Atmos 1020Slides9/10/2018

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.

Atmos 1020 – Lecture 2The Radiation Balance of the Atmosphere

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

•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 rate of change that is not measureable.

Visible Image

Infrared Image

Atmos 1020 – Lecture 2The Radiation Balance of the Atmosphere

What is electromagnetic radiation (light)? 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 (a 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 billionmiles 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 proposed using changes to the eclipses 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.

Atmos 1020 – Lecture 2The Radiation Balance of the Atmosphere

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

Atmos 1020 – Lecture 2The Radiation Balance of the Atmosphere

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

Atmos 1020 – Lecture 2The Radiation Balance of the Atmosphere

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

Atmos 1020 – Lecture 2The Radiation Balance of the Atmosphere

Relating this concept to everyday stuff….

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

Frequency

Wavelength

Atmos 1020 – Lecture 2The Radiation Balance of the Atmosphere

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: ? A small change in temperature can account for a large imbalance in energy.

Atmos 1020 – Lecture 2The Radiation Balance of the Atmosphere

In words: Temperature Change to the fourth power equals the change in Energy. or: 24=2x2x2x2=16

Implication: A small change in temperature can offset a large change in energy.

Example: doubling the absolute temperature results in how large a change in emitted energy?

Turn this around. Say we needed a 16 fold increase in Energy. What would the change in temperature need to be?

Graphic Source: Ribas, Ignasi (2010), "The Sun and stars as the primary energy input in planetary atmospheres", Solar and Stellar Variability: Impact on Earth and Planets, Proceedings of the International Astronomical Union, IAU Symposium, 264, pp. 3–1

How has the Earth’s temperature remained temperate as the Sun’s brightness has increased by 25%?

Temperature change=fourth root of the Energy change

1.251/4=1.057So a 25% increase in solar energy has resulted in only a 6% increase in Temperature

Atmos 1020 – Lecture 2The Radiation Balance of the Atmosphere

The 4th power dependence between temperature and energy is one of the most important physical relationships in the climate system (in all of physics, to be honest)!

Why?

Since Energy in=Energy out and Energy out depends on temperature to the 4th power, it takes relatively small changes in temperature to counter imbalances in the Ein=Eoutrelationship.

The implications of this are profound and help explain why the Earth has remained habitable even as the sun has brightened over geologic time.

Summary:

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