1. Advanced SynopticM. D. Eastin QG Analysis: Upper-Level Systems Will this upper-level trough intensify or weaken? Where will the trough 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 upper-level troughs and ridges Which QG Equation? We could use the QG omega equation Would require additional steps to convert vertical motions to structure change No prediction → diagnostic equation → we would still need more information! We can apply the QG height-tendency equation Ideal for evaluating structural change above the surface Prediction of future structure → exactly what we want! QG Analysis: Upper-Level Systems Vertical Motion Differential Thermal Advection Vorticity Advection Diabatic Forcing Topographic Forcing + +

4. Advanced SynopticM. D. Eastin Evaluate Total Forcing:  You must consider the combined effects from each forcing type in order to infer the expected total geopotential height change Sometimes one forcing will “precondition” the atmosphere for another forcing and the combination will enhance amplification of the trough / ridge Other times, forcing types will oppose each other, inhibiting (or limiting) any amplification of the trough / ridge Note: Nature continuously provides us with a wide spectrum of favorable and unfavorable combinations…see the case study and your homework QG Analysis: Upper-Level Systems Vertical Motion Differential Thermal Advection Vorticity Advection Diabatic Forcing Topographic Forcing + +

5. Advanced SynopticM. D. Eastin Evaluate Total Forcing: Forcing for height falls:→ PVA (trough amplification)→ Increase in WAA with height → Increase in diabatic heating with height → Increase in downslope flow with height Forcing for height rises:→ NVA (ridge amplification)→ Increase in CAA with height → Increase in diabatic cooling with height → Increase in upslope flow with height QG Analysis: Upper-Level Systems Vertical Motion Differential Thermal Advection Vorticity Advection Diabatic Forcing Topographic Forcing + +

6. Advanced SynopticM. D. Eastin Important Aspects of Vorticity Advection:  Vorticity maximum at trough axis: PVA and height falls downstream NVA and height rises upstream No height changes occur at the trough axis Trough amplitude does not change Trough simply moves downstream (to the east) QG Analysis: Upper-Level Systems

7. Advanced SynopticM. D. Eastin Important Aspects of Vorticity Advection:  Vorticity maximum upstream of trough axis: PVA (or CVA) at the trough axis Height falls occur at the trough axis Trough amplitude increases Trough “digs” equatorward  Vorticity maximum downstream of trough axis: NVA (or AVA) at the trough axis Height rises occur at the trough axis Trough amplitude decreases Trough ”lifts” poleward QG Analysis: Upper-Level Systems Digs Lifts AVA

8. Advanced SynopticM. D. Eastin QG Analysis: Upper-Level Systems Important Aspects of Vorticity Advection: Digging Trough 500mb Wind Speeds 500mb Absolute Vorticity t = 0 hr t = 24 hr

9. Advanced SynopticM. D. Eastin QG Analysis: Upper-Level Systems Important Aspects of Vorticity Advection: Lifting Trough 500mb Wind Speeds 500mb Absolute Vorticity t = 0 hr t = 24 hr

10. Advanced SynopticM. D. Eastin Example Case: Formation / Evolution Will this upper-level trough intensify or weaken?

11. Advanced SynopticM. D. Eastin Trough Axis Vorticity Advection: Example Case: Formation / Evolution

12. Advanced SynopticM. D. Eastin Trough Axis NVA Expect Height Rises Χ > 0 PVA Expect Height Falls Χ < 0 Weak PVA at trough axis Expect trough to “dig” slightly Vorticity Advection: Example Case: Formation / Evolution

13. Advanced SynopticM. D. Eastin 500mb Trough Axis System has westward tilt with height Differential Temperature Advection: Example Case: Formation / Evolution

14. Advanced SynopticM. D. Eastin 500mb Trough Axis Low-level CAA No temperature advection aloft Expect upper-level Height Falls Χ < 0 Low-level WAA No temperature advection aloft Expect upper-level Height Rises Χ > 0 Expect upper-level trough to “dig” System has westward tilt with height Differential Temperature Advection: Example Case: Formation / Evolution

15. Advanced SynopticM. D. Eastin Diabatic Forcing: 500mb Trough Axis Example Case: Formation / Evolution

16. Advanced SynopticM. D. Eastin Deep Convection Diabatic Heating Expect upper-level Height Falls Χ < 0 Expect northern portion of upper-level trough to “dig” Diabatic Forcing: Example Case: Formation / Evolution 500mb Trough Axis

