Advanced SynopticM. D. Eastin QG Analysis: Additional Processes

Advanced Synoptic M. D. Eastin

QG Analysis: Additional Processes


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


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

TVp

RfV

p

f

p

fggg

202

2202

PVA

PVA

PVA

Z-top

Z-400mb

Z-700mb

Z-bottom

ΔZ decreasesΔZ

HydrostaticBalance

Thicknessdecreasesmust occurwith coolingΔZ ΔZ decreases

RisingMotions

AdiabaticCooling

SinkingMotions

AdiabaticWarming


Review: The BASIC QG Omega Equation


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


TVp

RfV

p

f

p

fggg

202

2202

Z-400mb

Z-700mb

Z-bottom

ΔZ increase

SurfaceRose

Z-top

SurfaceFell

Z-400mb

Z-700mb

Z-bottom

Z-top

WAA ΔZ


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 increasesΔZ

SurfaceRose

SurfaceFell

Z-400mb

Z-700mb

Z-bottom

Z-top


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 decreasesΔZSurfaceRose

SurfaceFell Z-400mb

Z-700mb

Z-bottom

Z-top


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 increasesΔZ

SurfaceRose

SurfaceFell

Z-400mb

Z-700mb

Z-bottom

Z-top


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 decreasesΔZSurfaceRose

SurfaceFell 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



TVp

RfV

p

f

p

fggg

202

2202

VerticalMotion

ThermalAdvection

Differential VorticityAdvection

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?




Review: The BASIC QG Height Tendency Equation


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 PVA at a single level leads to height falls Using similar logic, NVA at a single level leads to height rises

TVp

Rf

pfVf

p

fg

oggo

2

2

2202

QG Analysis: System Evolution

0

tg

2

0

1p

g

ft

02 p 0 2


Review: The BASIC QG Height Tendency Equation


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 fallsAn increase in CAA advection with height leads to height

rises

TVp

Rf

pfVf

p

fg

oggo

2

2

2202



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 heightHeight Falls

Diabatic Heating maxlocated in upper-levelsdue to condensation

Diabatic cooling maxlocated below cloud base

due to evaporation

Z

Clear Regions

Diabatic Cooling maxlocated in upper-levels

due to radiational cooling

Diabatic heating maxlocated near surfacedue to surface fluxes

Z

Net Result: Increase in cooling with heightHeight Rises

Regions of Shallow Convection

Net Result: Increase in cooling with heightHeight Rises

ZDiabatic Cooling max

located in upper-levelsdue to radiational cooling

Diabatic heating maxlocated in lower-levelsdue to condensation


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 heatingNo topographic effectsabove the mountains

Adiabatic Heatingdue 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 heatingNo topographic effectsabove the mountains

Adiabatic Coolingdue 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


HeightTendency

Differential ThermalAdvection

VorticityAdvection


TVp

Rf

pfVf

p

fg

ogg

2

02

2202

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?




ReferencesBluestein, 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 WeatherSystems. 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.

Documents

Advanced SynopticM. D. Eastin QG Analysis: Additional Processes