#### Transcript Upper-Air Maps Newton`s Laws

NATS 101 Lecture 12 Newton’s Laws of Motion Upper-Air Maps and Winds QuickTime™ and a decompressor are needed to see this picture. Isobaric Maps • Weather maps at upper levels are analyzed on isobaric (constant pressure) surfaces. (Isobaric surfaces are used for mathematical reasons that are too advanced to include in this course!) • Isobaric maps provide the same information as constant height maps, such as: Low heights on isobaric surfaces correspond to low pressures on constant height surfaces! Cold temps on isobaric surfaces correspond to cold temperatures on constant height surfaces! Isobaric Maps (Constant height) 496 mb 504 mb Some generalities: 1) The 2) 3) Warm/Cold High/Low PGF on heights temps an isobaric on onan ansurface isobar isobaric surface correspond corresponds to the downhill to Warm/Cold High/Low direction temps pressures on a constant on aheight constant surface height surface Ahrens, Fig. 2, p141 Contour Maps How can we portray undulations of a 3D isobaric surface on a 2D plane without loss of information? Contour Maps QuickTime™ and a decompressor are needed to see this picture. Consider the terrain height of an island. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Contour Maps QuickTime™ and a decompressor are needed to see this picture. Denote the shoreline by a line. Labeled the line 0’ for zero feet above mean-sea-level. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Contour Maps QuickTime™ and a decompressor are needed to see this picture. Raise the water level by 500’. Denote the new shoreline by another line. Labeled that line 500’ forhttp://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html five-hundred feet above mean-sea-level. Contour Maps QuickTime™ and a decompressor are needed to see this picture. Raise the water level by another 500’ to 1,000’. Labeled that line 1000’ for one thousand feet above mean-sea-level. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Contour Maps QuickTime™ and a decompressor are needed to see this picture. Labeled another line 1500’ above mean-sea-level. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Contour Maps QuickTime™ and a decompressor are needed to see this picture. 2000’ above mean-sea-level. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Contour Maps QuickTime™ and a decompressor are needed to see this picture. 2500’ above mean-sea-level. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Contour Maps QuickTime™ and a decompressor are needed to see this picture. 3000’ above mean-sea-level. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Contour Maps QuickTime™ and a decompressor are needed to see this picture. 3500’ above mean-sea-level. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Contour Maps QuickTime™ and a decompressor are needed to see this picture. A 4000’ line is not needed since the island is completely submerged. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Contour Maps QuickTime™ and a decompressor are needed to see this picture. Lower the water level back to 0’. We are left with lines every 500’ at 0’, 500’, 1000’,... above MSL http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Contour Maps QuickTime™ and a decompressor are needed to see this picture. Rotate to a top-down perspective. We can see the entire island. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Contour Maps If lines every 500’ is good, would lines every 250’ be better? QuickTime™ and a decompressor are needed to see this picture. Extra precision could be of value, but the map starts to get busy. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/contourlabel.html Contour Maps Map can be clarified by accentuating every few contour lines QuickTime™ and a decompressor are needed to see thisand picture. QuickTime™ a decompressor are needed to see this picture. Contours every 250’; labeled and thickened every 1250’ http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/contourlabel.html Contour Spacing and Gradient Note differences in the steepness of the mountain slopes. QuickTime™ and a decompressor are needed to see this picture. Contours every 500’. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/contourspacing.html Contour Spacing and Gradient Note that tight spacing of contours corresponds to steep slopes. QuickTime™ and a decompressor are needed to see this picture. Contours every 500’. