
will discuss them when we study dynamic of join variability. Because the NIO, as mentioned
earlier, is most influenced by the Indian summer Asian monsoonn, thus, the variability of
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SSH and SST are likely to be tied firmly to the monsoonal winds. To identify the joint
variability, we performed joint analysis of the winds (zonal, WSX and meridional, WZY,
winds separately) with SSH. Figure 4 shows the LFV of this joint analysis. it is appropriate
to investigate joint variability between wind fields and SSH and SST. Here, we apply MTM-
SVD analysis on four pairs of joint fields -- between either zonal wind (WSX) or meridianal
wind (WSY) and either SSH or SST. Results of the analysis would give us information of any
dynamical link between the wind effects and SSH/SST.
We now analyze joint variability between wind fields and SSH in the NIO. The joint-
mode fractional variance spectrum based on weekly (green curve) and monthly (blue curve)
of joint WSX-SSH (panel a) and joint WSY-SSH (panel b) are shown in Figure 4. The LFV
of joint variability of both pairs (WSX-SSH and WSY-SSH) yield significant variance peaks
(over 99% confidence limit) at inter-annual, annual, and semi-annual periods where both
fields are simultaneously dominant, while seasonal and intra-seasonal (at 90% confidence
level). periods yield lower variances that only breach over 90% confidence limit. It is worth
noting that the dominant period at inter-annual frequency from weekly data is noticeably
separated into two significant peaks; at f = 0.4 and 0.6 cycle yr-1. The Note also that all
significant peaks observed in this joint analysis are same as the frequencies identified in the
individual analysis of SSH. Here too, the LFV spectra from the weekly and monthly data are
similar. variations between wind fields and SSH are also found to be significant in the
individual SSH variation.
To understand the joint variability in space and their evolution at these dominant
frequencies, we performed spatial reconstructions for the two fields at the frequencies
identified above. Spatial patterns of the zonal and meridional wind fields and the
corresponding SSH at the annual cycle (f = 1.0 cycle yr-1 ) frequency, from the respective joint
analyses are shown in Figure 5. The We next reconstruct spatial variation of the joint
variability between WSX (WSY) and SSH at dominant frequencies; annual mode, semi-
annual and inter-annual mode. Figure 5 shows the spatial patterns at annual ( f = 1.0 cycle yr-1)
cycle of (a) WSX on joint WSX-SSH; (b) SSH on joint WSX-SSH; (c) WSY on joint WSY-
SSH; and (d) SSH on joint WSY-SSH. vVector lengths in this (and subsequent spatial
reconstructions) figure are indicative of the magnitude of the signal and the phase (i.e.,
directions) are with respect to a reference location in (a) and (b) correspond to the magnitude
of each variable relative to size of WSX at a reference location (grid 529th at 7.25oN, 76.75oE)
– the vector at the reference location is always horizontal pointing right (i.e., at the 3 o’clock
position).. The direction of vectors at other locations Phase of the vectors corresponds to
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temporal difference (time lead/lag) relative to the reference vector (at 3 o’clock). In the
spatial pattern, clockwise vector rotation represents negative relative lag (or “lead”), and
counter-clockwise rotation represents positive lag (or “lag”). A complete rotation represents a
periodicity of the mode; e.g. 1 year for f = 1.0 cycle yr-1, and a grid point vector at 12 o’clock
(90o) experiences peaks at 4 months lag relative to the reference grid point.
Annual frequency
The zonal winds (Figure 5a) exhibit an out of phase relationship between the NIO
region and the Southern Indian Ocean region – this is indicative of the annual cycle in that the
winds in the northern hemisphere are always out of phase with the southern. The meridional
winds (Figure 5c) show a strong signal in the Arabian Sea region of the NIO the Bay of
Bengal region and the South China Sea – all active regions of the Asian monsoon, and Indian
monsoon in particular. In fact, these wind patterns are almost identical to the monsoon wind
features (xxx reference xxx). The vectors all in the same direction indicative of the feature
happening in the same period (i.e. the summer period), the slight changes in vector directions
between the South China Sea region and NIO shows the delay in the South China monsoon
relative to the Indian.
