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Introduction to Climatology Isaac (1642-1727) GEOGRAPHY 300

Tom Giambelluca University of Hawai‘i at Mānoa

Philosophiæ Naturalis Principia Mathematica (1687) "Mathematical Principles of Natural Philosophy” Atmospheric , , and • Newton’s Laws of Motion The General Circulation • Newton’s Law of Universal Gravitation • Theoretical Derivation of Kepler’s Laws of Planetary Motion • Laid the Groundwork for the Field of Calculus

Newton's Laws of Motion Newton's Laws of Motion

1st Law: Law of Inertia: If no net acts on a particle, the particle will Newton's Laws apply only in an inertial reference frame. not change . An inertial reference frame cannot be accelerating; must be at rest or An object at rest will stay at rest, and an object in motion, will continue at moving at a constant velocity (constant speed and direction). constant velocity unless acted on by external unbalanced force.

2nd Law: Law of Acceleration: The rate of change of velocity (acceleration) of a particle of constant is proportional to the net external force acting on the particle.

F a = m

or F = m⋅ a where a = acceleration, F = force, and m = mass.

1 Pressure Pressure

F The of an object is the force determined by gravitational P = A acceleration and the mass of the object:

Pressure = Force per Unit Area Weight = F = m × a

Pressure = Force per Unit Area = P = F/A In our environment, gravity is constantly accelerating objects downward. is the force exerted by the weight of the Gravitational acceleration (g) is approximately constant within the 's above a given point. atmosphere:

! m $ # & " s % m −2 g = 9.8 = 9.8 2 = 9.8 ms s s

Pressure Pressure

Measuring Atmospheric Pressure Pressure always decreases as you go up:

The Torricelli Tube: the original (invented in 1643 by )

Mean atmospheric pressure:

1013.2 mb = 101.32 kPa = 101,320 Pa

2 Pressure Pressure Gradients

Equation of State (): A Change in Pressure over a Distance

P = ρRT A pressure gradients is important because it exerts a force on air which acts to move air from high pressure to low pressure: where P = pressure (Pa), ρ = density (kg m-3), R = universal (287 J kg-1 K-1), and T = (K) Force

Changes in temperature or density cause changes in pressure.

High Pressure

Pressure Gradients Pressure Gradients

Vertical Pressure Gradient Hydrostatic Equilibrium

Because of the relationship between and pressure, a strong Upward vertical pressure gradient force is balanced by an equal force vertical pressure gradient is always present. oriented in the opposite direction.

Which direction is the resulting strong vertical pressure gradient force acting? The balance between vertical pressure gradient force and gravitational acceleration What effect does vertical pressure gradient force have on air motion? (Hydrostatic Balance) limits vertical motion in the atmosphere.

GRAVITY

3 Pressure Gradients Pressure Gradients

Horizontal Pressure Gradients Horizontal Pressure Gradients

Visualize the lower atmosphere seen from a cross sectional perspective. Connecting the points forms a 2-dimensional surface of all points having In the diagram below, upward in the atmosphere is toward the top. The the same pressure; we call this an isobaric surface; in profile, as in the horizontal line represents sea level. Go up from the ground until the drawing above, we see the edge of the isobaric surface; it is a line of pressure drops to 1000 mb. Do that from several different locations equal pressure, called an isobar.

Pressure Gradients Pressure Gradients

Horizontal Pressure Gradients Horizontal Pressure Gradients

In the pressure diagrams just shown, the isobaric surfaces were seen as flat and horizontal.

In that situation no horizontal pressure gradients are present.

Therefore, no wind would occur. The air would remain still.

If we went higher in the atmosphere, we would encounter isobaric surfaces with successively lower pressure values.

4 Pressure Gradients Pressure Gradients

Horizontal Pressure Gradients How Do We Get Horizontal Pressure Gradients?

In the previous diagram note that the distance between the 1000 and 900 We know that air density is affected by air temperature. Warm air is less mb surfaces is less than the distance between the 900 and 800 mb dense than cold air. The isobaric surfaces will have to be farther apart for surfaces. Why is that? warm air than for cold air.

Answer: As you go up, the decreases, therefore the distance necessary to reduce the pressure by 100 mb is greater as you go higher. Another way to think about this is that the mass of air between any 2 isobaric surfaces 100 mb apart is the same, i.e. you can equate the pressure difference with a given mass of air. But at higher , the air is less dense, so you have to go farther to reduce the mass of air above you by the amount necessary to lower the pressure by 100 mb.

