A COMPARISON OF VERTICAL MOTIONS A COMPARISON OF VERTICAL MOTIONS OBTAINED FROM DIFFERENT FORMS OF OBTAINED FROM DIFFERENT FORMS OF

THE OMEGA EQUATIONTHE OMEGA EQUATION

Christopher J. MelickChristopher J. Melickandand

Phillip J. SmithPhillip J. Smith

Department of Earth and Atmospheric Department of Earth and Atmospheric SciencesSciences

Purdue UniversityPurdue UniversityWest Lafayette, IndianaWest Lafayette, Indiana

OBJECTIVEOBJECTIVE

• Comparison of vertical motions obtained from: Four quasi-geostrophic (QG) forms and one ageostrophic form (‘extended’) of the omega equation.

• Case study: Strahl and Smith (MWR:2001)– Explosive cyclone development

accompanied by upper-air wave merger over North America (Nov. 2-3 1999)

INTRODUCTION

• Scale Analysis:

V: 10 m/sec

W: 1 cm/secToo small to be measured directly.

Computational methods required.

NOTE: Assumes synoptic-scale (large spatial and temporal) conditions.

COMPUTATIONAL COMPUTATIONAL TECHNIQUESTECHNIQUES

1. Kinematic – Integrated Divergence/Convergence in Continuity Equation

2. Vorticity – Integrated Vorticity Advection/Tendency

3. Adiabatic – Temperature Advection/Tendency

4. Isentropic – Pressure Advection along Potential Temperature Surface

5. Omega Equation – Combine Vorticity Equation and 1st Law of Thermodynamics

QG THEORYQG THEORY

• Ageostrophic motions and hence vertical motions are produced as the atmosphere progresses from one geostrophically balanced state to another

• Geostrophic Balance: PGF = CF

• zfgV og )/(

FORMS OF OMEGA EQUATIONFORMS OF OMEGA EQUATION

1. BASIC QUASIGEOSTROPHIC2. Q-VECTOR3. TRENBERTH (2) AND (3) ACCOUNTS FOR CANCELLATION

FEATURE FOUND IN (1).4. APPROXIMATE TRENBERTH

NEGLECTS DEFORMATION TERM 5. EXTENDED

INCLUDES AGEOSTROPHIC WIND

• Surface/Upper-Air Data: 0000 UTC Nov. 2nd to 0000 UTC Nov. 3rd

• 2-pass Barnes Analysis Scheme

• 25x17 grid• Dashed Box:

Computational Domain

• Solid Box:

Display Domain

Comparison MethodsComparison Methods

LAYER EXAMINED: 700-300mb AVERAGED VERTICAL MOTIONS

• CORRELATIONS/ MEAN ABSOLUTE VALUES

• SYNOPTIC PATTERNS

OMEGA vs. SYNOPTIC FEATURES• PRECIPITATION PATTERNS

% PRECIP IN UPWARD MOTION

12 UTC 2 Nov. 1999

(TOP):

SL Pressure & 6hr. Precip.

(MIDDLE):500-mb Height & Abs. Vort.

(BOTTOM): 200-mb Height & Winds

984 mb

0000 3rd

1000 mb

1200 2nd

1009 mb0000 2nd

CC (omega patterns)

QG Q T AT

E 0.66 0.59 0.59 0.62

QG 1.00 0.91 0.96 0.90

Q xxxxx 1.00 0.95 0.85

T xxxxx xxxxx 1.00 0.90

MAV (omega magnitudes)

QG Q T AT E

0.69 0.90 0.75 0.94 0.89

500MB Z: SOLID

700-300MB OMEGA: DASHED

SHADED: UPWARD MOTION

EXT

QG

Q

TREN

AT

% PRECIP IN UPWARD MOTION% PRECIP IN UPWARD MOTION

E QG Q T AT

93 87 97 91 82

• All results are similar in magnitude• No clear evidence of one form being superior

CONCLUSIONSCONCLUSIONS

• ALL VERTICAL MOTION FIELDS COMPARE FAVORABLY WITH SYNOPTIC FEATURES AND PRECIPITATION FIELDS.

• CANNOT DETERMINE SUPERIOR METHOD USING SIMPLE SYNOPTIC AND PRECIPITATION COMPARISONS.

• QG APPROXIMATION WORKS QUITE WELL EVEN FOR A CASE OF EXPLOSIVE CYCLONE DEVELOPMENT.