# Lecture 8 Climate Feedback Processes GEU 0136. Forcing, Response, and Sensitivity Consider a climate forcing (e.g., a change in TOA net radiation balance,

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Lecture 8 Climate Feedback Processes GEU 0136

Forcing, Response, and Sensitivity 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, dT s ) 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 Feedback S 0 T S OLR vapor albedo Sensitivity parameter depends on direct and indirect effects of forcing Changes in T S will also affect: –Outgoing longwave ( T e 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 S 0 : solar constant; y j = y j (S 0 )

Stefan-Boltzmann Feedback Simplest possible model of planetary radiative equilibrium Outgoing longwave radiation will increase to partly offset any increase in incoming radiation

Water Vapor Feedback As surface warms, equilibrium vapor pressure will increase (Clausius-Clapeyron) Increasing q increases LW down (higher ), so T s warms even more Air is not always saturated, but we can assume relative humidity remains fixed as T s increases, and calculate new T s from radiative-convective equilibrium

Water Vapor Feedback (contd) Water vapor is a positive feedback mechanism OLR is only linear wrt T S, 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 SW down, 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 T S resulting from any forcing Ice-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 Changes Ice age surface albedo was much higher than present!

Budyko Ice-Albedo Climate Model 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 Solutions 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, 1 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, 2 Ice-free albedo decreases toward the poles to account for cloud masking of surface Ice transition makes less difference

Tropical SSTs didnt 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 theyre not! Tropical SST and LW Feedback H 2 O window

Longwave and Evaporation Feedbacks Tropical SST energy balance: SW down – LW up = 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 Feedbacks 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 A i and temperatures T i of each surface (white daisies, black daisies, and bare ground) Biophysical Feedback: Daisyworld

Daisyworld More generally, = 0 : transport is perfect = (S0/4) : transport is zero

Biophysical Feedback: Daisyworld

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