Advanced SynopticM. D. Eastin QG Analysis: Additional Processes

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

Advanced SynopticM. D. Eastin Review: The BASIC QG Omega Equation Term A Term B Term 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 height will induce sinking motion QG Analysis: Vertical Motion PVA Z-top Z-400mb Z-700mb Z-bottom ΔZ decreases ΔZΔZ Hydrostatic Balance Thickness decreases must occur with cooling ΔZΔZΔZ decreases Rising Motions Adiabatic Cooling Sinking Motions Adiabatic Warming

Advanced SynopticM. D. Eastin Review: The BASIC QG Omega Equation Term A Term B Term 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  CAA will induce sinking motion QG Analysis: Vertical Motion Z-400mb Z-700mb Z-bottom ΔZ increase Surface Rose Z-top Surface Fell Z-400mb Z-700mb Z-bottom Z-top WAA ΔZΔZ

Advanced SynopticM. D. Eastin 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 Vertical Motion: Diabatic Heating/Cooling ΔZ increasesΔZΔZ Surface Rose Surface Fell Z-400mb Z-700mb Z-bottom Z-top

Advanced SynopticM. D. Eastin 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 Vertical Motion: Diabatic Heating/Cooling ΔZ decreases ΔZΔZ Surface Rose Surface Fell Z-400mb Z-700mb Z-bottom Z-top

Advanced SynopticM. D. Eastin 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 Vertical Motion: Topography ΔZ increasesΔZΔZ Surface Rose Surface Fell Z-400mb Z-700mb Z-bottom Z-top

Advanced SynopticM. D. Eastin 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 Vertical Motion: Topography ΔZ decreases ΔZΔZ Surface Rose Surface Fell Z-400mb Z-700mb Z-bottom Z-top

Update: The Modified QG Omega Equation + Diabatic + Topographic Forcing Forcing 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 Advanced SynopticM. D. Eastin QG Analysis: Vertical Motion Vertical Motion Thermal Advection Differential Vorticity Advection

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? Advanced SynopticM. D. Eastin QG Analysis: Vertical Motion

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

Advanced SynopticM. D. Eastin Review: The BASIC QG Height Tendency Equation Term A Term B Term 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 advection with height leads to height falls An increase in CAA advection with height leads to height rises QG Analysis: System Evolution

Advanced SynopticM. D. Eastin 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 System Evolution: Diabatic Heating/Cooling Regions of Deep Convection Net Result: Increase in heating with height Height Falls Diabatic Heating max located in upper-levels due to condensation Diabatic cooling max located below cloud base due to evaporation Z Clear Regions Diabatic Cooling max located in upper-levels due to radiational cooling Diabatic heating max located near surface due to surface fluxes Z Net Result:Increase in cooling with height Height Rises Regions of Shallow Convection Net Result: Increase in cooling with height Height Rises Z Diabatic Cooling max located in upper-levels due to radiational cooling Diabatic heating max located in lower-levels due to condensation

Advanced SynopticM. D. Eastin 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 System Evolution: Topography Downslope Flow Net Result: Decrease in heating with height above heating max → height rises Decrease in heating with height below heating max → height falls No adiabatic heating No topographic effects above the mountains Adiabatic Heating due to downslope flow Z Upslope Flow Net Result: Decrease in cooling with height above cooling max → height falls Decrease in cooling with height below cooling max → height rises No adiabatic heating No topographic effects above the mountains Adiabatic Cooling due to upslope flow Z

The Modified QG Height Tendency Equation + Diabatic + Topographic Forcing Forcing 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 Advanced SynopticM. D. Eastin Height Tendency Differential Thermal Advection Vorticity Advection 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? Advanced SynopticM. D. Eastin QG Analysis: System Evolution

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, Durran, D. R., and L. W. Snellman, 1987: The diagnosis of synoptic-scale vertical motionin an operational environment. Weather and Forecasting, 2, Hoskins, B. J., I. Draghici, and H. C. Davis, 1978: A new look at the ω–equation. Quart. J. Roy. Meteor. Soc., 104, Hoskins, B. J., and M. A. Pedder, 1980: The diagnosis of middle latitude synoptic development. Quart. J. Roy. Meteor. Soc., 104, 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,