# The Atmosphere: Energy Balance The photo shows knee-deep mud and debris clogging a pedestrian underpass near the flooded Boulder Creek, Colorado.

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The Atmosphere: Energy Balance The photo shows knee-deep mud and debris clogging a pedestrian underpass near the flooded Boulder Creek, Colorado. http://epod.usra.edu/blog/2013/09/flood- debris-along-boulder-creek-colorado.html

Thermal Energy Transfer Conduction = passage of thermal energy through a body without large-scale movement of matter within the body. Most effective in SOLIDS. Convection = passage of thermal energy through a fluid (liquid or gas) by means of large scale movements of material within the fluid, as in a convection cell. Most effective in Gases & Liquids. Radiation = The transfer of thermal energy by electromagnetic radiation. The only one of the three mechanisms of heat transfer that does not require atoms or molecules to facilitate the transfer process.

The equations we seek are the poetry of nature… Why is nature that way? Why is it possible for these powerful manifestations of forces to be trapped in a very simple, beautiful formula? This has been a question which many people have discussed, but there is no answer. ~Chen Ning Yang E =  T 4 (1/d 2 ) E = h c / m = a / T

Solar Energy Most of the environmental processes acting near the surface of the Earth derive their energy from exchanges of heat between the Earth and the atmosphere above. Much of this heat comes from radiant energy initially provided by the absorption of solar radiation. The absorbed energy is used to warm the atmosphere, evaporate water, warm the surface along with a host of other processes.

Solar Energy Temperature at surface of sun is 6000°C. Some if this thermal energy is converted to radiant energy. The top of the earth’s atmosphere receives the types of shortwave radiation from the sun: –Ultraviolet (7%) –Visible (43%) –Infrared (50%) The most intense radiation is visible.

Insolation Insolation is the amount of solar radiation reaching the earth’s surface. It varies because: 1.Solar radiation interacts with the earth’s atmosphere; and 2.There are changes in the orientation between the Earth and the Sun. On average, the Earth receives 1368 W/m 2 of solar radiation at the outer edge of the atmosphere, called the "solar constant".

The Radiation Laws The final key to understanding the Greenhouse Effect.

Tying it all together the Radiation Laws The Sun’s energy is emitted in the form of electromagnetic radiation. Mostly SW (but also some LW)

The Earth’s energy (terrestrial) is also emitted in the form of electromagnetic wavelengths. Mostly LW

Emission of radiation All substances emit radiation as long as their temperture is above absolute zero. LAW #1

LAW #2 Blackbody & Planck function concept The Sun is very similar to an “ideal emitter” (or “Black body”) (the Earth isn’t ideal as a “black body”) Black body = a hypothetical object that absorbs all of the radiation that strikes it. It also emits radiation (“Energy flux”) at a maximum rate for its given temperature.

Blackbodies (“ideal emitters”) exhibit a defined relationship between: The intensity of radiation energy (E) (i.e amount of radiation flux) they give off. And the wavelength of that radiation. This relationship is called the Planck function: E = h * speed of light / wavelength Or E = h c / (where h is Planck’s constant) h = 6.626 * 10 -34 m 2 kg / s

Planck Function: The Sun emits energy at ALL wavelengths… but the amount of Energy emitted is inversely related To the wavelength of emission The Sun radiates at the speed of light like a blackbody; but its energy flux is GREATEST at SHORTER wavelengths.

This is illustrated in this graph An emitting blackbody’s shorter wavelengths have higher intensity radiation (and greater energy flux) than the longer wavelengths. Intensity (radiation flux) peaks here

Easy way to remember the Planck Function/ Blackbody concept: The shorter the wavelength the greater the intensity of the energy flux.

1.True 2.False 3.Both wavelength bands have the same energy flux 4.We haven’t learned enough to answer this yet. Q1 - Gamma radiation involves a greater energy flux than microwave radiation.

1.True 2.False 3.Both wavelength bands have the same energy flux 4.We haven’t learned enough to answer this yet. Q1 - Gamma radiation involves a greater energy flux than microwave radiation.

