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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. Average Radiation Absorbed and Emitted vs Latitude Absorbed Solar Radiation Surplus Emitted Infrared Radiation Energy Deficit Deficit 90 40 0 40 90 Latitude Figure 10. The absorbed and emitted radiation vs. latitude 25 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. 26 Tropics Large Radiation Values Rnet Evaporate Water Heat Surface Moist and Unstable Air Evaporation Heat 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. 27 Clouds Release of Latent Heat Warm, Moist Air Rises Intertropical Convergence Zone -- ITCZ 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 28 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. Radiational Cooling Hadley Cells Radiational Cooling Cold and Dry Air Latent Heat Released Clouds Warm and Dry Air Warm and Dry Air Moist Air ~ 30 N ITCZ ~ 30 S 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. 29 Idealized Circulation for Non-rotating Earth Polar Cell Ferrel Cell Hadley Cell ICE ITCZ 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: 30 dq = c p dT - dP 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: 0 = c p dT - RT dP P dividing both sides of the above expression by T yields: cp dT dP =R T P Recall from Special Topic I. that the atmosphere is hydrostatic, meaning that pressure is defined by the weight of the air column above any point. This was expressed as: dp = - g dz This can be substituted for dP in the earlier expression, and the Gas Law used to substitute for as follows: cp dT R ( gdz) = T P P = RT 31 c p dT = - gdz dT g =dz cp 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 32 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 apparent acceleration 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. 2 The 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. 33 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: 2 x V 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: 2 sin 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. 2 sin . u 2 sin . v 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. 34 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. 35 Polar Easterlies Westerlies Subtropical High Subtropical High Trade Winds ITCZ Subtropical High Subtropical High 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 36 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. We will 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. The unequal heating of the Earth surface produces horizontal variations in pressure. The resulting horizontal pressure gradient imposes acceleration, causing the wind to blow initially towards the low pressure. Of course, the Coriolis effect will induce a deflection on the moving air. Figure 15 illustrates the balance of forces on the air. As the air moves towards lower pressure it increases in velocity in response to the acceleration from the pressure gradient. Recall that the Coriolis effect is proportional to the velocity. Hence, the magnitude of the Coriolis effect increases, causing a further increase in the deflection, until it eventually increases to a value equal to the acceleration caused by the pressure gradient. There is a then balance between the two. The resulting wind blows parallel to lines of constant pressure. This is called the geostrophic wind. This wind is often observed in the middle and upper troposphere, when the flow is not greatly curved. 37 Geostrophic Wind Balance Between Pressure Gradient and Coriolis Acceleration V P L P V C P P V V C C H C Figure 15. The evolution towards the balance of forces for the Geostrophic Wind Since the pressure field at the surface often has centers of high and low pressure, then the wind will often follow a curved or even circular path. Thus, we must consider another factor that is present when motions are along curved paths. Any circular motion, requires that a centripetal acceleration act inward to maintain the circular path. Hence, in addition to pressure gradient and Coriolis effect, we must include centripetal acceleration for flow around centers of high and low pressure. The resulting wind is called the gradient wind. The balance of forces in this case is shown in Figure 16 and 17. Note that centripetal acceleration is always directed inward by definition. However, pressure gradient is directed outward near a high pressure and inward near a low pressure. Coriolis of course is always to the right of the direction of motion. The centripetal acceleration can be viewed as the imbalance between the pressure gradient and Coriolis terms. 38 Gradient Wind Around Low Pressure Coriolis Acceleration does not balance Pressure Gradient and Centripetal Acceleration V Ce L P C Figure 16. Gradient wind around low pressure Gradient Wind Around High Pressure Pressure Gradient does not balance Centripetal Acceleration and Coriolis Acceleration Ce H P C V Figure 17. Gradient wind around high pressure 39 ______________________________ SPECIAL TOPIC V. Geostrophic and Gradient Winds: The geostrophic wind consists of a balance between the Coriolis effect and the pressure gradient, which can be expressed as: 1 P x 1 P f ug = y f vg = where f is the Coriolis acceleration or 2 sin , is density, P is pressure, and ug and vg are the x and y components of the geostrophic wind. Note that the wind in the x direction is defined by the pressure gradient in the y direction. This is because the Coriolis effect acts perpendicular to the wind. If we consider the flow around pressure centers, the centripetal acceleration must be considered. This term acts inward to hold the motion in a circle. The appropriate expression for the balance of forces are now given as: 2 V h 1 P f Vh+ = r n 40 where Vh is the horizontal wind vector, r is the radius of curvature of the circle, and n is the direction perpendicular to the flow. ______________________________ Horizontal Temperature Gradient and Thermal Wind: We need to consider the relationship between horizontal pressure gradients with height under the