GENERAL CIRCULATION OF THE ATMOSPHERE
Now that you have become acquainted with radiation and heat, let us examine how these processes act to produce the general motions of the atmosphere.
You must surely be familiar with the general geometry and motions of the earth and sun. Despite some notable historical attempts by organized religion to suppress the truth, the relative motions of the earth and sun are now well known. They lead to the observed spatial and temporal distributions of radiation balance at the planet surface.
The result is a distinct decrease in received solar radiation with increasing latitude. Recall that net radiation is energy received minus energy emitted. Figure 10 illustrates the approximate distribution of received solar and net emitted infrared versus latitude. This assumes a spatial average over an entire year for each latitude band.
Figure 10. The absorbed and emitted radiation vs. latitude
Notice that:
1.In the tropics, solar gains are greater than infrared losses. There exists a surplus of energy or positive net radiation.
2.The middle and high latitudes lose more infrared than they receive from solar. This deficit results in a net loss of radiation.
The cross over points lie at about 38 N and 38 S. So a majority of the Earth’s surface suffers a net loss of radiation, while the tropics are the continued beneficiary of a surplus. If no other processes were available to mediate this situation, the tropics would grow incredibly hot while the rest of the planet would experience extreme cold. Of course, this does not occur. Such a gradient in temperature cannot exist, as heat will flow in response. There must exist mechanisms to transport heat poleward from tropical regions. In fact, such transport is conducted through both atmospheric and oceanic processes. Let's consider the atmosphere first.
Idealized Atmospheric Motions For a Non-rotating Earth:
It is best to start with a simple situation, even if it isn't realistic. So assume for a moment that the Earth did not rotate. Of course the unequal distribution of radiation is still present.
Energy Balance and Transport in the Tropics
Consider the tropics where a large surplus of radiation is available. What happens to this free energy? Earlier it was noted that most net radiation was consumed to evaporate water over the globe. So most available energy in the tropics is used to evaporate water from the land and oceans (mainly oceans). Some of the energy is also absorbed by the surface waters, and used to heat them. The energy used in evaporation is not lost, but where does it go? It is stored and resides in a potential state in the water vapor itself. Since it is effectively hidden in such a state, it is called latent energy or latent heat. When water vapor condenses back into liquid, the same value of energy is released as heat.
Since such a large value of energy is required to evaporate water, the process of converting radiation to latent heat is very important to climate. The main processes involved in the energy balance of the surface in the tropical oceans are depicted below.
The warm and moist air near the surface is very unstable, leading to rising motion. The low density of the lower atmosphere in these regions is not only related to the warm temperatures, but also to the high water vapor contents. Water vapor is less dense than dry air. So adding water vapor to air reduces the density, and promotes vertical motion.
We can now look at the mechanisms that actually transfer energy upward and poleward in the tropics. Figure 11 is an illustration of the main transport processes in the tropics. The warm, evaporating ocean surface results in a vertical movement of very moist air. As this air rises, it expands (due to decreasing pressure) and cools. As the air cools, the maximum amount of water vapor that could be present in the air rapidly reduces. Recall that the maximum or saturation vapor pressure of air is a function only of temperature.
Eventually the rising air cools to a value where condensation begins, forming clouds. As condensation occurs, the heat energy absorbed during evaporation is now released, warming the air and causing further vertical motion. The radiation energy that was initially diverted into latent heat and resided in the water vapor is now released as heat. Eventually the air dries out, and diverges aloft towards the poles.
Figure 11. Transport of water vapor and energy from tropical waters
It is critical to note that heat has been transported vertically by two mechanisms:
- sensible heat flow from the warm water to the air
- vertical transport of `latent' heat of evaporation, later released in the clouds
The latter process is by far the most important. The amount of radiant energy at the surface is greatest in the tropics, and most of it is diverted into latent heat. Conversion of radiant energy into evaporation of water and subsequent transport, is the most important energy conduit that nature employs to drive the climate system. Latent heat and its transport is the most critical process that defines the climate of the planet.
Since the atmosphere is a continuous fluid, rising motions at the surface require a transport of air from the surroundings to replace the vertically moving air. This is required to conserve mass. The only way that this can happen is to have a flow into the region from the sides. As a result, a zone of converging air must exist in this region of rising air. This is called the Intertropical Convergence Zone (ITCZ). It is characterized by copious amounts of cloudiness and rainfall.