Pressure Gradients Pressure Gradients

Horizontal Pressure Gradients Horizontal Pressure Gradients

Suppose you have one area with warm air and another area with cold air: Now we see horizontal differences in pressure. Along the ground, the cold air has higher pressure:

5 Pressure Gradients Pressure Gradients

Horizontal Pressure Gradients Horizontal Pressure Gradients

Higher up, we see the pressure gradient is reversed: The resulting circulation, if no other were acting, would be a cell such as:

Pressure Gradients Pressure Gradients

Sea Breeze and Land Breeze and Land Breeze

SEA BREEZE LAND BREEZE

6 Pressure Gradients Pressure Gradients

Horizontal Pressure Gradients Horizontal Pressure Gradients The horizontal pressure gradient can also be represented by the slope of The spacing of the isobars indicates the strength of the gradient and, an isobaric surface. Regarding the height of a pressure surface, areas therefore, the speed of the wind. where it is higher correspond to high pressure areas and vice versa. The steeper the slope of the isobaric surface, the stronger the horizontal pressure gradient.

Pressure Gradients CORIOLIS EFFECT Horizontal Pressure Gradients

Horizontal pressure patterns in the upper atmosphere are shown using The rotation of the earth on its axis means that the pressure surface height maps. surface of the earth is constantly accelerating. In our non-inertial reference frame, large-scale motion such as atmospheric and currents appear to be deflected away from the direction of the forces acting.

7 CORIOLIS EFFECT CORIOLIS EFFECT Let's try to understand Coriolis effect by looking at the Earth from above the North Pole: How about in the Southern Hemisphere? Let's look at the Earth from above the South Pole:

At the start (t1), a force causes an object to start moving south. The object continues in the same direction, but the Earth is rotating. As a result, an hour later (t2), the path of the object Now the object appears to have veered to the left of its appears to have veered off to the right, as viewed from the original direction. ground.

CORIOLIS EFFECT

Up in the atmosphere, away from the frictional influence of the earth's surface, the two important forces controlling wind speed and direction are horizontal pressure gradient force and coriolis. The balance between these two forces is called Geostrophic Balance. The wind resulting from this balance is called the Geostrophic Wind.

8 Geostrophic Wind Geostrophic Wind

In the absence of other forces, the wind would therefore Take a situation where the isobars are running east-west with low blow from south to north. But, due to the earth's rotation, pressure towards the north and high pressure towards the south. In that coriolis acts on the moving air, always directed at 90° to the case, the pressure gradient force acting on air is directed from south to north: right of the direction of motion in the Northern Hemisphere. That changes the direction of the wind. The pressure gradient force and Coriolis force come into balance when they are oriented in opposite directions. That balance occurs when wind is directed at 90° to the right of the pressure gradient force in the Northern Hemisphere (and 90° to the left of the pressure gradient force in the Southern Hemisphere).

Geostrophic Wind Geostrophic Wind

The Geostrophic Wind always flows parallel to the isobars: Some other examples:

9 Geostrophic Wind Pressure Cells

Southern Hemisphere examples: Often the pressure distribution produces cells of low or high pressure. In that case, the isobars are more or less circular, and wind would flow around the cells parallel to the isobars. Strictly speaking, geostrophic wind only applies to straight wind flow. But for curved flow such as wind moving around low or high pressure cells, we can use the geostrophic wind as an approximation.

Pressure Cells Pressure Cells

For a low pressure cell, pressure gradient force is directed But, Coriolis will deflect the wind to the right of the pressure gradient in inward toward the center of the cell: the Northern Hemisphere:

10 Pressure Cells Pressure Cells

That produces a counterclockwise wind pattern around low The direction of flow is opposite (clockwise) for low pressure centers in the Northern Hemisphere: pressure cells in the Southern Hemisphere:

Pressure Cells Pressure Cells

For a high pressure cell, the pressure gradient force is Coriolis causes wind to be directed to the right of the oriented outwards from the center of the cell: pressure gradient force in the Northern Hemisphere:

11 Pressure Cells Pressure Cells In the Southern Hemisphere, air flows counterclockwise And that produces clockwise circulation of air around high around high pressure cells: pressure cells in the Northern Hemisphere:

In either hemisphere, we call high pressure cells and low pressure cells . The flow direction around an is always refered to as anticyclonic, and around a the flow is always called cyclonic.

Pressure Cells Gradient Wind

In either hemisphere, we call high pressure cells anticyclones and low pressure cells cyclones. The flow In reality, geostrophic balance is only possible with straight direction around an anticyclone is always referred to flow. Curved flow, such as that around a high or low as anticyclonic, and around a cyclone the flow is always pressure cell, requires that pressure gradient force and called cyclonic. Coriolis be out of balance. For flow around an anticyclone (high pressure), Coriolis has to be stronger than pressure gradient force. Therefore the wind speed has to be greater

than it would be for straight flow. Conversely, for flow around a cyclone, Coriolis has to be weaker than pressure gradient force, requiring wind speed to be lower than for straight flow.

