Global Energy Balance Chautauqua UWA-6, Dr. E.J. Zita 9-11 July 2007 Fire, Air, and Water: Effects of the Sun, Atmosphere, and Oceans in Climate Change and Global Warming
Review: Blackbody radiators Intensity of radiation = s T4
Review: Energy, power, and radiation Force = mass * acceleration [units: N = kg*m/s2] Energy = work [units: Joules = N*m = kg*m2/s2] Power = Energy / time = rate of doing work [Watts = Joules / sec] Intensity = Power / area [Watts / m2] Intensity of blackbody radiation = s T4 What must be the units of the constant s, if T is in Kelvin? s units =
Goldilocks Hypothesis: Earth is just the right distance from Sun. Venus is close Earth is intermediate Mars is far to the Sun distance from Sun from Sun TOO HOT JUST RIGHT TOO COLD (distances not to scale!)
Q0: What would be Earth’s equilibrium temperature without an atmosphere? Thermal equilibrium: unchanging temperature: Power received from Sun = Power emitted by Earth Power from Sun = Intensity of solar radiation * area of Earth irradiated Intensity of solar radiation = S = 1370 W/m2 Area of Earth hit by Sun = __________ Power received = radiation * area = S * ________
Note on radiative forcing Intensity of solar radiation = S = 1370 W/m2 Greenhouse gases’ radiative forcing ~ 3 W/m2 Projected increase in our lifetime ~ 1 W/m2 One xmas tree light per square meter could cause catastrophic warming
How much radiation does Earth emit? Power emitted by Earth = Intensity of Earth’s radiation * area of Earth radiating energy Area of Earth radiating = ______ Intensity of Earth’s radiation = s T4, where the Boltzmann constant s = 5.67 x 10-8 W/m2K4 Power emitted by Earth = ________________
Power received = power emitted p R2Earth S = 4 p R2Earths T4 Simplifying: Radiation emitted = radiation received s T4 = S/4
0. Solve for Goldilocks temperature: • T4 = S/4
0. Reality check on Goldilocks model: Too cold! (Earth’s average temperature is about 15º C.) Why? What did we leave out? Scientific method: • Observations and curiosity • hypotheses • models, quantitative reasoning, and tests • improve models bit by bit …
Goldilock Hypothesis is WRONG: Venus is close Earth is intermediate Mars is far Too hot STILL TOO HOT Too cold What do you predict we will find for the Earth’s equilibrium temperature if we take clouds into account? A warmer or colder planet?
Hypothesis 1: Clouds warm EarthHypothesis 2: Clouds cool Earth Both are partly right…
Q1: What would be Earth’s equilibrium temperature with reflective clouds? Radiation absorbed by Earth = radiation emitted by Earth Radiation emitted = s T4 Power absorbed by Earth = Power received from Sun – Power reflected by clouds, …
How much radiation does Earth absorb? Radiation reflected = radiation received * (reflectivity, or albedo) = S/4 * (A= albedo) So radiation absorbed = radiation received – radiation reflected = S/4 – S/4 *A = S/4 (1-A) Put it all together: radiation absorbed = radiation emitted S/4 (1-A) = s T4 To simplify notation in the future, we’ll label the effective solar radiation Earth absorbs: S’ = S/4 (1-A)
1. Reality check on reflective cloud model: The Earth is not really this cold! Its average surface temperature is actually about T = 15º C. What’s missing from this model? Brainstorm ideas, and we will analyze some of them quantitatively.
Q2: What effect do greenhouse gases have on Earth’s equilibrium temperature? Clouds do not merely reflect and transmit solar radiation – they also absorb Earth’s thermal radiation and re-radiate, especially in longer wavelengths. One-layer model: Assume the atmosphere absorbs all the Earth’s radiation, and re-radiates half of it back down to Earth (and half out to space), at an equilibrium temperature Te. Find Earth’s Surface temperature Ts. http://www.yourdictionary.com/ahd/g/g0258400.html
How? Greenhouse gases absorb infrared radiation Kenneth R. Koehler, Raymond Walters College http://www.rwc.uc.edu/koehler/biophys.2ed/dof.html Tohoku University http://www.tagen.tohoku.ac.jp/labo/arima/lecture/spectroscopy/gif/symmode.gif
Greenhouse Gases IPCC1 p.38
2. Greenhouse gases re-radiate heat At top of atmosphere, S’ = S(1-A)/4 = s Te4 At Earth’s surface, s Ts4 = S’ + s Te4 radiated by Earth = received from Sun + received from Atmosphere
2. Find greenhouse effect temperature: Eliminate s Te4 from the two equations and solve for Earth’s Ts: s Ts4 = 2 S’ → Reality check: This is certainly warmer – in fact it is about 15º C too warm. What’s missing from this improved model? Brainstorm ideas, and we will analyze some of them quantitatively. This is how science progresses – by gradually improving simple models and getting closer and closer approximations to nature’s reality.
Q3: What if the atmosphere also transmits some of Earth’s radiation? We found that the Earth is too cold without greenhouse gases, and too warm with them. What’s missing? Two-layer model: The atmosphere actually does not absorb all of Earth’s radiation – it transmits some energy out into space. This imperfect insulator should result in a slightly cooler surface temperature for the planet. We can quantify this effect by saying the atmosphere absorbs a fraction a of the Earth’s radiation (E= s Ts4), and transmits the rest (1-a). Meanwhile, the atmosphere continues to radiate with an intensity R= s Te4. Let’s see how this changes the results of our thermal equilibrium energy balance analysis.
