Lecture 14Lecture 14

Climate Sensitivity, thermal inertiaClimate Sensitivity, thermal inertia

Climate SensitivityClimate Sensitivity

The change in equilibrium temperature The change in equilibrium temperature per unit of radiative forcingper unit of radiative forcing

Tem

per

atu

re

TimeStart in equilibrium

Apply radiative forcing

Temp. risesChange in equilibrium temp

New Equilibrium Temp

ExampleExample

Suppose Sensitivity = 2Suppose Sensitivity = 2C per unit of C per unit of forcing (1 Wmforcing (1 Wm-2-2))

Radiative forcing = 3 WmRadiative forcing = 3 Wm-2-2

Then, Then, eventualeventual warming = 2 x 3 = 6 warming = 2 x 3 = 6C C

Differing SensitivitiesDiffering Sensitivities

Same radiative forcing applied at t= 0

System 2 is twice as sensitive

1 C

2 C

Comparing ModelsComparing Models

Double CODouble CO22 content of model atmosphere content of model atmosphere Radiative forcing ~ 4 W/mRadiative forcing ~ 4 W/m22

IPCC has compared many climate modelsIPCC has compared many climate models

Results used to estimate actual climate Results used to estimate actual climate sensitivity of Earthsensitivity of Earth

Sensitivity EstimatesSensitivity Estimates

Model sensitivities have a range of 2Model sensitivities have a range of 2C to C to 4.54.5C for a doubling of COC for a doubling of CO22

(A technical point – don’t memorize.)(A technical point – don’t memorize.)

The Role of FeedbacksThe Role of Feedbacks

Model sensitivity is determined by the Model sensitivity is determined by the strength of the strength of the feedbacksfeedbacks in the model in the model

PositivePositive feedbacks feedbacks increase increase sensitivitysensitivity

NegativeNegative feedbacks feedbacks decreasedecrease sensitivitysensitivity

Differences in Model SensitivityDifferences in Model Sensitivity

Main Cause of Variation: Cloud Main Cause of Variation: Cloud FeedbacksFeedbacks

In most models, cloud feedback is In most models, cloud feedback is positivepositive However, magnitude varies a lot from one However, magnitude varies a lot from one

model to anothermodel to another

Cloud

Albedo

Water Vapor

0.4

0.3

0.2

0.1

0.0

Fig. 2. Boxplot of feedback strengths in 12 climate models.

Feedback Strength

From IPCC ReportFrom IPCC Report

Cloud Feedback in various models

Thermal InertiaThermal Inertia

Determines Determines raterate of temperature of temperature changechange

RateRate of Warming of Warming

Thermal inertiaThermal inertia: resistance of system to : resistance of system to temp. changetemp. change Measured by Measured by heat capacityheat capacity

Higher heat capacity Higher heat capacity slower warming slower warming

System 1: 70% of warming has occurred at t = 1.2

Time

Tem

per

atu

re C

han

ge

(C)

System 2: 70% of warming has occurred at t = 2.4

Earth-Atmosphere SystemEarth-Atmosphere System

Most of the heat capacity is in oceansMost of the heat capacity is in oceans

Presence of oceans slows down warmingPresence of oceans slows down warming

ComparisonComparison

Look at two systems with same radiative Look at two systems with same radiative forcing and sensitivity, but different heat forcing and sensitivity, but different heat capacitiescapacities

Compare Two SystemsCompare Two Systems

T = 20C

Low Heat Capacity

High Heat Capacity

T=20C

t = 0

Incoming radiation Outgoing

radiation

Net radiation

T = 22C

Low Heat Capacity

High Heat Capacity

T = 21C

t = 1

Systems have warmed Systems have warmed emission has increased emission has increased

net radiation has decreased net radiation has decreased

T = 24C

Low Heat Capacity

High Heat Capacity

T = 22C

t = 2

Still warmingStill warming

T = 26C

Low Heat Capacity

High Heat Capacity

T = 23C

t = 3

Back in equilibrium Still warming

T = 26C

Low Heat Capacity

High Heat Capacity

T = 24C

t = 4

Back in equilibrium Still warming

T = 26C

Low Heat Capacity

High Heat Capacity

T = 25C

t = 5

Back in equilibrium Still warming

T = 26C

Low Heat Capacity

High Heat Capacity

T = 26C

t = 6

Back in equilibrium

Back in equilibrium, finally

SummarySummary

Positive (negative) radiative forcing causes Positive (negative) radiative forcing causes warming (cooling)warming (cooling)

System warms (cools) until equilibrium is System warms (cools) until equilibrium is restoredrestored

Amount of eventual warming (cooling) Amount of eventual warming (cooling) depends on radiative forcing and sensitivitydepends on radiative forcing and sensitivity Eventual warming (cooling) = sensitivity x rad. Eventual warming (cooling) = sensitivity x rad.

forcingforcing

RateRate of warming is inversely proportional to of warming is inversely proportional to heat capacityheat capacity

More Realistic SituationMore Realistic Situation

Previous examples assumed radiative Previous examples assumed radiative forcing applied instantaneouslyforcing applied instantaneously i.e., all g.h. gas and aerosols added i.e., all g.h. gas and aerosols added

instantaneouslyinstantaneously

Real life: g.h. gas & aerosols added Real life: g.h. gas & aerosols added graduallygradually

More laterMore later