A Comparison of Vertical Motions Obtained From Different ...

A Comparison of Vertical Motions Obtained From Different ...

A COMPARISON OF VERTICAL MOTIONS OBTAINED FROM DIFFERENT FORMS OF THE OMEGA EQUATION Christopher J. Melick and Phillip J. Smith Department of Earth and Atmospheric Sciences Purdue University West Lafayette, Indiana OBJECTIVE

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/sec Too small to be measured directly. Computational methods required. NOTE: Assumes synoptic-scale (large spatial and

temporal) conditions. COMPUTATIONAL TECHNIQUES 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 THEORY

Ageostrophic motions and hence vertical motions are produced as the atmosphere progresses from one geostrophically balanced state to another Geostrophic Balance: PGF = CF Vg ( g / f o )z FORMS OF OMEGA EQUATION 1. BASIC QUASIGEOSTROPHIC 2. Q-VECTOR 3. 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 Methods

LAYER EXAMINED: 700-300mb AVERAGED VERTICAL MOTIONS CORRELATIONS/ MEAN ABSOLUTE VALUES SYNOPTIC PATTERNS OMEGA vs. SYNOPTIC FEATURES PRECIPITATION PATTERNS % PRECIP IN UPWARD MOTION 984 mb 12 UTC 2 Nov. 1999 0000 3rd 1000 mb 1200 2nd

1009 mb 0000 2nd (TOP): SL Pressure & 6hr. Precip. (MIDDLE): 500-mb Height & Abs. Vort. (BOTTOM): 200-mb Height & Winds CC (omega patterns) QG Q T AT

E QG Q T 0.66 0.59 0.59 0.62 1.00 0.91

0.96 0.90 0.95 0.85 1.00 0.90 xxxxx 1.00 xxxxx

xxxxx MAV (omega magnitudes) QG Q T AT E 0.69 0.90 0.75 0.94 0.89

EXT QG Q TREN AT 500MB Z: SOLID 700-300MB OMEGA: DASHED SHADED: UPWARD MOTION % PRECIP IN UPWARD MOTION E

93 QG Q T AT 87 97 91 82

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

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