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following highly simplified equation of state obtained by drawing short lines tangent to the isopleths of a in Fig. 9.2 and writing:

where a0(T0, S0) is the density anomaly (at the point T0 and S0 in Fig. 9.2), about which we draw the tangent line to compute (small) variations in a. Note that pressure dependence in the above idealized expression is captured by making aT = aT(p) (see Table 9.4). Recall that a simplified form of Eq. 9-5 was used in our discussions of convection of an incompressible fluid in Section 4.2.2.

slope increasingly upward with increasing T) and at greater pressures (see Table 9.4).

The dependence of density on salinity is defined by:

Pref dS

(where T and p are kept constant). As can be seen in Fig. 9.2 and Table 9.4, PS varies very little and has a value close to 7.6 x 10-4psu-1.

It is sometimes useful to approximate the dependence of a on T, S, and p using the

9.1.4. Temperature, salinity, and temperature structure

Here we briefly describe the large-scale distribution of temperature and salinity at the surface of the ocean and its interior. We postpone an attempt at an "explanation" until Chapters 10 and 11.

Water has an albedo of around 10% (see Table 2.2) depending on surface conditions, and so absorbs solar radiation very efficiently. Not surprisingly sea surface temperatures, plotted in Fig. 9.3, are warmest in the tropics (up to almost 30°C) and coldest

(0°C) in high latitudes. The warmest water, that with a temperature greater than about 29° C, follows the Sun north and south. But there are also large east-west variations, particularly in the tropics, with relatively cool temperatures in the east, and the warmest temperatures west of the International Date Line. This latter region coincides with the location of greatest atmospheric convection (see Fig. 4.26), which can become very vigorous when ocean temperatures exceed about 27°C, an indication of the climatic importance of the tropical Pacific Ocean (to be discussed in Section 12.2). In middle latitudes there are large east-west differences in Sea Surface Temperature (SST) related, as we shall see, to the juxtaposition of cold boundary currents flowing toward the equation and warm boundary currents flowing toward the poles (e.g., in the region of the Gulf Stream in the Atlantic and the Kuroshio in the Pacific). There are also cold regions off California and Africa, which are not so obviously related to the advective influence of ocean currents. One also observes strong meridional gradients in SST in the Southern Ocean associated with the eastward flowing Antarctic Circumpolar Current. The coldest surface waters are found in the northern North Atlantic Ocean and around Antarctica. As will be discussed in Chapter 11, these are the regions of deepest ocean convection, where the surface ocean communicates with the abyss.

The annual mean salinity distribution at the surface of the ocean is shown in Fig. 9.4. Evaporation from the surface in the subtropics is vigorous and exceeds precipitation; since evaporation removes water, but not salt, the near-surface salinity is elevated here. In high latitudes and near the equator, there is an excess of precipitation over evaporation, so the surface waters are relatively fresh here. High values of salinity (> 38 psu) are found in the Mediterranean and the Persian Gulf. Low values of salinity (< 31 psu) are found near melting ice edges and at river outflows. Note that the surface salinity in the Atlantic is higher than that in the Pacific, making Atlantic surface waters more susceptible to convection.

Observed zonal-average mean distributions of T, S, and a in the interior of the ocean are shown3 in Figs. 9.5,9.6, and 9.7. Note that the top panel in each of these figures shows a blow-up of the upper 1000 m of the ocean; the bottom panel plots properties over the full ocean depth. The reason for this is that the largest vertical gradients of properties are found near the surface. In the abyss, vertical gradients are weak and horizontal gradients are almost nonexistent; for example, the deep ocean is everywhere very cold (0-2°C) and no more that 1°C warmer in the tropics than in high latitudes (see Fig. 9.5). In the upper kilometer of the ocean, however, shown in the top panels of Figs. 9.5, 9.6, and 9.7, there are strong vertical gradients (especially of temperature and density); this is the thermocline of the world's oceans, having a depth of about 600 m in middle latitudes but shoaling to 100-200 m in low latitudes. The temperature contrast between high and low latitudes is not surprising; the salinity contrast, as noted above and discussed in Chapter 11, reflects the pattern of evaporation and precipitation. Notice how, particularly around Antarctica, cold surface water can be less dense than warmer fluid beneath because it is so much fresher. Note also that the contours of temperature, salinity, and density anomaly "outcrop" (rise to the surface) in high latitudes, suggesting an important linkage between the high latitude surface waters and the deep ocean.

