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The All-Atlantic Temperature-Salinity-Pressure Relation and Patched Potential Density

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The All-Atlantic Temperature-Salinity-Pressure Relation and Patched Potential Density Journal of Marine Research, 63, 59–93, 2005 The all-Atlantic temperature-salinity-pressure relation and patched potential density by Roland A. de Szoeke1 and Scott R. Springer2 ABSTRACT The relation between temperature, salinity, and pressure in the Atlantic Ocean is examined. Most of the Atlantic resolves itself into three two-dimensional manifolds of three-dimensional thermody- namic space: a northern, more saline, branch, and a southern, fresher, branch, each quite independent of pressure, and between them a bridge, on which density is uniform at constant pressure. The properties of the branches are crucial to the construction of joint potential density surfaces, patched together at 1000 db intervals. By resolving more finely in pressure (illustrated with 200 db spacing), a finer system of patched potential density surfaces can be obtained, and indeed the continuous limit can be taken. This limit gives a form of orthobaric density, regionally differentiated because it is based on the duplicate regional branches. A mapping can be devised, using the properties of the bridge waters, that links the southern and northern forms of orthobaric density across the boundary between their respective regions of validity. The parallel of patched potential density surfaces to orthobaric density surfaces permits the use of measures developed for the latter to estimate quantitative measures of the material nature (or otherwise) of the former. Simply put, within the waters of the respective branches the patched isopycnals, or orthobaric isopycnals, are very nearly material, limited only by inherent irreversible mixing processes. However, where these isopycnals cross the bridge waters, significant, reversible, material exchange across them may occur. A difficulty may be encountered with coarsely resolved, regionally differentiated, patched potential density. This is that there exist ranges of density which cannot be consistently linked across the regional boundary. A solution for the difficulty, suggested by the continuous form (regionally differentiated orthobaric density), is proposed. 1. Introduction The regularity of the relation between potential temperature ␪ and salinity S in the ocean has long been remarked on (Helland-Hansen and Nansen, 1926; Wu¨st, 1933; Iselin, 1939; Sverdrup et al., 1942; Montgomery, 1958; Reid, 1981). Volumetric censuses of water types (finely resolved temperature-salinity combinations) have been published by Worth- ington (1981). Understanding the ␪ϪS relation is key to the mechanisms of the thermohaline circulation and mixing in the ocean (Stommel and Csanady, 1980; McDougall, 1. College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon, 97331, U.S.A. email: [email protected] 2. College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon, 97331, U.S.A. email: [email protected] 59 60 Journal of Marine Research [63, 1 1987). Water properties are frequently charted on core layers, defined by extrema of water characteristics such as salinity or oxygen, that are clearly delineated on ␪ϪS and other property-property relations (Wu¨st, 1933). These core layers are held to reveal the directions of spreading of water masses from their source regions. Alternatively, potential density surfaces, with which core layers often coincide, have been used instead to chart water mass spreading and mixing, particularly as density surfaces indicate dynamically neutral internal horizons in the ocean, and their slopes are related to geostrophic currents (Montgomery, 1938; Reid, 1965, 1981). However, this practice has raised the difficulty of potential density’s undue reliance on the thermal expansion coefficient at the reference pressure (Ekman, 1934). Reid and Lynn (1971) tried to overcome this difficulty by using patched potential density surfaces. These are composed of leaves of potential density surfaces in restricted ranges of pressure (typically 1000 db), referenced to the center of that range, and patched to neighboring leaves so as to minimize dislocation at the overlaps of the pressure ranges. De Szoeke et al. (2000) showed that the patching procedure is equivalent to selecting standard salinity functions of specific volume at the overlap pressures. Alternatively, these can be expressed as salinity vs. temperature functions at fixed pressure. Jackett and McDougall (1997) devised ways of calculating neutral density surfaces which they held to be the continuous analogue of patched potential density surfaces (see also Eden and Willebrand, 1999). These considerations motivate an examina- tion of ␪ϪS relations at fixed pressure to understand how the variable-reference potential density idea might work. Accordingly, in this paper we undertake a refinement of the traditional view of the ␪ϪS relation by differentiating the relation further by pressure (or depth). This reveals insights into the structure of the ocean perhaps more interesting than the original motivation, as we will