Formation of subantarctic mode water in the southeastern Indian Ocean

Abstract

Subantarctic Mode Water (SAMW) is the name given to the relatively deep surface mixed layers found directly north of the Subantarctic Front in the Southern Ocean, and their extension into the thermocline as weakly stratified or low potential vorticity water masses. The objective of this study is to begin an investigation into the mechanisms controlling SAMW formation, through a heat budget calculation. ARGO profiling floats provide estimates of temperature and salinity typically in the upper 2,000 m and the horizontal velocity at various parking depths. These data are used to estimate terms in the mode water heat budget; in addition, mode water circulation is determined with ARGO data and earlier ALACE float data, and climatological hydrography. We find a rapid transition to thicker layers in the central South Indian Ocean, at about 70°S, associated with a reversal of the horizontal eddy heat diffusion in the surface layer and the meridional expansion of the ACC as it rounds the Kerguelen Plateau. These effects are ultimately related to the bathymetry of the region, leading to the seat of formation in the region southwest of Australia. Upstream of this region, the dominant terms in the heat budget are the air–sea flux, eddy diffusion, and Ekman heat transport, all having approximately equal importance. Within the formation area, the Ekman contribution dominates and leads to a downstream evolution of mode water properties.

Appendix

Appendix I: objective analysis of the float displacements

We obtained 8,849 velocity components from the ARGO database and 11,667 from the ALACE/PALACE database. We deduced from them the velocities at 400 m by adding the climatological shear between their drifting depth and 400 m. The velocities were averaged into 2° longitude by 1° latitude bins. Values formed by at least five data points are retained.

We mapped the velocity field and a stream function from the ARGO data in the southern Indian Ocean using an objective analysis following Gille (2003a).We seek an estimate $\widehat{\psi }$ of the true streamfunction ψ using the key relation:

$$\widehat{\psi } = P{\left( {A + {{\in }} I} \right)}^{{ - 1}} \phi $$

(3)

with:

$$P = {\left\langle {\phi ,\psi } \right\rangle }$$

(4)

$$A = {\left\langle {\phi ,\phi ^{T} } \right\rangle }$$

(5)

where 〈.〉 is a scalar product, and Φ is a column vector containing all of the u and v measurements: Φ=[u ₁, u ₂,...u _n, v ₁, v ₂,...v _n ]. A is the covariance matrix of the measurement. We add an error ε to its diagonal, which represents the effective increase in autocovariance due to measurement noise. This simplification assumes that the measurement noise is independent between two different positions and between u and v at the same position.

As shown by Gille and Kelly (1996), in the Southern Ocean we can apply a Gaussian correlation function in space. Gille (2003a) shows that an isotropic decorrelation scale of 495 km gives the best results for an objective analysis in the Southern Ocean. In this study, we chose an isotropic decorrelation scale of 400 km.

The mean 10-day current velocities estimated from ARGO data at the parking depth contain errors, mainly due to the float drift at the surface. Furthermore, the float drift during the descent and ascent phase is also unknown. A study on the error in the drifting velocity at the float parking depth by Ichikawa et al. (2002) estimates this error to be between 10 to 25%. To be sure to overestimate this error, we chose 50% error level for the float velocities.

Appendix II: definition of the mixed layer depth

Accurate estimation of the mixed layer depth is a crucial part of the heat budget calculation. According to Thomson and Fine (2003), the threshold method with a finite difference criterion better approximates the “true” mixed layer depth, compared to the integral and regression methods. Experimental studies (see Brainerd and Gregg 1995) also find that the mixed layer depth based on a difference criterion is more stable because the gradient criterion method requires high-resolution profiles, which resolve the sharp vertical gradients. High-resolution in situ profiles are not always available, and ARGO profiles with a 10–20 m vertical resolution in the mixed layer cannot resolve sharp vertical gradients.

We chose to use a difference criterion method. The usual parameters used with this method are temperature and density; temperature is normally used when there is no equivalent salinity profiles. Most ARGO floats offer temperature and salinity profiles. We examined three different methods to find the mixed layer depth:

• a temperature difference criterion with a threshold 0.1°C; ΔT≤0.1°C

• a density difference criterion with a threshold 0.01 kg m⁻³; Δσ≤0.01 kg m⁻³

• a density difference criterion with a threshold 0.03 kg m⁻³; Δσ≤0.03 kg m⁻³

The first measurement closest to the surface was chosen as the reference for each profile if this measurement is in the range from 0 to 10 m. If not the profile is rejected.

Consider first the difference between the two density criteria: Δσ≤0.01 and Δσ≤0.03. The results obtained by these two criteria are similar over most of the southern Indian Ocean (not shown). Nevertheless, some 3% of the profiles reveal mixed layer depths, which vary by more than 50%. When these exceptional profiles are examined, the 0.03 threshold is consistently associated with the mixed layer that we seek (i.e., the mixed layer depth for monthly averaged applications).

In the southern Indian Ocean, there are big differences in the mixed layer depth depending on whether we use the temperature or the density criteria. To visually highlight these differences, we calculated the average of the mixed depth layer in bins (2° latitude by 4° longitude) for each criterion and then mapped the differences. Figure 16 shows the difference between the method ΔT≤0.1 and Δσ≤0.03.

