1-2: Evolution of the Earth's Atmosphere | 1-2: En Español | 1-2: Em Português |
GOAL:
To use some basic physics to help us understand the long-term characteristics of the atmosphere: why the atmosphere is what it is, how it got that way, and what is necessary to make significant changes in its structure and composition.
Escape Velocity
We begin by looking at the solar system, the physical properties of
planets, and their relationship to the sun.
Figure 1
gives various characteristics of bodies in our solar system that have
atmospheres, listed in order of their distance from the sun (except for
Titan, which is a satellite of Saturn). The first column gives the
size of the body as indicated by its radius, Rp. Size of the planet
determines its gravitational acceleration, as can be seen by the
correlation between radius and go in the second column. Gravity, in
turn, controls the escape velocity. Ve, given in column 3, which is the
minimum speed that molecules must move if they are able to escape from
the gravitational pull of the body. Earth, for example, being the
fourth smallest planet on this list, has the fourth smallest escape
velocity of 11.2 km/s or about 7 miles per second. If we wanted to
launch a spacecraft to be completely free of the earth's gravitational
field, it would have to have a speed of 7 miles per second. Just
putting a spacecraft in orbit, of course, is a quite different problem,
because the orbital parameters are determined by the balance of
gravitational force and the motion of the spacecraft as will be shown
in the unit on satellites.
The escape velocity can be calculated from a balance of gravitational energy at the planet surface and kinetic energy:
--> Ve = (2gRp)1/2
Where m is the mass of a molecule, Rp is the radius of the planet,
and Ve is escape velocity.
This shows that the escape velocity does not depend on the mass of the
particle trying to escape, so the escape velocity is the same for a
space ship as for a hydrogen molecule.
Albedo
Albedo (A), given in column 5, is the fraction of energy incident on
the planet that is reflected back to space. On the other hand,
1-A is the fraction of energy that is absorbed by the planet and its
atmosphere. A perfectly absorbing body has an albedo of zero, and a
perfectly reflecting body has an albedo of 1.0. The earth has an
albedo of 0.29, which is about average for most planets. Albedo and
distance from the sun are the factors determining the effective temperature of the body. Albedo is determined by the
combined effects of reflection from the planet's surface and the reflecting and absorbing properties of its atmosphere,
as determined by its composition.
Probable Velocity
The effective temperature of the body gives an approximation of the
temperature of the gaseous constituents at the "outer edge" of its
atmosphere. This temperature determines the most probable velocity of
each constituent in this region, as given by the following equation:
where
VM = most probable velocity for molecule of weight MNote that more massive molecules, such as CO2 with molecular weight 44, have much lower probable velocity than hydrogen with molecular weight 1 or helium with molecular weight 4. This means that for a given planet with a given gravitational acceleration and escape velocity, the lighter molecules are more likely to exceed the escape velocity and leave the planet's atmosphere. The seventh column in the table gives the most probable velocity of hydrogen (VH) for temperature corresponding to Te. Although the temperature at the "outer edge" of a planet's atmosphere may be quite different from Te , column 7 allows us to compare a typical most probable velocity with Ve for the planet. The closer the most probable velocity is to the escape velocity, the higher will be the fraction of molecules that are able to escape from the planet.k = Boltzmann's constant (1.38 x 10-23 J deg-1)
T = effective temperature
M = molecular weight of a particular gas species
mH = mass of the hydrogen atom ( 1.67 x 10-27kg)
Total Atmospheric Mass
Figure 2 gives a listing of the fractional contribution of each
of several gases to the total atmospheric mass of each body.
Comparison of these two tables explains why Venus, Earth, and Mars,
with their low escape velocities, have very low concentrations of
lighter elements. We don't expect to find, and we don't find, very
much hydrogen or helium on Venus,
Earth, or Mars because these light elements have relatively high
probable velocities in relation to the
escape velocities for these planets and there are no sources of light
elements on these planets. For more massive molecules, lower most
probable velocities mean that escape is less likely, For instance, for
CO2 (M=44) at the effective temperature of the earth, Vo (CO2) = 310
m/s or 0.31 km/s. The time for carbon dioxide to leave the planet is
long compared to the age of the earth, which is about 4-5 billion
years.
