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saturation.F90
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!-------------------------------------------------------------------------
!$Id$
!===============================================================================
module saturation
! Description:
! Contains functions that compute saturation with respect
! to liquid or ice.
!-----------------------------------------------------------------------
#ifdef GFDL
use model_flags, only: & ! h1g, 2010-06-18
I_sat_sphum
#endif
use clubb_precision, only: &
core_rknd ! Variable(s)
use model_flags, only: &
saturation_formula, & ! Variable
saturation_bolton, &
saturation_gfdl, &
saturation_flatau, &
saturation_lookup
implicit none
private ! Change default so all items private
public :: sat_mixrat_liq, sat_mixrat_ice, rcm_sat_adj, sat_vapor_press_liq
private :: sat_vapor_press_ice_flatau, sat_vapor_press_ice_bolton
interface sat_mixrat_liq
module procedure sat_mixrat_liq_k ! Works over a single vertical level
module procedure sat_mixrat_liq_2D ! Works over all vertical levels and columns
end interface sat_mixrat_liq
interface sat_mixrat_ice
module procedure sat_mixrat_ice_k ! Works over a single vertical level
module procedure sat_mixrat_ice_2D ! Works over all vertical levels and columns
end interface sat_mixrat_ice
! Lookup table of values for saturation
real( kind = core_rknd ), private, dimension(188:343) :: &
svp_liq_lookup_table
data svp_liq_lookup_table(188:343) / &
0.049560547_core_rknd, 0.059753418_core_rknd, 0.070129395_core_rknd, 0.083618164_core_rknd, &
0.09814453_core_rknd, 0.11444092_core_rknd, 0.13446045_core_rknd, 0.15686035_core_rknd, &
0.18218994_core_rknd, 0.21240234_core_rknd, 0.24725342_core_rknd, 0.28668213_core_rknd, &
0.33184814_core_rknd, 0.3826294_core_rknd, 0.4416504_core_rknd, 0.50775146_core_rknd, &
0.58343506_core_rknd, 0.6694946_core_rknd, 0.7668457_core_rknd, 0.87750244_core_rknd, &
1.0023804_core_rknd, 1.1434937_core_rknd, 1.3028564_core_rknd, 1.482544_core_rknd, &
1.6847534_core_rknd, 1.9118042_core_rknd, 2.1671143_core_rknd, 2.4535522_core_rknd, &
2.774231_core_rknd, 3.1330566_core_rknd, 3.5343628_core_rknd, 3.9819336_core_rknd, &
4.480713_core_rknd, 5.036072_core_rknd, 5.6540527_core_rknd, 6.340088_core_rknd, &
7.1015015_core_rknd, 7.9450684_core_rknd, 8.8793335_core_rknd, 9.91217_core_rknd, &
11.053528_core_rknd, 12.313049_core_rknd, 13.70166_core_rknd, 15.231018_core_rknd, &
16.91394_core_rknd, 18.764038_core_rknd, 20.795898_core_rknd, 23.025574_core_rknd, &
25.470093_core_rknd, 28.147766_core_rknd, 31.078003_core_rknd, 34.282043_core_rknd, &
37.782593_core_rknd, 41.60382_core_rknd, 45.771606_core_rknd, 50.31366_core_rknd, &
55.259644_core_rknd, 60.641174_core_rknd, 66.492004_core_rknd, 72.84802_core_rknd, &
79.74756_core_rknd, 87.23126_core_rknd, 95.34259_core_rknd, 104.12747_core_rknd, &
113.634796_core_rknd, 123.91641_core_rknd, 135.02725_core_rknd, 147.02563_core_rknd, &
159.97308_core_rknd, 173.93488_core_rknd, 188.97995_core_rknd, 205.18109_core_rknd, &
222.61517_core_rknd, 241.36334_core_rknd, 261.51108_core_rknd, 283.14853_core_rknd, &
306.37054_core_rknd, 331.27698_core_rknd, 357.97278_core_rknd, 386.56842_core_rknd, &
417.17978_core_rknd, 449.9286_core_rknd, 484.94254_core_rknd, 522.3556_core_rknd, &
562.30804_core_rknd, 604.947_core_rknd, 650.42645_core_rknd, 698.9074_core_rknd, &
750.55835_core_rknd, 805.55554_core_rknd, 864.0828_core_rknd, 926.3325_core_rknd, &
992.5052_core_rknd, 1062.8102_core_rknd, 1137.4657_core_rknd, 1216.6995_core_rknd, &
1300.7483_core_rknd, 1389.8594_core_rknd, 1484.2896_core_rknd, 1584.3064_core_rknd, &
1690.1881_core_rknd, 1802.224_core_rknd, 1920.7146_core_rknd, 2045.9724_core_rknd, &
2178.3218_core_rknd, 2318.099_core_rknd, 2465.654_core_rknd, 2621.3489_core_rknd, &