Fig. 16

Left pannel Normalized depth differences of the mixed layer depth identified by the Δσ≤0.03 and the ΔT≤0.1 criteria. A negative difference occurs when the ΔT≤0.1 criterion is shallower than the Δσ≤0.03 criteria. Right panel Selected density profiles in the region of mode water formation (upper) and south of the SAF (lower), which show large mixed layer depth differences using the density or temperature criteria. The red points correspond to the Δσ≤0.03 criterion and the black points correspond to the ΔT≤0.1 criterion

South of the SAF, the ΔT≤0.1 criterion shows a mixed layer depth far deeper than the density criteria; here there are small vertical temperature gradients but a strong halocline near the surface separating the fresh Antarctic Surface Waters from the saltier deep waters. In the region of mode water formation east of the Kerguelen Plateau between 80 and 120°E, the temperature criterion is shallower than the density criterion where the surface T–S compensates. Figure 16 also shows selected profiles in these two areas where there is a maximum depth difference between the two methods (ΔDepth>100 m). Clearly in both areas the density difference method is much better in identifying the mixed layer depth. For the following work, we will apply the 0.03-density criterion to find the mixed layer depth.

Appendix III: detailed heat budget calculations

Ekman heat transport

For the advective term of the heat budget Eq. 1, v the horizontal mean velocity can be decomposed into the Ekman and geostrophic components as v=v _E +v _g .The Ekman heat transport correspond to:

$${\int {{\bf v}_{{\it{E}}} \cdot \rho C_{p} \nabla } }Tdz$$

integrated over the mixed layer. Here

$${\bf v}_{{\it{E}}} \cdot \nabla T$$

can be written:

$${\bf v}_{{\it{E}}} \cdot \nabla T = u_{{\it{E}}} \frac{{\partial T}} {{\partial x}} + v_{{\it{E}}} \frac{{\partial T}} {{\partial y}} + w_{{\it{E}}} \frac{{\partial T}} {{\partial z}}$$

Assuming that the Ekman layer is included in the mixed layer, ρC _p has no dependency with the vertical and within the mixed layer $\frac{{\partial T}}{{\partial z}} = 0$. Thus:

$${\int_{{\it{EL}}} {{\bf v}_{{\it{E}}} \cdot \rho C_{{\text{p}}} \nabla Tdz} } = \rho C_{{\text{p}}} {\left( {U_{{\it{E}}} \frac{{\partial T}} {{\partial x}} + V_{{\it{E}}} \frac{{\partial T}} {{\partial y}}} \right)}$$

In the southern Indian Ocean, the Ekman transport is mainly northward (positive) with regard to the strong westerly winds, and ∇T is dominated by the strong (positive) meridional temperature gradient. So we expect $V_{{\rm{E}}} \frac{{\partial T}} {{\partial y}}$ to be much greater than $U_{E} \frac{{\partial T}}{{\partial x}}$ Consequently, the Ekman induced heat flux can be approximated by $\rho C_{{\rm{p}}} V_{{\rm{E}}} \frac{{\partial T}} {{\partial y}}$. We note from this equation that a positive Ekman heat transport (as in our case) will induce a negative temperature tendency, or cooling. In other words, a positive Ekman heat transport can induce a negative effective Ekman heat flux at the base of the Ekman layer.

Heat content variations from ARGO floats

The heat content variation is calculated for each ARGO float within the formation region, using pairs of float profiles separated by 30 days (three float cycles) that remain in our zone. The temperature is integrated down to the deepest mixed layer depth, which occurs for the two profiles.

Because the floats do not identically sample the water column, every profile has been vertically interpolated onto a regular 10-db grid. The shallowest value of each profile has also been extended to the surface.

Several techniques were applied to evaluate the heat content variation. A first possibility was to calculate a mean temperature profile for every month, which was used to calculate a mean mixed layer depth and thus a mean heat content. This method shows a poor ability to represent the cycle of the wintertime enhanced convection and was not retained. Instead, we adopted a second method where all of the 30-day heat content variations available for the different floats were binned to form the monthly average.

For each 30-day heat content calculation, the forcing terms (Ekman and air sea fluxes) are interpolated onto the 10-day float positions and then averaged over the 30 days. In other words, considering four profiles from the same float, Ekman advection and air sea fluxes are interpolated onto the first, the second, and the third profile and then averaged, and the heat content variation is computed between the first and the fourth profile. The average of the forcing terms and the variation of the heat content are stored with the date of the fourth profile. The monthly averages shown in Figs. 8 and 10 are the average of all float pairs within the formation region whose fourth profile occurs during the given month.

One problem encountered with this calculation concerns the Lagrangian behavior of our floats. The heat budget calculation assumes a local change of the mixed layer in the same location, but for our calculation, the floats move between two samples. The movement of the float from one water mass to another introduces a change of heat content due to the float’s advection. To assure that the floats remain in the same local area and water masses and to reduce this “relative advection,” we developed a series of tests.

• 1. First, we elimated pairs of profiles when their difference in SST (considering time and position) was 1°C greater than the local change of SST (at the last profile position) during the same period. This reduces the effects of floats close to the SAF crossing large SST gradients due to meanders or eddies.

• 2. We also added a deep density criteria. If the difference between the density at 1,000 m is greater than 0.1 kg m⁻³, we consider that the float doesn’t sample the same water mass.

• 3. We also calculated the monthly rms of the forcing terms and of the ARGO heat content variation. We then removed the individual ARGO profiles whose value plus one rms lay outside the range of the forcing terms plus one rms. We visually checked that this criterion removed most profiles crossing the SAF.

The net effect of these tests was to eliminate 36% of data pairs.