1. Introduction
Subantarctic Mode Water (SAMW) is a thick water mass generated in the Southern Ocean (McCartney 1977, 1982; Hanawa and Talley 2001), which plays a major role in global mass (Sloyan and Rintoul 2001), heat (Talley 2003), and material transport (Sabine et al. 2004; Ito et al. 2010). One of the generation regions of SAMW is south of Australia between the Subtropical and Subantarctic Fronts (Sloyan and Rintoul 2001; Cerovečki et al. 2013), where mixed layer temperature and salinity increase equatorward and tend to be density compensating, forming a region with almost uniform density between about 40° and 50°S (Figs. 1a,b). A low-potential-vorticity (PV) mode water is generated there in the wintertime thick mixed layer driven by surface cooling (Fig. 1c; McCartney 1977; Dong et al. 2008), subducts into the interior (Karstensen and Quadfasel 2002; Sallée et al. 2010b), and is transported toward the tropics via the advection of the subtropical gyre (Fig. 2a; McCarthy and Talley 1999; Herraiz-Borreguero and Rintoul 2011; Jones et al. 2016; Nagura and McPhaden 2018). SAMW in the south Indian Ocean is located on isopycnals between 26.6 and 26.9 σθ (Fig. 2b; Fine 1993; Cerovečki et al. 2013) sandwiched between high-PV waters of the south Indian subtropical water in the main pycnocline (Rochford 1964; Talley and Baringer 1997; Wijffels et al. 2002) and of the Antarctic Intermediate Water (AAIW) between 26.9 and 27.2 σθ (Fine 1993; Toole and Warren 1993; McCarthy and Talley 1999).
Climatological mixed layer (a) temperature, (b) salinity, and (c) depth in September. Mixed layer density in September is shown by contours. (d) Standard deviations (colors) and the mean (contours) of absolute satellite sea surface height. Contour intervals are 0.2 kg m−3 for (a)–(c) and 15 cm for (d). Boxes are the analysis region for the mixed layer heat budget (38°–48°S, 100°–150°E; see section 4). Mixed layer temperature, salinity, depth, and density were obtained from in situ hydrographic observations provided by the World Ocean Database (Boyer et al. 2018; Garcia et al. 2018) and objective mapping. Satellite sea surface height was provided by the Copernicus Marine and Environment Monitoring Service (Ducet et al. 2000; Rio and Hernandez 2004).
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
Climatological mixed layer (a) temperature, (b) salinity, and (c) depth in September. Mixed layer density in September is shown by contours. (d) Standard deviations (colors) and the mean (contours) of absolute satellite sea surface height. Contour intervals are 0.2 kg m−3 for (a)–(c) and 15 cm for (d). Boxes are the analysis region for the mixed layer heat budget (38°–48°S, 100°–150°E; see section 4). Mixed layer temperature, salinity, depth, and density were obtained from in situ hydrographic observations provided by the World Ocean Database (Boyer et al. 2018; Garcia et al. 2018) and objective mapping. Satellite sea surface height was provided by the Copernicus Marine and Environment Monitoring Service (Ducet et al. 2000; Rio and Hernandez 2004).
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
Climatological mixed layer (a) temperature, (b) salinity, and (c) depth in September. Mixed layer density in September is shown by contours. (d) Standard deviations (colors) and the mean (contours) of absolute satellite sea surface height. Contour intervals are 0.2 kg m−3 for (a)–(c) and 15 cm for (d). Boxes are the analysis region for the mixed layer heat budget (38°–48°S, 100°–150°E; see section 4). Mixed layer temperature, salinity, depth, and density were obtained from in situ hydrographic observations provided by the World Ocean Database (Boyer et al. 2018; Garcia et al. 2018) and objective mapping. Satellite sea surface height was provided by the Copernicus Marine and Environment Monitoring Service (Ducet et al. 2000; Rio and Hernandez 2004).
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(a) The mean planetary potential vorticity (PV; colors), streamlines (contour lines), and geostrophic velocity (vectors) on 26.85 σθ. Hatching shows the outcrop region, where the maximum of mixed layer density exceeds 26.85 σθ. (b) The mean planetary PV (colors), potential density (thin solid contours), and the maximum of mixed layer depth (thick solid line) along 100°E. PV is computed as |f(ρ0∂ρz)−1|, following McCarthy and Talley (1999). PV, potential density, and mixed layer depth were estimated from in situ hydrographic observations obtained from the World Ocean Database (Boyer et al. 2018; Garcia et al. 2018). Streamlines and geostrophic velocity were obtained from Nagura and McPhaden (2018).
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(a) The mean planetary potential vorticity (PV; colors), streamlines (contour lines), and geostrophic velocity (vectors) on 26.85 σθ. Hatching shows the outcrop region, where the maximum of mixed layer density exceeds 26.85 σθ. (b) The mean planetary PV (colors), potential density (thin solid contours), and the maximum of mixed layer depth (thick solid line) along 100°E. PV is computed as |f(ρ0∂ρz)−1|, following McCarthy and Talley (1999). PV, potential density, and mixed layer depth were estimated from in situ hydrographic observations obtained from the World Ocean Database (Boyer et al. 2018; Garcia et al. 2018). Streamlines and geostrophic velocity were obtained from Nagura and McPhaden (2018).
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(a) The mean planetary potential vorticity (PV; colors), streamlines (contour lines), and geostrophic velocity (vectors) on 26.85 σθ. Hatching shows the outcrop region, where the maximum of mixed layer density exceeds 26.85 σθ. (b) The mean planetary PV (colors), potential density (thin solid contours), and the maximum of mixed layer depth (thick solid line) along 100°E. PV is computed as |f(ρ0∂ρz)−1|, following McCarthy and Talley (1999). PV, potential density, and mixed layer depth were estimated from in situ hydrographic observations obtained from the World Ocean Database (Boyer et al. 2018; Garcia et al. 2018). Streamlines and geostrophic velocity were obtained from Nagura and McPhaden (2018).
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
It is known that the temperature and salinity (T/S) relationship of SAMW varies in time, which is related to ocean heat uptake. Variation in the T/S relationship of a water mass is referred to as spiciness anomaly, which can be measured by salinity variability on isopycnals and considered to be a dynamically passive tracer (Veronis 1972; Munk 1981; detailed discussions are presented in section 5d). Wong et al. (1999), Bindoff and McDougall (2000), and Bryden et al. (2003) examined repeated ship observations along 32°S and found spiciness anomalies of SAMW. Wong et al. and Bindoff and McDougall reported freshening and cooling of SAMW from 1962 to 1987, and Bryden et al. detected the increase of salinity from 1987 to 2002. Kolodziejczyk et al. (2019) also reported isopycnal temperature anomalies in the south Indian Ocean in the density range of SAMW using Argo float observations. For a 50-yr period, subsurface temperature tends to warm almost globally due to thermocline heave (Roemmich et al. 2015; Häkkinen et al. 2016). Spiciness anomalies in the density range of SAMW decrease in the southern Indian Ocean, whose cooling tendency counteracts the warming trend owing to thermocline heave (Durack and Wijffels 2010; Häkkinen et al. 2016). The climatic importance of spiciness anomalies of SAMW is further emphasized by Banks et al. (2000), who reported based on numerical model experiments that spiciness anomalies of SAMW are sensitive to anthropogenic carbon dioxide emissions. Previous studies also reported variability in thickness and volume of SAMW (Gao et al. 2018; Kolodziejczyk et al. 2019; Hong et al. 2020; Portela et al. 2020), whereas we focus on spiciness variations in this study.