2785.5596_core_rknd, 2958.6758_core_rknd, 3141.101_core_rknd, 3333.2534_core_rknd, &
3535.5657_core_rknd, 3748.4863_core_rknd, 3972.4792_core_rknd, 4208.024_core_rknd, &
4455.616_core_rknd, 4715.7686_core_rknd, 4989.0127_core_rknd, 5275.8945_core_rknd, &
5576.9795_core_rknd, 5892.8535_core_rknd, 6224.116_core_rknd, 6571.3926_core_rknd, &
6935.3213_core_rknd, 7316.5674_core_rknd, 7715.8105_core_rknd, 8133.755_core_rknd, &
8571.125_core_rknd, 9028.667_core_rknd, 9507.15_core_rknd, 10007.367_core_rknd, &
10530.132_core_rknd, 11076.282_core_rknd, 11646.683_core_rknd, 12242.221_core_rknd, &
12863.808_core_rknd, 13512.384_core_rknd, 14188.913_core_rknd, 14894.385_core_rknd, &
15629.823_core_rknd, 16396.268_core_rknd, 17194.799_core_rknd, 18026.516_core_rknd, &
18892.55_core_rknd, 19794.07_core_rknd, 20732.262_core_rknd, 21708.352_core_rknd, &
22723.592_core_rknd, 23779.273_core_rknd, 24876.709_core_rknd, 26017.258_core_rknd, &
27202.3_core_rknd, 28433.256_core_rknd, 29711.578_core_rknd, 31038.766_core_rknd /
!$acc declare create( svp_liq_lookup_table )
!$omp threadprivate( svp_liq_lookup_table )
contains
!-------------------------------------------------------------------------
! Wrapped in interface sat_mixrat_liq
function sat_mixrat_liq_k( p_in_Pa, T_in_K )
!$acc routine seq
! Description:
! Used to compute the saturation mixing ratio of liquid water.
! References:
! Formula from Emanuel 1994, 4.4.14
!-------------------------------------------------------------------------
use constants_clubb, only: &
ep
use constants_clubb, only: T_freeze_K
implicit none
! -------------------- Input Variables --------------------
real( kind = core_rknd ), intent(in) :: &
p_in_Pa, & ! Pressure [Pa]
T_in_K ! Temperature [K]
! -------------------- Output Variables --------------------
real( kind = core_rknd ) :: &
sat_mixrat_liq_k
! -------------------- Local Variables --------------------
real( kind = core_rknd ) :: &
T_in_C, &
T_in_C_sqd, &
T_in_K_clipped
integer :: &
T_in_K_int
! Constant parameters
! Relative error norm expansion (-50 to 50 deg_C) from
! Table 3 of pp. 1510 of Flatau et al. 1992 (Water Vapor)
! (The 100 coefficient converts from mb to Pa)
! real, dimension(7), parameter :: a = &
! 100.* (/ 6.11176750, 0.443986062, 0.143053301E-01, &
! 0.265027242E-03, 0.302246994E-05, 0.203886313E-07, &
! 0.638780966E-10 /)
! Relative error norm expansion (-85 to 70 deg_C) from
! Table 4 of pp. 1511 of Flatau et al.
!real( kind = core_rknd ), dimension(9), parameter :: a = &
!100._core_rknd * &
! Commented out because the form has been redone, causing these number to no longer be needed,
! leaving them in for now for reference.
! (/ 6.11583699_core_rknd, 0.444606896_core_rknd, 0.143177157E-01_core_rknd, &
! 0.264224321E-03_core_rknd, 0.299291081E-05_core_rknd, 0.203154182E-07_core_rknd, &
! 0.702620698E-10_core_rknd, 0.379534310E-13_core_rknd,-0.321582393E-15_core_rknd /)
real( kind = core_rknd ), parameter :: &
min_T_in_C = -85._core_rknd, & ! [deg_C]
min_T_in_K = 173.15_core_rknd ! Lowest temperature at which Goff-Gratch is valid [K]
! ---------------------- Output Variables ----------------------
real( kind = core_rknd ) :: &
esat ! Saturation vapor pressure over water [Pa]
! -------------------- Begin Code --------------------
! Calculate the SVP for water vapor.
select case ( saturation_formula )
case ( saturation_flatau )
! Using the Flatau, et al. polynomial approximation for SVP over vapor
! Determine deg K - 273.15
T_in_C = T_in_K - T_freeze_K
! Since this approximation is only good out to -85 degrees Celsius we
! truncate the result here (Flatau, et al. 1992)
T_in_C = max( T_in_C, min_T_in_C )
! Polynomial approx. (Flatau, et al. 1992)
! This is the generalized formula but is not computationally efficient.
