1. Advanced SynopticM. D. Eastin QG Analysis: Low-Level Systems Will these Surface Lows Intensify or Weaken? Where will they Move?

2. Advanced SynopticM. D. Eastin QG Analysis QG Theory Basic Idea Approximations and Validity QG Equations / Reference QG Analysis Basic Idea Estimating Vertical Motion QG Omega Equation: Basic Form QG Omega Equation: Relation to Jet Streaks QG Omega Equation: Q-vector Form Estimating System Evolution QG Height Tendency Equation Diabatic and Orographic Processes Evolution of Low-level Systems Evolution of Upper-level Systems

3. Advanced SynopticM. D. Eastin Goal:We want to use QG analysis to diagnose and “predict” the formation, evolution, and motion of low-level (or surface) cyclones and anticyclones Which QG Equation? We cannot apply the QG height-tendency equation Lower boundary condition assumes no height tendency at the surface Contrary to what we are trying to infer… We can use the QG omega equation Evaluate above the surface Then we can use QG theory to infer low-level (or surface) pressure changes QG Analysis: Low-Level Systems Vertical Motion Thermal Advection Differential Vorticity Advection Diabatic Forcing Topographic Forcing + +

4. Advanced SynopticM. D. Eastin Local application of the QG Theory at the Surface: If rising motion (ω < 0) is present above the surface (where ω = 0), then we know: Recall: We can then infer from the QG vorticity equation that: Recall: Using the relationship between vorticity tendency and height tendency we thus know: Recall: and Finally, using the height / pressure tendency relationship via hydrostatic balance: Since:via  Therefore:Rising motions aloft → Surface pressure decreases Sinking motions aloft → Surface pressure increases QG continuity equation Equivalent to low-level convergence QG Analysis: Low-Level Systems

5. Advanced SynopticM. D. Eastin Combined Effects of Forcing Evaluate Total Forcing:  You must consider the combined effects from each forcing type in order to infer the expected total vertical motion and surface pressure change Sometimes one forcing will “precondition” the atmosphere for another forcing and the combination will enhance low-level (or surface) cyclogenesis Other times, forcing types will oppose each other, inhibiting (or limiting) any low-level (or surface) cyclogenesis Note: Nature continuously provides us with a wide spectrum of favorable and unfavorable combinations…see the case study and your homework Vertical Motion Thermal Advection Differential Vorticity Advection Diabatic Forcing Topographic Forcing + +

6. Advanced SynopticM. D. Eastin Favorable Combinations of Forcing Vorticity Advection with Temperature Advection: Scenario: A region of increasing PVA with height (located downstream from a trough) is collocated with a region of strong warm air advection PVA Max Vort WAA Upper Levels Lower Levels

7. Advanced SynopticM. D. Eastin Favorable Combinations of Forcing Temperature Advection with Diabatic Heating: Scenario: A region of strong warm advection collocated with deep convection Commonly observed near warm fronts and in the warm sector WAA

8. Advanced SynopticM. D. Eastin Favorable Combinations of Forcing Vorticity Advection with Temperature Advection and Diabatic Heating: Scenario: A region of increasing PVA with height (located downstream from a trough) is collocated with a region of warm air advection and deep convection Max Vort WAA Upper Levels Lower Levels PVA

9. Advanced SynopticM. D. Eastin Favorable Combinations of Forcing Vorticity Advection with Downslope Motions: Scenario: A region of increasing PVA with height (located downstream from a trough) is located over the leeside of a mountain range PVA Max Vort Downslope Motions Upper Levels Lower Levels

10. Advanced SynopticM. D. Eastin Unfavorable Combinations of Forcing Vorticity Advection with Temperature Advection: Scenario: A region of increasing PVA with height (located downstream from a trough) is collocated with a region of strong cold air advection PVA Max Vort CAA Upper Levels Lower Levels

11. Advanced SynopticM. D. Eastin Unfavorable Combinations of Forcing Vorticity Advection with Downslope Motions: Scenario: A region of increasing NVA with height (located upstream from a trough) is located over the leeside of a mountain range NVA Max Vort Downslope Motions Upper Levels Lower Levels

12. Advanced SynopticM. D. Eastin Example Case: Formation / Evolution Will these Surface Lows Intensify or Weaken?

13. Advanced SynopticM. D. Eastin Differential Vorticity Advection: L L L Example Case: Formation / Evolution

14. Advanced SynopticM. D. Eastin Differential Vorticity Advection: L L PVA Assume NO vorticity advection below Rising Motion Surface Pressure Decreases L Example Case: Formation / Evolution NVA Assume NO vorticity advection below Sinking Motion Surface Pressure Increases

15. Advanced SynopticM. D. Eastin Thermal Advection: L L L Example Case: Formation / Evolution

16. Advanced SynopticM. D. Eastin Thermal Advection: L L L WAA Rising Motion Surface Pressure Decreases CAA Sinking Motion Surface Pressure Increases Example Case: Formation / Evolution

17. Advanced SynopticM. D. Eastin Diabatic Forcing: L L L Example Case: Formation / Evolution

18. Advanced SynopticM. D. Eastin Diabatic Forcing: L L L Diabatic Cooling Sinking Motion Surface Pressure Increases Diabatic Heating Rising Motion Surface Pressure Decreases Note the snow and cloud cover Note: Time is 12Z or 5:00-7:00 am (before or at sunrise) Note the clear skies Example Case: Formation / Evolution

19. Advanced SynopticM. D. Eastin Topographic Forcing: L L L Note direction of surface winds from the previous slide Example Case: Formation / Evolution

20. Advanced SynopticM. D. Eastin Topographic Forcing: L L L Downslope Flow Rising Motion Surface Pressure Decreases Note direction of surface winds from the two slides ago Example Case: Formation / Evolution