presence of horizontal temperature gradients. First let us look at a simple case where there are no horizontal variations in temperature. This is illustrated in Figure 18. Note that the pressure surfaces are parallel to each other as well as the surface. Change of Pressure With Height When Horizontal Temperature is Constant P4 = 200 mb P3 = 400 mb Height P2 = 600 mb P1 = 800 mb T = constant P0 = 1000 mb Horizontal Distance Figure 18. Pressure surfaces vs. height for uniform surface temperature When there is a gradient of temperature in the horizontal, the horizontal gradient of pressure and its variation with height are altered. An example is provided in Figure 19. Notice that the pressure lines become slanted with height, indicating a horizontal gradient of pressure. Also note the increase in the slope of the lines with height. The magnitude of the horizontal pressure gradient is now increasing with height. 41 P4 P3 Height P2 P1 Cold Warm Horizontal Distance Figure 19. Pressure surfaces vs. height under horizontal temperature gradient Recall that warmer air is less dense than cold air. Hence, the vertical thickness of atmosphere between any two pressure levels will be greater for a warmer air column. It requires a greater depth of low density air to provide the necessary mass between two pressure levels. The figure illustrates that the height of a given pressure level increases above warmer air, and decreases above the more dense colder air. So cold air is associated with a thinner atmosphere, while warm air is associated with a thicker atmosphere. So an increase in horizontal pressure gradient with elevation results from the horizontal temperature gradient. The slope of the lines of constant pressure increases with height. This indicates that the horizontal pressure gradient is increasing with height above a temperature gradient. To understand this you must recall that the pressure decreases exponentially with height. As a result, the density of air also reduces rapidly with height. So as one goes higher in the atmosphere, the change in height for a given drop in pressure increases rapidly. As a result, the difference in thickness between two pressure levels for air columns of different density increases with height. If pressure gradient increases with height, then so must the wind velocities. So the net result of a horizontal temperature gradient is to induce an increase in the geostrophic wind with height. This phenomenon is called the thermal wind. Clearly the 42 greater the horizontal temperature gradient, the greater the increase of winds with height. Such an atmosphere, characterized by horizontal gradients in temperature and density, is termed baroclinic. The horizontal temperature gradient is greatest in the middle latitudes, where it is cold air from the poles moves adjacent to the warm air from the subtropics. This gradient in temperature produces a belt of westerlies in the upper troposphere. At the actual interface between warm and cold air masses, the gradient of temperature is especially large, as shown in Figure 20. P4 P3 Height P2 P1 Cold Warm Horizontal Distance Figure 20. Pressure surfaces over narrow horizontal temperature gradient Over this sharp zone of temperature contrast the thermal wind process produces narrow zones of very high velocity winds within the westerlies in the upper troposphere. These are called jetstreams, and they exist in each hemisphere. Jetstreams and sharp horizontal temperature gradients in the middle latitudes are mutually arising features. That is to say, the existence of one defines the existence of the other. The upper air westerlies and embedded jetstreams move over each hemisphere in wave-like patterns. When the flow is mainly oriented east-west it is called zonal flow. In this case there is little wave structure to the flow. On the other hand, when there are large waves present, much of the flow is oriented north-south or parallel to the meridian lines. Hence, this is referred to as meridional flow. These waveforms are denoted by the terms troughs and ridges. Figure 21 shows examples of a trough and a ridge. 43 Upper Air Flow Ridge Trough Figure 21. Illustration of trough and ridge in upper air flow When the waves shown in Figure 21 are rather large in size, they are referred to as Rossby Waves. There may be a variable number of these waves across a hemisphere. The air flows in the direction indicated in these upper air winds. But the waves also move from west to east. So the troughs and ridges will move eastward at a phase velocity which is different from the velocity of air moving along the wave. The speed is variable, but in general the larger the wavelength the smaller rate of movement. Of course, the size and structure of the waves often changes as they move. It is a very dynamic system. Another way to view the flow of the upper air is to consider the spatial variation of height for a given pressure level. In other words at what height in the atmosphere a given pressure is reached. When this value is plotted for each location, the resulting map is that of a height field. The higher values in the field represent regions of the atmosphere where a large height value or thickness is required to reach a certain pressure level. It turns out that the flow of air is parallel to the lines of constant height, or contours. In fact, the velocity of the air will be proportional to the strength of the gradient of the height field. It is completely analogous to the relationship between horizontal pressure gradient and winds. 