! Based on Wexler's expressions(2.1)-(2.4) (See Flatau et al. p 1508)
! e_{sat} = a_1 + a_2 ( T - T_0 ) + ... + a_{n+1} ( T - T_0 )^n
! esat = a(1)
! do i = 2, size( a ) , 1
! esat = esat + a(i) * ( T_in_C )**(i-1)
! end do
! The 8th order polynomial fit. When running deep
! convective cases I noticed that absolute temperature often dips below
! -50 deg_C at higher altitudes, where the 6th order approximation is
! not accurate. -dschanen 20 Nov 2008
!esat = a(1) + T_in_C*( a(2) + T_in_C*( a(3) + T_in_C*( a(4) + T_in_C &
!*( a(5) + T_in_C*( a(6) + T_in_C*( a(7) + T_in_C*( a(8) + T_in_C*( a(9) ) ) ) ) ) ) ) )
! Factoring the polynomial above and changing it into this form allows the cpu
! to complete the calculations out of order. This is because modern cpus can complete
! multiple instructions at once if they do not depend on eachother, in the above case
! each instruction relies on the result of the last. In this version however, the terms
! in the parentheses could potentially be calculated in parallel by different execution
! units in the cpu, then only when those terms are being multiplied together do the
! instructions need to be done one at a time. See clubb issue 834 for more info.
! - Gunther Huebler, Aug 2018
T_in_C_sqd = T_in_C**2
esat = &
- 3.21582393e-14_core_rknd * ( T_in_C - 646.5835252598777_core_rknd ) &
* ( T_in_C + 90.72381630364440_core_rknd ) &
* ( T_in_C_sqd + 111.0976961559954_core_rknd * T_in_C + 6459.629194243118_core_rknd ) &
* ( T_in_C_sqd + 152.3131930092453_core_rknd * T_in_C + 6499.774954705265_core_rknd ) &
* ( T_in_C_sqd + 174.4279584934021_core_rknd * T_in_C + 7721.679732114084_core_rknd )
case ( saturation_bolton )
! Using the Bolton 1980 approximations for SVP over vapor
! Generally this more computationally expensive than the Flatau polnomial expansion
esat = 611.2_core_rknd &
* exp( (17.67_core_rknd *(T_in_K-T_freeze_K)) &
/ (T_in_K-29.65_core_rknd) ) ! Known magic number
! ---> h1g
case ( saturation_gfdl )
! Using GFDL polynomial approximation for SVP with respect to liquid
! Since the Goff-Gratch approximation is valid only down to -70 degrees Celsius,
! we threshold the temperature. This will yield a minimal saturation at
! cold temperatures.
T_in_K_clipped = max( min_T_in_K, T_in_K )
! Goff Gratch equation, uncertain below -70 C
esat = 10._core_rknd**(-7.90298_core_rknd*(373.16_core_rknd/T_in_K_clipped-1._core_rknd)+ &
5.02808_core_rknd*log10(373.16_core_rknd/T_in_K_clipped)- &
1.3816e-7_core_rknd*(10._core_rknd**(11.344_core_rknd &
*(1._core_rknd-T_in_K_clipped/373.16_core_rknd))-1._core_rknd)+ &
8.1328e-3_core_rknd*(10._core_rknd**(-3.49149_core_rknd &
*(373.16_core_rknd/T_in_K_clipped-1._core_rknd))-1._core_rknd)+ &
log10(1013.246_core_rknd))*100._core_rknd ! Known magic number
! <--- h1g
case ( saturation_lookup )
T_in_K_int = int( anint( T_in_K ) )
! Since this approximation is only good out to -85 degrees Celsius we
! truncate the result here
T_in_K_int = min( max( T_in_K_int, 188 ), 343 )
! Use the lookup table to determine the saturation vapor pressure.
esat = svp_liq_lookup_table( T_in_K_int )
case default
! Undefined approximation
esat = -99999.999_core_rknd
end select
! If esat exceeds the air pressure, then assume esat~=0.5*pressure
! and set rsat = ep = 0.622
if ( p_in_Pa-esat < 1.0_core_rknd ) then
sat_mixrat_liq_k = ep
else
#ifdef GFDL
! GFDL uses specific humidity
! Formula for Saturation Specific Humidity
if ( I_sat_sphum ) then ! h1g, 2010-06-18 begin mod
sat_mixrat_liq_k = ep * ( esat / ( p_in_Pa &
- (1.0_core_rknd-ep) * esat ) )
else
sat_mixrat_liq_k = ep * ( esat / ( p_in_Pa - esat ) )
endif ! h1g, 2010-06-18 end mod
#else
! Formula for Saturation Mixing Ratio:
!
! rs = (epsilon) * [ esat / ( p - esat ) ];
! where epsilon = R_d / R_v
sat_mixrat_liq_k = ep * esat / ( p_in_Pa - esat )
#endif
end if
return
end function sat_mixrat_liq_k
!-------------------------------------------------------------------------
!
function sat_mixrat_liq_2D( nz, ngrdcol, p_in_Pa, T_in_K, &
start_index_in )
!
! Description:
! Used to compute the saturation mixing ratio of liquid water.
!
