## Solar Radiation and the Earth's Energy Balance.

### Take away ideas and understandings:

1. Solar energy and gravitational energy are the fundamental sources of energy for the Earth's climate system.
2. In the ideal case (referred to as "black body") matter will absorb all the energy impinging on it in the form of electromagnetic waves and as a result will warm up and itself become a radiation source. This "give and take" of energy leads to a state of equilibrium, where the outgoing radiation balances the incoming one.
3. The energy radiated from a black body is distributed over all wavelengths, in a "bell-shaped" dependence on the wavelength. Maximum energy is radiated at a wavelength proportional to the inverse of the absolute temperature.
4. The total (integral over all wavelengths) energy radiated from a black body is proportional to the fourth power of its absolute temperature.
5. The energy flux radiating from a point source falls of as the square of the distance from it. This is why light dims fast as one moves away from its source.
6. Using these fundamental laws and knowing the Sun's temperature, we can calculate the so-called "effective" or "emission" temperature of any of its surrounding planets. This is the temperature that the plant will appear to have when viewed from outer space.
7. The Earth and other planets are not perfect black bodies, as they do not absorb all the incoming solar radiation but reflected part of it back to space. The ratio between the reflected and the incoming energies is termed the planetary albedo.
8. Because of its spherical shape incoming solar radiation is not equally distributed over the planet. At each instant, only the sun lights only half of the planet's surface, with maximum radiation coming in at local noon and less in other times of the day.
9. The total daily radiation decreases from equator to pole. Thus the Earth's surface should inherently be warmer at the equator than it is at the poles. However, …
10. The Earth's axis of rotation tilts at a 23.5° away from the plane of rotation around the sun, that makes the poles point towards the sun during solstice time. This is the reason for the seasons. During solstice, the pole pointing to the sun and the surrounding area receive radiation during all 24 hours of the day while the opposite pole does not receive any solar energy. This has the potential for making the poles as warm or warmer than the equator in their respective summer time if it were not for the large albedo of the Polar Regions.

### Introduction.

In the narrow sense of the word, Climate is the average or typical state of the weather at a particular location and time of year. Its description includes the average of such variables as temperature, humidity, windiness, cloudiness, precipitation, visibility etc., and also the expected range of the deviations of these variables from the mean. In the broadest sense however, climate is the state of the Earth's habitable environment consisting of the following components and the interactions between them:

• The atmosphere, the fast responding medium which surrounds us and immediately affects our condition.
• The hydrosphere, including the oceans and all other reservoirs of water in liquid form, which are the main source of moisture for precipitation and which exchange gases, such as CO2, and particles, such as salt, with the atmosphere.
• The land masses, which affect the flow of atmosphere and oceans through their morphology (i.e. topography, vegetation cover and roughness), the hydrological cycle (i.e. their ability to store water) and their radiative properties as matter (solids, liquids, and gases) blown by the winds or ejected from earth's interior in volcanic eruptions.
• The cryosphere, or the ice component of the climate system, whether on land or at the ocean's surface, that plays a special role in the Earth radiation balance and in determining the properties of the deep ocean.
• The biota - all forms of life - that through respiration and other chemical interactions affects the composition and physical properties air and water.

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 environmental conditions. These changes could well affect our health, comfort levels, and ability to grow and distribute food.

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 its governing processes in a quantitative manner, so that a better understanding of today's environmental issues can be achieved. The course will also provide a basis for further, more advanced study of the climate system and its individual components or processes. The Climate System course is mainly concerned with the properties of atmosphere and hydrosphere and the physical laws governing their behavior. Attention to the solid and living earth is also given, as far as they affect atmosphere and hydrosphere. Solid Earth and Life are dealt with in much more details in two separate courses under the EES umbrella.

Within the climate system the atmosphere plays the role of the efficient communicator. The atmosphere is capable of quickly moving and distributing mass and heat over large distances, horizontally and vertically and spread the effect of frequent perturbations to remote regions of the globe within hours to days from their occurrence. The atmosphere directly affects life on Earth by supplying the gases for the respiration of vegetation and animals and by moving water from oceanic regions to be deposited in liquid or solid form on land. The atmosphere also shelters life on Earth from the extreme and potentially harmful effects of direct solar radiation. The oceans are most important because of their tremendous heat storage potential and their ability to distribute that heat horizontally. The composition and motion of the water in the hydrosphere sustains a rich and diverse life system. The exchange of gases and heat between oceans and atmosphere determines the physical properties and composition of both these sub-systems and is one of the primary climate processes.

