Identification of Internal Tides in ECCO Estimates of Sea Surface Salinity in the Andaman Sea

Abstract

We used NASA’s high-resolution (1/48° or 2.3 km, hourly) Estimating the Circulation and Climate of the Ocean (ECCO) estimates of salinity at a 1 m depth from November 2011 to October 2012 to detect semi-diurnal and diurnal internal tides (ITs) in the Andaman Sea and determine their characteristics in three 2° × 2° boxes off the Myanmar coast (box A), central Andaman Sea (box B), and off the Thailand coast (box C). We also used observed salinity and temperature data for the above period at the BD12-moored buoy in the central Andaman Sea. ECCO salinity data were bandpass-filtered with 11–14 h and 22–26 h periods. Large variations in filtered ECCO salinity (~0.1 psu) in the boxes corresponded with near-surface imprints of propagating ITs. Observed data from the box B domain reveals strong salinity stratification (halocline) in the upper 40 m. Our analyses reveal that the shallow halocline affects the signatures of propagating semi-diurnal ITs reaching the surface, but diurnal ITs propagating in the halocline reach up to the surface and bring variability in ECCO salinity. In box A, the semi-diurnal IT characteristics are higher speeds (0.96 m/s) with larger wavelengths (45 km), that are closer to theoretical mode 2 estimates, but the diurnal ITs propagating in the box A domain, with a possible source over the shelf of Gulf of Martaban, attain lower values (0.45 m/s, 38 km). In box B, the propagation speed is lower (higher) for semi-diurnal (diurnal) ITs. Estimates for box C are closer to those for box A.

1. Introduction

Internal waves (IWs) are prominent features that undulate in the subsurface ocean in regions of well-defined density stratification [1,2,3]. The periods of IWs lie between the local buoyancy period (2π/N, where N is the buoyancy frequency) and inertial period (2π/f, where f is the Coriolis parameter) [4]. When these waves oscillate at tidal periods, they are referred to as internal tides (ITs). Their generation is influenced by bathymetry, atmospheric forcing, and gravitational forces to transport momentum and energy [5,6,7]. Osborne and Burch [7] made current meter observations in the Andaman Sea and identified the north Sumatra region as the source region of large-amplitude IWs with a semi-diurnal tidal period of 12.42 h. IT transport momentum in the near-shore coastal waters is associated with the breaking of ITs on the sloping topography and results in the initiation of turbulence at the density interface [8]. IWs can propagate hundreds of kilometers, where most of their energy dissipates into turbulent mixing [9]. The strength of ITs is derived from the contrast of the subsurface density gradient where strengthened stratification typically results in higher wave frequencies and faster phase speeds [10,11].

ITs displace the thermocline vertically, giving rise to near-surface flow convergence and divergence that affects local sea surface roughness [12]. Although their maximum amplitudes occur at the pycnocline boundary within the water column, their surface properties are observed as alternating smooth and rough bands [12]. These bands are the result of the convergence (divergence) of water parcels in the wave’s trough (above crest) as the ITs propagate at the thermocline [13]. The ITs also alter the vertical shear of the ocean and influence circulation processes, causing disturbances in nutrient mixing and bio-stimulation [14].

More recent observations allow us to analyze the surface effects of IWs through multi-parameter analysis using spectrometer imagery, remote sensing techniques such as synthetic aperture radar (SAR) [15], and ocean model simulations [16,17]. Using SAR data, IWs are detected near coastal areas in the western Bay of Bengal (BoB) in groups that are 10–60 km apart with crests that are 10–100 km long [13]. Using SAR data, da Silva and Magalhaes [15] gave a possible explanation for mode-2 IW generation in the Andaman–Nicobar Island chain system. Mohanty et al. [18] utilized Envisat ASAR (advanced SAR) true color imagery data (March 2010 and August 2011) to investigate the ITs in the Andaman Sea and around the Andaman–Nicobar Island chain. These researchers [18] utilized the BD12-moored buoy observation data from the central Andaman Sea to validate the three-dimensional Massachusetts Institute of Technology general circulation (MITgcm) simulations to study the ITs in the Andaman Sea. For this same study region, Raju et al. [19] utilized both MODIS true-color and SAR observations and studied the IWs and their propagation. From the Envisat SAR images in February 2012, Joshi et al. [20] estimated the phase speed of IWs as 0.75 m/s in the shallow waters off the western BoB. The researchers [21] reported large-amplitude (80 m) IWs of 2 km wavelengths off the northwestern coast of Sumatra.

In the northern Indian Ocean, the Andaman Sea is a marginal sea encompassed by coastlines and archipelago structures that are connected to wider continental shelves of Myanmar and Thailand coasts in the east and the underlying rugged topography of the Andaman and Nicobar Islands to the west, with Sumatra and the Malacca Strait in the south. In the Andaman Sea, Wyrtki [22] documented the occurrence of various tidal constituents of periods related to semi-diurnal principal lunar tides (M2; 12.42 h), semi-diurnal principal solar tides (S2; 12 h), diurnal lunisolar tides (K1; 23.93 h), and diurnal principal lunar tides (O1; 25.82 h), though semi-diurnal tides are dominant year-round with the greatest amplitudes during April and November [17,18,23,24]. Rizal et al. [6] studied the general circulation in the Malacca Strait and Andaman Sea using the HAMburg Shelf Ocean Model (HAMSM) and discussed that this area is influenced by the dominant semi-diurnal tide (M2: 12.42 h). The previous researchers [24] reported higher-amplitude (>2.0 m) semi-diurnal tides (M2, S2, and N2) in the Gulf of Martaban, the northeastern Andaman Sea, and also higher-amplitude (>2.0 m) diurnal tides (K1, O1) in the Malacca Strait, north of the Sumatra coast; thus, tidal amplitudes vary throughout the Andaman Sea, usually between 0.60 m and 2.0 m.

There are several studies on the tidal characteristics in the BoB and Andaman Sea involving their propagation, amplitude, and phases of major tides (semi-diurnal, diurnal) using sea level data at coastal stations [25], observations [18,23], and model data [6,17,24,26] mainly using temperature data. Mohanty et al. [18] studied the energetic estimates of the barotropic and baroclinic semi-diurnal ITs in the Andaman Sea using MITgcm model simulations and observed in situ data at the BD12-moored buoy in the central Andaman Sea and reported that the ITs are mainly generated north of the Sumatra coast, south of Car Nicobar Island, and north of Andaman Island. Previous researchers [17,27] analyzed the sea surface height and temperature gradients of ITs.

Recently, Subrahmanyam et al. [27] utilized the National Aeronautics and Space Administration’s (NASA’s) high-resolution (1/48° or 2.3 km and hourly) Estimating the Circulation and Climate of the Ocean (ECCO) model estimates of salinity data from November 2011 to October 2012 for the study of ITs in the BoB. These hourly data are advantageous over daily or even three-hour sampling for the studies of IWs and ITs. Previously, the ECCO estimates were used for identifying sub-mesoscale patterns with short-term ocean processes [28]. Though the ECCO model provides global simulations, the researchers [27] extracted the data only for the BoB and Andaman Sea, keeping in mind the focus of their investigations. We feel that an even finer resolution (than that of ECCO’s high resolution) of sea surface salinity (SSS), like that of sea surface temperature (SST), is not essential as it would lead to more noise because meso-scale processes such as evaporation (E), precipitation (P), freshwater discharge (R) from rivers, and advection by horizontal currents are involved in surface salinity changes.

These meso-scale processes are affected by the episodic disturbances of strong surface winds during the seasonal northeast monsoon in winter (December–February) and the southwest monsoon in summer (June–September), and also affect the depth variations in the mixed layer and thermocline/pycnocline layers [6,29,30,31]. Net freshwater flux (P+R-E) is a common contributor to the changes in salinity and hence to density fluctuations on seasonal or interannual scales [32]. In this study region, the Andaman Sea, the Irrawaddy River provides freshwater input and affects the SSS and surface layer salinity as well [32,33]. Varkey et al. [33] reported the climatological annual mean Irrawaddy River runoff as 13,020 m³/s and the seasonal mean runoff volumes. Latrubesse et al. [26] mentioned that the 15-year mean (2000–2015) maximum of Irrawaddy River discharge for August was 29,800 m³/s from observations. The annual mean discharge decreased from 15,440 m³/s in 2010 and 2011 to 13,900 m³/s in 2012. These authors also presented the daily highest Irrawaddy River discharge as 39,760 m³/s in 2011 and 38,210 m³/s in 2012 (our present study period). From this, we can see that the observed annual mean, maximum discharge, and the year-to-year variability in Irrawaddy River discharge in recent years (covering the 2011–2012 period) are higher than those of climatological river discharge. A higher SSS (31.8 psu) occurs in June in the northern Andaman Sea, prior to the southwest monsoon, while the minimum SSS (27.5 psu) occurs in October due to Irrawaddy River discharge [22]. In the southern Andaman Sea, the minimum SSS (31.9 psu) occurs in November, caused by advection of waters from the northern Andaman Sea, and the maximum SSS (32.8 psu) occurs in May, prior to the southwest monsoon, with an annual average SSS of 32.4 psu [22,30,32].