Spiciness anomalies were observed globally in midlatitude regions of the Pacific (e.g., Deser et al. 1996; Li et al. 2012; Kolodziejczyk and Gaillard 2012), Indian (Li and Wang 2015), and Atlantic Oceans (Qu et al. 2016), and their generation mechanisms have been discussed. One possible mechanism is the excursion of a T/S front (Schneider 2000; Li and Wang 2015). When two currents are confluent in the interior of the ocean, different water masses are located next to each other, which leads to a formation of a sharp T/S front on an isopycnal surface. Spiciness variations can be generated if variability in currents leads to the excursion of the front. Another possible cause is diapycnal forcing near the sea surface. In most of the regions, spiciness anomalies are generated in the formation region of mode water, where temperature and salinity near the surface tend to be density compensating in the meridional and/or vertical direction. In such a region, a water of higher (or lower) spiciness can be replaced with lower (or higher) spiciness virtually without changing density, giving rise to a spiciness anomaly in a subducted water mass. For example, interannual variability in surface heat flux leads to the meridional migration of the outcrop line of a density surface, which generates a spiciness anomaly when temperature and salinity at the sea surface tend to be density compensating in the meridional direction (Nonaka and Sasaki 2007; Laurian et al. 2009). In the region where temperature and salinity tend to be density compensating in the vertical direction, enhancement of vertical mixing near the surface injects saline water to subsurface and generates a positive spiciness anomaly, which is referred to as “spiciness injection” (Yeager and Large 2004, 2007; Kolodziejczyk and Gaillard 2012, 2013; Kolodziejczyk et al. 2015; Wang and Luo 2020). Interannual variability in surface heat and freshwater flux can generate a spiciness anomaly even if surface temperature and salinity are not density compensating (Nagura and Kouketsu 2018).
On the other hand, previous studies emphasized the importance of horizontal advection near the surface in the generation of spiciness anomalies in the formation region of SAMW. Mixed layer temperature and salinity tend to be density compensating in this region (Figs. 1a,b), and westerly winds drive equatorward Ekman currents. Rintoul and England (2002) proposed that variability in meridional Ekman transport in this region alters the T/S relationship of subducted water mass virtually without changing density, which results in spiciness anomalies. The Subantarctic Front is located just south of the formation region of SAMW (Nagata et al. 1988; Orsi et al. 1995; Belkin and Gordon 1996), where the eastward Antarctic Circumpolar Current (ACC) is intense (Nowlin and Klinck 1986; Stramma 1992), and eddies are vigorous (Fig. 1d; Morrow et al. 2003; Chelton et al. 2011; Frenger et al. 2015). Sallée et al. (2008a) and Herraiz-Borreguero and Rintoul (2010) pointed out that eddy advection and mixing can cause variability in the T/S relationship of the surface and subducted water mass. In addition, Wong et al. (1999) and Banks and Bindoff (2003) claimed that spiciness anomalies of intermediate water masses are attributable to variability in surface air–sea fluxes of heat and freshwater.
These previous studies focused only on an aspect of the mixed layer T/S budget, and a comprehensive view has not been provided. Wong et al. (1999) and Banks and Bindoff (2003) focused on surface air–sea fluxes and did not compare their effect with other terms, such as horizontal advection. Rintoul and England (2002) discussed the mixed layer heat budget using the typical values for mixed layer depth (MLD), horizontal gradient of temperature, and ocean currents because observational data were not available to them. Sallée et al. (2008a) focused on temperature variability tracked by one Argo float and did not relate results to the T/S relationship of a subducted water mass. Herraiz-Borreguero and Rintoul (2010) investigated eddy advection using observations along a ship section south of Tasmania. It is uncertain if their hypothesis is valid for variability in a larger domain. Also, different mechanisms have been proposed for the generation of spiciness anomalies in midlatitude regions and the formation region of SAMW, but this difference has not been discussed in detail.
To make a comprehensive discussion, the mixed layer heat or salinity budget should be estimated. Sallée et al. (2006) and Dong et al. (2007) estimated the mixed layer heat budget in the Southern Ocean on the seasonal time scale, using in situ observations and satellite measurements. Here we extend their methods to interannual time scales. At midlatitudes, the mixed layer is seasonally thin in summer and thick in winter. The subduction of a water mass occurs in spring, when the mixed layer thins. Owing to this seasonality, the property of a subducted water mass is determined by that of the surface water in winter (Stommel 1979). To discuss spiciness anomalies of a subducted water mass, we only need to examine year-to-year variability in wintertime mixed layer T/S. In this case, the idea of “effective MLD” proposed by Deser et al. (2003) is applicable in the estimation of the mixed layer heat budget, as is discussed in the rest of this paper. The forcing terms estimated in this study roughly account for interannual variability in mixed layer temperature, and we discuss relative importance of the forcing terms. We discuss the validity of this approach in various ways, including the examination of output from an ocean general circulation model (OGCM) and a reanalysis product. A different approach, which is a combination of observations and numerical integration, was adopted by Vivier et al. (2010), who examined the mixed layer heat budget on interannual time scales in the Southern Ocean. They provided general descriptions for the whole Southern Ocean, whereas we focus on the generation region of SAMW and conduct detailed examinations.
In addition, spreading patterns of spiciness anomalies of SAMW have not been fully described. Wong et al. (1999), Bindoff and McDougall (2000), and Bryden et al. (2003) examined observations from ship sections and did not examine spatial patterns of spiciness anomalies. Durack and Wijffels (2010), Häkkinen et al. (2016) and Kolodziejczyk et al. (2019) mainly examined long-term trends and did not discuss details of time evolution of spiciness anomalies.
The purpose of this study is to describe spreading of spiciness anomalies of SAMW, specify the generation region, and discuss generation mechanisms by estimating the mixed layer heat budget. Sections 2 and 3 introduce used datasets and adopted methods, respectively. Results are presented in section 4. The validity of the methods adopted in this study is discussed in section 5, and a summary is given in section 6.
2. Data
Spiciness anomalies were estimated using in situ hydrographic observations provided by the World Ocean Database (WOD; Boyer et al. 2018; Garcia et al. 2018). We used T/S profiles labeled as conductivity–temperature–depth (CTD) or profiling float (PFL) data in the region from 60°S to the equator and from 40° to 160°E for the period from 2004 to 2018. We first checked the quality flag of observations and discarded any that were not “accepted value” or “accepted cast.” Data provided by WOD underwent various tests including statistical tests, by which data that deviated from the mean by more than 4 standard deviations in a 5° × 5° box were flagged (Garcia et al. 2018). Data that did not pass this test were removed by our flag check. Still, we found apparently erroneous data in the remaining profiles. To remove them, we further conducted a statistical check using the mean and standard deviations on a 5° × 5° grid obtained from the World Ocean Atlas 2013 (Locarnini et al. 2013; Zweng et al. 2013) and eliminated data if they deviated from the mean by more than 3 standard deviations. In this study we focus on large-scale variability, and the use of the mean and standard deviation fields mapped on a 5° × 5° grid matches our purpose. The flag and standard deviation checks removed 18% and 0.7% of the total data, respectively. We used 246 431 profiles in this study that passed the checks. About 97% of observations were from PFL data, and almost all of PFL data were obtained from Argo float observations (Boyer et al. 2018). Note that WOD provides data that passed delayed-mode quality controls (Boyer et al. 2018), in which adjustments for various measurement errors, including salinity drifts, were conducted (Wong et al. 2020). In situ observations cover the basin, although observations are relatively sparse in the Indonesian Seas, coastal regions near Australia, west of Madagascar Island, and the Antarctic region south of about 50°S (Fig. 3a). The number of observations increased since the implementation of Argo float program, and observations are abundant in our analysis period (2004–18; Fig. 3b).