show. The data we use is the WOCE Atlantic hydrographic set. The three-dimensional temperature-salinity-pressure relation is shown, from a number of points of view. We show how the Atlantic Ocean data resolve into three two-dimensional manifolds of thermody- namic space, and confirm that Reid’s (1994) potential density patching method relies on the empirical relations of ␪ vs. S on two of these manifolds. We also confirm that there is a correspondence between patched potential density and regionally differentiated orthobaric density predicated on the same ␪ϪS relations (de Szoeke et al., 2000), and show how quantitative estimators of the degree of materiality of orthobaric density can be used to evaluate either kind of density. The Atlantic ␪؊S ؊ p relation .2 We used the 10-decibar hydrographic data file made available by the international World Ocean Circulation Experiment (WOCE) project to plot diagrams of potential temperature vs. salinity for pressures between 300 decibars (db) and 4000 db in the North and South Atlantic oceans (Fig. 1; maps of station locations are shown in Fig. 5). McDougall and Jackett (2005) show similar diagrams derived from atlas data (Gouretski and Koltermann, 2004). 2005] de Szoeke & Springer: All-Atlantic temperature-salinity-pressure relation 61 These diagrams show a number of interesting features. (i) A lower salinity branch extends from warm temperatures associated with the subtropical gyre to the salinity minimum associated with the Antarctic intermediate water, turns sharply toward higher salinity between 2.0–2.5°C, and then turns sharply again to join the cold, salty Antarctic bottom water. It is convenient to call this set of waters, usually called the south central waters (Sverdrup et al., 1942), the southern branch. By overlaying the diagrams for varying pressure, one sees that the form of this branch is virtually independent of pressure. (ii) A parallel branch, though without the twists at low temperature, of waters about 1–1.5 psu saltier than the southern branch, extends almost to the warmer end of the Antarctic bottom water. These waters—the north central waters—constitute the northern branch. Like the southern branch, the form of this branch is independent of pressure. (iii) Straddling the southern and northern branches, at each pressure from 300 db to about 2000 db, there is a bridge. At the low salinity end of the bridge, before reaching the southern branch, the bridge joins to a spur extending from and nearly parallel with that branch. The bridge shifts with pressure. At pressures deeper than 900 db, the bridge, the southern branch (of which only the line joining the Antarctic intermediate water to the Antarctic bottom water remains), and the northern branch form a triangle which gradually contracts to a small volume at 2000 db, although the line of the bridge is still discernible. (iv) At pressures deeper than 500 db, the bridge extends through and beyond the northern branch, with density increasing with salinity for pressures shallower than 1000 db. This bridge extension is a direct link to the Mediterranean outflow. Specific volume anomaly (SVA), defined by ␦ϭ␣(S, ␪, p) Ϫ␣(35, 0, p), has been re-plotted vs. salinity (Fig. 2). The diagrams show that the bridge at any pressure deeper than 500 db has an almost constant specific volume. At pressures shallower than 500 db, SVA increases slightly with salinity on the bridge. The extension of the bridge beyond the northern branch appears to have lower SVA. What seems most remarkable about the diagrams of Figure 1 is how little of ␪ϪS Ϫ p space the Atlantic Ocean actually occupies, as McDougall and Jackett (2005) also point out. The ocean is pretty flat in thermodynamic space, being composed, in idealized approximation, of the union of three two-dimensional manifolds, the northern and southern branches which are independent of pressure, and the bridge, joining the two and forming a ramp of SVA as a function of pressure. Deeper than a few hundred decibars, the pressure dependence of SVA of the bridge is described well by the profile shown in Figure 3. The value given by this profile is indicated on each panel of Figure 2. Variation from the idealized forms clearly occurs. In the bridge, this could be attributed to adiabatic heaving of isopycnals about their mean positions by internal motions that are aliased in the synoptic WOCE data. Such an explanation does not suffice in the southern 62 Journal of Marine Research [63, 1 Figure 1. Potential temperature ␪ vs. salinity S for numerous values of pressure, from the WOCE data. The southern and northern water masses describe a vertical shaft (independent of pressure) in ␪ϪS Ϫ p space, while a bridge joining them, and extending to higher salinity beyond the northern branch, forms a sloping ramp. Note the change of scale for pressures greater than 2000 db. Colors, for pressures Յ 1000 db: red denotes the bridge between the northern and southern branches; green (magenta), the parts of the northern and southern branches warmer (colder) than the bridge; dark blue, the high-salinity extension of the bridge; light blue, the intersection of the bridge with the northern branch.
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