Sea surface height (SSH) and sea surface temperature (SST) in the North Indian Ocean are affected predominantly by the seasonally reversing monsoons and in turn feed back on monsoon variability. In this study, a set of data generated from a data-assimilative ocean model is used to examine coherent spatiotemporal modes of variability of winds and surface parameters using a frequency domain technique, Multiple Taper Method with Singular Value Decomposition (MTM-SVD). The analysis shows significant variability at annual and semiannual frequencies in these fields individually and jointly. The joint variability of winds and SSH is significant at interannual (2-3 years) timescale related to the ENSO mode—with a “/dipole/” like spatial pattern. Joint variability with SST showed similar but somewhat weaker behavior. Winds appear to be the driver of variability in both SSH and SST at these frequency bands. This offers prospects for long-lead projections of the North Indian Ocean climate.
North Indian Ocean 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 variability of monsoonal winds in the North Indian Ocean greatly influence the variability of sea surface height (SSH) and sea surface temperature (SST) which have an impact on the regional rainfall and consequently, the socioeconomic well being of the large population in the surrounding regions. Thus, a better understanding of the nature of this variability is critical for improved resource planning and management.
The ENSO-monsoon relationship during 1997-1998 created climate and oceanic anomalies [
The SST anomaly is also an important key to climate change. One strong SST variation is an out-of-phase SST in the tropical Indian Ocean, the so-called Indian Ocean Dipole [
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) [
Unlike other univariate or multivariate methods, 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 [
In this study the joint variability and dynamics of wind and two surface parameters, SSH and SST, will be investigated using MTM-SVD. The paper is organized as follows. Data used in this study is first discussed, followed by a brief description of the MTM-SVD on joint variability. Results of MTM-SVD analysis are presented next. Discussions of the results conclude the paper.
Data used in this study is obtained from a data-assimilating numerical ocean model applied to the North Indian Ocean in a hindcast mode for the period 1993–2005 [
The North Indian Ocean hindcast model has 1/4° 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 [
The hindcast produced a continuous space-time data of wind and all the surface parameters (i.e., SST, SSH) for the 1993–2005 period, in addition to 3-D fields of water mass properties and currents. Weekly values are computed from the model data for use in this study. To keep the data size reasonable and maintain all the spatial information, data at every
Locations of data used for MTM-SVD analysis in the North Indian Ocean. Data locations are defaulted by
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 narrowband frequency domain structure [
In this study, the MTM-SVD approach is applied to examine the individual and joint spatiotemporal modes of variability of wind and sea surface parameters in the North Indian Ocean. 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 (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.
Consider a standardized spatiotemporal time series at the
With the set of eigenspectra, one can form an
The LFV spectrum is used to identify significant frequencies, and temporal and spatial reconstructions are carried out to understand the joint variability of the climate fields in the North Indian Ocean. In this study, the choice of bandwidth parameter
In the next section, the dominant frequencies of each individual surface parameters SSH and SST are isolated. Next the individual dynamics of SST and SSH will be discussed followed by the analysis of spatiotemporal variability jointly between a pair of zonal and meridional wind stresses, and SSH and SST which provide insight into possible dynamical processes governing such signals.
The MTM-SVD method is applied to the fields individually and also jointly. In this section results of the individual analysis of SSH and SST variability are first presented followed by the joint analysis of winds and SSH, and winds and SST.
The LFV spectrum of SSH based on the analysis of monthly data is shown in Figure
LFV spectra (relative variance explained by the first eigenspectra) of monthly SSH (a) and monthly SST (b) time series as a function of frequency. Thick dash-dot, thin dash-dot, dash, and solid lines denote 99%, 95%, 90%, and 50% confident limits from bootstrap procedure, respectively.