Number of in situ hydrographic observations (a) in each 1° × 1° box for the period from 2004 to 2018 and (b) in each year for the region from 60°S to the equator and from 40° to 160°E.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
Number of in situ hydrographic observations (a) in each 1° × 1° box for the period from 2004 to 2018 and (b) in each year for the region from 60°S to the equator and from 40° to 160°E.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
Number of in situ hydrographic observations (a) in each 1° × 1° box for the period from 2004 to 2018 and (b) in each year for the region from 60°S to the equator and from 40° to 160°E.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
We also used the mean absolute velocity data provided by Nagura and McPhaden (2018). In this dataset, mean velocity on isopycnal levels was computed from in situ hydrographic observations provided by WOD and Argo float trajectories at the parking depth (nominally 1000 m depth) provided by Lebedev et al. (2007). Hydrographic observations were objectively mapped on isopycnal levels, and vertical shear of geostrophic velocity was computed at the reference depth of 1000 m. Absolute velocity at 1000 m depth was estimated from Argo float trajectories using the method of Katsumata and Yoshinari (2010) and added to geostrophic velocity shear, resulting in absolute velocity on each isopycnal level.
We also used satellite measurements. Daily averages of sea surface temperature (SST) were obtained from the Remote Sensing Systems (RSS; http://www.remss.com/measurements/sea-surface-temperature/oisst-description/). This dataset uses SST measured by satellite microwave sensors and is constructed by optimal mapping onto a 0.25° × 0.25° grid. We chose microwave SST rather than infrared SST, because the former has better sampling than the latter in the southern subpolar region (Chelton and Wentz 2005). Sea surface height (SSH) was obtained from the Copernicus Marine and Environment Monitoring Service (CMEMS; Ducet et al. 2000; Rio and Hernandez 2004; CMEMS 2020). We also used surface geostrophic velocity data provided by CMEMS computed from satellite altimetry. SSH and geostrophic velocity data are on a 0.25° × 0.25° grid and daily averages.
We obtained surface wind stress, sea level pressure (SLP), and shortwave and longwave radiation data from the ECMWF interim reanalysis (ERA-Interim; Dee et al. 2011). These data are daily averages on a 0.75° × 0.75° grid. Turbulent heat fluxes were obtained from Objectively Analyzed Air–Sea Heat Fluxes (OAFlux; Yu and Weller 2007), which are daily averages mapped on a 1° × 1° grid. Renfrew et al. (2002) compared surface turbulent heat flux obtained from shipboard in situ observations with that from reanalysis products and pointed out that reanalysis turbulent heat flux is erroneous due to the inappropriate formulation of the bulk flux algorithm. They recommended to recalculate turbulent heat flux using meteorological fields obtained from a reanalysis dataset and an appropriate bulk algorithm. Dong et al. (2007) adopted this approach and examined the mixed layer heat budget in the Southern Ocean on the seasonal time scale. Turbulent heat flux of OAFlux is computed from meteorological data obtained from atmospheric reanalyses and satellite measurements using the bulk flux algorithm version 3.0 developed from the Coupled Ocean–Atmosphere Response Experiment (COARE3.0; Fairall et al. 2003), and we use this product following Dong et al. (2007). However, it is highly likely that the estimate of surface heat flux includes large uncertainty in the Southern Ocean, where observations are sparse (Bourassa et al. 2013). We discuss the accuracy of surface heat flux in section 5c, using in situ observations obtained from a moored buoy.
We examine the mixed layer heat budget using model output in section 5a. We used output from the OGCM for the Earth Simulator version 2 (OFES2; Sasaki et al. 2020). OFES2 is based on the Modular Ocean Model version 3 (Pacanowski and Griffies 1999). The model domain is from 76°S to 76°N. The bottom topography was obtained from ETOPO1 (Amante and Eakins 2009). The horizontal grid intervals are 0.1°, and the number of vertical levels is 105. Vertical mixing near the surface was parameterized by the scheme of Noh and Kim (1999). Surface heat flux was computed from meteorological data obtained from Japanese 55-year atmospheric reanalysis (Tsujino et al. 2018), simulated SST and the bulk formulas of Large and Yeager (2004). No data assimilation was applied. We used daily averages of output for the period from 2004 to 2016.
We also used output from the Estimating the Circulation and Climate of the Ocean version 4 (ECCO v4; Forget et al. 2015). ECCO v4 is based on the Massachusetts Institute of Technology general circulation model (Marshall et al. 1997; Adcroft et al. 2004) and assimilates various in situ and satellite observations by an adjoint method without introducing artificial sources of heat and buoyancy. The model domain is global. The horizontal grid intervals range from 0.5° to 1° in the tropical and midlatitude regions. The number of vertical levels is 50. We used output on the native grid. The turbulent closure scheme of Gaspar et al. (1990) and a simple convective adjustment scheme were adopted. Surface heat flux was computed meteorological fields of ERA-Interim and the bulk formula of Large and Yeager (2004). State estimation accounts for uncertainties of reanalysis meteorological fields. The ECCO v4 dataset provides monthly snapshots of temperature and salinity at the first day of each month and monthly averages of temperature, salinity, and advective and diffusive heat flux for the period from 1992 to 2017.
3. Methods
a. Gridding of in situ hydrographic observations
The T/S profiles obtained from in situ observations were interpolated onto 33 potential density levels from 21.5 to 27.74 σθ. Potential temperature and potential density were computed using the equation of the state of the International Thermodynamic Equation of Seawater 2010 (McDougall and Barker 2011). The resulting T/S data were objectively mapped on a 1° × 1° grid on each density surface, assuming a Gaussian covariance function with decorrelation scales of 6° in longitude and 3° in latitude. This mapping was done for each calendar year, which provides yearly estimates of T/S on isopycnals.
Using T/S profiles obtained from in situ observations, MLD was computed as the depth where density is larger than the value at 10 m depth by 0.03 kg m−3, following de Boyer Montégut et al. (2004). Averages of temperature, salinity, and density from the sea surface to the base of the mixed layer were also computed using obtained MLD. These variables were objectively mapped onto a 1° × 1° grid in the following two manners. First, MLD, mixed layer temperature, mixed layer salinity, and mixed layer density were mapped on a monthly basis from 2004 to 2018, results of which include interannual variability. Second, MLD was mapped on a monthly basis ignoring years, the results of which provided monthly climatologies. We refer to the first estimate as the “monthly estimate” and to the second as the “monthly climatological estimate.” For both, a Gaussian covariance function was assumed in objective mapping with decorrelation scales of 6° in longitude, 3° in latitude, and 45 days in time. The reason why we conducted the second estimate is sparseness of observations. In monthly estimates, data points are sometimes sparse, which leads to an erroneous estimate, such as negative MLD in summer. Such an erroneous estimate does not occur in monthly climatological estimate of MLD. For the monthly estimate of MLD, we replaced values less than 10 m with a constant value of 10 m.
Error for gridded fields was computed as standard deviation. First, nondimensional error for objective mapping was computed from assumed covariance function and the distance between data points and the grid point, following Bretherton et al. (1976). Nondimensional error ranges from 0 to unity depending on data density. Then, nondimensional error was converted to dimensional by multiplying standard deviations of data values around each grid point.