Law #3: The Stefan-Boltzmann Law If the substance is an ideal emitter (blackbody) The total Amount of radiation given off is Proportional To the fourth power of its absolute Temperature

Law #3: The Stefan-Boltzmann Law E =  T 4 Where  is a constant (the Stefan-Boltzmann constant) which has a value of: 5.67 x 10 -8 J / m 2 And T is the absolute temperature (in Kelvin) Energy =  T 4

The Stefan-Boltzmann Law (made easy) This law links: the total amount of energy flux that is emitted by a blackbody to the body’s temperature (actually, the 4th power of the body’s absolute temperature) The hotter the body, the greater the amount of energy flux or radiaton

The total amount of energy flux described by the Stefan- Boltzmann Law is proportional to the area under the Planck function curve

Stefan-Blotzmann Law The Sun is hot so it emits large amounts of high intensity energy. The Earth is cool so it emits lesser amounts of energy at a lower intensity.

Why is this concept important? Because it means that: The amount of radiation given off by a body is a very sensitive function of its temperature. Therefore…small changes in temperature can lead to BIG changes in the amount of radiation given off. E =  T 4

1.The Planck Function 2.The Stefan-Boltzmann Law 3.Both of them together 4.Neither one is appropriate because the Earth is NOT a blackbody Q2 - Which would you use: the Planck Function or the Stefan-Boltzmann Law to accurately compute the total amount of Energy emitted to space by planet Earth?

1.The Planck Function 2.The Stefan-Boltzmann Law 3.Both of them together 4.Neither one is appropriate because the Earth is NOT a blackbody Q2 - Which would you use: the Planck Function or the Stefan-Boltzmann Law to accurately compute the total amount of Energy emitted to space by planet Earth?

1.The Planck Function 2.The Stefan-Boltzmann Law 3.Neither one is appropriate because you would need to know the wavelengths of radiation the Earth emits 4.No idea Q3 - Which would you use: the Planck Function or the Stefan-Boltzmann Law to accurately compute the total amount of Energy emitted to space by planet Earth, IF you assume the Earth emits like a blackbody & you know the Earth’s temperature?

1.The Planck Function 2.The Stefan-Boltzmann Law 3.Neither one is appropriate because you would need to know the wavelengths of radiation the Earth emits 4.No idea Q3 - Which would you use: the Planck Function or the Stefan-Boltzmann Law to accurately compute the total amount of Energy emitted to space by planet Earth, IF you assume the Earth emits like a blackbody & you know the Earth’s temperature?

How to do it: E =  T 4 E = Energy per unit area, so all we need to know is the Area of the emitting Earth’s surface and what T is. From geometry we know that the formula for computing the area of a sphere is: 4  R 2 E = 4  R 2 *  T 4

Law # 4: Temperature and wavelength As substances get HOTTER, the wavelength at which radiation is emitted will become shorter. This is called Wien’s law.

Wien’s Law can be represented as: m = a / T Where m is the wavelength in the spectrum at which the energy peak occurs (m indicates “max”) T is the absolute Temperature (in Kelvin) And a is a constant (with a value of 2898) (if m is expressed in micrometers)

Note the inverse relationship between wavelength and temperature

Wien’s Law (made easy) max = constant / T (inverse relationship between wavelength and temperature) The hotter the body, the shorter the wavelength The cooler the body, the longer the wavelength

Why is Wien’s Law important? Because it means that very hot objects (like the sun) that radiate like blackbodies will radiate the maxium amount of energy at Short wavelengths, Whereas cooler bodies will radiate most of their energy at longer wavelengths.

Wein’s Law: The Sun is hot so it emits its maximum amount of radiation at shorter wavelengths The Earth is cool so it emits its maximum amount of radiation at longer wavelengths.

