Introduction to Climatology Isaac Newton (1642-1727) GEOGRAPHY 300 Tom Giambelluca University of Hawai‘i at Mānoa Philosophiæ Naturalis Principia Mathematica (1687) "Mathematical Principles of Natural Philosophy” Atmospheric Pressure, Wind, 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 force acts on a particle, the particle will Newton's Laws apply only in an inertial reference frame. not change velocity. 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 mass 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 weight 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. Atmospheric Pressure is the force exerted by the weight of the Gravitational acceleration (g) is approximately constant within the earth's atmosphere 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 barometer (invented in 1643 by Evangelista Torricelli) Mean sea level atmospheric pressure: 1013.2 mb = 101.32 kPa = 101,320 Pa 2 Pressure Pressure Gradients Equation of State (Ideal Gas Law): 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 gas constant (287 J kg-1 K-1), and T = temperature (K) Pressure Gradient 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 elevation 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 density of air 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 elevations, 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 forces were acting, would be a cell such as: Pressure Gradients Pressure Gradients Sea Breeze and Land Breeze Sea 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 winds and ocean 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 Geostrophic Wind 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 anticyclones and low pressure cells cyclones.