Take-home message(s): The amplitude of sea level seasonal cycle is much larger than the. 127 interannual variability along the WCI. The sea level interannualΒ ...
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Geophysical Research Letters
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Supporting Information for
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Sea level interannual variability along the west coast of India
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I. Suresh1, J. Vialard2, M. Lengaigne2,3, T. Izumo2,3, V. Parvathi1, and P.M. Muraleedharan1 1
CSIR-National Institute of Oceanography (CSIR-NIO), Goa, India
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LOCEAN-IPSL, Sorbonne UniversitΓ© (UPMC, Univ Paris 06)-CNRS-IRD-MNHN, Paris, France
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Indo-French Cell for Water Sciences, IISc-NIO-IITMβIRD Joint International Laboratory, CSIR-NIO, Goa, India
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Contents of this file
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1. Details of the linear, continuously stratified ocean model
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2. Details of the sensitivity experiments
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3. Figures in support of the main text
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a. Figure S1 shows the amplitude of seasonal and interannual sea level variability in the
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Indian Ocean
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b. Figure S2 shows that the interannual sea level variability 1st Empirical Orthogonal
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Function (EOF1) is dominated by the influence of the Indian Ocean Dipole (IOD)
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c. Figure S3 complements the main text Figure 2 by showing the patterns of sea level
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anomalies and wind-stress forcing associated with an IOD event for August, October,
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December, and February.
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d. Figure S4 provides theoretical travel times of first baroclinic mode Rossby waves in
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the Bay of Bengal (BoB) e. Figure S5 provides the process decomposition of west coast of India (WCI) signals
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separately for positive and negative IODs, allowing to discuss their asymmetrical
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influence on the WCI
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f.
Figure S6 completes the main text Figure 3 by showing typical IOD signals (and their process decomposition) in other relevant regions
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1. The linear, continuously-stratified ocean model
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We use the same linear, continuously stratified (LCS) model as that used to study the
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West Coast of India (WCI) intraseasonal variability and seasonal cycle in Suresh et al. (2013;
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2016). This model is a modified version of the one presented in McCreary et al. (1996). The
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equations of motion are linearized about a state of rest with a realistic background
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stratification derived from the averaged Indian Ocean (15oS-15oN, 40oE-100oE) World Ocean
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Atlas (Locarnini et al., 2010) climatological potential density profile, and the ocean bottom is
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assumed flat. With these conditions, the solutions are represented as a sum of vertical normal
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modes, which are eigenfunctions, π! (π§), satisfying the equation,
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subject to the boundary conditions, π!" βπ· = π!" 0 = 0, where π! (π§) is the Bruntβ
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VΓ€isΓ€lΓ€ frequency and D (= 4000 m) is the ocean depth. The eigenvalue, π! , of the above
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equation represents the characteristic Kelvin wave speed of the n-th mode. We use the first 5
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baroclinic modes, the characteristic speeds of which are 252 cm s-1, 155 cm s-1, 88 cm s-1, 69
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cm s-1, and 53 cm s-1, but a very similar solution is obtained when using 20 modes instead, as
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in Suresh et al. (2013; 2016).
! !!!
π!"
!
!
= β ! ! π! (π§), !
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The response of each mode is obtained on a regular, 0.25Β°-resolution grid over a domain
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that covers the Indian Ocean from 30Β°S to 30Β°N and from 30Β°E to 110Β°E, and with a coastline
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determined by the 200-m isobaths (Smith & Sandwell, 1997), a good proxy for the
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continental shelf break. Vertical mixing has the same form as McCreary et al. (1996), but
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with a 7-year dissipation time scale for the first baroclinic mode. The horizontal mixing
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coefficient is set to 5000 m2.s-1. Wind is introduced into the ocean as a body force with the
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same profile (constant down to 50 m and ramped to zero at 100 m) as in McCreary et al.
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(1996).
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The model is forced with daily TropFlux wind-stress anomalies (long-term mean
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removed) during 1979-2013 (available from http://www.incois.gov.in/tropflux/) (Praveen
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Kumar et al., 2013). We refer to this solution as the control (CTL) experiment.