As the rising air reaches the top of the troposphere it diverges horizontally, and moves poleward. It gradually cools by radiation loss, and subsequently sinks back to the surface at latitudes of about 30N and 30S. This defines a set of Hadley Cells. Of course the latitudinal position of these cells varies with time of year. The ITCZ will generally follow the location of maximum radiation. Figure 12 illustrates the structure of the Hadley Cells.
Figure 12. The circulation and processes defining the Hadley Cells
Now let's consider the poles, which suffer large radiation losses. The resulting cold, dense air slides equatorward. This flow must meet the poleward surface flow from the descending limbs of the Hadley Cells. As a result, two other cells are defined in each hemisphere, the Polar and Ferrel Cells. Figure 13 depicts this idealized circulation for a non-rotating earth. Although this simple view helps illustrate some of the important forces driving atmospheric motion, in fact this is not what is observed! Things are complicated by the rotation of the planet.
Figure 13. Simplified circulation if Earth did not rotate
SPECIAL TOPIC III.
Temperature Change of Rising Air
As air rises in the atmosphere, the pressure decreases. This reduction in pressure results in expansion of the air parcel. The kinetic energy of the air molecules is being spread into a larger volume. Hence, it makes sense that the temperature of this expanding air will decrease. For the moment let us consider unsaturated air. Using basic thermodynamic properties of air, we can express the rate of change of temperature in terms of the fundamental variables.
The 1st Law of Thermodynamics can be expressed for the atmosphere as:
where q is heat flow into or out of the parcel, T is temperature, P is pressure, is specific volume, which is 1/density or 1/, and cp is specific heat capacity of air. Generally a rising parcel of air can be assumed to have essentially no heat exchange with the surroundings. This is called an adiabatic process. In this case dq = 0. We can also substitute for or 1/ using the Gas Law defined in Special Topic I. This leads to:
dividing both sides of the above expression by T yields:
Recall from SpecialTopicI. that the atmosphere is hydrostatic, meaning that pressure is defined by the weight of the air column above any point. This was expressed as:
This can be substituted for dP in the earlier expression, and the Gas Law used to substitute for as follows:
So we now have a relationship for changes of temperature with height for a rising parcel of air that has not reached saturation. This turns out to be about -10 C / km, and is called the dry adiabatic lapse rate.
As the air rises, the amount of water that can exist in state of water vapor will also decrease. This is because the amount of water vapor present under saturated conditions rises rapidly with temperature. This value is usually expressed as the saturation vapor pressure. The reduction in temperature for rising air means a simultaneous reduction in the saturation vapor pressure. Of course, the actual water vapor content or vapor pressure of the air is constant during this process. At some height the saturation vapor pressure, which is reducing due to the decrease in temperature, will reach the actual vapor pressure. The air is now saturated, and condensation of water vapor into liquid water will begin.
During condensation, latent heat energy is now released. This is the same energy that was stored in the water vapor during evaporation. As a result, rising air that is saturated, cools more slowly than rising air that is unsaturated. Since the amount of condensation will slowly diminish with further rising motion, the actual rate of cooling will vary with height. This is termed the moist adiabatic lapse rate. This rate is not constant with height, since the rate of condensation changes with height. Eventually, when all the water vapor has condensed into liquid, the rate of cooling returns to the dry adiabatic lapse rate.
Effects of Earth Rotation:
Reality or Hallucination? A Question of Reference Frames
In order to interpret positions and motions in space, we always employ some frame of reference, whether we realize it or not. There are two main classes of reference frames. An inertial frame is absolute and might be considered fixed and unchanging. The background of deep space might be considered as an example. A non-inertial frame is relative and not fixed. It may be moving and changing constantly.
For obvious reasons the reference frame of choice for most macroscopic processes is the surface of our rotating planet. This is of course a moving reference frame, which presents difficulties in interpreting motions within such a system. Because of this curved and moving reference frame, motions in the atmosphere will appear to experience accelerations and changes in direction. Motions that actually occur in a straight line in absolute space, will appear to be deflected in our relative space.
The above phenomenon is called the Coriolis Effect. The name honors Gustav Gaspard de Coriolis, who first laid out a mathematical solution for moving reference frames in the early 19th century.
The Coriolis Effect is not a real physical force. It is an apparentacceleration or deflection due to our insistence upon using a moving frame of reference. The most important properties of this effect are:
1.It is 3-dimensional in nature. However, the horizontal components are much larger than the vertical ones.
2The apparent acceleration is small in actual value. Hence, the effect is only important for motions that occur over long time periods. In other words, it is critical for large-scale motions.
