1. ATS 621 Fall 2012 Lecture 8

2. Carbon dioxide, the key greenhouse gas http://edgar.jrc.ec.europa.eu/part_CO2.php#3degree Global gridded carbon dioxide emissions in the year 2005 (unit, ton CO2 per grid cell).

3. NH amplitude is larger Seasonal cycles in NH and SH

4. The heavier temperature lines 160,000 BP to present reflect more data points, not necessarily greater variability. Antarctic Ice Core Data CO 2 varies over geologic time, within the range 190 – 280 ppm for the last 420,000 years. The variations correlate with climate: cold  low CO 2. Is CO 2 driving climate or vice versa? CARBON DIOXIDE: GEOLOGICAL RECORD

5. ATMOSPHERIC CO 2 INCREASE OVER PAST 1000 YEARS, AND MORE RECENTLY…

6. Emissions have increased by more than 2X since 1970. But there has not been a corresponding rise in the annual increment of atmospheric CO 2. Interannual variability in the increment of atmospheric CO 2 is high. For example, in 1970 ~75% of the emitted CO 2 stayed in the atmosphere, but only ~40% in 2000. GLOBAL FUEL USE 8700 in 2008!

7. Arrows indicate El Nino events atmospheric increase is ~50% of fossil fuel emissions significant interannual variability HOW DOES GROWTH RELATE TO FOSSIL FUEL EMISSIONS? Where did the carbon go? On average, fraction in atmosphere ~1/2

8. Photosynthesis: CO 2 + H 2 O + light  "H 2 CO" + O 2 Respiration: "H 2 CO" + O 2  CO 2 + H 2 O + energy Very little organic matter is stored, on average. Dissolution/evasion CO 2(g) + H 2 O + CO 3(aq) =  2 HCO 3 ¯ CARBON CYCLE ON LAND CARBON CYCLE IN THE OCEAN This is not properly modeled as a first order sink…

9. How does ocean uptake work? CO 2 (g) CO 2 (aq), or CO 2  H 2 O CO 2 (aq), or CO 2  H 2 O Henry’s Law equilibrium; f(T) HCO 3 – (aq) H+H+ H+H+ CO 3 2– (aq) H+H+ H+H+ Because dissolved CO 2 can participate in these additional aqueous- phase reactions, MORE CO 2 than predicted by Henry’s Law can be dissolved into the ocean. How much more….?

10. Ocean pH controls the total amount of dissolved CO 2 CO 2 (g) CO 2 (aq), or CO 2  H 2 O CO 2 (aq), or CO 2  H 2 O Henry’s Law equilibrium; f(T) HCO 3 – (aq) H+H+ H+H+ CO 3 2– (aq) H+H+ H+H+ Increasing pH (more basic)

11. Ocean pH controls the total amount of dissolved CO 2 CO 2 (g) CO 2 (aq), or CO 2  H 2 O CO 2 (aq), or CO 2  H 2 O Henry’s Law equilibrium; f(T) HCO 3 – (aq) H+H+ H+H+ CO 3 2– (aq) H+H+ H+H+ Increasing pH (more basic)

12. Net uptake requires species to neutralize added acid Net uptake is charge neutral: CO 2 (g) + CO 3 2- 2HCO 3 -- CO 2. H 2 O HCO 3 - CO 3 2- H2OH2O Require CO 3 2- for overall reaction to proceed This CO 3 2- comes from dissolution of sediments: CaCO 3 = Ca 2+ + CO 3 2- (very slow!) This CO 3 2- comes from dissolution of sediments: CaCO 3 = Ca 2+ + CO 3 2- (very slow!)

13. UPTAKE OF CO 2 BY THE OCEANS CO 2 (g) CO 2. H 2 O HCO 3 - + H + HCO 3 - CO 3 2- + H + K H = 3x10 -2 M atm -1 K 1 = 9x10 -7 M K 2 = 7x10 -10 M pK 1 Ocean pH pK 2 Net uptake: CO 2 (g) + CO 3 2- 2HCO 3 -- CO 2. H 2 O HCO 3 - CO 3 2- OCEAN ATMOSPHERE H2OH2O