! References:
! Formula from Emanuel 1994, 4.4.14
!-------------------------------------------------------------------------
use constants_clubb, only: &
ep
use constants_clubb, only: T_freeze_K
implicit none
! -------------------- Input Variables --------------------
integer, intent(in) :: &
nz, &
ngrdcol
integer, intent(in), optional :: &
start_index_in
real( kind = core_rknd ), dimension(ngrdcol,nz), intent(in) :: &
p_in_Pa, & ! Pressure [Pa]
T_in_K ! Temperature [K]
! -------------------- Output Variables --------------------
real( kind = core_rknd ), dimension(ngrdcol,nz) :: &
sat_mixrat_liq_2D
! -------------------- Local Variables --------------------
real( kind = core_rknd ), dimension(ngrdcol,nz) :: &
esat
real( kind = core_rknd ) :: &
T_in_C, &
T_in_C_sqd, &
T_in_K_clipped
integer :: &
T_in_K_int
integer :: i,k
! Constant parameters
! Relative error norm expansion (-50 to 50 deg_C) from
! Table 3 of pp. 1510 of Flatau et al. 1992 (Water Vapor)
! (The 100 coefficient converts from mb to Pa)
! real, dimension(7), parameter :: a = &
! 100.* (/ 6.11176750, 0.443986062, 0.143053301E-01, &
! 0.265027242E-03, 0.302246994E-05, 0.203886313E-07, &
! 0.638780966E-10 /)
! Relative error norm expansion (-85 to 70 deg_C) from
! Table 4 of pp. 1511 of Flatau et al.
!real( kind = core_rknd ), dimension(9), parameter :: a = &
!100._core_rknd * &
! Commented out because the form has been redone, causing these number to no longer be needed,
! leaving them in for now for reference.
! (/ 6.11583699_core_rknd, 0.444606896_core_rknd, 0.143177157E-01_core_rknd, &
! 0.264224321E-03_core_rknd, 0.299291081E-05_core_rknd, 0.203154182E-07_core_rknd, &
! 0.702620698E-10_core_rknd, 0.379534310E-13_core_rknd,-0.321582393E-15_core_rknd /)
real( kind = core_rknd ), parameter :: &
min_T_in_C = -85._core_rknd, & ! [deg_C]
min_T_in_K = 173.15_core_rknd ! Lowest temperature at which Goff-Gratch is valid [K]
integer :: &
start_index
! -------------------- Begin Code --------------------
!$acc data create(esat) &
!$acc copyin(p_in_Pa,T_in_K), &
!$acc copyout(sat_mixrat_liq_2D)
! start_index is an optional argument and
! used for choosing the sub-arrays
if ( present(start_index_in) ) then
start_index = start_index_in
else
start_index = 1
end if
select case ( saturation_formula )
case ( saturation_flatau )
!$acc parallel loop gang vector collapse(2) default(present)
do k = start_index, nz
do i = 1, ngrdcol
! Determine deg K - 273.15
T_in_C = T_in_K(i,k) - T_freeze_K
! Since this approximation is only good out to -85 degrees Celsius we
! truncate the result here (Flatau, et al. 1992)
T_in_C = max( T_in_C, min_T_in_C )
! Polynomial approx. (Flatau, et al. 1992)
! This is the generalized formula but is not computationally efficient.
! Based on Wexler's expressions(2.1)-(2.4) (See Flatau et al. p 1508)
! e_{sat} = a_1 + a_2 ( T - T_0 ) + ... + a_{n+1} ( T - T_0 )^n
! esat = a(1)
! do i = 2, size( a ) , 1
! esat = esat + a(i) * ( T_in_C )**(i-1)
! end do
! The 8th order polynomial fit. When running deep
! convective cases I noticed that absolute temperature often dips below
! -50 deg_C at higher altitudes, where the 6th order approximation is
! not accurate. -dschanen 20 Nov 2008
!esat = a(1) + T_in_C*( a(2) + T_in_C*( a(3) + T_in_C*( a(4) + T_in_C &
!*( a(5) + T_in_C*( a(6) + T_in_C*( a(7) + T_in_C*( a(8) + T_in_C*( a(9) ) ) ) ) ) ) ) )
! Factoring the polynomial above and changing it into this form allows the cpu
! to complete the calculations out of order. This is because modern cpus can complete
! multiple instructions at once if they do not depend on eachother, in the above case
! each instruction relies on the result of the last. In this version however, the terms
! in the parentheses could potentially be calculated in parallel by different execution
! units in the cpu, then only when those terms are being multiplied together do the
! instructions need to be done one at a time. See clubb issue 834 for more info.
! - Gunther Huebler, Aug 2018
T_in_C_sqd = T_in_C**2
esat(i,k) = &
- 3.21582393e-14_core_rknd * ( T_in_C - 646.5835252598777_core_rknd ) &
* ( T_in_C + 90.72381630364440_core_rknd ) &
* ( T_in_C_sqd + 111.0976961559954_core_rknd * T_in_C + 6459.629194243118_core_rknd ) &
* ( T_in_C_sqd + 152.3131930092453_core_rknd * T_in_C + 6499.774954705265_core_rknd ) &
* ( T_in_C_sqd + 174.4279584934021_core_rknd * T_in_C + 7721.679732114084_core_rknd )
end do
end do
!$acc end parallel loop
case ( saturation_bolton )
! Using the Bolton 1980 approximations for SVP over vapor
! Generally this more computationally expensive than the Flatau polnomial expansion
!$acc parallel loop gang vector collapse(2) default(present)
do k = start_index, nz
do i = 1, ngrdcol
esat(i,k) = 611.2_core_rknd &
* exp( (17.67_core_rknd *(T_in_K(i,k)-T_freeze_K)) &
/ (T_in_K(i,k)-29.65_core_rknd) ) ! Known magic number
end do
end do
!$acc end parallel loop
! ---> h1g
case ( saturation_gfdl )
! Using GFDL polynomial approximation for SVP with respect to liquid
!$acc parallel loop gang vector collapse(2) default(present)
do k = start_index, nz
do i = 1, ngrdcol
! Since the Goff-Gratch approximation is valid only down to -70 degrees Celsius,
! we threshold the temperature. This will yield a minimal saturation at
! cold temperatures.
