Chapter 2 Heating Earth's Surface & Atmosphere

We need to address two questions:

  1. Why do different latitudes receive different amount of solar energy?
  2. Why does the amount of solar energy change to produce the seasons?
Earth's Motions
  1. The Earth rotates on its axis, once a day (24 hours)
  2. The Earth revolves around the Sun, taking 3651/4 days on average.
  3. The Earth is about 150 million km from the Sun, and travels in an elliptical orbit, with the Sun at one focus.
  4. Closest approach of Earth to Sun (147 million km), called Perihelion , occurs in January.
  5. Furthest distance from the Sun (152 million km), called Aphelion , occurs in July.
The Seasons
  1. The seasons arise because the Earth's axis of rotation is tilted (23.5 degrees) away from the perpendicular to the plane of the Earth's rotation (called the plane of the ecliptic ).
  2. Other factors that are less important - (1) the days are longer in summer, so the Earth is heated for a longer time, (2) the sun's rays have to pass through more atmosphere in the winter.
  3. The Earth's axis always points to the same point in space (currently the Pole Star).
  4. Northern summer occurs when the northern hemisphere of the Earth is closer to the Sun than the southern hemisphere is.
  5. Heat provided by the Sun is greatest when the Sun is overhead. (Greater insolation , less absorption by the atmosphere). Energy is spread over smaller area.
  6. Solstice - Sun is vertically overhead at noon at a latitude of 23.5 degrees (Tropic of Cancer) or -23.5 degrees (Tropic of Capricorn). Have Summer and Winter solstices. 23.5 degrees is the inclination of the Earth's axis.
  7. Equinoxes - Sun is vertically overhead at noon at the equator. March/September
  8. Sun Angle is the angle from the horizon to the Sun (complement of zenith angle)
  9. Noon sun angle depends on latitude and day of year
  10. Length of day can be determined from the Circle of Illumination . Length of day for a particular latitude depends on what fraction of the circle of latitude is in daylight.
  11. Days are shortest at mid-Winter, longest at mid-Summer, and equal to 12 hours in the Equinoxes (and nights are also 12 hours long)

SO - What would the seasons be like if the Earth's axis were not tilted?

Box 2-1 When are the Seasons?

Depends on who you are talking to:



March 22 to June 21



June 22 to Sep 21



Sep 22 - Dec 21

Sep, Oct, November


Dec 22 - Mach 21


The Noon Sun Angle
Noon Sun Angle (Fig 2-6)

Measured from the horizon to the position of the sun

Calculate the noon sun angle

(1) Find the latitude λ p where sun angle is 90 degrees.

(2) At latitude λ, the sun noon angle is 90 - |λ - λ p |

Noon sun angle at Lowell on June 21

Angle = 90 - |42.0 - 23.5| = 71.5. (Sun is vertical at +23.5)

Noon sun angle at Lowell on December 21

Angle = 90 - |42.0 + 23.5| = 25.5 (Sun is vertical at -23.5)

Noon sun angle at Hobart (42S) on Dec 21

Angle = 90 - |-42.0 -(-23.5)| = 90 -18.5 = 71.5 (same as Lowell, June 21)

SO - Does the Sun get directly overhead of any location in mainland USA?

Box 2-2 The Analemma

Show the latitude where the noon Sun is directly overhead for each day of the year.

Used for estimating the angle of the Sun for any location and any day of the year.

For example, what is the noon Sun angle for Boston (40N) on April 20?

Sun is overhead at 11 degrees N.

