Energy, Power, and Climate Change 8.9 The Greenhouse Effect

1. FYI: A photon of the "wrong" energy will pass right through the gas without interacting. FYI: A photon of the "right" energy will be absorbed by the atom, and the electron will jump to a new energy level. Energy, Power, and Climate Change8.9 The Greenhouse Effect INTERACTION BETWEEN LIGHT AND ATOMS FYI: This process is called EXCITING THE ELECTRON. The electron is in an EXCITED STATE. Recall that solar radiation strikes the earth at a rate of 1380 Wm-2 or less, the farther from the equator you are. FYI: If the "right" photon is of sufficiently large energy, the electron can be completely freed from the atom. This is called IONIZATION. That energy is carried in the form of photons, which are quanta of light. The atmosphere is made up of gases, which are the first layer of matter that the sun's rays interact with. If a photon is at the precise energy for an electron to jump to a different energy level in an atom, it will be absorbed.

2. N N N N N N N N N N N N N N FYI: A photon of the "right" energy will cause the molecule to vibrate with a larger amplitude. This is called RESONANCE. FYI: Resonant frequencies for molecules tend to be low, so the "right" photons are from the INFRARED region of the spectrum. Energy, Power, and Climate Change8.9 The Greenhouse Effect INTERACTION BETWEEN LIGHT AND MOLECULES Molecules can also absorb light energy. A relatively useful model of molecules (in this case diatomic) has two masses joined by a spring. First, we know that there is a potential energy associated with a spring given by U = (1/2)kx2, where k is the spring constant (representing how stiff the spring is) and x is the amount the spring is displaced from equilibrium. Second, we know that there is a kinetic energy associated with moving masses (two of them in this case). Note that a diatomic molecule has many modes of motion: Translation Rotation Linear Vibration

3. Albedo FYI: The albedo for snow is one of the highest, and about 0.9 or 90%. Cloud cover has about the same albedo as snow. FYI: The albedo for a dark forest is about 0.1 or 10%. Energy, Power, and Climate Change8.9 The Greenhouse Effect INTERACTION BETWEEN LIGHT AND SOLIDS Solids contain atoms which interact with each other in such a way that electrons do not need to exist in so few discrete energy levels. FYI: The average albedo for the earth is about 30%. Solids therefore can absorb photons of a very wide range of energies (and therefore frequencies: E = hf). The allowable energies of a solid are called bands. Solids will increase in temperature more readily than gases because of their increased absorption of photons. As the solid heatS up it emits low-energy radiation in the infrared region of the spectrum. Surfaces of solids, liquids, and clouds absorb and reflect light. The ratio of reflected to absorbed light is called the albedo. reflected light absorbed light albedo =

4. Wien's displacement law Energy, Power, and Climate Change8.9 The Greenhouse Effect INTERACTION BETWEEN LIGHT AND BLACK BODIES You may recall that black bodies are perfect absorbers of radiation (and also perfect emitters). Suppose we take our cavity blackbody and place a detector at the opening, and heat the cavity blackbody to successively higher temperatures, while measuring the frequencies of the emitted radiation. We get a family of graphs that looks like this: Two trends emerge: (1) The higher the temperature the greater the intensity at all wavelengths. (2) The higher temperature the smaller the wavelength of the maximum intensity. visible radiation Intensity UV radiation IR radiation maxT = 2.9010-3 mK 3000 4000 5000 1000 2000 Wavelength (nm)

5. FYI: Stefan's Power law Stefan-Boltzmann constant Energy, Power, and Climate Change8.9 The Greenhouse Effect POWER OUTPUT OF RADIATING MATTER Radiation emitted by hot objects is called thermal radiation. Recall that the total radiation power emitted is proportional to T4, where T is the absolute Kelvin temperature. P = AeT4 where = 5.6710-8 W/m2K4 A is the surface area of the object, and e is the emissivity of the object and is a unitless number between 0 and 1 that depends on the material emitting the radiation. FYI: Since all bodies are above absolute zero, all bodies emit thermal radiation.