T_in_K_clipped = max( min_T_in_K, T_in_K(i,k) )
! Goff Gratch equation, uncertain below -70 C
esat(i,k) = 10._core_rknd**(-7.90298_core_rknd*(373.16_core_rknd/T_in_K_clipped-1._core_rknd)+ &
5.02808_core_rknd*log10(373.16_core_rknd/T_in_K_clipped)- &
1.3816e-7_core_rknd*(10._core_rknd**(11.344_core_rknd &
*(1._core_rknd-T_in_K_clipped/373.16_core_rknd))-1._core_rknd)+ &
8.1328e-3_core_rknd*(10._core_rknd**(-3.49149_core_rknd &
*(373.16_core_rknd/T_in_K_clipped-1._core_rknd))-1._core_rknd)+ &
log10(1013.246_core_rknd))*100._core_rknd ! Known magic number
end do
end do
!$acc end parallel loop
! <--- h1g
case ( saturation_lookup )
!$acc parallel loop gang vector collapse(2) default(present)
do k = start_index, nz
do i = 1, ngrdcol
T_in_K_int = int( anint( T_in_K(i,k) ) )
! Since this approximation is only good out to -85 degrees Celsius we
! truncate the result here
T_in_K_int = min( max( T_in_K_int, 188 ), 343 )
! Use the lookup table to determine the saturation vapor pressure.
esat(i,k) = svp_liq_lookup_table( T_in_K_int )
end do
end do
!$acc end parallel loop
case default
! Undefined approximation
esat = -99999.999_core_rknd
end select
!$acc parallel loop gang vector collapse(2) default(present)
do k = start_index, nz
do i = 1, ngrdcol
! If esat exceeds the air pressure, then assume esat~=0.5*pressure
! and set rsat = ep = 0.622
if ( p_in_Pa(i,k)-esat(i,k) < 1.0_core_rknd ) then
sat_mixrat_liq_2D(i,k) = ep
else
#ifdef GFDL
! GFDL uses specific humidity
! Formula for Saturation Specific Humidity
if ( I_sat_sphum ) then ! h1g, 2010-06-18 begin mod
sat_mixrat_liq_2D(i,k) = ep(i,k) * ( esat(i,k) / ( p_in_Pa(i,k) &
- (1.0_core_rknd-ep) * esat(i,k) ) )
else
sat_mixrat_liq_2D(i,k) = ep(i,k) * ( esat(i,k) / ( p_in_Pa(i,k) - esat(i,k) ) )
endif ! h1g, 2010-06-18 end mod
#else
! Formula for Saturation Mixing Ratio:
!
! rs = (epsilon) * [ esat / ( p - esat ) ];
! where epsilon = R_d / R_v
sat_mixrat_liq_2D(i,k) = ep * esat(i,k) / ( p_in_Pa(i,k) - esat(i,k) )
#endif
end if
end do
end do
!$acc end parallel loop
!$acc end data
end function sat_mixrat_liq_2D
!-----------------------------------------------------------------
! Wrapped in interface sat_vapor_press_liq
subroutine sat_vapor_press_liq( T_in_K, &
esat )
! Description:
! Computes SVP for water vapor. Calls one of the other functions
! that calculate an approximation to SVP.
! References:
! None
!-----------------------------------------------------------------
use model_flags, only: &
saturation_formula, & ! Variable
saturation_bolton, &
saturation_gfdl, &
saturation_flatau
use clubb_precision, only: &
core_rknd ! Variable(s)
implicit none
! ------------------------ Input Variables ------------------------
real( kind = core_rknd ), intent(in) :: &
T_in_K ! Temperature [K]
! ------------------------ Output Variables ------------------------
real( kind = core_rknd ), intent(out) :: &
esat ! Saturation Vapor Pressure over Water [Pa]
! ------------------------ Being Code ------------------------
! Saturation Vapor Pressure, esat, can be found to be approximated
! in many different ways.
select case ( saturation_formula )
case ( saturation_bolton )
! Using the Bolton 1980 approximations for SVP over vapor
call sat_vapor_press_liq_bolton( T_in_K, &
esat )
!Earthworks case
case ( saturation_flatau )
! Using the Flatau, et al. polynomial approximation for SVP over vapor
call sat_vapor_press_liq_flatau( T_in_K, &
esat )
! ---> h1g
case ( saturation_gfdl )
! Using GFDL polynomial approximation for SVP with respect to liquid
call sat_vapor_press_liq_gfdl( T_in_K, &
esat )
! <--- h1g
case ( saturation_lookup )
! Use the lookup table to determine the saturation vapor pressure.
esat = sat_vapor_press_liq_lookup( T_in_K )
case default
! Undefined approximation
esat = -99999.999_core_rknd
end select
return
end subroutine sat_vapor_press_liq
!------------------------------------------------------------------------
subroutine sat_vapor_press_liq_flatau( T_in_K, &
esat )
! Description:
! Computes SVP for water vapor.
