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Advanced Research WRF (ARW) Technical Note - MMM - University ...

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Symbols Definition<br />

Wk regression coefficient<br />

z height<br />

zd depth of damping layer<br />

ztop height of model top<br />

α inverse density of air<br />

α ′ perturbation inverse density of air<br />

¯α inverse density of air for the reference state<br />

αd inverse density of dry air<br />

αr local rotation angle between y-axis and the meridian<br />

β off-centering coefficient for semi-implicit acoustic step<br />

γ ratio of heat capacities for dry air at constant pressure and volume<br />

γd divergence damping coefficient<br />

γe external mode damping coefficient<br />

γg damping coefficient for upper boundary gravity wave absorbing layer<br />

γr Rayleigh damping coefficient<br />

ɛ molecular weight of water over the molecular weight of dry air (Chapter 4);<br />

true background error (Chapter 9)<br />

η terrain-following hydrostatic-pressure vertical coordinate<br />

˙η contravariant ‘vertical’ velocity or coordinate velocity<br />

θ potential temperature<br />

θe equivalent potential temperature<br />

θm moist potential temperature<br />

Θ coupled potential temperature<br />

µ hydrostatic pressure difference between surface and top of the model<br />

¯µ reference state hydrostatic pressure difference between surface and top of the<br />

model<br />

µd dry hydrostatic pressure difference between surface and top of the model<br />

τ acoustic time (Chapter 3), vertical structure function for Rayleigh damping<br />

(Chapter 4)<br />

stress tensor (Chapter 4) where n.m = 1, 2 and 3<br />

τnm<br />

∆τ acoustic time step<br />

φ geopotential (Chapters 2, 3, 5); latitude (Chapter 9)<br />

¯φ geopotential for reference state<br />

φ ′ perturbation geopotential<br />

Φ generic prognostic variable (coupled)<br />

ψ generic variable (Chapter 6)<br />

ψ ′ streamfunction increment<br />

χ ′ velocity potential increment<br />

ω same as ˙η<br />

Ω coupled coordinate velocity<br />

angular rotation rate of the earth<br />

Ωe<br />

79

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