
The National Oceanic and Atmospheric Administration Extended Reconstructed SST version 5 (NOAA ERSST.v5) dataset provides monthly data on SST, with a resolution of 2.0° × 2.0° (Huang et al., 2017). Three other monthly SST datasets are obtained: the Hadley Centre Global Sea Ice and SST (HadISST) with a resolution of 1.0° × 1.0° (Rayner et al., 2003), NOAA Optimum Interpolation SST version 2 (NOAA OISST.v2) with a resolution of 1.0° × 1.0° (Reynolds and Smith, 1994), and Kaplan Extended SST version 2 with a resolution of 5.0° × 5.0° (Kaplan et al., 1998). The Global Ocean Data Assimilation System (GODAS) provides the monthly mean reanalysis dataset of sea temperature (40 levels in the upper 4500 m), currents (40 levels in the upper 4500 m), sea surface height (SSH), and wind stress with a resolution of 1.0° × 0.33° (Saha et al., 2006). Another monthly mean sea surface current data set is the Ocean Surface Current Analysis (OSCAR) dataset with a resolution of 1.0° × 1.0° (Johnson et al., 2007). The Japanese Meteorological AgencyTokyo (JRA) provides monthly surface heat flux data with a resolution of 1.25° × 1.25° (Onogi et al., 2007). The Objectively Analyzed air–sea Fluxes (OAFlux) of the Woods Hole Oceanographic Institution (WHOI) provides monthly surface heat flux data with a resolution of 1.0° × 1.0° (Yu et al., 2008). Unless noted otherwise, all anomalies are defined as the departure from the 1981–2010 climatological values for each month. The SWIO is defined over 34°–13°S, 54°–92°E.
To better understand the mechanism that causes the change in SSTAs, an upperlayer heat budget analysis method (Su et al., 2010) was used in this study. The heat budget is formulated as:
$$ \dfrac{\partial T’}{\partial t}=\left({V}^{{'}}\cdot\triangledown \overline{T}+\overline{V}\cdot\triangledown {T}^{{'}}\right)({V}^{{'}}\cdot\triangledown {T}^{{'}})+\dfrac{Q{’}_{\rm{net}}}{ {\textit{ρ}}{{c}}_{p} H}+R{,} $$ (1) where
$ T $ is the upperlayer temperature;$ V=(u,v,w) $ represents the threedimensional ocean current;$ \triangledown =\left(\dfrac{\partial }{\partial x}, \dfrac{\partial }{\partial y}, \dfrac{\partial }{\partial z}\right) $ represents the threedimensional gradient operator;$ \left( \right){'} $ represents the anomaly of a variable, which is the difference between the mean values in the last 11 years (2006–2016) and the previous 11 years (1996–2006);$ \overline{\left( \right)} $ represents the climatological annual cycle variables;$ \left({V}^{{{'}}}\cdot\triangledown \overline{T}+\overline{V}\cdot\triangledown {T}^{{{'}}}\right) $ represents a threedimensional linearized advection term;$ ({{{V}}}^{{{'}}}\cdot\triangledown {T}^{{{'}}}) $ represents a threedimensional nonlinear advection term;$ Q{’}_{\rm {net}} $ is the net air–sea heat flux anomaly, including the solar radiation flux, longwave radiation flux, sensible heat flux, and latent heat flux; ρ (assumed constant at 1026 kg m^{−3}) and$ c_{p} $ [assumed constant at 3850 J (kg K)^{−1}] represent the density and heat capacity of seawater, respectively;$ H $ is the depth of the mixed layer (50 m) or of the upper layer (100 m); and$ R $ is the residual.The heat flux formula is defined as:
$$ F=\sum {\textit{ρ}} {c}_{ p}uTS_{ij}{,} $$ (2) where i and j are the grid index along each section,
$ u $ is the current velocity,$ T $ is the sea temperature, and$ S $ is the area of a single grid in different sections of the SWIO. Then, the heat flux$ F $ of the total area of the boundary cross sections in the six sections of the SWIO is obtained. The mean value of temperature averaged within the SWIO threedimensional box is first removed from the sea temperature along each section before these heat flux calculations.To analyze the causes of the changes in ocean currents, geostrophic currents and Ekman currents are calculated. The formula for geostrophic currents is as below:
$$ \hspace{8pt} u_{\rm g}=\dfrac{\rm g}{f}\dfrac{\partial h}{\partial y},\quad v_{\rm g}=\dfrac{\rm g}{f}\dfrac{\partial h}{\partial x}{.} $$ (3) The formula for Ekman currents is as follows:
$$ {u}_{\rm E}=\dfrac{{\tau }_{y}}{f {\textit{ρ}} d_{\rm E}},\quad {v}_{\rm E}=\dfrac{{\tau }_{x}}{f {\textit{ρ}} d_{\rm E}}{,} $$ (4) where gravitational acceleration g is 9.8 m s^{−2}, the Coriolis parameter
$ f=2\varOmega {\rm{sin}}\varphi $ rad s^{−1} ($ {\rm{\varphi }} $ is latitude),$ h $ is the SSH,$ \tau $ is wind stress, and$ {{d}}_{\rm{E}} $ is the depth of the Ekman layer of the SWIO (50 m).
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Li, J. Y., and J. Z. Su, 2021: Sustained decadal warming phase in the southwestern Indian Ocean since the mid1990s. J. Meteor. Res., 35(2), 258–270, doi: 10.1007/s1335102101124 
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