3.The magnitude of the apparent acceleration varies with latitude. It is zero at the equator and increases with the sin of the latitude. Hence, it has a maximum value at the poles.
4.The apparent deflection is always to the right in the Northern Hemisphere, and to the left in the Southern Hemisphere.
So motions in tropical regions will experience small deflections by the Coriolis Effect, while those of the middle and high latitudes will appear to be deflected to a much greater extent. The above rules allow one to qualitatively understand the effects of Coriolis on motions over the planet. A more quantitative understanding will require some attention to the mathematical expressions. These are discussed briefly in the following section.
SPECIAL TOPIC IV.
The Coriolis Effect
The mathematical solution to the moving reference frame problem of concern here turns out to be fairly simple. The apparent acceleration vector due to the rotating Earth is given by:
where is the Earth rotation vector, and V is the velocity vector of the wind. This describes the 3-dimensional acceleration applied by the Coriolis effect. It is always operating at right angles to the direction of motion.
When the above cross product is carried out and the magnitude of each of the terms is examined, it turns out that the vertical component as well as terms involving the vertical wind are small. Hence, only the horizontal components are of interest here. The horizontal component is given as:
where is the rotation rate of the Earth, or 7.27 x 10-5 s-1, and is latitude. The acceleration at right angles to the motion is calculated by simply multiplying the above term by the appropriate horizontal velocity component.
Where u is the x or east-west component of velocity, and v is the y or north-south component of velocity. The top expression represents the acceleration in the y direction imposed on air moving in the x direction. The lower expression represents acceleration in the x direction imposed upon air moving in the y direction. In the N. Hemisphere, the acceleration will always act to the right, while in the S. Hemisphere the acceleration always acts to the left of the direction of motion. Please note that the above expressions are accelerations.
As an example, consider air moving northward at 10 m s-1, at 45N. The above expression would result in a calculated acceleration of about 10-3 m s-2 acting to the right or eastward. Hence, over time the moving air will appear to be deflected eastward from the original path.
In order for the trajectory of the air to be deflected any substantial amount, a significant amount of time will be required. This is because the actual value of the acceleration is so small, that it must operate for a long enough time period to appreciably alter the direction of the wind.
Clearly the acceleration term is zero at the equator and maximum at the pole. In the middle and upper latitudes the size of the term is around 10-4 s-1. This is a very small value of acceleration, which means that it will be important only for large-scale motions that persist for long periods of time.
Resulting Average Surface Circulations:
By applying the properties of the Coriolis Effect to the motions depicted in our simplistic circulation model of Figure 13, the mean surface circulation for a rotating planet can be depicted. The results are illustrated in Figure 14.
Figure 14. Resulting mean flows for the rotating Earth
We can examine the results for the tropics and middle and high latitudes separately.
Tropics
Near the equator the Coriolis effect is small, and gently deflects the flows converging on the ITCZ. They become the NE and SE Trade Winds. Note that there is still convergence of flow at the ITCZ.
The zones of subsiding warm and dry air at about 30 N and 30 S induce an arid region of high pressure. Because of thermal contrasts between continents and oceans, the subsiding air does not define a broad region of high pressure. Instead fairly distinct cells of high pressure are observed. These are called subtropical highs. Their locations are fairly predictable, and they move with the seasons. The dry and subsiding air associated with these subtropical highs, produces very warm and arid climates. Indeed, most of the major deserts on the Earth are located in these regions.
Middle and High Latitudes
When one moves to the middle and high latitudes, the Coriolis effect increases significantly. When we apply this to the idealized surface winds, the deflections produce zones of middle latitude westerlies and polar easterlies, as shown in Figure 14. There are two points to be made here:
1.These are mean or temporal average circulations. The actual winds at any moment in time could differ from these.
2.The mean flows are parallel to one another. Hence, the cold air in polar regions flows parallel to the warm air from the subtropical regions.
The 2nd observation is very significant. It indicates that there is no direct transport of heat between the subtropical and polar regions by the mean flow. Yet the observed temperatures on the planet indicate that a substantial poleward heat transport must be occurring in the middle and high latitudes. Wewill discuss oceans later, but they cannot account for this much transport. So there must be a different mechanism for meridional heat exchange in these regions.
Horizontal Temperature Gradients and Jetstreams:
Because of the east-west nature of the flows in the middle and polar latitudes the cold and warm air are not mixed by the mean flow. Hence, there must exist a zone of very large horizontal temperature gradient in each hemisphere. In order to understand how these temperature gradients affect the winds, we must first look at the forces that govern wind.