1 Weather, Climate & Society ATMO 325 Global Energy Balance Greenhouse Effect

2 General Laws of Radiation All objects above 0 K emit radiant energy Hotter objects radiate more energy per unit area than colder objects Stefan-Boltzman Law The hotter the radiating body, the shorter the wavelength of maximum radiation Wien’s Displacement Law Objects that are good absorbers of radiation are also good emitters

3 General Laws of Radiation Wien’s Displacement Law Stefan-Boltzman Law

4 What is Radiative Temperature of Sun if Max Emission Occurs at 0.5 µm? Apply Wien’s Displacement Law

5 What is Radiative Temperature of Earth if Max Emission Occurs at 10 µm? Apply Wien’s Displacement Law

6 Sun - Earth Radiation Spectra Ahrens, Fig. 2.8 Planck’s Law

7 Towards a Climate Model The energy of a gas is a function of its temperature only (vice versa). Therefore, if the atmosphere ’ s T changes, its energy balance has changed. It follows that if we can describe the sources and sinks of energy, then we can predict T. Courtesy J. Thornton UW

8 Energy Balance Energy Flux In = Energy Flux Out F in = F out F in =  T 4 Earth Assume Earth radiates like a blackbody Energy Balance: Halfway Done Courtesy J. Thornton UW

9 Earth’s Energy Balance: Towards F IN Need to account for a)Earth-Sun distance (inverse square law), b)Earth intercepts fraction of total solar flux at D SE c)Earth “reflects” some of the intercepted radiation D SE RSRS Courtesy J. Thornton UW

10 The sun emits about 6.3 X 10 7 W/m 2 of radiant energy How are we still here? Solar Emission Flux Courtesy J. Thornton UW

11 Radiant Energy Flux Far From Source vs r obj d1d1 d2d2 Flux decreases as inverse square of distance from source **this picture is a bit misleading ** Courtesy J. Thornton UW

12 Spectrum of Solar Radiation Flux Courtesy J. Thornton UW Flux Distribution (measured at Earth) Outside of atmosphere Reaching Earth’s surface Perfect blackbody ~30% “reflected”

13 Earth’s Energy Balance: Towards F IN Need to account for a)Earth-Sun distance (inverse square law), b)Earth intercepts fraction of total solar flux at D SE c)Earth “reflects” some of the intercepted radiation D SE RSRS Courtesy J. Thornton UW

14 If both a sphere and disc have the same radius, which will intercept more radiation? 1.disc 2.Sphere (hemisphere) 3.both intercept same “Area” =  r 2 “Area” = 2  r 2 Courtesy J. Thornton UW

15 Earth’s Energy Balance: Earth Sun Geometry Courtesy J. Thornton UW

16 Earth’s Energy Balance—No Atmosphere F in = F out Same approach for ANY planet! Courtesy J. Thornton UW

17 Earth’s Energy Balance—No Atmosphere Not a very good prediction! What’s wrong with our model? T E ~ 256 K (-17 o C below freezing) Plug in known values for S o, A, and  and predict Courtesy J. Thornton UW

18 Planet S o /4 = 341 Wm -2 (S o /4)A = 96 Wm -2 F IN ~ 245 Wm -2 F out =  T E 4 “Bare rock” Model (i.e. no atmosphere) Predict T E ~ 256 K when atmosphere is neglected Energy Balance Cartoon Courtesy J. Thornton UW

19 Where did we go wrong? 1.Radiation only form of energy 2.Sun only energy source, constant 3.Solar energy deposited uniformly 4.Atmosphere plays no role 5.F in = F out Examine the validity of our assumptions OK for global energy balance Very good for average state OK for global average energy balance Hmmm… Good for global long-term average

20 The Greenhouse Effect 289 K – 256 K = 33 K T true – T ”bare rock” The atmosphere increases the average surface temperature by about 13% Can we explain the physics and predict the right T? Courtesy J. Thornton UW

21 Surface T sf S o /4 (S o /4)A F sf IN F sf OUT Atmosphere T atm (1-  ) F sf OUT  F atm OUT Global Climate Model: Take 2 Let’s model the Earth system as a planetary surface with an absorbing atmosphere above the surface. Courtesy J. Thornton UW

22 Global Climate Model: Take 2 1.The atmosphere absorbs only Outgoing Long wave Radiation (no absorption of solar radiation) 2. The atmosphere absorbs the same fraction of OLR at each wavelength. 3. The atmosphere has a uniform temperature. 4. F in = F out for each component and whole system. Simplifying Assumptions Courtesy J. Thornton UW