14. How much CO 2 has been / will be taken up? In his text, Jacob treats the entire ocean as available for the equilibria we just wrote. Using these estimates, and for present-day pH= 8.2, he estimates that 28% of each mole of CO 2 that is added, remains in the atmosphere. This is an overestimate of uptake (i.e., more than this remains, on average): –Entire ocean is not participating on the same time scale –If we considered mixed layer only (first 100 m), 94% would remain in the atmosphere (but average is more like 50%) –Also, the pH of the ocean is changing – acidifying This creates a feedback such that LESS CO2 can be taken up as acidification occurs Eventually this acidity can be neutralized from sediment dissolution – but this takes a long time http://en.wikipedia.org/wiki/File:WOA05_GLODAP_del_pH_AYool.png Estimated change in annual mean sea surface pH between the pre-industrial period (1700s) and the present day (1990s). Δ pH here is in standard pH units. Calculated from fields of dissolved inorganic carbon and alkalinity from the Global Ocean Data Analysis Project climatology and temperature and salinity from the World Ocean Atlas (2005) climatology. Note that the GLODAP climatology is missing data in certain oceanic provinces including the Arctic Ocean, the Caribbean Sea, the Mediterranean Sea and the Malay Archipelago.pHindustrial1700s1990sdissolved inorganic carbonalkalinity Global Ocean Data Analysis Projectclimatology temperaturesalinityWorld Ocean Atlas Arctic OceanCaribbean SeaMediterranean SeaMalay Archipelago [Wikipedia entry for “ocean acidification”]

15. Estimate of where CO 2 ocean uptake has already occurred Vertically integrated anthropogenic dissolved inorganic carbon for the present day (1990s) from the Global Ocean Data Analysis Project climatology (the signal of anthropogenic DIC was separated from background, natural DIC by a mathematical technique [1] ). DIC here is in mol m -2.anthropogenicdissolved inorganic carbonGlobal Ocean Data Analysis Projectclimatology [1]molm

16. Next, consider uptake by land….

17. Sources and Sinks Half the CO 2 “goes away!” Some years almost all the fossil carbon goes into the atmosphere, some years almost none Interannual variability in sink activity is much greater than in fossil fuel emissions Sink strength is related to El Niño. Why? How?

18. Fate of Anthropogenic CO 2 Emissions (2010) 9.1±0.5 PgC y -1 + 0.9±0.7 PgC y -1 2.6±1.0 PgC y -1 26% Calculated as the residual of all other flux components 5.0±0.2 PgC y -1 50% 24% 2.4±0.5 PgC y -1 Average of 5 models Global Carbon Project 2010; Updated from Le Quéré et al. 2009, Nature Geoscience; Canadell et al. 2007, PNAS

19. NET UPTAKE OF CO 2 BY TERRESTRIAL BIOSPHERE (1.4 Pg C yr -1 in the 1990s; IPCC [2001]) is a small residual of large atm-bio exchange Gross primary production (GPP): GPP = CO 2 uptake by photosynthesis = 120 PgC yr -1 Net primary production (NPP): NPP = GPP – “autotrophic” respiration by green plants = 60 PgC yr -1 Net ecosystem production (NEP): NEP = NPP – “heterotrophic” respiration by decomposers = 10 PgC yr -1 Net biome production (NBP) NBP = NEP – fires/erosion/harvesting = 1.4 PgC yr -1 Atmospheric CO 2 observations show that the net uptake is at northern midlatitudes CO 2 + H 2 O  "H 2 CO" + O 2 Photosynthesis and Respiration NOTE: 1 Pg C = 1 Gt C = 3.66 Gt CO 2 = 0.47 ppm

20. Land Carbon Sink Issues If the land is taking up ¼ of the released fossil fuel CO 2, then the plants are growing faster than they are decomposing! What are some mechanisms? –CO 2 fertilization –Nitrogen fertilization –Season broadening –Fire Suppression –Forest Regrowth –“Woody Encroachment” (new biota growing in previously inaccessible areas) Where is the sink spatially? (Tropics, N.H.?) How will the sink behave in the future? Will it stay ~25% of human emissions?

