1000 hPa Z/Geo Rel Vort at t0

NEGATIVE Geo Rel Vort

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1000 hPa Z/Geo Rel Vort at t0 + 6-h

NEGATIVE Geo Rel Vort

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F00 GAVA (x 10-9 s-2); 500 hPa GRV F06 position

NEGATIVE Geo Rel Vort

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F00 GAVA (x 10-9 s-2); positive at F06 position (AVA in S.H.)

+0.5 x 10-9 s-2

Shading indicates NEGATIVE GAVA

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F00 nearly LTHAD (x 10-13 m-1s-1); negative at F06 position

OLD WAY!!

-[9.81 m s-2/ (-9.59x10-5 s-1)]*(-0. 475x10-13 m-1s-1) = -4.859 x 10-9 s-2

So, multiply by –g/f, giving a LTHAD contribution favoring cyclogenesis

Shading indicates NEGATIVE nLTHAD

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NEW WAY!!

THAD field shown

F00 nearly LTHAD (x 10-14 m-1s-1); positive at F06 position

So, multiply by –g/f, giving a LTHAD contribution to cyclogenesis

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NEW WAY!!

THAD field shownx 10-3 m s-1

F00 nearly LTHAD (x 10-13 m-1s-1); positive at F06 position

-[9.81 m s-2/ (-9.59x10-5 s-1)]*(-0.1341x10-13 m-1s-1) = -1.372 x 10-9 s-2

So, multiply by –g/f, giving a LTHAD contribution favoring cyclogenesis

-1.4

+0.8

-0.7

0.6

3.2

x

2o long. = 167.2 km

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d(THAD)/dx|pt6 = {(0.6 – [0.8])x10-3 m s-1}/{2x167.2x103 m}=-0.5981x10-9 s-1

d(THAD)/dx|pt4 = {(0.8 – [-1.4])x10-3 m s-1}/{2x167.2x103 m}=+6.579x10-9 s-1

d(THAD)/dy|pt2 = {(-0.7 – [0.8])x10-3 m s-1}/{2x167.2x103 m}=-4.486x10-9 s-1

d(THAD)/dy|pt8 = {(0.8 – [3.2])x10-3 m s-1}/{2x167.2x103 m}=-7.177x10-9 s-1

d2(THAD)/dx2|pt5 ={d(THAD)/dx|pt6 - d(THAD)/dx|pt4}/{2x167.2x103 m}=-0.2146x10-13 m-1 s-1

d2(THAD)/dy2|pt5 ={d(THAD)/dy|pt2 - d(THAD)/dy|pt8}/{2x167.2x103 m}=+0.0805x10-13 m-1 s-1

nLTHAD = d2(THAD)/dx2|pt5 + d2(THAD)/dy2|pt5 = -0.1341x10-13 m-1 s-1

So, multiply by –g/f, giving a LAD contribution favoring cyclogenesis

1.37 x 10-9 s-2 * 85% = -1.17 x 10-9 s-2

F00 nearly 700 hPa LAD (x 10-13 units); negative at F06 position

Shading indicates NEGATIVE nLAD

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F00 nearly LDIA; latent heat release at F06 position

1.17 x 10-9 s-2 * 70% = -0.82 x 10-9 s-2

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Calculations

Sum of terms on RHS = GAVA + LTHAD + LAD + LDIA= -2.854 x 10-9 s-2

Finite difference approximation of LHS = dGRV/dt= [(-24 – {-25}) x 10-5 s-1 ] / [6 h * 60 min/h * 60 s/min]= +0.4630 x 10-9 s-2

RHS = -6.165 x LHS

300 hPa Z, Div at F00

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300 hPa Z, GAVA at F00

[+]Shading indicates NEGATIVE GAVA

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300 hPa Z, Temp Adv at F00

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