Atmos 1020 - University of Utahmacegroup.chpc.utah.edu/class/1020/atmos1020_class_slides_20170911.pdf · 2017-09-11 · Atmos 1020 – Lecture 2 The Radiation Balance of the Atmosphere

Atmos 10209/11/2017

2017 Sea Ice Extent

https://neptune.gsfc.nasa.gov/csb/index.php?section=234

Atmos 1020 – Lecture 2The Radiation Balance of the Atmosphere

• We have already discussed the concept of energy conservation as it relates to the incoming solar energy and the outgoing thermal infrared energy.

• What are the magnitudes of typical energy fluxes?• Noontime sunny day solar energy at the surface:

~ 1000 watts/square meter• Upwelling infrared energy from a warm surface:

~ 400 watts/square meter

• Book speaks of an energy imbalance: For a doubling of CO2 in the next 50 years, we expect a total of 4 watts/square meter overall change – or 1/5 watt/square meter annual imbalance in energy – a change that is not measureable.

Newton: Force needed to accelerate a mass of one kilogram to a speed of one meter per second in a second.(1 N is the force of Earth's gravity on a mass of about 100 g – a small apple)

Joule: applying a force of one newton through a distance of one meter.(the energy required to lift a small apple one meter straight up.)

If 1 Joule is applied for 1 second then a Watt has been expended.

So a 100 Watt light bulb expends 100 Joules each second

For perspective:

It would take about an hour and 10 minutes for the energy that powers a 100 W bulb to take a kg of water (2.2 lbs) from freezing to boiling.

A 200 cal energy bar has 837,000 Joules. To consume that energy in an hour you would have to burn it at a rate of 232 Watts.


VisibleImage

InfraredImage


What is electromagnetic radiation? Oscillating electric and magnetic fields (waves) emitted by accelerating electrical charges or energy transitions from an energized state to a lower energy state.

Some properties of electromagnetic radiation: • propagates through a vacuum (volume empty of matter)• moves at the speed of light (c=3x108 m/s)• Has a characteristic wavelength (λ) (measure of distance from wave peak to peak).• Has a characteristic frequency (f) (number of wave peaks passing a point in some amount of time)• c= λf relates the speed, wavelength and frequency.• electromagnetic radiation with wavelengths between about 0.4 and 0.7 micrometers (10-6 meters) can be sensed by the human eye as visible light.

Exact valuesmetres per second 299,792,458

Approximate valueskilometres per second 299,792.5kilometres per hour 1,079 millionmiles per second 186,000miles per hour 671 millionastronomical units per day 173

Approximate light signal travel times

one kilometre 3.3 µsone statute mile 5.4 µsfrom geostationary orbit to Earth 119 msthe length of Earth's equator 134 msfrom Moon to Earth 1.3 sfrom Sun to Earth (1 AU) 8.3 minfrom Alpha Centauri to Earth 4.4 yearsfrom the nearest galaxy to Earth 25,000 yearsacross the Milky Way 100,000 yearsfrom the Andromeda Galaxy to Earth 2.5 million years

Historical attempts at estimating the speed of light:

•Prior to the mid 17’th century it was assumed that the speed of light was infinite

•Galileo proposes using changes to the eclipse of the moons of Jupiter as a way of determining longitude on Earth in 1616.

• Ole Christensen Rømer observed eclipses in Copenhagen while Cassini observed eclipses in Paris. They were able to confirm Galileo’s approach. However, there were inconsistencies. When the Earth was moving toward Jupiter they got one period and when Earth was moving away they got another.

•Rømer proposed in 1676 that these inconsistencies were due to the fact that light had a finite speed.

•Concept confirmed in 1727 and an accurate light speed derived in 1809 by Delambre using Jupiter’s moons and a precise clock.


Why do we care?

Visible Light carries energy from the sun to earth

Infrared Light is emitted by the earth to space

Meanwhile the climate happens


Because light is related to energy and energy is related to temperature, there is a natural equivalence between the color of light and temperature.

Fundamentally, the hotter something is, the more energy (light) it emits and the bluer the color is (bluer is equivalent to shorter wavelengths).