21. EMISSIONS: WHERE ARE WE NOW?

22. CHINA IS NOW THE WORLD’S LARGEST EMITTER OF CO 2 Population of China (1.3B) is more than 4x the US (307M). Per capita emissions are still 4 times higher in the US. US and China together currently make up 41% of global CO 2 emissions 2010 Growth Rates Carbon Emissions per year (C tons x 1,000,000) China USA Japan Russian Fed. India 0 500 1000 1500 2000 2500 1990 20002010 10.4% 9.4% 4.1% 5.8% 6.8%

23. Current LUC emissions ~10% of total CO 2 emissions CO 2 Emissions from FF and LUC (1960-2010) 42% Coal 34% Oil 19% Gas 5% Cement

24. SINKS: WHERE ARE WE NOW? Accumulation in the atmosphere trending up (ocean and/or land uptake efficiency declining? OR?) [Le Quéré et al., 2009] Ocean Models Atmosphere Obs Land “Missing Sink” is highly variable : 0 – 4 Gt C / yr

25. Coupled simulations of climate and the carbon cycle Given nearly identical human emissions, different models project dramatically different futures! Land Ocean Atmosphere 300 ppm! PROJECTED FUTURE TRENDS IN CO 2 UPTAKE BY OCEANS AND TERRESTRIAL BIOSPHERE

26. Lifetimes, IPCC (Third Assessment Report)

27. GLOBAL PREINDUSTRIAL CARBON CYCLE Inventories in PgC Flows in PgC yr -1 Where 5 years estimate comes from: surface exchanges only  = 615 / 120 ~ 5 years Where 5 years estimate comes from: surface exchanges only  = 615 / 120 ~ 5 years

28. More on the lifetime…. It is true that an individual molecule of CO2 has a short residence time in the atmosphere. However, in most cases when a molecule of CO2 leaves the atmosphere it is simply swapping places with one in the ocean. Thus, the warming potential of CO2 has very little to do with the residence time of CO2. What really governs the warming potential is how long the extra CO2 remains in the atmosphere. CO2 is essentially chemically inert in the atmosphere and is only removed by biological uptake and by dissolving into the ocean. Biological uptake (with the exception of fossil fuel formation) is carbon neutral: Every tree that grows will eventually die and decompose, thereby releasing CO2. (Yes, there are maybe some gains to be made from reforestation but they are probably minor compared to fossil fuel releases).dissolving into the ocean Dissolution of CO2 into the oceans is fast but the problem is that the top of the ocean is “getting full” and the bottleneck is thus the transfer of carbon from surface waters to the deep ocean. This transfer largely occurs by the slow ocean basin circulation and turn over (*3). This turnover takes 500-1000ish years. Therefore a time scale for CO2 warming potential out as far as 500 years is entirely reasonable (See IPCC 4th Assessment Report Section 2.10).IPCC 4th Assessment Report Section 2.10 http://www.skepticalscience.com/co2-residence-time.htm

29. Common Myth “ When we reduce or stop the burning of fossil fuel, the CO 2 will go away and things will go back to normal ” CO 2 from fossil fuel will react with oceans, but only as fast as they “mix” (1000s of years) Eventually, fossil CO 2 will react with rocks About 1/3 of today’s emissions will stay in the air ‘permanently’! Atmosphere for a 1000 GtC “pulse” of CO 2 Archer et al., 2009, Ann. Rev. Earth & Plan. Sci.

30. The fate of fossil fuel CO2 released into the atmosphere (Archer et al., Ann. Rev. Earth Planet. Sci, 2009): Equilibration with the ocean will absorb most of it on a timescale of 2 to 20 centuries. Even if this equilibration were allowed to run to completion, a substantial fraction of the CO 2, 20–40%, would remain in the atmosphere awaiting slower chemical reactions with CaCO 3 and igneous rocks. The remaining CO 2 is abundant enough to continue to have a substantial impact on climate for thousands of years. The changes in climate amplify themselves somewhat by driving CO 2 out of the warmer ocean. The CO 2 invasion has acidified the ocean, the pH of which is largely restored by excess dissolution of CaCO 3 from the sea floor and on land and, ultimately, by silicate weathering on land. The recovery of ocean pH restores the ocean’s buffer capacity to absorb CO 2, tending to pull CO 2 toward lower concentrations over the next 10,000 years. The land biosphere has its greatest impact within the first few centuries, which is when CO 2 peaks. Nowhere in these model results or in the published literature is there any reason to conclude that the effects of CO 2 release will be substantially confined to just a few centuries. In contrast, generally accepted modern understanding of the global carbon cycle indicates that climate effects of CO 2 releases to the atmosphere will persist for tens, if not hundreds, of thousands of years into the future.

