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Lecture 8Lecture 8Climate Feedback ProcessesClimate Feedback Processes
GEU 0136
Forcing, Response, and Forcing, Response, and SensitivitySensitivity
• Consider a climate forcing (e.g., a change in TOA net radiation balance, dQ)
• and a climate response(e.g., a resulting change in the globally averaged
annual mean surface air temperature, dTs)
• We can define a climate sensitivity parameter
• To know (i.e., forecast) expected climate change resulted from a forcing of Q, simply multiply by R
• Then the central question of “know how”:
What determine the magnitude of R?
Response, Sensitivity, and Response, Sensitivity, and FeedbackFeedback
S0 TS
OLR
vapor
albedo
• Sensitivity parameter depends on direct and indirect effects of forcing
• Changes in TS will also affect:– Outgoing longwave (Te
4)– Planetary albedo
(ice, snow, clouds)– Water vapor absorption
• Total sensitivity must take all these indirect effects into account
• Some will amplify sensitivity, and some will damp sensitivity
S0: solar constant; yj = yj(S0)
3 Basic Radiative Feedback 3 Basic Radiative Feedback ProcessesProcesses
Stefan-Boltzmann FeedbackStefan-Boltzmann Feedback
• Simplest possible model of planetary radiative equilibrium
• Outgoing longwave radiation will increase to partly offset any increase in incoming radiation
Water Vapor FeedbackWater Vapor Feedback
• As surface warms, equilibrium vapor pressure will increase (Clausius-Clapeyron)
• Increasing q increases LWdown (higher ), so Ts warms even more
• Air is not always saturated, but we can assume relative humidity remains fixed as Ts increases, and calculate new Ts from radiative-convective equilibrium
Water Vapor Feedback (cont’d)Water Vapor Feedback (cont’d)
• Water vapor is a positive feedback mechanism
• OLR is only linear wrt TS, not quartic as predicted by BB curves
R)FRH ~ 2 R)BB
• Cold temperatures make the surface turn white due to increased sea ice and snow cover on land
• White (high-albedo) surfaces reflect more SWdown, decrease energy absorbed , leading to colder surface temperatures
• Warmer temperatures tend to reduce planetary albedo, allowing more energy to be absorbed
• Positive feedback … tends to amplify changes in TS resulting from any forcing
Ice-Albedo FeedbackIce-Albedo Feedback
Ice-Albedo FeedbackIce-Albedo Feedback
• SH: ice sheet at pole, sea-ice from 50º to 80º
• NH: sea-ice at pole, seasonal snow from 40 º northward
Ice Age ChangesIce Age Changes
Ice age surface albedo was much higher than present!
Budyko Ice-Albedo Climate Budyko Ice-Albedo Climate ModelModel
• Solar rad is distribted according to latitude
• Energy transport is diffusive
• OLR is linear with TS
• Albedo switches between two values, depending on ice or no ice
Budyko Ice-Albedo Climate Budyko Ice-Albedo Climate SolutionsSolutions
• Stronger sun causes ice edge to retreat to higher lat, & vice versa
• Below 97% of current value, model produces a white Earth!
Budyko Feedback Sensitivities, Budyko Feedback Sensitivities, 11
• Ratio of meridional energy transport to longwave cooling
• Budyko used 2.6 … modern measurements suggest 1.7
• Less sensitive using recent data
= /B
Budyko Feedback Sensitivities, Budyko Feedback Sensitivities, 22
• Ice-free albedo decreases toward the poles to account for cloud masking of surface
• Ice transition makes less difference
• Tropical SSTs didn’t vary much during ice ages … why?
• Near 300 K, LW cooling decreases very fast with increasing SST
• Positive feedback should make tropical SSTs sensitive and variable …
• but they’re not!
Tropical SST and LW FeedbackTropical SST and LW Feedback
“H2O window”
Longwave and Evaporation Longwave and Evaporation FeedbacksFeedbacks
• Tropical SST energy balance:
SWdown – LWup = H + LE + F (200 W m-2) - (60 W m-2) = (10 W m-2 ) + (120 W m-2) + (20 W
m-2)
Compensating Tropical SST Compensating Tropical SST FeedbacksFeedbacks
Changes in LE with SST balance positive feedback with respect to longwave down
• Consider a planet populated by two kinds of plants: white “daisies” and black “daisies.”
• Write an energy balance for the planet, assuming – (1) it emits as a blackbody– (2) the albedo is an area-weighted average of the albedos
of bare ground, white, and black daisies
• The daisies grow at temperature-dependent rates (optimum at 22.5º C, zero at 5 º and 40º), and also proportional to the fraction of bare ground
• The daisies also die at a specified rate • Solve for areas Ai and temperatures Ti of each
surface (white daisies, black daisies, and bare ground)
Biophysical Feedback: Biophysical Feedback: “Daisyworld”“Daisyworld”
DaisyworldDaisyworld
More generally, = 0 : transport is perfect
= (S0/4) : transport is zero
Biophysical Feedback: Biophysical Feedback: “Daisyworld”“Daisyworld”