Noon Sun angle at Boston is 90 - (40 - 11) = 90 - 29 = 61 degrees

Energy, Heat & Temperature
  1. Energy is the ability to do work.
  2. Many different types of Energy (mechanical, chemical, nuclear, heat, kinetic, electromagnetic radiation)
  3. Total energy of a closed system is always conserved, but energy can change to another form.
  4. Kinetic energy is energy due to motion. If a gas is heated, its molecules move faster. For a mass m, KE = (1/2)mv 2 .
  5. Potential energy is energy possessed by a system of objects that act on each other. e.g,. a ball at the top of a hill has gravitational potential energy.
  6. Heat energy of a system of particles is the total kinetic energy of all the constituent particles
  7. Temperature is a measure of the average kinetic energy of the constituents
    KE = (3/2) kT, where T is the absolute temperature, and k is Boltzmann's constant (1.38x10 -23 joules/kelvin)
  8. When two bodies are in contact, heat flows from the one with the higher temperature to the one with the lower temperature.
Mechanisms of Heat transfer
  1. Conduction - transfer of heat through matter by molecular motion
  2. Convection - transfer of heat by mass motion or circulation
  3. Radiation - transfer of electromagnetic energy by electromagnetic waves
  4. Metals are good conductors. Poor conductors such as cork, wood, foam, and air are good insulators . The more air in a substance, the better the insulation.
  5. Convection is very important in the atmosphere. Large "parcels" of air warmed by the Sun will rise in altitude, while cooler air rushes in to take its place.
  6. The horizontal part of any convective flow (in a loop) is called advection, or wind.
  7. For example, hot air rises in the tropical zones, flows polewards (as a wind), while cool air from the polar regions moves towards the tropics and closes the loop.
  8. Solar radiation is the ultimate source of energy that drives the weather machine.
  9. The Sun emits EM radiation at all wavelengths, ranging from very short gamma rays to very long radio waves. The intensity is greatest between 0.4 and 0.7 micrometers, i.e., in the visible band of the spectrum.
  10. EM radiation travels (at the speed of light) 3x10 8 m/s - book says per hour )
  11. Infrared radiation has a wavelength longer than visible red light.
  12. Ultra-violet radiation has shorter wavelengths than the visible blue light.
Box 2-3 The Ultraviolet Index

Determined from

  1. The sun angle
  2. Predicted cloud cover
  3. Reflectivity of surface
  4. Extent of ozone layer
Laws of Radiation
  1. All objects with temperatures above absolute zero (0 kelvins, -273C) radiate energy to their surroundings
  2. A hot object radiates more total energy than a cold object (Stefan-Boltzmann Law)
  3. The hotter the radiating body, the shorter the wavelength of the maximum radiation (Wien's Displacement Law)
  4. Objects that are good emitters of radiation at all wavelengths are also good absorbers of radiation. The perfect absorber is called a Black Body .
Box 2-4 Radiation Laws

Planck's Law

All objects that are not at absolute zero radiate energy.

Stefan-Boltzmann Law E = σT 4

E is the rate of energy flow (watts/m 2 ). T is the absolute temperature. "σ" (sigma) is a constant of Nature called the Stefan-Boltzmann constant. The Sun (visible photosphere is 6000 K) emits more radiation per second per square meter than the Earth at 300 K, by a factor of (6000/300) 4 = 160,000.

Wien's Displacement Law λ max = C/T

λ max is the wavelength at which the radiation reaches its maximum intensity. C is Wien's constant, T is absolute temperature. For the Sun, T = 6000 k, so λ max = 0.483 μm (visible). For the Earth, T = 300 K, so λ max = 9.66 μm (infra-red).
λ max = 2898/T if wavelength is measured in μm.

Kirchoff's Law

A good emitter of radiation is also a good absorber.

What happens to Incoming Solar Radiation?