6. Energy of a photon of wavelength  Energy, Power, and Climate Change8.9 The Greenhouse Effect POWER OUTPUT OF RADIATING MATTER What is the energy of one photon of 450 nm light? we can get E in terms of : c = f and E = hf Using c  hc   f = E = (6.6310-34)(3108) 45010-9 E = E = 4.410-19 J 1 eV 1.610-19 J E = 2.8eV

7. Energy, Power, and Climate Change8.9 The Greenhouse Effect POWER OUTPUT OF RADIATING MATTER What is the wavelength of the most intense radiation coming from the sun if its surface temperature is 6000 K? maxT = 2.9010-3 mK max(6000) = 2.9010-3 max = 48310-9 m = 483 nm What is the power per square meter emitted by the sun? Treat the sun like a perfect emitter. e = 1 P = AeT4 P / A = eT4 P / A = (5.6710-8)(1)(6000)4 FYI: This is 74 MW per square meter! P / A = 7.35107 Wm-2

8. Energy, Power, and Climate Change8.9 The Greenhouse Effect POWER OUTPUT OF RADIATING MATTER The radius of the sun is 7108 m. What is the total power radiated by the sun? = 1.51018 m2 = (7108)2 A = r2 P / A = 7.35107 Wm-2 P = (7.35107 Wm-2)A P = (7.35107)(1.51018) P = 1.11026 W FYI: This is 1026 joules each second!

9. FYI: The radius of earth is R = 6.4106 m. Energy, Power, and Climate Change8.9 The Greenhouse Effect THE TEMPERATURE OF THE EARTH Our first model of the effect of the sun's energy on the temperature of the earth assumes no atmosphere. Ignoring the atmosphere we will estimate how warm the earth should be. The energy per second per unit area provided by the sun is 1360 W/m2. This energy is absorbed only by half of the earth. Why? This energy is contained in the disk in heavy yellow, which has a radius of the earth. 1360 W / m2 A = r2 = (6.4106)2 = 1.31014 m2 P = 1360A P = 1360(1.31014) P = 1.751017 W

10. FYI: The radius of earth is R = 6.4106 m. FYI: The surface area of a sphere is A = 4r2. Energy, Power, and Climate Change8.9 The Greenhouse Effect THE TEMPERATURE OF THE EARTH Since the average albedo of the earth is 30%, this means that 70% of this power is absorbed: Question: What assumption did we make about the emissivity of the earth? Question: If the temperature of the planet is to remain CONSTANT, at what rate must it be emitting energy if it is absorbing energy at a rate of 1.231017 W? P = (0.70)1.751017 W absorbed energy per second P = 1.231017 W To calculate the energy absorbed by the earth, we assume that the whole surface area of the planet is absorbing this energy. Why? A = 4r2 = 4(6.4106)2 = 5.21014 m2 From Stefan's power law we can get a handle of the expected temperature of earth (without atmosphere): P = AeT4 P = 5.6710-8(5.21014)(1)T4 P = 2.95107T4 1.231017 = 2.95107T4 T4 = 4.17109 FYI: The average temperature of the earth is 288 K = +15 C. T = 254 K = -19°C

11. FYI: The absorption of this radiated energy (or TRAPPING of it) by the ATMOSPHEREis called THE GREENHOUSE EFFECT, since a greenhouse also traps radiated energy. Energy, Power, and Climate Change8.9 The Greenhouse Effect THE EMISSIVITY OF THE EARTH This estimate is lower than the average temperature of the earth. FYI: The actual emissivity of earth depends on many things - not just the atmosphere. Clouds, ice packs, deserts, forests, lakes, etc. all contribute to a variable emissivity (and albedo). We may conclude that other factors contribute to increasing the average temperature of the earth. FYI: Another factor contributing to a higher surface temperature is the fact that the earth contains radioactive elements which produce heat as a byproduct of their disintegration. This is, after all, the energy behind volcanoes and plate tectonics! The atmosphere absorbs some of the energy radiated by the earth before it escapes to space. In our model we assumed that the emissivity was that of a block body. The earth does NOT have a perfect emissivity of 1. We can estimate the emissivity of earth using the Stefan power law and the actual temperature of 288 K: P = AeT4 P = 5.6710-8(5.21014)e(288)4 P = 2.031017e 1.231017 = 2.031017e e = 0.61

