Physical Oceanography: An Overview
2.4 Radiative, Thermodynamic, and Related Forces
The radiant energy that drives the earth’s fluid envelopes comes from only two major sources: (1) the sun, as an external source; and ( 2 ) the decay of radioactive matter within the earth’s interior, which maintains the material below the surface crust in either a plastic or a fluid condition (except for the inner, solid core). The latter energy influences, to a degree, the bottom temperature of the deep sea but is not an important source for dynamical effects.
The sun is approximately a graybody with an emissivity, e h , of 1 or less, characterized by an emission temperature, T,, of about 5900 K (Fig. 2.2);
the blackbody radiant intensity curve is modulated by the solar Fraunhofer
16 Principles of Ocean Physics
lines in the visible wavelength region. In this band, the radiative spectral in- tensity of a 5900 K blackbody has a maximum at a wavelength,
A,
in the blue at about X = 491 nm. The total solar radiative emission per unit area, M , or exitance (see Chapter 8 ) , isM = uSBTSj W m-’ , (2.1)
where the Stefan-Boltzmann constant is uSB = 5.67 x lo-’ W (m2 K 4 ) - ’ . At the earth’s surface, at a radius of one astronomical unit ( R , = 1.49598 x 10” m), the mean theoretical solar irradiance, (S,h ), is, according to the numbers above, uSB T$(R,lR,)’ = 1.487 kW m -*, where R , is the radius of the sun ( R , = 6.960 x 10’ m). The correct value at the top of the at- mosphere, i.e., the solar “constant” is, from observation,
( S ) = 1.376 kW m-’ , (2.2)
which is somewhat lower than the theoretical value because of the gray- bodiness of the sun. In addition, this insolation is not constant but varies by &3.2% annually because of the ellipticity of the earth’s orbit. The projec- tion of the disk of the earth in the sun’s direction receives an amount of so- lar power, P,y, of
of which a fraction, ( a ) , the mean albedo or reflected power, is reflected back to space, chiefly by clouds, snow, ice, and desert surface. Sfnce the total area of the earth’s surface is 4nR;, the average power flux absorbed per unit area is
%(s)(i - ( a ) ) = 240.8 W m - ’
.
(2.4)It is this energy that is responsible for the mean temperature of the earth, and since the planet is neither heating up nor cooling down (at least not on decadal or shorter time scales), the same amount of energy must be re-radiated to space as infrared radiation. If the earth, too, were a blackbody, its equilibri- um emission temperature, T , , would be found from the equation: re- radiation = insolation. Thus
For an average albedo, ( a ) = 0.3, as measured from spacecraft, Eq. 2.5 yields a theoretical value for T, of 260 K. However, the re-absorption of
emitted infrared energy by radiatively active constituents in the atmosphere (the greenhouse effect), coupled with convection, raises the observed value for T, to about 288 K. Figure 2.2 shows the spectral exitance of a 300 K blackbody as a n envelope for the observed IR emission from the earth. By the Wien displacement law, the wavelength, A,, of the maximum of the Planck distribution of blackbody radiation at temperature T is
a r
A , = - - , T
where a, = 2897.8 pm K. For the earth at T, = 288 K, the maximum oc- curs at
A,, = 10.1 pm
.
(2.7)This region of infrared emission is termed the thermal infrared, and it is coin- cidently a region of relatively high transparency of the atmosphere (see Fig.
2.2). One would then expect that the land and water would have a globally and seasonally averaged equilibrium temperature, in degrees Celsius, of
TeY = T, - 273.15 2 15°C
.
This temperature is not far from the observed average surface temperature of the oceans, which have extreme values of approximately -2°C to
+
35°Cand which have by far the largest heat capacity of the earth’s surface. Thus the processes of insolation, reflection, absorption, and re-radiation estab- lish the gross temperature balance of the earth.
Figure 2.3 is a schematic diagram of the flow of energy in the geophysical system consisting of atmosphere, hydrosphere (ocean, lakes, and other waters), lithosphere (land), and cryosphere (ice). Of the totality of incoming radiation, 30% is reflected by clouds, dust, and the earth’s surface (the al- bedo); 70% is re-radiated as IR radiation, which in turn is divided into 64%
emitted by the radiatively active gases and clouds in the atmosphere, and 6% by the earth’s surface, both land and water. Before this re-emission oc- curs, many transmutations of the incident energy have taken place, as the diagram suggests, with 20% of the total incident radiation being directly ab- sorbed by the atmosphere, and 50% entering the nonatmospheric portions of the system -mainly the oceans, where it heats the upper levels of the sea and directly contributes to the oceanic thermohaline circulation (tempera- ture- and salt-driven). As will be seen below, it also indirectly contributes to the wind-driven circulation via evaporation of water in the tropics and subtropics. Water has an enormous specific heat, the second highest of any
2 1 0.5
0.2 0.1 0.05
0.02
0.01
.-
-0 .kI
0.005P
R 0.002-
+ 0
0)
L- m
-
c% 0.001
(
Principles of Ocean Physics
' 1
6000 K blackbody irradiance lrradiance a t t o p of atmosphere lrradiance a t earth's surface
E
u
0.5 1300 K blackbody emission Radiant emission
2 5 10
surface
2
- +
0
20 50
Wavelength, A (pm)
Fig. 2.2 Incident solar spectral irradiances at top of atmosphere and at the earth's surface, compared with that from a6000 K blackbody (left). Spectral emittance from the earth's surface, compared with that from a300 K blackbody (right). [Adapted from Smith, D. G., Ed., The Cambridge Encyclopedia of Earth Sciences (1981).]