23 Non-Blackbodies (<100% absorption) The same springs (matter) forced with three different frequencies - emission - absorption Courtesy J. Thornton UW

24 A body will only emit the same wavelengths it absorbs. Radiation Flux Distribution Ideal Blackbody spectrum True spectrum Kirchoff’s Law: Imperfect Blackbody Courtesy J. Thornton UW

25 Surface T sf S o /4 (S o /4)A S o (1-A)/4 Atmosphere T atm (1-  ) F sf OUT  T atm 4 Global Climate Model: Take 2 A planetary surface with an absorbing atmosphere above the surface. (see pg 43 of textbook) F sf OUT =  T sf 4 Courtesy J. Thornton UW

26 Energy Balances Surface Balance Atmospheric Balance

27 Global Climate Model: Take 2 Wear it, sleep on it, put it on your cereal box, … Courtesy J. Thornton UW

28 Global Climate Model: Take 2 If  ~ 0.75, then T SFC ~ 289 K Courtesy J. Thornton UW

29 If the atmosphere’s absorptivity, , increases, Earth’s surface T 1.Increases 2.Decreases 3.Stays the same Courtesy J. Thornton UW

30 1. An OLR absorbing atmosphere slows the net energy flow out from surface (relative to no atm). 2. An increase in atmosphere’s absorptivity causes surface T to increase. 3. Radiation reaching space from the Earth is a combination of emission from a warm surface and colder atmosphere. It must be equivalent to 245 W/m 2 at equilibrium. 1-Layer Model Summary Courtesy J. Thornton UW

31 By how much must  increase in order to raise T SFC by 1˚C? If  ~ , then T SFC ~ 289 K + 1 K Courtesy J. Thornton UW

32 Figure SPM.3

33 Can increases in GHG’s alone explain observed warming? Increasing Greenhouse Gases

34 Can GHG increases explain warming? IPCC Fig. SPM.1 IPCC WG1 Fig. 6.10

35 Absorption Visible (  m) is absorbed very little O 2 an O 3 absorb UV (shorter than 0.3  m) Infrared (5-25  m) is selectively absorbed H 2 O & CO 2 are strong absorbers of IR Little absorption of IR around 10  m Visible IR Ahrens, Fig. 2.9

36 Total Atmospheric Absorption Visible radiation (  m) is not absorbed Infrared radiation (5-25  m) is selectively absorbed, but there is an emission window at 10  m Ahrens, Fig. 2.9

37 Greenhouse Effect Example (1-layer atmo., 100% IR, 0% SR absorbed) 1 Unit Incoming Solar 1 1/21/41/81/16 1/21/41/8 1/16 1 Unit Outgoing IR to Space 2 Units IR Emitted by Ground ½ emitted to space ½ emitted to ground

38 Greenhouse Effect Example (1-layer atmosphere,  IR absorbed) A = albedo - % solar reflected to space (1-  ) emitted to space  = emissivity - % absorbed by air F OUT SFC F IN SFC (S 0 /4) AS 0 /4 (1-  ) F OUT SFC Surface T SFC Atmosphere T ATM  F OUT ATM

39 Simplifying Assumptions Atmosphere only absorbs Outgoing Longwave Radiation (OLR) Atmosphere absorbs the same fraction of OLR at each wavelength Atmosphere has a uniform temperature distribution F IN = F OUT for each component and the whole system Each component obeys Stefan-Boltzmann

40 Greenhouse Effect Example (1-layer atmosphere, <100% IR absorbed) (1-  ) emitted to space  absorbed by air F OUT SFC =  T 4 SFC (1-A) S 0 /4 (S 0 /4)AS 0 /4 (1-  ) F OUT SFC Surface T SFC Atmosphere T ATM   T 4 ATM  F OUT ATM =   T 4 ATM

41 Energy Balances Surface Balance Atmospheric Balance

42 Simple Climate Balance Model

43 What Do Models Include?

44 Global Solar Radiation Balance Ahrens, Fig % solar absorbed by earth-atmosphere

45 The Atmosphere is Heated from Below Ahrens, Fig old ed.

46 Global Atmo Energy Balance Ahrens, Fig. 2.14

47 Summary Greenhouse Effect (It’s a Misnomer) Warmer than Rad. Equilibrium Temp Reason: selective absorption of air H 2 O and CO 2 most absorbent of IR Energy Balance Complex system All modes of Heat Transfer are important