The spatial pattern of 4.2.1 Annual of Wind-SSH
The primary mode of annual cycle (Figure 5) in the joint WSX-SSH data series accounts for
96% variance, while the joint WSY-SSH data series accounts for 97%. Recall that all vectors
in WSX and SSH as shown in panels (a) and (b) are related to the horizontal reference vector
of WSX in panel (a) at the grid 529th (as seen in Figure 1) near the southern tip of India. This
allows one to see a possible dynamical link between these two fields; while joint vectors of
WSY and SSH in panels (c) and (d) are related to a reference vector of WSY in panel (c).
At this mode, WSX shows latitudinal variations. Most of the year, there are two areas,
separated by the equator, with opposite sign. At every a few months, there are the WSX show
variations in three latitudinal bands with one sign in the middle strip locating between 0 oN-
10oN while the other two strips show another sign of variation. The three-band variation is
last for a month or so, and then the WSX variation returns to two-band variation with sign
reverse from previous. While the spatial variation of WSY within half-year cycle (6 months)
is dominant in three regions; Arabian Sea, Bay of Bengal and South China Sea with almost
in-phase in all regions with the largest in magnitude occurs in the Arabian Sea. This pattern is
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last for three months then it becomes weakening in a month or so before its magnitude
becomes strong again in the same three regions.
SSH variability at this mode as seen in (Figures 5b and 5d) from the joint analysis of the two
wind components is similar. panels (b) and (d) show the same pattern but the only difference
is that vector in each panel base on different references. The SSH signal is strong over most
of the basin except in the southern hemisphere where the winds are quite a bit weaker as seen
above. variability is dominant in most area of the NIO except area of 50o-80oE and 5oS-0oN.
From these plots, we see that the strong magnitude of SSH in the southwest region is not
locally affected by the zonal wind since the zonal wind in that region is weak during that
time. It may be affected from strong easterly wind in the south leading by about 2 months.
The propagation of the SSH signal at the annual cycle frequency is apparent and can
be explained as follows. While the dynamic of SSH alone in 1-year cycle can be described as
follow. One startsStarting in the black-vector area region in the southern of Indian Ocean and
it takes about ook 1-2 months (~30o-45o) to propagate westward into the southwest (green-
vector) area. . By that time, there are two large magnitudes of SSH along the west coast of
India and Gulf of Thailand. The large magnitude along the west coast of India propagates
westward into the red-vector area in the southern of Arabian Sea. Similarly,; the signal in the
while the smaller one in the southwest propagates northward along the Somali coast into
red/blue-vector areas. Then the red area near the Socotra Island propagates eastward into the
middle of Arabian Sea; while the blue area moves southward into the Equatorial region which
next propagates eastward along the equatorial waveguide into the Sumatra Island area and
completes the cycle with a stronger magnitude along the east coast of Bay of Bengal. The
propagation of the SSH signal lagged by a few months to the wind signal – which is
consistent, in that the SSH anomalies are driven in large part by the strong wind forcing in the
basin (xxx refs xxx).
Semi-annual
4.2.2 Semi-Annual of Wind-SSH
The spatial patterns of the wind and SSH fields at the Patterns of semi-annual
frequency mode (f = 2.0 cycle yr-1) are shown in Figure 6. At this period, the strongest signal
in the both the wind components are in the Arabian Sea region – which is the active Indian
monsoon region. This is more so in the meridional component where the amplitudes are
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strongest in Western Arabian Sea region and also a bit in the South China Sea. The main
aspect at the annual and semi-annual frequency is similar in terms of the winds in that the
variability is strongest in the regions of monsoonal winds and the phase lags are consistent
with spatial and temporal variability of monsoons in the region.
