Nonlinear processes reinforce extreme Indian Ocean Dipole events

Under global warming, climate models show an almost three-fold increase in extreme positive Indian Ocean Dipole (pIOD) events by 2100. These extreme pIODs are characterised by a westward extension of cold sea surface temperature anomalies (SSTAs) which push the downstream atmospheric convergence further west. This induces severe drought and flooding in the surrounding countries, but the processes involved in this projected increase have not been fully examined. Here we conduct a detailed heat budget analysis of 19 models from phase 5 of the Coupled Model Intercomparison Project and show that nonlinear zonal and vertical heat advection are important for reinforcing extreme pIODs. Under greenhouse warming, these nonlinear processes do not change significantly in amplitude, but the frequency of occurrences surpassing a threshold increases. This is due to the projected weakening of the Walker circulation, which leads to the western tropical Indian Ocean warming faster than the east. As such, the magnitude of SSTAs required to shift convection westward is relatively smaller, allowing these convection shifts to occur more frequently in the future. The associated changes in wind and ocean current anomalies support the zonal and vertical advection terms in a positive feedback process and consequently, moderate pIODs become more extreme-like.


Figures
| Heat budget analysis of extreme pIOD events in ECMWF-ORAS3 ocean reanalysis. Bar charts of the SON heat budget components during three extreme pIOD events (1961, 1994, and 1997) and the composite of the three extreme events. Table S2 provides a description of each heat budget term.  the multi-model ensemble mean historical SON sea surface temperature anomaly during strong nIODs. (b) As in (a) but for moderate nIODs. (c), (d) As in (a), (b) respectively but for the RCP8.5 period. A strong nIOD is when the DMI is less than -1.25 standard deviations. A moderate nIOD is when the DMI is less than -0.75 standard deviations but is not a strong event.

Figure S4 | Heat budget analysis of negative IOD (nIOD) events in CMIP5 models. (a)
Multi-model ensemble averaged historical SON heat budget components for strong nIODs. (b) As in (a) but for moderate nIODs. (c), (d) As in (a), (b) respectively but for the RCP8.5 period. Table S2 provides a description of each heat budget term.

Figure S5 | Nonlinear zonal advection during strong and moderate nIOD events. (a) Map
showing the multi-model ensemble mean historical SON nonlinear zonal advection term during strong nIODs. (b) As in (a) but for moderate nIODs. (c), (d) As in (a), (b) respectively but for the RCP8.5 period. The green contours in (c) and (d) denote where the difference between the historical and RCP8.5 periods is significant at the 95% confidence level based on a two-tailed Student's t-test.

Figure S6 | Nonlinear vertical advection during strong and moderate nIOD events. (a)
Map showing the multi-model ensemble mean historical SON nonlinear vertical advection term during strong nIODs. (b) As in (a) but for moderate nIODs. (c), (d) As in (a), (b) respectively but for the RCP8.5 period. The green contours in (c) and (d) denote where the difference between the historical and RCP8.5 periods is significant at the 95% confidence level based on a two-tailed Student's t-test.   The mixed layer depth is defined as the density at 10 m depth plus an increment in density equivalent to a 0.2°C cooling. Compared to ECMWF ORA-S3 reanalysis, the multi-model ensemble mixed layer depth is simulated reasonably well (not shown).  , the number of moderate pIOD events (2 nd column), the number of extreme pIOD events (3 rd column), the number of moderate nIOD events (4 th column), and the number of strong nIOD events (5 th column). The bold blue type indicates models that have a reduction in extreme pIOD events. The red type indicates models that have a decrease or no change in strong nIOD events. These models were selected based on their ability to simulate negative IODE SST skewness in the historical period  as well as the nonlinear relationship between rainfall EOF1 and EOF2.

Tables
Heat budget term

Description
The change in anomalous ocean temperature over time.
, , Anomalous zonal, meridional, and vertical advection of the anomalous ocean temperature, respectively. This can be thought of as the transport of anomalous heat by anomalous ocean currents. Collectively, these nonlinear advection terms form the nonlinear dynamic heating (NDH) process where: = − ( + + ) ̅ , ̅ , ̅ Mean zonal, meridional, and vertical advection of the anomalous ocean temperature, respectively. This can also be described as the transport of anomalous heat by the mean ocean currents. ̅ , ̅ , ̅ Anomalous zonal, meridional, and vertical advection of the mean ocean temperature, respectively. This is the transport of the mean heat by anomalous ocean currents.
Net incoming surface air-sea heat flux.
Residual terms such as eddy mixing and diffusion.