Causes of the interannual variability in the subduction rate within a constant subduction area
In this section, we explore possible causes of the interannual variability in the STUW subduction rate. As illustrated in the previous section, the temporal variability in the mixed layer (\(\partial h/\partial t\)) plays an important role in the interannual variability of the subduction rate (Fig. 4d). In this section, we consider the contribution of the interannual changes in the temporal rate of the mixed layer to changes in the subduction rate. The area-weighted \(\partial h/\partial t\) anomalies in each month of each year from 1992–2016 were calculated within the climatological subduction area to remove the possible nonlinear effects caused by interseasonal and interannual variations in the subduction area.
Based on Eq. (2), the changes in the temporal rate of the mixed layer anomalies can be attributed to the different variabilities in the MLD anomalies between austral winter and austral spring. The large difference in the MLD anomalies between austral winter and spring is generally associated with positive MLD anomalies in austral winter and negative MLD anomalies in austral spring. We emphasize that the averaged MLD anomalies over the entire winter-spring season do not imply changes in subduction, but the seasonal difference in the MLD anomalies accounts for changes in subduction. For example, the MLD during austral winter (from August to September) in 2009 was shallower than that in 2011 (Fig. 6), but the MLD in 2009 exhibited greater seasonal differences (positive value) than that in 2011 (Fig. 4d). This accounts for the stronger subduction in 2009 than in 2011. In 2011, a deeper MLD during November–December resulted in negative anomalies of the MLD difference (Fig. 6). These results are consistent with the smaller subduction rate observed in 2011. It should be noted that if a forward difference is applied in the calculation for \(\partial h/\partial t\), the magnitude of \(\partial h/\partial t\) changes, but the interannual variations remain the same. Positive MLD anomalies in winter and negative anomalies in spring sometimes do not indicate a strong subduction rate. Therefore, other processes must be at work during these years.
The deepening and shoaling of the MLD represent conversion between turbulent kinetic energy (TKE) and potential energy input by surface fluxes (Niiler 1975). During austral winter (July, August and September), the MLD deepens (Fig. 7a) due to surface convection (i.e., buoyancy loss) and TKE input by wind stirring. The buoyancy fluxes are extracted from the ocean surface and lead to the convective mixing by increasing the potential energy at the sea surface. During spring, the MLD shoals (Fig. 7a) due to warming (Fig. 7b) at the ocean surface (net surface heat flux > 0). The MLD is maintained by the TKE balance between the effects of wind stirring and stabilization due to surface buoyancy input. In summary, the driving forcing for the MLD varies depending on the season. In the next section, we investigate the causes of the interannual variability of the MLD during winter and spring, seperately.
The cause of MLD anomalies in winter
The MLD is an expression of the strength of convection during winter. The convection induced MLD is defined as (Marshall and Schott 1999):
$${H}_{conv}={\left[\frac{2{\int }_{{t}_{1}}^{{t}_{2}}{B}_{0}dt}{{N}^{2}}\right]}^{1/2}$$
(3)
where \({t}_{1}\) is April, \({t}_{2}\) is September, and \({N}^{2}\) is the averaged Brunt-Vaisala frequency between the maximum MLD over austral winter and the mean MLD over austral summer. \({B}_{0}\) represents the buoyancy flux and is calculated as follows:
$${B}_{0}=-\frac{g\alpha }{{C}_{p}{\rho }_{0}}{Q}_{net}+g\beta {S}_{m}\left(E-P\right)$$
(4)
where a positive \({B}_{0}\) indicates a buoyancy loss, and a negative value indicates a buoyancy gain. The variable \(g\) is the acceleration of gravity, \(\alpha\) is the thermal expansion coefficient, \({C}_{p}\) is the heat capacity, \({Q}_{net}\) is the net heat flux, \(\beta\) is the haline contraction coefficient, \({\rho }_{0}\) is the constant reference density (1027 kg/m3), \({S}_{m}\) is the mixed layer salinity, and \(E-P\) is the surface freshwater flux.
The TKE input can be estimated using the depth scale of the turbulent Ekman boundary layer (Rossby and Montgomery 1935). The turbulent Ekman depth is calculated as follows:
$${H}_{EKD}\sim \frac{{u}^{*}}{\left|f\right|}$$
(5)
where \({u}^{*}\) is the friction velocity, which is quantified as follows:
$${u}^{*} =\bigg({\frac{\left|{\tau }_{a}\right|}{\stackrel{-}{\rho }}\bigg)}^{1/2}$$
(6)
where \({\tau }_{a}\) is the wind stress magnitude.