31. HUMAN INFLUENCE ON THE CARBON CYCLE Natural fluxes in black; anthropogenic contribution (1990s) in red

32. Next topic: Photochemistry (Ch 3 notes)

33. Can these energies break chemical bonds? weak O 2 -O bond in ozone (~ 100 kJ/mol) moderately strong C-H bond in formaldehyde (~368 kJ/mol)  Corresponds to visible and shorter  But the shortest available in troposphere depends on screening by atmosphere

34. EXAMPLE: PHOTODISSOCIATION OF OXYGEN Estimate the wavelength of light at which photodissociation of O 2 into 2 ground-state oxygen atoms: O 2 + hv  O + O The enthalpy for this reaction is  H=498.4 kJ/mol (endothermic) So O 2 cannot photodissociate at wavelengths longer than about 240 nm Using:

35. What and energy reach the surface?

36. Vertical distribution of absorption

37. GASES: GHGs are absorbing in the IR(as seen for example for CO 2 ) Gases can scatter in the UV/visible  Rayleigh scattering LIGHT: REFLECTING, SCATTERING AND ABSORBING AEROSOLS: Absorption depends on composition (eg. black carbon) Scattering explained by Mie Theory  reduction in visibility

38. BEER-LAMBERT LAW AND OPTICAL DEPTH Beer-Lambert Law: Attenuation of radiation  This holds if number density does not vary significantly over dx I = radiation flux  =cross section [cm 2 /molecules] n = number density l = path length (x 2 -x 1 )  = optical depth [dimensionless]  = solar zenith angle (SZA)  z TOA Top of Atmosphere l=z TOA /cos(  ) If account for angle of light transmitted to Earth’s surface (at angle): n, σ

39. ACTINIC FLUX ACTINIC RADIATION: the integrated radiation (photon flux) from all directions to a sphere (sum of direct, scattered, reflected light) ACTINIC FLUX (J): Number of photons absorbed by species X:  ( )=absorption cross section [cm 2 /molecules] J( )=actinic flux [photons/cm 2 /s] F a ( )=number of photons abs by X [photons/cm 3 /s] [X] is in units of number density Actinic flux will be modified by SZA (thus time, season, latitude), as well as by scattering and absorption by gases and particles. The absorption is mostly from stratospheric O 3 (the ozone column). Must also consider not only direct solar, but also scattered/ reflected radiation  need surface albedo estimates  Computational codes developed to calculate actinic flux for different constituent profiles, angles, locations

40. MAJOR PHOTODISSOCIATING SPECIES NO 2 + hv  NO + O < 420 nm O 3 + hv  O( 3 P) + O 2 315 < < 1200 nm O( 1 D) + O 2 < 315 nm HNO 2 + hv  NO + OH < 400 nm H 2 O 2 + hv  2OH NO 3 + hv  NO + O 2 NO 3 “stores” NOx at night NO 2 + O HCHO + hv  HCO + H CO + H 2 dominant path for > 320 nm A photon (hv) is a reactant. Reminder: λ > 290 nm only in the troposphere!

41. COMPUTING RATES OF PHOTOLYSIS Molecule is excited into an electronically excited state by absorption of a photon: A + hv  A* The excited molecule may release the absorbed energy by any of: 1. DissociationA*  B1 + B2 2. Direct ReactionA* + B  C1 + C2 3. FluorescenceA*  A + hv 4. Collisional deactivationA* + M  A + M 5. IonizationA*  A + + e - The relative efficiency of each of these is described by the quantum yield (  i ): number of excited molecules of A* undergoing a process (i) to the total number of photons absorbed. By Stark-Einstein Law,  I = 1 You may come across the “overall quantum yield of a stable product A” (  A ) which is defined as the number of molecules of A formed over the number of photons absorbed.  A > 1 for a chain reaction

42. COMPUTING RATES OF PHOTOLYSIS (CONT’D) The total rate of photolysis of X: Rate [molecules/cm 3 /s] j = photolysis rate constant [s -1 ] Note, the use of j distinguishes the photolysis rate constant from other rate constants (k). Example: Two photochemical processes for formaldehyde to produce (H+HCO) or(H 2 +CO) thus,  ( )=  H+HCHO +  H2+CO To compute the rate of disappearance of HCHO according to 1 st rxn use only  H+HCHO