Surface Pressure
In Figure 1 of this summary information,
the column labeled Po gives
the surface pressure for each of the bodies. Note that Mars, the
smallest of the planets listed and having an escape velocity of only
about 5 km/s, has almost no atmosphere. Most of the atmospheric gases
from Mars have been able to escape, with the predominant remaining gas
being carbon dioxide. Earth, on the other hand, has a CO2
concentration of only 3.60 x 10-4, or about 360 molecules per million
total atmospheric molecules (parts per million by volume, or ppmv).
It is noteworthy that the earth is unusual because it is the only
planet that has a substantial amount of oxygen in its atmosphere. Venus
and Mars have trace amounts, but Earth has a remarkable amount of
oxygen and nitrogen.
Four Stages of the Earth's Atmosphere
Figure 3 gives four stages of the evolution of the earth's
atmosphere. Presumably the earth was formed as a product spinning off
from the sun, which is mostly hydrogen and helium. When the earth
formed and cooled, its earliest atmosphere (Atmosphere I) probably
consisted of primarily ammonia, and compounds of such elements as
bromine, chlorine, fluorine, and sulfur. Constituents of this
atmosphere would have been products of outgasing and are similar to the
kinds of gases coming out of volcanoes: hydrogen sulfide, hydrochloric
acid, hydrofluoric acid, hydrogen sulfide and ammonia. If you remember
any chemistry, you will recognize that these are not nice chemicals to
be around.
However this atmosphere didn't last long, quickly being replaced by an
atmosphere of water, CO2 , and nitrogen (Atmosphere II). As the earth
cooled further to conditions below the critical pressure and critical
temperature of water, the water of course started to condense and make
oceans and so water gradually over a period of time disappeared from
the atmosphere. This is the most interesting period for us, the period
between Atmospheres II and III, the latter revealing the appearance of
oxygen, possibly produced by photochemical breakdown of water. The
presence of oxygen to shield the earth's surface from ultraviolet light
allowed for the arrival of photosynthesizing plants that consumed the
abundant CO2 and gave off oxygen, thereby diminishing the former and
enhancing the relative abundance of the latter to give the atmosphere
we have today. A more extensive and precise list of current atmospheric constituents is given in a
table that will be discussed in Unit 1-4.
Determining the Temperature of a Planet
--1st
Approximation
Let's now consider the factors determining the temperature of a
planet. The sun has a temperature of about 6,000 K and is located 149
million km (93 million miles) from the earth. The flux density of
solar energy reaching the earth from the sun is 1367 Watts/m2 or 430
Btu/hr/ft2, which we refer to as the solar constant, S (although closer
inspection has revealed that it is, in fact, not constant). If the
earth absorbed all this energy over its disk area (π R2)
and
re-radiated it back to outer space as a sphere (of area 4
π R2), the
energy balance given by the Stefan-Boltzmann
law gives us an estimate
of the effective radiating temperature of the Earth:
--> (π R2) S =σ T4 (4 π R2)
--> T = [(0.25*S)/( 4 σ)]1/4
= 279 K, or 6 °C (40° F)
Determining the Temperature of a Planet
--2nd
Approximation
If we recognize that only a fraction of incident energy, given by (1-A)
where A is albedo, is absorbed by Earth, a second approximation
(Figure 4)
of the Earth's temperature gives 256 K or -17°C (1.6°F) as the
effective temperature. This is even further from the observed average
surface temperature of 283 K, or 15°C (59°F) than the first
approximation.
A more refined approximation is required to obtain a temperature for Earth that is close to the observed value. The factor not accounted for in the previous approximations is the effect of the atmosphere, for which we need to understand the relation of radiating temperature to dominant spectral wavelength.
Figure 5 gives a schematic representation of the radiated energy flux emitted by the sun (left-hand curve) radiating at about 6,000 K and the earth (right-hand curve) radiating at about 300 K. Note that the wavelength of radiated energy is 0.5 microns (0.5 x 10-6 m) for the sun and 10 microns for the earth. The sun radiates visible energy and the earth radiates infrared energy. The relationship between temperature and maximum radiating wavelength is given by Wien's Displacement Law, which is
where T is radiating temperature in K and lm is wavelength in microns. More information and simulations are available online.
An object or gas will absorb energy differently at different wavelengths, depending on the atomic structure of its molecules. At visible wavelengths, dark-appearing objects absorb more energy than light colored objects. An object that appears red to our eyes receives visible light from the sun or other source and absorbs all wavelengths except red, which is reflected. A black object absorbs almost all energy at all wavelengths.
