Decreased Stratification in the Abyssal Southwest Pacific Basin and Implications for the Energy Budget

As the abyssal oceans warm, stratification is also expected to change in response. This change may impact mixing and vertical transport by altering the buoyancy flux, internal wave generation, and turbulent dissipation. In this study, repeated surveys of three hydrographic sections in the Southwest Pacific Basin between the 1990s and 2010s are used to estimate the change in buoyancy frequency N2 . We find that below the θ=0.8 °C isotherm, N2 is on average reduced by a scaling factor of s=0.88±0.06 , a 12% reduction, per decade that intensifies with depth. At Θ=0.63 °C, we observe the biggest change: s=0.71±0.07 , or a 29% reduction per decade. Within the same period, the magnitude of vertical diffusive heat flux is also reduced by about 0.01Wm−2 , although this estimate is sensitive to the choice of estimated diffusivity. Finally, implications of these results for the heat budget and global ocean circulation are qualitatively discussed.

2 of 11 currents (DWBC) (Orsi et al., 1999;Talley, 2013). As AABW travels north, diapycnal mixing brings in heat from above, lightening the bottom water and creating upwelling (Lumpkin & Speer, 2007;Munk, 1966). This process ventilates the abyssal ocean, forming the upward branch of the overturning circulation (De Lavergne et al., 2016;Nikurashin & Ferrari, 2013). Since it was more recently at the surface, this bottom water is younger than the deep waters above (England, 1995). Changes in the surface conditions around the Antarctic margin, where AABW is produced including warming, increased glacial fresh water flux, or changes in sea ice production and export, can affect AABW production rates (Castagno et al., 2019;Jacobs & Giulivi, 2010;Purkey & Johnson, 2012;Thomas et al., 2020). While the time scale of the MOC is multicentennial, models have shown that a deep water production rate anomaly can propagate from the Adélie Coast to the North Pacific in as little as 40 years (Masuda et al., 2010). Therefore, recent climate shifts near Antarctica can have a global effect within a few decades, and fingerprints of these changes can be observed in the time-span of global data collection (Johnson et al., 2007;Purkey & Johnson, 2010).
Stratification change alters the medium of local dynamics, which can have feedback effects on the global climate. For example, background stratification sets the hydrostatic balance, a key component of the generation of internal waves from barotropic tidal flow over uneven topography (Baines, 1982;Bell, 1975;Garrett & Kunze, 2007). Globally, the tides input about 1 TW into the internal wave field, a significant portion of the total mixing required to close the MOC (Egbert & Ray, 2000;St. Laurent & Simmons, 2006;Waterhouse et al., 2014). Once generated, stratification also influences the internal wave's propagation, breaking, and subsequent turbulent dissipation (Gregg, 1989). Finally, it directly impacts the temperature gradient, setting the vertical heat flux. Due to the stratification's influence on the vertical transport of heat and other tracers such as oxygen and carbon, it is a key aspect of climate projections (Melet, Hallberg, et al., 2013).
While the processes discussed above are global, it is valuable to analyze their exact mechanisms on a sub-basin scale. This paper focuses on the Southwest Pacific Basin (SPB), a key pathway in the transport of AABW ( Figure 1) that connects deep waters in the Southern Ocean to the Pacific (Sloyan & Rintoul, 2001;Whitworth et al., 1999). As there is no deep water formation in the North Pacific, the bottom branch of the Pacific MOC is sourced exclusively from southern high latitudes and carried north via the DWBC. Between 60°S and 20°S, more than 70% of the water in the abyssal ocean is AABW in origin despite strong mixing by the  (Purkey & Johnson, 2010). Section identifiers (from World Ocean Circulation Experiment [WOCE] and now Global Ocean-Based Hydrographic Investigations Program [GO-SHIP]) used in this analysis are depicted, and key topographic features are labeled for reference. The gray arrow represents the approximate pathway of the Deep Western Boundary Current (Whitworth et al., 1999).

of 11
Antarctic Circumpolar Current (ACC) (Johnson, 2008). AABW is carried into the basin south of the Campbell Plateau, flowing northwards through the Kermadec and Tonga Trench, and exiting into the Pacific Basin via the Samoan Passage ( Figure 1). In the Samoan Passage, most of the northward flow is below 0.85°C (Roemmich et al., 1996;Voet et al., 2016). Since AABW warms as it travels north, within the scope of this paper we shall define AABW to be everything colder than 0.8°C.
Here, we quantify the stratification change in the SPB from the 1990s through 2017 and analyze the spatial pattern of this change. Basin wide averages of the change in both stratification and heat flux are estimated. Finally, we discuss the implications of these findings and potential feedbacks.