3In fact, what is shown in Figs. 9.5 and 9.7 are potential temperature and potential density, allowing for compressibility effects. Potential temperature, in direct analogy to its definition in a compressible fluid like the atmosphere (Section 4.3.2), is the temperature that a water parcel would have if moved adiabatically to a reference pressure, commonly chosen to be the sea surface. We define potential density as the density a parcel would have when moved adiabatically to a reference pressure. If the reference pressure is the sea surface, we compute the potential temperature of the parcel, and evaluate the density at zero pressure. The measured salinity is used because it has very little pressure dependence.

FIGURE 9.5. Annual-mean cross-section of zonal average potential temperature (in °C ) in the world's oceans. The top shows the upper 1 km. The bottom shows the whole water column. Dark shading represents warm water. Note the variable contour interval in the bottom plot. Data from the Levitus World Ocean Atlas (1994).

FIGURE 9.5. Annual-mean cross-section of zonal average potential temperature (in °C ) in the world's oceans. The top shows the upper 1 km. The bottom shows the whole water column. Dark shading represents warm water. Note the variable contour interval in the bottom plot. Data from the Levitus World Ocean Atlas (1994).

In summary, the zonal average picture reveals a warm, salty, light lens of fluid in the subtropics of each hemisphere, shoaling on the equatorial and polar flanks, "floating'' on a cold, somewhat fresher abyss. These lenses exist in each ocean basin but exhibit considerable regional characteristics and variability. For example, Fig. 9.8 maps the depth of the a = 26.5 kgm-3 surface over the global ocean; we chose the depth of this surface because, as can be seen in the zonal-average plot, Fig. 9.7, it lies roughly in the middle of the thermocline. One can readily observe the geography of the subtropical lenses of light fluid in both the northern and southern hemispheres. Note that the lens is deeper in the Pacific than the Atlantic; and outcrops in the Atlantic near 40° N and around the Southern Ocean.

Figure 9.9 shows a detailed hydrographic section4 of T and S along (nominally) 30° W

4A hydrographic section is a section of T and S as a function of depth, obtained by lowering a CTD (a device that measures Conductivity—hence salinity—Temperature, and Depth) from a ship to the bottom of the ocean. It takes about

1 month to complete a section such as Fig. 9.9 and so gives us a snap-shot of the interior T, S structure of the ocean. The average sections shown in, for example, Figs. 9.5 and 9.6 are obtained by zonally averaging hundreds of such sections crisscrossing the ocean. Such zonal-average sections give us a coarse, blurred, but nevertheless instructive view of the meridional structure.

Zonal Average Salinity in World Oceans (psu)

Zonal Average Salinity in World Oceans (psu)

LMKud*

LMKud*

uttudt

uttudt

FIGURE 9.6. Annual-mean cross-section of zonal average salinity (in psu) in the world's oceans. The top shows the upper 1 km. The bottom shows the whole water column. Dark shading represents salty water. Data from the Levitus World Ocean Atlas (1994).

in the Atlantic. The thermocline is clearly visible, deep in the subtropics (± 30° ), shallow in equatorial regions and has much more detailed structure than the zonally averaged view of the thermocline evident in Fig. 9.5. The salinity field reveals an interesting layering of subsurface flow, which we discuss in more detail in Section 11.2.

### 9.1.5. The mixed layer and thermocline

At the surface of the ocean there is a well-defined mixed layer in direct contact with the overlying atmosphere, stirred by winds and convection, in which properties are relatively uniform in the vertical. The mixed layer depth varies with latitude and season, but is typically 50-100 m deep (see Fig. 9.10). Over the bulk of the ocean the mixed layer communicates with the underlying thermocline, except in high latitudes (particularly in the northern North Atlantic and around Antarctica) where it can get very deep (> 1 km) and thus comes into direct contact with the abyss.

The processes forming the mixed layer are illustrated schematically in Fig. 9.11. Radiation entering the ocean surface is absorbed mostly in the top few meters (depending on wavelength; IR is absorbed within a few mm, blue/green light may penetrate to almost 100 m in especially clear water, but is usually attenuated much more

Zonal-Average, Annual-Mean, Potential Density (kg/m:l)

Zonal-Average, Annual-Mean, Potential Density (kg/m:l)

FIGURE 9.7. Annual-mean cross-section of zonal average potential density anomaly a = p - pref (inkgm-3) for the world's oceans (referenced to the surface). The top shows the upper 1 km . The bottom shows the whole water column. Note that the contour interval is not uniform. Data from the Levitus World Ocean Atlas (1994).