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2. Details of sensitivity experiments
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The processes that influence the sea level along the WCI are discussed in detail in the
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main text (refer to Section 3.2). The contribution of each process is isolated using set of
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experiments with dampers and/or special boundary condition applied in specific regions. 2
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The dampers are constructed as in McCreary et al. (1996) from a Newtonian damping
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which allows the waves to decay over a region of interest with an e-folding scale of 1.5 Ξx,
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where Ξx is the grid size. To avoid distortions in the solutions, the Newtonian damping
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coefficients are ramped linearly to zero within 1o from the edges of the damping region. As
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demonstrated in Suresh et al. (2016), our results are not very sensitive to the specific choice
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of these dampers or ramp. The solution obtained with such a damper will thus be free from
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the effect of waves emanating from this region. The dampers in our experiments are designed
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such that their edges match and the ramping coefficients add up to 1 there. That is, the sum of
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the various process solutions is exactly equal to the CTL experiment, owing to the linearity of
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the model.
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As in McCreary et al. (1996), we also use the following special boundary condition in some sensitivity experiments: ππ = π β ππ = βπ. πΓ
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ππ π
π£! = (πΓπ) β ππ = 0, 75
where n is a unit vector perpendicular to the coast, k is an upward-directed unit vector, and f
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is the Coriolis parameter. ππ = π’! , π£! π€ππ‘β π’! , π£! the horizontal components of velocity
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perpendicular and parallel to the coast. ππ = πΉ! , πΊ! π€βπππ πΉ! and πΊ! are given by
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πΉ! = π ! π! /(ππ»! ) and πΊ! = π ! π! /(ππ»! ) . π ! and π ! are the zonal and meridional wind
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stresses, and π»! =
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vertical profile, Ξ(π§), used here follows that of McCreary et al. (1996), which is constant
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down to 50 m and ramped to zero at 100 m. The second equation in the above represents no
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slip condition. The effect this boundary condition is to filter out alongshore forcing of coastal
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Kelvin waves, by allowing the Ekman flow to pass through the boundaries and hence
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generating no convergence and sea level anomaly at the coast.
! π! !! !
ππ§ and π! =
! π !!
π§ π! π§ ππ§ are the coupling factors. The
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In this paper, we carry out a series of sensitivity experiments to separate out the
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processes mentioned in Section 3.2. These experiments are essentially the same ones
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presented in Suresh et al. (2016).
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The equatorial forcing process (EQ) is isolated using a damper over the entire
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equatorial region between 4oS and 4oN (light blue box on Fig. 2c in the main text; experiment
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EXP1), with a 1o ramp at the northern and southern edges to minimize distortion of the signal
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near the edges. The solution obtained with this damper has no signals emanating from the 3
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equatorial region, i.e. no equatorial forcing. CTL-EXP1 thus yields northern Indian Ocean
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sea-level variations resulting from equatorial forcing.
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The BoB forcing process (BB) is isolated in an experiment with both the equatorial
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and BoB dampers (light blue and green boxes on Fig. 2cd; EXP2). EXP2 will thus be free
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from both EQ and BB signals. EXP1-EXP2 hence yields the BB contribution to sea-level
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variability. We further isolate the contribution of the BoB alongshore forcing (ABB) by
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applying the special boundary condition described above within the BoB (green box on Fig.
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2d; EXP2β). CTL-EXP2β hence isolates the effect of ABB forcing. The BoB interior Ekman
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pumping contribution (IBB) is further obtained by subtracting ABB from BB solution.
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The ST process, which includes the alongshore forcing (AST) near the southern tip of
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India and Sri Lanka and the Ekman pumping due to wind-stress curl off the east coast of Sri
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Lanka (IST), is separated out by using an additional damper near the southern tip of India,
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extending up to 90oE (purple box on Fig. 2b; EXP3; i.e. EXP3 has dampers in the EQ, BB &
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ST regions). The difference EXP2-EXP3 thus yields the effect of ST (both alongshore
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forcing and Ekman pumping east of Sri Lanka). We further isolate the contribution of AST in
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the ST process in an experiment EXP3β in which we impose the special boundary condition
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described above within the purple box. CTL-EXP3β hence isolates the effect of alongshore
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forcing. The IST contribution is further obtained by subtracting this AST contribution from
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the ST process.
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The effect of local alongshore forcing along the WCI is finally obtained by applying
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the special boundary condition along the entire WCI, in addition to all the above dampers
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(EXP4). EXP3-EXP4 thus isolates the effect of WCI winds. At the same time, EXP4 does
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not have the effect of equatorial, BoB and southern tip of India forcing and is also free from
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the effect of WCI alongshore winds. It has only the effect of interior wind forcing in the
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Arabian Sea. Both the above processes constitute the AS process.
