Energy to drive the Climate Earth’s Energy Budget, Solar Radiation, The Greenhouse Effect Martin Visbeck DEES, Lamont-Doherty Earth Observatory [email protected]

Energy to drive the Climate

Earth’s Energy Budget, Solar Radiation,

The Greenhouse Effect

Martin VisbeckDEES, Lamont-Doherty Earth Observatory

[email protected]

Take away ideas and understandings

Energy cycle of absorbed sunlight, emitted heat, and transport drives weather and climate.

• Intensity of sunlight decreases with distance according to inverse square law.

• Clouds and surface types regulate absorption of sunlight.

• Emitted energy is very sensitive to small changes in temperature.

• Hot objects (e.g., Sun) radiate more, and radiate at shorter wavelengths than cool objects (e.g., Earth).


• 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.


• 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.

INTRODUCTION (SYSTEM)

The Earth is a complex dynamic system consisting of three closely interacting subsystems:

• the solid earth, or rock, subsystem,

• enveloped by the climate subsystem

consisting of three fluids - air, water and ice -

• which contains the life subsystem, encompassing all life, including ourselves. • All subsystems are dynamic, with processes operating on time scales ranging from seconds to billions of years, and space scales ranging from the atomic to the global.

Elements of the Climate system

INTRODUCTION (ENERGY)

All subsystems are powered by gravitational energy and energy generated at the atomic level, either within the Earth or within the Sun.

Radiant energy from the Sun streams through 93 million miles of nearly empty interplanetary space to warm our planet's surface and to drive the climate subsystem, most of the life subsystem, and part of the rock subsystem.

The Earth's energy, through conduction and convection, drives most of the rock subsystem and a small part of the life subsystem, but not much of the climate subsystem.

INTRODUCTION (Interaction)

The flow of matter and energy is continuous between the subsystems. The climate subsystem's fluids originated in the solid earth and continue to recycle through it. Life most likely originated in these fluids and draws chemicals from both the climate and rock subsystems, thereby modifying their composition. Today, the life subsystem is responsible for maintaining the non-equilibrium composition of the atmosphere.

The boundaries between subsystems are largely transitional. The top of the atmosphere, more than one hundred kilometers above the Earth's surface, merges imperceptibly with interplanetary space. Water, air, and, in polar regions, ice extend kilometers below the solid Earth's surface, and recent data indicate that life does too.

INTRODUCTION (Whole System)

The traditional disciplines of biology, meteorology, oceanography, and geology look at various pieces of the Earth system and so we have had a tendency to arbitrarily divide it into compartments that correspond to the domains of these disciplines. This compartmentalization of a single system into arbitrary subsystems tends to obscure the properties of the whole system and in this course we will make an effort to put the system back together, recognizing that we must of necessity focus on aspects of the system and processes within the system. We will draw from the traditional disciplines of physics, chemistry and biology for concepts to help us understand the planet's processes and history.

Why is climate important?

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n u cleu sA. What is climate?

Important characteristics of all the planets are controlled by their climates.

Local climate - long term average of local weather.

Global climate - long term average of global weather.

B. How can we understand the Earth’s climate?

The Climate System and Humans

In our generation climate is receiving unprecedented attention due to the possibility that human activity on Earth during the past couple hundred years will lead to significantly large and rapid changes in our environmental conditions, changes that will affect our health, comfort levels, and ability to grow and distribute food.

The Climate System part of the Water and Climate course

This course introduces the climate system and the processes that determine its state as a problem in physical science.

Our goal is to explain the properties of the climate system and the processes governing it in a quantitative manner, so that a better understanding of today's environmental issues can be achieved.

The climate part of the course is mainly concerned with the properties of atmosphere and hydrosphere and the physical laws governing their behavior.

Where does the Energy come from?

We begin this course in a study of the primary energy source for Earth and its climate system - solar radiation.

We examine the properties of the Sun and its energy and the laws governing the transfer of this energy through space to Earth.

We then study in detail the transformation of this solar energy on Earth and gain first appreciation on how this energy shapes the properties of Earth's climate.

Outline of this Lecture

The Earth Radiation Budget Part 1: Energy from the Sun

The Sun and its EnergyThe Physics of Radiative Heat TransferRadiation from Sun to Earth

The Earth Radiation Budget Part 2: Energy from Earth

The Earth's AlbedoEffective TemperatureThe "greenhouse" effect

What is Energy?

Energy is an abstract quantity that matter or a wave possesses. We can measure its effects but we can not measure it directly.

Energy is always conserved.