43. DISCOVERY OF PHOTOCHEMICAL REACTIONS IN THE ATMOSPHERE Some observations which remained unexplained until ~1960: 1.NO is oxidized to NO 2 in photochemical smog  the known thermal oxidation rxn is too slow: 2NO + O 2  2NO 2 2.Organics are rapidly oxidized during smog formation Known before 1970, for example for propylene were rxns: a. C 3 H 6 + O 3  products b. C 3 H 6 + O  products with rates too slow compared to propylene loss rates Leighton (1961) speculated that free radicals might be formed from organics and involved in oxidation: Ralkyl (formed from any hydrocarbon group, eg. CH 4, C 2 H 8 ) RO 2 alkyl peroxy ROalkoxy OHhydoxyl HO 2 hydroperoxy Hhydrogen free radical Time (min) Propylene Loss Rate Observed Reaction a Reaction b

44. DISCOVERY OF PHOTOCHEMICAL REACTIONS IN THE ATMOSPHERE (cont’d) In mid 1960’s reactions of CO or hydrocarbons with OH were found to be rapid. Chain reactions were proposed in 60’s which regenerate OH, convert NO  NO 2 and involve HC species: CO + OH  H + CO 2 (1) H + O 2 + M  HO 2 + M(2) HO 2 + NO  OH + NO 2 (3) Note the chemical effects: oxidation of CO (CO  CO 2 ) conversion of NO  NO 2 (as observed to occur in atmosphere) reactions are fast (as observed in atm) free radicals are used up, but also created in each step This sequence (1-3) is important in the clean troposphere. In the polluted air, organic species play a role similar to that of CO.

45. GENERATION OF OH OH radical drives the daytime chemistry of both polluted and clean atmosphere What is the source of OH (and other radicals)? Major source: O 3 + hv (  320 nm)  O( 1 D) + O 2 O( 1 D) + H 2 O  2OH Other sources: HONO + hv ( < 400 nm)  OH + NO nitrous acid (photodissociation) H 2 O 2 + hv ( < 370 nm)  2OH hydrogen peroxide HO 2 + NO  OH +NO 2 (sources and sinks of HO 2 effectively sources and sinks of OH  HOx)

46. What is steady state [O 3 ]? SS for O:R2=R1  [O] depends on [NO 2 ] SS for NO 2 :R1=R3 SS for NO:R3=R1 SS for O 3 :R3=R2  sub R1 for R2 from above: BASIC PHOTOCHEMICAL CYCLE OF NO 2, NO AND O 3 NOx is released in combustion processes, also saw that there are natural sources, such as lightning. The following is a “fast” photochemical cycle with no net consumption or production of species: NO 2 + hv  NO + O(1) O + O 2 + M  O 3 + M(2) O 3 + NO  NO 2 + O 2 (3) NO NO 2 hv O3O3 O3O3 This is the photostationary state relation. The steady state concentration of ozone is controlled by the ratio of NO 2 to NO here. However, 3 rxn cycle is incomplete for predicting ozone concentrations  don’t forget carbon compounds!

47. FREE RADICAL KINETICS EXAMPLE: ETHANE PYROLYSIS Step 1: inititation (generates free radicals) C 2 H 6 + M  2 CH 3 + M(1) (thermal initiation step) 1.Products we expect are generated in (3), (4), (5) and (7) 2.“Side products are generated in (2), (8), (9), (10) 3.If there were no termination reaction, (1) would only need to occur once to start the “chain” 4.The “chain length” is the average number of times the chain sequence is repeated before a chain-propagating radical is terminated 5.Rate is NOT equal to k[C 2 H 6 ]! Need reaction mechanism to describe the kinetics, even if net result is described by (*) C 2 H 6  C 2 H 4 + H 2 (*) C2H6C2H6 C2H4C2H4 H2H2 Step 2: chain propagation (free radical  free radical) CH 3 + C 2 H 6  CH 4 + C 2 H 5 (2) C 2 H 5 + M  C 2 H 4 + H + M(3) H + C 2 H 6  H 2 + C 2 H 5 (4) Step 3: termination: two free radicals combine to form a stable molecule 2H  H 2 (5) H + C 2 H 5  C 2 H 6 (6) H + C 2 H 5  C 2 H 4 + H 2 (7) H + CH 3  CH 4 (8) CH 3 + C 2 H 5  C 3 H 8 (9) 2C 2 H 5  C 4 H 10 (10)