The SSH signal is stronger with the meridional winds (Figure 6d). of joint WSX-SSH
and WSY-SSH, as shown in Figure 6, account for 91% and 90%, respectively. Variability of
WSX, in panel (a), is large in all area except in the eastern area, i.e. area south of the Bay of
Bengal with the largest in magnitude occurs in the Arabian Sea. The present of WSX
variations displays in latitudinal bands with opposite signs; one sign in area north of 5oN, and
another sign central of the Indian Ocean south west of India. This is last for a month or so.
Then the strong variation in the central area is moving westward and northward into the
Arabian Sea and this takes about a month. Then the latitudinal variations with sign reverse
reoccur again. This is a complete half cycle (3 months) of WSX variation. While the WSY
variability, in panel (c), shows large magnitude in the western the Arabian Sea and the South
China Sea as well as the southern tip of India but the largest in magnitude is found in the
Arabian Sea. While the SSH variability is relatively weak compare to WSX variation but its
variation is comparable to WSY.
The large magnitude of SSH between 2o-10oN and 50o-77oE (referred as area A1
thereafter) is affected by strong WSY in the western Arabian Sea, which leads the highthis by
about a month or so. The strong magnitude of SSH in the southern region on the other hand is
forced by zonal wind stress locally and is also affected by the strong magnitude of SSH in the
area A1. The last region affected by from these winds is the eastern coast near the Sumatra
Island. It is affected by remote WSX in the central region where the wind leads by a month or
so.
4.2.3 Inter-Annual of Wind-SSH (Snapshots)
Interannual band
The primary mode of joint variances of WSX-SSH and WSY-SSH at dominant
frequency in the inter-annual band is mode (f = 0.4 cycle yr-1). We show a snap-shot
reconstruction for this frequency, in that snap shots of the magnitudes of the two fields at
several times in the entire cycle are shown. account for 87% and 85%, respectively. A
possible dynamical link observed from spatial variations between winds and SSH, occurs in
the east of NIO near the Sumatra Island. However, the phases difference between large WSY
and SSH variations occur in this area are large (about 180o or 15 months) compared a few
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months (about 30o-45o) of the relationship between large magnitude in WSX and SSH
variations. It leads us to believe that WSX favors this pattern. Thus we choose to compare
spatial patterns between WSX and SSH at this inter-annual mode.
Figure 7 shows the reconstruction of spatial snapshots of joint WSX (left panels) and
SSH (right panels) variations of 2.5-year (f = 0.4 cycle yr-1) period at various times, spanning
one-half of a complete cycle (~1.25 years or 15 months). Squares and triangles indicate sign
differences and the sizes of these symbols represent magnitude of each variable that is
relative to value of WSX at a reference grid point (grid 529th). The initial snapshots (at 0o)
correspond to peaks WSX anomalies in the east-central of the NIO and the corresponding
SSH anomalies. Next snapshots reveals the evolution of WSX and SSH anomalies. The WSX
anomalies are weakening in the next few months and reverse the signs in about 6-7 months
(at about 90o); though the SSH anomalies are also weakening but at slower rate. While the
final snapshots correspond to the opposite conditions reveals at about 15 months later.
At the phase between 112.5o and 135o, large magnitude of SSH anomalies occur
within the stripe of 10oS - 10oN across the ocean with one sign covering most of the western
side of equatorial region and the other sign occurs next to the Sumatra Island. These
anomalies in the eastern side intrude into the middle of this region. These This is reminiscent
of the patterns exhibit the situations so called “dipole” feature (Saji et al., 1999; Webster et
al., 1999; Yu and Rienecker 1999 and 2000) identified in the wind fields. which are the
effects of WSX anomalies, in the area south of Sri Lanka, that lead this event by a few
months.
The spatial patterns between wind fields and SSH at f = 0.6 cycle yr-1 period (are not
shown) is similar to those at f = 0.4 cycle yr-1 period but its dynamics is different. Large
magnitudes of SSH are found in the eastern side of Indian Ocean but once it propagates
westward into the south of Sri Lanka area and western region, their magnitudes are relative
small compared to the magnitude along the east coast.
