Download Chap 6 Forcing and feedback

Chapter 6
Radiative forcing and climate feedbacks
Recall: equation … Ts = [(S(1-α)(n+1)]/(4 σ)]1/4
Humans are increasing “n” … expected to cause warming
Other factors:
6.1 Timelag
Pot on the stove doesn’t boil immediately.
Earth does not warm up immediately (SHC of ocean, land)
Planet has not yet reached equilibrium with what we’ve already emitted
(Each CO2 molecule lasts hundreds of years in the atmosphere)
Ein > Eout by about 0.9 W/m2
Committed warming = 0.5 K; unavoidable
Timelag: as increase n, Ein > Eout for a few decades (presently 0.9 W/m2
Decades for temperature increase (70% water)
6.2 Radiative forcing
Imagine that the sun suddenly becomes brighter … what happens?
(a) Zero layer atmosphere
238 W/m2 in and out; suddenly, Ein increases to 243 W/m2 (5 W/m2 increase)
Eout does not immediately change, meaning that Ein > Eout
Oceans cause response lag; eventually Ein = Eout
Climate change: global temperature adjusts until Ein = Eout
Lag of decades has important policy consequences
Radiative forcings: imposed changes on Ein or Eout (unconnected with surface temp)
Planet’s T must change to reestablish energy balance
Define: RF = ΔEin - ΔEout : positive radiative forcings warm the planet
Ex 1: How much does Ein change if S increases by 5%?
Answer: Ein = 1360(1-0.3)/4 = 238; Ein=1360*1.05*(1-0.3)/4=250; change = 12 W/m2.
Note: time independent
Ex 2: What increase in solar constant would cause a radiative forcing of +1 W/m2 ?
(zero-layer planet with equilibrium temperature of 300 K)
Note: +4 W/m2 is the RF for doubled CO2
What other factors can cause radiative forcing?
Total radiative forcing between 1750 and 2005
Factors
1. Aerosols: particles so small they have negligible fall speed
Burning coal increases aerosol sulfates
Highly reflecting, increases albedo  cools climate (-0.5 W/m2 )
Indirect aerosol effect: sulfates combine with water to form droplets within clouds
Increases reflectivity of clouds (-0.7 W/m2)
Don’t stay in the atmosphere too long, so they are mainly near their sources
Efforts to clean up air pollution will reduce the amount of aerosols in the
atmosphere, and therefore increase radiative forcing
2. Black carbon or soot comes from incomplete combustion;
absorbs sunlight & IR; reduces albedo and increases “n”  warms climate
3. CO2 forcing: from 280->380 ppm
4. CH4 forcing: from 0.8->1.8 ppm
Total GHGs = +3 W/m2 : CO2 is about +1.6 W/m2
Total Aerosols = -1.2 W/m2 (-0.5 W/m2 direct, -0.7 W/m2 indirect) 40%offset
Total net forcing = +1.6 W/m2
Net human RF is +1.6 W/m2
Aerosol reflectivity as a function of latitude and longitude
Example of radiative forcing; sulfur gases from volcanic eruptions
Radiative forcing from volcanoes (1880-2000)
Summary
RF is an imposed energy imbalance to the climate system. In response, the temperature
of the planet will change
Defined as the change in planetary energy imbalance before system has responded.
Total RF = +1.6 W/m2
Earth has warmed up about 0.8°C, 2/3rds of the energy imbalance wiped out.
Present energy imbalance is about 0.5 W/m2.
Not finished warming from previous emissions — another 0.5 K of committed warming.
Problem: calculate T for planet with Ein = 238 W/m2 (254.5 K) and for Ein = 242 W/m2
(255.6 K); a warming of 1.1 K
What is Eout for the planet? sigma(255)^4 = 239.74 W/m2
What is Ein for the planet? also 239.74 W/m2
Hence: +4 W/m2 RF is applied …
Ein increases to 243.74 W/m2, so Eout also increases (eventually). New temperature is
(243.74/sigma)^(1/4) = 256 K … +1 K increase
Note: RF of doubled CO2 is +4 W/m2
6.3 Feedbacks
Feedback processes amplify or ameliorate an initial perturbation
Example: Zero-layer model (n = 0) with S = 2000 W/m2, α = 0.6. What is Ts?
