Energy Balance and Climate Energy Balance and Climate EES 3310/5310 - - PowerPoint PPT Presentation

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Energy Balance and Climate Energy Balance and Climate

EES 3310/5310 EES 3310/5310 Global Climate Change Global Climate Change Jonathan Gilligan Jonathan Gilligan

Class #3: Class #3: Friday January 10 Friday January 10 2020 2020

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Looking for a Good Home Looking for a Good Home

Bad Good Worst

− F 28∘ F 71∘ F 800∘

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Basic Concepts Basic Concepts

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Vocabulary Vocabulary

Energy, Heat: Heat = energy flowing spontaneously from hot to cold Power: speed at which energy flows or transforms Intensity: Concentration of power

Power, Flux = Heat flow/Time Heat, Energy = Power × Time Intensity = Power/Area Power = Intensity × Area

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Temperature of a planet Temperature of a planet

Basic principle: Steady temperature if and only if How can heat get in or out? Electromagnetic radiation

= Powerin Powerout

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Electromagnetic Waves Electromagnetic Waves

Color and brightness Color: Two ways to measure color: Wavelength ( ) Wavenumber ( ) Archer mostly uses wavenumber Math is simpler that way Brightness: Intensity (power/area, Watts/square meter)

λ n = 1/λ

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Colors Colors

All you need to think about is All you need to think about is shortwave shortwave vs.

• vs. longwave

longwave radiation. radiation.

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Shortwave Shortwave and and longwave longwave:

Shortwave: Near-infrared, visible, ultraviolet (cycles per centimeter) Longwave: Mid-infrared, far-infrared More on this in the next class …

λ < 3μm n > 3, 300cm−1 λ > 3μm n < 3, 300cm−1

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4 Laws of Radiation 4 Laws of Radiation

• 1. All objects continually radiate energy
• 2. Hotter objects are brighter
• 3. Hotter objects radiate at shorter wavelengths
• 4. Objects that are good absorbers are also good emitters

Black objects emit & absorb the most Transparent and white objects emit & absorb the least

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Blackbody Radiation Blackbody Radiation

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Blackbody Radiation Blackbody Radiation

Emissivity ( ) measures how black something is: for perfectly black for perfectly white or transparent In between for gray. Black, white, and gray: is the same for all wavelengths. Colored objects: is a function of wavelength. For simplicity: start by assuming everything is black, white, or gray. Remember: Good emitters are good absorbers Fundamental rule: Temperature and emissivity determine radiation.

ε ε = 1 ε = 0 ε ε

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Heating Up: What Changes?? Heating Up: What Changes??

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Heating Up: What Changes? Heating Up: What Changes?

Hotter temperature: Brighter (greater intensity) Bluer (greater wavenumber, shorter wavelength) A curious thing: A hot black object glows with color! Total intensity = area under curve

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Mathematical Description Mathematical Description

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Blackbody Radiation Blackbody Radiation

Intensity (brightness): Stefan-Boltzmann law after Josef Stefan and Ludwig Boltzmann = emissivity Different for different objects. = Stefan-Boltzmann constant. = absolute (Kelvin) temperature.

Color: Peak wavenumber proportional to (Kelvin) temperature.

I = εσT 4 ε σ T

Helpful Hint: Fourth power on a calculator: press the button twice.

x 2

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Sun and Earth Sun and Earth

Longwave ( ) 2% Visible & Near-IR ( ) 91% Ultraviolet ( ) 7% Total Shortwave (UV + Vis + Near-IR) 98%

λ > 3 micron 0.4 < λ < 3 micron λ < 0.4 micron

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Earth and Radiation Earth and Radiation

False-color images of radiation from Earth, seen by NASA Terra satellite: Left: Thermal radiation (blue → red → yellow = dim → bright) Right: Reflected sunlight (blue → green → white = dim → bright)

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Efciency of Light Bulbs Efciency of Light Bulbs

Type of Bulb Efficiency Standard 40W 1.8% Standard 60W 2.1% Standard 100W 2.6% Quartz Halogen 3.5% Ideal black body @ 7000K 14.0% Compact Fluorescent 8–12% LED 20–44%

7000K is the optimal temperature for a black body to emit visible light, but it will melt every known substance. Standard light bulbs operate at around 2000–3300 K.

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Calculating Earth’s Temperature: Calculating Earth’s Temperature: Bare-Rock Model Bare-Rock Model

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Basics Basics

Steady Temperature Steady Temperature

Heat in must balance heat out Total heat flux in ( ): Intensity depends on solar constant and albedo Does not depend on earth’s temperature Total heat flux out ( ): Intensity depends on earth’s temperature and emissivity Strategy:

• 1. Figure out

.

