QG Analysis: Additional Processes

1. QG Analysis: Additional Processes M. D. Eastin

2. 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 M. D. Eastin

3. QG Analysis: Vertical Motion • Review: The BASIC QG Omega Equation • Term ATerm BTerm C • Term B: Differential Vorticity Advection • Therefore, in the absence of geostrophic vorticity advection and diabatic processes: • An increase in PVA with height will induce rising motion • An increase in NVA with heightwill induce sinking motion Z-top Hydrostatic Balance Thickness decreases must occur with cooling PVA Adiabatic Warming Adiabatic Cooling Rising Motions Sinking Motions Z-400mb PVA ΔZ ΔZ decreases Z-700mb PVA ΔZ ΔZ decreases Z-bottom M. D. Eastin

4. QG Analysis: Vertical Motion • Review: The BASIC QG Omega Equation • Term ATerm BTerm C • Term C: Thermal Advection • WAA(CAA) leads to local temperature / thickness increases (decreases) • In order to maintain geostrophic flow, ageostrophic flows and mass continuity • produce a vertical motion through the layer • Therefore, in the absence of geostrophic vorticity advection and diabatic processes: • WAA will induce rising motion • CAAwill induce sinking motion Z-top Z-top Surface Rose Z-400mb Z-400mb ΔZ increase WAA ΔZ Surface Fell Z-700mb Z-700mb Z-bottom Z-bottom M. D. Eastin

5. Vertical Motion: Diabatic Heating/Cooling • What effect does diabatic heating or cooling have? • Diabatic Heating: Latent heat release due to condensation (Ex: Cumulus convection) • Strong surfaces fluxes (Ex: CAA over the warm Gulf Stream) • (Ex: Intense solar heating in the desert) • Heating always leads to temperature increases → thickness increases • Consider the three-layer model with a deep cumulus cloud • Again, the maintenance of geostrophic flow requires rising motion through the layer • Identical to the physical response induced by WAA • Therefore: Diabatic heating induces rising motion Z-top Surface Rose Z-400mb ΔZ ΔZ increases Surface Fell Z-700mb Z-bottom M. D. Eastin

6. Vertical Motion: Diabatic Heating/Cooling • What effect does diabatic heating or cooling have? • Diabatic Cooling: Evaporation (Ex: Precipitation falling through sub-saturated air) • Radiation (Ex: Large temperature decreases on clear nights) • Strong surface fluxes (Ex: WAA over snow/ice) • Cooling always leads to temperature decreases → thickness decreases • Consider the three-layer model with evaporational / radiational cooling • Again, maintenance of geostrophic flow requires sinking motion through the layer • Identical to the physical response induced by CAA • Therefore: Diabatic cooling aloft induces sinking motion Z-top Surface Fell Z-400mb ΔZ decreases ΔZ Z-700mb Surface Rose Z-bottom M. D. Eastin

7. Vertical Motion: Topography • What effect does flow over topography have? • Downslope Motions: Flow away from the Rockies Mountains • Flow away from the Appalachian Mountains • Subsiding air always adiabatically warms • Subsidence leads to temperature increases → thickness increases • Consider the three-layer model with downslope motion at mid-levels • Again, maintenance of geostrophic flow requires rising motion through the layer • Identical to the physical response induced by WAA and diabatic heating • Therefore: Downslope flow induces rising motion Z-top Surface Rose Z-400mb ΔZ ΔZ increases Surface Fell Z-700mb Z-bottom M. D. Eastin

8. Vertical Motion: Topography • What effect does flow over topography have? • Upslope Motions: Flow toward the Rockies Mountains • Flow toward the Appalachian Mountains • Rising air always adiabatically cools • Ascent leads to temperature decreases → thickness decreases • Consider the three-layer model with upslope motion at mid-levels • Again, maintenance of geostrophic flow requires sinking motion through the layer • Identical to the physical processes induced by CAA and diabatic cooling • Therefore: Upslope flow induces sinking motion Z-top Surface Fell Z-400mb ΔZ decreases ΔZ Z-700mb Surface Rose Z-bottom M. D. Eastin

