Feedback Dynamics Feedback Dynamics & the Amplification & the Amplification of Climate Changeof Climate Change

At equilibrium,energy received

just balances the amount of energy radiated back to space

Increase in GHGconcentration raises

efficiency of insulating envelope,reducing net global radiation

Increase in GHGconcentration raises

efficiency of insulating envelope,reducing net global radiation

Surfacetemperature

rises, driven byretained solar energy

until resultantradiation recoversto establish a new

thermal equilibrium

Except that weare accelerating the

accumulation of GHGs.

Except that weare accelerating the

accumulation of GHGs.

Except that weare accelerating the

accumulation of GHGs,and feedbacks are also pushing

the system even further from balance

Except that weare accelerating the

accumulation of GHGs,and feedbacks are also pushing

the system even further from balance

Temperature

RadiativeForcing

MethaneConcentration

Carbon DioxideConcentration

Water VapourConcentration

Other GHGsConcentration

AlbedoEffect

Contrails &Aerosols

CloudEffects

Geo-thermalenergy

Solarenergy

Spatial Sink

Temperature

RadiativeForcing

MethaneConcentration

Carbon DioxideConcentration

Water VapourConcentration

Other GHGsConcentration

AlbedoEffect

Contrails &Aerosols

CloudEffects

F.1

F.2

F.3 F.4

F.5

F.6

F.GGeo-thermalenergy

Solarenergy

Spatial Sink

F.R

Temperature

RadiativeForcing

MethaneConcentration

Carbon DioxideConcentration

Water VapourConcentration

Other GHGsConcentration

AlbedoEffect

Contrails &Aerosols

CloudEffects

F.1

F.2

F.3 F.4

F.5

F.6

F.GGeo-thermalenergy

Solarenergy

Spatial Sink

F.R

Temperature

RadiativeForcing

MethaneConcentration

Carbon DioxideConcentration

Water VapourConcentration

Other GHGsConcentration

AlbedoEffect

Contrails &Aerosols

CloudEffects

F.1

F.2

F.3 F.4

F.5

F.6

F.GGeo-thermalenergy

Solarenergy

Spatial Sink

F.R

Temperature

RadiativeForcing

MethaneConcentration

Carbon DioxideConcentration

Water VapourConcentration

Other GHGsConcentration

AlbedoEffect

Contrails &Aerosols

CloudEffects

F.1

F.2

F.3 F.4

F.5

F.6

F.GGeo-thermalenergy

Solarenergy

Spatial Sink

F.R

Thermal InertiaThermal Inertia

Temperature

RadiativeForcing

MethaneConcentration

Carbon DioxideConcentration

Water VapourConcentration

Other GHGsConcentration

AlbedoEffect

Contrails &Aerosols

CloudEffects

F.1

F.2

F.3 F.4

F.5

F.6

F.GGeo-thermalenergy

Solarenergy

Spatial Sink

F.R

F.Ti

Thermal InertiaThermal Inertia

T h eT h e

P r o j e c tP r o j e c t

Feedback Dynamics Feedback Dynamics SimulatorSimulator

NRINRI(t)

The value of Net Radiative Imbalance at time (t) is governed by:

3: Consequential Feedback at time (t)

4: Radiative Damping Coefficient x ΔTt

1: Change in Solar Radiance from (t0) to (t)

2: Anthropogenic Forcing at time (t)

ΔSRt RDC.ΔTt

AFt CFt

NRINRI(t)

The Core Structure

The Fundamental Equation

NRINRI(t)AFt CFtΔSRt RDC.ΔTt= + + -

Climate SensitivityClimate Sensitivity

Amplification of the AnthropogenicAmplification of the AnthropogenicDisturbance of the Climate SystemDisturbance of the Climate System

Wa

ter

Va

po

ur

Oz o

ne

Wa

ter

Va

po

ur

Ca

rbo

n D

iox

i de

0 1 1400.1 1.071773 150.04830.2 1.148698 160.81780.3 1.231144 172.3602

0.36 1.283426 179.67960.4 1.319508 184.73110.5 1.414214 197.98990.6 1.515717 212.20030.7 1.624505 227.43070.8 1.741101 243.75420.9 1.866066 261.2492

1 2 2801.1 2.143547 300.09661.2 2.297397 321.63551.3 2.462289 344.72041.4 2.639016 369.46221.5 2.828427 395.97981.6 3.031433 424.4006

1.65 3.138336 439.36711.7 3.24901 454.86131.8 3.482202 487.50831.9 3.732132 522.4985