Utilizing a time series of observed data at the BD12-moored buoy (10.5°N, 94°E) location during March 2014–March 2018, Ashin et al. [32] studied the upper ocean variability in the central Andaman Sea and presented the depth–time sections of observed salinity in the upper 120 m, wherein narrow bands of high-salinity waters rose to the surface (1 m depth) from subsurface depths (halocline) in many instances. These researchers [32] reported several freshening events at the BD12-moored buoy location resulting from the spread of Irrawaddy River discharge and surface freshwater flux (P-E) under the influence of surface circulation during the southwest monsoon and its subsequent period from August 2016 to January 2017 and August 2017 to January 2018. These freshening events lasted over 5 days to 25 days and the associated decrease in SSS was around 1 psu to 2.5 psu, leading to large horizontal salinity gradients at the sea surface in SMAP SSS maps [32]. Similar freshening events with low SSS also led to the formation of a layer of strong salinity stratification, and the associated vertical profiles of the computed Brunt–Väisäla frequency (N, cph) at the BD12 location during 5–25 December 2011 showed a higher peak of N (14 cph, cycles per hour) at 50–75 m depth [18]. In a recent study [27], the profiles of the computed N using the observed temperature and salinity data in November 2011 and April 2012 at the same BD12-moored buoy location showed a maximum N value (10–11 cph) at a shallow depth of 20 m within the halocline formed due to salinity stratification and a secondary maximum of 12.5 cph at a 100 m depth within the thermocline. Yadidya et al. [34], in their study on ITs in the Andaman Sea during March 2017 to February 2018 using observed data at the BD12-moored buoy location, pointed out that the Brunt–Väisäla frequency (N, cph) computed using varying salinity, while keeping temperature constant, shows dominant salinity stratification in the upper layers (30–50 m depth) during the southwest monsoon and subsequent period (July–February), and the temperature variability (while salinity is kept constant) influences the stratification below a depth of 50 m. These researchers [34] also noted the presence of a double pycnocline in all seasons and the computed profiles of N show two peaks, one in the halocline at 30–50 m depth during July–February, and the other peak at a 75–100 m depth in the thermocline.

From the above, we see that the near-surface salinity in the Andaman Sea is very much influenced by the seasonal freshwater flux (R+P-E), and as a result, a halocline is developed in the upper ocean due to salinity stratification [32,33]. In the present study, using the observed salinity and temperature data at the BD12-moored buoy location in the central Andaman Sea, monthly mean profiles of temperature, salinity, and the computed density and Brunt–Väisäla frequency (N, cph) in the upper 200 m are presented for November 2011, May 2012, July 2012, and October 2012 (Figure 1a–d). From Figure 1a–d, one can notice warmer and saline waters in November and May in the upper 80 m and relatively colder and less saline waters in July and October. A shallow pycnocline is present at a 45 m depth and a deeper pycnocline at 100 m and correspondingly, the profiles of N show its first maximum within 50 m due to the presence of a halocline (and hence a shallow pycnocline) and the second maximum at 100 m is due to a thermocline (a seasonal pycnocline).

It will be interesting to investigate whether this near-surface layer salinity stratification in the Andaman Sea plays any role on the surface signatures of the propagating ITs at depth, and whether the presence of both a halocline and thermocline make any distinction in the propagation of ITs of different periods. In this study, we have attempted to address these with a focus on the surface attributes of ITs in the Andaman Sea. For this purpose, we use NASA’s high-resolution (in space and time) ECCO near-surface salinity estimates for the period of November 2011 to October 2012 (same data period as was used in [27] for the BoB) together with high-resolution observed salinity and temperature data at the BD12-moored buoy for the same period in the Andaman Sea. The objectives of this study are as follows: (1) to extract the semi-diurnal and diurnal ITs from the hourly ECCO estimates of salinity at a 1 m depth and from the observed salinity and temperature data at the BD12-moored buoy and at RAMA mooring with a specified bandpass filtering technique [27], (2) subjecting the filtered time series data to a continuous wavelet power spectrum and 2D–FFT spectral analysis as that described in [27], (3) to understand whether the salinity stratification in the upper ocean plays any role on the surface impressions of the propagating semi-diurnal and diurnal ITs at depth, and (4) to determine the characteristics of the semi-diurnal and diurnal ITs. This study is structured as follows. In Section 2, we briefly describe the data and methodology. Section 3 provides the results of our research analyses of the detection and characteristics of ITs. Section 4 gives a brief discussion and Section 5 states the conclusions of this study.

2. Data and Methods

2.1. ECCO Estimates

NASA’s high-resolution (1/48° or 2.3 km and hourly) ECCO model (https://ecco-group.org (accessed on 29 March 2020)) project’s MITgcm (https://mitgcm.org (accessed on 29 March 2020)) simulation LLC4320 (available through https://data.nas.nasa.gov/ecco/data.php (accessed on 29 March 2020)) is used in this study. The KPP scheme was used for the ECCO LLC4320 simulations, but the non-local transport term was turned off. This model’s bottom topography was derived from Smith and Sandwell v14.1 [35] and IBCAO v2.23. LLC4320 refers to the latitude–longitude polar cap (LLC) grid at a 4320 resolution along each common face direction such as one-quarter of the Earth’s circumference at the Equator with 4320 points every 90° at this resolution [36,37]. Details on the description of ECCO estimates can be found in [27]. ECCO’s surface level thickness is 1 m, and this is considered as the ECCO near-surface salinity or ECCO SSS. In this study, we have used the available-on-hand hourly ECCO salinity at a 1 m depth only (no subsurface 3D data on temperature, salinity, and currents) for a one-year period from 1 November 2011 to 31 October 2012. This study period was chosen as it is the only temporal period for which ECCO was run with hourly 1/48° resolution as a precursor for the NASA Surface Water Topography mission (SWOT), which was launched on 16 December 2022. These ECCO estimates resolve ITs and sub-mesoscale dynamics. The one-hour temporal resolution was chosen intentionally to increase the stability limit (guided by the combination of staggered time stepping and tracer advection schemes) related to the speed of ITs [38], which gives us additional confidence in using this dataset for the study of ITs in the BoB [27] and in this study.

2.2. Observations

We used the NOAA’s Blended Seawinds dataset that has synthesized multiple satellite observations since June 2002. Wind data are provided at daily intervals with a 0.25° gridded spatial resolution, and we used the wind data for the duration of the ECCO model simulation. The blending data fills in spatiotemporal data gaps between each source. The research delayed mode product from the wind directions comes from the NCEP-DOE Reanalysis 2 product, while the near-real-time products use the ECMWF weather predictions [39].

Satellite surface salinity data were obtained from the European Space Agency’s (ESA) Soil Moisture and Ocean Salinity (SMOS) mission and NASA’s Aquarius mission. We used the SMOS surface salinity version 5.0 at Level 3 (as detailed in Boutin et al. [40]) with a spatial resolution of 25 km x 25 km. We also used NASA’s Jet Propulsion Laboratory (JPL), which produced Aquarius Combined Active-Passive (CAP) surface salinity version 5.0 at Level 3 (as detailed in [41]) at a spatial resolution of 1° × 1° for our study period, and we obtained this Aquarius salinity from the Physical Oceanography Distributed Active Archive Center (PO.DAAC).

We used the NOAA–Pacific Marine Environmental Laboratory (PMEL) (https://www.pmel.noaa.gov/gtmba/pmel-theme/indian-ocean-rama (accessed on 14 April 2020))-provided RAMA mooring [42] observed hourly salinity data at 1 m below the surface at 12°N, 90°E for the same study period as that covered by the ECCO estimates.

We used the same high-resolution observational data of temperature and salinity at various depths at the BD12-moored buoy location (10.5°N, 94°E) in the central Andaman Sea [23,43,44,45] as those used and described in [27]. These observed data were collected using the self-contained Seabird-MicroCAT SBE37 sensors for conductivity–temperature-depth at different depths starting from 5 m, 10 m, 15 m, 20 m, 30 m, 50 m, 75 m, 100 m, and 200 m depths. While scrutinizing the data, doubtful salinity data at 5 m from 1 November 2011 to 30 April 2012 were discarded from our analysis. These observed data were acquired by the National Institute of Ocean Technology (NIOT), India, and distributed through the Indian National Centre for Ocean Information Services (INCOIS), India, through their service portal (https://incois.gov.in/portal/datainfo/mb.jsp (accessed on 14 September 2021)).

