1. CE 401 Climate Change Science and Engineering solar input, mean energy budget, orbital variations, radiative forcing 18-20 January 2011

2. a quick business item: CE 401 is NOT a Tier III class. So anyone taking it to meet the Tier III requirement will not be given credit for this class as a Tier III

3. any questions from last time? we did the entire science section

4. homework 3: due Thursday 1/27 read Houghton Chapter 2 do some computations (see website)  (1) use the Stefan-Boltzmann law as described in class: (a) if the solar output as measured at the top of the Earth’s atmosphere (1368 W m -2 ) were reduced by 1 W m -2, then how much would the equilibrium temperature of the Earth be changed (assuming no atmospheric gases)? (b) if the amount of solar radiation reflected by clouds, aerosols, and atmospheric gases were changed from the current 31% to 30%, then how much would the equilibrium temperature of the Earth change [K]? (2) use Houghton Fig 2.5 to estimate the change in Earth equilibrium temperature that would occur if CO 2 were completely removed from the atmosphere. Hint: the total energy radiated by the Earth plus atmosphere should remain the same  the area under the radiation curve should not change. (3) The solar flux S arriving at the top of the atmosphere varies by +/-3.3% as the Earth revolves around the sun. By how many degrees should the effective temperature of the Earth vary each year as a result? Read chapter 2 of Houghton due Tuesday, 1/25 HW 2 due on Thursday

6. what cause natural variations in the climate system

7. natural variations in Earth energy balance are caused by (at least): changes in the radiation balance of the Earth-Sun system intrinsic changes in solar flux long term - must be modeled using sunspot numbers solar cycle - only two cycles measured + 0.05% changes in Earth orbital parameters - Milankovitch cycles periods of 20k - 100k years explain all the major ice ages – dramatic changes in temperature changing aerosol concentrations (e.g. volcanic activity)

8. the solar energy input to the Earth system

9. 1000 nm = 1 µm

10. solar and earth spectra 1000 nm = 1 µm

12. why would solar energy output vary?

13. the sun is a dynamic object

14. Sun varies in output on an 11 yr and 22 yr cycle, but also over longer periods that are not understood number of sunspots vs time

15. modeled solar irradiance at top of the atmosphere

16. satellite measurements of solar brightness 0.1% variation individual instruments vary in calibration – so bring them to a normalization, usually 1368 w/m 2

17. Stefan-Boltzmann law: Let S = rate at which the Sun produces energy as measured at the Earth’s orbital distance = solar constant = 1368 w m -2 then rate at which solar energy strikes the Earth = S  R 2 (watts) where R is the radius of the Earth (6370 km) energy reflected back into space by Earth = S  R 2  where  is the Earth’s average albedo (reflectivity) ~ 0.31 on average energy absorbed by Earth system = S  R 2 (1-  )

18. the Earth cannot get rid of energy by conduction or convection to space, so must radiate its energy to space thermally energy radiated to space is =  4  R 2 T e 4 [the Stefan-Boltzmann law] where  = Stefan-Boltzmann constant = 5.67 x 10 -8 [w m -2 K -4 ] Earth in equilibrium (temp not changing with time), rate of absorption = rate of emission  S  R 2 (1-  ) =  4  R 2 T e 4 solving for T e using  = 0.31 gives T e = 255K = -18°C this is the equilibrium temperature of the Earth in the absence of the atmosphere and it is much lower than observed

19. distributed over the entire surface of the Earth, average incoming solar radiation is: [incoming solar/surface area of Earth] = S  R 2 /4  R 2 = 1368/4 = 342 w m -2 since albedo  is 0.31, amount of incoming radiation reflected back to space is: [solar energy reflected/surface area of Earth] = S  R 2  / 4  R 2 = 107 w m -2 absorbed energy: [solar energy absorbed/surface area of Earth] = S  R 2 (1-  ) / 4  R 2 = 235 w m -2

