A Climate Senior Project Presentation

Simulating Climate UsingA Simple Model

Jonathan Fivelsdal

May 12, 2010

Jonathan Fivelsdal Simulating Climate Using A Simple Model 1/44

General Outline

• Introduction

• Basic Facts About Climate

• Climate Model Equation

• Results

• Future Work


Introduction

• My Research Focuses on Global Climate

• I use a Computer Model of a 1-D EBM

• I Investigate How Land Configs Affect TemperatureChange Across the Globe

• Simulation Runs Over 1-Year Period


1-D Energy Balance Model

1-D Energy Balance Model

• Used to Examine Properties of Earth’s Climate System

• Based on Equilibrium Condition

• Considers Temperature Variations Across Lines of LatitudeOnly


Physics of Heat Exchange

• Energy is the ability to do work

• Heat flux is the process of energy transfer from one body toanother

• Example: Earth Receives Energy From the Sun and inResponse to the Energy Exchange Heats Up


Specific Heat

C =ΔQ

mΔT

• Specific heat capacity: heat energy required to raise thetemperature of a substance

Terms DescriptionΔQ Heat required to raise substance to a given temperaturem Mass of a given substanceΔT Amount of temperature change in a given substanceC Specific Heat Capacity


Specific Heat (Examples)

• specific heat of rock is 850 J (kg K)−1

• specific heat of water 4186 J (kg K)−1

• Since the specific heat of water > specific heat of rock;more energy to increase temp of oceans vs. land


Albedo

Albedo (�)

• ratio of radiation reflected by a surface

• 0 ≤ � ≤ 1

• Net Albedo of Earth is determined by factors such as % ofland vs. ocean and glacier coverage

• Earth’s Average Albedo is .3


Blackbody Radiation

• A blackbody is a surface that completely absorbs allincident radiation

• Earth absorbs most of the radiation it receives (about 70%)

• Earth can be approximately described as a blackbody

• The amount of energy released by a blackbody over agiven area is obtained by the Stefan-Boltzmann law


Stefan Boltzmann LawAmount of Energy Emitted by a Blackbody

E = ��T 4

• E: Flux Density• �: Emissivity (Ability to radiate as a blackbody (�bb = 1)• �: Stefan-Boltzmann Constant *• T: Temperature

* � = 5.67 ⋅ 10−8 Wm−2 K−4


Greenhouse Effect

• Ability of Atmosphere to Absorb and Reflect Heat RadiatedFrom Earth’s Surface

• Atmosphere is a layer of gas

• (ie. 78% Nitrogen,21% Oxygen, and < 1% Carbon Dioxide)

• Thicker Atmosphere Absorbs Heat More Effectively


Greenhouse Effect


Facts About Earth’s Temperature

• Earth’s Effective Blackbody Temperature (No Atmosphere)is 255 K

• Freezing Temperature of Water 273 K

• Earth’s Temperature With Atmosphere (Actual) is 288 K

• Earth’s Temperature With Atmosphere (Model) is 303 K


More Facts About Earth’sTemperature

• Difference Between Actual Mean Temperature (288 K) andEffective (255 K) is 30 K

• The Temp Difference is due to the Greenhouse Effect


Incoming Solar Radiation

• Amount of Solar Radiation Earth Receives in Units Wm−2

• Solar Radiation is also referred to as Short Wave(SW)



• Amount of SW that reaches Top of Atmosphere is 1380Wm−2

• Total Amount of SW Received by an Average Point onEarth is 343 Wm−2



• Only 25 % of the SW at the Top of the Atmosphere(TOA)Reaches Earth’s Surface

• This is because Earth’s Sphericity and only half of theearth is lit by the sun

• (ie. day and night)

Solar Radiation ValuesRadiation at TOA 1380 Wm−2

Incoming Radiation 343 Wm−2


Geographic Features and Climate

Geographic Features that Affect Climate are

• Distribution of Land and Sea• Ocean Currents• Orientation of Land Masses


Climate Models

Advantages of Simple Climate Models VS Complex Models

• Easier to Interpret• Less Computationally Expensive• Easier to Implement

• Complex Models use Systems of PDE’s• My Model is Based on 1 Partial Differential Equation


The Model Equation

Climate Model Equation

∂T

∂t=

1

�cpℎ[Qs(1− �)− I +D]

Model Parameters Description�cpℎ Thermal Capacity FactorQ Insolations = s(y) Latitude Distribution� AlbedoI OLRD Difffusion


Model Parameters Explained

∂T

∂t=

1

�cpℎ[Qs(1− �)− I +D]

• Q = 343 Wm−2: (Incoming Solar Radiation)• s(y): Describes How Solar Radiation is Distributed Over

Latitudes• y = sin(�): where � is Latitude• (1-�): Ratio Solar Radiation Absorbed by the Earth• I: Outgoing Long Wave Radiation• D: Diffusion (Heat Transport Term)