17. Advanced SynopticM. D. Eastin Topographic Forcing: 500mb Trough Axis Example Case: Formation / Evolution

18. Advanced SynopticM. D. Eastin Topographic Forcing: 500mb Trough Axis Example Case: Formation / Evolution Upslope flow (CAA) at low-levels No “topo” flow at 500mb Increase in WAA with height Expect upper-level Height Falls Χ < 0 Expect northern portion of upper-level trough to “dig”

19. Advanced SynopticM. D. Eastin Will this upper-level trough intensify or weaken? Trough Axis Initial Time Expect upper-level trough to “dig” Summary of Forcing Expectations: Example Case: Formation / Evolution

20. Advanced SynopticM. D. Eastin Initial Trough Axis Trough “dug” (intensified) “Results” 6-hr Later Example Case: Formation / Evolution

21. Advanced SynopticM. D. Eastin QG Analysis: Upper-Level System Motion Initial Trough Axis Current Trough Axis Trough moved east Why?

22.  Whether the relative or planetary vorticity advection dominates the height changes determines if the wave will “progress” or “retrograde” Advanced SynopticM. D. Eastin QG Analysis: Upper-Level System Motion Vertical Motion Differential Thermal Advection Vorticity Advection Diabatic Forcing Topographic Forcing + + OR Relative Vorticity Advection Planetary Vorticity Advection

23. Advanced SynopticM. D. Eastin Scale Analysis for a Synoptic Wave: Term B Absolute Vorticity Advection OR Relative Vorticity Advection Planetary Vorticity Advection Assume waves are sinusoidal in structure:U = basic current (zonal flow) L = wavelength of wave β = north-south Coriolis gradient Ratio of relative to planetary vorticity is: QG Analysis: Upper-Level System Motion

24. Advanced SynopticM. D. Eastin Scale Analysis for a Synoptic Wave: For the Mid-Latitudes:U ~ 10 m s -1 β ~ 10 -11 s -1 m -1  Whether relative or planetary vorticity advection dominates the height changes is a function of the wavelength Short Waves:L < 6000 km Relative vorticity dominates Long Waves:L > 6000 km Planetary vorticity dominates QG Analysis: Upper-Level System Motion

25. Advanced SynopticM. D. Eastin Short Waves: Most synoptic waves are short waves with wavelengths less than 6000 km Relative vorticity maxima (minima) are often located near trough (ridge) axes PVA and height falls east of troughs NVA and height rises east of ridges Short waves move eastward Trough Ridge L < 6000 km L L Adapted from Bluestein (1993) Vort Max Vort Min Note: Several “short waves” can stretch across the entire US at one time QG Analysis: Upper-Level System Motion

26. Advanced SynopticM. D. Eastin Long Waves: Long waves, with wavelengths greater than 6000 km, occur during stationary weather patterns Planetary vorticity maxima (minima) are located at ridge (trough) axes NVA and height rises west of ridges PVA and height falls west of troughs Long waves move westward Trough Ridge L > 6000 km Adapted from Bluestein (1993) Vort Max Vort Min Note: A single “long wave” would stretch across the entire US and beyond QG Analysis: Upper-Level System Motion

27. Advanced SynopticM. D. Eastin The “Kicker”: Long waves are often associated with stationary weather patterns When a short wave “kicker” approaches a stationary long wave trough, the wavelength associated with the long wave is effectively decreased Hence, the long wave becomes a short wave and begins to move eastward The short wave “kicked out” the long wave, and the stationary weather pattern ends From Bluestein (1993) QG Analysis: Upper-Level System Motion

28. Advanced SynopticM. D. Eastin Example Case: Motion Where will this upper-level trough move?

29. Advanced SynopticM. D. Eastin Trough Ridge L < 6000 km Short Wave Trough Examine relative vorticity advection Is it a “short wave” or a “long wave”? Initial Time Example Case: Motion

30. Advanced SynopticM. D. Eastin Trough Axis NVA Expect Height Rises Χ > 0 PVA Expect Height Falls Χ < 0 Expect trough to move east Effects of Vorticity Advection: Assume “local” absolute vort max are relative vort maxima Initial Time Example Case: Motion

31. Advanced SynopticM. D. Eastin Initial Trough Axis Current Trough Axis 6-hr Later Trough moved east Results: 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: Upper-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.