: A REALLY TOUGH SCIENTIFIC PROBLEM

Stephen E. Schwartz

Upton NY USA

Physics 311: Connections in Science “Energy Problems” Stony Brook University September 26, 2013 http://www.ecd.bnl.gov/steve GLOBAL TEMPERATURE CHANGE SINCE 1850

0.8

0.6

0.4 0.8 K 0.2

0.0

-0.2

Temperature anomaly vs. 1850-1900, K 1860 1880 1900 1920 1940 1960 1980 2000 Climatic Research Unit, East Anglia, UK Global carbon dioxide concentration over thelastthousand years Global carbondioxide concentration ATMOSPHERIC CARBONDIOXIDEISINCREASING CO2 concentration (ppm) 180 200 220 240 260 280 300 320 340 360 380 800 1000 310 320 330 340 350 360 370 380 390 400 1960 C. D.Keeling Antarctic icecores 1200 1970 1980 1990 1400 2000 2010 an LoaHawaii Mauna 1600 a Dome Law ot Pole South Siple Land Adelie 802000 1800 400 EXPECTED AND OBSERVED TEMPERATURE CHANGE OVER THE TWENTIETH CENTURY Expected warming for forcing by long-lived greenhouse gases only

3.0 Externally imposed change in Earth radiation budget

2.5 Decades to centuries: CO2 , CH , N 24 O, CFCs

2.0 Expected 1.5 Range 1.0

0.5

0.0 Observed Temperature anomaly relative to 1850, K 1860 1880 1900 1920 1940 1960 1980 2000 Observations: Climatic Research Unit, East Anglia, UK Expected increase substantially exceeds observed. 2009 COPENHAGEN ACCORD AGREES ON 2˚C MAXIMUM TEMPERATURE RISE The Heads of State, Heads of Government, Ministers . . . present at the Climate Change Conference 2009 in Copenhagen: Albania, Algeria, Armenia, Australia, Austria, . . . [106 countries] . . . , of America, Uruguay and Zambia, have agreed on this Copenhagen Accord. . . . We underline that climate change is one of the greatest challenges of our time. We emphasise our strong political will to urgently combat climate change. . . . To . . . stabilize concentration in the atmosphere at a level that would prevent dangerous anthropogenic interference with the climate system, we shall, recognizing the scientific view that the increase in global temperature should be below 2 degrees Celsius . . . enhance our long-term cooperative action to combat climate change. 4 DEGREES OF SEPARATION 1850 1870 1890 1910 1930 1950 1970 1990 2010 2

1 Observed 0 Expected -1 Range -2

-3 Last Glacial Maximum (21 000 years before present) -4

-5 Best estimate Uncertainty range

Temperature Difference to Preindustrial, K -6 Expected increase equals or exceeds 2 degree threshold. KEY QUESTION

• How much more CO2 can be emitted without committing Earth to a temperature increase of 2 ˚C above preindustrial?

ATMOSPHERIC RADIATION Power per area

Unit: Watt per square meter W m-2

Photo: S. E. Schwartz THE SOLAR SPECTRUM Outside Earth’s atmosphere – Compare Planck spectrum at 255 K Wavenumber, cm-1 100000 10000 1000 100

-1 600 m)

/ (1/4) Solar spectral irradiance at 1 AU λ Planck function at 5770 K normalized to 340 W m-2 10 500 Planck function at 255 K normalized to 240 W m-2 (log -2 400 5770 K

300 255 K

200

100

TOA Spectral irradiance, W m 0 0.1 1 10 100 Wavelength, m Data source: Gueymard, Solar Energy, 2004 Short- and longwave spectra are nearly non-overlapping. EARTH’S RADIATION BUDGET AND THE Shortwave Longwave absorbed = emitted T = (J/ σ )1/4 1360 Radiative Fluxes Stefan-Boltzmann Solar in W m -2 Radiation law constant 340 240 70.6% = 1-α 1/4 solar 255 K constant 240 σ 4 α J = T = 29.4% Stefan-Boltzmann Radiation law 100 78

Rayleigh 36 . . . Aerosol 4 H2O, CO 2 , CH4 31 47 Greenhouse effect 385 302 ≈ 287 K 162 13 Latent heat 88 Sensible heat 21 Atmosphere WHAT IT REALLY LOOKS LIKE Measurements for a single day, March 10, 2012, W m-2 Shortwave upwelling Net daytime, positive downward

16 121 225 330 435 540 644 749 854 958 1063 -300 -169 -38 93 224 355 486 617 748 879 1010 Longwave upwelling Net 24-hr, positive downward

67 99 131 163 195 227 259 291 323 335 387 -200 -150 -100 -50 0 50 100 150 200 NASA CERES Program, courtesy Norman Loeb An externally imposed change in Earth’s radiation budget, W m-2.

Working hypothesis: Global temperature change is proportional to forcing.

On a global basis radiative forcings are additive and interchangeable.