! References:
! ``Polynomial Fits to Saturation Vapor Pressure'' Falatau, Walko,
! and Cotton. (1992) Journal of Applied Meteorology, Vol. 31,
! pp. 1507--1513
!------------------------------------------------------------------------
use constants_clubb, only: T_freeze_K
use clubb_precision, only: &
core_rknd ! Variable(s)
implicit none
! Constant parameters
! Relative error norm expansion (-50 to 50 deg_C) from
! Table 3 of pp. 1510 of Flatau et al. 1992 (Water Vapor)
! (The 100 coefficient converts from mb to Pa)
! real, dimension(7), parameter :: a = &
! 100.* (/ 6.11176750, 0.443986062, 0.143053301E-01, &
! 0.265027242E-03, 0.302246994E-05, 0.203886313E-07, &
! 0.638780966E-10 /)
! Relative error norm expansion (-85 to 70 deg_C) from
! Table 4 of pp. 1511 of Flatau et al.
!real( kind = core_rknd ), dimension(9), parameter :: a = &
!100._core_rknd * &
! Commented out because the form has been redone, causing these number to no longer be needed,
! leaving them in for now for reference.
! (/ 6.11583699_core_rknd, 0.444606896_core_rknd, 0.143177157E-01_core_rknd, &
! 0.264224321E-03_core_rknd, 0.299291081E-05_core_rknd, 0.203154182E-07_core_rknd, &
! 0.702620698E-10_core_rknd, 0.379534310E-13_core_rknd,-0.321582393E-15_core_rknd /)
real( kind = core_rknd ), parameter :: min_T_in_C = -85._core_rknd ! [deg_C]
! ---------------------- Input Variables ----------------------
real( kind = core_rknd ), intent(in) :: &
T_in_K ! Temperature [K]
! ---------------------- Output Variables ----------------------
real( kind = core_rknd ), intent(out) :: &
esat ! Saturation vapor pressure over water [Pa]
! ---------------------- Local Variables ----------------------
real( kind = core_rknd ) :: T_in_C, T_in_C_sqd
! ---------------------- Begin Code ----------------------
! Determine deg K - 273.15
T_in_C = T_in_K - T_freeze_K
! Since this approximation is only good out to -85 degrees Celsius we
! truncate the result here (Flatau, et al. 1992)
T_in_C = max( T_in_C, min_T_in_C )
! Polynomial approx. (Flatau, et al. 1992)
! This is the generalized formula but is not computationally efficient.
! Based on Wexler's expressions(2.1)-(2.4) (See Flatau et al. p 1508)
! e_{sat} = a_1 + a_2 ( T - T_0 ) + ... + a_{n+1} ( T - T_0 )^n
! esat = a(1)
! do i = 2, size( a ) , 1
! esat = esat + a(i) * ( T_in_C )**(i-1)
! end do
! The 8th order polynomial fit. When running deep
! convective cases I noticed that absolute temperature often dips below
! -50 deg_C at higher altitudes, where the 6th order approximation is
! not accurate. -dschanen 20 Nov 2008
!esat = a(1) + T_in_C*( a(2) + T_in_C*( a(3) + T_in_C*( a(4) + T_in_C &
!*( a(5) + T_in_C*( a(6) + T_in_C*( a(7) + T_in_C*( a(8) + T_in_C*( a(9) ) ) ) ) ) ) ) )
! Factoring the polynomial above and changing it into this form allows the cpu
! to complete the calculations out of order. This is because modern cpus can complete
! multiple instructions at once if they do not depend on eachother, in the above case
! each instruction relies on the result of the last. In this version however, the terms
! in the parentheses could potentially be calculated in parallel by different execution
! units in the cpu, then only when those terms are being multiplied together do the
! instructions need to be done one at a time. See clubb issue 834 for more info.
! - Gunther Huebler, Aug 2018
T_in_C_sqd = T_in_C**2
esat = &
- 3.21582393e-14_core_rknd * ( T_in_C - 646.5835252598777_core_rknd ) &
* ( T_in_C + 90.72381630364440_core_rknd ) &
* ( T_in_C_sqd + 111.0976961559954_core_rknd * T_in_C + 6459.629194243118_core_rknd ) &
* ( T_in_C_sqd + 152.3131930092453_core_rknd * T_in_C + 6499.774954705265_core_rknd ) &
* ( T_in_C_sqd + 174.4279584934021_core_rknd * T_in_C + 7721.679732114084_core_rknd )
return
end subroutine sat_vapor_press_liq_flatau
!------------------------------------------------------------------------
subroutine sat_vapor_press_liq_bolton( T_in_K, &
esat )
! Description:
! Computes SVP for water vapor.
