Download
1 / 29
290 likes | 308 Views
Explore the intricate relationship between ocean heat budget, solar radiation, and heat transfer mechanisms while examining factors influencing solar flux interactions. Gain insights into longwave radiation, cloud cover effects, and empirical formulas for solar energy distribution.
E N D
An evaporation rate of 1.2 m/yr is equivalent to removing about 0.03% of the total ocean volume each year. An equivalent amount returns to the ocean each year, about 10% by way of rivers and the remainder by rainfall. The yearly salt exchange is less than 10-7 of the total salt content of the ocean.
Thermodynamic Equation Heat Content H=cpT (Joule/m3) Heat per unit volume cp is the specific heat of sea water
Heat budget Temperature (Potential Temperature) Equation . where : specific heat capacity at constant pressure. , vertical eddy diffusion coefficient. , horizontal eddy diffusion coefficient. , Molecular thermal diffusivity . ( ) Define , we have and
, heat storage. , heat convergence by currents and sub-scale transport. , penetrating solar radiation. , surface heat flux. Qsa: solar radiation absorbed at the sea surface. Qb: net heat loss due to long wave radiation. Qe: latent heat flux. Qh: sensible heat flux. , geothermal heat flux (neglected). We also take Qs=Qsp+Qsa as total solar radiation. Then the heat budget is:
Solar radiation: Basics Planck’s law: Black body irradiance (absorptance ) h~ Planck’s constant. k~ Boltzmann’s constant. c~ light speed in vacuum. T~ temperature (Kelvin), λ~wavelength. Total irradiance (Stefan-Boltzmann law): Stefan-Boltzmann constant: The wavelength of maximum irradiance (Wien’s law): Temperature at sun’s surface: T=5800K λm=0.5μm. , Solar radiation is in shortwave band: 50% visible, 0.35μm ≤ λ ≤ 0.7μm; 99%, λ ≤ 4μm
Solar flux at the top of the atmosphere: FS=1365-1372 W/m2 Solar constant: (mean solar flux on 1 square meter of earth) Usually, we choose . Not all of the radiation received at the top of atmosphere is available to the ocean
Factors influencing QS 1). Length of the day (depending on season, latitude) 2). Atmospheric absorption. Absorption coefficient (gas molecules, dust, water vapor, etc). Elevation of the sun θ: angle of the sun above the horizon. 3). Cloud absorption and scattering. 4). Reflection at the sea surface. direct sunlight (from one direction) reflection depends on elevation of the sun and the state of the sea (calm or waves). skylight (scattered sunlight from all directions) reflected about 8%. (A few percent of the radiation entering the sea may also be scattered back to the atmosphere)
Empirical Formula (Parameterization) (shortwave flux averaged over 24 hours): Qso is clear sky solar radiation at sea surface. F is an empirical function of the fractional cloud cover. Example: 1). Clear sky radiation QSO: clear sky radiation. An: noon altitude of the sun in degree. tn: length of the day from sunrise to sunset in hours. 2). Cloud reduction is the solar flux arriving at the sea surface. C=8, C=4, 3). Reflection at the sea surface 4). Shortwave radiation into the sea 5). Original algorithm overestimates. Multiply by 0.7.
Another example: Reed (1977) n~ fractional cloud cover (0.3 ≤n≤1). Otherwise Qs=Qso. φ~ solar elevation in degrees. cn~ cloud attenuation factor (≈0.62). α~ albedo.
Distribution daily inflow of solar radiation • The highest value (>300 W/m2) occur at 30oS and 30oN in respective summer hemispheres. • There is no shortwave input at high latitudes during the polar winter. • The amount of energy input is greater in the southern hemisphere than in the northern hemisphere. (In its elliptic orbit, earth is closer to the sun in southern summer).
Absorption in the sea reduces the light level rapidly with depth. 73% reaches1 cm depth 44.5% reaches1 m depth 22.2% reaches10 m depth 0.53% reaches100 m depth 0.0062% reaches200 m depth
Long-wave radiation (Qb) The difference between the energy radiated from the sea surface (σT4, T ocean skin temperature) and that received from the sea by the atmosphere, mostly determined by water vapor in lower atmosphere. The outgoing radiation from the sea is always greater than the inward radiation from the atmosphere. Qb is a heat loss to ocean. The outgoing radiation is “longwave” Mean sea surface temperature is T= 12oC=285K, λm=10.2μm. Most of the longwave radiation is in the range 3μm ≤ λ ≤ 80μm Longwave radiation is much smaller than the shortwave solar radiation
Empirical Formula of Qb tw=water temperature (oC). ea=relative humidity above the sea surface. C=cloud cover in oktas (1-8). Qbo=Qb(C=0) ranges from 70-120 W/m2. Qb (Qbo) decreases with tw and ea. ea increases exponentially with tw. Due to the faster increase of ea, inward atmospheric flux is larger than outgoing surface radiation). The net heat loss decreases with tw.
Another formula: ε=0.98, λ increases with latitude (0.5, equator; 0.73, 50o). e water vapor pressure (mb): Saturated water vapor pressure Nonlinearity in water vapor dependence: The water vapor content (humidity) increases exponentially with TS, which could result in a more rapid increase in the atmosphere’s radiation into the sea than the sea’s outward radiation (proportional to TS4. Thus Qb could decrease as TS increases, leading to a “super greenhouse” effect. It should be noted that this is still a highly speculated process, which has not been substantiated with a significant amount of measurements.
Properties of long wave radiation • Qb does not change much daily, seasonally, or with location. This is because (1) Qb ~T4, for T=283K, ΔT=10K, , which is only 15% increase. (2) Inward radiation follows outgoing radiation. • Effect of cloud is significant. The big difference between clear and cloudy skies is because the atmosphere is transparent to radiation range from 8-13μm while clouds are not. • Ice-albedo feedback Effect of ice and snow cover is relatively small for Qb but large for Qs due to large albedo (increase from normally 10-15% to 50-80%). Therefore, net gain (Qs-Qb) is reduced over ice. ice once formed tends to maintain.