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/contourspacing.html Topographic Map Google maps Grand Canyon Village 570 dam contour 576 dam contour 570 and 576 dam contours All contours at 6 dam spacing All contours at 6 dam spacing -20 C and –15 C Temp contours -20 C, –15 C, -10 C Temp contours All contours at 5o C spacing Region of Low Heights TROUGH and Cold Region of High Heights RIDGE and Warmth Height contours Temps shaded PGF Wind Do Rocks BegsAlways the Question…. Roll Downhill? PGF Gedzelman, p 247 The Empirical Evidence Shows • Wind Direction and PGF Relationship Winds more than 1 to 2 km above the ground are perpendicular to PGF! Analogous a marble rolling not downhill, but at a constant elevation with lower altitudes to the left of the marble’s direction How can we explain observations? Why does the wind blow? To begin the answer to this question we first have to revisit Sir Isaac Newton Newton’s Laws of Motion • Newton’s 1st Law An object at rest will remain at rest and an object in motion will remain at a constant velocity (same speed and same direction) if the net force exerted on it is zero An external force is required to speed up, slow down, or change the direction of air Newton’s Laws of Motion • Newton’s 2nd Law The net force exerted on an object equals its mass times its acceleration Sum of All Forces = Mass Acceleration Acceleration = Velocity Change / Time Acceleration = Change in Either Speed or Direction Velocity, Acceleration and Force are Vectors • Speed/Size Change New Velocity Original New Velocity Velocity Original Velocity • Direction Change New Velocity Original Velocity New Velocity Original Velocity Acceleration and Force Acceleration and Force Uniform, Circular Motion Requires Acceleration New Velocity Circular Path Original Velocity New Velocity Original Velocity Acceleration directed toward center of circle Centripetal Centripetal Force CENTRIFUGAL FORCE CENTRIPETAL FORCE You experience acceleration without a change in speed, for example, on a tilt-a-whirl carnival ride. The force is directed toward the center of the wheel. An equal an opposite (fictitious) centrifugal force is exerted by the inertia of your body on the wheel—so you stay put and don’t fall off even when upside down. Important when considering curved flows, as well see later… Newton’s 2nd law can be used to derive a governing equation for atmospheric motion The simplified form in the horizontal that we’ll consider has four terms. By understanding how each of these terms works, we’ll be able to explain why the wind blows. Simplified equation of horizontal atmospheric motion 1 p V2 Total Force 2V sin Fr d r (1) (2) (3) (4) Term Force Cause 1 Pressure gradient force Spatial differences in pressure 2 Coriolis force Rotation of the Earth 3 Centripetal force Curvature of the flow 4 Friction force FOCUS Acts TODAY… against direction of motion ON FIRST TWO due to interaction with surface Force Balance What we’re looking for in the equation of motion is the condition where the forces exactly balance—or the sum of the forces is equal to zero. When this happens, there is no net acceleration and the wind speed is constant, by Newton’s first law. 1 p V2 0 2V sin Fr d r 0 = Pressure gradient force + Coriolis force + Centripetal Force + Friction 0 = Pressure gradient force + Coriolis force Geostrophic Balance Pressure gradient force 1 p1 p d d Definition: Force to the difference in pressure (Δp) over a distance (d). (In the equation ρ is the density of air) The pressure gradient force is directed perpendicular to lines of constant pressure (isobars), toward lower pressure. Strength of the pressure gradient force How strong the pressure gradient is depends on distance between the areas of high and low pressure, or how close the lines of constant pressure are spaced. STRONG PRESSURE GRADIENT WEAK PRESSURE GRADIENT Strong pressure gradient: Isobars are close together Weak pressure gradient: Isobars are far apart. The pressure gradient force is why the wind blows, but you need the other terms to complete the picture… Upper Level Chart for Surface Arctic Air Outbreak (300-mb) Observations for upper level winds: Wind DOES NOT follow the pressure gradient. Wind runs parallel to the lines of constant height (i.e. isobars). DENVER 105 knots LOW HIGH PRESSURE GRADIENT AT DENVER ALBUQUERQUE 90 knots Strength of the wind IS related to the closeness, or packing, of the isobars. For example, compare the wind speed at Denver (105 knots) to some of the surrounding upper air observations, like Albuquerque. NEED AT LEAST ONE OF THE OTHER THREE FACTORS TO ACCOUNT FOR WIND MOTION Coriolis Force 22V Vsin sin Definition: Apparent force due to rotation of the Earth (Ω). Depends on the speed (V) and the latitude (Φ). Gaspard Coriolis Causes apparent deflection in reference of an observer at a fixed point on Earth Coriolis force on a merry-go-round From perspective of person NOT on the merry-go-round, path of ball is straight. From perspective of person on merry-go-round, path of ball deflects. It accelerates. This is an apparent (fictitious) force. Life on a Rotating Platform QuickTime™ and a YUV420 codec decompressor are needed to see this picture. (left click picture for animation) World Weather Project 2010 Courtesy of M. Ramamurthy U of Illinois, Urbana-Champaign • From