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

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 /

Looking for a Good Home Looking for a Good Home Bad Good Worst 28 ∘ 71 ∘ 800 ∘ − F F F /

Basic Concepts Basic Concepts /

Vocabulary Vocabulary Energy, Heat: Heat = energy flowing spontaneously from hot to cold Power: speed at which energy flows or transforms Power, Flux = Heat flow/Time Heat, Energy = Power × Time Intensity: Concentration of power Intensity = Power/Area Power = Intensity × Area /

Temperature of a planet Temperature of a planet Basic principle: Steady temperature if and only if Power in = Power out How can heat get in or out? Electromagnetic radiation /

Electromagnetic Waves Electromagnetic Waves Color and brightness Color: Two ways to measure color : Wavelength ( ) λ Wavenumber ( ) n = 1/ λ Archer mostly uses wavenumber Math is simpler that way Brightness: Intensity (power/area, Watts/square meter) /

Colors Colors All you need to think about is All you need to think about is shortwave shortwave vs. vs. longwave longwave radiation. radiation. /

Shortwave Shortwave and and longwave longwave : Shortwave : Near-infrared, visible, ultraviolet λ < 3 μ m (cycles per centimeter) n > 3, 300cm − 1 Longwave : Mid-infrared, far-infrared λ > 3 μ m n < 3, 300cm − 1 More on this in the next class … /

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 /

Blackbody Radiation Blackbody Radiation /

Blackbody Radiation Blackbody Radiation Emissivity ( ) measures how black something is: ε for perfectly black ε = 1 for perfectly white or transparent ε = 0 In between for gray. Black, white, and gray: is the same for all wavelengths. ε Colored objects: is a function of wavelength. ε For simplicity: start by assuming everything is black, white, or gray. Remember: Good emitters are good absorbers Fundamental rule: Temperature and emissivity determine radiation. /

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

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 /

Mathematical Description Mathematical Description /

Blackbody Radiation Blackbody Radiation Intensity (brightness): Stefan-Boltzmann law I = εσ T 4 after Josef Stefan and Ludwig Boltzmann = emissivity ε Different for different objects. = Stefan-Boltzmann constant. σ = absolute (Kelvin) temperature. T Color: Peak wavenumber proportional to (Kelvin) temperature. Helpful Hint: Fourth power on a calculator: press the button twice. x 2 /

Sun and Earth Sun and Earth Longwave ( ) 2% λ > 3 micron Visible & Near-IR ( ) 91% 0.4 < λ < 3 micron Ultraviolet ( ) 7% λ < 0.4 micron Total Shortwave (UV + Vis + Near-IR) 98% /

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) /

Ef�ciency of Light Bulbs Ef�ciency 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. /

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

Basics Basics Steady Temperature Steady Temperature Heat in must balance heat out Total Heat Flux (Power) = Area × Intensity Total heat flux in ( ): F in Intensity depends on solar constant and albedo Does not depend on earth’s temperature Total heat flux out ( ): F out Intensity depends on earth’s temperature and emissivity Strategy: 1. Figure out . F in 2. Figure out temperature that makes . T F out = F in /

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

What is What is ? F in in F in = Area × Intensity absorbed Intensity absorbed = (1 − α ) × I in m 2 I in = 1350 W/ Average albedo (30% of sunlight is reflected) α = 0.30 What is area? What is area? Area = silhouette or shadow Circle: π r 2 /

What is What is ? F in in r 2 F in = π × (1 − α ) I in Earth 10 14 m 2 r 2 π = 1.3 × α = 0.30 ⇒ (1 − α ) = 0.70 m 2 I in = 1350 W/ 10 17 F in = 1.2 × Watt 11,000 times total human energy production. /

What is What is ? F out out F out = Area × I out T 4 I out = εσ (blackbody) ε = 1 m 2 K 4 10 − 8 σ = 5.67 × W/ / What is area? Sphere: 4 π r 2 r 2 T 4 F out = 4 π × εσ earth /

Putting it all together Putting it all together F out = F in r 2 T 4 r 2 4 π × εσ = π (1 − α ) I in r 2 T 4 r 2 4 π × εσ = π (1 − α ) I in T 4 4 εσ = (1 − α ) I in (1 − α ) I in T 4 = 4 εσ − − − − − − − − (1 − α ) I in 4 √ T = 4 εσ /

Temperature of Earth Temperature of Earth Steady Temperature: Heat flux in must balance heat flux out ( ). F out = F in : F in Does not depend on earth’s temperature. Depends on solar constant and earth’s albedo. : Helpful hint: F out Depends on earth’s temperature. To take the fourth root on a calculat press the square-root key ( ) twic adjusts until heat out = heat in. √ T − − − − − − − − (1 − α ) I in 4 √ T = 4 εσ /

/

Temperature of Earth Temperature of Earth − − − − − − − − (1 − α ) I in 4 √ T = 4 εσ Earth: Earth: (Note: My numbers are slightly different from Archer’s textbook) m 2 I in = 1350 W/ α = 0.30 ε = 1 m 2 K 4 10 − 8 σ = 5.67 × W/( ) Calculate : T . 19 ∘ 2 ∘ T = 254 K = − C = − F /

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? − − − − − − − − (1 − α ) I in 4 √ T = 4 εσ Normal: : m 2 I in = 1350 W/ T = 254 K 5% Brighter: : m 2 m 2 I in = 1.05 × 1350 W/ = 1418 W/ T = 257 K 6 ∘ Δ T = 3 K = F /

Temperature of Earth Temperature of Earth − − − − − − − − (1 − α ) I in 4 √ T = 4 εσ Earth: Earth: (Note: My numbers are slightly different from Archer’s textbook) m 2 I in = 1350 W/ α = 0.30 ε = 1 m 2 K 4 10 − 8 σ = 5.67 × W/( ) . 19 ∘ 2 ∘ T = 254 K = − C = − F How does this compare to Earth’s actual temperature? How does this compare to Earth’s actual temperature? /

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 71 ∘ 295 K = F significantly different from the radiative, or bare-rock, temperature. /

The Terrestrial Planets The Terrestrial Planets Mars Earth Venus 240 K 295 K 700 K /

Terrestrial Planets Terrestrial Planets Earth Mars Venus Distance from sun 1 AU 1.5 AU 0.72 AU 1.00 0.44 1.9 1/Distance 2 Solar constant 1350 W/m 2 600 W/m 2 2604 W/m 2 Albedo 0.30 0.17 0.71 2 ∘ 70 ∘ 27 ∘ T bare rock 254 K ( − F) 216 K ( − F) 240 K ( − F) 71 ∘ 28 ∘ 800 ∘ T surface 295 K ( F) 240 K ( − F) 700 K ( F) 42 ∘ 828 ∘ 74 ∘ Δ T 41 K ( F) 24 K ( F) 460 K ( F) Total flux (power) radiated from sun doesn’t change with distance. At a distance total flux spreads over sphere of radius r r Intensity = Total Flux / Area: Proportional to . 1/ r 2 At edge of Earth’s atmosphere, solar intensity = . 1350 W/m 2 /