2.3. Methodology

To understand the variability in ITs and their characteristics using ECCO salinity in the Andaman Sea, we selected three boxes, as outlined in Figure 2a—one box (A: 13°N–15°N, 96°E–98°E) was on the outer shelf of Gulf of Martaban, off the Myanmar coast, in the northeastern Andaman Sea; the second box (B: 9°N–11°N, 94°E–96°E) was in the central Andaman Sea, closer to the Andaman Islands; and the third box (C: 7°N–9°N, 96°E–98°E) was in the southeastern Andaman Sea off the Thailand coast. During the northeast monsoon season (November–February) (Figure 2a–c) and the following southwest monsoon season (June–September) (Figure 2d–f), the Irrawaddy River discharge enters the northern Andaman Sea mostly through the eastern Gulf of Martaban and the box A region. The seasonal reversal of winds during the northeast monsoon (Figure 2a–c) and southwest monsoon (Figure 2d–f) and the associated seasonal reversal of surface currents exchange the waters between the BoB and the Andaman Sea through the Preparis Channel, the Ten Degree Channel, and the box B region. Also, the waters from the BoB and the southern Andaman Sea are exchanged through the Six Degree Channel and the waters from the Malacca Strait enter the southern Andaman Sea where the box C region is selected. The choice of these boxes is also based on regions of high internal solitary wave activity as reported by Jensen et al. [25] and Apel et al. [46].

As we are interested in studying the IT characteristics in the Andaman Sea and their variability in box A, box B, and box C, the hourly time series of ECCO salinity estimates at a 1 m depth are subjected to fourth-order recursive Butterworth 11–14 h bandpass filtering and 22–26 h bandpass filtering directly to the raw ECCO salinity estimates to extract the signals of semi-diurnal and diurnal ITs, as that applied in [27]. Earlier studies reported the dominance of semi-diurnal tides and diurnal tides in the Andaman Sea [18,22,23,24,25].

The bandpass filtering procedure, as described in [27], is also applied to the observed data sets at the BD12-moored buoy (10.5°N, 94°E location) in the Andaman Sea and at the RAMA-moored buoy (12°N, 90°E location) in the eastern BoB. This type of filtering is commonly used, as evidenced in many previous studies in this region [27,47,48,49,50] and is permitted for an isolated analysis of ITs [51,52]. This bandpass filter was applied twice, once forward in time and once backward in time for the full time series duration to reduce edge effects related to phase shifts [53]. With larger-period events or insufficient temporal sampling, a cone of influence (COI) signifies regions where the oscillation is poorly resolved due to edge effects. However, when a full year of hourly data is used to study periods less than 27 h, the sampling frequency is high enough that the COI is negligible.

A continuous wavelet analysis provides additional insight regarding the timing, frequency, and periodicity of the identified signals [27]. Cross-wavelet power spectra and continuous wavelet transforms are more useful for extracting individual features rather than a discrete wavelet transform [54]. As described in Morlet [55], a continuous wavelet transform is expressed as

$$\mathsf{\psi }\left(\mathsf{\eta }\right)={\mathsf{\pi }}^{-1/4}{\mathrm{e}}^{\mathrm{i}{\mathsf{\omega }}_0\mathsf{\eta }}{\mathrm{e}}^{{\displaystyle \frac{-1}{2}}{\mathsf{\eta }}^2}$$

(1)

where ω₀ is the dimensionless frequency and η is dimensionless time [54,56].

A Pearson product–moment correlation coefficient analysis was applied to compute the lead–lag and correlation relationships between the filtered signals in boxes A, B, and C (see Figure 2 for locations) following the methodology in Paris et al. [57] and Trott et al. [58]. Power spectral density was computed using Welch’s overlapped segment averaging estimator [59,60] to compute power at each frequency. Welch’s approach applies a modified periodogram to overlapping segments and then averages these estimates [60]. This approach results in uncorrelated estimates of true power spectral densities and averaging results in reduced variability [60]. An additional benefit is the protection against a loss of information due to windowing because of the presence of multiple overlapping segments [59]. A two-dimensional fast Fourier transform (2D FFT) was applied to the time series of filtered ECCO salinity estimates [27] along the central longitudinal (latitudinal) transects in boxes A, B, and C to estimate the IT parameters (zonal wavenumber (k_x), meridional wavenumber (k_y), resultant wavenumber (k = SQRT(k_x² + k_y²), wavelength, frequency, period, and phase speed). This technique follows the methodology described in Belonenko et al. [61] and Wang et al. [62].

Following the study of Ashin et al. [32] on the upper ocean variability in the Andaman Sea based on observations at the BD12 location, we computed the mixed-layer depth (MLD) as the depth where the density is greater than 0.125 kg/m³ from the surface density. The isothermal layer depth (ILD) is also computed with a temperature criterion as the depth where the temperature is 0.5 °C lower than the surface temperature [63].

3. Results

3.1. Spatial Variation in Sea Surface Salinity from ECCO, SMOS, and Aquarius

High-resolution ECCO salinity estimates during November 2011–October 2012 are analyzed to identify ITs, their characteristics, and propagation direction in the Andaman Sea. We have taken up the comparison of high-resolution ECCO salinity variability with the available satellite-derived surface salinity from SMOS and Aquarius sensors, though these data sets are of coarser temporal and spatial resolution. Comparisons of the seasonal variation in surface salinity from ECCO, SMOS, and Aquarius for the northeast (or winter) monsoon (November 2011–February 2012) and southwest (or summer) monsoon (June–September 2012) are shown in Figure 2a–f. Various geographical settings of the Andaman Sea are shown in Figure 2d. Furthermore, boxes A, B, and C and the locations of the RAMA buoy and OMNI buoy are marked in Figure 2a. The seasonal mean NOAA Blended Seawinds surface wind vectors are overlaid on each map of seasonal surface salinity.

During the winter monsoon season, ECCO salinity distribution shows low-salinity waters in the eastern Andaman Sea in the Gulf of Martaban (Irrawaddy River delta), and high-salinity (32.5–33.0 psu) waters offshore of the southern Myanmar coast, west of the Andaman–Nicobar Islands and in the western Andaman Sea. High-salinity waters are also observed in the coastal region of Thailand due to coastal upwelling induced by northeasterly winds. The ECCO salinity distribution during the summer monsoon looks similar to that of the winter monsoon, but with more saline waters (33.0–34.0 psu) west of the Andaman–Nicobar Islands under the influence of eastward advection of Arabian Sea waters via the Southwest Monsoon Current (SMC, [31]). Very-low-salinity (29.5–30.5 psu) waters occupy the Gulf of Martaban delta and the adjacent Thai coast region. This freshening is due to the local summer monsoon precipitation over the Andaman Sea and the Irrawaddy River discharge [22]. Seasonal mean surface salinity spatial variation patterns in the SMOS salinity and Aquarius salinity (Figure 2b,c and Figure 2e,f) are similar to the ECCO salinity. Among the three boxes, box A lies in the northeastern Andaman Sea and registers very-low-salinity waters in association with the southwest monsoon precipitation and the highest daily Irrawaddy River discharge in 2011 and 2012 [26,27].

3.2. Spatial Variation in Weekly Averaged ECCO Salinity in Different Seasons

Figure 3 presents the weekly averaged spatial variations in ECCO salinity in May, August, and October 2012, with superposed boxes A, B, and C. In these weekly averages, the ECCO salinity over the shallow Gulf of Martaban is higher in May, relatively high in August, and shows reduced salinity in October. These relatively high-salinity waters can be attributed to the surface wind forced coastal upwelling [64] along the Myanmar coast and over the Gulf of Martaban and could be due to coastally trapped equatorial upwelling Kelvin waves [65]. Furthermore, these authors reported a more significant impact of upwelling at the sea surface with high-salinity waters due to the prevailing strong salinity stratification. In May, prior to the SW monsoon season, higher-salinity waters are present in the southern Andaman Sea and occupy boxes B and C (Figure 3a). In August, low-salinity waters along the Myanmar coast up to the central region are the result of horizontal advection of monsoonal discharge from the Irrawaddy River (Figure 3b) and by October, these low-salinity waters appear over a wider portion of the northeastern BoB and northeastern and central Andaman Sea regions, which occupy box A and reach up to box B, the BD12 buoy location, and box C (Figure 3c).

3.3. Spatial Variations in 11–14 h and 22–26 h Bandpass-Filtered ECCO Salinity

The 51 h high-pass filtered ECCO salinity attained notable highest minimum values in box A on 4 May 2012 (−0.116 psu), 7 September 2012 (−0.106 psu), and in box B and box C, the highest minimum salinity amplitude (−0.13 psu) occurred on 12 November 2011 and 6 April 2012 (Figure is not shown).

Spatio-temporal variations in 11–14 h bandpass-filtered ECCO salinity at a 1 m depth on the date of the highest minimum salinity amplitude, i.e., on 12 November 2011, are presented for six-hour intervals, i.e., at 00:00, 06:00, 12:00, and 18:00 (Figure 4a–d), and their six-hour differences between 00:00 of 12 November 2011 and 00:00 of 13 November 2012 are shown in Figure 4e–h. One can see bands of alternating positive and negative salinity amplitudes representing the possible surface imprints of semi-diurnal IT propagation.