A gas will absorb some fraction of radiant energy incident on it. Figure 6 gives the absorptivity of various gases, ranging from 0 to 1.0, for various wavelengths of radiant energy in the visible and infrared spectrum. The sun, radiating most strongly at wavelengths around its maximum at about 0.5 microns, has essentially all of its energy absorbed by ozone below 0.3 microns (ultraviolet light), but none of the atmospheric constituents absorb very much in the "visible window" between 0.3 and 0.7 microns.
Energy from the earth, on the other hand, radiates over a range of wavelengths centered on about 10 microns, which, according to the absorption graph, is a region where energy is absorbed strongly by water vapor (H2O) and carbon dioxide (CO2) and, at certain wavelengths, by methane (CH4), nitrous oxide (N2O), oxygen (O2) and ozone (O3). The graph at the bottom of the figure gives the aggregate absorptivity for all gases in the atmosphere.
Determining the Temperature of a Planet
--3rd Approximation
The absorbing properties of the earth's atmosphere allow us to develop
a third approximation to the radiating temperature for the earth. The
atmosphere behaves like a one-way blanket that lets in solar energy and
absorbs outgoing infrared energy emitted by the earth. It should be
noted that all the energy emitted by the earth does ultimately escape
to outer space, but the spherical shell of atmosphere interrupts this
flow of energy by radiating some of it back toward the earth, thereby
raising its temperature and causing it to emit even more (as required
by the Stefan-Boltzmann equation). The ultimate balance that is
achieved has a higher surface temperature but the same amount escaping
from the top of the atmosphere to outer space.
If we assume the atmosphere absorbs 90% of energy upwelling from the earth but none coming in from the sun, we get a third approximation to the surface temperature as given in Figure 7. This model of the earth energy budget gives the same effective temperature for radiation to space (256 K or 1.6°F) from the "outer edge" of the atmosphere, but the surface temperature in this model is 283 K, (59°F), the correct present value. This simple model demonstrates the important role of the atmosphere in determining the surface temperature of the planet. And the exact type of gases that compose the atmosphere is the critical factor in determining its overall absorptivity. The important factor, as we will see later, is that the resulting surface temperature allows H2O to exist in all three phases in abundant quantities, thereby simultaneously allowing some H2O to exist as water vapor to trap infrared radiation in the atmosphere and some to exist in condensed form to create global oceans .
To summarize the two main points so far in this unit, (1) the
gravitational field and escape velocity for a planet will determine the
amount of atmosphere it is able to retain, and (2) the laws of
radiation and absorbing properties of the atmosphere determine both the
effective radiating temperature and the surface temperature of the
planet.
Gas Concentrations
Concentrations of gases expected to occur in the earth's atmosphere
can be calculated by use of some concepts of thermal and chemical
equilibrium from freshman chemistry. However, the results of such
calculations, shown in Figure 8
, give equilibrium concentrations of constituents that are nowhere near
the observed present fractional concentrations. For example, the
equilibrium calculation suggests nitrogen should have a concentration
of 10-10, whereas, in fact, it makes up 78% (0.78). Equilibrium
calculations suggest there would be no oxygen, but the present value is
almost 22%. Methane would be expected to comprise only 10-35 rather
than the observed amount of 1.7 parts per million. Likewise, nitrous
oxide, ammonia, and hydrogen calculated by these methods give values
far below present levels. We can only conclude that our assumption of
equilibrium is wrong, and that, in fact, the atmosphere must be in a
constant state of chemical reaction with inputs and outputs. Knowledge
of the equilibrium concentrations and rates of the inputs and outputs
allows for an estimate of the residence time for each molecule. As
shown, in the table, these range from 10 days to 107 years.
Distribution of Temperature
Figure 9
gives the vertical distribution of temperature in the Earth's
atmosphere. This plot is a global average that overlooks spatial
(different locations on Earth) and temporal changes, which will be
discussed in the unit on atmospheric
structure and circulation. Notice
that the temperature decreases rather linearly from about 15°C at the
surface to about -55°C at an altitude of 10 km above the Earth's
surface. This region of the atmosphere, called the troposphere,
contains about three-fourths of the mass of the atmosphere, and its top
is called the tropopause. Above the tropopause is a 10-km thick region
of constant temperature, and above this layer the temperature increases
with height to about 0°C at a height of 50 km. This region above the
tropopause and below the stratopause at 50 km is called the
stratosphere. Ninety nine percent of the atmosphere is confined in the
lowest 30 km, and 99.9% is below 50 km. The extremely low density of
the atmosphere in the upper stratosphere and beyond give a different
meaning to the concept of temperature. The portion of the atmosphere
that is relevant to global change issues is the lowest 30 km.