If S increases by 2% to 1.02(2000)=2040 W/m2. New Ts = ?
S (W/m2)
2000
2040
α
0.6
0.6
T (K)
243.7
244.9
Increase in S leads to a T increase of 1.2 K
However: other things do not remain the same …
As T increases -> ice melts -> albedo decreases -> more solar energy is absorbed -> T
increase -> loop back to ice melts:
Positive feedback loop
Let’s assume that α(T) = 0.6-(T-243.7)/150.
T4=S(1-α(T))/4 ; 4th-order polynomial.
S (W/m2)
α
T(K)
2000
2040
0.6
0.6
0.595
0.592
0.590
243.7
244.9
245.6
246.1
246.3
2040
0.588
246.6
Warming with the ice-albedo feedback is 2.9 K, compared to 1.2 K without it
The ice-albedo feedback amplifies the perturbation due to S increase (positive feedback)
Negative feedback; suppose two kinds of flowers cover the planet: black and white. As
the climate warms, white flowers begin to take over regions previously covered by black
flowers. Here reflectivity increases with warming.
In general, now Ts = [ (n(Ts)+1).S(1-α(Ts))/(4σ)]1/4
This is what makes climate change hard to predict …
Fast feedbacks:
Ice-albedo (positive), water vapor (positive), clouds (uncertain)
Water vapour: humidity increases with temperature
i.e. warmer atmosphere can hold more water vapour
Since water vapour = GHG, feeback loop
Tropical water vapour tracks temperature as a function of time (2002-10)
Cloud feedbacks; both positive and negative
Sunlight reflected (cooling effect)
IR absorption (heating effect)
Net effect: currently negative (- 20 W/m2)
Expect: net positive effect in the future…
Slow feedbacks: occur over centuries
Ice sheet response: v slow melting (?)
Permafrost melting (Arctic): releases CO2 and methane
Methane clathrates in ice (land and under oceans); methane release
Carbon cycle feedback:
Initial warming leads to release of frozen GHGs , more warming, further release
Compare past warmings
Feedbacks vs forcings:
Feedbacks change Ein and Eout, but are responding to surface T; do not initiate
Forcings change Ein and Eout, but are unconnected to surface warming
Carbon dioxide (1750-2005): forcing
Carbon dioxide (past climates): not forcing but positive feedback
Future: once warming underway, carbon dioxide as feedback?
6.4 Climate sensitivity:
Relates change in T to emission of a standard amount of CO2
Climate sensitivity = CO2
The standard CO2 is a doubling in conc. from 280 ppm (1850) to 560 ppm
Doubling CO2 without feedbacks gives us about 1.2°C warming
Some feedback math:
Tf = Ti + g Ti + g2 Ti + g3 Ti …
Tf = Σ gkTi
Summing over the series
Tf = Ti/(1-g)
If g = 0, Tf = Ti
If 0 < g < 1, Tf > Ti : positive feedback
If g < 0, Tf < Ti : negative feedback
If g approaches 1, Tf very large: runaway greenhouse effect
Earth: g = gia (+0.1) + gwv (+0.6) + gcloud ( 0 to +0.3) + glr ( -0.3)
Total feedback factor: g = [0.4 to 0.7]
Applying this to the initial temperature perturbation of 1.2°C, get Tf = [2 to 4°C]
- uncertainty related primarily to uncertainty in cloud feedbacks
IPCC estimate Tf = [2°C to 4.5°C], with best estimate of 3°C.
Very unlikely to be less than 1.5°C. Values substantially higher than 4.5°C possible.
Recall: doubled CO2 has RF = +4 W/m2.
Can express climate sensitivity as warming per unit RF units: [0.5 to 1.1] °C/(W/m2)
or best estimate 0.75 K/(W/m2)
Example: if solar constant increases by 5%, S = + 12 W/m2
For climate sensitivity of 0.75 K/(W/m2), get C
Final Note : Sensitivity including “slow” feedbacks may be higher.