The six-hour variation in bandpass-filtered salinity shows the typical pattern of longer bands and curved bands of alternating positive- and negative salinity amplitudes, and their change in 6 h intervals. In 6 h intervals, the positive bands of salinity are replaced by negative bands of salinity and the patterns of the bands are the same. In the next 6 h, these negative bands of salinity are once again replaced by positive salinity bands, like those at 00:00. This pattern of variations in the bands represents the surface imprints of semi-diurnal ITs (Figure 4a–d) propagating at depth as shown in Section 3.9. South of 12°N, the positive and negative salinity patches also change in 6 h intervals near the Nicobar Islands and north of the Sumatra coast (Figure 4a,b and Figure 4c,d). If the higher positive salinity band is considered as the leading edge of the propagating semi-diurnal ITs, it represents the crest of the near-surface imprint of the semi-diurnal ITs propagating at depth, while the higher negative salinity band represents the trough of these ITs. The smaller bands form the trailing of the large-amplitude progressing ITs. North of 10°N, the propagating IT period is about 12 h (as seen from the repetition of positive and negative bands in 6 h intervals). South of 10°N, the persistence of the same bands over 12 h and their change in the next 6 h suggests the presence of a 12 h period (semi-diurnal) for ITs, particularly near the generating source regions, the Nicobar Islands, and north of the Sumatra coast. Off the southern Thailand coast, the 6 h alternating bands of positive- and negative-salinity bands suggest that semi-diurnal ITs are approaching the coast [66,67].

In the northern Andaman Sea (north of 10°N), the patterns of positive (negative)-salinity amplitude represent the crests (troughs) of semi-diurnal ITs. Semi-diurnal ITs are seen reaching the Gulf of Martaban continental shelf from the 6 h differences in the filtered salinity (Figure 4e–h). As seen in the weekly averaged ECCO salinity maps for May, August, and October (Figure 3a–c), wherein relatively high-salinity waters are noticed over the Gulf of Martaban and attributed to the upwelling process [64,65], are also affected by the propagating ITs onto the shallow continental shelf break supporting the vertical mixing of shelf waters. At a given location, the band of the IT crest is replaced by the band of the IT trough in 6 h and hence, the 6 h salinity difference yields a large negative salinity band (e.g., northern Andaman Sea, Preparis Channel, etc., in Figure 4e). When the IT trough is replaced by its crest in 6 h, this gives rise to a large positive salinity band (adjacent to the Myanmar coast in Figure 4e). At times, a crest may be replaced by another crest or a trough by another trough in 6 h, then the 6 h salinity differences are minimal. The semi-diurnal IT troughs of low-salinity bands are conspicuous in the northern Andaman Sea on November 12 (Figure 4e–h). Specifically, one notices a negative salinity band at the outer shelf of the Gulf of Martaban, and across the Preparis Channel and in the open northern Andaman Sea (Figure 4e). This negative salinity band, again by the semi-diurnal IT, brings out low-salinity waters from the Gulf of Martaban into the interior Andaman Sea. The negative salinity band is replaced by the positive salinity band after 6 h (Figure 4f), and after 6 h, the pattern (Figure 4g) once again becomes the negative salinity band (Figure 4e). After another 6 h, the salinity difference pattern (Figure 4h) becomes similar to the previous 6 h (as seen in Figure 4g). These 6 ho salinity differences over a day (i.e., from 00:00 12 November to 00:00 13 November) suggest a dominant semi-diurnal IT in the high-resolution ECCO salinity data in the northern Andaman Sea and the southern Andaman Sea (Figure 4e,g and Figure 4f,h). In the southwestern Andaman Sea, the Great Channel, and north of the Sumatra region, semi-diurnal ITs originated around the Nicobar Islands and propagated into the interior southern Andaman Sea [19,21,67,68].

Figure 5a,b presents the spatio-temporal variations in 22–26 h bandpass-filtered ECCO salinity on 12 November at 12:00 and 13 November at 00:00, and the patterns of bands of positive salinity and bands of negative salinity on both the dates is almost the same in the northern Andaman Sea, north of 10°N. The 12 h difference in filtered salinity (12 November at 12:00 minus 12 November at 00:00) (Figure 5c) shows a patch of higher positive salinity at 10°N near the Nicobar Islands, the source region of IT generation. Each band of positive and negative salinity from the source region propagates toward the northern Andaman Sea and the Gulf of Martaban shelf region and toward the east. These patterns of bands are the leading edges of the propagating diurnal ITs, which are agreeable to those predicted from the model studies [19,68,69]. The next 12 h differences in filtered salinity (13 November at 00:00 minus 12 November at 12:00) (Figure 5d) show the opposite pattern of salinity bands in the northern Andaman Sea, while positive salinity bands persist in the southern Andaman Sea. However, north of the Sumatra coast, the pattern of salinity bands changes to positive from negative salinity in the 12 h salinity differences (Figure 5c,d), while over the Gulf of Martaban, positive salinity differences persisted for over 24 h (Figure 5c,d). This suggests that the diurnal tidal periods of ITs also are generated in the Nicobar Island region and propagate toward the southern Andaman Sea and toward the Thailand coast.

3.4. Continuous Wavelet Power Spectra of Bandpass-Filtered ECCO Salinity

In Section 3.3, we have inferred the presence and propagation of semi-diurnal ITs in the region north of 10°N and diurnal ITs in the southeastern Andaman Sea distinctly from the patterns of bands of positive and negative salinity amplitudes in the bandpass-filtered ECCO salinity (Figure 4 and Figure 5). To confirm these inferences, the box-averaged hourly time series of 11–14 h bandpass-filtered ECCO salinity for each of the three boxes (Figure 6a–c) were subjected to a continuous wavelet power spectral analysis (Figure 6d–f and Figure 6g–i). Wavelet power spectra for box A, in the northeastern Andaman Sea, confirm the dominance of higher wavelet power occurring during November 2011 and during June-October 2012 (Figure 6d) in association with the higher (±0.05 psu) salinity amplitudes (Figure 5a) and a higher wavelet power spectral peak (14 × 10⁻¹⁰ psu²·day) at semi-diurnal (2 cycles/day, 12.42 h) ITs (Figure 6g). For box B, in the central Andaman Sea, near the generating source region (closer to the Nicobar Islands), the ECCO salinity amplitudes are moderate (±0.015 psu) in November 2011 and April 2012 (Figure 6b). The continuous wavelet power spectrum and the associated wave power spectral peak (0.04 × 10⁻¹⁰ (psu)²·day) confirm the weaker signal of semi-diurnal IT propagation through box B (Figure 6e,h), compared to that for box A (Figure 6g). Interestingly, for box C, the ECCO salinity amplitudes of the semi-diurnal ITs are relatively high (±0.02 psu) in November 2011, January 2012, and April 2012 (Figure 6c). The continuous wavelet power spectrum shows higher values in these months (Figure 6f). The associated spectra confirm the existence of semi-diurnal ITs with moderate wave power (0.2 × 10⁻¹⁰ (psu)²·day).

Similarly, the box-averaged hourly time series of the 22–26 h bandpass-filtered ECCO salinity for each of the three boxes (Figure 7a–c) were subjected to a continuous wavelet power spectral analysis (Figure 7d–f and Figure 7g–i). The wavelet power spectra for box A, in the northeastern Andaman Sea, confirm the dominance of a higher wavelet power peak (3.5 × 10⁻¹⁰ (psu)²·day) at the diurnal (1 cycle/day, 24 h) ITs (Figure 7g) in correspondence with a higher wavelet power spectrum in November 2011, February 2012, May 2012, and October 2012 (Figure 7d) and higher ECCO salinity amplitudes (Figure 7a). For box B, in the central Andaman Sea, near the generating source region (closer to the Nicobar Islands), ECCO salinity amplitudes are high (±0.02 psu) only in April 2012 due to diurnal ITs and also the continuous wavelet power spectrum has a higher intensity in April 2012 (Figure 7e), giving rise to a weaker wave power peak (0.7 × 10⁻¹⁰ (psu)²·day) (Figure 7h) compared to the highest wavelet power spectral peak in box A (Figure 7g). In box C, the ECCO salinity amplitudes are large (±0.02 psu to ±0.03 psu) in December 2012 and April 2012, together with the continuous wavelet power spectrum intensities (Figure 7c,f) in association with the propagation of diurnal ITs through box C. The resulting wavelet power spectral peak of diurnal ITs attains the value of (1.9 × 10⁻¹⁰ (psu)²·day) (Figure 7i).

3.5. 2D–FFT Spectra of Bandpass-Filtered ECCO Salinity

Each category of box-averaged bandpass-filtered time series is further subjected to 2D–FFT in the wavenumber vs. frequency domain. Once the propagating barotropic tides (mode 1) interact with sloping shallow bottom topography (such as the Nicobar Islands, the Andaman–Nicobar Island chain or the Greater Channel or shallow continental shelf slope region of the Andaman Sea), baroclinic ITs are generated at the density interface layer (a pycnocline due to haloclines and thermoclines) and propagate in all directions. Surface winds and air–sea interactions would also generate near-inertial period IWs [70], and they propagate at the base of the mixed layer that falls in the halocline. These higher frequency IWs are not considered here due to the specific selection of the bandpass filtering procedure adopted here.

