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Chapter 9: Climate Sensitivity and Feedback Chapter 9: Climate Sensitivity and Feedback Mechanisms Mechanisms
This chapter discusses:This chapter discusses:
1.1. Climate feedback processesClimate feedback processes2.2. Climate sensitivity and climate feedback Climate sensitivity and climate feedback
parameterparameter3.3. ExamplesExamples
((Materials are drawn heavily from D. Hartmann’s textbook and online materials Materials are drawn heavily from D. Hartmann’s textbook and online materials by J.-Y. Yu of UCI. Guo-Yue Niu contributed significantly to the by J.-Y. Yu of UCI. Guo-Yue Niu contributed significantly to the preparation of this lecture.)preparation of this lecture.)
Climate Feedback and Sensitivity
Feedback is a circular causal process whereby some proportion of a system's output is returned (fed back) to the input.
ΔTfinal = ΔT + ΔTsensitivity
Climate System ΔT
ΔQ
ΔTfinal
ΔQfeedback can be either negative or positive
input
output
ΔQfinal = ΔQ + ΔQfeedback
ΔQfinal
An objective measure of climate feedback and sensitivity
The strength of a feedback depends on how sensitive the change in input (Q) responds to the change in output (T) :
Feedback strength: λ = ΔQ / ΔT
Climate sensitivity: λ-1 = ΔT / ΔQ
1. Positive values negative feedbacks, stable
Negative values positive feedbacks, unstable
λBB = 4σT3 = 3.75Wm-2K-1
2. The larger λ, the stronger feedback.
Stefan-Boltzmann feedback
Outgoing longwave radiation: F = σT4
σ = 5.67x10-8
The strength of the feedback:
1. A negative feedback, stable2. 1K increase in T would increase F by 3.75 Wm-2
(see Fig. 9.1)
λBB = ∂F / ∂T = 4σ T3 = 3.75 Wm-2K-1
Water vapor feedback
Clausius-Clapeyron relationship: es = f(T) 1% increase in T would increase 20% in es
Water vapor is the principal greenhouse gases.
The feedback strength: λv= – 1.7 Wm-2K-1
1. A positive feedback, unstable 2. Weaker than λBB
3. λBB + λv = 2.05 Wm-2K-1 (see Fig. 9.1)
Ice (snow) albedo feedback
Striking contrast between ice-covered and ice-free surfaces
In ice-covered regions, more solar energy reflected back to space:
Feedback strength: λice= –0.6 Wm-2K-1
1. Positive feedback, unstable
2. λBB + λv + λice=1.45 Wm-2K-1
An example of climate feedback
Global Temperature Anomalies
Northern Hemisphere Snow Cover Anomalies
ΔT
ΔQ
Snow (ice)-albedo climate feedback
Chapin et al. (2005), Science
1. Decrease in snow-cover and snow season
2. Tundra trees
Snow cover change Temperature change
Total feedback
λtotal =1.45 Wm-2K-1
3.75 Wm-2K-1
Positive feedback negative feedback
λtotal
Doubling of atmospheric CO2 2.9 KWithout ice-albedo feedback 2.0 K
−31−48−17
+15%
Cloud feedbackCloud feedback
1. It is unclear what is the strength and even directions (negative or positive). From GCM simulations, λcloud = 0 ─ −0.8.
2. Could effects can be either “umbrella” or “blanket”.
umbrella blanket
Low cumulus cloudsNegative feedback
High cirrus cloudsPositive feedback
Cloud feedback (con.)Cloud feedback (con.)
3. It is uncertain whether an increased temperature will lead to increased or decreased cloud cover.
4. It is generally agreed that increased temperatures will cause higher rates of evaporation and hence make more water vapor available for cloud formation, the form (e.g., type, height, and size of droplets) which these additional clouds will take is much less certain.
Energy-balance climate modelsEnergy-balance climate models
1. Zero-dimensional EBMs
(1-α) S0 /4 = σTe4
shortwave in = Longwave out
The surface T: Ts = Te + ΔT (greenhouse effects)
The Erath: S0 = 1376 Wm-2, α = 0.3, Te= 255 K, Ts =288 K
Venus: S0 = 2619 Wm-2, α = 0.7, Te = 242 K,
greenhouse gases Ts = 730 K
Energy balance climate models (con.)