12 Gradient Wind Surface Wind Near the earth's surface, frictional force comes into play. Friction acts to slow the wind, and therefore can be thought of as always acting in the direction opposite of the . When the friction vector is added into the picture, the force vectors are no longer balanced:

Surface Wind Surface Wind

Balance is achieved when the wind direction changes so that wind is And for the Southern Hemisphere: directed across the isobars at an angle instead of flowing parallel to the isobars. The direction of Coriolis and friction depend on the wind direction. So when the wind shifts, they shift. With the wind crossing the isobars at an angle toward low pressure, the forces come into balance:

13 Surface Wind Surface Wind Near surface winds when isobars are straight and parallel: Near surface winds when isobars are straight and parallel: Northern Hemisphere: Sothern Hemisphere:

Surface Wind Surface Wind For curved flow around high or low pressure cells: For curved flow around high or low pressure cells: Northern Hemisphere: Southern Hemisphere:

14 Surface Wind Surface Pressure Patterns and Wind

Surface Pressure Patterns and Wind Upper Level Pressure Patterns and Wind

15 The General Circulation of the Atmosphere The General Circulation of the Atmosphere

Hadley: 1-cell model of 3-cell model of atmospheric circulation • Hadley cell • Ferrel Cell • Polar Cell

George Hadley (1682-1744)

William Ferrel (1817-1891)

The General Circulation of the Atmosphere The General Circulation of the Atmosphere

3-cell model of atmospheric circulation See animation of idealized atmospheric circulation:

• Hadley cell http://kingfish.coastal.edu/marine/Animations/Hadley/hadley.html • Ferrel Cell • Polar Cell

William Ferrel (1817-1891)

16 The General Circulation of the Atmosphere The General Circulation of the Atmosphere Mean Pressure Patterns Belts of Pressure and Zonal Winds January Pressure Belts • Intertropical Convergence Zone (ITCZ, Low Pressure) • Sub-Tropical High Pressure Belt • (Low Pressure) • Zonal Winds • Trade Winds: Tropical Easterlies • Mid-Latitude Westerlies •

The General Circulation of the Atmosphere The General Circulation of the Atmosphere Mean Pressure Patterns Components of the Hadley-Cell Circulation July • ITCZ – vigorously lifted air in the equatorial region – produces huge – visible in satellite images as a line of – shifts seasonally – shifts more over land areas – remains in the Northern Hemisphere over the central and eastern Pacific Ocean

17 The General Circulation of the Atmosphere The General Circulation of the Atmosphere Components of the Hadley-Cell Circulation Components of the Hadley-Cell Circulation • Poleward flowing air aloft • Trade winds – gradually cools by radiation – return flow of air from decending limb of Hadley cell – starts to sink due to cooling, and convergence back to the equator • Subtropical high pressure belt – flow has strong easterly component in both hemispheres due to Coriolis – zone of subsiding (sinking) air and high pressure around 30 degrees north and south – subsiding air causes this region to have very little – the great subtropical deserts, such as the Sahara and Kalahari Deserts are located in this zone – subsiding air also produces the trade wind inversion

The General Circulation of the Atmosphere The General Circulation of the Atmosphere Movement of the ITCZ Upper-Level Westerly Winds • Thickness Patterns • Seasonal shifts – The pressure gradient force, and hence the wind velocity, is – Moves north during northern determined by the slope of the isobaric surfaces. hemisphere summer and vice versa – In the presence of a horizontal temperature gradient, the thickness of each pressure layer changes horizontally. As a result – Over land, the seasonal shift is the isobaric surfaces tilt more and more toward the colder air. greater – Lines of constant thickness are parallel to lines of constant – Accounts for seasonal rainfall temperature, i.e. the thickness pattern and the temperature in some equatorial/tropical land pattern are the same. This is because the temperature pattern areas, such as the Amazon creates the thickness pattern. basin and the Sahel

18 The General Circulation of the Atmosphere The General Circulation of the Atmosphere

Upper-Level Westerly Winds Upper-Level Westerly Winds • The Thermal Wind • The Thermal Wind – The Thermal Wind can be thought of as a vector added to wind at – As a consequence of the Thermal Wind, air flow in the mid- one level to give the wind at a higher level. The size and direction latitudes becomes more and more westerly as you go up in of the Thermal Wind vector are determined by the thickness . pattern (temperature pattern) of the air layer in between. – The Thermal Wind is always pointed so that warm air is on its right side (in the Northern Hemisphere).

The General Circulation of the Atmosphere The General Circulation of the Atmosphere

Upper-Level Westerly Winds Upper-Level Westerly Winds • The Polar Front Jet Stream • Meanders in the upper level westerly winds – The north-south temperature gradient is strongest along the Polar – Mid-latitude isotherms do not always run exactly east-west, for Front. example,because of ocean-continent temperature contrasts. – As a result, the Thermal Wind is strongest there, and the upper- – Wave-patterns are common in the westerly wind flow. level westerlies become extremely strong. – The Polar Front Jet is a narrow stream of very fast moving air in the upper atmosphere.