! References:
! Bolton 1980
!------------------------------------------------------------------------
use constants_clubb, only: T_freeze_K
use clubb_precision, only: &
core_rknd ! Variable(s)
implicit none
! --------------------- Input Variables ---------------------
real( kind = core_rknd ), intent(in) :: &
T_in_K ! Temperature [K]
! --------------------- Output Variables ---------------------
real( kind = core_rknd ), intent(out) :: &
esat ! Saturation vapor pressure over water [Pa]
! --------------------------- Begin Code ---------------------------
! (Bolton 1980) approx.
! Generally this more computationally expensive than the Flatau polnomial expansion
esat = 611.2_core_rknd &
* exp( (17.67_core_rknd *(T_in_K-T_freeze_K)) &
/ (T_in_K-29.65_core_rknd) ) ! Known magic number
return
end subroutine sat_vapor_press_liq_bolton
! ---> h1g, 2010-06-16
!------------------------------------------------------------------------
subroutine sat_vapor_press_liq_gfdl( T_in_K, &
esat )
! Description:
! copy from "GFDL polysvp.F90"
! Compute saturation vapor pressure with respect to liquid by using
! function from Goff and Gratch (1946)
! Polysvp returned in units of pa.
! T_in_K is input in units of K.
!------------------------------------------------------------------------
use clubb_precision, only: &
core_rknd ! Variable(s)
implicit none
! --------------------------- Input Variables ---------------------------
real( kind = core_rknd ), intent(in) :: &
T_in_K ! Absolute temperature [K]
! --------------------------- Output Variables ---------------------------
real( kind = core_rknd ), intent(out) :: &
esat ! Saturation vapor pressure over water [Pa]
! --------------------------- Local Variables ---------------------------
real( kind = core_rknd ), parameter :: &
min_T_in_K = 203.15_core_rknd ! Lowest temperature at which Goff-Gratch is valid [K]
real( kind = core_rknd ) :: &
T_in_K_clipped ! Absolute temperature with minimum threshold applied [K]
! --------------------------- Begin Code ---------------------------
! Since the Goff-Gratch approximation is valid only down to -70 degrees Celsius,
! we threshold the temperature. This will yield a minimal saturation at
! cold temperatures.
T_in_K_clipped = max( min_T_in_K, T_in_K )
! Goff Gratch equation, uncertain below -70 C
esat = 10._core_rknd**(-7.90298_core_rknd*(373.16_core_rknd/T_in_K_clipped-1._core_rknd)+ &
5.02808_core_rknd*log10(373.16_core_rknd/T_in_K_clipped)- &
1.3816e-7_core_rknd*(10._core_rknd**(11.344_core_rknd &
*(1._core_rknd-T_in_K_clipped/373.16_core_rknd))-1._core_rknd)+ &
8.1328e-3_core_rknd*(10._core_rknd**(-3.49149_core_rknd &
*(373.16_core_rknd/T_in_K_clipped-1._core_rknd))-1._core_rknd)+ &
log10(1013.246_core_rknd))*100._core_rknd ! Known magic number
return
end subroutine sat_vapor_press_liq_gfdl
! <--- h1g, 2010-06-16
!------------------------------------------------------------------------
elemental function sat_vapor_press_liq_lookup( T_in_K ) result ( esat )
! Description:
! Computes SVP for water vapor, using a lookup table.
!
! The lookup table was constructed using the Flatau approximation.
! References:
! ``Polynomial Fits to Saturation Vapor Pressure'' Falatau, Walko,
! and Cotton. (1992) Journal of Applied Meteorology, Vol. 31,
! pp. 1507--1513
!------------------------------------------------------------------------
implicit none
! External
intrinsic :: max, min, int, anint
! Input Variables
real( kind = core_rknd ), intent(in) :: T_in_K ! Temperature [K]
! Output Variables
real( kind = core_rknd ) :: esat ! Saturation vapor pressure over water [Pa]
! Local Variables
integer :: T_in_K_int
! ---- Begin Code ----
T_in_K_int = int( anint( T_in_K ) )
! Since this approximation is only good out to -85 degrees Celsius we
! truncate the result here
T_in_K_int = min( max( T_in_K_int, 188 ), 343 )
! Use the lookup table to determine the saturation vapor pressure.
esat = svp_liq_lookup_table( T_in_K_int )
return
end function sat_vapor_press_liq_lookup
!------------------------------------------------------------------------
! Wrapped in interface sat_mixrat_ice
function sat_mixrat_ice_k( p_in_Pa, T_in_K )
! Description:
! Used to compute the saturation mixing ratio of ice.
