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# Hollow earth, contrails & global warming calculations lecture

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http://www.marcusmoon2022.org/designcontest.htm
Shoot for the moon and if you miss you'll land among the stars...

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• Need to supplement with one of those diagrams…indicating that total radiation flux at the ground includes a lot of longwave.
• Question: How many watts/m 2 radiated to space on a clear night in the Niger with the surface still at 320K? (200 cm -1 x 150x10 -3 W/m 2 ) x 2  = 6 x (30+20) = 300 Wm -2 . [ + 200x100x10 -3 ?] Question: What would be the emission rate if T=280 instead of 320 (a cool clear winter night)? Estimate that it goes at T 4 : (7/8) 4 = .58 =&gt; 100 Wm -2 . How much does that cool the air? Assume snow cover (perfect insulator), effect through 100 m depth of air. Heat capacity of air = 1005 J/kg/K. In 1 hour each sq. meter loses 36 KJ. 7000m of air = 10,000 kg/m 2 , so 200m is 300 kg. DelT= 360KJ/300/1.005 = 1.2 K/hr. In a night, 12 hr, 14K; 16 hr, 19K T decline!
• “ official chart”
• Question: How many watts/m 2 radiated to space on a clear night in the Niger with the surface still at 320K? (200 cm -1 x 150x10 -3 W/m 2 ) x 2  = 6 x (30+20) = 300 Wm -2 . [ + 200x100x10 -3 ?] Question: What would be the emission rate if T=280 instead of 320 (a cool clear winter night)? Estimate that it goes at T 4 : (7/8) 4 = .58 =&gt; 100 Wm -2 . How much does that cool the air? Assume snow cover (perfect insulator), effect through 100 m depth of air. Heat capacity of air = 1005 J/kg/K. In 1 hour each sq. meter loses 36 KJ. 7000m of air = 10,000 kg/m 2 , so 200m is 300 kg. DelT= 360KJ/300/1.005 = 1.2 K/hr. In a night, 12 hr, 14K; 16 hr, 19K T decline!
• Accumulation mode—happens to be in visible range; also repirable!. Growth rate is proportional to 1/r.
• Highest when particle r = wavelength (pi*d)—surface wave, diffraction. Rayleigh=inefficient
• Absorbing (right panel) ; Jfk jr; particle size and composition.
• ### Hollow earth, contrails & global warming calculations lecture

1. 2. Millenial NH temperature trend [IPCC, 2001]
2. 3. GLOBAL CLIMATE CHANGE SINCE 1850 [IPCC, 2007] IPCC [2007]
3. 4. EMISSION OF RADIATION <ul><li>Radiation is energy transmitted by electromagnetic waves; all objects emit radiation </li></ul><ul><li>One can measure the radiation flux spectrum emitted by a unit surface area of object: </li></ul>Here  is the radiation flux emitted in [  is the flux distribution function characteristic of the object Total radiation flux emitted by object:
4. 5. BLACKBODY RADIATION <ul><li>Objects that absorb 100% of incoming radiation are called blackbodies </li></ul><ul><li>For blackbodies,   is given by the Planck function: </li></ul>   <ul><li>  k 4 /15c 2 h 3 is the </li></ul><ul><li>Stefan-Boltzmann constant </li></ul> max = hc/5kT Wien’s law Function of T only! Often denoted B(  T )  max
5. 6. KIRCHHOFF’S LAW: Emissivity  T ) = Absorptivity Illustrative example: Kirchhoff’s law allows determination of the emission spectrum of any object solely from knowledge of its absorption spectrum and temperature For any object: … very useful!
