*IF DEF,A15_1A DTHDP1A.2
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CLL Subroutine dthe_dp ----------------------------------------------- DTHDP1A.3
CLL DTHDP1A.4
CLL Purpose: To compute dtheta_dp on model half-levels DTHDP1A.5
CLL for use in potential vorticity calculation. DTHDP1A.6
CLL These are the natural definition of static stability DTHDP1A.7
CLL given that theta is held on model levels. DTHDP1A.8
CLL The subroutine calculates both dtheta/dp and the DTHDP1A.9
CLL half-levels (called e_levels) between the top and DTHDP1A.10
CLL bottom full levels. Therefore there are p_levels-1 DTHDP1A.11
CLL e_levels and dtheta/dp's. DTHDP1A.12
CLL DTHDP1A.13
CLL Not suitable for single column use. DTHDP1A.14
CLL DTHDP1A.15
CLL 13/9/93 Written by Terry Davies DTHDP1A.16
CLL DTHDP1A.17
CLL Model Modification history: DTHDP1A.18
CLL version Date DTHDP1A.19
CLL 3.3 14/12/93 Original version DTHDP1A.20
CLL DTHDP1A.21
CLL Programming Standard: UM DOC Paper3, Version 4 (05/02/92) DTHDP1A.22
CLL DTHDP1A.23
CLL Logical Component Covered: D415 DTHDP1A.24
CLL DTHDP1A.25
CLL System Task: D4 DTHDP1A.26
CLL DTHDP1A.27
CLL Documentation: U.M.D.P No 13. Derivation and Calculation of DTHDP1A.28
CLL Unified Model Potential Vorticity. DTHDP1A.29
CLL by Simon Anderson and Ian Roulstone. DTHDP1A.30
CLL DTHDP1A.31
CLLEND DTHDP1A.32
DTHDP1A.33
C*L ARGUMENTS: --------------------------------------------------------- DTHDP1A.34
subroutine dthe_dp 1DTHDP1A.35
1 (pstar,theta,p_field,p_levels, DTHDP1A.36
2 ak,bk,akh,bkh,n_levels, DTHDP1A.37
3 e_levels,dthe_dph) DTHDP1A.38
DTHDP1A.39
implicit none DTHDP1A.40
DTHDP1A.41
C Input variables ------------------------------------------------------ DTHDP1A.42
DTHDP1A.43
integer DTHDP1A.44
& p_field !IN Size of field on pressure points. DTHDP1A.45
&,p_levels !IN Number of pressure levels. DTHDP1A.46
&,n_levels !IN Number of half-levels (p_levels-1) DTHDP1A.47
C for dtheta/dp and e_levels. DTHDP1A.48
DTHDP1A.49
real DTHDP1A.50
& pstar(p_field) !IN Surface pressure field. DTHDP1A.51
&,theta(p_field,p_levels) !IN Theta field on p_levels DTHDP1A.52
DTHDP1A.53
real DTHDP1A.54
& ak(p_levels) !IN A coefficient of hybrid DTHDP1A.55
& ! coordinates at full levels. DTHDP1A.56
&,bk(p_levels) !IN B coefficient of hybrid DTHDP1A.57
& ! coordinates at full levels. DTHDP1A.58
&,akh(p_levels+1) !IN A coefficient of hybrid DTHDP1A.59
& ! coordinates at half levels. DTHDP1A.60
&,bkh(p_levels+1) !IN B coefficient of hybrid DTHDP1A.61
& ! coordinates at half levels. DTHDP1A.62
DTHDP1A.63
C Output variables ----------------------------------------------------- DTHDP1A.64
DTHDP1A.65
real DTHDP1A.66
& e_levels(n_levels) !OUT Model half-levels over range. DTHDP1A.67
&,dthe_dph(p_field,n_levels) !OUT dtheta/dp on half levels DTHDP1A.68
DTHDP1A.69
DTHDP1A.70
C*---------------------------------------------------------------------- DTHDP1A.71
C*L Workspace Usage: 2 arrays are required. DTHDP1A.72
real DTHDP1A.73
& pressure(p_field,2) ! Pressure on model levels DTHDP1A.74
&,thetae(p_field,2) ! thetate on model levels DTHDP1A.75
C ! 2 levels used, IL, IU used to switch DTHDP1A.76
DTHDP1A.77
C*---------------------------------------------------------------------- DTHDP1A.78
C*L External subroutine calls: DTHDP1A.79
DTHDP1A.80
C*---------------------------------------------------------------------- DTHDP1A.81
C*L Call comdecks to get required variables: DTHDP1A.82
DTHDP1A.83
C*---------------------------------------------------------------------- DTHDP1A.84
C*L Define local variables. DTHDP1A.85
integer i,j,ii ! Loop variables. DTHDP1A.86
& ,il,iu,is ! Pointers for pressure arrays DTHDP1A.87
DTHDP1A.88
C ---------------------------------------------------------------------- DTHDP1A.89
CL Section 1 Compute model half-levels over required range DTHDP1A.90
CL ~~~~~~~~~ DTHDP1A.91
C ---------------------------------------------------------------------- DTHDP1A.92
DTHDP1A.93
CL Section 1.1 DTHDP1A.94
CL ~~~~~~~~~~~ Half-levels in e_levels DTHDP1A.95
DTHDP1A.96
do i=1,p_levels-1 DTHDP1A.97
ii=i+1 DTHDP1A.98
e_levels(i)=0.00001*akh(ii)+bkh(ii) DTHDP1A.99
end do DTHDP1A.100
DTHDP1A.101
CL Section 1.2 Calculate pressure at bottom of range DTHDP1A.102
CL Store in pressure(p_field,1) DTHDP1A.103
DTHDP1A.104
do j=1,p_field DTHDP1A.105
pressure(j,1)=ak(1)+bk(1)*pstar(j) DTHDP1A.106
end do DTHDP1A.107
DTHDP1A.108
C ---------------------------------------------------------------------- DTHDP1A.109
CL Section 2 Calculate dtheta/dp on model half-levels DTHDP1A.110
CL ~~~~~~~~~ DTHDP1A.111
C ---------------------------------------------------------------------- DTHDP1A.112
DTHDP1A.113
is=1 DTHDP1A.114
il=2 DTHDP1A.115
do i=1,p_levels-1 DTHDP1A.116
iu=il DTHDP1A.117
il=is DTHDP1A.118
ii=i+1 DTHDP1A.119
do j=1,p_field DTHDP1A.120
pressure(j,iu)=ak(ii)+bk(ii)*pstar(j) DTHDP1A.121
dthe_dph(j,i)=(theta(j,ii-1)-theta(j,ii))/ DTHDP1A.122
2 (pressure(j,il)-pressure(j,iu)) DTHDP1A.123
end do DTHDP1A.124
is=iu DTHDP1A.125
end do DTHDP1A.126
DTHDP1A.127
return DTHDP1A.128
end DTHDP1A.129
DTHDP1A.130
*ENDIF DTHDP1A.131