The MLD anomalies (Fig. 8a and b) generally show consistent changes with the convective MLD (\({H}_{conv}\), Fig. 8c and d) in August and September. The correlation coefficients between the convective MLD and the MLD are 0.88 and 0.81 for August and September, respectively. The p-values of the two correlation coefficients are smaller than 0.05, indicating that the correlation is significant. The root-mean-square errors (RMSEs) between the two types of MLDs are 11.35 m and 20.65 m for August and September, respectively. The time series of the turbulent Ekman depth (\({H}_{EKD}\), Fig. 8e) shows a large difference with MLD in August (Fig. 8a). The correlation is not significant between the MLD and turbulent Ekman depth. In September, the correlation between the two types of depths is significant. However, the correlation coefficient between the two types of depths in September is 0.62, which is smaller than that of the convective MLD. Thus, convection plays a more important role in regulating the winter MLD than turbulence induced by wind stress. According to Eq. (3), convection is determined by buoyancy and stratification. We also compared the magnitude of the heat and freshwater fluxes and found that heat fluxes show stronger variations than the freshwater fluxes (figures not shown here). Thus, heat fluxes control the buoyancy fluxes in August and September. In summary, heat fluxes and stratification play the leading role in the interannual variability of the MLD during August and September, respectively.
Cause of the MLD anomalies in Spring
According to Morioka et al. (2011), the MLD in the subtropical South Atlantic during austral spring and summer can be determined based on the Monin–Obukhov depth. The Monin–Obukhov depth can be calculated as follows (Nurser et al. 1999):
$${H}_{mo}=\left({m}_{0}{{u}^{*}}^{3} +\frac{\alpha g}{{\rho }_{0}{c}_{p}}{\int }_{-{H}_{m0}}^{0}q\left(z\right)dz\right)/\frac{\alpha g}{2{\rho }_{0}{c}_{p}}({Q}_{net}+qd)$$
(7)
where \({q}_{d}\) is the penetrating shortwave radiation (Paulson and Simpson 1977), and \({m}_{0}\) is 0.5. The contribution of heat fluxes and wind stress to the variation of the Monin–Obukhov depth can be examined by decomposing it into three components as follows:
$$\delta \left({H}_{mo}\right)\left[=\delta \left(\frac{{m}_{0}{u}_{*}^{3}+{q}_{*}}{{Q}_{*}}\right)\right]=\frac{\delta ({m}_{0}{u}_{*}^{3})}{\overline{{Q}_{*}}}+\frac{\delta {q}_{*}}{\overline{{Q}_{*}}}-\frac{\delta {Q}_*\left(\overline{{m}_{0}{u}_{*}^{3}}+\overline{{q}_{*}}\right)}{{\overline{{Q}_{*}}}^{2}}+Res$$
(8)
where \({Q}_{*}=\frac{\alpha g}{2\rho {c}_{p}}({Q}_{net}+{q}_{d})\), and \({q}_{*}=\frac{\alpha g}{\rho {c}_{p}}{\int }_{-{H}_{clim}}^{0}q(z)dz\). \({H}_{clim}\) is the climatological seasonal cycle of the MLD.
The Monin–Obukhov depth shows a good correlation with the MLD in October, November, and December, with magnitudes of 0.88, 0.8, and 0.89, respectively (Fig. 9). All correlations are significant. The RMSE of the Monin–Obukhov depth is large in October, with a magnitude of 84.43 m. During November and December, the RMSEs are relatively small, with magnitudes of 52.98 m and 37.15 m, respectively. Although the RMSE is large, the Monin–Obukhov depth still shows a consistent change with the MLD, indicating that the Monin–Obukhov depth can express the interannual variability of the MLD during its shoaling phase. Next, we compare the contribution of heat fluxes (the second and third terms in Eq. (8)) and wind stress to changes in the Monin–Obukhov depth. The time series of the heat flux terms match well with those of the Monin–Obukhov depth in October, November, and December. Furthermore, the STDs of the heat fluxes in October, November, and December are 17 m,13 m, and 7 m, respectively. The STDs of the wind stress term are 6 m, 3 m, and 2 m. The STDs of the residual term are 7 m, 4 m, and 2 m. Thus, the STDs of the heat fluxes have a larger magnitude than the sum of the wind stress term and the residual term. As a result, the Monin–Obukhov depth is controlled by the variability in the heat fluxes in October, November, and December.