6. 7. SOLAR RADIATION SPECTRUM: blackbody at 5800 K
7. 8. TERRESTRIAL RADIATION SPECTRUM FROM SPACE: composite of blackbody radiation spectra for different T Scene over Niger valley, N Africa
8. 9. SHORT QUESTIONS <ul><li>For an object of given volume, which shape emits the least radiation? </li></ul><ul><li>If the Earth were hollow, would it emit less radiation? </li></ul><ul><li>The Sun, with a temperature of 5800 K, emits radiation peaking at a wavelength of 0.5  m. What is the wavelength of peak emission for an object with a temperature of 290 K? </li></ul>
9. 10. RADIATIVE EQUILIBRIUM FOR THE EARTH Solar radiation flux intercepted by Earth = solar constant F S = 1370 W m -2 Radiative balance  effective temperature of the Earth: where A is the albedo (reflectivity) of the Earth = 255 K
10. 11. ABSORPTION OF RADIATION BY GAS MOLECULES <ul><li>… requires quantum transition in internal energy of molecule. </li></ul><ul><li>THREE TYPES OF TRANSITION </li></ul><ul><ul><li>Electronic transition: UV radiation (<0.4  m) </li></ul></ul><ul><ul><ul><li>Jump of electron from valence shell to higher-energy shell, sometimes results in dissociation (example: O 3 +h   O 2 +O) </li></ul></ul></ul><ul><ul><li>Vibrational transition: near-IR (0.7-20  m) </li></ul></ul><ul><ul><ul><li>Increase in vibrational frequency of a given bond </li></ul></ul></ul><ul><ul><ul><li>requires change in dipole moment of molecule </li></ul></ul></ul><ul><ul><li>Rotational transition: far-IR (20-100  m) </li></ul></ul><ul><ul><ul><li>Increase in angular momentum around rotation axis </li></ul></ul></ul>Gases that absorb radiation near the spectral maximum of terrestrial emission (10  m) are called greenhouse gases; this requires vibrational or vibrational-rotational transitions
11. 12. NORMAL VIBRATIONAL MODES OF CO 2 forbidden allowed allowed IR spectrum of CO 2 bend asymmetric stretch
12. 13. GREENHOUSE EFFECT: absorption of terrestrial radiation by the atmosphere <ul><ul><li>Major greenhouse gases: H 2 O, CO 2 , CH 4 , O 3 , N 2 O, CFCs,… </li></ul></ul><ul><ul><li>Not greenhouse gases: N 2 , O 2 , Ar, … </li></ul></ul>
13. 14. SIMPLE MODEL OF GREENHOUSE EFFECT Earth surface ( T o ) Absorption efficiency 1- A in VISIBLE 1 in IR Atmospheric layer ( T 1 ) abs. eff. 0 for solar (VIS) f for terr. (near-IR) Incoming solar Reflected solar Surface emission Transmitted surface Atmospheric emission Atmospheric emission <ul><li>Energy balance equations: </li></ul><ul><li>Earth system </li></ul><ul><li>Atmospheric layer </li></ul>Solution: T o =288 K  f=0.77 T 1 = 241 K VISIBLE IR
14. 15. SHORT QUESTIONS <ul><li>In our calculation of the effective temperature of the Earth we viewed the Earth as a blackbody. However, we also accounted for the fact that the Earth absorbs only 72% of solar radiation (albedo = 0.28), so obviously the Earth is not a very good blackbody (which would absorb 100% of all incoming radiation). Nevertheless, the assumption that the Earth emits as a blackbody is correct to within a few percent. How can you reconcile these two results? </li></ul><ul><li>2. Soot particles absorb solar radiation and have little effect in the infrared. Explain how this can have either a warming or cooling effect on the surface temperature of the Earth. </li></ul>
15. 16. RADIATIVE AND CONVECTIVE INFLUENCES ON ATMOSPHERIC THERMAL STRUCTURE In a purely radiative equilibrium atmosphere T decreases exponentially with z , resulting in unstable conditions in the lower atmosphere; convection then redistributes heat vertically following the adiabatic lapse rate
16. 17. EQUILIBRIUM RADIATIVE BUDGET FOR THE EARTH
17. 18. TERRESTRIAL RADIATION SPECTRUM FROM SPACE: composite of blackbody radiation spectra emitted from different altitudes at different temperatures
18. 19. HOW DOES ADDITION OF A GREENHOUSE GAS WARM THE EARTH? 1. 1. Initial state 2. 2. Add to atmosphere a GG absorbing at 11  m; emission at 11  m decreases (we don’t see the surface anymore at that  but the atmosphere) 3. At new steady state, total emission integrated over all  ’s must be conserved  Emission at other  ’s must increase  The Earth must heat! 3. Example of a GG absorbing at 11  m
19. 20. EFFICIENCY OF GREENHOUSE GASES FOR GLOBAL WARMING The efficient GGs are the ones that absorb in the “atmospheric window” (8-13  m). Gases that absorb in the already-saturated regions of the spectrum are not efficient GGs.