In each box domain, along the central latitude, ITs propagate eastward/westward, and similarly, along the central longitude, they propagate northward/southward from the center of the box domain. Accordingly, positive zonal (meridional) wavenumbers denote eastward (northward) radiating ITs, and negative zonal (meridional) wavenumbers denote westward (southward) radiating ITs. For box A, box B, and box C, the central latitudes are 14°N, 10°N, and 8°N, respectively, and the central longitudes are 97°E, 95°E, and 97°E, respectively. The 2D–FFT plots were prepared for both semi-diurnal and diurnal ITs using the respective bandpass-filtered ECCO salinity time series data. We selected the wavenumber on the X-axis corresponding to the given frequency (or semi-diurnal and diurnal period) on the Y-axis and the highest spectral density value. It is shown by vertical dashed lines for clarity in Figure 8 and Figure 9. Along the central longitude or latitude, the total length of the box domain is 3.0° and from the center of the box, the distance is 1.5° (or 166.5 km) on the north side/south side and 1.5° (166.5 km) on east side/west side. This distance in degrees is taken as the wavenumber, and along the central longitude, it is the meridional wavenumber; along the central latitude, it is the zonal wavenumber. From these plots, corresponding to the given frequency (semi-diurnal or diurnal periods) and having the maximum spectral energy density value, we picked the zonal wavenumber (k_x) and meridional wavenumber (k_y) values for the estimation of the resultant wavenumber (k = SQRT(k_x² + k_y²)). We chose the k_x and k_y values in the same quadrant. Using these k and frequency values, other parameters of ITs, namely the wavelength, period, and phase speed, were estimated. For each box, the respective IT parameters for each category are given in

Table 1. Estimates of the semi-diurnal internal tide parameters of wavelength, frequency, period, speed, and the dominant propagation direction for box A, box B, and box C in the Andaman Sea. The unit for wavenumbers is 1/degree (1 degree = 111 km). Positive (negative) zonal wavenumbers mean eastward (westward) radiation of propagating ITs. Positive (negative) meridional wavenumbers mean northward (southward) radiation of propagating ITs. This table is related to Figure 8.

Box	Wavenumber (1/Degree)	Wavelength (km)	Frequency (1/Day)	Period (Hour)	Phase Speed (m/s)	Propagation Direction in the Box Domain
A	2.623	42.318	1.959	12.251	0.960	Eastward and Westward
B	8.393	13.225	1.794	13.378	0.275	Northward
C	3.410	32.551	1.959	12.251	0.738	Eastward and Westward

and

Table 2. Estimations of the diurnal internal tide parameters of wavelength, frequency, period, speed, and the dominant propagation direction for box A, box B, and box C in the Andaman Sea. The unit for wavenumbers is 1/degree (1 degree = 111 km). Positive (negative) zonal wavenumbers mean eastward (westward) radiation of propagating ITs. Positive (negative) meridional wavenumbers mean northward (southward) radiation of propagating ITS. This table is related to Figure 9.

Box	Wavenumber (1/Degree)	Wavelength (km)	Frequency (1/Day)	Period (Hour)	Phase Speed (m/s)	Dominant Propagation Direction from the Box Domain
A	2.953	37.589	1.041	23.066	0.453	Southwestward
B	3.158	35.149	1.046	22.956	0.425	Northeastward
C	5.193	21.375	0.939	25.573	0.232	Southwestward

.

3.6. Characteristics of Semi-Diurnal ITs for the Boxes A to C

In the case of semi-diurnal ITs, the 11–14 h bandpass-filtered time series of ECCO salinity were subjected to 2D–FFT and the corresponding spectra for boxes A to C are shown in Figure 8. In box A, spectral energy density is higher at 2 (psu/degree)² in the zonal wavenumber vs. frequency domain compared with almost negligible spectral energy density in the meridional wavenumber vs. frequency domain. That means the ITs are radiating mostly in the zonal direction (east–west) in the domain of box A. In Figure 8a, it is seen that the harmonics of spectral energy density are radiating dominantly both eastward and westward from the center of box A. For this reason, we consider the zonal wavenumber (k_x, 2.6 degree⁻¹) to estimate the semi-diurnal IT characteristics in the northeastern Andaman Sea, which are given in Table 1. The wavelength of the semi-diurnal IT, dominantly westward, is about 42 km, and the phase speed is 0.96 m/s in box A. Compared to box A, the spectral energy density in box B for the semi-diurnal IT is fivefold less (Figure 8b). It is seen that in box B, relatively higher spectral energy density is associated with the meridional wavenumber (k_y) compared to that of the zonal wavenumber (k_x). Considering the k_y as 8 degree⁻¹, the estimated wavelength and phase speed are 13 km and 0.28 m/s at the resultant k value (8 degree⁻¹), which are far lower than those of box A (Table 1), and the IT is radiating northward in the box B domain in the central Andaman Sea. In box C, in the southeastern Andaman Sea, the spectral energy density is tenfold less (Figure 8c) than that for box A and two times higher than that for box B. The spectral energy radiates eastward/westward from the center of box C as weaker spectral energy is associated with the meridional wavenumber. Considering the k_x as −3 degree⁻¹ with a higher spectral energy density for box C, the estimated wavelength and phase speed for the resultant k value (3 degree⁻¹) are 33 km and 0.74 m/s, respectively. The eastward radiating semi-diurnal ITs from the center of box C reach the Thailand coast shelf region and break over the shelf. The westward radiating ITs from the box C domain reach the Andaman−Nicobar Island chain.

From Table 1, it is seen that the average phase speed of the semi-diurnal ITs in the Andaman Sea from the three boxes A, B, and C is around 0.66 m/s. This is in the range reported [15] from Envisat ASAR imageries where the average phase speed (0.56–0.67 m/s) was retrieved for a semi-diurnal IT. These authors [15] also reported that the linear theory provided theoretical values for the phase speed and wavelength for the first four vertical modes of semi-diurnal ITs. For the barotropic mode 1 semi-diurnal IT, the phase speed is 2.37 m/s and its wavelength is 106 km. Our estimates of phase speeds and wavelengths for semi-diurnal ITs (Table 1) are closer to those reported under the linear theory [15]. The estimated relatively higher speed and wavelength for the semi-diurnal ITs for box A, in the northeastern Andaman Sea, are closer to theoretical mode 2, while estimates for box C, in the southeastern Andaman Sea, agree with the theoretical (linear theory) vertical mode 3. However, in the central Andaman Sea (box B), these estimates are lower than those for vertical mode 4. Therefore, our study suggests the possible existence of higher-mode baroclinic semi-diurnal ITs in the central Andaman Sea.

3.7. Characteristics of Diurnal ITs for Boxes A to C

In the case of diurnal ITs, the 22–26 h bandpass-filtered time series of ECCO salinity were subjected to 2D–FFT and the resultant spectra for boxes A to C are shown in Figure 9a–f. Among the three boxes, spectral energy density is higher at 0.1 (psu/degree)² in box A, fivefold less in box B, and tenfold less in box C for this category (Figure 9a–f). In box A, the harmonics of spectral energy density are seen radiating dominantly in the zonal direction from the center of the box at a frequency of 1 cycle/day, i.e., a 24 h period (Figure 9a). To estimate the parameters of diurnal ITs, we chose −2.088 as k_x and k_y (marked by dashed vertical lines in Figure 9a,d) and the estimated values are shown in Table 2. For box A, the resultant wavenumber is 2.953 degree⁻¹ and the wavelength is 38 km, and the phase speed is 0.45 m/s (Table 2, for box A). From the center of box B, the diurnal ITs appear to radiate dominantly in the meridional direction. For box B, we chose k_x and k_y to be 2.098 and 2.361 (marked by vertical dashed lines in Figure 9b,e); the corresponding diurnal IT parameters are a wavelength of 35 km and a phase speed of 0.42 m/s (Table 2, for box B); and the dominant direction of propagation is northeastward. In box C, the spectral energy density associated with the diurnal ITs is very weak and the estimated parameters and inferred directions are to be viewed cautiously. The diurnal ITs appear to radiate both zonally and meridionally from the center of box C. For box C, the chosen k_x and k_y are -3.672 (marked by vertical dashed lines in Figure 9c,f) and the estimated parameters are a 21.4 km wavelength and a 0.23 m/s phase speed. From the center of box C, the diurnal ITs propagate dominantly in the southwestward direction in the southeastern Andaman Sea. For diurnal ITs, we could not compare our estimates of phase speed and wavelength (Table 2) as there are no theoretical estimates from the linear theory. The average phase speed of diurnal ITs in the Andaman Sea from the three boxes A, B, and C is around 0.37 m/s.

