Energy to drive the Climate

Earth’s Energy Budget, Solar Radiation

Nili HarnikDEES, Lamont-Doherty Earth Observatory

nili@ldeo.columbia.edu

Where does the Energy come from?The primary energy sources for the Earth’s climate system are gravitational energy

and solar radiation. The Earth absorbs solar radiation and after transformation, emits it back to space. How this energy is transformed and distributed on Earth shapes its climate.

Earth’s energy balance

Outline

The Earth Radiation Budget Part 1: Energy from the Sun

• Energy, and the Physics of Radiative Heat Transfer • Black Body radiation• The Sun and its Energy• Radiation from Sun to Earth

The Earth Radiation Budget Part 2:Energy from Earth

• The Earth's Albedo• Effective Temperature• The "greenhouse" effect

What is Energy?Energy is a latent property of every physical system,

describing its ability to perform work. When energy is released it is converted to either work

(which implies motion of bodies or matter) or another form of energy such that the sum of work and energy is always conserved.

In other words, energy is never destroyed but it can be transformed from one kind to another.

Units of EnergyEnergy is measured in units of work:

The MKS unit for energy is the Joule (J): 1 Joule is equal to the work spent by moving a body with a forceof 1 Newton over a distance of 1 meter, or the work that could be gotten from bringing to halt a mass of 1 kg moving at a speed of 1 m/sec, or the work that has to be invested to increase the elevation of a body weighing 1 kg by 10.2 cm.

Other units of energy are the calorie and the Btu (British thermal unit).The calorie is defined as the energy spent raising the temperature of 1 gram of

pure water by 1 degree Centigrade. 1 calorie = 4.185 JoulesThe Btu is defined as the energy required to raise the temperature of 1 lb of pure

water by 1 degree Fahrenheit. 1 Btu = 251.996 calories = 1054.6 joules

Forms of Energy:

Thermal energy: the ability to do work through the release of heat. It is related to temperature and to the phase of matter. Electromagnetic wave energy: energy embedded in electromagnetic wave motion (such as light, microwaves, or x-rays). When this kind of energy impinges on matter part or all of is converted to thermal energy.Nuclear/atomic/molecular energies: associated with to the nuclear, atomic, and molecular states of matter - related to electromagnetic wave energy. Kinetic energy: the ability to do work due to motion.Gravitational (or potential) energy: the ability to do work through changes in a body's location within a gravitational field (elevation).Electrical energy: Related to the position of charged particles in an electrical field (in meteorology it is responsible for lightening and thunder).Chemical energy: the ability to do work via a chemical interactions - that is, the forming or breaking of chemical bonds.

The sun is composed mainly of hydrogen and helium. In the Sun's interior a thermonuclear fusion reaction converts the hydrogen into helium releasing huge amounts of energy. The energy created by the fusion reaction is converted into thermal energy (heat) and raises the temperature of the sun to levels that much larger that of the earth's surface. The solar heat energy travels through space in the form of electromagnetic waves enabling the transfer of heat through radiation.

http://seds.lpl.arizona.edu/nineplanets/nineplanets/sol.html

Radiation: Electromagnetic WavesElectromagnetic waves are generated by moving electrons. Since all matter contains electrons, which are in motion, as are the atomic nuclei they spin around, all matter generates electromagnetic waves.

Properties of Waves

Properties of Electromagnetic waves

The wavelength is usually measured in microns (one millionth of a meter, 10-6) or nanometers (one billionth of a meter, 10-9) and is denoted by the Greek letter lambda (λ).

The frequency is denoted by the Greek letter mu (µ).

The product of wave number and frequency is referred to as the wave speed, denoted by the latin letter c. Thus we can write:

λ * µ = c

The speed of electromagnetic waves is a constant equal to 3 x 108 m/s (also known as the speed of light).

Energy of Electromagnetic waves

Since all electromagnetic waves travel at the same speed (c) thefrequency of the waves is determined by the frequency of the vibrating electrons that generate them. The higher the frequency, the shorter the wavelength.

