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”