After salinity drifts are adjusted in delayed mode quality check, error for salinity of each profile is about 0.01 psu or less (Wong et al. 2003, 2020). It is considered that this is a random measurement error and reduced by gridding (e.g., Kouketsu et al. 2017). Typically, about 50 profiles are located within 6° × 3° decorrelation scales around each grid point in a year. The resulting measurement error for the gridded salinity field can be roughly estimated using the propagation of error formula (Emery and Thomson 2004) as
In this study, isopycnal salinity and mixed layer variables were first computed from each T/S profile and then objectively mapped. This is to avoid artificial variability in the T/S characteristic of a water mass, which is caused by isobaric averaging (Lozier et al. 1994), and to avoid errors for mixed layer variables, which occur when MLD is computed from spatially and temporally smoothed gridded fields (de Boyer Montégut et al. 2004; Toyoda et al. 2017). Widely distributed datasets that are based on Argo float observations, such as Roemmich and Gilson’s (2009) dataset, the Grid Point Value of the Monthly Objective Analysis using Argo float data (MOAA-GPV; Hosoda et al. 2008) and the In Situ Analysis System (ISAS; Gaillard et al. 2016; Kolodziejczyk et al. 2017), are mapped onto isobaric surfaces, and thus we chose to construct our own gridded dataset. However, these distributed datasets are constructed by more sophisticated methods of quality controls and gridding procedure than those adopted here. For check, we repeated the analysis using Roemmich and Gilson’s (2009) dataset, MOAA-GPV, and ISAS and found that the gross features presented in this study were obtained from these datasets, although details differed from dataset to dataset. This shows that results presented here are insensitive to adopted methods. Below we show results obtained from the dataset gridded in this study.
b. Mixed layer heat budget
The most straightforward way to compute the right-hand side terms in Eq. (1) is to obtain monthly estimates of h and Tb from in situ observations and calculate the entrainment term, with computing the surface heat and horizontal advection terms using Q,
We computed each term of Eq. (2) as follows. The temporal tendency of mixed layer temperature anomalies [left-hand side of Eq. (2)] was computed from monthly estimates of mixed layer temperature obtained from in situ hydrographic observations. Surface heat fluxes were obtained from OAFlux and ERA-Interim. The penetration of shortwave radiation was computed using the formula of Paulson and Simpson (1977) for water type IB. Effective MLD was obtained as the maximum of monthly climatological estimate of MLD at each grid point. Geostrophic velocity and wind stress data were obtained from CMEMS and ERA-Interim, respectively. To resolve the Subtropical and Subpolar Front in the Antarctic region, we used RSS’s microwave SST to compute horizontal gradient of mixed layer temperature. Each term on the right-hand side of Eq. (2) was integrated from September in a year to August in the next year (i.e., t0 is September in a year, and t1 is August in the next).
The residual term R includes the effects of processes neglected in our estimate. One of them is horizontal diffusion. We computed this term using RSS’s SST with an eddy diffusivity of 500 m2 s−1 following Dong et al. (2007), but contributions were negligibly small, which is consistent with results of Dong et al. (2007) and Tamsitt et al. (2016). The horizontal diffusion term is omitted to show in the rest of the paper. Another process neglected in this study is the effects of interannual variability in wintertime MLD, which are discussed in detail in section 5b. To validate our approach, we computed the mixed layer heat budget based on Eq. (1) using output from OFES2 and ECCO v4 and compared results with those based on Eq. (2). Results of this examination are presented in section 5a.
4. Results
We first describe the spreading patterns of spiciness anomalies and specify their generation region. Then, the mixed layer heat budget in the generation region is presented. Here we use salinity anomalies on isopycnal surfaces as a measure of spiciness variability. The validity of this choice is discussed in section 5d.
On 26.2 and 26.4 σθ, spiciness anomalies are large in amplitude along 15°S from the northwestern coast of Australia to about 60°E (Figs. 4a,c). The mean salinity on these isopycnals is high south of 15°S and low north of 15°S, forming a sharp front at about 15°S (Figs. 4b,d). These patterns suggest that spiciness anomalies along 15°S are generated by meridional excursions of the salinity front. The salinity front becomes weaker (Fig. 4f) or absent (Fig. 4h) on density surfaces related to SAMW. On 26.6 σθ, spiciness anomalies are large in amplitude in the southeastern Indian Ocean (20°–35°S, 80°–110°E), and the amplitude is relatively small along 15°S (Fig. 4e). On 26.8 σθ, a large amplitude of spiciness anomalies is in the south Indian Ocean along the streamline of the mean flow, whose upstream end is the outcrop region south of Australia (Fig. 4g). These patterns suggest that spiciness anomalies of SAMW are not the consequence of meridional excursions of a salinity front, but generated in the outcrop region and spread toward the interior via the advection of the mean current. The amplitude of spiciness anomalies is small all over the basin on 27.0 σθ (Figs. 4i,j), which is the density range of AAIW.
(left) Standard deviations of salinity anomalies and (right) the mean salinity at (a),(b) 26.2, (c),(d) 26.4, (e),(f) 26.6, (g),(h) 26.8, and (i),(j) 27.0 σθ obtained from in situ observations. Contours show the streamlines of the mean isopycnal velocity obtained from Nagura and McPhaden (2018). Hatching indicates outcrop region, where the maximum of mixed layer density exceeds the density of the isopycnal.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(left) Standard deviations of salinity anomalies and (right) the mean salinity at (a),(b) 26.2, (c),(d) 26.4, (e),(f) 26.6, (g),(h) 26.8, and (i),(j) 27.0 σθ obtained from in situ observations. Contours show the streamlines of the mean isopycnal velocity obtained from Nagura and McPhaden (2018). Hatching indicates outcrop region, where the maximum of mixed layer density exceeds the density of the isopycnal.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(left) Standard deviations of salinity anomalies and (right) the mean salinity at (a),(b) 26.2, (c),(d) 26.4, (e),(f) 26.6, (g),(h) 26.8, and (i),(j) 27.0 σθ obtained from in situ observations. Contours show the streamlines of the mean isopycnal velocity obtained from Nagura and McPhaden (2018). Hatching indicates outcrop region, where the maximum of mixed layer density exceeds the density of the isopycnal.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
In our analysis period, positive spiciness anomalies are prevalent from 2004 to 2009, and negative anomalies occupy the basin after 2012 (Fig. 5). The decreasing trend of spiciness anomalies in the south Indian Ocean was also reported by Kolodziejczyk et al. (2019, their Fig. 5i). Negative anomalies first appear south of Australia in 2007 and 2008 (Figs. 5d,e) and then spread over the south Indian Ocean (Figs. 5g–o).
Yearly estimates of salinity anomalies on 26.8 σθ from 2004 to 2018 obtained from in situ observations. Anomalies are masked if they are smaller than analysis error in magnitude. Symbols illustrate positions of artificial particles, which are deployed on 1 Jan 2011 and advected by the mean absolute velocity on 26.8 σθ obtained from Nagura and McPhaden (2018). Hatching indicates the outcrop region, where the maximum of mixed layer density for respective year exceeds 26.8 σθ.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
Yearly estimates of salinity anomalies on 26.8 σθ from 2004 to 2018 obtained from in situ observations. Anomalies are masked if they are smaller than analysis error in magnitude. Symbols illustrate positions of artificial particles, which are deployed on 1 Jan 2011 and advected by the mean absolute velocity on 26.8 σθ obtained from Nagura and McPhaden (2018). Hatching indicates the outcrop region, where the maximum of mixed layer density for respective year exceeds 26.8 σθ.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
Yearly estimates of salinity anomalies on 26.8 σθ from 2004 to 2018 obtained from in situ observations. Anomalies are masked if they are smaller than analysis error in magnitude. Symbols illustrate positions of artificial particles, which are deployed on 1 Jan 2011 and advected by the mean absolute velocity on 26.8 σθ obtained from Nagura and McPhaden (2018). Hatching indicates the outcrop region, where the maximum of mixed layer density for respective year exceeds 26.8 σθ.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
To see if the spreading speed of spiciness anomalies is consistent with the mean flow speed, we deployed 23 artificial particles in the region of negative anomalies on 1 January 2011 and advected them by the mean current provided by Nagura and McPhaden (2018). Seasonal variability in meridional velocity is small south of 20°S (Nagura 2018), and the amplitude of interannual variability in subtropical gyre transport in the south Indian Ocean is about 17% of the mean (Nagura 2020). We expect that the use of the mean velocity is a good approximation. Note that Nagura and McPhaden’s (2018) velocity dataset is constructed with objective mapping with a zonal decorrelation scale of 6° and does not resolve detailed structure of coastal currents. Here, if a particle hits the coast, we stopped the computation for the particle. This computation ignores the exchange of water between coastal currents and interior circulation, although such an exchange is found by a numerical study (Domingues et al. 2007).