2 4 560

Column 1

Incremental power

Column 2

2 raised to power

Column 3

Column 2 x 140

Semi-log (base 2) scale construction

Pre-Industrial Benchmark

Half Benchmark

Double Benchmark

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

180

440

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

440

180

*

*

CO2 only: amplification x 1.0

1.2

Equilibrium Temperature for CO2 concentrations with no feedbacks°C °C

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180

*

*

Charney Sensitivity: amplification x 2.5

CO2 only: amplification x 1.0

1.2

3

Equilibrium Temperature for CO2 concentrations with fast feedbacks°C °C

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180

*

*

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

CO2 only: amplification x 1.0

1.2

3

4.5

Equilibrium Temp. for CO2 concentrations with fast + C-cycle f-backs°C °C

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

CO2 only: amplification x 1.0

1.2

3

4.5

6

Equilibrium Temp. for CO2 concentrations + fast & some slow f-backs°C °C

Earth System Sensitivity?

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

CO2 only: amplification x 1.0

1.2

3

4.5

6

7.8

Equilibrium Temp. for CO2 concentrations with all system feedbacks°C °C

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

*

CO2 only: amplification x 1.0

1.2

3

4.5

6

7.8

Equilibrium Temp. for CO2 concentrations with all system feedbacks°C °C

Ice Age Minimum point: [180, -5.0]

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

*

CO2 only: amplification x 1.0

1.2

3

4.5

6

7.8

Equilibrium Temp. for CO2 concentrations with all system feedbacks°C °C

*

Ice Age Minimum point: [180, -5.0]

Pre-Industrial Benchmark: [280, -0]

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

*

*

*CO2 only: amplification x 1.0

1.2

3

4.5

6

7.8

Equilibrium Temp. for CO2 concentrations with all system feedbacks°C °C

*

Ice Age Minimum point: [180, -5.0]

Pre-Industrial Benchmark: [280, -0]

Earth System Sensitivity: amp. x 6.5

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

*

*

*CO2 only: amplification x 1.0

1.2

3

4.5

6

7.8

Equilibrium Temp. for CO2 concentrations with all system feedbacks°C °C

*

Earth System Sensitivity: amp. x 6.5

Engelbeen point: [534, 7.1]

Ice Age Minimum point: [180, -5.0]

*

Pre-Industrial Benchmark: [280, -0]

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

*

*

*CO2 only: amplification x 1.0

1.2

3

4.5

6

7.8

Equilibrium Temp. for CO2 concentrations with all system feedbacks°C °C

*

Earth System Sensitivity: amp. x 6.5

Engelbeen point: [534, 7.1]

Pagani point: [360, 3.0]

*

Ice Age Minimum point: [180, -5.0]

*

Pre-Industrial Benchmark: [280, -0]

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

*

*

*CO2 only: amplification x 1.0

1.2

3

4.5

6

7.8

Equilibrium Temp. for CO2 concentrations with all system feedbacks°C °C

*

Earth System Sensitivity: amp. x 6.5

Engelbeen point: [534, 7.1]

Pagani point: [360, 3.0]

*

Ice Age Minimum point: [180, -5.0]

*

Pre-Industrial Benchmark: [280, -0]

Mathematical Cross-Check:Mathematical Cross-Check:

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

*

*

*CO2 only: amplification x 1.0

1.2

3

4.5

6

7.8

Equilibrium Temp. for CO2 concentrations with all system feedbacks°C °C

*

Earth System Sensitivity: amp. x 6.5

Engelbeen point: [534, 7.1]

Pagani point: [360, 3.0]

*

Ice Age Minimum point: [180, -5.0]

*

Pre-Industrial Benchmark: [280, -0]

Mathematical Cross-Check:Mathematical Cross-Check: Radiative Damping Coefficient = 3.3wm-2°C-1

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

*

*

*CO2 only: amplification x 1.0

1.2

3

4.5

6

7.8

Equilibrium Temp. for CO2 concentrations with all system feedbacks°C °C

*

Earth System Sensitivity: amp. x 6.5

Engelbeen point: [534, 7.1]

Pagani point: [360, 3.0]

*

Ice Age Minimum point: [180, -5.0]

*

Pre-Industrial Benchmark: [280, -0]

Mathematical Cross-Check: Mathematical Cross-Check: Radiative Damping Coefficient = 3.3wm-2°C-1

Radiative increase (Ice-age minimum to Pre-Industrial Benchmark) = 16.5wm-2

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

*

*

*CO2 only: amplification x 1.0

1.2

3

4.5

6

7.8

Equilibrium Temp. for CO2 concentrations with all system feedbacks°C °C

*

Earth System Sensitivity: amp. x 6.5

Engelbeen point: [534, 7.1]

Pagani point: [360, 3.0]

*

Ice Age Minimum point: [180, -5.0]