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The linearity of our model ensures that EQ+BB+ST+AS=CTL, except for numerical
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errors, which are orders of magnitude smaller than any of the components. As noted above,
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the BB, ST and AS contributions can further be decomposed into interior (I) and alongshore
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(A) contributions, e.g. ST=IST+AST.
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Figure S1: Standard deviation of the observed sea level a) seasonal cycle and b) interannual
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anomalies.
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Take-home message(s): The amplitude of sea level seasonal cycle is much larger than the
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interannual variability along the WCI. The sea level interannual variability is much larger in
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the BoB than along the WCI. This probably explains why previous studies discussed the
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seasonal cycle on the WCI (e.g. Suresh et al. 2016; because of its high amplitude) or the
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interannual variability in the Bay of Bengal (e.g. Aparna et al. 2012; because it has a high
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amplitude) but not the interannual variability on the WCI (because of its relatively weaker
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amplitude). While the WCI SLA interannual variability is weak, it has strong societal
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impacts. Parvathi et al. (2017) indeed showed that even small perturbations in the WCI
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thermocline/oxycline depths during SON can potentially trigger/suppress anoxic conditions,
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due to the upwelling-driven shallow thermocline/oxycline depths at this time of the year.
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Those anoxic conditions have strong societal impacts, owing to their adverse influence on
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ecosystems and fisheries. This emphasizes the need for better understanding of the WCI
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interannual sea level variability (see introduction section in the text for more details)
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Figure S2: Normalized first principal component (PC1, black) of the northern Indian Ocean
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interannual monthly sea-level anomalies from the CTL experiment, along with the normalized
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Dipole Mode index (DMI, red) and multivariate ENSO Index (MEI, blue).
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Take-home message(s): PC1 has a higher correlation with DMI Index during the IOD peak
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(SON; 0.95) than with MEI index during ENSO peak (NDJ; 0.81). In line with the previous
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literature on the subject (see the main text), this indicates that the EOF1 captures the intrinsic
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sea-level variability associated with the IOD, rather than that associated with the ENSO.
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Figure S3: Maps of (left column) CTL SLA (cm) and wind-stress (N.m-2) vectors and (right
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column) wind-stress curl (N.m-3; shading) and alongshore wind stresses (N.m-2; shading along
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the coastline) lead-lag regression onto the normalized SON-averaged DMI during (a, b)
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August; (c, d) October; (e, f) December; and (g, h) February. Red boxes marked on panel a
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will be used in Figure S5.
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Take-home message(s): Typical sequence of wind forcing and sea-level response associated
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with a positive IOD event. Note that the west coast of India signals shift from positive in
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boreal fall to negative in winter. 7
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Figure S4: a) Sketch showing the pathways of coastal Kelvin and mid-latitude Rossby waves
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travelling from one given latitude on the eastern rim to the same latitude on the western rim of
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the BoB. Also shown, as a function of latitude, are b) Rossby wave phase speed, computed
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with a typical first baroclinic wave speed of 2.5 m.s-1, c) distance across BoB basin, d) Rossby
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wave travel time to cross the basin.
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Take-home message(s): A first-baroclinic mode coastal Kelvin wave typically takes ~20
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days (with 2.5 m.s-1) to travel around the BoB coastal waveguide (~4300 km), while Rossby
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waves typically need 2 to 6 months, depending on the latitude, to cross the BoB basin.
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Figure S5: Regression of WCI CTL interannual sea-level anomalies in SON to the
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normalized SON-averaged DMI during a typical positive (red; i.e. regression only for DMI >
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0) and negative (blue; i.e. regression only for DMI < 0) IOD events, and its decomposition
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into the ST, EQ, BB, and AS processes.
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Take-home message(s): For a given IOD amplitude, the WCI sea-level response is larger for
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positive IODs, due to stronger ST and BB processes, which can be linked to zonal equatorial
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wind anomalies that extend more northward during positive IOD than their negative
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counterpart.
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Figure S6: Same as Figure 3 in the main text, but for coastal locations on the a) eastern BoB;
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b) east coast of India; c) southeastern Arabian Sea, indicated by red frames in Figure S3a.
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Take-home message(s): Sea-level signals are almost entirely associated with equatorial
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remote forcing in the eastern BoB. Local BoB forcing starts contributing (but rather weakly)
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along the east coast of India, where EQ is still the most dominant process. The contributing
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processes to the sea level interannual variability in the southeastern Arabian Sea are very
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similar to those along the WCI (Fig. 3 in the main text), i.e., the ST and EQ, but with a
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slightly stronger contribution of Arabian Sea local forcing.
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