Energy emitted by an object is proportional to the 4th power of the temperature

So, a doubling of temperature means that the energy emitted increases by a factor of …

24=2x2x2x2=4x4=16


Back to the Earth….

Fundamentally, the cooler something is, the redder the color is….

Temperature of the sun – 5700 KTemperature of the Earth – 250 K Frequency

Wavelength


Relating this concept everyday stuff….

Fundamentally, the cooler something is, the longer the wavelength is….

Frequency

Wavelength


Because light is related to energy and energy is related to temperature, there is a natural equivalence between the color of light and temperature.

Energy emitted by an object is proportional to the 4th power of the temperature

So, a doubling of temperature means that the energy emitted increases by a factor of …

24=16

Implication: ? Asmallchangeintemperaturecanaccountforalargeimbalanceinenergy.

Takeaway from our discussion of Friday:

An imbalance in energy can be balanced by a proportionally MUCH smaller change in temperature.

For instance:

Doubled CO2 is expected to change the surface energy balance by about 2%.

This can be balanced by a temperature change of 0.5%.

For a surface temperature of 290K (23 C, 75 F) this equates to a change in temperature change of 1.5 K (1.5 C, 1.1 F).

This is smaller than what is predicted from climate models (~ 4-6 K). Why?

Inverted IR Image:

White means a lot and black means little IR reaching the satellite sensor.

Both Sides of the Energy Balance Equation…

White is equivalent to energy moving away from the earth

Infrared or Energy to Space

Solar or Energy Absorbed

Both Sides of the Energy Balance Equation…

Black is equivalent to energy retained within the earth

Infrared or Energy to Space

Solar or Energy Absorbed

The Sun


Fundamentally, the hotter something is, the more energy (light) it emits and the bluer the color is.

http://earthsky.org/brightest-stars/blue-white-rigel-is-orions-brightest-star

600 ly3100K

860 ly12,000K


Electromagnetic energy falling on or emanating from a surface is usually described in terms of the amount of energy of a certain color interval flowing to or from an element of surface area during some time interval.

This quantity is termed intensity (I) and typically has units of Joules per second per square meter per unit wavelength

Or Watts per Square Meter when summed over all colors…

Consider a 100 watt light bulb at the center of a circular light shade. The shade has a radius of 1/2 meter. The intensity of the light from the bulb falling on the shade is the number of watts divided by the area the shade:

100/(4*pi*r2)=100/(4*3.14*0.25)=32 Watts/m2.

What happens if we double the radius (r) of the lamp shade?

How much total energy is hitting the larger shade?

But how has the area of the shade increased?


Still 100 Watts

By the change in the radius (a factor of 2) squared – or 22=4


So by doubling the radius of the lampshade we are putting the same amount of energy into a factor of 4 larger area – so we had 32 W/m2 but now we have 32 divided by 4 or just 8 Watts/m2!

The amount of energy per unit area decreases as the square of the distance from the source.


How is all this relevant?

Think of the sun as the bulb and the earth as occupying a tiny fraction of a circular lamp shade 193 million miles from the bulb!


To determine what the energy balance is, we need to start by determining how much solar energy reaches the top of the earth’s atmosphere:

This will depend on how much energy the sun puts out and also the area over which that energy is spread after it reaches a distance equal to the earth’s distance from the sun – imagine the earth plastered to a lampshade surrounding the sun.

At the sun’s surface:I=total solar output/area of the sunI=3.9x1026 W/6.01x1018 m2=65,000,000 Watts/meter2

At the top of Earth’s Atmosphere:I=total solar output/(4*pi*(earth to sun distance)2)I=3.9x1026 W/(4*3.14*(1.5x1011meters)2)=1368 Watts/meter2

Sizeofthe”lampshade”


1368 w/m2 is the energy hitting a flat plate perpendicular to the solar energy stream at the top of the earth’s atmosphere.

This number is known as the solar constant.

The figure to the right shows measurements of the solar constant from several satellites.

Documents

Atmos 1020 - University of Utahmacegroup.chpc.utah.edu/class/1020/atmos1020_class_slides_20170911.pdf · 2017-09-11 · Atmos 1020 – Lecture 2 The Radiation Balance of the Atmosphere