3.8. Cross-Wavelet Analysis between the Filtered ECCO Salinity Data among the Three Boxes

Previous studies [17,18,19,69,71] revealed that semi-diurnal and diurnal ITs are generated in the shallow topographic region of the Andaman−Nicobar Island chain around 10°N. These studies show that once these ITs are generated in this region, they propagate into the interior Andaman Sea. In this study, following the methodology presented by Grinsted et al. [54], we examined this feature through the localized correlations of the wavelet energy between the box-averaged time series of bandpass-filtered ECCO salinity for the pair of box B and box A and the pair of box B and box C for each case of semi-diurnal and diurnal ITs. Box B is located closer to the generation site of ITs in the Andaman−Nicobar chain region. Cross-wavelet analyses between box B and box A and between box B and box C reveal the timing and magnitude of signal coherence between the filtered signals.

Figure 10a represents the wavelet coherence plots of localized correlation between box B and box A and between box B and box C in the case of semi-diurnal IT propagation. In this figure, arrow centers indicate the period at which they are positioned, and our 12 h period of interest for semi-diurnal ITs is shown by the white dashed horizontal line. Black arrows indicate phase relations of the second time series to the first time series by pointing right (in phase), up (time series 2 leads 1), left (out of phase), and down (time series 1 leads 2). From the region of higher correlations (red shading) that cross the white dashed line, we see the in-phase coherence in November 2011, January 2012, April 2012, and July 2012 (with arrows pointing upward and oriented right; box A time series leads box B time series), indicating that a semi-diurnal IT is propagating from box A (northeastern Andaman Sea), with its source located over the Gulf of Martaban shelf region, toward the domain of box B (central Andaman Sea). However, in-phase coherence with a higher correlation is also noticed in August 2012 and October 2012 with the semi-diurnal IT propagating from the source region of the Andaman−Nicobar Island chain (Figure 10a) through the domain box B to box A (as is evident with the arrows pointing downward and oriented right; box B time series leads box A time series).

Similarly, the time series of localized correlations of wavelet coherences between box B and box C in the case of semi-diurnal ITs is shown in Figure 10b. One can see higher correlations with in-phase coherence (with arrows pointing downward and oriented right crossing the 12 h period white dashed line; box B time series leads box C time series) in November 2011, February 2012, April 2012, May 2012, July 2012, September 2012, and October 2012, indicating the propagation of semi-diurnal ITs from the generating source region of the Andaman−Nicobar Island chain through the central Andaman Sea (box B) to the southeastern Andaman Sea (box C).

Wavelet coherence plots of localized correlation between the box-averaged time series of 22–26 h bandpass-filtered ECCO salinity for the pair of box B and box A and for the pair of box B and box C are shown in Figure 11. Also in this figure, arrow centers indicate the period at which they are positioned and our period of interest of 24 h for diurnal ITs is shown by the white dashed horizontal line. Black arrows indicate phase relations of the second time series to the first time series by pointing right (in phase), up (time series 2 leads 1), left (out of phase), and down (time series 1 leads 2). One can see in-phase coherence with higher correlations in November 2011, December 2011, April 2012, July 2012, and October 2012 (with arrows pointing downward and oriented right; box B time series leads box A time series), indicating the propagation of diurnal ITs from the source region of the Andaman–Nicobar Island chain through the box B domain in the central Andaman Sea toward the domain of box A in the northeastern Andaman Sea (Figure 11a). However, in-phase coherence with a higher correlation is also seen between box B and box A during February–March 2012, May 2012, June 2012, and occasionally in August 2012 and October 2012 (with arrows pointing upward and oriented right; box A time series leads box B time series), indicating the diurnal ITs propagate from the northeastern Andaman Sea to the central Andaman Sea (Figure 11a). This is consistent with the inferred propagation direction (northeast–southwest) of diurnal ITs in the box A domain. It is to be mentioned that the direction of propagation of ITs appears to be linked to the seasonal salinity stratification and circulation in the region between box A and box B [34].

In the case of diurnal ITs’ propagation from the box B domain to the box C domain, in-phase coherence with higher correlations is seen in November–December 2011, January 2012, March–April 2012, and May–June 2012 (Figure 11b). Occasional in-phase coherence with a higher correlation is seen in October 2012 between box C and box B (Figure 11b).

3.9. Inferences from BD12 OMNI Buoy Time Series Salinity and Temperature Observations

The time series of 11–14 h bandpass-filtered and 22–26 h bandpass-filtered observed salinity and temperature data at the BD12-moored buoy at various depths in the upper 200 m is analyzed and presented in this section. Figure 12a presents the time series of the 11–14 h bandpass-filtered observed salinity at a 5 m depth (blue color) and the ECCO salinity at a 1 m depth (black color) for the period of May to October 2012. It is seen that the amplitudes of filtered ECCO salinity at a 1 m depth are in phase with and in the same range as that of the filtered observed salinity at 5 m in May and October. However, they are less than those of the observed salinity during June-–September (Figure 12a). This suggests that the variations in the filtered ECCO salinity at a 1 m depth are responding to propagating semi-diurnal ITs at depth. Figure 12b,c present the depth–time sections of the 11–14 h bandpass-filtered observed salinity and temperature in the upper 80 m during the study period of November 2011–October 2012. Superimposed on these depth–time sections are the six-hour averages of the MLD and ILD (see section c. Methodology for their computing method). The 11–14 h bandpass-filtered salinity and temperature show the narrow bands of salinity and temperature emanating from the halocline (black line, MLD variation) and thermocline (green line, ILD variation), respectively. It is interesting to note that the narrow bands in salinity reach closer to the surface compared to those in temperature (Figure 12b,c). The 11–14 h bandpass-filtered salinity structure shows the bands of salinity reach up to a 5 m depth from 1 May 2012 to 31 October 2012. During certain timings, these bands have not reached up to these shallow depths. Associated with the shallower MLD, coinciding with the halocline (Figure 12b,c), the amplitudes in ECCO salinity at 1 m are large, as evident in May, July, and October (Figure 12a), and a deeper MLD gives rise to smaller salinity amplitudes. The ILD is deep (>40 m depth) in May, June, July, and October (Figure 12b,c). A upward rise of high-salinity bands from subsurface depths is seen throughout the study period, but some narrow bands reach up to a 5 m depth on some occasions (Figure 12b). One can also notice that following the upward rising of these narrow bands, the MLD is deep (Figure 12b).

Large amplitude signals in temperature are centered at deeper depths and their upward extension is well seen below 20 m (Figure 12c). The ILD variations coincide with the higher amplitude salinity variations, i.e., halocline depth variations. From May to October, the MLD becomes shallow at around 20–30 m and the vertical salinity bands reach above a 20 m depth toward the surface. Associated with the semi-diurnal ITs, filtered observed salinity amplitudes are relatively higher at shallower depths, as seen from narrow salinity bands, compared to those of filtered observed temperature amplitudes, wherein higher amplitudes are at deeper depths (Figure 12b,c).

Figure 13 shows a detailed time series of the 11–14 h bandpass-filtered ECCO salinity (at a 1 m depth) superimposed with the 11–14 h bandpass-filtered observed salinity at a 5 m depth at the BD12 location during the selected shorter times. The filtered ECCO salinity amplitude variations and their pattern agree with that of the observed salinity amplitude variations. From May to October, observed salinity amplitudes are relatively higher than those of the ECCO salinity. Occasionally, when the ECCO salinity amplitudes are large, the observed salinity amplitudes are weaker, and vice versa. It is seen that larger amplitudes (±0.05 psu) of ECCO salinity occur during the second week of November (Figure 13a) and in the fourth week of January (Figure 13b). The filtered salinity amplitude variations in the ECCO salinity and the observed salinity at a 5 m depth are in phase in April–June 2012 and September–October 2012, but observed salinity amplitudes are large (Figure 13c,d). During this period of May to October, both the MLD and ILD are located at shallower depths. It can be understood that the upward rising salinity bands propagating through the halocline reach up to near-surface depths. This feature is also reflected in the observed salinity and the model estimated salinity. Thus, high temporal resolution in the model estimates of salinity variations is very much essential for the study of IWs, particularly ITs.

The time series of 22–26 h bandpass-filtered ECCO salinity at a 1 m depth and the BD12 buoy-measured salinity at a 5 m depth show higher salinity amplitudes in the observed salinity and weaker amplitudes in the ECCO salinity (Figure 14a). The depth–time sections of the bandpass-filtered observed salinity and temperature show lower amplitude signals (Figure 14b,c) compared to those of semi-diurnal tidal period variability in salinity and temperature (Figure 12b,c). These diurnal IT signals reach up to halocline depths (~20–40 m depth), wherein salinity amplitudes attain higher (±1 psu) magnitudes (Figure 14b) compared to those of temperature amplitudes (±0.75 °C) (Figure 14c). The 6 h averaged MLD and ILD variations superimposed on both the salinity and temperature sections (Figure 14b,c) show MLD variations between 20 m and 30 m, and the ILD variations are between 20 m and 50 m from May to October 2012 (Figure 14b,c). ILD variations are affected by the circulation patterns; a deeper (shallower) ILD is associated with anticyclonic (cyclonic) circulation patterns. When the ILD is deep, the amplitudes of both the ECCO salinity and observed salinity attain the same magnitudes.