Results show that particles migrate northwestward from the southeastern Indian Ocean, which is roughly consistent with the spreading of negative spiciness anomalies (Figs. 5h–o). This result suggests that spiciness anomalies are advected by the mean current as a passive tracer, rather than generated by the meridional excursion of a salinity front. A discrepancy is found in 2017 and 2018 (Figs. 5n,o), in which negative spiciness anomalies spread within 15°–35°S, 55°–110°E, but artificial particles are not present east of 90°E between 15° and 30°S. This is likely because of the lack of detailed representation of coastal currents and the resulting absence of migration of particles from south of Australia to west of Australia. Except for this discrepancy, the spreading of spiciness anomalies is consistent with migration of artificial particles.
Note that there is a decadal time lag between spiciness anomalies in the interior and those in the generation region. Negative anomalies south of Australia in 2007–08 reach the interior of the south Indian Ocean in 2013–18. This time scale is consistent with the estimate of Jones et al. (2016), who tracked passive tracers in an OGCM. It is expected that positive anomalies south of Australia in 2016–18 will spread to the interior in the next decade, resulting in a warming of the interior water. Häkkinen et al. (2016) reported that the cooling tendency of spiciness anomalies in the Southern Ocean counteracts the warming tendency due to thermocline heave in the last 50 years. It is possible that warming signals of spiciness anomalies will reinforce the warming tendency in coming years.
Mixed layer salinity, temperature, and density anomalies in the outcrop region are shown in Fig. 6. We chose 38°–48°S, 100°–150°E as the analysis region because the surface density in this region is 26.6 to 26.8 σθ (Figs. 1a–c), which is the typical density range of SAMW (Fig. 2b), and also this region is the upstream end of interior spiciness anomalies (Fig. 4g). We plot values in September because the mixed layer is thickest in this month, and the T/S relationship of subducted SAMW is determined by the surface water in this month. We confirmed that results presented below were not sensitive to the choice of the domain.
Mixed layer (a) salinity, (b) temperature, and (c) density in September averaged over 38°–48°S, 100°–150°E obtained from in situ observations (black lines). The red line in (a) shows anomalies of mixed layer salinity on isopycnals averaged over 100° to 150°E and 26.6 to 26.8 σθ. Analysis error for area-averaged values is shown by vertical bars. The temporal means for the period from 2004 to 2018 were subtracted from the time series in (a) and (b). A three-point running-mean filter was applied.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
Mixed layer (a) salinity, (b) temperature, and (c) density in September averaged over 38°–48°S, 100°–150°E obtained from in situ observations (black lines). The red line in (a) shows anomalies of mixed layer salinity on isopycnals averaged over 100° to 150°E and 26.6 to 26.8 σθ. Analysis error for area-averaged values is shown by vertical bars. The temporal means for the period from 2004 to 2018 were subtracted from the time series in (a) and (b). A three-point running-mean filter was applied.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
Mixed layer (a) salinity, (b) temperature, and (c) density in September averaged over 38°–48°S, 100°–150°E obtained from in situ observations (black lines). The red line in (a) shows anomalies of mixed layer salinity on isopycnals averaged over 100° to 150°E and 26.6 to 26.8 σθ. Analysis error for area-averaged values is shown by vertical bars. The temporal means for the period from 2004 to 2018 were subtracted from the time series in (a) and (b). A three-point running-mean filter was applied.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
Mixed layer salinity is anomalously low in the former half of the analysis period and high in the latter half (Fig. 6a). To compare area-averaged salinity anomalies with isopycnal salinity anomalies, we interpolated mixed layer salinity onto density surfaces and averaged over 100°–150°E and 26.6–26.8 σθ. The resulting isopycnal salinity anomalies (Fig. 6a, red line) show a consistent time evolution with area-averaged mixed layer salinity anomalies. Note that negative isopycnal salinity anomalies in the former half of the analysis period spread into the interior in subsequent years, as shown in Fig. 5. Mixed layer temperature anomalies averaged over the analysis region are negative from 2004 to 2009 and positive from 2011 to 2015 (Fig. 6b), nearly in phase with mixed layer salinity anomalies, and tend to be density compensating. Consistently, mixed layer density is almost constant and remains to be within the density range of SAMW (Fig. 6c). Results show that the mixed layer heat or salinity budget analysis in a fixed domain can be used for the discussion of the generation mechanism of spiciness anomalies, as is done by Schneider et al. (1999) and Katsura et al. (2013) for the subtropical Pacific Ocean. This is in contrast to Nagura and Kouketsu (2018), who investigated the region where variability in SST and sea surface salinity (SSS) is not density compensating and thus conducted a Lagrangian analysis.
Here we chose to examine the mixed layer heat budget, rather than the mixed layer salinity budget. The calculation of the horizontal advection term in the budget requires satellite measurements of SST or SSS to resolve the narrow Subantarctic Front and mesoscale variability. Satellite SST measurements obtained from RSS is available for the period from 1998 to the present, whereas the longest records of satellite SSS can be obtained from the European Space Agency’s Soil Moisture and Ocean Salinity mission but available only for the period from May 2010 to March 2016, which does not cover the analysis period of this study.
Results of the mixed layer heat budget computed using the method described in section 3b are shown in Fig. 7a. The temperature tendency term is close to zero in 2005–07, positive from 2008 to 2012 and negative after 2013 (thick black line). Positive tendency in 2008–12 corresponds to warming and the generation of positive spiciness anomalies. The sum of the surface heat flux and horizontal advection terms compares well with the temperature tendency term both in phase and magnitude (thick gray line). The sum of the surface heat flux and horizontal advection terms tends to be smaller than the temperature tendency term in 2008–09 and larger in 2011–15, but the discrepancy is minor.
(a) The mixed layer heat budget terms averaged over 38°–48°S, 100°–150°E computed using the concept of effective MLD and observations. The black line shows the temperature tendency term. The red and blue lines are for the surface heat flux term and the horizontal advection term, respectively. The gray line shows the sum of the surface heat flux term and the horizontal advection term. (b) The horizontal advection term averaged over 38°–48°S, 100°–150°E (black), the contribution from Ekman current advection (red), and that from geostrophic current advection (blue). The temporal mean was subtracted, and the time series were smoothed by a three-point running-mean filter.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(a) The mixed layer heat budget terms averaged over 38°–48°S, 100°–150°E computed using the concept of effective MLD and observations. The black line shows the temperature tendency term. The red and blue lines are for the surface heat flux term and the horizontal advection term, respectively. The gray line shows the sum of the surface heat flux term and the horizontal advection term. (b) The horizontal advection term averaged over 38°–48°S, 100°–150°E (black), the contribution from Ekman current advection (red), and that from geostrophic current advection (blue). The temporal mean was subtracted, and the time series were smoothed by a three-point running-mean filter.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(a) The mixed layer heat budget terms averaged over 38°–48°S, 100°–150°E computed using the concept of effective MLD and observations. The black line shows the temperature tendency term. The red and blue lines are for the surface heat flux term and the horizontal advection term, respectively. The gray line shows the sum of the surface heat flux term and the horizontal advection term. (b) The horizontal advection term averaged over 38°–48°S, 100°–150°E (black), the contribution from Ekman current advection (red), and that from geostrophic current advection (blue). The temporal mean was subtracted, and the time series were smoothed by a three-point running-mean filter.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
The comparison of the surface heat flux term and the horizontal advection term indicates that the latter is the main contributor (red and blue lines in Fig. 7a). In particular, the advection term contributes to warming of mixed layer temperature from 2008 to 2012, which shows that positive spiciness anomalies are mainly generated by horizontal advection. The decomposition of the advection term indicates that both Ekman and geostrophic flow contribute to warming (Fig. 7b). Below we examine these advection terms.