Global carbon dioxide concentration over thelastthousand years Global carbondioxide concentration CO2 concentration (ppm) ATMOSPHERIC CARBONDIOXIDEISINCREASING 180 200 220 240 260 280 300 320 340 360 380 800 1000 Antarctic icecores 1200 1400 1600 a Dome Law ot Pole South Siple Land Adelie 802000 1800 400

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Forcing, W m W Forcing, -2 CLIMATE FORCINGS OVER THE INDUSTRIAL PERIOD Extracted from IPCC AR4 (2007)

Long Lived Greenhouse Gases N2O CFCs CO2 CH4

-2 -1 0 1 2 3 Forcing, W m-2 Greenhouse gas forcing is considered accurately known. Gases are uniformly distributed; radiation transfer is well understood. EARTH’S RADIATION BUDGET AND THE GREENHOUSE EFFECT Shortwave Longwave absorbed = emitted T = (J/ σ )1/4 1360 Radiative Fluxes Stefan-Boltzmann Solar in W m -2 Radiation law constant 340 240 70.6% = 1-α 1/4 solar 255 K constant Albedo 240 σ 4 α J = T = 29.4% Stefan-Boltzmann Radiation law 100 78

Rayleigh 36 . . . Aerosol 4 H2O, CO 2 , CH4 31 47 385 302 + 2.8 Forcing ≈ 287 K 162 13 Latent heat 88 Sensible heat 21 Atmosphere HOW MUCH WARMING IS EXPECTED?

Steady-state change Climate in global mean = sensitivity × Forcing surface temperature ΔT =S × F S is “equilibrium” sensitivity. Units: K/(W m-2)

Sensitivity is commonly expressed as “CO2 doubling temperature” ΔTS2× ≡ × F2×

-2 where F2× is the “CO2 doubling forcing” ca. 3.7 W m . EARTH’S RADIATION BUDGET AND THE GREENHOUSE EFFECT Shortwave Longwave Co-albedo absorbed = emitted γ = 1- α = 0.706 T = (J/ σ )1/4 1360 Radiative Fluxes Stefan-Boltzmann Solar in W m -2 Radiation law constant 340 240 70.6% = 1-α 1/4 solar 255 K Emissivity constant ε = 240/385 = 0.61 Albedo 240 σ 4 α J = T = 29.4% Stefan-Boltzmann Radiation law 100 78

Rayleigh 36 . . . Aerosol 4 H2O, CO 2 , CH4 31 47 Greenhouse effect 385 302 ≈ 287 K 162 13 Latent heat 88 Sensible heat 21 Atmosphere ENERGY BALANCE MODEL OF EARTH’S CLIMATE SYSTEM

dH γJ Global energy balance: =−=QE S −εσT 4 dt 4 s

Ts is global mean surface temperature H is global heat content Q is absorbed solar energy E is emitted longwave flux γ JS is solar constant is planetary co-albedo σ is Stefan-Boltzmann constant ε is effective emissivity γJ At radiative steady state: S = εσT 4 4 s γJ /4 γ =−107α ≈. ; ε = S ; for T = 288 K, ε ≈ 061. σ 4 s Ts

NO FEEDBACK

In absence of feedbacks γ and ε do not depend on Ts Change in emitted flux per change in temperature: 4 dE d(εσTs ) 3 4 4 γJS γJS = = 4εσTs = E = = dTs dTs Ts Ts 4 Ts −1 dTs dTs ⎛ dE ⎞ Ts No-feedback sensitivity: SNF ≡ = = ⎜ ⎟ = dQ dE ⎝dTs ⎠ γJS -2 JS =1360 Wm ; Ts = 287 K; γ = 0.7; -2 SNF = 0.30 K / (Wm ) -2 -2 ΔT2× = F2×SNF = 3.7 Wm × 0.30 K / (Wm ) = 1.1 K

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€ Water Vapor Feedback: Pretty Well Understood

Higher temperature, More water vapor. More infrared is absorbed

Positive Feedback Higher Sensitivity Cloud Feedbacks: A Big Mystery in Climate Sensitivity

Higher temperature, Higher temperature, Clouds evaporate. More water vapor, More sunlight More clouds. is absorbed Less sunlight is absorbed

Positive Feedback Negative Feedback Higher Sensitivity Lower Sensitivity CLIMATE SENSITIVITY ESTIMATES THROUGH THE AGES Estimates of central value and uncertainty range from major national and international assessments 6 Charney , K 5 Arrhenius NRC – – – – IPCC – – –– ×

2 1 sigma T 4 "Likely" > 66% Δ 3 2 Stefan- ? Boltzmann 2013 1 Sensitivity 0 1880 1890 1900 1980 1990 2000 2010

Despite extensive research, climate sensitivity remains highly uncertain. ESTIMATES OF EARTH’S CLIMATE SENSITIVITY AND ASSOCIATED UNCERTAINTY Major national and international assessments and current climate models K ,

× 6 2 T

Δ Charney 19 IPCC AR4 Models 5 NRC – – IPCC – –

4 > 66%

3 "Likely" 2 1 σ

1

Doubling Temperature 0 2 1980 1990 2000 2010 CO

Current estimates of Earth’s climate sensitivity are centered about a CO2 doubling temperature ΔT2× = 3 K, but with substantial uncertainty. Range of sensitivities of current models roughly coincides with IPCC “likely” range. ?? QUESTION ?? • Why is there such a large range of sensitivities in current climate models and why hasn’t this situation improved much in thirty years? ANSWER • This is a really tough scientific problem! A REALLY TOUGH SCIENTIFIC PROBLEM • Determine the consequences of a systematic change of less than 1% in a quantity that is highly variable in time and space applied to a noisy dynamic system. • Right now we do not even know the sign of how much more CO2 can be added to the atmosphere without committing Earth to a temperature increase ≥ 2˚ C. • Even at the low end of the climate sensitivity range, expected temperature increase from long-lived greenhouse gases ~ 1.4 ˚C, the consequences would be severe. • Why has Earth not warmed up the expected amount, 1.4 to 3.2 ˚C? We don’t know, but that’s another lecture.