The LFV spectrum of SST (Figure
North Indian Ocean, as mentioned earlier, is most influenced by the Indian summer monsoon, thus, the variability of SSH and SST is likely to be tied firmly to the monsoonal winds. To identify the joint variability, the joint analysis of the winds (zonal, WSX and meridional, WSY winds separately) with SSH is performed. Figure
The same as Figure
The LFV of joint variability of both pairs (WSX-SSH and WSY-SSH) yield significant peaks (over 99% confidence limit) at interannual, annual, and semiannual periods and at seasonal and intraseasonal (at 90% confidence level). The significant peaks observed in this joint analysis are the same as the frequencies identified in the individual analysis of SSH. Here too, the LFV spectra from the weekly and monthly data are similar.
To understand the joint variability in space and their evolution at these dominant frequencies, the spatial reconstructions for the two fields at the frequencies identified above are performed. Spatial patterns of the zonal and meridional wind fields and the corresponding SSH at the annual cycle (
Spatial variations at annual (
WSX from joint WSX-SSH at
SSH from joint WSX-SSH at
WSY from joint WSY-SSH at
SSH from joint WSY-SSH at
The zonal winds (Figure
The spatial pattern of SSH variability at this mode (Figures
The propagation of the SSH signal at the annual cycle frequency is apparent and can be explained as follows. Starting in the black-vector region in the southern Indian Ocean, it takes about 1-2 months (~30°–45°) to propagate westward into the southwest (green-vector) area. The large magnitude along the west coast of India propagates westward into the red-vector area in the southern Arabian Sea. Similarly, the signal 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 [
The spatial patterns of the wind and SSH fields at the semiannual frequency (
The same as Figure
WSX from joint WSX-SSH at
SSH from joint WSX-SSH at
WSY from joint WSY-SSH at
SSH from joint WSY-SSH at
The SSH signal is stronger with the meridional winds (Figure
The dominant frequency in the interannual band is 0.4 cycle
Spatial patterns shown at progressive intervals (~56 days or 22.5° 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 that magnitudes 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 are obtained at one-half cycle later.
Clarke and Liu [
Locations of reconstructed time series, WSX at southeast of Sri Lanka (grid 450th) in yellow squares and SSH at west equatorial region (grid 346th), west Sumatra Island (grid 416th), and west India (grid 484th) in green circles.
Time series reconstruction at interannual mode (
The LFV spectra of the joint analysis of WSX-SST and WSY-SST are shown in Figure
The same as Figure
The spatial reconstructions of the SST fields at the annual frequency periods (not shown) show large anomalies with a phase difference of 4-5 months between the Northern Arabian Sea, Northwestern Bay of Bengal and South China Sea, and the Southwest region near the Tanzanian coast. The wind fields lead the SST variations in the Northern areas by a few months and that the strong SST variation in the southwest region of the domain is affected by both local WSX and WSY variation. At the semiannual (
In this study, the MTM-SVD technique was applied to decimated weekly and monthly data of individual and joint fields of winds and surface variables. The MTM-SVD technique provides an attractive and complementary alternative to the traditional time domain analysis methods. Especially, its capability in isolating narrowband propagating features in the joint fields is unique unlike the traditional methods.
This analysis was able to identify significant frequencies bands that are shared by a majority of spatial locations in the joint fields. It showed significant variability at semiannual, annual, and interannual frequencies in these fields individually and jointly. At the semiannual and annual frequency bands, the variability is largely linked to the seasonal reversing monsoons in the basin, which is a strong factor. The variability at the interannual frequency band is related to ENSO and the evolution of the SST spatial pattern resembles at time to a nonstanding so-called the Indian Ocean dipole. Furthermore, it appears that the winds are the main drivers of variability in both SSH and SST, which propagate around the basin. The spatial and temporal reconstructions offer prospects for long lead simulation and forecast of the climate in the North Indian Ocean which can be of great help to societies in the region that support a large part of the world’s population.
One can extend the analysis of MTM-SVD technique to more than two fields but it requires more 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 a few spatial locations with strong variability participating at that frequency, that area will not be dominant.
This work was partially supported by the US Office of Naval Research Grant N00014-06-10287 (LK), and the Faculty of Science, Burapha University, Thailand for partially support as well as the Center of Excellence in Mathematics (TR).