44 Linkage of Jetstreams to Surface Pressure Pattern The patterns of the upper air westerlies such as illustrated in Figure 21 have a connection to the pressure fields and winds of the surface. How can wave-like patterns in the upper air flow connect with surface pressure systems? There are several processes that explain the connections. We can treat one of the processes in a somewhat descriptive fashion, while the other process directly applies mathematics and physics. Changes in Thickness and Vertical Motions First consider the eastward movement of a trough in the upper air flow, and a location upwind of this trough. As the trough approaches the height of any pressure surface is decreasing. Thus, the depth of atmosphere is lowering with time at this location. The atmosphere is getting thinner. If this is true, then the atmosphere must also be getting more dense and colder. If the atmosphere ahead of the advancing trough is getting colder, there must be a process or mechanism at work to reduce the temperature. Given that we have already shown that the atmosphere obeys the hydrostatic and adiabatic approximations, there is only one possible process that could result in cooling the atmosphere in this case. This process is rising motion. So the lowering heights of pressure surfaces with time are associated with upward vertical motions of the air. Vorticity and Vertical Motions Another approach to examine the connections between upper air waves and vertical motions involves looking at changes in the curvature of the wind. The rotation of a fluid is expressed by a mathematical property called vorticity. A rotation in a counterclockwise direction is defined as positive. We call this flow cyclonic in the Northern Hemisphere, since it is the same direction as flow around a low pressure. Conversely, a rotation in a clockwise direction is defined as negative. This flow is called anticyclonic. Since the Earth spins, it imparts a natural rotation to air. This means the Coriolis Effect will result in the presence of vorticity. The amount will depend upon the sin of the latitude. The direction of rotation caused by Earth rotation will be counterclockwise in the Northern Hemisphere, and it will induce a positive vorticity. So moving air always has a background value of positive vorticity at all locations in the Northern Hemisphere save the equator. Any rotations that exist due to the curvature of the flow, will either add or subtract from this background value. 45 SPECIAL TOPIC V. The mathematical expression for rotation of a fluid is given by: V where V is the velocity vector. The usual notation for the x, y, and z components of wind are u, v, and w. So the above can be expanded as: iˆ ˆj kˆ x u y v z w v u w w v u iˆ ˆj kˆ y z z x x y As we will be using vorticity to explain why air horizontally diverges and converges, the term of most interest is the horizontal rotation around a vertical axis. This is the last term in the above expression. So we are left with; v u x y This contribution to vorticity by the gradients in wind is called relative vorticity. 46 Vorticity Measure of the spin or rotation of a fluid We are interested in the rotation around vertical axis Anticyclonic or Negative Vorticity Cyclonic or Positive Vorticity The diagram below shows how horizontal changes of u and v can indeed induce a rotation. The change in v with x is positive, while u is decreasing with y, and is negative. Since the second term is subtracted from the first, they add to produce positive relative vorticity. Y Induces Positive Vorticity u decreasing with y v increasing with x X 47 The vorticity can be separated into the effects of the Earth’s rotation and the relative vorticity due to the gradients in the wind. The sum of these is called the absolute vorticity. Recall that the vorticity induced by the Coriolis in the Northern Hemisphere is always positive, and increases with the latitude. The relative vorticity can be either zero, positive, or negative, depending on the degree of curvature of the flow. Now let us return to an upper air flow with a trough and a ridge. As the air flows over the top of a ridge the relative vorticity reaches a maximum negative value. So the absolute vorticity is at the lowest value at that point. As the air moves towards the trough, the relative vorticity is increasing from negative to positive. This means the absolute vorticity is increasing. As the air flows around the bottom of the trough, the relative vorticity reaches the maximum positive value, and absolute vorticity reaches its largest value. As the air moves ahead of the trough, the relative vorticity is decreasing as is the value of absolute vorticity. So ahead of a ridge the rotation is increasing. However, ahead of a trough the rotation is decreasing. This is illustrated in Figure 22. Negative Vorticity Absolute Vorticity Decreasing Divergence Convergence Absolute Vorticity Increasing Positive Vorticity Figure 22. Changes in vorticity and associated divergence and convergence Notice that there is a zone of convergence ahead of the ridge, and divergence ahead of the trough. How are these connected to vorticity changes? This can be discussed in a descriptive way by recalling the principle of conservation of angular momentum. This states that the product of the angular velocity and the radius squared is conserved during rotation. 48 Ahead of the ridge the vorticity or rotation rate is increasing, which implies the radius of curvature of the flow must decrease. In other words, the flow must be converging in order to spin faster. So convergence is observed ahead of the ridge. The opposite effect is observed ahead of the trough. Here the vorticity is decreasing, and the rate of rotation is slowing. The radius must be growing larger, which means the air is spreading out or diverging. So divergence is observed in front of the trough. In the Southern Hemisphere the same physical processes apply, but the signs change. The Coriolis parameter is negative, so the vorticity values produced by the Earth’s rotation are negative. For example, the structure we define as a ridge, when present in the upper air flow in the Southern Hemisphere is physically the same as a trough in the Northern Hemisphere. Since cold air now comes from the south, the center of a ridge is actually an indication of cold air and low heights. At the ridge center the background vorticity and relative vorticity are both negative. Ahead of the ridge to the east, the relative vorticity gradually increases to positive