To analyze the temporal variability, we reconstructed the time components of these
fields at locations (see Figure 8) from regions exhibiting strong magnitudes in Figure 7. The
temporal reconstructions are shown in Figure 9. Relationship between WSX and SSH at the
western equatorial (top) locations are almost in-phase, while the WSX in this region leads
SSH at Sumatra by 10-12 weeks. There is a rather sudden change in WSX during the late
1997 that can be seen with an anomalous high in SSH at that time. This potentially could be
driven by the strongest ENSO event in 1997-98.
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4.3 Wind fields and SST
Next we apply MTM-SVD to weekly and monthly data of wind fields and sea surface
temperature. The LFV spectra of the joint analysis of Local fractional variance of joint WSX-
SST and WSY-SST are shown in Figure 8 (Plan to omit). The spectra is very similar to that
of joint wind and SSH analysis from before. Significant peaks are found at the annul, semi-
annual and interannual bands. There are only two significant peaks at annual and semi-annual
periods which breach over 99% confidence interval in both fields. Unlike the joint variability
between wind fields and SSH, the inter-annual mode of joint variability between wind fields
and SST hardly reach the 90% confidence interval. The founds of the annual and semi-annual
peaks are not surprise since the NIO locates covers in the tropic region, therefore, the
temperature does not vary much.
The spatial reconstructions of the SST fields (Figure not shown) shows anomalies of
opposite sign in the Northern Arabian Sea, Northwestern Bay of Bengal and South China Sea
and; near the Tanzanian coast.
4.3.1 Annual of Wind-SST
The annual cycle of joint wind fields and SST accounts for 97% variance. Spatial
patterns of WSX (and WSY) are same as discussed in the annual mode of WSX (and WSY)
from joint wind fields and SSH. The corresponding SST variances of joint WSX-SST at this
mode (are not shown) only show significant variance with opposite signs near the continents;
one sign in north of the Arabian Sea, northwest-west of the Bay of Bengal, South China Sea
and the other sign in southwest region near Tanzania coast.
We observed that the wind fields lead the SST variations by a month to a few months
and that the strong SST variantionce in the southwest region of the domain is affected by both
local WSX and WSY variation. The dominant variation in the southwest area is extended
along the eastern African coast while the variations in the northern regions do not spread out.
This situation is last for three month. Once the wind field variations are weakening and
reverse their signs, the SST variation becomes weakening all over the domain.
4.3.2 Semi-Annual of Wind-SST
At the The ssemi-annual (f = 2.0 cycle yr-1) frequency the SST anomalies are small
everywhere except in Western Arabian Sea. mode of joint wind fields and SST accounts for
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95% variance. Spatial patterns of WSX (and WSY) are same as discussed in the semi-annual
mode of WSX (and WSY) from joint wind fields and SSH. Their corresponding SST
variances of joint WSX-SST at this mode (are not shown) is relatively low in all area except
in the Arabian Sea. The largest in magnitude is found in the western side of the Arabian Sea
which is last by almost two months.
4.4 Time series of WSX and SSH at inter-annual mode
We have seen that there are large variations in WSX and SSH at the inter-annual
mode. We are now investigating relationship between these two variables by reconstructing
time series at inter-annual mode (f = 0.4 cycle yr-1 or about 2.5 year period) of WSX and SSH
within the dominant area. Here we reconstruct time series of WSX at southeast of Sri Lanka
-- grid 450th and times series of dominant SSH at three locations; western equatorial, western
of Sumatra Island, and south of India -- at grids 345th, 416th, and 484th respectively. Note that
locations of the reconstructed time series can be seen in Figure 9.
Time series reconstruction at inter-annual mode (f = 0.4 cycle yr-1 or about 2.5 year
period) comparing WSX and SSH at three different locations are shown in Figure 10.