perspective of person not on merrygo-round, path of ball is straight. • From perspective of person on merry-goround, path of ball deflects to left. There is an apparent force. Merry Go Round Link Rotation of the Earth (from the polar perspective) NORTHERN HEMISPHERE deflection SOUTHERN HEMISPHERE deflection (Getzelman) COUNTERCLOCKWISE ROTATION Deflection to the right CLOCKWISE ROTATION Deflection to the left SAME IDEA AS THE MERRY-GO-ROUND! Coriolis Effect: An Apparent Force Cannonball follows a straight path to an observer in space Earth rotates counter-clockwise underneath cannonball (in Northern Hemisphere) Cannonball appears to deflect to the right to an observer on earth Shot misses Paris to the right Coriolis Force and Latitude All three airplanes travel in a straight line with respect to an outside observer (from space). The largest deviation, or deflection to the right, with respect to an observer on Earth occurs for the one traveling closest to the pole. The higher the latitude, the greater the Coriolis force. Accounted for by the sine term in the mathematical expression. Zero at equator (sin 0° = 0) Maximum at poles (sin 90° = 1) Coriolis force and speed The Coriolis force is proportional to the wind speed. The faster the speed (or velocity), the greater the amount of Coriolis force. Note also the dependence on latitude here. Coriolis Force vs. Wind Direction NORTHERN HEMISPHERE WIND SOUTHERN HEMISPHERE CORIOLIS FORCE (TO LEFT) WIND CORIOLIS FORCE (TO RIGHT) Coriolis force acts perpendicular (at a right angle) to the wind direction, to the right or left depending on which hemisphere. Key Points: Coriolis Force • Introduced to account for the earth’s rotation. • Only deflects a moving object. Never changes the speed of an object. • Zero if the velocity of an object relative to the earth’s surface is zero. • Zero at the equator. For given speed, it is maximum at the poles. Geostrophic Adjustment QuickTime™ and a YUV420 codec decompressor are needed to see this picture. (left click picture to animate) World Weather Project 2010 Courtesy of M. Ramamurthy U of Illinois, Urbana-Champaign A. Parcel at rest initially accelerates toward lower pressure. B. Coriolis Force rotates parcel to right in NH. C. As parcel speeds up, Coriolis Force increases. D. Eventually (about a day), PGF equals CF and flow is parallel to isobars. Animate Picture Geostrophic Wind PARCEL RELEASED Positions 1 and 2: Pressure gradient force accelerates the parcel towards the low pressure. Coriolis force acts to the right of the velocity of the parcel, making it curve to the right. Geostrophic Wind Positions 3 and 4: Pressure gradient force continues to accelerate the parcel towards the low pressure. As the velocity of the parcel increases, the Coriolis force increases, making the parcel continue to curve to the right. Geostrophic Wind Position 5: FINAL STATE Pressure gradient force is balanced by the Coriolis force. Velocity of the parcel is constant (no acceleration). Direction is parallel to the isobars. FINAL STATE is called geostrophic balance. Geostrophic Wind PRESSURE GRADIENT FORCE Isobar 2 WIND Isobar 1 CORIOLIS FORCE Pressure gradient force is equally balanced by the Coriolis force, so net force is zero. Wind speed and direction (velocity) is constant (no acceleration). Direction of wind is parallel to the isobars, or lines of constant pressure. PRESSURE GRADIENT FORCE Isobar 2 WIND Isobar 1 WEAK GEOSTROPHIC WIND Isobars far apart CORIOLIS FORCE PRESSURE GRADIENT FORCE Isobar 2 WIND STRONG GEOSTROPHIC WIND Isobar 1 Isobars close together CORIOLIS FORCE Geostrophic Wind and Upper Level Charts CORIOLIS FORCE PRESSURE GRADIENT FORCE GEOSTROPHIC WIND Winds at upper levels are pretty close to being geostrophic: Wind is parallel to isobars Wind strength dependents on how close together isobars are Simplified equation of horizontal atmospheric motion 1 p V2 Total Force 2V sin Fr d r GEOSTROPHY:(1) No centripetal force or friction X (2) (3) (4) Term Force Cause 1 Pressure gradient force Spatial differences in pressure 2 Coriolis force Rotation of the Earth 3 Centripetal force Curvature of the flow 4 Friction force Acts against direction of motion due to interaction with surface DoNot Rocks if the Always Hill isRoll Big Downhill? Enough! PGF Gedzelman, p 247 Fundamental Concepts for Today • Rotation of Earth Geocentric =Accelerated Frame of Reference • Introduce Coriolis “Force” Apparent Force to Account for Deflection Depends on Rotation, Latitude, Wind Speed • Geostrophic Balance and Wind Balance Between PGF and Coriolis Force Geostrophic Wind Blows Parallel to Contours About One Day Required to Reach Balance Assignment Next Lecture Surface Wind,Vertical Air Motions • Reading - Ahrens 3rd: 155-162 4th: 157-164 5th: 158-164 • Problems - HW05 D2L (Due Wed. Mar. 3) 3rd-Pg 162: 6.23, 6.24 4th-Pg 164: 6.23, 6.24 5th-Pg 165: 6.24, 6.25