values at the trough. So the absolute vorticity value is changing from very negative to less negative. This means that the total rotation is growing smaller, and divergence should be observed in the upper air flow ahead of the ridge. So the physics are the same in the Southern Hemisphere as they must be. But the change in sign of the Coriolis and opposite meaning of critical flow patterns, require careful attention. Increasing Vorticity Values -- Relate to Convergence Decreasing Vorticity Values -- Relate to Divergence As area or radius gets smaller due to convergence -- rotation rate increases Convergence So how do the divergence and convergence in the upper air lead to vertical motion? If air is converging aloft the collision will force air outwards. There must be a flow of air directed downwards. Conversely, if the air is diverging aloft, then it must be 49 replaced by air rising from below. So we now have vertical motions resulting from the changes in rotation in the upper air. Note that it is changes in vorticity with distance that cause divergence and convergence aloft, which induces vertical motions. Another way to express this is that the advection or transport of vorticity towards a region, causes vertical motions. So waves in the upper air induce vertical motions by two processes: Changes in thickness with time Transport or advection of vorticity These are the processes by which waves in the upper-air flow cause vertical motions. Figure 23 shows the relationship between the resulting vertical motions and surface pressure. Convergence Upper Air Divergence High Pressure Divergence Convergence Low Pressure Surface Figure 23. Connections between vertical motions and surface pressures The rising and sinking air will induce low and high pressures at the surface. The resulting pressure gradients will often cause the formation of a center of surface high pressure in front of a ridge, and center of surface high pressure in front of a trough. Let us look at the situation in advance of an upper air trough. The resulting gradient winds near the surface will blow counterclockwise around the low pressure system. Considering for a moment the N. Hemisphere, this means that warm air will be moved northward, while cold air will move southward. A cold front is likely to form at the southern boundary of the cold air mass, and a warm front at the northern boundary of the warm air mass. This is depicted in Figure 24. 50 Cold Initial Formation of Low Low Upper Air Flow Developed Low Pressure System Figure 24. L Surface Warm Overunning Clouds-Precip Latent Heat Relationship between trough and developing low pressure system It should be clear that the wave-like behavior of the upper air in the vicinity of the jetstream, is crucial to vertical motions surface pressure systems. The key issues that we have discussed in the last few sections can be summarized as follows: Divergence ahead of upper air trough induces surface convergence and low pressure -- rising motion Divergence aloft related to curvature of flow or vorticity Rising motion also related to atmosphere becoming thinner and colder Upper air ridge causes convergence, which leads to surface divergence and high pressure -- sinking motion Related to curvature or vorticity changes in upper air flow Sinking motion also related to atmosphere becoming thicker and warmer The surface weather near the low will be unsettled, with precipitation and strong winds common due to the rising motion associated with low pressure and the collisions of cold and warm air. The condensation of water vapor into liquid water occurring during 51 the forced rise of air masses, releases additional latent heat. This latent heat release is very substantial, and provides further energy for the storms. Hence, latent heat plays a significant role in energy transport, even in the middle latitudes. These are baroclinic storms, which are the necessary result of strong horizontal temperature gradients. As the trough in the jetstream moves eastward, so does the surface low and the associated flow pattern and weather. Of course, the lifetime of the upper air feature is limited to a matter of days, since the upper air wave pattern is always changing. Hence, these systems result in a transient movement of heat towards the pole. If we consider the situation upstream of an advancing ridge in the jetstream, the opposite effects will be observed. Now heights will be rising, implying that the atmosphere must be growing thicker and less dense. Such warming of the atmosphere is associated with subsiding air, leading to higher surface pressure. The surface winds will then flow clockwise around the high pressure. This circulation also moves cold air south, and warm air north. Importance to Global Heat Transport So, low pressure disturbances or baroclinic storms, and high pressure centers, both caused by the waves in the upper air flow and jetstream induce transient meridional flows of heat. These flows are very transient, but they are large! In addition, a substantial part of the heat transport is in the form of latent heat released during the storms. This is the indirect mechanism that transfers heat poleward in the middle latitudes. Note that this has been a very simplified and qualitative approach to these processes. We have only considered horizontal temperature gradients, and not discussed the angular momentum imparted to the atmosphere by the rotating planet. This momentum is transported poleward, and plays a role in formation of jetstreams. But that topic is beyond our scope in this class. We have considered what is normally called the polar front or polar jetstream. This is associated with the largest horizontal temperature gradient that exists along the boundary between the cold polar air and warmer air from the subtropics. In reality, there is sometimes a second jetstream. The subtropical jetstream exists just poleward of the Hadley cells. It is much weaker than the polar jet, but still induces baroclinic disturbances and transports heat meridionally. 52