Note: this is a logarithmic scale-- values increase exponentially Wein’s law is the law behind this process

The Radiation Laws Re-cap of Laws 2-4

Planck Function E = h c / The Sun can emit energy at All wavelengths, but the amount of energy emitted is inversely related to its wavelength. The Sun radiates at the speed of light like a blackbody; but its energy flux is GREATEST at SHORTER wavelengths.

Stefan-Blotzmann Law The Sun is hot so it emits large amounts of high intensity energy. The Earth is cool so it emits lesser amounts of energy at a lower intensity. E =  T 4

Wein’s Law: The Sun is hot so it emits its maximum amount of radiation at shorter wavelengths The Earth is cool so it emits its maximum amount of radiation at longer wavelengths. m = a / T

Q4 - Which choice correctly matches the Stefan-Boltzmann Law with its “mantra”? 1.The hotter the body, the shorter the wavelength. The cooler the body, the longer the wavelength 2.Shorter wavelengths have higher intensity radiation than longer wavelengths 3.The hotter the body the greater the amount of energy flux or radiation

Q4 - Which choice correctly matches the Stefan-Boltzmann Law with its “mantra”? 1.The hotter the body, the shorter the wavelength. The cooler the body, the longer the wavelength 2.Shorter wavelengths have higher intensity radiation than longer wavelengths 3.The hotter the body the greater the amount of energy flux or radiation

Law #5: Radiation & distance --the inverse-square law The inverse square law describes how solar Flux of Energy Decreases With increasing Distance From the source of The flux (i.e., the radiation), The Sun.

Inverse-Square Law The amount of radiation passing through a particular unit area is: Inversely proportional to the Square of the distance Of that unit area from the source (1/d 2 )

Inverse-Square Law (made easy If we double the distance from the source to the interception point, the intensity of the radiation decreases by a factor of (1/2) 2 = 1/4 If we triple the distance from the source to the interception point, the intensity decreases by a factor of (1/3) 2 = 1/9

Or if we reduce the distance from the source to the interception point by a factor of 2 or 3, the intensity of the radiation increases by a factor of 2 2 = 4 Or 3 2 = 9

Why is this concept important? Because it means that relatively small changes in distance from the source of the energy (e.g., the Sun) Can result in large changes in the amount of energy received by a planet’s surface.

Goldilocks and the 3 planets

Q5 -The inverse-square law applied to the distance between a planet and the Sun is what determines that planet’s temperature 1.Yes, this is what the Goldilocks Effect is illustrating 2.No, how much solar energy a planet reflects back must also be taken into account 3.No, whether or not the planet has a greenhouse effect must also be taken into account.

Q5 -The inverse-square law applied to the distance between a planet and the Sun is what determines that planet’s temperature 1.Yes, this is what the Goldilocks Effect is illustrating 2.No, how much solar energy a planet reflects back must also be taken into account 3.No, whether or not the planet has a greenhouse effect must also be taken into account.

Law #6: Selective emission and absorption Some substances emit and absorb radiation at certain wavelengths only. This is mainly true of gases. Recall the concept of the quantum properties of molecules and their bending, rotation and vibration.

Insolation and the Atmosphere As solar radiation travels through the earth’s atmosphere, three things can happen to the radiation: 1)Scattering 2)Reflection 3)Absorption

Scattering Radiation "bumps" into molecules and produces a large number of weaker waves traveling in many different directions but mainly forward. Blue light the most scattered length in sky (hence the blue sky) Scatter radiation is called Diffused Light

Reflection Reflected light bounces back from a surface at the same angle at which it strikes that surface and with the same intensity. Albedo is the fraction of radiation that is reflected by a substance. Expressed as a percentage (see next slide)

Albedo

Albedo = a measure of the reflectivity of the Earth’s surface. Darker objects have a lower albedo (reflectivity), lighter objects have a higher albedo (reflectivity).