Energy of Electromagnetic wavesHigher frequency (shorter wavelength) waves have higher energy.Hot substances have more energy and their component atoms vibrate more rapidly than those of cold bodies.

Power, and Energy Flux

Power is Energy per unit of time. The MKS unit for power is Watts (1 W=1 Joule/sec)

Flux is the amount of energy that passes perpendicularly through a unit surface area, per unit of time. We measure it in Watts per square meter (W m-2)

Black Body RadiationAll bodies in the universe radiate energy at a rate which is proportional to the absolute temperature of the body. For a body to be in thermal equilibrium with a source of radiation it must radiate as much energy as it receives. Thus, the efficiency with which abody absorbs radiation must equal the efficiency with which a body radiates radiation. So if a body absorbs with 100% efficiency then it should also radiate at 100% efficiency. Such a body is called a black body.

Radiation and TemperaturePlanck's law states a complex (and non-linear) relationship

between the energy flux per unit wavelength, the wavelength and the temperature.

Wien's law states that the wavelength of the maximum intensity is inversely proportional to the temperature:

λmax= a / T λmax is in µm, T is in K, and a=2897 µm K.

The Stefan-Boltzman law states that the energy flux released by a black body is proportional to the fourth power of its absolute temperature.

I = σ T4

I is in W/m2, T is in K, and σ = 5.67 x 10-8 W m-2 K-4.

Black Body Emission

Stephen-Boltzman:The area under the

curve: I = σ T4 Wavelength

Rad

iatio

n flu

x

Weins law: λmax= a / Tλmax (sun) < λmax(earth)

I(sun) > I(earth)

Planck’s law: relating radiation flux to wavelength

5780 K

288 K

The Sun and its Energy

The Sun is a black body of 5780K.

Solar radiation is rather sharply centred on the wavelength band of 0.2-2(µm). Its range includes ultraviolet radiation (UV, 0.001-0.4 µm), visible radiation (light, 0.4-0.7 µm), and infrared radiation (IR, 0.7-100 µm).

The total energy flux at the surface energy flux at the surface of the Sun is approximately of the Sun is approximately 63 x 1063 x 1066 W/m2 (StephanW/m2 (Stephan--Boltzman'sBoltzman's Law).Law).

Radiation from Sun to EarthWhile the energy flux leaving the sun is 63x106 W/m2,

the energy flux reaching the top of the Earth's atmosphere is only about 1360 W/m2. Why?

When electromagnetic radiation spreads from a localized source, such as the Sun, it usually does so in a directionally uniform way.

Far enough from the source, the radiated energy will be equally distributed on a surface of a sphere centered on the emitting object. Assuming that the total radiative energy emitted from the source is fixed, then as the distance from the emitting object increases, the same total amount of radiation is distributed over a larger sphere.

Spreading of RadiationThe decrease of flux is inversely proportional to the increase in the surface area of the sphere. The area of a sphere of radius r is: 4πr2.

Therefore, radiation follows an inverse square law:

I (r) = I0r02 / r2

I - energy flux at a distance r from the source.

Io – energy flux at a reference distance ro.

Geometric effects on the amount of solar radiation reaching the Earth

A. Effect of orbit's shape:

The radiation at the top of the atmosphere varies by about 3.5% over the year, as the Earth spins around the Sun. This is because the Earth's orbit is not circular but elliptical, with the Sun located in one of the foci of the ellipse.

The point where Earth is closest to the sun is the perihelion, and the point where the earth is furthest from the sun is called aphelion.

The time-of-year when the Earth is at perihelion moves continuously around the calendar with a period of 21000 years. At present it occurs in the middle of the Northern Hemisphere winter. Aphelionoccurs in the middle of the Northern Hemisphere summer.

B. Effect of Earth’s spherical shape

1

2

The effect of the tilting earth surface is equivalent to the

tilting of the light source

If the Earth were a disk with its surface perpendicular to the rays of sunlight, each point on it would receive the same amount of radiation, equal to the Solar constant (S).However, the Earth is a sphere and aside from the part closest to the sun, its surface tilts with respect to the incoming rays.The area over which radiation spreads varies as the cosine of latitude.

