Transfer of Heat Across the Ocean Surface

1. Transfer of Heat Across the Ocean Surface Lecture 4 OEAS-604 September 19, 2011 • Outline: • The Solar Constant • Shortwave Radiation (insolation) • Longwave Radiation (infrared) • Latent Heat Flux • Sensible Heat Flux • Total Heat Budget • Problem Set #1

2. Heat in the Ocean • Nearly all heat entering the ocean occurs at the air-sea interface (except for the small amount at the ocean-sediment interface ~ 0.1 Watts/m2). • To a first approximation, the mean temperature of the ocean does not change on an annual basis (i.e. it is in steady state, so the flux in equals the flux out). • This steady state balance only applies at annual time scales, as the heat content of the ocean can change substantially on daily to seasonal time scales. And it only applies in an integrative sense. Flux out Flux in

3. Heat is exchange between the ocean and the atmosphere by the following processes: • Short-wave radiation (insolation) received from the sun [Qs] • Longwave radiation (infrared) [Qb] • Latent heat flux (evaporation) [Qe] • Sensible heat flux (air-sea temperature difference) [Qh] Change in Heat content with time Flux in Flux out At annual time scales and average over the ocean, the heat entering the ocean is balanced by the heat leaving, so:

4. This balance is approximate and does not hold for any given location in the ocean or over short time periods. Significant heat is transported by atmosphere and ocean Averaged over an entire year this balance holds, but there are seasonal changes in oceanic heat content.

5. 1. Short-wave radiation (insolation) received from the sun [Qs] The sun radiates energy as a blackbody with a temperature of 5800°K Wien’s Law: The wavelength of maximum transmission is inversely proportional to the absolute temperature b=2,897,768.5 nm·K. • About 49% is in the visible spectrum (400-700 nm) • About 9% is in the UV (~100-400 nm) • Remainder in IR (~700-2500 nm)

6. The Solar Constant. • 1. A flat plate just beyond the earth’s atmosphere, perpendicular to the rays of the sun receives about 1368 Watts/m2 (the solar constant). • But Earth is not a flat disk (area = πR2), but a sphere with surface area of 4πR2, so the energy is spread over larger area. • On average, the top of the atmosphere receives 342 Watts/m2. • This varies with at any given spot on Earth due to declination of the sun.

7. Less irradiance reaches surface of Earth because of absorption by molecules, clouds or aerosols. Average loss by absorption is roughly 19%.

8. Measured summer time Irradiance (Sterling Virginia)

9. Albedo: the ratio of the amount of radiation reflected by an object to the energy incident upon it. Albedo varies considerably, but planetary average is about 30 percent.

10. 2. Longwave radiation (infrared) or Back Radiation [Qb] All bodies with a temperature above absolute zero radiate heat energy. The amount is proportional to the fourth power of the absolute temperature. This is known as the Stefan-Boltzmann law: where cs = 5.67 × 10-8 W/m2K4 ( Stefan-Boltzmann constant) and K is degrees Kelvin

11. Using average temperature of the oceans of 18°C (~ 291 Kelvin), what is the back radiation of the oceans? But I thought that the Ocean was only absorbing about 50 percent of the incoming 342 Watts/m2. Is the ocean radiating more than twice the amount it absorbs? WHY?

12. Greenhouse Effect Short wave length incoming radiation (mostly visible) passes through the atmosphere. Longer wave length back radiation (infrared) is more effectively absorbed and reflected back to earth by the gases in the atmosphere. Because atmosphere effectively traps the longer wave infrared wave lengths, the effective back radiation is roughly 50 to 75 W/m2

13. 3. Latent heat flux (evaporation) [Qe] Remember from Lecture 2: Latent Heat is the heat required to change state. Sensible Heat is the heat added/removed that changes the temperature When water evaporates, it removes significant amounts of heat. The energy that is added to break the hydrogen bonds to allow evaporation is removed by the water vapor. Can be estimated from “Bulk Formula”: ρa = Density of air (~1.2 kg/m3) Le = Latent heat of vaporization (~ 2260 kJ/kg) CL = Bulk transfer coefficient (Stanton number) U10 = wind speed @ 10 m qs = specific humidity at saturation qa = specific humidity of overlying air

14. 1. Latent Heat Flux is very difficult to measure. 2. Biggest loss term in budget. 3. Estimated as about 100 W/m2

15. Surface of the Ocean usually has a “cool skin” layer, also called thermal sublayer.

16. 3. Senisible heat flux [Qh] • Sensible heat is heat energy transferred between the ocean surface and air when there is a difference in temperature between them. • The flux is proportional to the temperature gradient • Flux is also dependent on the turbulence in the ocean and atmosphere. Also can be estimated from “Bulk Formula”: ρa = Density of air (~1.2 kg/m3) cp = specfic heat capacity of air (~ 1 J/g°K) CS = Bulk transfer coefficient (Dalton number) U10 = wind speed @ 10 m Ts = Temperature of water Ta = Temperature of air

17. Global Heat Budget

18. MATLAB Has Tools for Calculating Heat Fluxes http://woodshole.er.usgs.gov/operations/sea-mat/air_sea-html/index.html “Air Sea Toolbox” Click on “air_sea.zip” to download. Save this folder and add to path.

19. Function “hfbulktc.m” Calculates Sensible and Latent Heat Fluxes (among other things)

20. How to use the ‘bulk fluxes’ in the MATLAB air-sea toolbox. Heat_fluxes=hfbulktc(W,Zw,Ta,ZT,RH,ZH,P,Th20); W = wind speed (m/s) Zw = Height of wind measurement (m) Ta = Air temperature (C) ZT = Height of temperature measurement (m) RH = Relative Humidity (%) ZH = Height of humidity measurement (m) P = Atmospheric Pressure Th20 = Sea Surface Temperature This function returns a matrix “Heat_fluxes”, where the first column is the Sensible Heat Flux and the second column is the Latent Heat Flux. You can ignore the other columns.