Chapter 5 - The Oceanic Heat Budget

Chapter 5 Contents

5.2 Heat Budget Terms

Let's look at the factors influencing each term in the heat budget.

Factors Influencing Insolation Incoming solar radiation is primarily determined by latitude, season, time of day, and cloudiness. The polar regions are heated less than the tropics, areas in winter are heated less than the same area in summer, areas in early morning are heated less than the same area at noon, and cloudy days have less sun than sunny days.

The following factors are important:

  1. The height of the sun above the horizon, which depends on latitude, sea-son, and time of day. Don't forget, there is no insolation at night!
  2. The length of day, which depends on latitude and season.
  3. The cross-sectional area of the surface absorbing sunlight, which depends on height of the sun above the horizon.
  4. Attenuation, which depends on:
    • Clouds, which absorb and scatter radiation.
    • Path length through the atmosphere, which varies as csc φ , where φ is angle of the sun above the horizon.
    • Gas molecules which absorb radiation in some bands (Figure 5.2). H2O, O3, and CO2 are all important.
    • Aerosols which scatter and absorb radiation. Both volcanic and marine aerosols are important.
    • Dust, which scatters radiation, especially Saharan dust over the Atlantic.
  5. Reflectivity of the surface, which depends on solar elevation angle and roughness of sea surface.
Figure 5.2 Insolation (spectral irradiance) of sunlight at top of the atmosphere and at the sea surface on a clear day. The dashed line is the best-fitting curve of blackbody radiation the size and distance of the sun. The number of standard atmospheric masses is designated by m. Thus m = 2 is applicable for sunlight when the sun is 30° above the horizon. From Stewart (1985).

Solar inclination and cloudiness dominate. Absorption by ozone, water vapor, aerosols, and dust are much weaker.

The average annual value for insolation (Figure 5.3) is in the range:

30 W/m2 < QSW < 260 W/m2
(5.5)

Figure 5.3 Monthly average of clear-sky, downward flux of sunlight through the sea surface in W/m2 during 1989 calculated by the Satellite Data Analysis Center at the NASA Langley Research Center (Darnell et al., 1992) using data from the International Satellite Cloud Climatology Project.

Factors influencing Infrared Flux
The sea surface radiates as a blackbody having the same temperature as the water, which is roughly 290K. The distribution of radiation as a function of wavelength is given by Planck s equation. Sea water at 290K radiates most strongly at wavelengths near 10 µm. These wavelengths are strongly absorbed by clouds, and somewhat by water vapor. A plot of atmospheric transmittance as a function of wavelength for a clear atmosphere but with varying amounts of water vapor (Figure 5.4) shows the atmosphere is nearly transparent in some wavelength bands called windows.

Figure 5.4 Atmospheric transmittance for a vertical path to space from sea level for six model atmospheres with very clear, 23km, visibility, including the influence of molecular and aerosol scattering. Notice how water vapor modulates the transparency of the 10mm - 14mm atmospheric window, hence it modulates QLW, which is a maximum at these wavelengths. From Selby and McClatchey (1975).

The transmittance on a cloud-free day through the window from 8 µm to 13 µm is determined mostly by water vapor. Absorption in other bands, such as those at 3.5 µm to 4.0 µm depends on CO2 concentration in the atmosphere. As the concentration of CO2 increases, these windows close and more radiation is trapped by the atmosphere.

Because the atmosphere is mostly transparent to incoming sunlight, and somewhat opaque to outgoing infrared radiation, the atmosphere traps radiation. The effect is known as the greenhouse effect. If the earth were in radiative equilibrium, with an atmosphere, the surface temperature would be 77°C. This does not happen because water evaporates from the surface, mostly from tropical seas, cooling the surface (Philander, 1998: 78).

The simple picture of the greenhouse mechanism is seriously oversimplified. Many of us were taught in elementary school that heat is transported by radiation, convection, and conduction. The above representation [of the simple greenhouse effect] only refers to radiative transfer. As it turns out, if there were only radiative heat transfer, the greenhouse effect would warm the Earth to about seventy-seven degrees centigrade rather than to fifteen degrees centigrade. In fact, the greenhouse effect is only about 25 percent of what it would be in a pure radiative situation. The reason for this is the presence of convection (heat transport by air motions), which bypasses much of the radiative absorption ... The surface of the Earth is cooled in large measure by air currents (in various forms including deep clouds) that carry heat upward and poleward. One consequence of this picture is that it is the greenhouse gases well above the Earth's surface that are of primary importance in determining the temperature of the Earth. That is especially important for water vapor, whose density decreases by about a factor of 1,000 between the surface and ten kilometers above the surface. Another consequence is that one cannot even calculate the temperature of the Earth without models that accurately reproduce the motions of the atmosphere. Indeed, present models have large errors here--on the order of 50 percent. Not surprisingly, those models are unable to calculate correctly either the present average temperature of the Earth or the temperature ranges from the equator to the poles. Rather, the models are adjusted or "tuned'' to get those quantities approximately right. Richard S. Lindzen, Alfred P. Sloan Professor of Meteorology at the Massachusetts Institute of Technology.

See Hartmann (1994: 24-26) for a simple discussion of the radiative balance of a planet. CO2, water vapor, methane, and ozone are all important greenhouse gasses.

The net infrared flux depends on:

  1. Clouds thickness. The thicker the cloud deck, the less heat escapes to space.
  2. Cloud height, which determines the temperature at which the cloud radiates heat back to the ocean. The rate is proportional to t4, where t is the temperature of the radiating body in Kelvin. High clouds are colder than low clouds.
  3. Atmospheric water-vapor content. The more humid the atmosphere the less heat escapes to space.
  4. Water Temperature. The hotter the water the more heat is radiated. Again, radiation depends of t4.
  5. Ice and snow cover. Ice emits as a black body, but it cools much faster than open water. Ice-covered seas are insulated from the atmosphere.

Water vapor and clouds are more important for determining the net loss of infrared radiation than are changes in surface temperature. Hot tropical regions lose less heat than cold polar regions. The temperature range from poles to equator is 0°C < T < 25°C or 273K < T < 298K, and the ratio of maximum to minimum temperature in Kelvin is 298/ 273 = 1.092. Raised to the fourth power this is 1.42. Thus there is a 42% increase in emitted radiation from pole to equator. Over the same distance water vapor can change the net emitted radiance by 200%.

The average annual value for net infrared flux is in the narrow range:

- 60W/m2 < QLW < - 30W/m2
(5.6)

Factors influencing Latent-Heat Flux
Latent heat flux is influenced primarily by wind speed and relative humidity. High winds and dry air evaporate much more water than weak winds with relative humidity near 100%. In polar regions, evaporation from ice covered oceans is much less than from open water. In the arctic, most of the heat lost from the sea is through leads (ice-free areas). Hence the percent open water is very important for the arctic heat budget.

The average annual value for latent-heat flux is in the range:

- 130W/m2 < QL < - 10W/m2
(5.7)

Factors influencing Sensible-Heat Flux
Sensible heat flux is influenced primarily by wind speed and air-sea temperature difference. High winds and large temperature differences cause high fluxes. Think of this as a wind-chill factor for the oceans.

The average annual value for sensible-heat flux is in the range:

- 42 W/m2 < QS < - 2 W/m2
(5.8)

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