2. One-dimensional EBMs (Sellers and Budyko in 1969)
Shortwave in = Transport out + Longwave out
S(x) [1 - α(x) ] = C [ T(x) - Tm ] + [ A + B T(x) ]
S(x) = the mean annual radiation incident at latitude (x) = S0/4 *s(x)
α(x) = the albedo at latitude (x)
for ice-free (Ts > −10°C) : 0.3
for ice (Ts < −10°C) : 0.62
C = the transport coefficient (3.81 W m-2 °C-1)
T(x) = the surface temperature at latitude (x)
Tm = the mean global surface temperature
A and B are constants A = 204.0 W m-2 and B = 2.17 W m-2 K-1
This B is equivalent to λBB (3.75) or λBB + λv = 2.05 (see Fig. 9.1)
Energy balance climate models (con.)
Changeable parameters:
S0
α(x) (0.62)
C (3.81 W m-2 °C-1)
A and B are (B = 2.17 W m-2 K-1)
The model contains four kinds of climate feedbacks:
1) Ice-albedo feedback (Ts> − 5°C ; 0.8) (see Fig. 9.5)
2) Stefan-Boltzmann feedback: B (λBB) = 3.75
3) water-vapor feedback: B (λBB + λv) = 2.05 ; 1.45 (Budyco, 1969); 1.6 (Cess, 1974)
4) dynamical feedbacks and zonal energy transport: C=0 means no such a feedback
You may also add cloud feedbacks by changing: B smaller (positive feedbacks)
B larger (negative feedbacks)
Try Toy Model 4 at the course website
Biogeochemical feedbacks – A Daisyworld model
Biogeochemical feedbacks – A Daisyworld model
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xAdt
dA
xAdt
dA
bbb
www
Biogeochemical feedbacks – A Daisyworld model
Growth Factorwhite = 1 - 0.003265*(295.5K -Twhite)2
Global mean temperature:
σTe4 = S0 (1 – αp) /4
αp=Agαg + Awαw+ Abαb
Local temperature:
σTi4 = S0 (1 – αi) /4
Ti4 = η(αp – αi) + Te
4
where 0<η < S0/(4σ) represents the allowable range between the two extremes in which horizontal transport of energy is perfectly efficient (0) and least efficient [S0/(4σ)].
A Daisyworld model
Global mean emission temperature is remarkably stable for a wide range of solar constant values. (see Fig. 9.9d); Run Toy Model 1 at the course website.
Climate Trend 1976 to 2000
Increase in T melting of snow and frozen soil larger area of wetlandsmore soil carbon released as CH4 increase in TTogether with ice-albedo feedback, the warming trend will be accelerated
Other feedbacks at regional scales
Albedo
Increase in albedo
SW radiation absorbed decreases
Rn decreases
H, LE decreases
Reduction in:CloudnessPrecipitationconvergence
Increase in insolation
Increase in Rn Increase in albedo
Reduction in:Soil moisture
Other feedbacks at regional scales
Soil Moisture
Decrease in soil moisture
LE decreasesH IncreasesTs IncreasesRn decreases
Reduction in:CloudnessPrecipitationconvergence
Increase in insolation
Increase in Rn Decrease in soil
moisture
Equilibration times of the climate systems
Radiative forcing
Climate System
Atmosphere 10 days
Atmosphere boundary layer 1dayOcean Land
Mixed layer mths-yrs
Sea ice days to 100 y
Ice/snow 10 days
Lakes 10 days
Deep ocean 1000 years glacier 100s yrs
Biosphere 10 d to 100
yrs
Three-dimensional atmospheric general circulation models (AGCMs)
1. Computer programs•Describing atmosphere at >150,000 grid cells
2. Operate in two alternate stages:•Dynamics: for whole global array, simultaneously solves: • Conservation of Energy Conservation of Momentum Conservation of Mass Ideal Gas Law Physics: for each independent column, computes mass/energy divergences, surface inputs, buoyant exchange, e.g., Radiation Transfer Boundary Layer Surface Processes Convection (cloud) Precipitation
3. Coupling withOcean, Land, Biosphere, Sea Ice, and Ice Sheets
Grid spacing: ~ 3°×3° horizontally
~ meters/km vertically
Time step ~ 30 minutes
Concluding Remarks
The inclusion or exclusion of a feedback mechanism could dramatically alter the climate modeling results.
Some important feedbacks may have not been included in GCMs.
Global climate models are getting more complex as more feedback mechanisms are included.
Analyses on climate feedbacks and sensitivity can help
1) understand the mechanisms of climate change.2) select important processes and limit the
complexity of climate models.