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Abstract: The southeastern Indian Ocean is characterized by the warm barrier layer (BL) underlying the cool mixed layer water in austral winter. This phenomenon lasts almost half a year and thus provides a unique positive effect on the upper mixed layer heat content through the entrainment processes at the base of the mixed layer, which has not been well evaluated due to the lack of proper method and dataset. Among various traditional threshold methods, here it is shown that the 5 m fixed depth difference can produce a reliable and accurate estimate of the entrainment heat flux (EHF) in this BL region. The comparison between the daily and monthly EHF warming indicates that the account for high-frequency EHF variability almost doubles the warming effect in the BL period, which can compensate for or even surpass the surface heat loss. This increased warming is a result of stronger relative rate of the mixed layer deepening and larger temperature differences between the mixed layer and its immediate below in the daily-resolving data. The interannual EHF shows a moderately increasing trend and similar variabilities to the Southern Annular Mode (SAM), likely because the mixed layer deepening under the positive SAM trend is accompanied by enhanced turbulent entrainment and thus increases the BL warming.
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Figure 1. The barrier layer thickness (BLT) distribution in the southeastern Indian Ocean from May to October. The black box indicates the barrier layer (BL) area for the subsequent analysis.
Figure 2. The entrainment heat flux (EHF) seasonal variation from May to October calculated by K05 method (exact) and different threshold methods listed in Table 1.
Figure 3. Spatial distributions of the entrainment heat fluxes (EHFs) from May to October using K05 method and the 20 m depth difference threshold method.
Figure 4. Seasonal entrainment heat fluxe (EHF) warming calculated from daily (black) and monthly (red) Southern Ocean state estimates (SOSE) data (a) and comparison between the daily EHF warming (blue) and the surface net heat flux (SNHF) cooling (red) (b). The black dashed line represents the ratio between the EHF and SNHF.
Figure 5. The temperature difference between the mixed layer average and the mixed layer base (a); the daily and monthly relative variation of the mixed layer depth (MLD) (b).
Figure 7. Annual variation of entrainment heat flux (EHF) deduced from the daily and monthly Southern Ocean state estimates (SOSE) data (a) and the annual observation-based Southern Annular Mode (SAM) index obtained from
https://legacy.bas.ac.uk/met/gjma/sam.html (b).
Figure 6. Interannual variation of the entrainment heat flux (EHF) anomaly from May to October.
Table 1. The EHF calculations based on various definitions
No. Definition of $ \Delta \mathit{T} $ Reference 1 $ \Delta T = 1$℃ Qiu and Kelly (1993) 2 $ \Delta T = 0.75 $℃ Swenson and Hansen (1999) 3 $ \Delta T = 0.2 $℃ Dong and Kelly (2004) 4 $ \Delta T = {T}_{\mathrm{m}\mathrm{l}} - {T}_{5} $ Qu (2001); Girishkumar et al. (2013) 5 $ \Delta T = {T}_{\mathrm{m}\mathrm{l}} - {T}_{10} $ Qu (2003); Close and Goosse (2013) 6 $ \Delta T = {T}_{\mathrm{m}\mathrm{l}} - {T}_{20} $ Yasuda et al. (2000); McPhaden (2002) Note: $ {T}_{N} $ is the temperature at the depth of N (unit in m) below the mixed layer base. ${T}_{\mathrm{m}\mathrm{l}} $ is the mixed layer average temperature. 
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