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subroutine da_sfc_pre_lin (psfcm_prime, psm_prime, tsm_prime, qsm_prime, psm, tsm, qsm, hsm, ho, to, qvo) 3,2
!---------------------------------------------------------------------------
! Purpose: Correct pressure between two levels.
!
! Reference: make use of the hydrosatic equation:
!
! P2 = P1 * exp [-G/R * (z2-z1) / (tv1 + tv2)/2)
!
! Where:
! z1 = height at level 1
! z1 = height at level 2
! tv1 = temperature at level 1
! tv2 = temperature at level 2
! P1 = Pressure at level 1
! P2 = Pressure at level 2
!---------------------------------------------------------------------------
implicit none
! Perturbation:
real, intent (out) :: psfcm_prime ! model pressure at ho
real, intent (in) :: psm_prime, tsm_prime, qsm_prime ! model surface p, t, q
! Basic state:
real, intent (in) :: psm, tsm, qsm ! model pressure at ho and
! model surface p, t, q
real, intent (in) :: hsm, ho
real, intent (in), optional :: to, qvo
! working array:
real :: tvo, tvsm, tv, dz, arg0
real :: tvsm_prime, tvo_prime, tv_prime, arg, arg_prime
real, parameter :: GASR = gas_constant
real, parameter :: G = gravity
if (trace_use) call da_trace_entry
("da_sfc_pre_lin")
! 1. MODEL AND OBSERVATION VIRTUAL TEMPERATURE
! ---------------------------------------------
tvsm_prime = tsm_prime * (1.0 + 0.608 * qsm) &
+ qsm_prime * tsm * 0.608
tvsm = tsm * (1.0 + 0.608 * qsm)
if (present(to) .and. present(qvo)) then
tvo_prime = 0.0
tvo = to * (1.0 + 0.608 * qvo)
else if (present(to) .and. .not.present(qvo)) then
tvo_prime = 0.0
tvo = to
else
tvo_prime = tvsm_prime
tvo = tvsm
end if
tv_prime = 0.5 * (tvsm_prime + tvo_prime)
tv = 0.5 * (tvsm + tvo)
! 2. HEIGHT DifFERENCE BEWTEEN MODEL SURFACE AND OBSERVATIONS
! ------------------------------------------------------------
dz = hsm - ho
arg0 = dz * g / gasr
! 3. EXTRAPOLATE PRESSURE OBS TO MODEL SURFACE
! ---------------------------------------------
arg_prime = - arg0 * tv_prime / (tv * tv)
arg = arg0 / tv
psfcm_prime = exp(arg) *(psm_prime + psm * arg_prime)
if (trace_use) call da_trace_exit("da_sfc_pre_lin")
end subroutine da_sfc_pre_lin