*

Pre-Industrial Benchmark: [280, -0]

Mathematical Cross-Check:Mathematical Cross-Check: Radiative Damping Coefficient = 3.3wm-2°C-1

Radiative increase (Ice-age minimum to Pre-Industrial Benchmark) = 16.5wm-2

CO2 contribution = 2.54wm-2

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

*

*

*CO2 only: amplification x 1.0

1.2

3

4.5

6

7.8

Equilibrium Temp. for CO2 concentrations with all system feedbacks°C °C

*

Earth System Sensitivity: amp. x 6.5

Engelbeen point: [534, 7.1]

Pagani point: [360, 3.0]

*

Ice Age Minimum point: [180, -5.0]

*

Pre-Industrial Benchmark: [280, -0]

Mathematical Cross-Check:Mathematical Cross-Check: Radiative Damping Coefficient = 3.3wm-2°C-1

Radiative increase (Ice-age minimum to Pre-Industrial Benchmark) = 16.5wm-2

CO2 contribution = 2.54wm-2 Feedback contribution = 13.96wm-2

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

*

*

*CO2 only: amplification x 1.0

1.2

3

4.5

6

7.8

Equilibrium Temp. for CO2 concentrations with all system feedbacks°C °C

*

Earth System Sensitivity: amp. x 6.5

Engelbeen point: [534, 7.1]

Pagani point: [360, 3.0]

*

Ice Age Minimum point: [180, -5.0]

*

Pre-Industrial Benchmark: [280, -0]

Mathematical Cross-Check:Mathematical Cross-Check: Radiative Damping Coefficient = 3.3wm-2°C-1

Radiative increase (Ice-age minimum to Pre-Industrial Benchmark) = 16.5wm-2

CO2 contribution = 2.54wm-2 Feedback contribution = 13.96wm-2

Hence Amplification Factor = 6.49Amplification Factor = 6.49

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

*

*

*CO2 only: amplification x 1.0

1.2

3

4.5

6

7.8

Equilibrium Temp. for CO2 concentrations with all system feedbacks°C °C

*

Earth System Sensitivity: amp. x 6.5

Engelbeen point: [534, 7.1]

Pagani point: [360, 3.0]

*

Ice Age Minimum point: [180, -5.0]

*

Pre-Industrial Benchmark: [280, -0]

Mathematical Cross-Check:Mathematical Cross-Check: Radiative Damping Coefficient = 3.3wm-2°C-1

Radiative increase (Ice-age minimum to Pre-Industrial Benchmark) = 16.5wm-2

CO2 contribution = 2.54wm-2 Feedback contribution = 13.96wm-2

Hence Amplification Factor = 6.49 Sensitivity = 7.79 Amplification Factor = 6.49 Sensitivity = 7.79 °°CC

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

*

*

*350

CO2 only: amplification x 1.0

1.2

3

4.5

6

7.8

Equilibrium Temp. for CO2 concentrations with all system feedbacks°C °C

Earth System Sensitivity: amp. x 6.5

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

*

*

*350

CO2 only: amplification x 1.0

1.2

3

4.5

6

7.8

Equilibrium Temp. for CO2 concentrations with all system feedbacks°C °C

Earth System Sensitivity: amp. x 6.5

Correlations and Consequences

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

*

*

*350

CO2 only: amplification x 1.0

1.2

3

4.5

6

7.8

Equilibrium Temp. for CO2 concentrations with all system feedbacks°C °C

Earth System Sensitivity: amp. x 6.5

690

°C

CO2

ppm0

4

6

8

2

12

14

16

10

0

+4

+6

+8

+2

-2

-4

-6

-8280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

*

*

440

180*

*

*

*

*

*

*

*

*350

1.2

3

4.5

6

7.8

1120

15.6

12

9

6

2.4

°C

600

643

739

792

849

910

975

1045

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

CO2 only: amplification x 1.0

Equilibrium Temperatures up to second doubling of CO2 concentrations

690

Earth System Sensitivity: amp. x 6.5

0

+4

+6

+8

+2

-2

-4

-6

-8

280

560

522

487

455

424

396

369

345

322

300

261

244

227

212

198

185

172

161

150

140

°C

CO2

ppm

*

*

440

180*

*

*

*

Hansen Upgrade: amplification x 5.0

Charney Sensitivity: amplification x 2.5

Hadley +C f-backs: amplification x 3.75

*

*

*

*

*350

NB. All lines refer to change that is slow and close to equilibrium

Those conditions no longer apply

CO2 only: amplification x 1.0

1.2

3

4.5

6

7.8

Equilibrium Temp. for CO2 concentrations with all system feedbacks°C °C

Earth System Sensitivity: amp. x 6.5