ESCI 340 Physical Meteorology Radiation Lesson 5 Terrestrial Radiation and Radiation Balance Dr. DeCaria

Transcription

1 ECI 30 Physica Meteoroogy Radiation Lesson 5 errestria Radiation and Radiation Baance Dr. DeCaria References: Atmospheric cience: An Introductory urvey, Waace and Hobbs An Introduction to Atmospheric Radiation, Liou A First Course in Atmospheric Radiation, Petty Reading: Petty, Chapter 8 (don t focus on equations in book) CHWARZCHILD EQUAION he radiative transfer equation is di k I ds k J ds. If we make the foowing assumptions: Ignore mutipe scattering (so there is no scattering back into the beam) Assume the medium is a backbody, so the source function is the Panck function for radiance, B. then the radiative transfer equation becomes di k I B ds. he equation above is known as chwarzschid s equation. We woud ike to appy chwarzschid s equation to a pane parae atmosphere, for both upward and downward propagating radiation. For downward propagating radiation ds so that chwarzschid s equation is di dz k I B For upward propagating radiation and the chwarzschid equation is di ds dz / k I B dz. Downward propagating radiation dz. Upward propagating radiation

2 EMIION FROM AN OPICALLY HICK LAYER In genera, the chwarzschid equation does not have an anaytica soution. However, it is instructive to sove it for the case of an isotherma atmosphere, in which case B = constant. For upward propagating radiation the intensity at some eve z in the atmosphere is found by integrating chwarzschid s equation from the ground to eve z, I di k dz I B. I0 0 he Panck function, B, depends on the temperature, so the eft side can t easiy be integrated. However, if we assume an isotherma atmosphere then B is constant, and the integra is I ( z) B I B exp( ), 0 z where z is the vertica optica thickness from the ground to eve z. From this resut, we see that as the optica thickness of a ayer increases, then I(z) approaches B. hus, an opticay thick ayer behaves as though a the radiation were being emitted by the upper surface of the ayer. hough this resut was derived in terms of an isotherma ayer, in genera it is true for any opticay thick ayer. his is why couds appear cod on an IR sateite image, because the sateite is ony seeing the radiation emitted by the coud top, not a the radiation that was emitted at higher temperatures beow the coud top. z GLOBAL RADIAION BALANCE he amount of soar power received by the entire Earth is P in R 2 (1 ) where R is the radius of the Earth, is the abedo, and is the soar constant. he amount of power radiated by the Earth is P out, 2 R e where e is the temperature at which the Earth/atmosphere system is radiating ( is the tefan-botzmann constant). 2

3 If the Earth s temperature is not changing, then the power in must equa the power out. his eads to an expression for the radiation temperature, (1 ). e For the Earth, the radiation temperature is approximatey 255 K (18C), which is the temperature at about 500 mb. he surface temperature of the Earth averages about 288 K (15C). he reason the surface temperature is much warmer than the radiation temperature is that the atmosphere contains greenhouse gasses. On a panet without an atmosphere, the radiation and surface temperatures woud be identica. RADIAION BALANCE AND HE GREENHOUE GAE o further iustrate the roe of greenhouse gasses, imagine an atmosphere that consists of a singe, homogeneous sab such as that shown beow. In this mode, the atmosphere has an abedo of. he surface of the panet is a backbody at a temperature of 0. he atmosphere is a gray body, with an absorptivity of s for short-wave radiation and an absorptivity of for ongwave radiation (from Kirchhoff s aw, the absorptivity and emissivity are equa). he temperature of the atmosphere is a. 3

4 We can write a set of equations for the radiation baance at the top of the atmosphere and at the surface. At the top of the atmosphere: Incoming soar radiation (after refection) is (1) Radiation emitted by the atmosphere and escaping to space is a Radiation emitted by the surface and escaping to space is (1 ) 0 (note that absorptivity equas emissivity, so the amount absorbed by the atmosphere is 0, eaving one minus this amount to escape to space. Radiation baance at top of atmosphere: (1) 0 0 a At the surface: Incoming soar radiation is (1)(1 s )0 (note that absorptivity equas emissivity, so the amount absorbed by the atmosphere is (1) s, eaving one minus this amount to reach the surface.) Incoming radiation emitted by atmosphere is a Outgoing radiation emitted by surface is 0 Radiation baance at surface: (2) s 0 a 0 Equations (1) and (2) can be soved for a and 0, with the foowing resuts: a s s s 1 2. he figure beow shows a pot of these temperatures as a function of (for this pot s is set to 0.1 and = 3 W m 2 ).

5 An increase in greenhouse gasses resuts in an increase of, and therefore, a monotonic increase in the surface temperature, 0. he effect of the greenhouse gasses on the atmospheric temperature is not monotonic. At first, increasing greenhouse gasses actuay decreases atmospheric temperature, whie ater it increases. hough the rea atmosphere is certainy more compex than the simpe sab mode, the sab mode remains a usefu iustration. DAILY AND YEARLY RADIAION BALANCE A ocation on Earth receives its maximum soar radiation at oca noon, yet the hottest time of day is in the afternoon. his apparent discrepancy can be expained in terms of radiation baance. 5

6 During those times when the outgoing radiation exceeds the incoming, the temperature fas. When the incoming radiation exceeds the outgoing, the temperature rises. When the two components of radiation are equa, there is no change in temperature. A simiar concept appies to the annua cyce, where the maximum incoming soar radiation occurs at the ostice (June in Northern Hemisphere), but the hottest month of the year is actuay ater in the summer (Juy or August in Northern Hemisphere). LAIUDINAL RADIAION BALANCE At the top of the atmosphere, the poes actuay receive more insoation throughout the year than does the Equator. However, at the surface of the Earth the Equatoria regions receive far more insoation. A sketch of the soar and terrestria radiation fuxes vs. atitude ooks ike he ropica regions receive more energy than they radiate, and so shoud become increasingy hotter. he Poar regions radiate more energy than they receive, and so shoud become increasingy coder. herefore, the atmosphere and oceans must somehow transport the excess heat from the ropics to the Poes. his is what utimatey drives the circuation of the atmosphere and oceans. 6

7 EXERCIE 1. Find the radiation temperature of the Earth for a soar constant of 1373 W/m 2 and an abedo of 30%. 2. Why is this temperature so much ess than the surface temperature? 3. If the abedo increased, woud the radiation temperature increase or decrease?. If the soar constant increased, woud the radiation temperature increase or decrease? 5. If the Earth became coudier, woud the radiation temperature increase or decrease? What about the surface temperature? 6. For the sab mode a. show that a s s 1 2. and 0 2s 1 2. b. Using the vaues in the tabe beow, find 0 and a. vaue 3 W-m s c. Expain physicay why, if there are very few greenhouse gasses, the temperature of the atmosphere in the sab mode gets extremey arge. 7