# Solar Flux and Flux Density. Lecture 3: Global Energy Cycle. Solar Energy Incident On the Earth. Solar Flux Density Reaching Earth

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1 Lecture 3: Global Energy Cycle Solar Flux and Flux Density Planetary energy balance Greenhouse Effect Vertical energy balance Latitudinal energy balance Seasonal and diurnal cycles Solar Luminosity (L) the constant flux of energy put out by the sun L = 3.9 x W Solar Flux Density (S d ) the amount of solar energy per unit area on a sphere centered at the Sun with a distance d S d = L / ( π d 2 ) W/m 2 sun d Solar Flux Density Reaching Earth Solar Energy Incident On the Earth Solar Constant (S) The solar energy density at the mean distance of Earth from the sun (1.5 x m) S= L / ( π d 2 ) = (3.9 x W) / [ x 3.1 x (1.5 x m) 2 ] = 1370 W/m 2 Solar energy incident on the Earth = total amount of solar energy can be absorbed by Earth = (Solar constant) x (Shadow Area) = S x π R 2 Earth 1

2 Zenith Angle and Insolation Solar Energy Absorbed by Earth (from Meteorology: Understanding the Atmosphere) The larger the solar zenith angle, the weaker the insolation, because the same amount of sunlight has to be spread over a larger area. (from The Earth System) Solar Constant (S) = solar flux density reaching the Earth = 1370 W/m 2 Solar energy incident on the Earth = S x the flat area of the Earth = S x π R 2 Earth Solar energy absorbed by the Earth = (received solar flux) (reflected solar flux) = S π R 2 Earth S π R2 Earth x A = S π R 2 Earth x (1-A) A is the planetary albedo of the Earth, which is about 0.3. Albedo = [Reflected] / [Incoming] Sunlight What Happens After the Earth Absorbs Solar Energy? The Earth warms up and has to emit radiative energy back to the space to reach a equilibrium condition. Albedo is the percentage of the sunlight that is reflected back to the space by the planet. The radiation emitted by the Earth is called terrestrial radiation which is assumed to be like blackbody radiation. 2

3 Blackbody Radiation Energy Emitted from Earth Blackbody A blackbody is something that emits (or absorbs) electromagnetic radiation with 100% efficiency at all wavelength. Blackbody Radiation The amount of the radiation emitted by a blackbody depends on the absolute temperature of the blackbody. The Stefan-Boltzmann Law The energy flux emitted by a blackbody is related to the fourth power of the body s absolute temperature F = σt where σ is 5.67x10-8 W/m 2 /K Energy emitted from the Earth = (blackbody emission) x (total area of Earth) = (σt e ) x (π R 2 Earth ) (from The Earth System) Planetary Energy Balance Greenhouse Effect (from Global Physical Climatology) Earth s surface temperature T S = 288 K (15C) Energy emitted by Earth = Energy absorbed by Earth σt e x (π R 2 Earth ) = S π R2 Earth x (1-A) σt e = S/ * (1-A) = 1370/ W/m 2 * (1-A) = 32.5 W/m 2 * (1-A) = 20 W/m 2 Earth s blackbody temperature greenhouse effect (33C)!! T e = 255 K (-18C) Greenhouse sunlight heat allow sunlight to come in trap heat inside the house S/ * (1-A) Atmosphere σt S σt A σt A For Earth s surface: S/*(1-A) + σt A = σt S For the atmosphere: σt S = 2σT A T A =T e = 255K T s = 2 ¼ T A = 303K 3

4 Greenhouse Gases Earth, Mars, and Venus Global Temperature Factors Determine Planet Temperature distance + albedo + greehouse Distance from the Sun Albedo Greenhouse effect distance + albedo distance only

5 Greenhouse Effects On Venus 510 K (very large!!) On Earth 33 K On Mars 6 K (very small) Why Large Greenhouse Effect On Venus? Venus is very close to the Sun Venus temperature is very high Very difficult for Venus s atmosphere to get saturated in water vapor Evaporation keep on bringing water vapor into Venus s atmosphere Greenhouse effect is very large A run away greenhouse happened on Venus Water vapor is dissociated into hydrogen and oxygen Hydrogen then escaped to space and oxygen reacted with carbon to form carbon dioxide No liquid water left on Venus Why Small Greenhouse Effect on Mars? Vertical Distribution of Energy Mars is too small in size Mars had no large internal heat Mars lost all the internal heat quickly No tectonic activity on Mars Carbon can not be injected back to the atmosphere Little greenhouse effect A very cold Mars!! (from Global Physical Climatology) Incoming solar energy (100) 70% absorbed 50% by Earth s surface 20% by atmosphere 3% in stratosphere (by ozone and O 2 ) 17% in troposphere (water vapor & cloud) 30% reflected/scattered back 20% by clouds 6% by the atmosphere % by surface 5