Outward Longwave Radiation

Since �rock ≈ 1 and �water ≈ 1 we represent I as

I = ��T 4

= (1)�T 4

= �T 4


Thermal Capacity Factor

∂T

∂t=

1

�cpℎ[Qs(1− �)− I +D]

• �cpℎ is the thermal capacity factor

• Amount of Heat Per Unit Surface Area needed to Raise theSurface Temperature of the Earth by 1∘ C

• Units are in J K−1 m−2


Properties of Rock and Water

• Rock radiates heat differently from water

• Specific Heat of Rock (cpr) is 850 J K−1 kg−1

• Specific Heat of Water (cpw) is 4198 J K−1 kg−1

• Specific Heat of Water is about 5 times larger than SpecificHeat of Rock


Capacity Factors: Rock and Water

∂T

∂t=

1

�cpℎ[Qs(1− �)− I +D]

Rock Thermal Capacity Factor

rc = �rcprℎr

Water Thermal Capacity Factor

wc = �wcpwℎw


Radiative Imbalance

• Excess Radiation (Tropics) Deficit (Poles)


Hadley Circulation

• A Physical Manifestation of Heat Transport

• Large Scale Circulations Develop in the Atmosphere due toUneven Heating

• 1. Air Rises Near The Equator

• 2. Then Air Flows Poleward and Cools

• 3. Air Sinks Near The Poles

• 4. Air Flows Close to Surface Back Towards Equator


Gulf Stream

• Series of Fast Moving Ocean Currents in the Atlantic• Carry Warm Air Poleward• Results in Mild Climates in North America and Europe• The Diffusion term (D) Represents this Process


Model Diffusion Compared toRealistic Diffusion

• Model Diffusion is Given by the equation D = C(T − T )

• Realistic Diffusion is Represented by

D ∝ ∂2T

∂x



Figure:Dark Line ≡ Temp. DistributionA,B ≡ Specfic Temps.Dotted ≡ Mean Temperature



• With Model Diffusion A and B are Treated the Same• Due to (T − T ) for A equaling (T − T ) for B



• With Realistic Diffusion Negative Diffusion at A andPositive Diffusion at B

• A: Neg. Curvature and B: Pos. CurvatureJonathan Fivelsdal Simulating Climate Using A Simple Model 32/44

Land Configurations

Land Types

• Type 1: Land in Poles Only (land > 55 S and land > 55 N)

• Type 2: Land in Poles and Tropics

• Type 3: Land in Tropics Only (23.5 S < land < 23.5 N)

• Type 4: Land mostly in Northern Hemisphere (MostlyAbove the Equator)

• Land types were run for each initial temperature


Percentage Land Vs. Water

Land Type: Type 1 Type 2 Type 3 Type 4Land 39% 65% 26% 39%Water 61 % 35 % 74 % 61%

• Notice: Land Type 3 has the most water


Initial Condition 1

Annual Average Temperatures With Initial Temperature 255 K

250

255

260

265

270

275

280

285

290

-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90

Latitude

Tem

pera

ture

(Kel

vin)

Land Type 1Land Type 2Land Type 3Land Type 4Initial Temp


Results for Initial Condition 1

• Land Type 3 Changes the Least From the InitialTemperature of 255 K

• This is because Land Type 3 has the most water and thehigh heat capacity of water

• Land Type 2 Changes the Most Since it has the Most Land• Land Type 1 and 4 have similar Temp. Distributions since

same amount of land



Initial Condition 2


260

265

270

275

280

285

290

-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90

Latitude

Tem

pera

ture

(Kel

vin)




Land Type 3 Changes the Least From the Initial Temp.

Again this is likely due to the higher heat capacity of water



Initial Condition 3


260

265

270

275

280

285

290

295

-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90

Latitude

Tem

pera

ture

(Kel

vin)




Land Type: Type 1 Type 2 Type 3 Type 4Average Temps. 279.30 K 278.88 K 282.20 K 279.25 KΔ Initial Temp. -8.7 K -9.12 K -5.8 K -8.75 K

• Land types 1,2, and 4 have average temperatures about 10K less than 288 K.

• Land type 3 has an average temperature about 6 K lessthan 288 K

• Therefore Land Type 3 changes the least from the initialtemperature


Initial Condition 4


260

265

270

275

280

285

290

295

300

305

-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90Latitude

Tem

pera

ture

(Kel

vin)




One difference from other graphs is all temp. distributions liebelow initial temp.


Discussion

All temp. distributions have a similar shape (indicatesdominance of solar term Qs(y))

Every temp. distribution has cold temperatures in poles andwarm temperatures in tropics

Land Type 3 is the most distinct distribution

Land Type 3 Changes Least from Initial Temperature (has themost water)


Future Work

Test if large percent of water coverage is sole reason for smalltemp. changes

Method 1: Keep ratio of land to water constant but changedistributions of land

Method 2: Keep land distribution constant but change ratio ofland to water


A Climate Senior Project Presentation

Documents

Transcript of A Climate Senior Project Presentation