20. global energy balance – bold black numbers are W/m 2 342-107=235 absorbed

21. no atmosphere  T e = 255K = -18°C Earth radiates 235 w m -2 at this temperature and this radiation is in the infrared spectral region where many atmosphere gases absorb radiation Thus, energy balance is NOT achieved at -18°C, and the Earth temp must increase to get rid of the energy and achieve a balanced equilibrium Measured average Earth temperature is 288K = +15°C. Using Stefan- Boltzmann, we compute the radiated energy is  T e 4 = 390 w m -2 of the 390 w m -2, only 40 passes directly through (gases do not absorb ALL radiation)  350 w m -2 is absorbed by atmospheric gases, and 324 w m -2 is radiated back to the surface

22. checks on our numbers: rate of gain = rate of loss at Earth surface: 168 + 324 + 30 = 78 + 24 + 30 + 390 OK Atmosphere: 67 + 78 + 24 + 350 + 40 = 165 + 30 + 324 + 40 OK Space: 107 + 165 + 30 + 40 = 342 OK

23. Earth ~33°C (60°F) warmer than without GHG

24. thermal radiation curves (T) measured thermal Earth radiation over the Mediterranean sea H2O CH4 N2O O3 CO2 H2O GHG absorbers are indicated with atmospheric transmission “windows”

25. what physical parameters affect the ability of an atmospheric gas to be a greenhouse gas? see http://www.ciesin.columbia.edu/docs/003-074/003-074.html for GH effect: science and policy

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27. radiative forcing: IPCC “Radiative forcing is a measure of the influence a factor has in altering the balance of incoming and outgoing energy in the Earth-atmosphere system and is an index of the importance of the factor as a potential climate change mechanism. In this report radiative forcing values are for changes relative to preindustrial conditions defined at 1750 and are expressed in watts per square meter (W/m 2 )”

28. factors that influence the radiative equilibrium of the Earth system average solar input: 342 w/m 2

29. global warming potential (GWP) of a gas GWP g : a weighting factor to compare the GHG efficiency of a gas relative to CO 2 GWP g = F g x R g (t) dt / F CO2 x R CO2 dt where F g = radiative forcing efficiency of the gas in question [w m -2 kg -1 ] F CO2 = radiative forcing efficiency of CO 2 [w m -2 kg -1 ] R g = fraction of the 1 kg of gas remaining in the atmosphere at time t R CO2 = fraction of the 1 kg of CO 2 remaining in the atmosphere at time t radiative forcing efficiency is usually an exponential decay function, or ~ constant with time, depending on the gas. For CO 2 the decay is rapid the first few decades as the biosphere absorbs the carbon, then it decays at a much slower rate corresponding to the slow CO 2 uptake of the oceans Choice of time horizon for GWP depends on what a policy maker is interested in e.g. CH 4 GWP is 62 for 20 yr horizon, 23 for 100 yr, and 7 for 500 yr

31. astronomical forces drive global climate change seasons are driven by astronomical causes, as is the 24 h da/night cycle

32. Earth orbital changes that vary the solar input and cause the ice ages: the Milankovich cycles – these cycles change the solar input to the Earth system

33. shape of earth’s orbit changes during a cycle of about 100,000 years eccentricity changes varies from nearly circular to high eccentricity 0.058 with mean 0.028. Caused by perturbations from the other planets

34. axis of rotation changes from about 21.5° to 24.5° --> seasonal variations over a period of 41,000 years. Tilt is the most significant cause of seasonal temp change. Modulates the seasons, does not change climate overall axial tilt (obliquity) – increased obliquity  increased seasonal amplitude change

35. the earth’s rotation axis precesses (wobbles) with a period of about 26,000 years due to tidal forces exerted by sun and moon on solid Earth since Earth is not spherical affects climate extremes axial precession – trend in direction of axis of rotation in inertial space – gyroscopic motion

37. problems with the Milankovitch theories: 100,000 yr problem: eccentricity variations should have a smaller impact that the other mechanisms, but this is the strongest climate signal in the data record 400,000 yr problem: eccentricity variations also show a 400,000 yr cycle but that cycle is only visible in climate records > 1My ago observations of climate changes show behavior much more intense than calculated the 23,000 yr cycle dominates, the opposite of what is observed so the explanation is not 100% - there are still issues with the explanation

38. deg change obliquity=axial tilt long of perihelion precession index calc. insolation to TOA Benthic and Vostok ice cores