Causes of the subduction zone variations
The previous section showed that changes in the subduction area were consistent with the interannual variability in the subduction rate in most years. For example, the low subduction rate observed in 2012 is attributed to the small size of the subduction area in September and November 2012 (Fig. 4b).
This analysis determines the total subduction area based on the number of released water particles remaining within the permanent thermocline for 1 year. Under this definition, two possible variables could affect the size of the subduction area: (1) the total number of particles released from the outcropping area and (2) modulation of the total number of particles that penetrate the permanent thermocline due to variability in three-dimensional advection and the MLD downstream.
The total number of particles released from the outcropping area from 1992–2016 was 647,225, with an average of 24,893 ± 2546 particles released in each year. The number of particles used in tracing during each year depends on the size of the outcropping area because particles are released regularly every 0.25° × 0.25° within the outcropping area. A comparison between the normalized subduction area and the normalized outcropping area is displayed in Fig. 10. During September 1992–2016, the outcropping area showed changes consistent with but slightly different than the subduction area. For example, the maximum in the outcropping area occurred in 2009, whereas the maximum in the subduction area occurred in 2003. The correlation coefficients of the two time series are 0.69, satisfying the 95% confidence level. During October, November, and December, the two time series do not have any significant correlation. Significant discrepancies exist between the outcropping area and the subduction area during October, November, and December from 1992–2016. Hence, the size of the STUW outcropping area does not play the leading role in controlling the size of the subduction area from October-December.
Next, we explore the relationship between the downstream dynamics (including the spatial/temporal pattern of the MLD and three-dimensional velocities) and the size of the subduction area. Generally, the route of the particles alone, derived from the three-dimensional velocities, cannot determine whether the particles are entrained back to the mixed layer or penetrate the thermocline after one year of tracing. The MLD downstream must be taken into consideration. However, the South Atlantic STUW is a unique water mass according to Liu and Qu (2020). STUW outcropping area sits on the SEC, which bifurcates when encountering the western South Atlantic coast. Thus, the STUW particles after release from the outcropping area are transported in two directions (Fig. 11a). The STUW particles headed northward are preferably subducted because the MLD in the northern flank (north of 21°S, according to Liu and Qu 2020) of the outcropping area is shallow (Fig. 1). These particles are counted as being subducted because they reach as deep as the permanent thermocline. In contrast, the STUW particles headed southward (south of 21°S, according to Liu and Qu 2020) are preferably transported to the seasonal thermocline because the MLD is deep in the southern side of the outcropping area. Whether the STUW particles are subducted or entrained into the seasonal thermocline is determined by the meridional direction of the particles’ route. Thus, the unique characteristics of the STUW transport allow us to assess the meridional velocities alone to identify the downstream flows’ contribution to the subduction area.
In this section, we analyze the causes of the subduction area in November 2012 as an example to illustrate the possible impact of the downstream velocity on the variability in the number of subducted particles. November 2012 is selected because it shows one of the lowest percentages (5%) of subducted particles during 1992–2016 (Supplementary Figure S3), as derived from the number of subducted STUW particles divided by the total number of released particles during each month of every year. In Fig. 11, a schematic diagram of the STUW particle route and the effect of the meridional velocities on the route is displayed. From a climatological mean perspective, the STUW particles head toward the northwest immediately after being released because the climatological subsurface meridional velocity averaged between 50 and 150 m is directed northward (Fig. 11c). Then, the route of the particles encounters the western coast of South America and bifurcates into two components: the northern one and the southern one. 84% of the released STUW particles are entrained into the mixed layer, and 16% of them are subducted into the permanent thermocline. 59.92% of the non-subducted STUW particles (i.e., 50.63% of the total released number of particles in Fig. 11a) are transported to the south of 21°S. From November 2012 to October 2013, abnormal poleward meridional velocity anomalies occurred at 40°W and 22°S–30°S and 20°W and 20°S (Fig. 11d). The non-subducted particles increase to 95%. 64% (i.e., 61.13% of the total released number) of them are transported to the south. However, particles headed to the north of the 21°S zonal line do not show a large difference between the climatological mean value (32.92% in Fig. 11a) and November 2012 (33.53% in Fig. 11b). Thus, the southward meridional velocity anomalies lead to more particles heading to the south of 21°S. This further results in an increase in the percentage of particles being entrained back to the mixed layer (deeper MLD to the south of 21°S) and fewer particles get subducted.