Lecture7_Radiation - EAS 1600 Introduction to Environmental...

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Unformatted text preview: EAS 1600 Introduction to Environmental Sciences We now begin an investigation of the Earth's climate, by focusing on the so-called Earth's energy budget. The fundamental physical law that underpins this discussion is the First Law of Thermodynamics; that is, the conservation of energy. The next two lectures focus on how electromagnetic radiation (e.g., light) interacts with the Earth and helps determine climate. Class 6 Solar Radiation and Effective Temperature Today, we introduce some basic concepts about electromagnetic radiation and how solar radiation interacts with a planet like the Earth. BASIC CONCEPTS: 1. Electromagnetic Radiation Propagation of energy involving coupled electric and magnetic waves Waves are characterized by: Wavelength, Frequency, Speed, c where c = = 3 x 108 m/s Radiation also acts as stream of photons E = h = hc/ Where h = Planck's constant = 6.63 x 10-34 Js Select all the correct statements about electro-magnetic radiation. A. As wavelength increases, phase speed increases B. As wavelength increases, photon energy decreases C. As wavelength increases, frequency decreases. D. Phase speed is independent of wavelength. BASIC CONCEPTS: 2. Electromagnetic Spectrum Forms of electromagnetic radiation determined by and Unit of wavelength: nanometers or nm, micrometers, m In the visible, different wavelengths are perceived as different colors Electromagnetic Spectrum BASIC CONCEPTS: 3. Radiative Flux Flux is rate at which energy or mass passes through a unit area. Radiative flux has units of Wm-2; i.e.., power/unit area Flux depends upon: Angle of incidence of radiation upon surface are S = So cos(q), where q is the angle of incidence And, distance from source S = So(ro/r)2 (See example on next page) http://cimss.ssec.wisc.edu/satmet/modules/spectrum/spectrum.html Dependence upon angle of incidence of radiation S = So cos(q), where q is the angle of incidence Dependence upon distance from source: S = So(ro/r)2 The key thing to know in order to understand this concept is that the surface area of a sphere is 4r2, where r is the radius of the sphere Example Given that Radiant flux leaving sun, Ssun is 6.34 x 107 W/m2 (t4) Radius of sun is 7 x 108 m Distance from Earth to sun is 1.5 x 1011 m 1. Calculate the total radiant energy leaving the sun (Luminosity) Energy = 6.34 x 107 W/m2 (4) (7 x 108 m)2 ~ 3.9 x 1026 W 2. Calculate the solar flux reaching the Earth (Brightness) SS-E = 3.9 x 1026/[4 (1.5 x 1011)2] ~ 1,370 W/m2 {SS-E referred to as the "solar constant"} Important: Brightness varies with 1/R2 where R is the distance from the source. How constant is the "solar constant" (SS-E)? The top panel in the figure below illustrates the most recent analysis of observations of the "solar constant" over the past twenty years. Willson, R.C., and A.V. Mordinov, Time frequency analysis of Total Solar Irradiance variations, Geophys. Res. Lett., 24, 3613-3616, 1999. BASIC CONCEPTS: 4. Temperature Temperature is a macroscopic property of a substance that describes the average amount of internal energy in the substance. You can think of this internal energy as random kinetic energy. BASIC CONCEPTS: 4. Temperature Scales Celsius: defined by freezing and boiling point of water Kelvin: defined by absolute zero; i.e., temperature at which all motion stops Fahrenheit: used in US, but not by scientific community BASIC CONCEPTS: 5. Blackbody Radiation BASIC CONCEPTS: 5. Blackbody Radiation All substances at temperatures above 0 K radiate energy A blackbody is an idealized substance that radiates at all wavelengths with maximum efficiency. Important things to know Planck function: dependence of radiative flux on wavelength Wien's Law max(m) ~ 2898/Teff (Note 1m = 10-6 m) Stefan-Boltzman Law S = T4 (Radiative Flux W/m2) where = Stefan-Boltzman constant = 5.67 x 10-8 W/m2/K4 The Planck Function for Sun and Earth: Example of application of Stefan-Boltzman Law: Key concept: Effective temperature, Teff This is average temperature of a body at which it radiates energy For example: Given that the average surface temperature of the sun = 5780 K Calculate the radiant flux leaving the sun S = (5780 K)4 ~ (5.67 x 10-8 W/m2/K4) (1.12 x 1015 K4) ~ 6.3 x 107 W/m2 Note: These curves define an effective temperature for each body; that is the average temperature at which the body radiates. Do you know why? How would you use these curves to derive the sun's and the Earth's effective temperatures? Note: this is same value we had in earlier example The Effective Temperature of a Planet: Key concept: Effective temperature, Teff The average temperature of a body at which it radiates energy For a planet it is also the temperature the planet would have in the absence of an atmosphere to maintain thermal balance We can calculate a planet's effective temperature by demanding a simple energy balance Energy absorbed = Energy emitted Energy absorbed = SS-P x Areaeffective x (1 - albedo) Areaeffective = (RPlanet)2 (See next page) Energy emitted = 4 (RPlanet)2 x x (Teff of Planet)4 Solving we obtain: (Teff of Planet)4 = (SS-E/4) (1/) (1 - albedo) Energy absorbed by Earth: The effective area for absorbing radiation is the equivalent 2dimensional circle facing the sun; i.e., (RPlanet)2 Note: Sun's rays only illuminate the 2-d circle surrounding Earth. Rays hitting at oblique angles (i.e., high latitudes) are spread out and thus are less effective. Energy absorbed by Earth: (continued) So ...Energy absorbed = SS-P x x (Rplanet)2 x (1 - albedo) Energy emitted: Energy emitted = 4 (RPlanet)2 x x (Teff of Planet)4 Figure from Turco, R.P., Earth Under Siege: From Air Pollution to Global Change, Oxford University Press, New York, 527pp, 1997 Simple model of planet's energy balance: System's diagram for planet's energy balance: Solar Irradiance Effective Temperature (-) Outgoing IR flux Albedo Figure from Turco, R.P., Earth Under Siege: From Air Pollution to Global Change, Oxford University Press, New York, 527pp, 1997 The answers to these questions are found in our next lecture when we consider the GREENHOUSE EFFECT. But first we will have Exam 1 Turco, R.P., Earth Under Siege: From Air Pollution to Global Change, Oxford University Press, New York, 527pp, 1997 Why does Teffective differ from the observed temperature? Why does the size of the difference vary between planets? If Venus is closer to the sun than the Earth, why is its Teffective so close to that of the Earth? ...
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