9. QG Analysis: Vertical Motion • Update: The Modified QG Omega Equation • + Diabatic + Topographic • ForcingForcing • Note: The text includes a modified equation • with only diabatic effects [Section 2.5] • Application Tips: • Differential vorticity advection and thermal advection are the dominant terms • in the majority of situations → weight these terms more • Diabatic forcing can be important when deep convection or dry/clear air are present • Topographic forcing is only relevant near large mountain ranges Vertical Motion Differential Vorticity Advection Thermal Advection M. D. Eastin

10. QG Analysis: Vertical Motion • Application Tips: • Diabatic Forcing • Use radar → more intense convection → more vertical motion • Use IR satellite → cold cloud tops → deep convection or high clouds? • → warm cloud tops → shallow convection or low clouds? • Use VIS satellite → clouds or clear air? • Use WV satellite → clear air → dry or moist? • Topographic Forcing • Topographic maps → Are the mountains high or low? • Use surface winds → Is flow downslope, upslope, or along-slope? M. D. Eastin

11. QG Analysis: System Evolution • Review: The BASIC QG Height Tendency Equation • Term ATerm BTerm C • Term B: Vorticity Advection • Positive vorticity advection (PVA) PVA → • causes local vorticity increases • From our relationship between ζg and χ, we know that PVA is equivalent to: • therefore: PVA → or, since: PVA → • Thus, we know that PVAat a single level leads toheight falls • Using similar logic, NVA at a single level leads to height rises M. D. Eastin

12. QG Analysis: System Evolution • Review: The BASIC QG Height Tendency Equation • Term ATerm BTerm C • Term C: Differential Thermal Advection • Consider an atmosphere with an arbitrary vertical profile of temperature advection • Thickness changes throughout the profile will result from the type (WAA/CAA) and • magnitude of temperature advection though the profile • Therefore: An increase in WAA advectionwith height leads to height falls • An increase in CAA advection with height leads to height rises M. D. Eastin

13. System Evolution: Diabatic Heating/Cooling • Recall: • Local diabatic heating produces the • same response as local WAA • Likewise local diabatic cooling is • equivalent to local CAA • Evaluation: • Examine / Estimate the vertical profile • of diabatic heating / cooling from all • available radar / satellite data Clear Regions Z Diabatic Coolingmax located in upper-levels due to radiational cooling Diabatic heatingmax located near surface due to surface fluxes Net Result: Increase in cooling with height Height Rises Regions of Deep Convection Regions of Shallow Convection Z Z Diabatic Heating max located in upper-levels due to condensation Diabatic cooling max located below cloud base due to evaporation Diabatic Coolingmax located in upper-levels due to radiational cooling Diabatic heatingmax located in lower-levels due to condensation Net Result: Increase in heating with height Height Falls Net Result: Increase in cooling with height Height Rises M. D. Eastin

14. System Evolution: Topography • Recall: • Local downslop flow produces the • same response as local WAA • Likewise local upslope flow is • equivalent to local CAA • Evaluation: • Examine / Estimate the vertical profile • of heating due to topographic effects Downslope Flow Upslope Flow Z Z No adiabatic heating No topographic effects above the mountains Adiabatic Heating due to downslope flow No adiabatic heating No topographic effects above the mountains Adiabatic Cooling due to upslope flow Net Result: Decrease in heating with height above heating max → height rises Decrease in heating with height below heating max → height falls Net Result: Decrease in cooling with height above cooling max → height falls Decrease in cooling with height below cooling max → height rises M. D. Eastin

15. QG Analysis: System Evolution • The Modified QG Height Tendency Equation • + Diabatic + Topographic • ForcingForcing • Application Tips: • Differential vorticity advection and thermal advection are the dominant terms • in the majority of situations → weight these terms more • Diabatic forcing can be important when deep convection or dry/clear air are present • Topographic forcing is only relevant near large mountain ranges Height Tendency Vorticity Advection Differential Thermal Advection M. D. Eastin

16. QG Analysis: System Evolution • Application Tips: • Diabatic Forcing • Use radar → more intense convection → more vertical motion • Use IR satellite → cold cloud tops → deep convection or high clouds? • → warm cloud tops → shallow convection or low clouds? • Use VIS satellite → clouds or clear air? • Use WV satellite → clear air → dry or moist? • Topographic Forcing • Topographic maps → Are the mountains high or low? • Use surface winds → Is flow downslope, upslope, or along-slope? M. D. Eastin

17. 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. M. D. Eastin