We begin this course in a study of solar radiation, the primary energy source for Earth and its climate system. We examine the properties of the Sun and its energy and the laws governing the transfer of this energy through space from the Sun to the 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.

Review: What is energy?

### The Earth Radiation Budget Part 1: Energy from the Sun.

The energy that drives the climate system comes from the Sun. When the Sun's 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. Solar radiation absorption is uneven in both space and time and this gives rise to the intricate pattern and seasonal variation of our climate. To understand the complex patterns of Earth's radiative heating we begin by exploring the relationship between Earth and the Sun throughout the year, learn about the physical laws governing radiative heat transfer, develop the concept of radiative balance, and explore the implications of all these for the Earth as a whole. We examine the relationship between solar radiation and the Earth's temperature, and study the role of the atmosphere and its constituents in that interaction, to develop an understanding of the topics such as the "seasonal cycle" and the "greenhouse effect". We complement this lecture by a set of two laboratory assignments that explore in much more detail the spatially and seasonally varying elements of the Earth radiation budget as they are revealed through satellite observations of the Earth.

#### The Sun and its 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 about twenty 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 through a process known as radiation.

Review: electromagnetic waves.

Solar radiation occurs over a wide range of wavelengths. However, the energy of solar radiation is not divided evenly over all wavelengths but, as Figure 1 shows, is rather sharply centered on the wavelength band of 0.2-2 micrometers (μm=one millionth of a meter). As can be seen from Figure 2, the main range of solar radiation 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 physics of radiative heat transfer.

Before proceeding to investigate the effect of solar radiation on Earth we should take a moment to review the physical laws governing the transfer of energy through radiation. In particular we should understand the following points:

• The radiative heat transfer process is independent of the presence of matter. It can move heat even through empty space.
• All bodies emit radiation and the wavelength (or frequency) and energy characteristics (or spectrum) of that radiation are determined solely by the body's temperature.
• The energy flux drops as the square of distance from the radiating body.
• Radiation goes through a transformation when it encounters other objects (solid, gas or liquid). That transformation depends on the physical properties of that object and it is through this transformation that radiation can transfer heat from the emitting body to the other objects.

#### Radiation transfer from Sun to Earth.

Properties of Solar radiation: 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 (degrees Kelvin = degrees C + 273.15), the energy flux at the surface of the Sun is approximately 63 x 106 W/m2 (Do you know what law of radiative transfer do we use to calculate this number? Check the link to radiative heat transfer.) This radiative flux maximizes at a wavelength of about 0.5 μm (can you show that this is true based on the laws of radiative heat transfer?) which is at the center of the visible part of the spectrum.

Solar radiation on Earth: As the Sun's energy spreads through space its spectral characteristics do not change because space contains almost no interfering matter. However the energy flux drops monotonically as the square of the distance from the Sun. Thus, when 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 (Can you calculate this number from the flux at the surface of the Sun and the distance to the Earth? Can you figure out the flux on Pluto, which is 39 times as far from the sun as 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 perihelion) than at the "opposite" time (a point referred to as aphelion). The time-of-year when the Earth is at perihelion moves continuously around the calendar year with a period of 21,000-years. At present perihelion occurs in the middle of the Northern Hemisphere winter. The annual average radiative solar flux at the top of the Earth's atmosphere (=1360 W/m2) is sometimes referred to as the Solar Constant because it has changed by no more than a few percent over the recent history of the Earth (last few hundred years). There are however important variations in this flux over longer, so-called "geological", time scales, to which the Earth glaciation cycles are attributed.

Effect 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 (Figure 5).

The tilt of the Earth's axis and the seasons: If the axis of Earth was perpendicular to the plane of its orbit (and the direction of incoming rays of sunlight), then the radiative energy flux would drop as the cosine of latitude as we move from equator to pole. However, as seen in Figure 6, the Earth axis tilts at an angle of 23.5° with respect to its plane of orbit, pointing towards a fix point in space as it travels around the sun. Once a year, on the Summer Solstice (on or about the 21st of June), the North Pole points directly towards the Sun and the South Pole is entirely hidden from the incoming radiation. Half a year from that day, on the Winter Solstice (on or about the 21st of December) the North Pole points away from the Sun and does not receive any sunlight while the South Pole receives 24 hours of continued sunlight. During Solstices, incoming radiation is perpendicular to the Earth surface on either the latitude of Cancer or the latitude of Capricorn, 23.5° north or south of the equator, depending on whether it is summer or winter in the Northern Hemisphere, respectively. During the spring and fall (on the Equinox days, the 21st of March and 23rd of September) the Earth's axis tilts in parallel to the Sun and both Polar Regions get the same amount of light. At that time the radiation is largest at the true equator. Averaged over a full 24-hour period, the amount of incoming radiation varies with latitude and season as shown in Figure 7. Note that the figure combines the effect of the change in incidence angle with latitude and time of year and the number of hours of sunlight during the day. 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.

