Atmospheres of the solid worlds II: Structure and heat transport


The surface of Venus from The Daily Galaxy
We continue our consideration of the atmospheres of:

From Effective Temperature to Actual Temperature:

Effective temperature: The ideal temperature at which a planet precisely re-radiates all of the energy it receives from the sun. For an idealized black-body, it is:

Te = (L / (16πσD2))1/4

Where:

Thus, in our solar System, the only real variable in computing effective temperature is distance from the Sun.

If we treated real planets like idealized black-bodies, we get these effective temperature:

Not crazy sounding except when you consider that in reality, these planets don't absorb all of the solar radiation that hits them


Iapetus: High and low albedo on a single world
Albedo: However, to know incoming solar radiation, we must also consider Albedo, the amount of radiation reflected back into space. Clouds and surface features like ice caps have high albedo. Likewise:

Albedo is measured on a scale from 0.0 (no reflectivity - a physicist's ideal "black body") to 1.0 (all light reflected). Modest examples:

To factor is into effective temperature, we calculate

Te = (L(1-a) / (16πσD2))1/4

Where a = albedo.

Incorporating albedo we get the following estimates of effective temperature:

Again, makes sense. Mars is farther from the sun than Earth, and Venus has much greater albedo. For Mars, it also approximates mean surface temperature well.


From The Koshland Science Museum
The Greenhouse Effect:

But for Venus and Earth, true mean surface temperature is:

Yikes. Earth is 33 K warmer than expected. Venus is 500 K warmer. This difference is because of the greenhouse effect - the ability of planetary atmospheres to trap heat. Solar energy usually reaches planet's surface in the form of visible light. Whatever fraction is not reflected by albedo heats whatever opaque surface absorbs it.

Hot objects reradiate energy as infrared radiation, however many atmospheric gasses that are transparent to visible light (allowing the energy in) are opaque to infrared, preventing this energy from radiating back into space. The result is that the atmospheric gasses opaque to infrared are warmed up. These are greenhouse gasses. Foremost among them:

Although most sunlight hitting Venus is reflected into space, much of that which penetrates is trapped by its massive CO2 atmosphere. On Earth, even trace amounts of CO2 and water increase temperature significantly. Note: Without this, mean Earth temperature would be below freezing.

So, how is this heat distributed vertically in the atmosphere?

Atmospheric Structure

Stratification

On any planet, atmospheric pressure (density) decreases smoothly with increasing elevation. Temperature is more complex, and allows us to define distinct atmospheric layers:
  • Troposphere: The zone of rapid temperature decrease with increasing height. Also the zone of atmospheric convection and, consequently, of weather - variable atmospheric conditions (E.G. of temperature, humidity, precipitation, wind characteristics, and atmospheric pressure) in a particular regions at a specific times.

    The troposphere is warmed by infrared radiation from the planet's surface (which has been directly illuminated by visible sunlight) With increasing elevation, heat from this source diminishes rapidly, causing rapid cooling.

  • Mesosphere: Becomes cooler with increasing altitude but at a much lower rate. Convective motion or weather is absent.

  • Thermosphere: The "air" is so thin that it mixes with the solar wind, the flow of very hot charged particles from the sun, and is heated and, to various degrees ionized by it.

    With two notable exceptions, the atmospheres of the Solar System conform to this schematic:



    Earth's atmosphere from Astrobiology Magazine
    Why is there an upper limit to convection? Consider the relationship between heat and pressure - heat of compression. When a volume of gas is compressed, the energy of the work of compression is transferred to the gas molecules, increasing their thermal energy. Common practical applications of this include:

    The converse of heat of compression is the cooling that results from decompression. If a location on the planet's surface is particularly warm:

    Because this cooling occurs even if there is no transfer of heat to surrounding air, it is termed adiabatic cooling. (Adiabatic means "without transfer.") This is the minimum rate at which rising air cools. In practice, there is usually some heat transfer to surrounding air, also.

    Adiabatic lapse rate: The rate at which rising air cools adiabatically. As long as the surrounding air cools faster with increasing height than the adiabatic lapse rate, that parcel will continue to rise. Typically, the adiabatic lapse rate is slightly less than general cooling in the lower atmosphere. Once the adiabatic lapse rate exceeds the general rate of cooling, the parcel will no longer rise. This places an upper limit on convection and defines the top of the troposphere.

    The Mesosphere: Here, the transfer of heat is relatively straightforward. There is no convection, only conduction - the absorption and re-radiation of energy.

    The Thermosphere: In its thin outer reaches, an atmosphere mixes and interacts with the solar wind with the result that it is heated and ionized. (Regions of extensive ionization are called the ionosphere). Heated molecules re-radiate energy at different rates depending on their physical characteristics, such that some retain their heat longer than others.