Meridional advection dominates the Ekman flow advection term, and advection due to zonal Ekman currents is negligible in amplitude (Fig. 8a). This is owing to the fact that the isolines of the mean mixed layer temperature are almost zonal (Fig. 1a). Zonal wind stress anomalies are negative from 2007 to 2012 and positive after 2013 (Fig. 8b). The meridional advection term due to Ekman flow is roughly out of phase with zonal wind stress anomalies. In this region, the mean wind is westerly, which excites northward Ekman flow and equatorward advection of polar cool water. A weaker westerly wind leads to a weaker northward Ekman flow and anomalous warming. This result supports the idea of Rintoul and England (2002).
(a) The horizontal advection term due to Ekman currents averaged over 38°–48°S, 100°–150°E (−ue ⋅ ∇hT,; thick black line), contributions from zonal (−ue∂xT; red line) and meridional (−υe∂yT; blue line) Ekman currents obtained from observations. (b) Zonal wind stress anomalies averaged over 38°–48°S, 100°–150°E. (c) The SAM index. (d) The December–February mean of SST anomalies averaged over the Niño-3.4 region (5°N–5°S, 120°–170°W; Trenberth 1997) obtained from NOAA Optimum Interpolation SST V2 (Reynolds et al. 2002). The mean was subtracted, and all the time series were smoothed by a three-point running-mean filter. The average over December 2015 to February 2016 is shown as the value for 2015 in (d), for example.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(a) The horizontal advection term due to Ekman currents averaged over 38°–48°S, 100°–150°E (−ue ⋅ ∇hT,; thick black line), contributions from zonal (−ue∂xT; red line) and meridional (−υe∂yT; blue line) Ekman currents obtained from observations. (b) Zonal wind stress anomalies averaged over 38°–48°S, 100°–150°E. (c) The SAM index. (d) The December–February mean of SST anomalies averaged over the Niño-3.4 region (5°N–5°S, 120°–170°W; Trenberth 1997) obtained from NOAA Optimum Interpolation SST V2 (Reynolds et al. 2002). The mean was subtracted, and all the time series were smoothed by a three-point running-mean filter. The average over December 2015 to February 2016 is shown as the value for 2015 in (d), for example.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(a) The horizontal advection term due to Ekman currents averaged over 38°–48°S, 100°–150°E (−ue ⋅ ∇hT,; thick black line), contributions from zonal (−ue∂xT; red line) and meridional (−υe∂yT; blue line) Ekman currents obtained from observations. (b) Zonal wind stress anomalies averaged over 38°–48°S, 100°–150°E. (c) The SAM index. (d) The December–February mean of SST anomalies averaged over the Niño-3.4 region (5°N–5°S, 120°–170°W; Trenberth 1997) obtained from NOAA Optimum Interpolation SST V2 (Reynolds et al. 2002). The mean was subtracted, and all the time series were smoothed by a three-point running-mean filter. The average over December 2015 to February 2016 is shown as the value for 2015 in (d), for example.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
A climate mode that can be influential in surface wind variability in the Antarctic region is the southern annular mode (SAM; Hall and Visbeck 2002; Lovenduski and Gruber 2005; Verdy et al. 2006; Ciasto and Thompson 2008; Sallée et al. 2010a; Meijers et al. 2019). We computed the SAM index following Limpasuvan and Hartmann (1999), Gong and Wang (1999), and Thompson and Wallace (2000) by applying empirical orthogonal function analysis to SLP from 2004 to 2018 in the region poleward of 20°S. We used the time series of the first mode as the SAM index. We defined the sign of the SAM index such that pressures over Antarctica are relatively low (or high) compared to those at midlatitudes during its positive (negative) phase. Results were almost the same if we used the SAM index of Marshall (2003). Anomalies of the obtained SAM index tend to be negative from 2005 to 2013 and positive after 2014. The correlation between the SAM index and zonal wind stress anomalies is not apparent (Figs. 8b,c). Sallée et al. (2010a) showed Ekman heat flux anomalies regressed onto the SAM index, which are relatively weak in magnitude in the region south of Australia (their Fig. 3b). It is suggested that the influence of SAM is weak in this region.
Another climate mode that affects wind variability in the Southern Ocean is ENSO (Karoly 1989; Fogt and Bromwich 2006; Verdy et al. 2006; Ciasto and Thompson 2008; Sallée et al. 2008b; Meijers et al. 2019). Niño-3.4 SST anomalies tend to be negative from 2006 to 2012 and positive afterward (Fig. 8d), which is in phase with zonal wind stress anomalies. However, the correlation coefficient with the two indices for a longer period (1982–2018) is 0.41, which is not significant even at the 70% level. We also conducted the multiple regression analysis using the SAM index and Niño-3.4 SST anomalies as the independent variables and zonal wind stress anomalies averaged over the analysis region as the dependent variable. Note that the correlation between the SAM index and Niño-3.4 SST anomalies is 0.08, and these two can be treated as independent variables. Results explain only 32% of the variance, which further suggests weak influences of these climate modes. More elaborated study is necessary to clarify the factor that controls zonal wind stress variability south of Australia.
It is expected that variability in geostrophic flow can be decomposed into large-scale and mesoscale variability, the former of which is variability in the strength of the mean flow, and the latter is due to eddies, meanders, and rings. The spatial scale of mesoscale eddies is about 80 km (Frenger et al. 2015), and that of meanders is about 500 km (Phillips and Rintoul 2000). The time scale of mesoscale variability is from 20 to 120 days (Phillips and Rintoul 2000). We define the large-scale field (denoted by
Decomposition of the horizontal advection term due to geostrophic velocity. Advection terms are averaged over 38°–48°S, 100°–150°E. Total (thick black line; −ug ⋅ ∇hT), contributions from the large-scale field (red line;
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
Decomposition of the horizontal advection term due to geostrophic velocity. Advection terms are averaged over 38°–48°S, 100°–150°E. Total (thick black line; −ug ⋅ ∇hT), contributions from the large-scale field (red line;
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
Decomposition of the horizontal advection term due to geostrophic velocity. Advection terms are averaged over 38°–48°S, 100°–150°E. Total (thick black line; −ug ⋅ ∇hT), contributions from the large-scale field (red line;
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
Meridional advection is the primary contributor to advection due to large-scale geostrophic currents (Fig. 10a) because the isolines of the mean mixed layer temperature are almost zonal (Fig. 1a). Variability in the large-scale component of geostrophic meridional velocity (
(a) The horizontal advection term owing to large-scale variability in geostrophic flow and SST (
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(a) The horizontal advection term owing to large-scale variability in geostrophic flow and SST (
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(a) The horizontal advection term owing to large-scale variability in geostrophic flow and SST (
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
Finally, we discuss advection due to mesoscale fields of geostrophic currents. It is known that poleward transport of eddy-induced velocity counteracts equatorward Ekman transport near the surface in the ACC region (Karsten and Marshall 2002; Marshall and Radko 2003; Sallée et al. 2010b). Considering that eddy-induced velocity advects large-scale tracer field (e.g., Gent et al. 1995), it is expected that eddy-induced velocity advects low-latitude warm water to the south and results in warming. Consistently, the mean of the advection term due to the mesoscale fields (
The time series of (a) mesoscale geostrophic velocity squared [
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
The time series of (a) mesoscale geostrophic velocity squared [
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
The time series of (a) mesoscale geostrophic velocity squared [
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
5. Discussion
a. Mixed layer heat budget estimated from output of OFES2 and ECCO v4
In this study we computed the mixed layer heat budget using the effective MLD approach. We discuss the validity of this approach using output from OFES2 and ECCO v4 in this subsection. We computed the mixed layer heat budget using daily averages of OFES2 output and the discrete version of Eq. (1), which is presented in Kim et al. (2006) and Nagura et al. (2015). OFES2 computed vertical diffusion using an implicit scheme, and it is impossible to retrieve the vertical diffusion term from daily averages of output. Here, the vertical diffusion term is estimated as the residual of the budget. We computed the mixed layer heat budget using ECCO v4 output using the method described in the appendix B. For both OFES2 and ECCO v4, MLD is computed as the depth where density is larger than the value at the topmost level by 0.03 kg m−3, which is consistent with the definition for in situ observations. Results were integrated from September in a year to August in the next year.