IkBim")

FIGURE 9.7. Annual-mean cross-section of zonal average potential density anomaly a = p - pref (inkgm-3) for the world's oceans (referenced to the surface). The top shows the upper 1 km . The bottom shows the whole water column. Note that the contour interval is not uniform. Data from the Levitus World Ocean Atlas (1994).

rapidly). Heat loss, through IR radiation, sensible heat loss to the atmosphere, and latent heat loss through evaporation (see Chapter 11 for a more detailed discussion), occur at or within a few mm of the surface. The cooling and salinization of the surface water increases its density. Since, in an incompressible fluid, our criterion, Eq. 4-5, for the onset of convection is dp/dz > 0, surface buoyancy loss drives con-vective motions which stir the mixed layer and tend to homogenize its temperature and other properties, just as studied in GFD Lab II in Section 4.2.4. These turbulent motions within the mixed layer may entrain cold water upward across the mixed layer base. In addition, wind stress at the surface drives turbulent motions within the mixed layer, which mix vertically and entrain fluid from below. Furthermore, because the base of the mixed layer slopes (Fig. 9.10), horizontal currents can carry properties to and from the mixed layer in a process known as "subduction."

Beneath the mixed layer, T and S rapidly change over the depth of the thermocline to match the properties of the relatively homogeneous abyss. Fig. 9.12(a) shows the

FIGURE 9.8. Depth in m of the annual-mean a = 26.5 kgm-3 surface over the global ocean. Note the position of the outcrop—the line along which the a surface cuts the sea surface—in the North Atlantic and in the southern ocean. Data from the Levitus World Ocean Atlas (1994).

FIGURE 9.9. Hydrographie section along (roughly) 25° W through the Atlantic Ocean (see inset). Top: Potential temperature contoured every 2.5°C (solid) and every 0.5°C (dotted). Bottom: Salinity (in psu). Values greater than 35 are contoured every 0.5 psu (solid); values less than 35 are plotted every 0.1 psu (dotted). Figure produced using Ocean Data View.

FIGURE 9.9. Hydrographie section along (roughly) 25° W through the Atlantic Ocean (see inset). Top: Potential temperature contoured every 2.5°C (solid) and every 0.5°C (dotted). Bottom: Salinity (in psu). Values greater than 35 are contoured every 0.5 psu (solid); values less than 35 are plotted every 0.1 psu (dotted). Figure produced using Ocean Data View.

Mixed Layer Depth (m)

1000 900 800 700 800 500 400 300 200 100 0

mixed layer depth [mj

FIGURE 9.10. Mixed layer depth (in m) in (top) JFM (January, February, March, northern hemisphere winter) and (bottom) JJA (June, July, August, Southern hemisphere winter). Black contours mark the 100 and 200 m mixed layer depth isopleths. Data from the Levitus World Ocean Atlas 1994.

1000 900 800 700 800 500 400 300 200 100 0

mixed layer depth [mj

FIGURE 9.10. Mixed layer depth (in m) in (top) JFM (January, February, March, northern hemisphere winter) and (bottom) JJA (June, July, August, Southern hemisphere winter). Black contours mark the 100 and 200 m mixed layer depth isopleths. Data from the Levitus World Ocean Atlas 1994.

annual mean T and S profile at 50° W, 30° N in the Atlantic Ocean. The thermocline is clearly evident in the upper 1 km of the water column. Since density increases sharply downward across the thermocline, it is very stable, rather like the stratosphere.

We can estimate the buoyancy frequency of the thermocline as follows. Starting from Eq. 4-19 of Section 4.4 and noting that s{pp~pE) ~ =frddiiA _ n2a, the appro-

priate definition for our incompressible fluid is:

pref dz dz

Pe dz if thermocline density gradients are dominated by temperature gradients and Eq. 9-5 is used. From Fig. 9.12(a), if there is a 15°C temperature drop across the top 1000 m of the ocean, then (using aT _ 2 x 10-4 K-1 from Table 9.4) we obtain an N of, in round

FIGURE 9.11. A schematic diagram showing processes at work in the mixed layer of the ocean. Note that the vertical scale of the mixed layer relative to the thermocline is greatly exaggerated.

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