21. Advanced SynopticM. D. Eastin Moderate NVA D Weak CAA D Diabatic CoolingD Downslope FlowU ----------------------------------------------------------- Net Pressure RiseD/R ----------------------------------------------------------- 15Z: Pressure rose 2 mb Moderate NVAD Weak WAAU Diabatic CoolingD Downslope FlowU ----------------------------------------------------------- Net Pressure RiseD/R ----------------------------------------------------------- 15Z: Pressure rose 3 mb Weak PVAU Moderate CAAD Diabatic HeatingU Downslope FlowU ----------------------------------------------------------- Net Pressure FallU/F ------------------------------------------------------------ 15Z: Pressure fell 1 mb Example Case: Formation / Evolution

22. Advanced SynopticM. D. Eastin Will this Surface Low Move? QG Analysis: Low-level System Motion

23. Advanced SynopticM. D. Eastin Goal:Use QG theory to diagnose the motion of low-level (or surface) systems Application of QG Theory: Surface cyclones always move away from regions with pressure increases toward regions with pressure decreases In essence, surface cyclones “move down the pressure change gradient” CycloneRegions of sinking motion→ Regions or rising motion MotionRegions of NVA aloft → Regions of PVA aloft (From → To)Regions of CAA→ Regions of WAA Regions of diabatic cooling → Regions of diabatic heating Regions of upslope flow→ Regions of downslope flow AnticycloneRegions of rising motion→ Regions of sinking motion MotionRegions of PVA aloft→ Regions of NVA aloft (From → To) Regions of WAA→ Regions of CAA Regions of diabatic heating→ Regions of diabatic cooling Regions of downslope flow→ Regions of upslope flow QG Analysis: Low-level System Motion

24. Advanced SynopticM. D. Eastin Influence of Topography: Consider a cyclone (low pressure system) east of a mountain range: Motion will be to the south along the range Consider an anticyclone east of a mountain range Motion will be to the south along the range L Upslope Flow → Pressure Increase Downslope Flow → Pressure Decrease H Upslope Flow → Pressure Increase Downslope Flow → Pressure Decrease QG Analysis: Low-level System Motion

25. Advanced SynopticM. D. Eastin Influence of Topography and Temperature Advection: Consider a low pressure system initially just east of a mountain range: Motion will be to the southeast Consider the low at a later time southeast of the mountain range Motion will now be to the east-southeast  As the low moves further away from the mountain range, it begins to feel less topographic effects and more temperature advection effects → acquires a more northeastward motion L Upslope Flow → Pressure Increase Downslope Flow → Pressure Decrease WAA → Pressure Decrease T T-ΔT T-2ΔT L Weaker Upslope Flow → Pressure Increase Weaker Downslope Flow → Pressure Decrease WAA → Pressure Decrease T T-ΔT T-2ΔT QG Analysis: Low-level System Motion

26. Advanced SynopticM. D. Eastin Example Case: Motion Where will this Surface Low Move?

27. Advanced SynopticM. D. Eastin Differential Vorticity Advection: L Example Case: Motion Maximum PVA Assume NO vorticity advection below Expect motion toward the south

28. Advanced SynopticM. D. Eastin Thermal Advection: L Maximum WAA Expect motion toward the southeast Example Case: Motion

29. Advanced SynopticM. D. Eastin Diabatic Heating: L Maximum Heating Expect motion toward the northwest Example Case: Motion

30. Advanced SynopticM. D. Eastin Flow over Orography: L Maximum Downslope Flow Expect motion toward the southwest Example Case: Motion

31. Advanced SynopticM. D. Eastin Motion Summary LL WAA PVA Heating Downslope Expected Motion Initial Location Later Location Example Case: Motion

32. Advanced SynopticM. D. Eastin Application Tips: Evolution and Motion ALL relevant forcing terms should be analyzed in each situation!!! Differential vorticity advection and thermal advection are the dominant terms in the majority of situations → weight these terms more Diabatic forcing can be important for system evolution when deep convection or dry/clear air are present. Diabatic forcing can be important for system motion when the forcing is asymmetric about the system center Topographic forcing is only relevant near large mountain ranges or rapid elevation changes over a short horizontal distance QG Analysis: Low-level Systems

33. Advanced SynopticM. D. Eastin References Bluestein, H. B, 1993: Synoptic-Dynamic Meteorology in Midlatitudes. Volume I: Principles of Kinematics and Dynamics. Oxford University Press, New York, 431 pp. Bluestein, H. B, 1993: Synoptic-Dynamic Meteorology in Midlatitudes. Volume II: Observations and Theory of Weather Systems. Oxford University Press, New York, 594 pp. Charney, J. G., B. Gilchrist, and F. G. Shuman, 1956: The prediction of general quasi-geostrophic motions. J. Meteor., 13, 489-499. Durran, D. R., and L. W. Snellman, 1987: The diagnosis of synoptic-scale vertical motionin an operational environment. Weather and Forecasting, 2, 17-31. Hoskins, B. J., I. Draghici, and H. C. Davis, 1978: A new look at the ω–equation. Quart. J. Roy. Meteor. Soc., 104, 31-38. Hoskins, B. J., and M. A. Pedder, 1980: The diagnosis of middle latitude synoptic development. Quart. J. Roy. Meteor. Soc., 104, 31-38. Lackmann, G., 2011: Mid-latitude Synoptic Meteorology – Dynamics, Analysis and Forecasting, AMS, 343 pp. Trenberth, K. E., 1978: On the interpretation of the diagnostic quasi-geostrophic omega equation. Mon. Wea. Rev., 106, 131-137.