Q-G Theory: Using the Q-Vector Patrick Market Department of Atmospheric Science University of Missouri-Columbia

Introduction Q-G forcing for  –Vertical motions (particularly in an ETC) complete a secondary ageostrophic circulation forced by geostrophic and hydrostatic adjustments on the synoptic-scale. Evaluation –Traditional Laplacian of thickness advection Differential vorticity advection –PIVA/NIVA (Trenberth Approximation) –Q-vector

Q-vector Strengths Eliminates competition between terms in the Q-G  equation Unlike PIVA/NIVA, deformation is retained as a forcing mechanism Q-vectors are proportional in strength and lie along the low level V ag. Analysis of Q-vectors with isentropes can reveal areas of frontogenesis/frontolysis. Only one isobaric level is needed to compute forcing.

Q-vector Weaknesses Diabatic heating/cooling are neglected Variations in f are neglected Variations in static stability are neglected  is still not calculated; its forcing is Although one may employ a single level for the process, layers are thought to be better for Q evaluation –So, which layer to use?

Q-vector: Choosing a layer… RECALL: Q-G forcing for  –Vertical motions complete a secondary ageostrophic circulation… Inertial-advective adjustments with the ULJ Isallobaric adjustments with the LLJ Deep layers can be useful –Max vertical motion should be near LND (~550 mb) Ideally that layer will be included

Q-vector: Choosing a layer… Avoid very low levels (PBL) –Friction –Radiative/sensible heating/cooling Look –low enough to account for CAA/WAA –deep enough to account for vertical change in vorticity advection Typical layer: mb –Brackets LND (~550 mb) –Deep enough to Capture low level thermal advection Significant differential vorticity advection

Q A Definition of Q Q is the time rate of change of the potential temperature gradient vector of a parcel in geostrophic motion (after Thaler)

Simple Example 1 True gradient vector points L  H Equivalent barotropic environment (after Thaler) Z Z+  Z Z+2  Z T T+  T

Simple Example 2 (after Thaler) Z Z+  Z Z+2  Z T T+  T

Q A Purpose for Q If Q exists, then the thermal gradient is changing following the motion… So… thermal wind balance is compromised So… the thermal wind is no longer proportional to the thickness gradient So… geostrophic and hydrostatic balance are compromised So… forcing for vertical motion ensues as the atmosphere seeks balance

Known Behaviors of Q Q often points along V ag in the lower branch of a transverse, secondary circulation Q often proportional to low-level |V ag | Q points toward rising motion Q plotted with a field of  can reveal regions of F –F Q-G Q points toward warm air – frontogenesis Q points toward cold air – frontolysis

Q Q Components Q n – component normal to  contours Q s – component parallel to  contours    QnQn QsQs Q

Q Aspects of Q n Indicates whether geostrophic motion is frontolytic or frontogenetic –Q n points Cold  Warm Frontogenesis –Q n points Warm  Cold Frontolysis For f=f 0, the geostrophic wind is purely non-divergent –Q-G frontogenesis is due entirely to deformation

Q Aspects of Q s Determines if the geostrophic deformation is rotating the isentropes cyclonically or anticyclonically –Q s points with cold air on left Q rotates cyclonically –Q s points with cold air on right Q rotates anticyclonically Rotation is manifested by vorticity and deformation fields

A Case Study: April 2002

27/23Z Synopsis

27/23Z P MSL & Thickness

27/23Z 850 mb Hght & V ag

27/23Z 300 mb Hght & |V |

27/23Z 300 mb Hght & V ag

J 27/23Z Cross section of , Normal |V|, V ag, & 

27/23Z Layer Q and 550 mb 

27/23Z Layer Q, Q n, Q s, and 550 mb 

27/23Z Divergence of Q and 550 mb 

27/23Z Layer Q n, and 550 mb 

27/23Z Layer Q s, and 550 mb 

27/23Z 550 mb Heights and 

27/23Z 550 mb F

LDF (THTA) 27/23Z Stability (d  /dp) vs ls

ADV(LDF (THTA), OBS) 27/23Z Advection of Stability by the Wind

OMEG  b s -1 27/23Z 700 mb 

27/23Z Layer Mean RH

Outcome Convection initiates in western MO –Left exit region of ~linear jet streak –Q n points cold  warm Frontogenesis present but weak –Q s points with cold to left  cyclonic rotation of  –Relative low stability –Modest low-level moisture

28/00-06Z IR Satellite

28/00-06Z RADAR Summary

Summary VQ aligns along low-level V ag in well- developed systems Div(Q) –Portrays  forcing well –Plotting stability may highlight regions where Q under-represents total  forcing –Plotting moisture helps refine regions of inclement weather Q proportional to Q-G F