Relationship between WSX and SSH at the western equatorial (top) reveal almost in-phase
with the WSX leads SSH at this location by 10-12 weeks. We notice the sudden change of
WSX during the late 1997 while there was an anomalous high in SSH at that time. Time
reconstruction of WSX and SSH at the west of Sumatra Island (middle) shows in-phase with
the WSX slightly lead SSH by 1-2 weeks. Time reconstruction of WSX and SSH at the west
of India reveals 180o out of phase. From time series, we notice that the effect of WSX
anomalous in 1997-98 directly affects SSH in the west of Sumatra Island but it is not affect
the SSH at the west of India.
5. Conclusion
The MTM-SVD was applied to the joint fields of winds and variables at the surface.
This analysis was able to identify frequencies where an unusual concentration of a
narrowband variance occurs. In this study, we performed MTM-SVD along with bootstrap
procedure on decimated weekly and monthly data. The results revealed higher energy of local
fraction variance in weekly data at the high frequency as expected; while at other low
frequency, the LFVs of both data are relatively comparable. The LFVs from joint MTM-SVD
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simultaneously revealed dominant cycles at annual and semi-annual frequencies which
should be expected in the NIO because the variability in this region are strongly affected by
seasonal reversing monsoons.
The LFVs of winds and SSH also reveal dominant variability in the inter-annual
frequency, which relates to the ENSO cycle; while variation of the wind components and SST
at this mode are not statistically significant. This is not a surprise result since the NIO locates
in the tropic region, thus SST is usually warm most of the time and the variability of SST in
this region does not vary much from year to year.
Reconstructed spatial patterns reveal the dynamics of joint variation at specific
frequency. The phase and magnitude differences in each pair allow us to understand the
relationship between the two fields. We observed that the anomalous wind during 1997-98
strongly affected in the eastern side of NIO which can be seen from signature of SSH
anomaly.
One can extend the analysis of MTM-SVD to more than two fields but it requires
higher computer resources. However, a disadvantage of MTM-SVD technique is that the
dominant variability at any frequency requires strong variance in many spatial locations. If
there are only few spatial locations with strong variability participating at that frequency, that
area will not be dominant.
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summer monsoon and some meteorological variables, Clim. Dyn., 13, 635–648.
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Figure Captions:
Figure 1
Locations of data used for MTM-SVD analysis in the North Indian Ocean. Data locations are
defaulted by with reference location at the 529th grid point which is just below the tip of
Indian.
Figure 2
Comparing LFV spectra (relative variance explained by the first eigenspectra) of weekly
(green) and monthly (blue) SSH time series as a function of frequency. Black, red, cyan, and
magenta lines denote 99%, 95%, 90%, and 50% confident limits from bootstrap procedure,
respectively.
Figure 3 (not shown)
Same as Figure 2 but for SST.
Figure 4
LFVs for joint variability between WSX and SSH (a) and between WSY and SSH (b).
Figure 5
Spatial variations at annual (f = 1.0 cycle yr-1) cycle of (a) WSX on joint WSX-SSH; (b) SSH
on joint WSX-SSH; (c) WSY on joint WSY-SSH; and (d) SSH on joint WSY-SSH. Vector
lengths in (a) and (b) correspond to the magnitude of each variable relative to size of WSX at
a reference location (grid 529th at 7.25oN, 76.75oE). Phase of the vectors correspond to
temporal difference (time lead/lag) relative to the reference vector (at 3 o’clock). In the
spatial pattern, clockwise vector rotation represents negative relative lag (or “lead”), and
counter-clockwise rotation represents positive lag (or “lag”). A complete rotation represents a
periodicity of the mode; e.g. 1 year for f = 1.0 cycle yr-1, and a grid point vector at 12 o’clock
(90o) experiences peaks at 4 months lag relative to the reference grid point. Same analogous
is applied for a patterns in (c) and (d), where all vectors are related to vector at grid 529th of
WSY.
Figure 6
Same as Figure 5, but for semi-annual (f = 2.0 cycle yr-1) period.
