Introductory Climate Modeling

Presented by Dr. Robert MacKayClark College physics and meteorology

rmackay@clark.edu

Earth in space

See the first 4 videos at:http://earthobservatory.nasa.gov/Experiments/PlanetEarthScience/GlobalWarming/GW.php

These are a very nice introduction to radiation from Earth and Sun.

Earth in space

The rate of Solar energy absorption by Earth is

R2*(1-)So where

R is Earth’s radius is the mean planetary albedoSo is the solar constant ~1365 W/m2

The mean emission rate for terrestrial (longwave) radiation is

R2*T4 where

=5.67x10-8 W/m2/K4

T is Earth’s mean annual temperature

Earth in space

Setting absorption equal to emission gives

R2*(1-)So =R2*T4

or

K 255

4σ

α1ST

41

0

This is about 33 K lower than Earth’s mean surface temperature of 288 K

Adding an atmosphere

A “flat” earth with an atmosphere that absorbs no solar radiation but absorbs all long-wave radiation coming from Earth’s surface. Both the earth’s surface and the atmosphere are assumed to be black bodies for longwave radiation. The atmosphere emits radiant energy equally towards and awy from Earth’s surface.

4A2

4E1

σTF

σTF

A “flat” earth with an atmosphere that absorbs no solar radiation but absorbs all long-wave radiation coming from Earth’s surface. Both the earth’s surface and the atmosphere are assumed to be black bodies for longwave radiation. The atmosphere emits radiant energy equally towards and awy from Earth’s surface.

4A2

4E1

σTF

σTF

KmKWx

mW303

)/(1067.5

/239*2Tor

2SF gives Ffor Solving

unknowns as F and Fwith

equationst independen just tworeally are equations above the

)atmosphere of at top balance(energy SF 3)

)atmospherefor balance(energy F2F 2)

surface)at balance(energy FSF 1)

41

248

2

E

11

21

2

12

21

This is about 15 K higher than Earth’s mean surface temperature of 288 K

S

From K. Trenberth, J. Fasullo, and J. Kiehl, EARTH’S GLOBAL ENERGY BUDGET BAMS 2009

Atmosphere absorbs a fraction, ,of the total solar radiation absorbed by the planet

Atmosphere absorbs a fraction, of all long-wave radiation coming from Earth’s surface. Through Kirchoff’s radiation law the emissivity of the atmosphere for long-wave radiation equals its absorptivity.

Earth’s surface is assumed to be a black bodies for long-wave radiation.

The atmosphere emits radiant energy equally towards and away from Earth’s surface.

4A2

4E1

σTF

σTF

S

A “flat” earth with an atmosphere that absorbs no solar radiation but absorbs all long-wave radiation coming from Earth’s surface. Both the earth’s surface and the atmosphere are assumed to be black bodies for longwave radiation. The atmosphere emits radiant energy equally towards and awy from Earth’s surface.

4A2

4E1

σTF

σTF

unknowns as F and Fwith

equationst independen just tworeally are equations above the

)atmosphere of at top balance(energy S)F-(1F 3)

)atmospherefor balance(energy SF2F 2)

surface)at balance(energy FS)1(F 1)

21

12

12

21

Estimating =0.29 and =0.9 from Khiel and Trenberth Energy Balance diagram

A “flat” earth with an atmosphere that absorbs no solar radiation but absorbs all long-wave radiation coming from Earth’s surface. Both the earth’s surface and the atmosphere are assumed to be black bodies for longwave radiation. The atmosphere emits radiant energy equally towards and awy from Earth’s surface.

4A2

4E1

σTF

σTF

K5.284S

2ε

1

2γ

1Tor S

2ε

1

2γ

1F

2) and 1) equations (combining S2

F2

S)1(F

41

E1

11

Estimating =0.29 and =0.9 from Khiel and Trenberth Energy Balance diagram

This is about 3.5 K lower than Earth’s mean surface temperature of 288 K

Thermal Inertia Of Oceans

d C

I

t

T

T dA C tA I

I Net radiation intensity (W/m2)A Area of surfaced depth of ocean mixed layerC specific heat capacity of oceans the density of water

day

Co

14

I

t

T

If d=100 m

http://www.atmosedu.com/Geol390/physlets/GEBM/EBMGame.htm

http://www.youtube.com/watch?v=y2m7OTv-cAc

http://www.atmosedu.com/Geol390/physlets/GEBM/ebm.htm

Stella version: http://www.atmosedu.com/WSU/esrp310-550/Activities/Gebm.STM

Feedbacks

Feedbacks

http://www.thesystemsthinker.com/tstcld.html

http://www.atmosedu.com/ENVS109/PP/CausalLoopDiagramsA.ppt

Diagram from VUE.Visual Understanding environment

Conclusions

• Simple conceptual climate models can help students learn about climate modeling and the climate system.

• Climate models of all sort provide Interactive engagement opportunities for students.

• Causal loop diagrams offer an excellent visual communication tool for both student and instructor.