48. FREE RADICAL KINETICS EXAMPLE: ETHANE PYROLYSIS C 2 H 6 + M  2 CH 3 + M(1) CH 3 + C 2 H 6  CH 4 + C 2 H 5 (2) C 2 H 5 + M  C 2 H 4 + H + M(3) H + C 2 H 6  H 2 + C 2 H 5 (4) 2H  H 2 (5) H + C 2 H 5  C 2 H 6 (6) H + C 2 H 5  C 2 H 4 + H 2 (7) H + CH 3  CH 4 (8) CH 3 + C 2 H 5  C 3 H 8 (9) 2C 2 H 5  C 4 H 10 (10) To determine overall rate: Each step is an “elementary” reaction so can be written: R1 = k1[C 2 H 6 ][M] d[C 2 H 6 ]/dt = -R1 + …. OPTIONS: 1.Write mass conversation eqns for all species and solve ODEs numerically to get [C 2 H 6 ](t) 2.Use simplifying assumptions to get analytical expression for d[C 2 H 6 ]/dt Assumption: SS applies to free radicals: for H:R3 = R4 (consider only propogation reactions for now) analysis shows k3[M] << k4[C 2 H 6 ] so can argue that for termination (10) is most important for CH 3 :R2 = 2R1 for C 2 H 5 :R3 + 2R10 = R2 + R4  sub in above, find R10=R1 Plug results into rate equation for ethane to get: rxn order = 1/2 If assume long chain lengths, can ignore initiation (R1)

49. Extra slides More detail on some topics from Prof. Heald’s course PPTs

50. LIMIT ON OCEAN UPTAKE OF CO 2 : CONSERVATION OF ALKALINITY Equilibrium calculation for Alk = 2.25x10 -3 M pCO 2, ppm 100 200 300 400 500 8.6 8.4 8.2 2 3 4 1.4 1.6 1.8 1.9 2.0 2.1 Ocean pH [CO 3 2- ], 10 -4 M [HCO 3 - ], 10 -3 M [CO 2. H 2 O]+[HCO 3 - ] +[CO 3 2- ], 10 -3 M Ca 2+ + CO 3 2- …which takes place over a time scale of thousands of years The alkalinity is the ability of solution to neutralize an acid (or excess positive charge in the ocean balanced by dissolved C): Alk = [Na + ] + [K + ] + 2[Mg 2+ ] + 2[Ca 2+ ] - [Cl - ] – 2[SO 4 2- ] – [Br - ] = [HCO 3 - ] + 2[CO 3 2- ] It is conserved upon addition of CO 2  uptake of CO 2 is limited by the existing supply of CO 3 2- Increasing Alk requires dissolution of sediments: CaCO 3 Often called carbonate alkalinity

51. EQUILIBRIUM PARTITIONING OF CO 2 BETWEEN ATMOSPHERE AND GLOBAL OCEAN Fraction of CO 2 in atmosphere (Equilibrium for present-day ocean, pH=8.2):  only 3% of total inorganic carbon is currently in the atmosphere But CO 2 (g)  [H + ]  F  … positive feedback to increasing CO 2 Pose problem differently: how does a CO 2 addition dN partition between the atmosphere and ocean at equilibrium?  28% of added CO 2 remains in atmosphere! varies roughly as [H + ] varies roughly as [H + ] 2 moles

52. FURTHER LIMITATION OF CO 2 UPTAKE: SLOW OCEAN TURNOVER (~ 200 years) Inventories in 10 15 m 3 water Flows in 10 15 m 3 yr -1 Uptake by oceanic mixed layer only (V OC = 3.6x10 16 m 3 ) would give f = 0.94 (94% of added CO 2 remains in atmosphere)

53. BLACKBODY RADIATION Objects that absorb 100% of incoming radiation are called blackbodies For blackbodies,   is given by the Planck function:   k 4 /15c 2 h 3 is the Stefan-Boltzmann constant max = hc/5kT Wien’s law Function of T only! Often denoted B(  T) max

54. KIRCHHOFF’S LAW: Emissivity  T) = Absorptivity For any object:…very useful! Illustrative example: Kirchhoff’s law allows determination of the emission spectrum of any object solely from knowledge of its absorption spectrum and temperature

55. SUN AND EARTH E/M SPECTRA As we saw last class…Emission = f(T) [Stefan-Boltzmann Law] NOTE: Sun Planck function actually much larger (higher T), normalized here