The 22–26 h bandpass-filtered time series of ECCO salinity at a 1 m depth superimposed with the observed salinity at a 5 m depth at the BD12 buoy location for selected periods are shown in Figure 15a–d. In November 2011 and February 2012, the amplitudes of ECCO salinity are smaller (±0.02 psu) and are lower than those (±0.045 psu) corresponding to the semi-diurnal IT time series salinity (Figure 13a,b), wherein there is no observed salinity data for comparison. However, during May to October, the observed salinity amplitudes are larger than the ECCO salinity and both the time series are in phase (Figure 15c,d).

The computed wavelet power spectra for both the time series of 11–14 h bandpass-filtered and 22–26 h bandpass-filtered ECCO salinity and the observed salinity at the BD12 buoy location (top panel) and RAMA mooring location (bottom panel) are compared and shown in Figure 16a–d. The spectra show the peaks corresponding to the semi-diurnal period (2 cycles/day) and diurnal periods (1 cycle/day) both in the observations and ECCO model simulations. Though the spectral peak periods are coinciding in both the cases, the wavelet power spectral density of the ECCO salinity is weaker compared to that in the observations because of higher values of the bandpass-filtered observed salinity amplitudes.

The continuous wavelet power spectrum and the corresponding wave power vs. frequency plots examined for the time series of 11–14 h bandpass-filtered observed salinity data (Figure 17) and the 22–26 h bandpass-filtered observed salinity data (Figure 18) at the depths of 5 m, 10 m, and 20 m (in the halocline), and 50 m and 75 m (in the thermocline) reveal that the wavelet power and spectral peak values are reduced greatly at 5 m in the halocline from those at 50 m, indicating that the impact of salinity stratification (halocline) impeding the vertical lifting of the crests of semi-diurnal and diurnal ITs from the thermocline depths to the surface (Figure 17 and Figure 18). The signals of higher wavelet power for semi-diurnal ITs reach up to a 20 m depth in November, January, May, and September–October (Figure 17e), and further upward up to a 5 m depth between May and October 2012 but with reduced wavelet power (Figure 17a). Similarly, the magnitude of the spectral peak of wavelet power also decreased drastically at a 5 m depth (Figure 17b). We can expect a further decrease in wavelet power up to a 1 m depth, as noticed in the ECCO salinity (Figure 16a,c). Interestingly, the signals of peak wavelet power in the continuous wavelet power spectrum (Figure 18a,c,e,g,i) and the corresponding wavelet spectral peaks (Figure 18b,d,f,h,j) for diurnal ITs decreased from a 50 m depth (Figure 18g) to a 10 m depth (Figure 18c) and maintained the same trend up to a 5 m depth (Figure 18a,b). This suggests that the impact of semi-diurnal ITs and diurnal ITs reach up to 20 m depths, but the semi-diurnal ITs lose their strength drastically toward a 5 m depth, while the diurnal ITs maintain their strength up to 5 m depth in the halocline. This vital information is also seen in the vertical structures of bandpass-filtered observed salinity at the BD12 buoy (Figure 12b and Figure 14b) and supports the above inferences drawn from the analysis of the ECCO salinity and the impact of the halocline or salinity stratification hindering the vertical lifting of crests of propagating ITs at deeper depths. The high-resolution ECCO model estimating salinity at a 1 m depth could capture the signals of propagating ITs at depth (Figure 16a–d), but the associated wavelet power spectral density is lower than that associated with the observed salinity at a 5 m depth. The observed salinity also reveals a gradual reduction in wavelet power spectral density up to 5 m from thermocline depths, but the spectral density peaks associated with the diurnal IT at 10 m and 5 m depths are relatively higher than those of semi-diurnal ITs at these depths. This shows the impact of diurnal ITs at the sea surface at the BD12 buoy location in the box B domain in the central Andaman Sea, while the impact of semi-diurnal ITs is limited to 20 m. The signature of semi-diurnal ITs is not felt at the sea surface at the BD12 location and is not captured in the ECCO salinity at a 1 m depth. Thus, the signature of diurnal ITs is felt at the sea surface at the BD12 location and is captured in the ECCO salinity as well. Since the wavelet power density associated with the diurnal IT is small in the halocline, the amplitudes in the ECCO salinity are also weak. The same inferences of salinity stratification (due to the halocline) can be extended to the regions of box A and box C as well, wherein strong salinity stratification is expected.

4. Discussion

Subrahmanyam et al. [27] studied the propagation of ITs in the BoB by selecting specific regions in the Andaman Sea and BoB. In this study, we utilized the same datasets and conducted a similar analysis but focused exclusively on the Andaman Sea to understand the propagation and characteristics of the semi-diurnal and diurnal ITs in this region. We have also analyzed the observed salinity and temperature data from two locations, namely the BD12-moored buoy in the central Andaman Sea and the RAMA mooring in the eastern BoB. Our findings reveal that variations in ECCO salinity (1 m depth) compared well with skin salinity measurements from SMOS and Aquarius (Figure 2). However, in the northeastern Andaman Sea, off the Myanmar coast (box A), satellite-derived skin salinity maps indicate low-salinity waters because of combined influences of local freshwater flux (R+P-E) from in situ Irrawaddy River discharge (R), local precipitation (P), and local evaporation (E). The ECCO estimates are forced with climatological seasonal freshwater discharge from rivers and daily ERA5 data (P and E), as well as AVHRR SST.

The 6 h spatial variations in the 11–14 h bandpass-filtered ECCO salinity suggested first-hand information of progressing semi-diurnal ITs, both toward the northeast and southwest in the north Andaman Sea (north of 12°N) (Figure 4a–d), and eastward propagating semi-diurnal ITs off the southern coast of Thailand. These observations agree with those of Raju et al. [19,68], Yang et al. [66], and Nielsen et al. [67]. The weekly averaged ECCO salinity maps for the months of May, August, and October (Figure 3a–c) reveal the presence of relatively high-salinity surface waters, and we attribute the presence of these high-salinity waters prior to, during, and post-southwest monsoon months as due to the coastward propagating semi-diurnal ITs over to the shallow Gulf of Martaban shelf region that would lead to the vertical mixing of shelf waters besides the other upwelling processes [64,65] on longer time scales (wind forcing and coastally trapped Kelvin waves). These inferences about the presence and propagation of semi-diurnal ITs north of 10°N and diurnal ITs in the southeastern Andaman Sea are distinctly supported by the patterns of bands of positive and negative salinity amplitudes in the bandpass-filtered ECCO salinity (Figure 4 and Figure 5). This has been well supported by the box-averaged hourly time series of the 11–14 h bandpass-filtered ECCO salinity and the 22–26 h bandpass-filtered ECCO salinity for each of the three boxes (A, B, and C), the continuous wavelet power spectra, and the 2D–FFT spectra in the wavenumber vs. frequency domain.

The patterns in 12 h differences of filtered salinity variations (Figure 5c) confirm the source region of ITs near the Nicobar Islands. This also demonstrates the propagation of diurnal ITs from the source region toward the northern Andaman Sea in the Gulf of Martaban shelf region. These patterns of bands signify the leading edges of propagating diurnal ITs and agree with those predicted from the model studies [19,67,69]. Additionally, we notice the propagation of diurnal ITs from the source region of Nicobar Islands toward the southern Andaman Sea and the Thailand coast (Figure 5c,d).

In the case of semi-diurnal ITs (Figure 8), in box A, we see these ITs are radiating mostly in the zonal (east–west) direction. In the northeastern Andaman Sea (Table 1), the semi-diurnal ITs propagate westward in the box A domain with estimated characteristics of a 42 km wavelength and a phase speed of 0.96 m/s. These ITs radiating westward reach the northern Andaman Islands. The eastward radiating semi-diurnal ITs from the box A domain propagate with the same speed and reach the Myanmar shelf region (or the Gulf of Martaban), where they would break over the shallow region and affect the mixing processes there, as is supported in Figure 3a–c. In the box B domain, semi-diurnal ITs radiate northward, with an estimated wavelength of 13 km and phase speed of 0.28 m/s. These estimates are lower compared to those for box A. In box C, spectral energy is seen radiating in both eastward and westward directions from the center of box C and their estimated wavelength and phase speed are 33 km and 0.74 m/s, respectively. These estimates are closer to those of box A. The eastward radiating semi-diurnal ITs reach the Thailand coast shelf region and would break over the shelf.

In the case of diurnal ITs (Figure 9), within the box A domain, the spectral energy density radiates dominantly in the zonal direction and the estimated diurnal IT characteristics (Table 2) are a wavelength of 38 km and a phase speed of 0.45 m/s. This phase speed is significantly lower than the semi-diurnal ITs. However, the wavelengths of the semi-diurnal and diurnal ITs are comparable (Table 1 and Table 2). These observations align with those reported earlier [69,71]. From the center of box B, diurnal ITs appear to radiate dominantly in the northward direction with a propagation phase speed of 0.42 m/s and a wavelength of 35 km, which are closer to those of semi-diurnal ITs in box B (Table 1). Similarly, in box C, the diurnal ITs’ estimated characteristics are a wavelength of 21.4 km and a phase speed of 0.23 m/s (Table 2).

