NATS 101 Lecture 12 Newton’s Laws of Motion Upper-Air Maps and Winds

1. NATS 101Lecture 12Newton’s Laws of MotionUpper-Air Maps and Winds

2. 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!

3. (Constant height) Downhill 496 mb PGF 504 mb Ahrens, Fig. 2, p141 Isobaric Maps Some generalities: 1) High/Low heights on an isobar surface correspond to High/Low pressures on a constant height surface 2) Warm/Cold temps on an isobaric surface correspond to Warm/Cold temps on a constant height surface 3) The PGF on an isobaric surface corresponds to the downhill direction

4. Contour Maps How can we portray undulations of a 3D isobaric surface on a 2D plane without loss of information?

5. Contour Maps Consider the terrain height of an island. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html

6. Contour Maps 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

7. Contour Maps Raise the water level by 500’. Denote the new shoreline by another line. Labeled that line 500’ for five-hundred feet above mean-sea-level. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html

8. Contour Maps 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

9. Contour Maps Labeled another line 1500’ above mean-sea-level. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html

10. Contour Maps 2000’ above mean-sea-level. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html

11. Contour Maps 2500’ above mean-sea-level. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html

12. Contour Maps 3000’ above mean-sea-level. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html

13. Contour Maps 3500’ above mean-sea-level. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html

14. Contour Maps A 4000’ line is not needed since the island is completely submerged. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html

15. Contour Maps 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

16. Contour Maps Rotate to a top-down perspective. We can see the entire island. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html

17. Contour Maps If lines every 500’ is good, would lines every 250’ be better? Extra precision could be of value, but the map starts to get busy. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/contourlabel.html

18. Contour Maps Map can be clarified by accentuating every few contour lines Contours every 250’; labeled and thickened every 1250’ http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/contourlabel.html

19. Contour Spacing and Gradient Note differences in the steepness of the mountain slopes. Contours every 500’. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/contourspacing.html

20. Contour Spacing and Gradient Note that tight spacing of contours corresponds to steep slopes. Contours every 500’. http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/contourspacing.html

21. Topographic Map Google maps Grand Canyon Village

22. 570 dam contour

23. 576 dam contour

24. 570 and 576 dam contours

25. All contours at 6 dam spacing

26. All contours at 6 dam spacing

27. -20 C and –15 C Temp contours

28. -20 C, –15 C, -10 C Temp contours

29. All contours at 5o C spacing

30. Region of Low Heights TROUGH and Cold Region of High Heights RIDGE and Warmth Height contours Temps shaded

31. PGF Wind Wind doesn’t blow downhill!

32. Begs the Question…. Do Rocks Always Roll Downhill? PGF Upper-Level Winds Gedzelman, p 247

33. 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?

34. Why does the wind blow?To begin the answer to this question we first have to revisit Sir Isaac Newton

35. 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

36. 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

37. New Velocity Acceleration and Force Original Velocity Original Velocity New Velocity New Velocity Acceleration and Force Original Velocity New Velocity Original Velocity Velocity, Acceleration and Force are Vectors • Speed/Size Change • Direction Change

38. New Velocity Acceleration directed toward center of circle Centripetal New Velocity Original Velocity Original Velocity Uniform, Circular Motion Requires Acceleration Circular Path

39. 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… CENTRIFUGAL FORCE CENTRIPETAL FORCE

40. 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.

41. Simplified equation of horizontal atmospheric motion (1) (2) (3) (4) FOCUS ON FIRST TWO TODAY…

42. 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. 0 = Pressure gradient force + Coriolis force + Centripetal Force + Friction Geostrophic Balance 0 = Pressure gradient force + Coriolis force

43. Pressure gradient force Definition: Force to the difference in pressure (Δp) over a distance (d). (In the equation ρis the density of air) The pressure gradient force is directed perpendicular to lines of constant pressure (isobars), toward lower pressure.

44. 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: Isobars are close together Weak pressure gradient: Isobars are far apart. WEAK PRESSURE GRADIENT STRONG PRESSURE GRADIENT

45. The pressure gradient force is why the wind blows, but you need the other terms to complete the picture…

46. Upper Level Chart for Surface Arctic Air Outbreak (300-mb)

47. Observations for upper level winds: Wind DOES NOT follow the pressure gradient. Wind runs parallel to the lines of constant height (i.e. isobars). 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 DENVER 105 knots LOW HIGH PRESSURE GRADIENT AT DENVER ALBUQUERQUE 90 knots

48. Coriolis Force 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

49. 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.

50. Life on a Rotating Platform • From perspective of person not on merry-go-round, path of ball is straight. • From perspective of person on merry-go-round, path of ball deflects to left. There is an apparent force. (left click picture for animation) World Weather Project 2010 Courtesy of M. Ramamurthy U of Illinois, Urbana-Champaign Merry Go Round Link