! References:
! Formula from Emanuel 1994, 4.4.15
!-------------------------------------------------------------------------
use constants_clubb, only: &
ep ! Variable(s)
use clubb_precision, only: &
core_rknd ! Variable(s)
implicit none
! ------------------------ Input Variables ------------------------
real( kind = core_rknd ), intent(in) :: &
p_in_Pa, & ! Pressure [Pa]
T_in_K ! Temperature [K]
! ------------------------ Output Variables ------------------------
real( kind = core_rknd ) :: &
sat_mixrat_ice_k
! ------------------------ Local Variables ------------------------
real( kind = core_rknd ), dimension(1,1) :: &
p_in_Pa_col, &
T_in_K_col
real( kind = core_rknd ), dimension(1,1) :: &
sat_mixrat_ice_col
integer :: i, k ! Loop indices
! ------------------------ Begin Code ------------------------
! Copy inputs to 2D arrays
p_in_Pa_col(1,1) = p_in_Pa
T_in_K_col(1,1) = T_in_K
! Call 2D version
sat_mixrat_ice_col = sat_mixrat_ice_2D( 1, 1, p_in_Pa_col, T_in_K_col )
! Copy 2D result into output
sat_mixrat_ice_k = sat_mixrat_ice_col(1,1)
return
end function sat_mixrat_ice_k
!------------------------------------------------------------------------
! Wrapped in interface sat_mixrat_ice
function sat_mixrat_ice_2D( nz, ngrdcol, p_in_Pa, T_in_K )
! Description:
! Used to compute the saturation mixing ratio of ice.
! References:
! Formula from Emanuel 1994, 4.4.15
!-------------------------------------------------------------------------
use constants_clubb, only: &
T_freeze_K, & ! Variable(s)
ep
use clubb_precision, only: &
core_rknd ! Variable(s)
implicit none
! ------------------------ Input Variables ------------------------
integer, intent(in) :: &
nz, &
ngrdcol
real( kind = core_rknd ), dimension(ngrdcol,nz), intent(in) :: &
p_in_Pa, & ! Pressure [Pa]
T_in_K ! Temperature [K]
! ------------------------ Output Variables ------------------------
real( kind = core_rknd ), dimension(ngrdcol,nz) :: &
sat_mixrat_ice_2D
! ------------------------ Local Variables ------------------------
! Relative error norm expansion (-90 to 0 deg_C) from
! Table 4 of pp. 1511 of Flatau et al. 1992 (Ice)
real( kind = core_rknd ), dimension(9), parameter :: a = &
100._core_rknd * (/ 6.09868993_core_rknd, 0.499320233_core_rknd, 0.184672631E-01_core_rknd, &
0.402737184E-03_core_rknd, 0.565392987E-05_core_rknd, 0.521693933E-07_core_rknd, &
0.307839583E-09_core_rknd, 0.105785160E-11_core_rknd, 0.161444444E-14_core_rknd /)
real( kind = core_rknd ), parameter :: &
min_T_in_C = -90._core_rknd, & ! [deg_C]
min_T_in_K = 173.15_core_rknd ! Lowest temperature at which Goff-Gratch is valid [K]
real( kind = core_rknd ) :: &
T_in_C, & ! Temperature [deg_C]
T_in_K_clipped ! Absolute temperature with minimum threshold applied [K]
real( kind = core_rknd ), dimension(ngrdcol,nz) :: &
esat_ice
integer :: i, k ! Loop indices
! ------------------------ Begin Code ------------------------
!$acc data create( esat_ice ) &
!$acc copyin( p_in_Pa, T_in_K ) &
!$acc copyout( sat_mixrat_ice_2D )
! Determine the SVP for the given temperature
select case ( saturation_formula )
case ( saturation_bolton )
! Using the Bolton 1980 approximations for SVP over ice
!$acc parallel loop gang vector collapse(2) default(present)
do i = 1, ngrdcol
do k = 1, nz
! Exponential approx.
esat_ice(i,k) = 100.0_core_rknd * exp( 23.33086_core_rknd - &
(6111.72784_core_rknd/T_in_K(i,k)) + (0.15215_core_rknd*log( T_in_K(i,k) )) )
end do
end do
!$acc end parallel loop
case ( saturation_flatau )
! Using the Flatau, et al. polynomial approximation for SVP over ice
!$acc parallel loop gang vector collapse(2) default(present)
do i = 1, ngrdcol
do k = 1, nz
! Determine deg K - 273.15
T_in_C = T_in_K(i,k) - T_freeze_K
! Since this approximation is only good out to -90 degrees Celsius we
! truncate the result here (Flatau, et al. 1992)
T_in_C = max( T_in_C, min_T_in_C )
! Polynomial approx. (Flatau, et al. 1992)
! esati = a(1)
! do i = 2, size( a ), 1
! esati = esati + a(i) * ( T_in_C )**(i-1)
! end do
esat_ice(i,k) = a(1) + T_in_C*( a(2) + T_in_C*( a(3) + T_in_C*( a(4) + T_in_C &
*( a(5) + T_in_C*( a(6) + T_in_C*( a(7) + T_in_C*( a(8) + T_in_C*a(9) ) ) ) ) ) ) )
end do
end do
!$acc end parallel loop
! ---> h1g, 2010-06-16
case ( saturation_gfdl )