Cross-wavelet analyses between box B and box A and between box B and box C for the propagation of semi-diurnal ITs and diurnal ITs reveal in-phase coherence with a higher correlation in some months (Figure 10a,b and Figure 11a,b). This implies that the semi-diurnal ITs and diurnal ITs propagate from the source region of the Andaman–Nicobar Island chain through the box B domain toward the northeastern Andaman Sea (box A) and toward the southeastern Andaman Sea (box C). It should be noted that the direction of IT propagation seems to be linked to seasonal salinity stratification and circulation in between box A and box B [34].

The continuous wavelet power spectrum and the corresponding plots of wave power vs. frequency constructed for the hourly time series of the 11–14 h bandpass-filtered and the 22–26 h bandpass-filtered observed salinity (at the BD12-moored buoy, box B) at different depths in the upper 200 m (Figure 17 and Figure 18) revealed that wavelet power and spectral peak values significantly reduce at a 5 m depth in the halocline compared to those at 50 m. This indicates the impact of salinity stratification (halocline) impeding the vertical lifting of the crests of semi-diurnal ITs and diurnal ITs from the thermocline depths to the surface. Signals of higher wavelet power for semi-diurnal ITs reach up to 20 m in depth in November, January, May, and September–October (Figure 17e), and further upward up to a 5 m depth between May and October 2012 but with reduced wavelet power (Figure 17a). Similarly, the magnitude of the spectral peak of wavelet power decreases drastically at a 5 m depth (Figure 17b). We can expect a further decrease in wavelet power up to a 1 m depth, as noticed in the ECCO salinity (Figure 16a).

Interestingly, the signals of peak wavelet power in the continuous wavelet power spectrum (Figure 18a,c,e,g,i) and corresponding wavelet spectral peaks (Figure 18b,d,f,h,j) for diurnal ITs decrease from a 50 m depth (Figure 18g) to a 10 m depth (Figure 18c) and maintain the same up to a 5 m depth (Figure 18a,b). This suggests that the impact of semi-diurnal and diurnal ITs reaches up to a 20 m depth, but semi-diurnal ITs lose their strength drastically toward a 5 m depth, while diurnal ITs maintain their strength up to a 5 m depth in the halocline. This highlights the impact of diurnal ITs at the sea surface at the BD12-moored buoy location in the box B domain in the central Andaman Sea, while the impact of semi-diurnal ITs is limited to a 20 m depth. The signature of semi-diurnal ITs is not felt at the sea surface at the BD12 location and is not captured in the ECCO salinity at a 1 m depth. This vital information is also reflected in the vertical structures of bandpass-filtered observed salinity at the BD12-moored buoy (Figure 12b and Figure 14b) and supports the above inferences drawn from the ECCO salinity analysis regarding the impact of the halocline or salinity stratification hindering the vertical lifting of crests of propagating ITs at deeper depths. The high-resolution ECCO model estimating salinity at a 1 m depth could capture the signals of propagating diurnal ITs at depth at the box B region (Figure 16a–d), but the associated wavelet power spectral density is lower than the observed salinity at a 5 m depth in the halocline and hence, the ECCO salinity amplitudes are also weak. The same inferences of salinity stratification (due to the halocline) can be extended to the regions of box A and box C as well, wherein strong salinity stratification is expected.

5. Conclusions

We have utilized high temporal (hourly) and spatial (1/48° or 2.3 km) resolution ECCO estimates of salinity at a 1 m depth in the Andaman Sea, a semi-enclosed marginal sea in the northern Indian Ocean, for a limited period during 1 November 2011–31 October 2012 to detect semi-diurnal and diurnal ITs in ECCO salinity and to determine their parameters in three selected 2° × 2° boxes (A to C). The selected box A is off the Myanmar coast in the northeastern Andaman Sea, box B in the central Andaman Sea (off the Nicobar Islands), and box C off the Thailand coast in the southeastern Andaman Sea. We also made use of the moored buoy-observed salinity and temperature data for the study period at the BD12 OMNI buoy location in the central Andaman Sea. This BD12-moored buoy (10.5°N, 94°E) lies on the western boundary of box B. This study is different from previous research on ITs in the Andaman Sea as we have shown the impact of salinity stratification due to the halocline in the upper 40 m on limiting the signature of semi-diurnal ITs up to 20 m from deeper depths, while the signature of diurnal ITs was shown to reach up to a 5 m depth and then to the sea surface. Spatial variations in seasonal mean high-resolution ECCO salinity provided rich information on the horizontal salinity structure compared to the spatial variations in seasonal mean satellite-derived coarse-resolution salinity from the SMAP and Aquarius missions.

Our analysis reveals that the pattern of bands of spatial variations in 11–14 h bandpass-filtered and 22–26 h bandpass-filtered ECCO salinity on selected days in different months are agreeable to those of IT radiation patterns [17] and those of leading waves in each solitary IT packet [19,71]. The bands of positive salinity amplitude represent the vertical lifting of subsurface high-salinity waters under the crests of large-amplitude ITs at depth. The bands of negative salinity coincide with the troughs of ITs where surface salinity waters are converged and pushed downward.

The continuous wavelet power spectra and the 2D–FFT spectra in the wavenumber vs. frequency domain applied to the time series of 11–14 h and 22–26 h bandpass-filtered ECCO salinity in each box (A to C) revealed semi-diurnal IT propagation in an eastward direction in box A toward the Myanmar shelf region and also westward into the interior northern Andaman Sea. The westward propagation agrees well with the semi-diurnal energy flux vectors in the northeastern Andaman Sea [18] and is in line with that reported earlier in [69,71], where the authors identified the IT generating site in the northeastern Andaman Sea. In the box A domain, semi-diurnal ITs propagate with a higher phase speed (0.96 m/s) and wavelength (42 km) (see Table 1, box A). These estimates are closer to those in the linear theory-estimated theoretical mode 2 values [15]. Though box B is closer to the IT generating source region (Nicobar Islands chain), its surface imprints are weak in the spatial maps of filtered ECCO salinity in the box B domain, and weaker-amplitude semi-diurnal ITs propagate northward and agree with [18]. Their estimated parameters are lower (13 km and 0.28 m/s) compared to those of box A and are lower than those of theoretical vertical mode 4 [15]. Our study suggests the existence of higher-mode (>4) baroclinic ITs in the central Andaman Sea. Further understanding is necessary from observed datasets and model simulations.

In box C in the southeastern Andaman Sea, the estimated parameters for semi-diurnal ITs are 33 km for the wavelength and 0.74 m/s for the phase speed and are closer to those estimated for box A and the theoretical mode 3 values [15].

In the case of diurnal ITs, the estimated wavelength and phase speed are 38 km and 0.45 m/s, respectively, and their propagation direction is southwestward in the box A domain (Table 2). In box B, the diurnal IT attains relatively higher wavelet power in April–May and propagates northeastward and its wavelength and speed are 35 km and 0.43 m/s, respectively, and closer to box A estimates (see Table 2). In box C, the estimated wavelength and phase speed for the diurnal IT are 21 km and 0.23 m/s, respectively, and the propagation direction is southwestward into the southern Andaman Sea (Table 2).

In the central Andaman Sea (box B domain), ITs are less discernable in the ECCO salinity (weaker salinity amplitudes) due to presence of salinity stratification with a shallow (20–30 m) pycnocline (or halocline) as revealed from BD12-moored buoy observations. This salinity stratification with a shallow pycnocline appears to restrict the uplifting of the crests of ITs propagating at the thermocline depth (a seasonal pycnocline), reaching to the surface. This gets support from the drastic reduction in peak wavelet power by manyfold, from a 50 m depth to a 5 m depth for the semi-diurnal IT. Observations at BD12 also reveal that subsurface high-salinity waters occasionally rise upward to the near-surface (5 m depth) by the large-amplitude semi-diurnal ITs; however, the impact of semi-diurnal ITs is limited to 20 m for most of the observational period. Therefore, signatures of semi-diurnal ITs are not felt at the sea surface at the BD12 location and are not captured in the ECCO salinity at a 1 m depth. The diurnal ITs, however, show their impact at the sea surface at the BD12-moored buoy location in the box B domain and is well captured in the ECCO salinity. Since the wavelet power density associated with the diurnal IT is small in the halocline, the amplitudes in the ECCO salinity are also weak. These inferences could be drawn in our study with the use of high-resolution observed data together with the high-resolution ECCO salinity data. This study envisages more high-resolution observed data in the high salinity stratified regions such as the northeastern Andaman Sea and the southeastern Andaman Sea.

Overall, this study provides insight into the characteristics of ITs in the Andaman Sea in the presence of salinity stratification and thus can be very useful for further IT studies elsewhere in the global ocean.