• 2. Figure out temperature

that makes .

Total Heat Flux (Power) = Area × Intensity Fin Fout Fin T = Fout Fin

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Solar Constant and Solar Constant and Inverse Square Law Inverse Square Law

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What is What is ?

Average albedo (30% of sunlight is reflected)

What is area? What is area?

Area = silhouette or shadow Circle:

Fin

in = Area × Intensity absorbed Fin Intensity absorbed = (1 − α) × Iin = 1350 W/ Iin m2 α = 0.30

πr 2

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What is What is ?

11,000 times total human energy production.

Fin

in = π × (1 − α) Fin r 2

Earth

Iin π = 1.3 × r 2 1014m2 α = 0.30 ⇒ (1 − α) = 0.70 = 1350 W/ Iin m2 = 1.2 × Watt Fin 1017

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What is What is ?

(blackbody) What is area? Sphere:

Fout

• ut

= Area × Fout Iout = εσ Iout T 4 ε = 1 σ = 5.67 × W/ / 10−8 m2 K4 4πr 2 = 4π × εσ Fout r 2

earth

T 4

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Putting it all together Putting it all together

= Fout Fin 4π × εσ = π (1 − α) r 2 T 4 r 2 Iin 4π × εσ = π (1 − α) r 2 T 4 r 2 Iin 4εσ = (1 − α) T 4 Iin = T 4 (1 − α)Iin 4εσ T = (1 − α)Iin 4εσ − − − − − − − − √

4

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Temperature of Earth Temperature of Earth

Steady Temperature: Heat flux in must balance heat flux out ( ). : Does not depend on earth’s temperature. Depends on solar constant and earth’s albedo. : Depends on earth’s temperature. adjusts until heat out = heat in.

= Fout Fin Fin Fout T T = (1 − α)Iin 4εσ − − − − − − − − √

4

Helpful hint: To take the fourth root on a calculat press the square-root key ( ) twic

√

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Temperature of Earth Temperature of Earth

Earth: Earth:

(Note: My numbers are slightly different from Archer’s textbook) Calculate : .

T = (1 − α)Iin 4εσ − − − − − − − − √

4

= 1350 W/ Iin m2 α = 0.30 ε = 1 σ = 5.67 × W/( ) 10−8 m2K4 T T = 254 K = − C = − F 19∘ 2∘

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If the sun got 5% brighter, If the sun got 5% brighter, how much warmer would the earth become? how much warmer would the earth become?

Normal: : 5% Brighter: :

T = (1 − α)Iin 4εσ − − − − − − − − √

4

= 1350 W/ Iin m2 T = 254 K = 1.05 × 1350 W/ = 1418 W/ Iin m2 m2 T = 257 K ΔT = 3 K = F 6∘

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Temperature of Earth Temperature of Earth

Earth: Earth:

(Note: My numbers are slightly different from Archer’s textbook) .

T = (1 − α)Iin 4εσ − − − − − − − − √

4

= 1350 W/ Iin m2 α = 0.30 ε = 1 σ = 5.67 × W/( ) 10−8 m2K4 T = 254 K = − C = − F 19∘ 2∘ How does this compare to Earth’s actual temperature? How does this compare to Earth’s actual temperature?

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Radiative Temperature Radiative Temperature

Satellites orbiting in space can measure longwave radiation from earth To the satellites, the earth looks very much like a blackbody at the bare-rock temperature (254 K). Thus, scientists generally call the bare-rock temperature the radiative temperature because it describes the radiation coming off the earth. However, the surface temperature of the earth is around , which is significantly different from the radiative, or bare-rock, temperature.

295 K = F 71∘

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The Terrestrial Planets The Terrestrial Planets

Mars Earth Venus

240 K 295 K 700 K

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Total flux (power) radiated from sun doesn’t change with distance. At a distance total flux spreads over sphere of radius Intensity = Total Flux / Area: Proportional to . At edge of Earth’s atmosphere, solar intensity = .

r r 1/r 2 1350 W/m2

Terrestrial Planets Terrestrial Planets

Earth Mars Venus Distance from sun 1 AU 1.5 AU 0.72 AU 1.00 0.44 1.9 Solar constant Albedo 0.30 0.17 0.71

1/Distance2 1350 W/m2 600 W/m2 2604 W/m2 Tbare rock 254 K (− F) 2∘ 216 K (− F) 70∘ 240 K (− F) 27∘ Tsurface 295 K ( F) 71∘ 240 K (− F) 28∘ 700 K ( F) 800∘ ΔT 41 K ( F) 74∘ 24 K ( F) 42∘ 460 K ( F) 828∘