Oxygen and Ozone
The lowest 50 km of the atmosphere is relatively well stirred by
convection and turbulent processes, so the mixture of atmospheric gases
is quite homogenous over this region. Masses of nitrogen and oxygen
decrease exponentially with height throughout the troposphere. Ozone
is produced by photochemical processes in the stratosphere, so its
concentration increases from the base of the stratosphere to a maximum
around 30 km and then decreases. Monatomic oxygen and monatomic
hydrogen exist at low concentrations above these levels.
Perhaps one of the most famous experiments in science was done by Stanley Miller who took water, methane, and ammonia put it in a jug and subjected it to solar radiation. His discovery of the development of complex molecules from such a situation suggests that these are the ingredients for life to form. Similarly, about 3 billion years ago, oxygen began appearing on Earth. Figure 10 gives the reactions in the earth's prebiotic atmosphere that allow an initial atmosphere of H2O and CO2 to form O2. Solar radiation decomposes water into H and OH. Carbon monoxide and OH give CO2 back again plus H. The OH can give water and monatomic oxygen, and the monatomic oxygen together with a third species (M) can produce diatomic oxygen and hydrogen which could then escape. So it would be theoretically possible for sunlight in an atmosphere with water and CO2 to produce oxygen, but probably not more than a few tenths of a percent of what we now find.
Figure 11 starts at 100 million years before the present and goes back in time to show what happened to oxygen and ozone over time. Two processes began to occur: first, nitrogen could be fixed, and secondly CO2 could be absorbed by plants, like green algae, thereby producing oxygen allowing biological activity to expand. Ocean plants appeared first, then land plants, ocean animals, and land animals. Land animals did not appear until the oxygen concentration of the atmosphere reached some critical level to feed cells by diffusion processes. Microbial organisms played a dominant role in the evolution of the early atmosphere of the Earth. Note that the abundance of ozone (O3) relative to the present atmosphere is high compared to diatomic oxygen (O2) in this early part of the record. We later will see the critical role of ozone in protecting the biosphere from ultraviolet radiation, and that this early-evolutionary protection was important for subsequent plant development.
Therefore, living matter gradually produced oxygen over a period of 1.5 billion years, leading to a situation on earth unique from other planets in our solar system. In the process of producing the oxygen, plants absorbed CO2 in the green plant cycle and converted atmospheric nitrogen to plant nitrogen, thereby driving down the atmospheric levels of both of these constituents.
Another way of getting an overview of the different forms and transformations of oxygen is to look at the oxygen cycle (Figure 12). In future summary informations we will examine cycles of other molecules, but the oxygen cycle is one of the most interesting. Circles in the accompanying figure represent present estimates of flows, and boxes represent present estimates of reservoirs. The atmosphere itself is a large reservoir, 1019 moles, but an even larger reservoir exists in sedimentary rocks. Oxygen may be chemically combined in these reservoirs whereas in the atmosphere it's free. The reservoir of oxygen in fossil fuels is about 3 times larger than that of the biosphere, which consists of plants and animals - both living and dead - at the Earth's surface.
The largest flows of oxygen, photosynthesis and respiration/decay, are about 1016 moles per year. The atmosphere gains oxygen by weathering of rocks, and a comparable amount is lost from the surface by burial, such as marine plant parts and animal skeletons that drift to the bottom of the deep ocean. Burning of fossil fuels (oil, coal, natural gas) in production of energy represents a loss of oxygen for the atmosphere. Finally, a small amount of O2 is gained by the atmosphere when water vapor is broken down by sunlight (photolysis), with hydrogen released to space in the process.
The concept of a material cycle is very helpful in evaluating the
impact of human activity in comparison with natural processes. In
future learning units we will apply this concept to global
distributions of carbon, nitrogen, sulfur, and water substance.
Similar reasoning will be used to evaluate global flow of energy, and
ultimately we will see how these cycles or budgets of materials and
energy all are connected in the earth/atmosphere/ocean/ice system.
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