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, season, 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: i) Clouds, which absorb and scatter radiation. ii) Path length through the atmosphere, which varies as \(\csc \varphi\), where \(\varphi\) is angle of the sun above the horizon. iii) Gas molecules which absorb radiation in some bands (figure \(\PageIndex{1}\)). H₂O, O₃, and CO₂ are all important. iv) Aerosols which scatter and absorb radiation. Both volcanic and marine aerosols are important. And v) 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 \(\PageIndex{1}\): 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\(^{\circ}\) above the horizon. After Stewart (1985: 43).

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

The average annual value for insolation (figure \(\PageIndex{2}\)) is in the range: \[30 \ \text{W/m}^{2} < Q_{SW} < 260 \ \text{W/m}^{2} \nonumber \]

Figure \(\PageIndex{2}\): Monthly average of downward flux of sunlight through a cloud-free sky and into the ocean 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 290 K. The distribution of radiation as a function of wavelength is given by Planck’s equation. Sea water at 290 K radiates most strongly at wavelengths near 10 \(\mu\)m. 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 \(\PageIndex{3}\)) shows the atmosphere is nearly transparent in some wavelength bands called windows.

Figure \(\PageIndex{3}\): Atmospheric transmittance for a vertical path to space from sea level for six model atmospheres with very clear (23 km) visibility, including the influence of molecular and aerosol scattering. Notice how water vapor modulates the transparency of the 10-14 \(\mu\)m atmospheric window, hence it modulates \(Q_{LW}\), which is a maximum at these wavelengths. After Selby and McClatchey (1975).

The transmittance on a cloud-free day through the window from 8 \(\mu\)m to 13 \(\mu\)m is determined mostly by water vapor. Absorption in other bands, such as those at 3.5 \(\mu\)m to 4.0 \(\mu\)m, 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 trapped radiation, coupled with convection in the atmosphere, keeps earth’s surface 33\(^\circ}\) warmer than it would be in the absence of a convecting, wet atmosphere but in thermal equilibrium with space. The atmosphere acts like the panes of glass on a greenhouse, and the effect is known as the greenhouse effect. 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.

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 \(t^{4}\), where \(t\) is the temperature of the radiating body in Kelvins. 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 \(t^{4}\).
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 influence the net loss of infrared radiation more than surface temperature. Hot tropical regions lose less heat than cold polar regions. The temperature range from poles to equator is \(0^{\circ}\text{C} < t < 25^{\circ}\text{C}\) or \(273 \ \text{K} < t < 298 \ \text{K}\), and the ratio of maximum to minimum temperature in Kelvins 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: \[-60 \ \text{W/m}^{2} < Q_{LW} < -30 \ \text{W/m}^{2} \nonumber \]

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 ocean 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: \[-130 \ \text{W/m}^{2} < Q_{L} < -10 \ \text{W/m}^{2} \nonumber \]

Factors Influencing Sensible Heat Flux

Sensible heat flux is influenced 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 ocean. The average annual value for sensible-heat flux is in the range: \[-42 \ \text{W/m}^{2} < Q_{S} < -2 \ \text{W/m}^{2} \nonumber \]