Surface density obtained from OFES2 and ECCO v4 shows a region of uniform density between 38° and 48°S (Figs. 12a,b). The wintertime mixed layer obtained from these products is thick between 40° and 55°S with the maximum of MLD being about 550 m (Figs. 12c,d). These patterns are similar to observations (Fig. 1). OFES2 simulates the northward bend of a density contour of 26.8 σθ between 120° and 130°E (Fig. 12a). A similar northward bend is seen in observations (Fig. 1a), but a contour of 26.8 σθ is closer to that of 26.6 σθ between 120° and 140°E in the simulation. OFES2 and ECCO v4 reproduce the increase of mixed layer temperature anomalies in the analysis region between 2008 and 2012 (Figs. 12e,f), which compares well with observations (Fig. 6b), although OFES2 tends to underestimate the magnitude of mixed layer temperature anomalies.
(a) Climatological SST (colors) and surface density (contours) and (c) MLD in September obtained from OFES2. (e) Mixed layer temperature anomalies in September averaged over the analysis region (38°–48°S, 100°–150°E) obtained from OFES2. (b),(d),(f) As in (a), (c), and (e), respectively, but for ECCO v4. Boxes in (a)–(d) show the analysis region (38°–48°S, 100°–150°E).
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(a) Climatological SST (colors) and surface density (contours) and (c) MLD in September obtained from OFES2. (e) Mixed layer temperature anomalies in September averaged over the analysis region (38°–48°S, 100°–150°E) obtained from OFES2. (b),(d),(f) As in (a), (c), and (e), respectively, but for ECCO v4. Boxes in (a)–(d) show the analysis region (38°–48°S, 100°–150°E).
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(a) Climatological SST (colors) and surface density (contours) and (c) MLD in September obtained from OFES2. (e) Mixed layer temperature anomalies in September averaged over the analysis region (38°–48°S, 100°–150°E) obtained from OFES2. (b),(d),(f) As in (a), (c), and (e), respectively, but for ECCO v4. Boxes in (a)–(d) show the analysis region (38°–48°S, 100°–150°E).
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
OFES2 and ECCO v4 have their own advantages and disadvantages. OFES2 simulates the mean field and variability near the surface well (Figs. 12a,c,e), but it is not able to simulate spiciness anomalies in the interior of the south Indian Ocean in the density range of SAMW. Interior spiciness anomalies simulated by OFES2 tend to be out of phase with observed anomalies (figure not shown). This discrepancy indicates an error in generation, subduction, and/or spreading processes of spiciness anomalies in the model. However, daily averages are available as output of OFES2, from which the terms in Eq. (1) can be computed directly. ECCO v4 reproduces the surface fields (Figs. 12b,d,f) and interior spiciness anomalies well, as it assimilates observational data. However, we need to compute MLD from monthly averages of temperature and salinity, which likely leads to nonnegligible errors for the mixed layer heat budget terms, in particular for the entrainment term (appendix B). Here, we present results from both of OFES2 and ECCO v4.
The mixed layer heat budget estimated from OFES2 output shows positive anomalies of the temperature tendency term in 2008–11 (Fig. 13a, thick black line), which corresponds to the increase of mixed layer temperature anomalies shown in Fig. 12e. The surface heat flux term shows anomalous cooling in 2008–10 (red line). The entrainment term (green line) and the diffusion term (orange line) show anomalous warming in 2008 and 2009, which tend to offset anomalous cooling due to the surface heat flux term. This is consistent with the idea of effective MLD, which claims that heat given to the surface mixed layer is redistributed to the depth of effective MLD by entrainment, and thus the effect of surface heat flux is counteracted (appendix A). Also, as discussed in the appendix A, vertical diffusion likely plays a similar role to that of entrainment, which is consistent with results in Fig. 13a. Anomalies of the entrainment (diffusion) term tend to be out of phase with those of the surface heat flux term in 2005–09 and 2012–13 (2008–09 and 2013). The horizontal advection term shows anomalous warming in 2006–11 (blue line), which contributes to the increase of mixed layer temperature anomalies. This supports the conclusion derived in section 4 that horizontal advection is the main driver of anomalous warming of the mixed layer. Warming due to the horizontal advection term is larger in magnitude than that of the temperature tendency term, which is likely owing to the fact that Ekman flow is trapped in a thin mixed layer and swift in summer. Meridional velocity averaged over the surface mixed layer and 38°–48°S, 100°–150°E obtained from OFES2 output tends to be larger in magnitude in summer than in winter (figure not shown). The advection term across the base of the mixed layer is relatively small in amplitude (gray line).
(a) The mixed layer heat budget terms obtained from OFES2 based on Eq. (1) and averaged over the analysis region (38°–48°S, 100°–150°E). The temperature tendency term (
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(a) The mixed layer heat budget terms obtained from OFES2 based on Eq. (1) and averaged over the analysis region (38°–48°S, 100°–150°E). The temperature tendency term (
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(a) The mixed layer heat budget terms obtained from OFES2 based on Eq. (1) and averaged over the analysis region (38°–48°S, 100°–150°E). The temperature tendency term (
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
Results from ECCO v4 also show the out-of-phase relationship between the surface heat flux term and the entrainment (diffusion) term in 2005, 2009, and 2011–15 (2008–10 and 2013) (Fig. 13b). The horizontal heat advection term shows anomalous warming in 2006–11, which contributes to the increase of mixed layer temperature anomalies. The surface heat flux term obtained from OFES2 shows anomalous cooling in 2008–10 and anomalous warming in 2012, but that from ECCO v4 shows anomalous warming in 2008–10 and cooling in 2011–15. This discrepancy may be due to the difference in the method of surface heat flux computation. ECCO v4 corrects surface heat flux using ocean state estimate, whereas given meteorological data were used to compute surface heat flux in the integration of OFES2.