    Earth's atmosphere from Annenberg Learner
    An Earth idiosyncrasy - the stratosphere: (15 - 50 km) Solar ultraviolet radiation impinges on the stratosphere. Through a complex series of reactions, this radiation causes the dissociation of O2 molecules which recombine as O3, ozone, which forms an ozone layer. Happily, ozone is opaque to ultraviolet light. As a result, the biosphere is protected from ultraviolet radiation that would otherwise render Earth's surface sterile. However, as ultraviolet light strikes the stratosphere, its energy is absorbed by the ozone, which heats up, then re-radiates in the infrared. The warming effect on the upper atmosphere is similar to that of the ground surface on the troposphere, warming surrounding air. This gives Earth an atmospheric structure in which air actually gets warmer in the stratosphere - a layer between the troposphere and mesosphere.

    Atmospheric circulation:

    But sunlight does more than heat atmospheres, it causes them to circulate. Atmospheric circulation is driven by two things:

    Latitudinal differential in incoming sunlight: The amount of solar energy received per unit area of Earth's surface is a function of the angle at which the light strikes. The most concentrated energy is delivered to equatorial regions whereas polar regions receive very little. Resulting circulation is, in part, the atmosphere's attempt to equalize that heat distribution.

    The Coriolis effect: The greatest solar heating occurs near the equator. Picture a rising parcel of air in Earth's equatorial troposphere. It reaches the top of the troposphere then circulates toward higher latitudes. At the equator, its motion equalled that of the Earth's equator. At it moves north, this momentum is conserved even though it is now moving over a surface that is not moving as fast. As a result, to conserve momentum, it seems to accelerate with respect to Earth's surface. Viewed from the surface, it appears to follow a curved path, as it is deflected toward the east.


    Global convection cells: On Earth, the interaction of the latitudinal differential and Coriolis force breaks global circulation into three convection cells per hemisphere, forming globe girdling belts:

    The cells meet in broad zones roughly 30 and 60 deg. north and south. These zones are the location of the tropical and polar jet streams, respectively - rapid high altitude westerly air currents.

    When we translate the schematic above into three dimensions, we see that on Earth's surface we perceive the atmospheric circulation cells as latitudinal wind zones, with easterly trade winds at the bottom of the Hadley cells, westerlies with the Ferrel cells, and polar easterlies at high latitudes.

    Variations on other worlds:


    Planetary idiosyncrasies:


    Mars dust storms from Space Today

    Mars:

    As we have seen, Mars displays a normal atmospheric profile with vigorous convection in the troposphere on most days. Two circumstances sometimes disrupt this:


    Titan in visible light from Wikipedia

    Titan:

    Stranger and stranger.

    Processes that alter atmospheric composition over time:

    Atmospheric retention the distribution of atmospheres in the Solar System can still be puzzling:

    A planet's ability to retain its atmosphere is a function of two variables:

    Generally, we expect more massive planets (stronger gravity), and colder ones (slower gas molecules) to retain their gasses more effectively.


    Escape velocity from Hyperphysics
    Escape velocity: The speed that any body (rocket or gas molecule) must attain to escape the pull of a planet's gravity. Escape velocity is described as:

    Vesc = (2 G M / R)1/2

    Where:

    Notice that the escape velocity depends only on the ratio M/R of the planet. It has nothing to do with characteristics of the object that may escape. The escape velocity is the same for a rocket and for a gas molecule.

    Some escape velocities:

    These are the speeds that a gas molecule must attain to escape from a planet's atmosphere. How do they attain those speeds?

    Thermal energy: So, what is the velocity of a gas molecule? It depends on the temperature and the molecular mass of the gas. Hot gas molecules move at higher velocities than cold gases, and heavy molecules move more slowly than light ones. Note that this is an average velocity. Gas molecules do not all move at one speed; there is a wide distribution of speeds at any temperature.

    With this in mind, we can see by pairwise comparison that:


    Artist's impression of the Moon, 3.5 Ga. From Phys.org
    Caveat: But note that a planetary body may acquire an atmosphere only to lose it. Needham and Kring, 2017, calculated the amount of gas released on Earth's Moon during its period of giant volcanic eruptions around 3.5 Ga and determine that these could have formed an atmosphere denser that Mars' that could have lasted for 70 ma.


    Misleading textbook figure with confused x-axis

    Bad Graph!

    For an atmosphere to remain bound to its planet over the age of the solar system (4.56 Ga), the average speed of gas molecules should be less than 1/6 of the escape velocity.

    Note: The temperatures we use here are temperatures of the upper atmosphere - the region from which gas molecules actually have a clear shot at escaping. Nevertheless a glance at the x-axis figures of this graph from your text shows that something is horribly wrong.


    Use this version based on information from The University of Nebraska Lincoln

    Good Graph!

    Here is a correct version. To learn more, play with the applet from the University of Nebraka Lincoln


    Key concepts and vocabulary:
  • Tropical and polar jet streams