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

#### The Earth's albedo.

The Earth's surface reflects (that is, returns the radiation back to space in more or less the same spectrum) part of the solar energy. This is what makes the part of the Earth lit by the sun visible from space (Figure 8) in the same way that the moon and the other members of the solar system are visible to us, despite their lack of an inner source of visible radiation. The most obvious aspect of Figure 8 is the brightness of the Earth's cloud cover. A significant part of the Earth's reflectivity can be attributed to clouds (this is but one reason why they are so important in the Earth's climate). In climate texts the reflectivity of a planet is referred to as the albedo (that is, albedo = reflectivity) and is expressed as a fraction. The albedo of Earth depends on the geographical location, surface properties, and the weather (can you tell from Figure 7 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.

#### Effective temperature.

By absorbing the incoming solar radiation, the Earth warms up, like a black body (see radiative heat transfer) 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 little warmth on the dark side would come from the limited amount of heat stored in the ground from the previous daytime - this is, to some extent, what we experience in a cloud-free, land locked desert climate).

All heated objects must emit electromagnetic radiation, particularly so if they are surrounded by empty space. This radiation is referred to as outgoing. 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:

First let us denote the solar radiative flux at the top of the planets atmosphere by So (for solar constant) and the albedo of the planet by a. Then let us figure out the total amount of radiation absorbed by the planet. To overcome the difficulty posed by the fact that the planets are spherical and their surface tilts with respect to the incoming radiation, note that the amount distributed over the sphere is equal the amount that would be collected on the planets surface if it was a disk (with the same radius as the sphere), placed perpendicular to the sunlight. If the planet's radius is R the area of that disk is πR2. Thus:

heat absorbed by planet = (1 - a) πR2So

The total heat radiated from the planet is equal to the energy flux implied by its temperature, Te(from the Stefan-Boltzman law) times the entire surface of the planet or:

heat radiated from planet = (4πR2) σT4

In radiative balance we thus have:

(4πR2 ) σTe4 = (1 - a) πR2So

Solving this equation for temperature we obtain:

Te = [(1-Aa)So / 4σ] 1/4

We have added a subscript e to the temperature to emphasize that this would be the temperature at the surface of the planet if it had no atmosphere. It is referred to as the effective temperature of the planet. According to this calculation, the effective temperature of Earth is about 255 K (or -18 °C). With this temperature the Earth radiation will be centered on a wavelength of about 11 μm, well within the range of infrared (IR) radiation.

Because of the spectral properties of the Sun and Earth radiation we tend to refer to them as "shortwave" and "longwave" radiation, respectively.

#### The greenhouse effect.

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 planet is about 288 K (or 15°C). This difference is in the effect of the heat absorbing components of our atmosphere. This effect is known as the greenhouse effect, referring to the farming practice of warming garden plots by covering them with a glass (or plastic) enclosure.

Here is how the greenhouse effect works: The Earth's atmosphere contains many trace (or minor) components (see Figure 9 for the composition of the atmosphere). While the major atmospheric components (Nitrogen and Oxygen) absorb little or no radiation, some of the minor components are effective absorbers (Figure 10). Particularly effective is water vapor, which absorb effectively in the IR wavelength range (Figure 10).

Because the atmosphere is almost transparent to sunlight, all that is absorbed at the surface results in warming and the emission of IR radiation; this radiation cannot freely escape into space because of absorption in the atmosphere by trace gases such as water vapor and carbon dioxide (CO2). These absorbing gases and their surrounding air warm up, emitting radiation downward, towards the Earth's surface, as well as upward, towards space. This effectively traps part of the IR radiation between ground and the lower 10 km of the atmosphere. This reduction in the efficiency of the Earth to lose heat causes the surface temperature to rise above the effective temperature calculated above (Te) until finally, enough heat is able to escape to space to balance the incoming solar radiation. The effect is analogous 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.

All that the IR absorbing gases do is make it more difficult for heat to escape, they don't (and can't) stop the heat output, because half of their emission is directed upward towards space. The greenhouse effect forced the planet to raise its surface temperature until the amount of heat radiated from the top of the absorbing layer is equal to the solar radiation at the top of the atmosphere. It is at the top of the absorbing layer that the effective temperature is reached, while down at the surface of the Earth it is much warmer.

Text by Yochanan Kushnir, 2000.