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. thermal haline

where aT, pS are defined in Eqs. 9-3 and 9-4, respectively. The units of buoyancy flux are m2 s-3, that of velocity x acceleration. We see that the buoyancy flux is made up of both thermal and haline components.

The net heat flux through the sea surface is itself made up of a number of components:

shortwave longwave sensible flux

latent flux

Estimates of the various terms from observations are shown in Figs. 11.2, 11.3, and 11.4. The units are in Wm-2.

The shortwave flux is the incoming solar radiation that reaches the sea surface and penetrates the ocean (the ocean has a low albedo; see Table 2.2), warming it down to a depth of 100-200 meters, depending on the transparency of the water. The longwave flux is the net flux of longwave radiation at the sea surface due to the radiation beamed out by the ocean according to the black-body law, Eq. 2-2, less the ''back radiation'' from the atmospheric cloud and water vapor layer (see Chapter 2).

The sensible heat flux is the flux of heat through the sea surface due to turbulent exchange. It depends on the wind speed and g g

Ocean Loss

FIGURE 11.2. Upper: Zonal averages of heat transfer to the ocean by insolation Qsw, and loss by long-wave radiation Qlw, sensible heat flux Qs, and latent heat flux Ql, calculated by DaSilva, Young, andLevitus (1995) using the COADS data set. Lower: Net heat flux through the sea surface calculated from the data above (solid line) and net heat flux constrained to give heat and fresh water transports by the ocean that match independent calculations of these transports. The area under the lower curves ought to be zero, but it is 16 Wm-2 for the unconstrained case (solid line) and -3 Wm-2 for the constrained case (dotted line). From Stewart (2005).

Ocean Loss

FIGURE 11.2. Upper: Zonal averages of heat transfer to the ocean by insolation Qsw, and loss by long-wave radiation Qlw, sensible heat flux Qs, and latent heat flux Ql, calculated by DaSilva, Young, andLevitus (1995) using the COADS data set. Lower: Net heat flux through the sea surface calculated from the data above (solid line) and net heat flux constrained to give heat and fresh water transports by the ocean that match independent calculations of these transports. The area under the lower curves ought to be zero, but it is 16 Wm-2 for the unconstrained case (solid line) and -3 Wm-2 for the constrained case (dotted line). From Stewart (2005).

the air-sea temperature difference according to the following (approximate) formula:

where pair is the density of air at the surface, cS is a stability-dependent bulk transfer coefficient for heat (which typically has a value of about 10-3), cp is the specific heat of air, Tair and Ui0 are, respectively, the air temperature and wind speed at a height of 10 m and SST is the sea surface temperature. Note that if SST > Tair, Qs > 0 and the sensible heat flux is out of the ocean which therefore cools. The global average temperature of the surface ocean is indeed 1 or 2 degrees warmer than the atmosphere and so, on the average, sensible heat is transferred from the ocean to the atmosphere; see the zonal-average curves in Fig. 11.2.

The latent heat flux is the flux of heat carried by evaporated water. The water vapor leaving the ocean eventually condenses into water droplets forming clouds, as described in Chapter 4 and sketched in Fig. 11.5, releasing its latent heat of vaporization to the atmosphere. The latent heat flux depends on the wind-speed and relative humidity according to Eq. 11-6,

where cL is a stability-dependent bulk transfer coefficient for water vapor (which, like cS in Eq. 11-6, typically has a value ~ 10-3), Le is the latent heat of evaporation, qar is the specific humidity (in kg vapor per kg air), and q* is the specific humidity at saturation which depends on SST (see Section 4.5.1). High winds and dry air evaporate much more water than weak winds and moist air. Evaporative energy loss rises steeply with

Net Upward Heat Flux (W/m*)

FIGURE 11.3. Global map of Qsw + Qlw, Ql and Qs across the sea surface in Wm-2. Areas in which the fluxes are upward, into the atmosphere, are positive and shaded green; areas in which the flux is downward, into the ocean, are negative and shaded brown. Contour interval is

Net Upward Heat Flux (W/m*)

FIGURE 11.3. Global map of Qsw + Qlw, Ql and Qs across the sea surface in Wm-2. Areas in which the fluxes are upward, into the atmosphere, are positive and shaded green; areas in which the flux is downward, into the ocean, are negative and shaded brown. Contour interval is

Net Upward Heat Flux (W/m2)

taffE 130 e tan isovv igo'w sow oo W snw o so e doe we 120 e i»e

Longitude taffE 130 e tan isovv igo'w sow oo W snw o so e doe we 120 e i»e

Longitude

—2b0 —240 -300 -»80 -120 -80 -40 ^if) 40 80 120 '80 200 240 280

FIGURE 11.4. Global map of net annual-mean constrained heat flux, Qnet, across the sea surface in Wrn-2. Areas in which the fluxes are upward, into the atmosphere, are shaded green; areas in which the flux is downward, into the ocean, are shaded brown. Contour interval is water temperature due to the sensitivity of saturation vapor pressure to temperature (see Fig. 1.5) and the concomitant increase in vapor density gradient between the sea and air. At higher latitudes where these gradients are smaller, evaporative transfer is of lesser importance and sensible heat transfer, which can be of either sign, becomes more important (see Fig. 11.3).