Earth reflects 30% of incoming solar radiation back to space. -Fresh Snow: 75-95% -Old Snow: 40-60% -Open Water: 2-6% -Dense Forest: 5-10% How would melting Sea Ice change Earth’s albedo? Albedo

Albedo ~30% Albedo ~90%

Absorption Absorption a process in which solar radiation is retained by a substance and converted into Thermal Energy. The creation of heat energy also causes the substance to emit its own radiation In general, the absorption of solar radiation by substances in the Earth's atmosphere results in temperatures that get no higher than 1800° Celsius. Bodies with temperatures at this level or lower would emit their radiation in the long wave band.

Absorption of Incoming Solar Radiation by Atmosphere

Average distribution of incoming solar radiation

5% Scatted by Atmosphere 20% Absorbed by Atmosphere 20% Reflected by Atmosphere 5% Reflected by Surface 50% Absorbed by the surface of the earth –Mainly visible (shortwave) radiation strikes the surface. –Solar radiation is transformed into thermal molecular motion or thermal energy at the surface.

Surface – Atmosphere Heat Exchange Thermal Energy is transferred from the surface into the atmosphere in three ways: 1) Evaporation –Water evaporates at the surface and then condenses to form clouds which releases latent heat 2) Conduction/Convection –Warm surface air will rise to higher altitudes 3) Terrestrial Radiation –Due to the increase in temperature, the surface reemits infrared (long wave) radiation. –MOST COMMON

The Greenhouse Effect

Atmospheric Greenhouse Effect Step 1 Solar shortwave radiation is absorbed by the earth’s surface

Earth's surface radiates long wave radiation which is absorbed by the greenhouse gasses. Atmospheric Greenhouse Effect Step 2

Greenhouse gasses reradiated some of the energy earthward, thus trapping heat in the lower atmosphere. Atmospheric Greenhouse Effect Step 3

Atmospheric Greenhouse Effect The absorption of outgoing terrestrial infrared radiation increase the surface temperature of the atmosphere about 30°C. The average surface temperature is about 15°C. If we did not have greenhouse gasses, the surface temperature of the earth would be about -15°C!

Variations in Insolation Variations on insolation also occur due to changes in the orientation between the earth and the sun. These changes are based on: 1.Latitude 2.Time of Day 3.Time of Year

Latitude and Insolation A significant impact on insolation is the thickness of the atmosphere on depletion of a beam of light. As the amount of atmosphere through which the beam passes increases, the greater the chance for reflection and scattering of light, thus reducing insolation at the surface. Due to the curvature of the Earth, a beam of light striking the Equator passes through less atmosphere than one at a higher latitude.

Latitude and Insolation The lower the latitude, the less the path length, the higher the insolation. Thus insolation is greater at the equator (0° latitude) than at the poles (90° latitude).

Daily and Seasonal Changes in Insolation

Seasons and Sun (Azimuth) Angle Sun angle for Peoria (40°N) at the summer solstice and winter solstice. Note how the angle changes seasonally.

Seasons and Sun (Azimuth) Angle

Earth Revolution and Rotation Earth revolves around the Sun once every 365 1/4 days. The elliptical orbit of the earth varies from 147.5 million kilometers on January 3 called "perihelion", to 152.5 million kilometers on July 4 called "aphelion" for an average earth- sun distance of 150 million kilometers. The elliptical path causes only small variations in the amount of solar radiation reaching the earth.

Earth Revolution and Rotation

The Reason for the Seasons The tilt of the Earth is the reason the Northern and Southern Hemisphere have opposite seasons. Summer occurs when a hemisphere is tipped toward the Sun and winter when it is tipped away from the Sun. Day length changes through the year as the orientation of the Earth to the Sun changes

Axial Tilt

August 26 th 2011 (~1:00 am) Latitude: 76° N

June 21st Latitude: 69° N

The Reason for the Seasons

December 12 th 2011 (~3:00 pm) Latitude: 61° N

Obliquity of Earth’s Axis (axis tilts 23.5 degrees from plane of eclipic)

Earth-Sun Orbital Relationships “astronomical climate forcing” Drives natural climate variability (ice ages, etc.) on LONG time scales (geologic time, past 10,000 to 100,000 years, etc., etc.)

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