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Figure 7
Spatial patterns shown at progressive intervals (~56 days or 22.5o from top to bottom),
spanning one-half of a complete cycle (~1.25 years or 15 months). Left and right panels show
variations of WSX and SSH, respectively. Sizes of square and triangle represents magnitude
of both variables are relative to value of WSX at a reference grid point (grid 529th). The
squares and triangles indicate different in signs. The initial snapshots correspond to peaks
WSX anomalies in the east-central of the North Indian Ocean and SSH anomalies. While the
final snapshot corresponds to the opposite conditions that obtain at one-half cycle later.
Figure 8 (Plan to omit)
LFVs for joint variability between WSX and SST (a) and between WSY and SST (b).
Figure 9
Locations of reconstructed time series, WSX at southeast of Sri Lanka (grid 450 th) in yellow
squares and SSH at west equatorial region (grid 346 th), west Sumatra Island (grid 416th), and
west India (grid 484th) in green circles.
Figure 10
Time series reconstruction at inter-annual mode (f = 0.39 cycle yr-1) comparing WSX at
southeast of Sri Lanka and SSH at three other locations; western of equatorial region (top),
western Sumatra Island (middle), and western India (bottom).
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Figures
Figure 1: Locations of data used for MTM-SVD analysis in the North Indian Ocean. Data locations are defaulted by with reference location at the 529th grid point which is just below the tip of Indian.
Figure 2: Comparing LFV spectra (relative variance explained by the first eigenspectra) of weekly (green) and monthly (blue) SSH time series as a function of frequency. Black, red, cyan, and magenta lines denote 99%, 95%, 90%, and 50% confident limits from bootstrap procedure, respectively.
739
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Figure 3 (Plan to omit): Same as Figure 2 but for SST.
Figure 4: LFVs for joint variability between WSX and SSH (a) and between WSY and SSH (b).
Page 2 of 34
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Figure 5: Spatial variations at annual (f = 1.0 cycle yr-1) cycle of (a) WSX on joint WSX-SSH; (b) SSH on joint WSX-SSH; (c) WSY on joint WSY-SSH; and (d) SSH on joint WSY-SSH. Vector lengths in (a) and (b) correspond to the magnitude of each variable relative to size of WSX at a reference location (grid 529th at 7.25oN, 76.75oE). Phase of the vectors
Page 3 of 34
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correspond to temporal difference (time lead/lag) relative to the reference vector (at 3 o’clock). In the spatial pattern, clockwise vector rotation represents negative relative lag (or “lead”), and counter-clockwise rotation represents positive lag (or “lag”). A complete rotation represents a periodicity of the mode; e.g. 1 year for f = 1.0 cycle yr-1, and a grid point vector at 12 o’clock (90o) experiences peaks at 4 months lag relative to the reference grid point. Same analogous is applied for a patterns in (c) and (d), where all vectors are related to vector at grid 529th of WSY.
Page 4 of 34
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Figure 6: Same as Figure 5, but for semi-annual (f = 2.0 cycle yr-1) period.
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Figure 7: Spatial patterns shown at progressive intervals (~56 days or 22.5o from top to bottom), spanning one-half of a complete cycle (~1.25 years or 15 months). Left and right panels show variations of WSX and SSH, respectively. Sizes of square and triangle represents magnitude of both variables are relative to value of WSX at a reference grid point (grid 529th). The squares and triangles indicate different in signs. The initial snapshots correspond to peaks WSX anomalies in the east-central of the North Indian Ocean and SSH anomalies. While the final snapshot corresponds to the opposite conditions that obtain at one-half cycle later.
Page 6 of 34
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Figure 7: (continue)
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Figure 7: (continue)
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Figure 8: (Plan to omit) LFVs for joint variability between WSX and SST (a) and between WSY and SST (b).
Figure 9: Locations of reconstructed time series, WSX at southeast of Sri Lanka (grid 450 th) in yellow squares and SSH at west equatorial region (grid 346 th), west Sumatra Island (grid 416th), and west India (grid 484th) in green circles.
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Figure 10: Time series reconstruction at inter-annual mode (f = 0.39 cycle yr-1) comparing WSX at southeast of Sri Lanka and SSH at three other locations; western of equatorial region (top), western Sumatra Island (middle), and western India (bottom).
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