It is very difficult to directly measure the terms that make up Eq. 11-5. Estimates can be made by combining in situ measurements (when available), satellite observations, and the output of numerical models constrained by observations. Zonal-average estimates of each term in Eq. 11-5 are shown in Fig. 11.2. We see that QSW peaks in the tropics and is somewhat balanced by the evaporative processes QL and outgoing longwave radiation, Qlw, with Qs making only a small contribution. Note that solar radiation is the only term that warms the ocean. The major source of cooling is QL. Its typical magnitude can be estimated by noting that the net upward transfer of H2O in evaporation must equal precipitation (see Fig. 11.5). This

FIGURE 11.5. Latent heat is taken from the ocean to evaporate water that is subsequently released into the atmosphere when the vapor condenses to form rain.

suggests that the upward flux of energy in latent form is:

dm ql ~ Le-r-, dt where Le is the latent heat of evaporation and m is the mass of water falling per square meter (note that the precipitation rate P = (l/pref) (dm/dt) and has units of velocity, most often expressed in meters peryear). Inserting numerical values from Table 9.3, the previous equation yields 71Wm-2 for every m y-l of rainfall. This is broadly in accord with Fig. 11.2, because the annual mean rainfall rate is around 1 my-1.

Note that if the ocean is not to warm up or cool down in the long-run, the net air-sea heat flux integrated over the surface of the ocean, the area beneath the continuous black line in the lower panel in Fig. 11.2, should be zero. In fact, due to uncertainties in the data, it is 16Wm-2. That this is an unrealistically large net flux can easily be deduced as follows. If the global ocean were heated by an air-sea flux of magnitude Qnet to a depth h over time At, it would warm (assuming it to be well mixed) by an amount AT given by, see Eq. 11-2:

AT = Qnet At hprefcw or 0.75°C for every 1 W m-2 of global imbalance sustained for a 100 year period, assuming h = 1 km, and the data in Table 9.3. This is a full 12°C if the imbalance is 16Wm-2! The "observed" warming of the ocean's thermocline during the second half of the 20th century is an almost imperceptible few tenths of a °C. Clearly Qnet integrated over the global ocean must, in reality, be very close to zero. Thus, in the lower panel of Fig. 11.2, a constrained (adjusted) zonalaverage estimate of Qnet is shown by the dotted line, the area under which is close to zero. This is much the more likely distribution. We now see that the ocean gains heat in the tropics and loses it at high latitudes, as seems intuitively reasonable.

The geographical distribution of Qnet and E — P are shown in Figs. 11.4 and 11.6. Both fields are constrained to have near-zero global integral. We generally see cooling of the oceans in the northern subtrop-ics and high latitudes, and particularly intense regions of cooling over the Kuroshio and Gulf Stream extensions, exceeding 100 W m-2 in the annual mean. These latter regions are places where, in winter, very cold air blows over the ocean from the adjacent cold land-masses and where the western boundary currents of the ocean carry warm fluid from the tropics to higher latitudes. Such intense regions of heat loss are not seen in the southern hemisphere because the juxtaposition of land and sea is largely absent. Moreover, because the 'fetch' of ocean is so much larger there, the air-sea temperature difference and hence air-sea flux is much reduced. In the tropics we observe warming of the ocean due to incoming shortwave solar radiation.

The pattern of E - P, Fig. 11.6, shows excess of evaporation over precipitation in the subtropics, creating the region of high salinity seen in Fig. 9.4. Precipitation exceeds evaporation in the tropics (in the rising branch of the Hadley circulation), and also in high latitudes. This creates anomalously fresh surface water (cf. see Fig. 9.4) and acts to stabilize the water column.

Another perspective on the forcing of thermohaline circulation is given by Fig. 11.7 which shows the zonally averaged air-sea buoyancy flux Bsurface defined by Eq. 11-4, and the thermal and haline components that make it up. Buoyancy loss from the ocean peaks in the subtropics, yet we do not observe deep mixed layers at these latitudes (see Fig. 9.10). Evidently here buoyancy loss is not strong enough to ''punch through'' the strong stratification of the main thermocline (cf. Fig. 9.7). It is clear from Fig. 11.7 that the haline component stabilizes the polar oceans (excess of precipitation over evaporation at high latitudes), but is generally considerably weaker in magnitude than the thermal contribution to the buoyancy flux. Nevertheless, in the present climate, the weak stratification of the polar oceans enables the buoyancy lost there to trigger deep-reaching convection which ventilates the abyssal ocean. In past climates it is thought that the freshwater supply to the polar oceans may have been different (due to, for example, enhanced atmospheric moisture transport in a warm climate or melting of polar ice releasing fresh water) and could be an important driver of climate variability (see Section 12.3.5).

Global Precipitation and Evaporation (m/y)

120 E 160 E 180 160 W 130'W 90 V* COW DOW 0' 30 E 60 E 90 E 120 E 19TE

Longitude

120 E 160 E 180 160 W 130'W 90 V* COW DOW 0' 30 E 60 E 90 E 120 E 19TE

Longitude

120 £ 150 E IB0 150 W 120 W SOW SOW WW V 30 E 60 E DOE 120 E ISO E

Longitude

120 £ 150 E IB0 150 W 120 W SOW SOW WW V 30 E 60 E DOE 120 E ISO E

Longitude

120'E 1S0E 160 1 50 W 1Ï0W 90 W 60W 30 W 0 30 E 60'E 90 E 1Î0E 150 E

Longitude

120'E 1S0E 160 1 50 W 1Ï0W 90 W 60W 30 W 0 30 E 60'E 90 E 1Î0E 150 E

Longitude

FIGURE 11.6. A map of anual-mean evaporation (E), precipitation (P), and evaporation minus precipitation (E - P) over the globe. In the bottom map, E> P over the green areas; P > E over the brown areas. The contour interval is 0.5 my-1. From Kalnay et al. (1996).

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