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

)(

)(

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.