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Geophysical Fluid Dynamics: Atmospheric Dynamics

This lecture covers topics such as thermal wind, vertical wind, and thermal circulation in geophysical fluid dynamics, specifically focusing on atmospheric dynamics. The lecture includes approximated equations of motion, geostrophic wind, hydrostatic balance, and the relationship between temperature and wind.

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Geophysical Fluid Dynamics: Atmospheric Dynamics

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  1. AOSS 401Geophysical Fluid Dynamics:Atmospheric DynamicsPrepared: 20131029Thermal Wind / Vertical Wind / Thermal Circulation Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Cell: 301-526-8572

  2. Class News • Ctools site (AOSS 401 001 F13) • Second Examination on December 10, 2013 • Homework • Watch for Ctools / Email

  3. Weather • National Weather Service • Model forecasts: • Weather Underground • Model forecasts: • NCAR Research Applications Program

  4. Outline • Thermal wind • Revisit the Tour of the Earth • Vertical structure • Vertical wind • Formation of a circulation feature

  5. Approximated equations of motion in pressure coordinates

  6. Geostrophic wind

  7. Hydrostatic Balance

  8. Schematic of thermal wind. Thickness of layers related to temperature. Causing a tilt of the pressure surfaces. from Brad Muller

  9. What is a tactic for exploring vertical behavior?

  10. Geostrophic wind Take derivative wrt p. Links horizontal temperature gradient with vertical wind gradient.

  11. Thermal wind p is an independent variable, a coordinate. Hence, x and y derivatives are taken with p constant.

  12. A excursion to the atmosphere.Zonal mean temperature - Jan approximate tropopause north (winter) south (summer)

  13. A excursion to the atmosphere.Zonal mean temperature - Jan ∂T/∂y ? north (winter) south (summer)

  14. A excursion to the atmosphere.Zonal mean temperature - Jan ∂T/∂y ? north (winter) south (summer)

  15. A excursion to the atmosphere.Zonal mean temperature - Jan ∂T/∂y ? <0 <0 <0 <0 <0 >0 north (winter) south (summer)

  16. A excursion to the atmosphere.Zonal mean temperature - Jan ∂T/∂y ? ∂ug/∂p ? <0 >0 <0 <0 >0 <0 <0 <0 > 0 >0 <0 >0 north (winter) south (summer)

  17. A excursion to the atmosphere.Zonal mean wind - Jan north (winter) south (summer)

  18. Relation between zonal mean temperature and wind is strong • This is a good diagnostic – an excellent check of consistency of temperature and winds observations. • We see the presence of jet streams in the east-west direction, which are persistent on seasonal time scales. • Is this true in the tropics?

  19. Thermal wind

  20. Thermal wind

  21. Thermal wind

  22. Thermal wind ?

  23. From Previous LectureThickness Note link of thermodynamic variables, and similarity to scale heights calculated in idealized atmospheres Z2-Z1 = ZT ≡ Thickness - is proportional to temperature is often used in weather forecasting to determine, for instance, the rain-snow transition.

  24. Similarity of the equations There is a direct relationship between thermal wind and thickness.

  25. Schematic of thermal wind. Thickness of layers related to temperature. Causing a tilt of the pressure surfaces. from Brad Muller

  26. In class problems • Group A • Scott • Anna • Alex • James • Justin • Kevin • Group B • John • Ross • Rachel • Trent • Jordan

  27. Another excursion into the atmosphere. 850 hPa surface 300 hPa surface • Identify: Surface low and trough / Upper troposphere low and trough • Using state boundaries: describe position or surface and upper trop features • Describe surface temperature advection from Brad Muller

  28. Another excursion into the atmosphere. X X X 850 hPa surface 300 hPa surface

  29. Another excursion into the atmosphere. X X X 850 hPa surface 300 hPa surface

  30. Another excursion into the atmosphere. 850 hPa surface 300 hPa surface

  31. Another excursion into the atmosphere. 850 hPa surface 300 hPa surface

  32. A summary of ideas. • In general, these large-scale, middle latitude dynamical features tilt westward with height. • The way the wind changes direction with altitude is related to the advection of temperature, warming or cooling in the atmosphere below a level. • This is related to the growth and decay of these disturbances. • Lifting and sinking of geopotential surfaces.

  33. Schematic of thermal wind. Thickness of layers related to temperature. Causing a tilt of the pressure surfaces. from Brad Muller

  34. Outline • Vertical Motion • Rotation in Fluid, Vorticity

  35. Vertical motions: The relationship between w and  = 0 hydrostatic equation ≈ 1m/s 1Pa/km≈ 1 hPa/d ≈ 100 hPa/d ≈ 10 hPa/d

  36. Link between  and the ageostrophic wind = 0 Links the horizontal and vertical motions. Since geostrophy is such a good balance, the vertical motion is linked to the divergence of the ageostrophic wind (small).

  37. Vertical pressure velocity : Kinematic method For synoptic-scale (large-scale) motions in midlatitudesthehorizontal velocity is nearly in geostrophic balance.Recall: the geostrophic wind is nondivergent (for constant Coriolis parameter), that isHorizontal divergence is mainly due to small departures from geostrophic balance (ageostrophic wind). Therefore: small errors in evaluating the winds <u> and <v> lead to large errors in . The kinematic method is inaccurate.

  38. Think about this ... • If I have errors in data, noise. • What happens if you average that data? • What happens if you take an integral over the data? • What happens if you take derivatives of the data?

  39. Estimating the vertical velocity: Adiabatic Method Start from thermodynamic equation in p-coordinates: Assume that the diabatic heating term J is small (J=0), re-arrange the equation - (Horizontal temperature advection term) Sp:Stability parameter

  40. Estimating the vertical velocity: Adiabatic Method Horizontal temperature advection term Stability parameter • If T/t = 0 (steady state), J=0 (adiabatic) and Sp > 0 (stable): • then warm air advection:  < 0, w ≈ -/g > 0 (ascending air) • then cold air advection:  > 0, w ≈ -/g < 0 (descending air)

  41. Adiabatic Method • Based on temperature advection, which is dominated by the geostrophic wind, which is large. Hence this is a reasonable way to estimate local vertical velocity when advection is strong.

  42. Estimating the vertical velocity: Diabatic Method Start from thermodynamic equation in p-coordinates: If you take an average over space and time, then the advection and time derivatives tend to cancel out. Diabatic term

  43. An example that connects it all

  44. Equations of motion in pressure coordinates(plus hydrostatic and equation of state)

  45. Let’s think about growing and decaying disturbances. Mass continuity equation.

  46. Let’s think about growing and decaying disturbances. Formally links vertical wind and divergence.

  47. Remember • What is the definition of omega, ω?

  48. Let’s think about growing and decaying disturbances. Convergence (divergence) of mass into (from) column above the surface will increase (decrease) surface pressure.

  49. In class problems • Group A • Scott • Anna • Alex • James • Justin • Kevin • Group B • John • Ross • Rachel • Trent • Jordan

  50. Initiation of flow pressure surfaces Earth’s surface

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