Q3: What if the atmosphere also transmits some of Earth’s radiation? (Find a) Solving any two equations, we find that assuming Ts =288K. This means that 23% of Earth’s radiation must be transmitted out into space by the insulating atmosphere, if this two-layer model fully explains why the Earth’s surface temperature currently averages about 288K. What other factors might be involved? Top of atmosphere: S’ = R + (1-a)E Earth’s surface: E = S’ + R
Q4: What is the effect of ocean and ice albedo on Earth’s global energy balance? We actually included some reflection (r) from the Earth’s surface in our original albedo term (A). Surface albedo is complicated, however, by several factors, including (1) seasonal changes and (2) positive feedback effects.
Ice-albedo feedback http://www.bbc.co.uk/portuguese/especial/1126_clima/page4.shtml
Feedback systems Positive feedback destabilizes Earth system (bad) Negative feedback stabilizes Earth system (good)
Physics is not the whole story!Gaia hypothesis: Biota help regulate Earth’s climate Ex: Faint young Sun Paradox
Q5: How do phytoplankton contribute to climate regulation? Plankton contribute to absorption and emission of CO2, cloud formation, ocean albedo, and more. Coccolithophores under the Scanning Electron Microscope http://oceanworld.tamu.edu/NMEA_Talk/
Phytoplankton → ocean albedo Coccolithophore bloom off the Coast of Britanny: Due to their unusually high reflectivity, “special algorithms have been developed specifically for the remote-sensing detection of coccolithophorid blooms in the ocean. If the data indicates the presence of such a bloom, the data is [flagged to note] this anomalous condition.” http://disc.gsfc.nasa.gov/oceancolor/scifocus/classic_scenes/12_classics_blooms.shtml http://visibleearth.nasa.gov/view_rec.php?id=705
Phytoplankton → atmospheric composition Phytoplankton production is an important sink of atmospheric CO2. Sinking of phytoplankton biomass below the pycnocline (“biological pump”) removes CO2 from atmospheric circulation. Biological factors (production, predation, decomposition) and physical/chemical factors (density stratification, acidity of the ocean, wind speed, etc.) affect the efficiency of the biological pump. www.msrc.sunysb.edu/octet/BP_Fig_1.gif
Phytoplankton → sulfur compounds → cloud formation Marine algae produce dimethylsulfoniopropionate (DMSP), which is converted to dimethylsufide (DMS) by phytoplankton and bacterial enzymes during decomposition. DMS then enters the atmosphere where it is photo-oxidized to sulfate aerosols. DMS accounts for 95% of the natural marine input of sulfur gases to the atmosphere, and about 50% of the total global biogenic source of sulfur to the atmosphere. Sulfur compounds act as cloud condensation nuclei. Climate Change Workshops, Zita + Chin-Leo, SORCE, Sept 2006, Orcas Island, WA
SUMMARY • In Q0, we found that without an atmosphere, Earth’s equilibrium temperature would be about 279 K, or 9º C too cold. • In Q1, we found that an Earth with reflective clouds but no greenhouse gas trapping was about 255 K, or 33º C too cold. • In Q2, we found that an Earth with reflective clouds and an insulating layer of greenhouse gas atmosphere was about 15º C too warm. (One-layer model) • Two-layer model:If the atmosphere is an imperfect insulator, transmitting about 23% of Earth’s radiation into space, this yields Earth’s observed temperature of 288 K. • Positive feedback tends to warm Earth: melting ice decreases albedo; increased water vapor increases greenhouse effect. • Negative feedback stabilizes: warmer Earth radiates more. • Biota such as plankton also contribute to ocean albedo, atmospheric composition, and cloud formation, all of which have impacts on the global energy balance.
References and sources of figures Shindell et al. (http://www.people.virginia.edu/%7Emem6u/ssmrw02.html) Robert Stewart (http://oceanworld.tamu.edu/NMEA_Talk/NMEA_Talk_2004.html) ETE team (http://www.cotf.edu/ete/modules/coralreef/CRatmo.html) Judith Lean and David Rind, Sun-Climate Connections: Earth's Response to a Variable Sun, Science, Vol 292, Issue 5515, 234-236 (2001) Friis-Christensen, E.; Lassen, K., Science, 254, 698-700 (1991) D. Rind (from J. Lean), The Sun's Role in Climate Variations Science, Vol 296, Issue 5568, 673-677 (2002)
The Earth System, Lee R. Kump, James F. Kasting, Robert G. Crane, Ed.2, pub. Pearson/Prentice Hall The Earth Institute, Columbia University (http://www.earth.columbia.edu/news/2005/images/conveyor_belt.gi) Atelier Changement Climatique, ENPC (http://www.enpc.fr/fr/formations/ecole_virt/trav-eleves/cc/cc0304/cycle-carbone/cycle-carbone.htm) Richard Dewey, UVic, BC (http://web.uvic.ca/~rdewey/eos110/webimages.html) Scott Rutherford, Roger Williams Univ., RI, Milankovitch Cycles in Paleoclimate, (http://deschutes.gso.uri.edu/~rutherfo/milankovitch.html) E.J. Zita, solar physics research at Evergreen and HAO/NCAR http://academic.evergreen.edu/z/zita/research.htm, http://www.hao.ucar.edu/