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

From the reference temperature and pressure, the reference potential temperature is then defined
as
θd = T0 + A ln pd p0
p0
and the reciprocal of the reference density using (5.4) and (5.5) is given by
αd = 1
ρ d
= Rd θd
p0
pd
p0
p d
R d
Cp
, (5.5)
− Cv
Cp
. (5.6)
The base state difference of the dry surface pressure from (5.3) and the model top is given as
µ d = pdhs − pdht. (5.7)
From (5.6) and (5.7), the reference state geopotential defined from the hydrostatic relation is
δηφ = −αd µ d.
One of the total fields provided to the real-data cases by the SI is µd. The perturbation field
given the reference value (5.7) is
µ ′ d = µd − µ d. (5.8)
Starting with the reference state fields (5.4, 5.6, and 5.7) and the dry surface pressure perturbation
(5.8), the perturbation fields for pressure and inverse density are diagnosed. The pressure
perturbation includes moisture and is diagnosed from the hydrostatic equation
1 + qv η
+ qv η µ d,
δηp ′ = µ ′ d
which is integrated down from at the model top (where p ′ = 0) to recover p ′ . The total dry
inverse density is given as
αd = Rd
p0
θ
1 + Rv
qv
Rd
which defines the perturbation field for inverse density
α ′ d = αd − αd.
p ′ d + p d
p0
− Cv
Cp
,
The perturbation geopotential is diagnosed from the hydrostatic relation
δηφ ′ = − µdα ′ d + µ ′
dαd
by upward integration using the terrain elevation as the lower boundary condition. In future
versions of the real-data pre-processor, p ′ will be re-diagnosed consistent with the method used
in the model (2.21) as a final step. No modifications to the original µd, u, v, qv, or θ from the
SI are performed. The vertical component of velocity is initialized to zero.
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