Radiation may be absorbed, transmitted, or re-directed

  1. 50% of sunlight reaches the Earth's surface
  2. 20% absorbed by atmosphere and clouds
  3. 20% reflected by clouds
  4. 5% reflected from land-sea surface
  5. 5% scattered back into space by the atmosphere
Reflection and Scattering
  1. Reflection is the process whereby light bounces back from an object at the same angle at which it encounters that surface, and with the same intensity. Snell's Law,
    i = r. Surface is much larger than the wavelength of the light.
  2. Scattering occurs when light encounters an object with a rough surface, or a collection of particles. Energy is scattered in all directions, but mainly in the forward direction. Surface is much smaller than the wavelength of the light.
  3. Albedo of a surface is the fraction of incident radiation that is reflected by that surface.
  4. Albedo of the Earth varies from place to place, and from time to time. On average, it is 30% (reflections - 20% by clouds; 5% by land/sea; 5% back-scatter)
  5. Fresh snow has the highest albedo, water the lowest when the Sun is nearly overhead)
  6. Scattering by the atmosphere - depends on 1/λ 4 . Blue light scattered more than red.
  7. Blue sky is caused by scattering of the blue part of the Sun's white light by nitrogen molecules.
  8. Red sunsets are caused by the scattering of the blue light out of the Sun-observer path. Light passes through a lot of atmosphere.
Radiation Emitted by the Earth
  1. Gases are selective absorbers - they absorb radiation at only particular wavelengths, and get hotter
  2. Most absorption is due to water vapor, oxygen and ozone (not nitrogen)
  3. Atmosphere is almost transparent to visible light, which therefore does not heat the atmosphere
  4. Oxygen & ozone absorb UV radiation
  5. Water vapor absorbs infrared radiation
  6. Infrared radiation at 8 to 11μm can escape from the Earth (the atmospheric window ) - can also reach the Earth from space; used by "infrared astronomers"
  7. Sunlight heats the Earth, then the Earth heats the atmosphere from below , hence the temperature decrease with altitude (normal lapse rate of 6.5 O C/km)

SO - what causes leaves to change color each Fall?

The Greenhouse Effect
  1. Most of the energy reradiated by the Earth's surface is in the infrared
  2. This radiation is absorbed by water vapor, carbon dioxide, and a few trace gases
  3. These gases get hot, so radiate heat back to the Earth (but some to space)
  4. Earth gets hotter, emits more radiation (Stefan-Boltzmann), and cycle goes on
  5. This effect is called the Greenhouse Effect , which keeps the Earth's average temperature 30 C warmer than it otherwise would be - a good thing
  6. Not the same process as occurs in garden greenhouses
Why is Venus so hot?
  1. Venus has a runaway greenhouse effect
  2. Surface temperature 480 C
  3. Atmosphere is mostly carbon dioxide, and has no water or life to change the carbon dioxide to oxygen
  4. Will the burning of fossil fuel (carbon) on the Earth, raise the Earth's temperature?
Role of Clouds in Heating the Earth
  1. Daytime - High thin clouds (thin) trap the Earth's radiation, and make the Earth warmer
  2. Daytime - Thick clouds (dark) reflect solar radiation, so Earth is cooler
  3. Night - Thick cloud cover absorbs heat from Earth, re-radiates it back to Earth, so Earth keeps warm
  4. Night - Clear skies mean that the Earth's radiation can escape to space, cooling the Earth
  5. Day and night temperatures can be very close during cloudy weather
Box 2-5 Infrared Imaging
  1. We "look" at the world at different wavelengths
  2. Visible - animals
  3. Infrared - astronomers, meteorologists
  4. Ultra-violet, X-ray, Radio Waves - astronomers
Earth's Heat Budget / Latitudinal Heat Balance
  1. Average temperature of Earth remains "constant" because the Earth re-emits almost all incoming solar radiation
  2. Earth's Heat Budget is balanced
  3. Tropical regions actually lose less energy than they gain from the Sun, while polar regions lose more energy
  4. Difference between incoming and outgoing radiation is called the heat surplus
  5. Latitude of heat surplus changes with the seasons - e.g., large in northern hemisphere in June (summer)
  6. Tropics are not getting hotter and hotter, and the poles are not getting colder and colder, because heat is carried from the tropics towards the poles (and vice versa) by winds (called the general atmospheric circulation )
Solar Radiation hitting the Earth

Radiation is power per square meter. (kWh/m2/day used in figures)

Fig 2-23 top shows June, northern Summer

These are false-color-images - our eyes cannot see infrared radiation

Measurements by satellites over ~10 years

Fig 2-23 bottom shows December, northern Winter, southern Summer

Box 2-6 Solar Power
  1. Solar collectors focus large amounts of solar radiation onto a body containing circulating fluid (such as water)
  2. Photovoltaic cells convert solar energy into electricity
  3. Solar power is not always available
  4. Initial costs are high
  5. Most people choose the cheapest solution if possible