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

Units of Energy1. Energy 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 force of 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 Joules

The 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

Kinds of Energy:

Kinetic energy,

Chemical energy,

Gravitational energy,

Electrical energy,

Mass energy,

Thermal energy,

Elastic energy,

Nuclear energy,

Radiant energy. Electromagnetic waves

Electromagnetic Waves

Properties of Waves

Properties of Electromagnetic waves

The wavelength is usually measured in microns (or micro meters m with 1 m = one millionth, or 10-6 of a meter) and is denoted by the Greek letter lambda The frequency denoted by the Greek letter mu

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

The Sun and its Radiation Energy

The Sun is the star located at the center of our planetary system. It 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 are one hundred times 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 trough radiation.

The Sun and its Energy

Solar radiation occurs over a wide range of wavelengths. However, the energy of solar radiation is not divided evenly over all wavelength but, is rather sharply centered on the wavelength band of 0.2-2 micrometers (m). Its range includes ultraviolet radiation (UV, which encompasses the range 0.001-0.4 m), visible radiation (light, encompassing the range 0.4-0.7 m), and infrared radiation (IR, which encompasses the range 0.7-100 m).

The Electromagnetic Spectrum

Black Body Radiation

All 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 at a particular wavelength. Thus, the efficiency with which a body 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.

The Sun and its Energy Spectrum

It was the physicist Max Planck who determined the relationship between the radiative energy flux emitted from a blackbody and its absolute temperature. This expression is known as the Planck blackbody radiation law. It is by using this law that the spectra of Sun and Earth emitted radiation were calculated in the figure. We substituted in Planks law values of 5780 K and 288 K for the Sun's and Earth's temperatures, respectively.

Radiation and Temperature

Planck's law states a complex (and non-linear) relationship between the energy flux per unit wavelength, the wavelength and the temperature.

Two derivatives of this law, useful for our discussion, are the Wien law, stating the relationship between the wavelength corresponding to the maximum energy flux output by a blackbody (max) and its absolute temperature (T), and the Stefan-Boltzman law stating the relationship between absolute temperature and the total energy flux emitted by a blackbody, over the entire wavelength range (I).

Radiation max. Wavelength

Wien's law states that:

The wavelength of the maximum intensity is inversly proportional to the temperature

max= a / T

where maxis given in m, T is in units of K, and a is a constant equal 2897 m K.

Total Radiation versus Temperature

The Stefan-Boltzman law states that:

The total energy (flux) released by a black body is proportional to the fourth power of its absolute temperature.

I = T4 where I is in units of W/m2, T is in units of K, and (the

Greek letter sigma) is a constant equal to5.67 x 10-8 with units of W m-2 K-4.

Black Body Emission

Wien's law states that:

max= a / T where maxis given in m, T is in units of K, and

a is a constant equal 2897 m K.

The Stefan-Boltzman law states that:

I = T4 where I is in units of W/m2, T is in units of K,

and (the Greek letter sigma) is a constant equal to5.67 x 10-8 with units of W m-2 K-4.

Area ~ Energy(integrate over log ofwavelength)

Spreading of Radiation

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 thus 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.


Thus the energy flux decreases as the energy moves further away from the source. The rate of energy flux decrease with increasing distance from the emitting object, is directly related to the rate of increase in the area of the sphere, centered on that object with distance. Because the surface area of a sphere increases in proportional to the square of the radius we have:

I (at distance r from source) = I0 r0

2 / r2 Where I is the energy flux and r is the distance from the source. In the same way:

I (r2) / I(r1) = r12 / r2

2

Where r1 and r2 are two distances along the path of the radiation from the source.


As the sphere gets larger, the energy per square meter decreases. Since 4 and ,p are constants it follows that

the intensity per square meter is

inversely proportional to r2,

the square of the distance to ( .the source ie

proportional to1/r2).

Radiation of Sun

The Sun is located at the center of our Solar System, at a distance of about 150 x 106 kilometers from Earth.

With a surface temperature of 5780 K, the energy flux at the surface of the Sun is approximately 63 x 106 W/m2 (Stephan-Boltzman's Law).

This radiative flux maximizes at a wavelength of about 0.5 m which is at the center of the visible part of the spectrum (Wien's Law).

Radiation from Sun to Earth

As the Sun's energy spreads through space the energy flux drops as the same total radiated energy spreads over the surface of an ever growing sphere. As the radiation reaches the outer limit of the Earth's atmosphere, several hundred kilometers over the Earth's surface, the radiative flux is approximately 1360 W/m2

Radiation transfer from Sun to Earth

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 Earth is closer to the sun at one time of year (a point referred to as perihilion) than at the "opposite" time (a point referred to as aphelion). The time-of-year when the Earth is at perihilion moves continuously around the calendar with a period of 21000-years. At present it occurs in the middle of the Northern Hemisphere winter.