The seasonsC. The effect of the tilt of the Earth's axis (obliquity):The obliquity causes the length of day to vary with latitude.

This effect is largest during winter/summer solstice, and is zero during vernal/autumnal equinox.

The difference between day and night is zero at the equator, and increases poleward. The day is longer than the night on the hemisphere tilting towards the Sun, leading to more incoming Solar energy (per day/month) than in the other hemisphere.

Daily incoming solar radiation at the top of the atmosphere (W/m2)

Averaged over a full 24-hour period, the amount of incoming radiation varies with latitude and season. At the poles, during solstice, the earth is either exposed to sunlight over the entire (24-hours) day or is completely hidden from the Sun throughout the entire day. This is why the poles get no incoming radiation during their respective winter or more than the maximum radiation at the equator during their respective summer.

Latit

ude

Time of yearBased on ERBE data

OutlineThe Earth Radiation Budget Part 1:

Energy from the Sun

• Energy, and the Physics of Radiative Heat Transfer • Black Body radiation• The Sun and its Energy• Radiation from Sun to Earth

The Earth Radiation Budget Part 2:Energy from Earth

• The Earth's Albedo• Effective Temperature• The "greenhouse" effect

Three Aspects of Radiationinteracting with matter

The processes that affect incoming solar radiation in the Earth’s atmosphere, and their value in %

Reflection of Solar Radiation: The Earth’s Albedo

The fact that the Earth is visible from space indicates that it reflects incoming solar radiation.

The ratio between incoming and reflected radiation at the top of the atmosphere (TOA) is referred to as the planetary albedo, and is denoted by alpha (α).

The albedo varies between 0 and 1.The albedo of the Earth depends on the

geographical location (land/ocean, vegetation, type of surface, clouds). On the average, it is about 0.3.The other 0.7 of the incoming solar radiation is absorbed by our planet: Iabs=S(1-α)

Absorption of solar radiation by the Earth: The Effective Temperature

The response of the Earth to the incoming solar radiation sets the planetary temperature and its climate.

By absorbing the incoming solar radiation, the Earth warms up and its temperature rises.Since the Earth is a Black Body, the amount of radiation it emits will also rise (Stephan-Boltzman law). This process stops when an equilibrium is reached: when the total emitted radiation equals the total absorbed radiation. Thetemperature at which this happens is called the Effective Temperature.

The Effective Temperature: the geometric factor for a Spherical Planet

Total energy received from the

Sun after reflection:

Iabs=πr2S(1-α)

Total energy emitted to space from the earth:

Iem=4πr2σTe4

Iabs=Iem πr2S(1 - α) = 4πr2σTe4

Solving for Te we obtain the effective temperature:

Te = [ (1-α) S / 4 σ ] 1/4

The year-round averaged energy flux at the top of the atmosphere is S0 =1367 W m-2. With an albedo of a=0.3, we have Te=255 K or -18°C.

This temperature is much lower than the average surface temperature of Earth (288 K or 15°C). The reason for the difference lies in the greenhouse effect.

The Effective Temperature

Take away ideas and understandings

• Understand the law of conservation of energy • Solar energy and gravitational energy are the ultimate

sources of energy to power all climate subsystem processes.

• Understand black body radiation. • The relationship between the absolute temperature of a

black body and the energy flux it radiates.• The relationship between the wave length of the maximum

energy output of a black body and its absolute temperature.• Why the intensity of a light dims as you move away from it.

Take away ideas and understandings

• You should be able to use these relatively simple relationships to calculate the effective temperature of the Earth (or any other planet) given the temperature of the sun, and the Earth(planet)-to-Sun distance.

• You should know why the Earth is warmer at the equator than it is at the poles.

• You should know, in a qualitative way, why the energy of a beam of electromagnetic radiation is proportional to its frequency and why this is important.