20. 21. RADIATIVE FORCING OF CLIMATE CHANGE Incoming solar radiation Reflected solar radiation (surface, air, aerosols, clouds) F out F in IR terrestrial radiation ~ T 4 ; absorbed/reemitted by greenhouse gases, clouds, absorbing aerosols EARTH SURFACE <ul><li>Stable climate is defined by radiative equilibrium: F in = F out </li></ul><ul><li>Instantaneous perturbation  Radiative forcing  F = F in – F out </li></ul><ul><li>Different climate models give  = 0.3-1.4 K m 2 W -1 , insensitive to nature of forcing; </li></ul><ul><li>differences between models reflect different treatments of feedbacks </li></ul>Increasing greenhouse gases   F > 0 positive forcing <ul><li>The radiative forcing changes the heat content H of the Earth system: </li></ul>where T o is the surface temperature and  is a climate sensitivity parameter eventually leading to steady state
21. 22. CLIMATE CHANGE FORCINGS, FEEDBACKS, RESPONSE Positive feedback from water vapor causes rough doubling of 
22. 23. CLIMATE FEEDBACK FROM HIGH vs. LOW CLOUDS convection T o T cloud ≈ T o Clouds reflect solar radiation (  A > 0)  cooling; … but also absorb IR radiation (  f > 0)  warming WHAT IS THE NET EFFECT?  T o 4  T cloud 4 ≈  T o 4 LOW CLOUD: COOLING  T cloud 4 <  T o 4  T o 4 HIGH CLOUD: WARMING
23. 24. IPCC [2007]
24. 25. SHORT QUESTIONS <ul><li>Stratospheric ozone has both a cooling and warming effect on the Earth’s surface temperature. Explain. </li></ul><ul><li>The total radiative forcing of climate from human activities since 1750 has been +1.6 W m -2 . What fractional increase in cloud albedo would completely offset the associated warming? </li></ul>
25. 26. TERRESTRIAL RADIATION SPECTRUM FROM SPACE: composite of blackbody radiation spectra emitted from different altitudes at different temperatures
26. 27. ORIGIN OF THE ATMOSPHERIC AEROSOL Soil dust Sea salt Aerosol: dispersed condensed matter suspended in a gas Size range: 0.001  m (molecular cluster) to 100  m (small raindrop) Environmental importance: health (respiration), visibility, radiative balance, cloud formation, heterogeneous reactions, delivery of nutrients…
27. 28. SCATTERING OF RADIATION BY AEROSOLS: “DIRECT EFFECT” By scattering solar radiation, aerosols increase the Earth’s albedo <ul><li>Scattering efficiency is maximum when particle diameter =  </li></ul><ul><li>particles in 0.1-1  m </li></ul><ul><li>size range are efficient scatterers of solar radiation </li></ul>2 (diffraction limit)
28. 29. EVIDENCE OF AEROSOL EFFECTS ON CLIMATE: Observations NASA/GISS general circulation model Temperature decrease following large volcanic eruptions Mt. Pinatubo eruption 1991 1992 1993 1994 -0.6 -0.4 -0.2 0 +0.2 Temperature Change ( o C)
29. 30. SCATTERING vs. ABSORBING AEROSOLS Scattering sulfate and organic aerosol over Massachusetts Partly absorbing dust aerosol downwind of Sahara Absorbing aerosols (black carbon, dust) warm the climate by absorbing solar radiation
30. 31. AEROSOL “INDIRECT EFFECT” FROM CLOUD CHANGES Clouds form by condensation on preexisting aerosol particles (“cloud condensation nuclei”)when RH>100% <ul><li>clean cloud (few particles): </li></ul><ul><li>large cloud droplets </li></ul><ul><li>low albedo </li></ul><ul><li>efficient precipitation </li></ul><ul><li>polluted cloud (many particles): </li></ul><ul><li>small cloud droplets </li></ul><ul><li>high albedo </li></ul><ul><li>suppressed precipitation </li></ul>
31. 32. EVIDENCE OF INDIRECT EFFECT: SHIP TRACKS  Particles emitted by ships increase concentration of cloud condensation nuclei (CCN)  Increased CCN increase concentration of cloud droplets and reduce their avg. size  Increased concentration and smaller particles reduce production of drizzle  Liquid water content increases because loss of drizzle particles is suppressed  Clouds are optically thicker and brighter along ship track N ~ 100 cm -3 W ~ 0.75 g m -3 r e ~ 10.5 µm N ~ 40 cm -3 W ~ 0.30 g m -3 r e ~ 11.2 µm from D. Rosenfeld
32. 33. SATELLITE IMAGES OF SHIP TRACKS AVHRR, 27. Sept. 1987, 22:45 GMT US-west coast NASA, 2002 Atlantic, France, Spain
33. 34. OTHER EVIDENCE OF CLOUD FORCING: CONTRAILS AND “AIRCRAFT CIRRUS” Aircraft condensation trails (contrails) over France, photographed from the Space Shuttle (©NASA).