12. Energy, Power, and Climate Change8.9 The Greenhouse Effect ATMOSPHERIC HEAT ABSORPTION Obviously the atmosphere is the first layer of earth to be struck by incoming light, and so the atmosphere has first dibs on extracting energy from the sun. incoming solar radiation Different gases in the atmosphere absorb different frequencies of light - this is because of the resonant properties of each gas. 20% UV and X-rays (Ozone) The atmosphere absorbs about 50% of the incoming solar radiation before it strikes the ground. The Sankey diagram for incoming solar radiation looks like this: 30% IR (H2O, CO2) 30% arrives at ground

13. Energy, Power, and Climate Change8.9 The Greenhouse Effect ATMOSPHERIC HEAT ABSORPTION incoming solar radiation 20% UV and X-rays (Ozone) 30% IR (H2O, CO2) 50% arrives at ground

14. FYI: This is in the IR region of the spectrum. FYI: Do not confuse the radiation REFLECTED by the ground with the radiation PRODUCED by the ground. Energy, Power, and Climate Change8.9 The Greenhouse Effect SURFACE HEAT ABSORPTION FYI: You can think of the ground as a frequency converter. It absorbs radiation of a variety of frequencies and converts it to infrared radiation. Not all of the remaining 50% of the solar radiation is absorbed by the ground. incoming solar radiation Depending on the albedo of the ground, some of the radiation is reflected back to the atmosphere. The atmosphere WILL NOT absorb and of the ground-reflected radiation. Why? 20% UV and X-rays (Ozone) The remaining radiation is absorbed by the ground, increasing its temperature. The ground temperature will radiate its own heat according to Wien's displacement law: 30% IR (H2O, CO2) maxT = 2.9010-3 mK max(288) = 2.9010-3 max = 1.0110-6 m = 10100 nm Note that CO2 and H2O can both absorb IR radiation. 50% arrives at ground

15. Energy, Power, and Climate Change8.9 The Greenhouse Effect SURFACE HEAT ABSORPTION Absorption by the ground is very complex. Ice, snow, water, sand, forest, crops, cities, etc. all have different heat capacities. incoming solar radiation We can lump all of the specific heat capacities into one overall surface heat capacityCs, which is defined to be the amount of heat Q needed to raise the temperature of 1 m2 of the ground by 1K. 20% UV and X-rays (Ozone) For earth, Cs is estimated to be about 4108 J/Km2. 30% IR (H2O, CO2) 50% arrives at ground

16. Energy, Power, and Climate Change8.9 The Greenhouse Effect THE GREENHOUSE EFFECT It is the absorption in the atmosphere of the IR radiation produced by the warm earth that we call the greenhouse effect. incoming solar radiation Since H2O and CO2 are the gases in the atmosphere that are able to absorb IR, we call them greenhouse gases. FYI: Water vapor and carbon dioxide are the principal greenhouse gases. 20% UV and X-rays (Ozone) FYI: If it wasn't for the greenhouse gases, all of the heat radiated by the earth would pass through the atmosphere and be lost to space. 30% IR (H2O, CO2) FYI: The greenhouse gases account for much of the difference between the earth's calculated temperature of 254 K, and the earth's actual temperature of 288 K. 30% arrives at ground

17. FYI: By the way, since the greenhouse gases absorb IR (both incoming and outgoing) they radiate IR just as the ground does, contributing to the overall temperature of the earth. This makes for a rather involved Sankey diagram! FYI: At each interface the energy in equals the energy out: Energy, Power, and Climate Change8.9 The Greenhouse Effect THE GREENHOUSE EFFECT FYI: This means that the temperature of the earth is constant. 235 235 incoming solar radiation 342 W/m2 342 77 30 77 30 absorbed by greenhouse gases 67 40 reflection by atmosphere reflection by atmosphere radiated by earth greenhouse gases reflection by ground reflection by ground radiated by earth the atmosphere 324 390 235 168 the ground WITHOUT GREENHOUSE GASES WITH GREENHOUSE GASES