known substance; for seawater, the specific heat at constant pressure,
C,,
is 0.955 cal (g 'C)-', or 3998 J (kg "C)-' at a temperature, T , of 2 0 ° C , a surface pressure, p , of 1.024x
10' Pa, and a salinity, s, of 35 practical salinity units (psu, or 35 parts per thousand). It also has a very large latent heat of vaporization, L,:Infrared radiation
Fig. 2.3 Schematic diagram of the flow of energy in the components of the cli- mate system. Numbers show the percentages of incoming solar radiation entering into the energy transformation processes illustrated. [From Piexoto, J. P., and A. H.
Oort, Rev. Mod. Phys. (1984).]
L , = (2.501 - 0.00239 T ) x lo6
= 2.453 x lo6 J k g - ' at 20°C
= 586 cal g - '
.
(2.9)These two seemingly simple facts have important consequences for the en- tire ocean-ice-atmosphere system on both short and long time scales, as much of the subsequent discussion in this book will reveal. The thermodynamic properties of water in its solid, liquid, and vaporous states establish the ther- mal inertia of the climate system and the ability of that system to redistrib- ute and transform heat, energy, and momentum.
Returning to Fig. 2.3, our ledger showing the energy budget of the sys- tem: It is seen that 50% of the incoming solar radiation is deposited in the surface, mostly via warming of the surface waters of the sea. A quantity of 6%
+
14% is re-radiated as infrared radiation, with the former percentage escaping to space and the latter being absorbed by the atmosphere; 30% is transported by ocean currents to areas removed from the immediate regions of deposition. Essentially all of the latter is eventually surrendered t o the atmosphere, 24% as latent heat of vaporization and 6% as sensible heat,20 Principles of Ocean Physics
i.e., direct thermal conduction across the air/sea interface. Thus, on the aver- age, 83 W m - 2 , or nearly one-third of the incoming solar radiation of 241 W m - * , is deposited within the atmosphere via the agent of water vapor.
In the tropics, the actual amounts are nearer 120 W m - ' of evaporative flux, which is four times more effective in air/sea energy interchange than sensible heat conduction. The heat of vaporization is surrendered to the at- mosphere as internal thermal energy upon condensation, i.e., cloud forma- tion and rainfall, whereupon it is immediately available to drive the atmospheric circulation.
The discussion to this point has been along the lines of globally averaged quantities. The obliqueness of the polar regions t o solar radiation, the seasonally varying tilt of the spin axis, the interruption of flow by the con- tinental land masses, and the large asymmetry in the land/water ratio be- tween the Northern and Southern Hemispheres also have profound influences on both oceanic and atmospheric dynamics. We shall now consider some of these.
The solar energy absorbed in the ocean is deposited in the upper levels of the sea and is mixed downward by wind waves, convective overturning, and turbulent processes, as well as being forced downward by Ekman pump- ing in certain regions, a process to be considered later. Figure 2.4 shows six typical vertical profiles of temperature for Northern Hemisphere summer and winter, in the tropics (15"N), at mid-latitudes (40"N), and in the polar North Atlantic (75 ON). The three vertical regimes are: the near-surface mixed
-lO0Oo
,
15 25Mid-latitudes
Permanent Thermocline
-
5 Temperature, 15 T/z) 25 ("C)Polar
rJ--
I I I
y
u
5 15 25
Fig. 2.4 Schematic temperature distributions with depth for tropical, mid-latitude, and polar regions, for summer (solid) and winter (dashed) conditions. The major re- gimes in the vertical are termed the near-surface mixed layer, the seasonal thermocline, and the deep, permanent thermocline.
layer, which is isothermal (or nearly so); the seasonal thermocline, where the temperature changes relatively rapidly below the base of the mixed lay- er; and the deep permanent thermocline, where the temperature changes are more gradual with depth and exceedingly slow with time. While there are only small variations between the summer and winter thermoclines in the tropics, there are very large alterations in the subpolar and even the mid- latitude profiles. It is in this upper region of the sea that the main portion of the incoming solar energy is stored and redistributed by currents and air/sea interchanges.