DOC PREVIEW
UT GEO 387H - Chapter 2 The global energy balance

This preview shows page 1-2-21-22 out of 22 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 22 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 22 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 22 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 22 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 22 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Chapter 2The global energy balanceWe consider now the general p roblem of the radiative equilibrium tempera-ture of the Earth. The Earth is bathed in solar radiation and absorbs m u chof that incident upon it. To m aintain equilibrium it m ust w a rm up and radi-ate energy a wa y at the same rate as it is received , as depicted in Fig.2.1. Wewill see that the emission temperature of the Earth is 255 K and that a bodyat this temperature radiates ener gy primarily in the infrared (IR). But theatmosph ere is strongly absorbing at these wavelengths due to the presenceof trace gases – principally the triatomic molecu les H2OandCO2–whichabsorb and emit in the infrared, this raising the surface temperature abov ethat of the emission temperatur e, a mechanism that has becom e know n asthe ‘greenhouse effect’.2.1 Planetary emission temperatureThe E arth receives almost all of its energy from the Sun. At the presen t timein its ev o lution the Sun emits energy at a rate of Q =3.87 × 1026W. Theflux of solar energy at the Earth – called the ‘solar constan t’ – dependson the distance of the Earth from the Sun, r, and is given by the in versesquare la w: S0=Q4πr2. O f course, because of variations in the Earth’s orbit(see Sections 5.1.1 and 12.3.5) the solar constan t is not really constant; theterrestrial value S0= 1367 W m−2set out in Table 2.1, along with that forother planets, is an av erage corresponding to the average distance of Earthfrom the Sun, r =150× 109m.The w ay in which radia tion interac ts with an atmosphere depends on3738 CHAPTER 2. THE GLOBAL ENER GY BALANCEFigure 2.1: The Earth radiates energy away at the same rate as it is received fromthe Sun. The Earth’s emission temperature is255 K; that of the Sun, 6000 K.Theoutgoing terrestrial radiation peaks in the infrared; the incoming solar radiationpeaks at shorter wavelengths, in the visible.r S0αpTeTm109m W m−2K KVenus 108 2632 0.77 227 230Earth 150 1367 0.30 255 250Mars 228 589 0.24 211 220Jupiter 780 51 0.51 103 130TsK760288230134τEarth da ys2431.001.030.41Table 2.1: Properties of some of the planets. S0is the solar constant at a dis-tancer from the Sun, αpis the planetary albedo, Teis the emission temperaturecomputed from Eq.(2.4),Tmis the measured emission temperature and Tsis theglobal mean surface temperature. The rotation period,τ, is given in Earth days.2.1. PLA N ETARY EMISSIO N TEMP E R ATU R E 39Figure 2.2: The energy emitted from the sun plotted against wavelength basedon a black body curve withT = TSun. Most of the energy is in the visible and95% of the total energy lies between0.25 and 2.5 µm (10−6m).the wavelength as w ell as the inten sity of the radiative flux. The relationbet ween the energy flux and wa velength – the spectrum – is plotted inFig.2.2. The Sun emits rad ia tion that is primarily in the visible part of thespectrum, corresponding to the colors of the rain bow – red, orange, yellow,green, blue, indigo and violet – with the energy flux decreasing towardlonger (infrared, IR) and shorter (ultrav iolet, UV ) wa velengths.W hy does the spectrum have this pattern? Suc h behavior is c hara cteristicof the radiation emitted b y incan descent material, as can be observ ed, forexample, in a coal fire. The hottest parts of the fire are almost white andemit the most inten se radiation, with a wa velength that is shorter than thatcoming from the war m par ts of the fire, which glo w red. The coldest partsof the fire do not seem to be radiating at all, but are, in fact, radiating inthe infrared. Experimen t and theory sho w that the wa velength at wh ic hthe intensit y of radiation is a maximum, and the flux of emitted radiation,depend only on the temperature of the source. The theoretical spectrum,40 CHAPTER 2. THE GLOBAL ENER GY BALANCEFigure 2.3: Theenergyemittedatdifferent wavelengths for black bodies at severaltemperatures. The functionBλ(T ), Eq.(13.1) is plotted.one of the jewels of ph ysics, was worked out b y Planck1,andisknownasthe ‘Planck ’ or ‘blackbody’ spectrum. (A brief theoretical background to thePlanc k spectrum is giv en in Appendix 13.1.1). It is plotted as a function oftemperature in Fig.2.3. N ote that the hotter the radiating body, the moreenergy it emits at shorter w avelengths. If the observ ed radiation spectrumof the Sun is fitted to the black body curve by using T as a free parameter,w e deduce that the blac kbody temperature of the sun is about 6000 K.Let us consider the energy balance of the Earth as in Fig.2.5, whic h show sthe Earth in tercepting the solar energy flux and radiating terrestrial energya way. If at the location of the (mean) Earth orbit, the incoming solar energy1In 1900 Max Planck (1858-1947) combined the formulae of Wienand Rayleigh describing the distribution of energy as a function of w avelength of theradiation in a cavity at temperature T , to arriv e at what is now known as Planck’s radiationcurve. He went on to a complete theoretical deduction, introduced quanta of energy andset the scene for the development of Quantum Mechanics.2.1. PLA N ETARY EMISSIO N TEMP E R ATU R E 41Type of surface Albedo (%)Ocean 2 − 10Forest 6 − 18Cities 14 − 18Grass 7 − 25Soil 10 − 20Grassland 16 − 20Desert (sand) 35 − 45Ice 20 − 70Cloud (thin, thick stratus) 30, 60 − 70Sno w (old) 40 − 60Sno w (fresh) 75 − 95Table 2.2: Albedos for different surfaces. Note that the albedo of clouds is highlyvariable and depend on the type and form. See also the horizontal map of albedoshowninFig.2.4.flux is S0=1367W m−2, then, given that the cross-sectional area of theEarth in tercepting the solar energy flux is πa2where a is the radius of theEarth (Fig. 2.5),Solar power incident on the Earth = S0πa2=1.74 × 1017Wusing the data in Table 1.1. Not all of this radiation is absorbed by theEarth; a significant fraction is reflected. The ratio of reflected to incidentsolar energy is called the albedo, α. As set out in Table 2.2 and the map ofsurface albedo show n in Fig.2.4, α depends on the nature of the reflectingsurface and is large for clouds, ligh t surfaces such as deserts and (especially)snow and ice. Under the present terrestrial conditions of cloudiness and sno wand ice cover, on a verage a fraction αp' 0.30 of the incoming solar radiationat the Earth is reflected back to space; αpis known as the planetary alb edo(see table 2.1). Th u sSolar radiation absorbed by the Earth =(1− αp)S0πa2=1.22 ×


View Full Document

UT GEO 387H - Chapter 2 The global energy balance

Documents in this Course
Impacts

Impacts

2 pages

Load more
Download Chapter 2 The global energy balance
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Chapter 2 The global energy balance and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Chapter 2 The global energy balance 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?