Friday 8 September, :00-4:00 Class#05

Transcription

1 Friday 8 September, :00-4:00 Class#05 Topics for the hour Global Energy Budget, schematic view Solar Radiation Blackbody Radiation notes.html 1

2 ** Global Energy Balance Pathways of energy transfer in a global average Figure 2.8 Slide from Neelin, Climate Change and Climate Modeling, Cambridge UP After Kiehl and Trenberth, 1997, Bull. Amer. Meteor. Soc.

3 Energy movement above the Top of Earth s atmosphere

4 First Law of Thermodynamics - Energy is Conserved dq = du dw Heat added to system Change in internal energy of system Work extracted from system SMALL dq Radiation - no mass exchanges or media needed Conduction - no mass exchanged, need media for transfer Convection - mass exchanges but net usually zero Consider Only Radiation to get Energy Balance of Earth 4

5 Energy movement above the Top of Earth s atmosphere & within

6 Review Wavelength and Frequency Relationship Frequency is inversely (1/cm) proportional to wavelength (cm) 6

7 Electromagnetic Spectrum Shortwave: µm Longwave: 7-25 µm 7

8 Seasons results from degree tilt of earth s axis Ruddiman, 2001 Sun is closest to earth in January and farthest in July What if the earth s axis did not tilt? 8

9 Solar radiation at each latitude related to axis of rotation Ruddiman,

10 Amount of Solar radiation arriving at earth inversely proportional to distance squared 149,600,000 km from Sun 1.49 x m (R S-E ) Solar Luminosity (L 0 ) 3.9 x W Radius of sun (R s ) 7.0 x 10 8 m Radiance at sun s surface (S s ) is 6.3 x 10 7 W/m 2 Hartmann Eq (2.3) Flux = L 0 = S d 4πd 2 S - Flux density S R 2 0 S E = S s R s 2 S 0 = S s R 2 s 1380Wm 2 R 2 S E Solar Constant - amount of solar radiation reaching the top of the earths atmosphere. 10

11 Schematic of Sun's rays arriving at disk and spherical Earth Summarized Solar energy flux (integrated across all wavelengths) at Earths orbit S o 1366 Wm -2 Insolation averaged over one day, and over all latitudes = global average solar flux S o / Wm -2 (round to 342 Wm -2 below) [Neelin 2011] Decrease of intensity is inversely proportional to distance squared

12 Planetary Albedo is total amount of Solar radiation reflected by earth Average global albedo is 30% (α p = 0.3) function of clouds and reflectivity of surfaces Average solar radiation reaching surface is 241W/m 2 Approximate by Area of Earth s shadow (a circle) Incoming/4 TOA 1380/4 = 342 (1 A)S 0 πr E 2 = (0.7)(1380) 4πR 2 4 E = 241Wm 2 Total Area of Earth s surface Average radiation at TOA is 342 W/m 2 Average solar radiation reaching surface is 241W/m 2 12

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14 Summary of Numbers From Sun to Earths surface Solar Radia*on Component Radiance at sun s surface is 6.3 x 10 7 W/m 2 Radiance at Earth s Orbit is 1366 W/m 2 Radiance at the top of the earths atmosphere is 342 W/m 2 Radiance at the surface of the earths is 241 W/m 2

15 Distribution of Solar Energy at surface Watts per meter squared Pexito & Oort, 1992 Net Solar 3 times greater in Tropics than at Poles 241 W/m 2 on average 15

16 ** Global Energy Balance Pathways of energy transfer in a global average Figure 2.8 Slide from Neelin, Climate Change and Climate Modeling, Cambridge UP After Kiehl and Trenberth, 1997, Bull. Amer. Meteor. Soc.

17 Solar Insolation at Top of the Atmosphere (TOA) with Latitude/Month Pole equator contrast NH SH contrast Hartmann, 1994 Subsolar point- point where sun perceived to be directly overhead (dash) June compare 90 and 0 lat, 17

18 Main concepts thus far today Why do we have seasons? What are the geometric factors that impact solar radiation reaching the earth? What are the values? Flux density at sun s surface is: 6.3 x 10 7 W/m 2 Flux density arriving at the earth is 1380 W m -2 Flux density at TOA is 342 W m-2 (1380/4) Flux density at surface is 241 W m-2 (1380/4)*0.7 Annual average solar flux at the surface is >300 W m -2 in tropics and <100 W m -2 in polar regions. Two parts of the Radiation budget, incoming shortwave (solar) radiation and outgoing longwave (terrestrial).. 18

19 Blackbody Radiation Blackbody radiation - perfect absorber and emits a maximum of energy at a particular temperature Dependence of total blackbody emission (over all wavelengths) on temperature follows Stefan-Boltzman Law ( Tell us how quickly energy is radiated from an object): E R = εσt 4 σ = Wm 2 K 4 ER is the total rate of energy emission from the object at all frequencies in Watts/m2. ε is emissivity, a number between 0 & 1 telling us how good a blackbody we have (1=best) σ is the Stefan-Boltzman constant T is emission temperature Compare spectra of Sun and Earth 19

20 Theoretical Blackbody Spectra wave number is the reciprocal of wavelength [Archer 2011] Wien s Law, Maximum wavelength - Temperature relationship 20

21 Emission Temperature Temperature at which a planet needs to emit in order to achieve energy balance. Solar radiation absorbed = planetary radiation emitted 21

22 Emission Temperature of Earth Set Solar in equal to Terrestrial out! T e = S 0 4 (1 α p ) = σt e (1367 /4)(1 0.3) 4 255K = 18C σ W/m 2 Factor of 1/4 comes from the ratio of shadow area of sphere to the surface area of a sphere (π RE 2 /4 π RE 2 ) Hmmm Emission Temperature is much less than observed Surface temperature of Earth (~288K)??? WHY?? 22

23 Normalized Spectra of Sun and Earth (same heights) Visible not absorbed Ozone absorbs most incoming solar radiation 4 micron break CO 2 vibration-rotation absorption key wavelength Water vapor absorption between microns You can imagine that radiation is NOT easy to model! 23

24 Layer Model of the Atmosphere Recall bare rock model had an emission temperature of 255 K, much cooler than real temperature of 288 K. Atmosphere is transparent to visible light (solar) Solar energy all reaches the surface and converts into Terrestrial radiation and emits upward. Terrestrial radiation (LW) is absorbed in atmosphere and emitted upwards and downwards 24

25 Solve for temperature of surface and atmosphere. Simple energy balance model Assume LW blackbody Solar transparent Hartmann, 1994 S 0 4 (1 α ) = σt 4 4 p A = σt Energy Balance TOA e σt 4 = 2σT 4 Energy Balance of Atmosphere S A sd S 0 4 (1 α ) + σt 4 4 p A = σt S Energy Balance of Surface Te=Ta=255K TS= is ~20% warmer 25

26 Concepts/Numbers shortwave radiation albedo, earth s albedo Solar radiation at the TOA, at surface of earth Emission temperature Questions???? Summary Top 30 Figures visited in this lecture: Surface Energy Balance 26