Finally, we estimated the mixed layer heat budget using model/reanalysis output and the effective MLD approach. The MLD, mixed layer temperature, surface heat flux, and surface wind stress were obtained from model and reanalysis output. Surface geostrophic velocity was computed from output of SSH. We used daily averages of OFES2 output and monthly averages of ECCO v4 output. Results show the contribution of horizontal advection to anomalous warming in 2008–12 (Figs. 13c,d), which is consistent with observational results (Fig. 7a) and the heat budget estimate based on Eq. (1) (Figs. 13a,b). The surface heat flux term computed from OFES2 output shows weak anomalous cooling from 2007 to 2014 (red line in Fig. 13c), which compares well with observational results in Fig. 7a. On the other hand, the surface heat flux term computed from ECCO v4 output shows anomalous warming before 2009 (red line in Fig. 13d), which partly contributes to the increase of mixed layer temperature anomalies. It is difficult to determine which result is correct. We confirmed that this discrepancy is due to the differences in surface heat flux data. The sum of the surface heat flux and horizontal advection terms computed using the effective MLD approach agrees only roughly with the temperature tendency term (black and gray lines in Figs. 13c and 13d), which shows that the effective MLD approach is valid only qualitatively.
b. Effects of interannual variability in wintertime MLD on the mixed layer heat budget
As discussed in appendix A, we assumed that MLD can be replaced with its seasonal cycle plus the mean in the computation of the mixed layer heat budget terms. However, wintertime MLD averaged over the analysis region varies from about 220 to 320 m, which is comparable to seasonal variability in MLD in amplitude (Fig. 14). The following errors can be caused by ignoring interannual variability in wintertime MLD. First, we estimated heff from monthly climatological estimates of MLD, but wintertime MLD and thus heff change from year to year. This can affect the magnitude of the surface heat flux term and the Ekman flow advection term in Eq. (2). Second, if wintertime MLD is larger in a year than in the previous year, anomalously more subsurface water is entrained into the surface, which can cause interannual variability in mixed layer temperature. Third, interannual variability in MLD and the resulting variability in vertical mixing can generate spiciness anomalies by spiciness injection. In this subsection, we discuss these three issues.
Monthly estimate of MLD obtained from in situ observations and averaged over 38°–48°S, 100°–150°E. Values in September are marked by asterisks.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
Monthly estimate of MLD obtained from in situ observations and averaged over 38°–48°S, 100°–150°E. Values in September are marked by asterisks.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
Monthly estimate of MLD obtained from in situ observations and averaged over 38°–48°S, 100°–150°E. Values in September are marked by asterisks.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
1) Interannual variability in effective MLD
As described in appendix A, the formulation of Eq. (2) is defined as the time integral of the forcing terms from winter in a year (t = t0) to that in the next (t1). Thus, it is possible to define effective MLD for each year and compute the right-hand side terms of Eq. (2). Here we define the maximum of MLD in each calendar year as effective MLD in the year and refer to it as “yearly” effective MLD. We refer to effective MLD obtained from monthly climatological MLD as “climatological” effective MLD. Yearly effective MLD defined for 2010 was used to compute the right-hand side terms of Eq. (2) from September in 2009 to August in 2010, for example. The mixed layer heat budget was computed using yearly effective MLD using observations and output of OFES2 and ECCO v4. Results obtained from OFES2 and ECCO v4 show that the surface heat flux term estimated from yearly effective MLD (Figs. 15b,c, red line) is almost identical to that from climatological effective MLD (Figs. 13c,d, red line). The horizontal advection term estimated from yearly effective MLD compares well with that from climatological MLD, both of which show anomalous warming in most years after 2007 (Figs. 15b,c, blue line). This result indicates that interannual variability in effective MLD has a small effect on the estimate of the mixed layer heat budget.
(a)–(c) As in Fig. 7a, Fig. 13c, and Fig. 13d, respectively, but computed with yearly effective MLD. See text for the definition of yearly effective MLD.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(a)–(c) As in Fig. 7a, Fig. 13c, and Fig. 13d, respectively, but computed with yearly effective MLD. See text for the definition of yearly effective MLD.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(a)–(c) As in Fig. 7a, Fig. 13c, and Fig. 13d, respectively, but computed with yearly effective MLD. See text for the definition of yearly effective MLD.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
On the other hand, some discrepancy can be found in results obtained from observations. The surface heat flux term computed from observations and yearly effective MLD significantly contributes to anomalous warming of mixed layer temperature in 2009–11 (Fig. 15a), which is in contrast to results obtained from climatological effective MLD (Fig. 7a). This discrepancy likely reflects errors for yearly effective MLD obtained from in situ observations, as discussed below.
We compared the surface heat flux term computed with climatological effective MLD with that computed with yearly effective MLD obtained from observations (Fig. 16a). The difference is largest between about 115° and 135°E north of 43°S, where the wintertime mixed layer is thinnest in the analysis region (Fig. 16b). The surface heat flux term is proportional to the reciprocal of heff, and it is sensitive to variability in heff if the mean heff is small. The analysis error for monthly estimates of wintertime MLD (defined in section 3a) ranges from about 10 to 40 m (Fig. 16c), and the ratio of error to the mean is largest between 120° and 140°E north of about 44°S (Fig. 16d). The region with large noise-to-signal ratio approximately coincides with the region of the large difference between the two estimates of the surface heat flux term. Standard deviations of yearly effective MLD in this region are about 40 m (Fig. 16e), which is comparable to analysis error. The amplitude of surface heat flux anomalies (Q′) is almost the same in the analysis region (figure not shown), and it is likely that errors for MLD in the region of a thin mixed layer give rise to the difference between the two estimates of the surface heat flux term computed from observations. The noise-to-signal ratio is much smaller in monthly climatological estimate (Fig. 16f), which indicates that results obtained from climatological effective MLD suffer less from error. The horizontal advection term obtained from observations is less sensitive to these errors for MLD (Fig. 15a, blue line). These results show that yearly effective MLD obtained from in situ observations is erroneous. Considering this, we estimated the mixed layer heat budget from observations using climatological effective MLD.
(a) Standard deviations of the difference of the surface heat flux term between the one computed from climatological effective MLD and that from yearly effective MLD. See text for the definitions of climatological and yearly effective MLD. (b) The mean MLD in September. (c) The mean of dimensional error for monthly estimates of MLD in September for the period from 2004 to 2018. (d) Ratio of dimensional MLD error to the mean MLD in September obtained from monthly estimates. (e) Standard deviations of monthly estimates of MLD in September for the period from 2004 to 2018. (f) As in (d), but obtained from monthly climatological estimates. Box illustrates the analysis region (38°–48°S, 100°–150°E). Results were obtained from in situ observations.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(a) Standard deviations of the difference of the surface heat flux term between the one computed from climatological effective MLD and that from yearly effective MLD. See text for the definitions of climatological and yearly effective MLD. (b) The mean MLD in September. (c) The mean of dimensional error for monthly estimates of MLD in September for the period from 2004 to 2018. (d) Ratio of dimensional MLD error to the mean MLD in September obtained from monthly estimates. (e) Standard deviations of monthly estimates of MLD in September for the period from 2004 to 2018. (f) As in (d), but obtained from monthly climatological estimates. Box illustrates the analysis region (38°–48°S, 100°–150°E). Results were obtained from in situ observations.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
(a) Standard deviations of the difference of the surface heat flux term between the one computed from climatological effective MLD and that from yearly effective MLD. See text for the definitions of climatological and yearly effective MLD. (b) The mean MLD in September. (c) The mean of dimensional error for monthly estimates of MLD in September for the period from 2004 to 2018. (d) Ratio of dimensional MLD error to the mean MLD in September obtained from monthly estimates. (e) Standard deviations of monthly estimates of MLD in September for the period from 2004 to 2018. (f) As in (d), but obtained from monthly climatological estimates. Box illustrates the analysis region (38°–48°S, 100°–150°E). Results were obtained from in situ observations.
Citation: Journal of Climate 34, 10; 10.1175/JCLI-D-20-0482.1
2) Entrainment
(a) Climatological MLD averaged over the analysis region (38°–48°S, 100°–150°E). (b) The entrainment term estimated by Eq. (4). A three-point running-mean filter was applied. (c) The difference between mixed layer temperature and temperature at the base of the mixed layer ave