6 Selective Absorption and Emission Vertical Distribution of Energy The atmosphere is not a perfect blackbody, it absorbs some wavelength of radiation and is transparent to others (such as solar radiation). Greenhouse effect. Net=0 Outgoing radiation (70 units) 10 units by the surface 60 units by the atmosphere Objective that selectively absorbs radiation usually selectively emit radiation at the same wavelength. For example, water vapor and CO2 are strong absorbers of infrared radiation and poor absorbers of visible solar radiation. (from The Atmosphere) (from Global Physical Climatology) Net=-29 5 units by troposphere 6 units by stratosphere Greenhouse effect (89 units) from the atmosphere back to the surface Water vapor and cloud provide 80% of the greenhouse effect Greenhouse Effect and Diurnal Cycle The very strong downward emission of terrestrial radiation from the atmosphere is crucial to main the relatively small diurnal variation of surface temperature. Important Roles of Clouds In Global Climate If this large downward radiation is not larger than solar heating of the surface, the surface temperature would warm rapidly during the day and cool rapidly at the night. a large diurnal variation of surface temperature. The greenhouse effect not only keeps Earth s surface warm but also limit the amplitude of the diurnal temperature variation at the surface. (from The Earth System) 6

7 Latitudinal and Seasonal Variations Angle of Inclination = the Tilt The amount of energy absorbed and emitted by Earth geographically and seasonally. Seasonal variations: the angle of inclination is responsible for the seasonal variation in the amount of solar energy distributed at the top of the atmosphere. Latitudinal variations: the variations of solar energy in latitude is caused by changes in: (a) the angle the sun hits Earth s surface = solar zenith angle (b) albedo (c) the number of day light hours At present-day, the axis is tilted at an angle of 23.5, referred to as Earth s obliquity, or tilt. The Sun moves back and forth through the year between 23.5 N and 23.5 S. Earth s 23.5 tilt also defines the 66.5 latitude of the Artic and Antarctic circles. No sunlight reaches latitudes higher than this in winter day. The tilt produces seasons!! (from Earth s Climate: Past and Future) Seasons and the Elliptical Orbit Solar Zenith Angle Seasons Solstices: mark the longest and shortest days of the years (June 21 and December 21 in the northern hemisphere, the reverse in the southern) Equinoxes: the length of night and day become equal in each hemisphere. Solar zenith angle is the angle at which the sunlight strikes a particular location on Earth. This angle is 0 when the sun is directly overhead and increase as sun sets and reaches 90 when the sun is on the horizon. At the present-day orbit, the winter and summer solstices differ from the aphelion and perihelion by about 13 days. (from Earth s Climate: Past and Future) (from Meteorology: Understanding the Atmosphere) 7

8 Zenith Angle and Insolation What Determine Zenith Angle? The solar zenith angle is a function of time of day, time of year, and latitude. (from Meteorology: Understanding the Atmosphere) The larger the solar zenith angle, the weaker the insolation, because the same amount of sunlight has to be spread over a larger area. (from Meteorology Today) Insolation at Top of Atmosphere Insolation in Summer Solstice (from Global Physical Climatology) (from Meteorology Today) 8

9 Albedo = [Reflected] / [Incoming] Sunlight Solar Zenith Angle Affects Albedo Albedo is the percentage of the sunlight that is reflected back to the space by the planet. (from Meteorology Today) The larger the solar zenith angle, the larger the albedo. When the zenith angle is large, sunlight has to pass through a thicker layer of the atmosphere before it reaches the surface. The thinker the atmospheric layer, more sunlight can be reflected or scattered back to the space. Surface Types Affect Albedo Global Distribution of Albedo Northern Winter The brighter a color, the more it reflects sunlight. (from Earth s Climate: Past and Future) (from Global Physical Climatology) 9

10 Latitudinal Variations of Net Energy Polarward Energy Transport Annual-Mean Radiative Energy Polarward Heat Flux (from Meteorology: Understanding the Atmosphere) Polarward heat flux is needed to transport radiation energy from the tropics to higher latitudes. Polarward heat flux is needed to transport radiative energy from the tropics to higher latitudes (figures from Global Physical Climatology) (1 petawatts = W) The atmosphere dominates the polarward heat transport at middle and high latitudes. The ocean dominates the transport at lower latitudes. How Do Atmosphere and Ocean Transport Heat? Atmospheric Circulation Ocean Circulation Global Atmospheric Circulation Model (from USA Today) (top from The Earth System) (bottom from USGCRP) 10

11 Diurnal Temperature Variations Ocean Circulation (from Meteorology: Understanding the Atmosphere) 11

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