Data and Methods
We use deep ocean temperature, salinity, and pressure data from repeated ship-based hydrographic surveys to determine the decadal rate of change of stratification and heat flux. The first surveys were collected in the 1990s by the World Ocean Circulation Experiment (WOCE), which conducted full-depth high resolution CTD surveys along sections transecting the global oceans. This effort, along with a sub-set of selected WOCE sections was sustained through the 2000s by the Climate Variability and Predictability (CLIVAR) program, and since the 2010s has been coordinated by the Global Ocean-Based Hydrographic Investigations Program (GO-SHIP).
We consider a latitudinal section, P06, and two longitudinal sections, P15 and P16 ( Figure 1). P06 (blue line) provides a zonal cross section of northward bottom water transport while P15 and P16 (purple and green lines) capture a meridional view. P06 was occupied in 1992, 2003, 2010, and 2017; P16 in 1992, 2005, and 2014; and P15 in 1996, 2001, 2009, and 2016. Only the 1996 and 2016 occupations of P15 extend further are respectively the thermal expansion and saline contraction coefficients, sp E V is the specific volume calculated using a 75-term polynomial expression, and E P is pressure (Roquet et al., 2015).
For each grid point, we also calculate vertical heat flux ( E Q ) using the equation, where  E and p E c are respectively the density and heat capacity of seawater, both assumed constant.   Θ E z is the difference in conservative temperature between successive pressure grids. The diffusivity  E is parameterized in two different ways. The first method uses the canonical constant value of 10 4 2  m /s , which produces a heat flux estimate proportional to the temperature gradient (Munk, 1966;Waterhouse et al., 2014). The second method uses an estimate of the local diffusivity calculated from a finescale parametrization of the strain in each temperature profile (Gregg & Kunze, 1991;Henyey et al., 1986;Kunze et al., 2006;Osborn, 1980; 4 of 11 Polzin et al., 1995Polzin et al., , 2014Whalen et al., 2015) with the bottom boundary layer removed using a method inspired by de Boyer Montegut et al. (2004) (see Supporting Information S1 and S2 for details). Once the diffusivity is estimated, it is interpolated onto the 40 dbar by 2° grid (same grid used for temperature and stratification). Then all estimates of the same section across occupations are averaged together. As diffusivity is a log-normal variable and we have a limited number of estimates for each location, a geometric mean is used for this average (McAlister, 1879). The second method for calculating heat flux allows for a wide range of abyssal diffusivities driven by various bathymetric features. This implies that areas with rougher bathymetry are weighted more compared to areas with a smoother seafloor.

Isotherm Grid
To eliminate the potential effects of smaller scale density perturbations, we reparametrize the gridded 2 E N and heat flux values by temperature, which we use as a proxy for density. Since small errors in salinity have a significant impact on density, particularly in the deep ocean, temperature is chosen to avoid amplifying the salinity errors (Purkey & Johnson, 2013). Using Θ E from each occupation, the values, initially binned by pressure, are piecewise cubic interpolated onto a 0.01°C temperature grid. We will refer to each of the these temperature bins as a temperature class. This shift in perspective allows for direct comparisons between properties within a water mass over time, regardless of the vertical movement of the water mass.

Decadal Trends
The trend of 2 E N or heat flux over time at each grid point in a section is estimated as the slope of the linear fit across all occupations following the methods of Purkey and Johnson (2010). Since sections are reoccupied about once every decade, the trend is calculated on a decadal scale. To smooth small scale fluctuations of the profile, we average the value of each bin with that of the bins above and below (except along boundaries). The smoothed profile is used to calculate the trend.
Because 2 E N is a log-normal value (Gregg, 1989) The heat flux trend throughout each section is calculated using the same method as the stratification trend, albeit in linear space. This produces the standard linear trend and does not need to be expressed as a scale.
To estimate a basin average profile of the stratification or heat flux trend, the spatially variable trends across each section are re-gridded from the original pressure bins into 0.01°C temperature bins as described in Section 2.1. The mean profile and error is calculated using the length weighted mean and standard deviation of the trends in each temperature class across all three sections constrained within the boundaries of the SPB as defined by Purkey and Johnson (2010).
Confidence intervals are determined by calculating the degree of freedom (DOF) along each temperature class using a horizontal decorrelation length scale of 163 km, originally calculated using temperature changes (Purkey & Johnson, 2010). If the isotherm is segmented by topography, each portion is assumed to be statistically independent and to contribute at least one DOF. The standard error is then calculated by dividing the standard deviation by the square root of the DOF. The 95% confidence interval is then found using a Student's t distribution.

