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

…………………………………..

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.

6. References

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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).

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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.

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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.

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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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