19 The General Circulation of the Atmosphere The General Circulation of the Atmosphere

Upper-Level Westerly Winds Rossby Waves • , Upper-Level Divergence and Convergence • Rossby Waves – Vorticity is a measure of the rotation of a parcel of air. – Large waves in the westerly flow are known as Rossby waves. – Vorticity can be positive (cyclonic) or negative (anticyclonic). – Rossby waves constantly change in position and amplitude with major consequences for mid-latitude .

The General Circulation of the Atmosphere The General Circulation of the Atmosphere Rossby Waves Rossby Waves • Vorticity, Upper-Level Divergence and Convergence • Vorticity, Upper-Level Divergence and Convergence – Earth Vorticity: – Relative Vorticity: • is the rotation imparted by the earth’s rotation. • is the additional rotation due to the spin of the air, curved flow of air, • is related to Coriolis. or shear in the air flow • is maximum at the poles and zero at the equator • Is cyclonic (counterclockwise in the Northern Hemisphere) • Is anticyclonic in the Southern Hemisphere

20 The General Circulation of the Atmosphere The General Circulation of the Atmosphere Rossby Waves Rossby Waves • Vorticity, Upper-Level Divergence and Convergence • Vorticity, Upper-Level Divergence and Convergence – Absolute Vorticity: – The Law of Conservation of Angular Momentum: • is the sum of Earth Vorticity and Relative Vorticity • when applied to air, can be simply stated as: The absolute vorticity of – The Law of Conservation of Angular Momentum: an air column divided by the height of the air column must remain constant. Or another way of stating it is: The absolute vorticity of an • a familiar example of conservation of angular momentum is the air column multiplied by the area of the air column must remain increase in spin rate of an ice skater when the arms and leg are constant. pulled in closer to the axis of rotation: – Level of Non-Divergence: • Generally, air is either divergent or convergent aloft (in the upper atmosphere) and the opposite in the lower atmosphere. There is a gradual change from divergence to convergence, or vise versa as you go from the surface upward. Somewhere in between the surface and the upper atmosphere is a level where the air is neither convergent nor divergent: The Level of Non-Divergence.

The General Circulation of the Atmosphere The General Circulation of the Atmosphere Rossby Waves Rossby Waves • Vorticity, Upper-Level Divergence and Convergence • Vorticity, Upper-Level Divergence and Convergence – The Law of Conservation of Angular Momentum: – These waves in the westerly flow are known as Rossby waves. • Conservation of Angular Momentum requires that air crossing a – Rossby waves can also be triggered by SST anomalies. mountain barrier must compensate for the decreased height of the air – Cyclogenesis: Above the level of non-divergence, angular momentum column by curving in an anticyclonic direction (clockwise in the N. conservation can be maintained by convergence or divergence of the air, i.e. by increasing or decreasing the air column height, or in other words, by decreasing Hemisphere). (converging) or increasing (diverging) the horizontal area of the air column. Air • For example, westerly flow encountering the Rocky Mountains of moving downstream of a Rossby wave is moving from high positive relative western North America, will turn to the right as it passes the vorticity (cyclonic curvature) to zero relative vorticity (straight flow). The resulting mountains, becoming northwesterly. As a result, the air is flowing decrease in absolute vorticity is compensated for (above the level of non- toward lower latitudes, and its Earth Vorticity is decreasing as a divergence) by a decrease in the air column height, i.e. an increase in the area or result. At the level of non-divergence, the air must turn in a cyclonic diameter of the column. In other words the air aloft diverges. This causes air below to rise, setting in motion the process of developing a low pressure center at the direction (counterclockwise in the northern hemisphere) to conserve surface. As air rises, surface air will converge: lower level convergence. But as angular momentum. This causes the flow to change direction, long as the upper level divergence is greater than the lower level convergence, the becoming southwesterly. Succeeding changes in latitude will cause low pressure center (cyclone, ) will continue to strengthen. alternating anticyclonic and cyclonic changes in direction, setting up a series of waves downstream of the mountain barrier. The equatorward dips in the flow are called "troughs" and the poleward meanders are called "ridges".

21 The General Circulation of the Atmosphere Rossby Waves • Vorticity, Upper-Level Divergence and Convergence – As a result of this relationship between the voriticy changes in upper level flow and surface pressure, Rossby waves exert strong control on the formation and movement of midlatitude . These storms tend to form beneath the area of upper-level divergence downstream of a Rossby wave trough, and subsequently move in a path that tracks the upper-level wind. In the northern hemisphere, midlatitude cyclones tend to move from southwest to northeast as they go from intitial disturbance to maturity and occlusion.

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