Radiation transfer from Sun to EarthEffect of Earth's spherical shape:

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, an energy flux equal to the solar constant. However, the Earth is a sphere and aside from the part closest to the sun, where the rays of sunlight are perpendicular to the ground, its surface tilts with respect to the incoming rays of energy with the regions furthest away aligned in parallel to the radiation and thus receiving no energy at all.


Effect of Earth's spherical shape:

Radiation transfer from Sun to EarthThe tilt of the Earth's axis and the seasons:


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.

Three Aspects of Radiationinteracting with matter

Interaction of Energy from the Sun with

Earth’s Atmosphere

The energy that drives the climate system comes from the Sun. When the Sun energy reaches the Earth it is partially absorbed in different parts of the climate system. The absorbed energy is converted back to heat which causes the Earth to warm up and makes it habitable.

The Earth Radiation Budget Part 2: Energy from Earth and Earth's

temperature.A.The Earth's albedo.

If the Earth had no atmosphere, then the entire

energy received from the sun would reach the surface undisturbed, to be reflected from and/or absorbed by it. As it stands, the Earth's surface reflects part of the solar energy. The Albedo of Earth depends on the geographical location (can you tell from the Figure which has higher albedo, the land or the ocean?). On the average however, the Earth's albedo is about 0.3. This fraction of incoming radiation is reflected back into space. The other 0.7 part of the incoming solar radiation is absorbed by our planet.


temperature.A.The Earth's albedo.


temperature.

B.Effective temperature.

By absorbing the incoming solar radiation, the Earth warms up and its temperature rises.

If the Earth would have had no atmosphere or ocean, as is the case for example on the moon, it would get very warm on the sunlit face of the planet and much colder than we experience presently, on the dark side.

The Effective Temperature

We have seen that all heated objects emit (outgoing) radiation. As long as the incoming radiative flux is larger than the outgoing, the radiated object will continue to warm, and its temperature will continue to increase. This in turn will result in an increase in the outgoing radiation (according to the Stefan-Boltzman law the outgoing radiation increases faster than the temperature). At some point the object will emit as much radiation as the amount incoming and a radiative equilibrium (or balance) will be reached.


Using what we have learned about radiative heat transfer and some geometric calculation we can calculate the equilibrium temperature of an object if we know the amount of incoming energy. Here is how we do that in the case of a planet rotating around the Sun:

heat absorbed by "disk" planet = heat emitted by surface of planet


heat absorbed by "disk" planet = (1 - A) R2 I

heat radiated from planet = (4 R2 ) T4

In radiative balance:

(4 R2 ) T4 = (1 - A) R2 I

Solving this equation for temperature we obtain:

Te = [ (1-A) I / 4 ] 1/4


The effective temperature of Earth is much lower than what we experience. Averaged over all seasons and the entire Earth, the surface temperature of our plane is about 288 K (or 15 oC). This difference is the effect of our atmosphere, or more precisely, the heat absorbing components of our atmosphere. This effect is traditionally referred to as the greenhouse effect referring to the warming of garden plots by covering them with a glass enclosure.


Here is how the greenhouse effect works: The Earth's atmosphere contains many trace (or minor) components While the major atmospheric components (Nitrogen and Oxygen) absorb little or no radiation, some of the minor components are effective absorbers. Particularly effective is water vapor, which absorb effectively in the IR wavelength range.


Because the atmosphere is almost transparent to sunlight most of it is absorbed at the surface (some is reflected, as we saw earlier, from the surface and by clouds and other light particles suspended in the air). When the surface warms and emits IR radiation, this radiation can not freely escape into space because trace gases such as water vapor absorb it. These gases (and their surrounding air) warm up, emitting radiation towards the Earth's surface, as well as upward, towards space (half is emitted up and half down).


This effectively traps part of the IR radiation between ground and the lower 10 km of the atmosphere.

The surface temperature then rises above the effective temperature calculated above (Te).

The effect is similar to that of a blanket that traps the body heat preventing it from escaping into the room and thus keeps us warm on cold nights.


Documents

Energy to drive the Climate Earth’s Energy Budget, Solar Radiation, The Greenhouse Effect Martin Visbeck DEES, Lamont-Doherty Earth Observatory [email protected]