Results
Warming between the 1990s and 2010s is more prominent near the bottom, a trend which has been observed in all three sections in this analysis and noted by multiple previous studies (D. G. Desbruyeres (Figure 2a), while the observed temperature change between the 0.8°C and 1.0°C isotherms is negligible. Abyssal warming is most prominent in the western side of the basin along the path of the DWBC (Figure 2a). Within the layer of AABW, warming is strongest near the sea floor. As a result, colder isotherms deeper in the water column have deepened at a faster rate. For example, between 1992 and 2017, the  Θ 0.65 E °C isotherm has deepened by 562 m, while the  Θ 0.8 E °C isotherm only by 14 m. Further down in the water column, the  Θ 0.6 E °C isotherm completely disappeared by 2017, indicating an absence of the coldest waters. In contrast, warmer isotherms such as  Θ 1.0 E °C have remained relatively stationary due to minimal temperature changes. The two meridional sections that intersect P06 in the SPB, P15 (to the west) and P16 (to the east) can provide additional context for the observed zonal variation (Figures 3a and 3b). P15 follows the DWBC which carries AABW and, as a result, below 4,000 dbar it is on average 0.1°C colder than P16. At depth, P15 is warming 90% more per decade than P16. Overall, the spatial patterns of the bottom intensified warming are similar to that of the 2 E N reduction. Compared to P06, the 2 E N trends of P15 and P16 exhibit more variability.
While both sections P15 and P16 show a near bottom reduction in 2 E N , particularly below 5,000 dbar, the trend in P15 is much larger. A strong 2 E N decrease is observed south of 55°S where AABW is advected into the basin, and in the deepest region between 20°S and 35°S (Figure 3c). In P16, we observe the most substantial 2 E N reduction between 45°S and 35°S.
Averaged across all sections, we find a statistically significant ( ) E s N below  Θ 0.75 E °C. Despite variability across isobaths (Figures 2 and 3), 2 ( ) E s N shows a consistent trend across isotherms in all sections, as indicated by the overlapping confidence intervals (Figure 4). There is an intensified stratification reduction in colder temperature classes at depth. At the AABW boundary (   (Figure 4b). Despite having more spatial variability across the section, the 2 E N trend of P15 decreases significantly down to  Θ 0.63 E °C, agreeing well with the trend seen in P06. Below this isotherm, the only data in the basin come from a small region at the southern end of P15, causing greater uncertainty.  A changing stratification may alter the medium of internal wave generation, propagation, and dissipation, the main drivers of mixing in the deep ocean (St. Laurent & Garrett, 2002;Waterhouse et al., 2014). The energy conversion from barotropic tidal flow over uneven topography to internal gravity waves scales with E N (Bell, 1975;Garrett & Kunze, 2007;Melet, Nikurashin, et al., 2013). Once generated, the average energy dissipation rate of internal waves   E  is proportional to 2 E N (Gregg, 1989;Polzin et al., 2014). In the upper ocean, increased surface heating has created a stronger stratification, which is linked to more internal wave activity and turbulent energy dissipation (Capotondi et al., 2012;DeCarlo et al., 2015). In contrast, we find a significant 2 E N reduction along near bottom isotherms that is enhanced with depth. Consequently, we expect a decrease in both internal wave tidal energy conversion and turbulent energy dissipation rate by the respective scaling relations of Bell (1975) and Gregg (1989 averaged across all three study sections. The large error interval is a product of low signal-to-noise ratio and the sensitivity of tidal energy conversion to topographic variations within the basin (Melet, Nikurashin, et al., 2013). However, recent studies have shown that warming in the Southwest Pacific has accelerated in the 2010s compared to previous decades Purkey et al., 2019). Since we find that 2 E N decrease correlates to bottom intensified warming, the accelerated warming may lead to an accelerated 2 E N reduction. If this trend continues, the impact on internal waves could become more significant in the coming decades.
The weakening temperature gradient associated with the stratification decrease results in a smaller downward heat flux. The magnitude of the estimated trend is dependent on whether the diffusivity  E is assumed to be spatially uniform or varying. With uniform diffusivity, the estimated heat flux change is proportional to the changing temperature gradient. In contrast, considering the spatial variation of diffusivity accounts  for enhanced mixing over rough topography (Ledwell et al., 2000). Since abyssal temperature profiles are relatively homogeneous, a single temperature class may reside in both strong and weak mixing environments, increasing the variance of heat flux change along each Θ E value, widening the confidence interval. Heat flux change estimates using both a constant and spatially variable parameterization of diffusivity show a decreasing trend in downward heat diffusion over the past three decades (Lele et al., 2021). As a result, less heat (and thus buoyancy) is mixed into the deep ocean from above. Over time, this may allow the water column to re-stratify, potentially reversing the observed trend. Additionally, the observed decrease of abyssal heat flux could reduce the ability of the deep ocean to act as a heat sink for the warming upper ocean, although this may be corrected by the negative feedback loop. More research is needed to examine the timescales of these changes and feedbacks, which should be considered both locally and on a global scale.
This study suggests a connection between stratification and heat flux change, which is potentially linked to future changes in internal wave generation and dissipation. Both 2 E N and turbulent dissipation are important for upwelling, and an alteration of these terms will have consequences for the strength of the abyssal MOC (Furue & Endoh, 2005;Hieronymus et al., 2019;Jayne, 2009;Oka & Niwa, 2013). However, current efforts have yet to untangle these interconnected contributions. While bottom warming is almost ubiquitous in the world's oceans, much is still unknown about stratification change in other basins, and how it relates to global mixing processes, heat flux, and ocean circulation. Since vertical transport of heat and water is key for accurate climate projections (Melet, Hallberg, et al., 2013), more deep ocean research, and data, such as the establishment of a Deep Argo program (Johnson et al., 2015), is critical for improving predictions of future climate scenarios.

Data Availability Statement
Data Accessibility Statement CTD data from each each individual cruise along lines P06, P15, and P16 are accessed through https://cchdo.ucsd.edu. Data were collected and made publicly available by the International Global Ship-based Hydrographic Investigations Program (https://www.go-ship.org/; https://cchdo. ucsd.edu) and the national programs that contribute to it.