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module_diag_functions.F
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module_diag_functions.F
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!WRF:MEDIATION_LAYER:PHYSICS
#if (NMM_CORE == 1)
MODULE diag_functions
CONTAINS
SUBROUTINE diag_functions_stub
END SUBROUTINE diag_functions_stub
END MODULE diag_functions
#else
MODULE diag_functions
CONTAINS
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
!~
!~ Name:
!~ calc_rh
!~
!~ Description:
!~ This function calculates relative humidity given pressure,
!~ temperature, and water vapor mixing ratio.
!~
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
FUNCTION calc_rh ( p, t, qv ) result ( rh )
IMPLICIT NONE
REAL, INTENT(IN) :: p, t, qv
REAL :: rh
! Local
! -----
REAL, PARAMETER :: pq0=379.90516
REAL, PARAMETER :: a2=17.2693882
REAL, PARAMETER :: a3=273.16
REAL, PARAMETER :: a4=35.86
REAL, PARAMETER :: rhmin=1.
REAL :: q, qs
INTEGER :: i,j,k
! Following algorithms adapted from WRFPOST
! May want to substitute with another later
! -----------------------------------------
q=qv/(1.0+qv)
qs=pq0/p*exp(a2*(t-a3)/(t-a4))
rh=100.*q/qs
IF (rh .gt. 100.) THEN
rh=100.
ELSE IF (rh .lt. rhmin) THEN
rh=rhmin
ENDIF
END FUNCTION calc_rh
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
!~
!~ Name:
!~ uv_wind
!~
!~ Description:
!~ This function calculates the wind speed given U and V wind
!~ components.
!~
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
FUNCTION uv_wind ( u, v ) result ( wind_speed )
IMPLICIT NONE
REAL, INTENT(IN) :: u, v
REAL :: wind_speed
wind_speed = sqrt( u*u + v*v )
END FUNCTION uv_wind
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
!~
!~ Name:
!~ Theta
!~
!~ Description:
!~ This function calculates potential temperature as defined by
!~ Poisson's equation, given temperature and pressure ( hPa ).
!~
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
FUNCTION Theta ( t, p )
IMPLICIT NONE
!~ Variable declaration
! --------------------
REAL, INTENT ( IN ) :: t
REAL, INTENT ( IN ) :: p
REAL :: theta
REAL :: Rd ! Dry gas constant
REAL :: Cp ! Specific heat of dry air at constant pressure
REAL :: p0 ! Standard pressure ( 1000 hPa )
Rd = 287.04
Cp = 1004.67
p0 = 1000.00
!~ Poisson's equation
! ------------------
theta = t * ( (p0/p)**(Rd/Cp) )
END FUNCTION Theta
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
!~
!~ Name:
!~ Thetae
!~
!~ Description:
!~ This function returns equivalent potential temperature using the
!~ method described in Bolton 1980, Monthly Weather Review, equation 43.
!~
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
FUNCTION Thetae ( tK, p, rh, mixr )
IMPLICIT NONE
!~ Variable Declarations
! ---------------------
REAL :: tK ! Temperature ( K )
REAL :: p ! Pressure ( hPa )
REAL :: rh ! Relative humidity
REAL :: mixr ! Mixing Ratio ( kg kg^-1)
REAL :: te ! Equivalent temperature ( K )
REAL :: thetae ! Equivalent potential temperature
REAL, PARAMETER :: R = 287.04 ! Universal gas constant (J/deg kg)
REAL, PARAMETER :: P0 = 1000.0 ! Standard pressure at surface (hPa)
REAL, PARAMETER :: lv = 2.54*(10**6) ! Latent heat of vaporization
! (J kg^-1)
REAL, PARAMETER :: cp = 1004.67 ! Specific heat of dry air constant
! at pressure (J/deg kg)
REAL :: tlc ! LCL temperature
!~ Calculate the temperature of the LCL
! ------------------------------------
tlc = TLCL ( tK, rh )
!~ Calculate theta-e
! -----------------
thetae = (tK * (p0/p)**( (R/Cp)*(1.- ( (.28E-3)*mixr*1000.) ) ) )* &
exp( (((3.376/tlc)-.00254))*&
(mixr*1000.*(1.+(.81E-3)*mixr*1000.)) )
END FUNCTION Thetae
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
!~
!~ Name:
!~ The2T.f90
!~
!~ Description:
!~ This function returns the temperature at any pressure level along a
!~ saturation adiabat by iteratively solving for it from the parcel
!~ thetae.
!~
!~ Dependencies:
!~ function thetae.f90
!~
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
FUNCTION The2T ( thetaeK, pres, flag ) result ( tparcel )
IMPLICIT NONE
!~ Variable Declaration
! --------------------
REAL, INTENT ( IN ) :: thetaeK
REAL, INTENT ( IN ) :: pres
LOGICAL, INTENT ( INOUT ) :: flag
REAL :: tparcel
REAL :: thetaK
REAL :: tovtheta
REAL :: tcheck
REAL :: svpr, svpr2
REAL :: smixr, smixr2
REAL :: thetae_check, thetae_check2
REAL :: tguess_2, correction
LOGICAL :: found
INTEGER :: iter
REAL :: R ! Dry gas constant
REAL :: Cp ! Specific heat for dry air
REAL :: kappa ! Rd / Cp
REAL :: Lv ! Latent heat of vaporization at 0 deg. C
R = 287.04
Cp = 1004.67
Kappa = R/Cp
Lv = 2.500E+6
!~ Make initial guess for temperature of the parcel
! ------------------------------------------------
tovtheta = (pres/100000.0)**(r/cp)
tparcel = thetaeK/exp(lv*.012/(cp*295.))*tovtheta
iter = 1
found = .false.
flag = .false.
DO
IF ( iter > 105 ) EXIT
tguess_2 = tparcel + REAL ( 1 )
svpr = 6.122 * exp ( (17.67*(tparcel-273.15)) / (tparcel-29.66) )
smixr = ( 0.622*svpr ) / ( (pres/100.0)-svpr )
svpr2 = 6.122 * exp ( (17.67*(tguess_2-273.15)) / (tguess_2-29.66) )
smixr2 = ( 0.622*svpr2 ) / ( (pres/100.0)-svpr2 )
! ------------------------------------------------------------------ ~!
!~ When this function was orinially written, the final parcel ~!
!~ temperature check was based off of the parcel temperature and ~!
!~ not the theta-e it produced. As there are multiple temperature- ~!
!~ mixing ratio combinations that can produce a single theta-e value, ~!
!~ we change the check to be based off of the resultant theta-e ~!
!~ value. This seems to be the most accurate way of backing out ~!
!~ temperature from theta-e. ~!
!~ ~!
!~ Rentschler, April 2010 ~!
! ------------------------------------------------------------------ !
!~ Old way...
!thetaK = thetaeK / EXP (lv * smixr /(cp*tparcel) )
!tcheck = thetaK * tovtheta
!~ New way
thetae_check = Thetae ( tparcel, pres/100., 100., smixr )
thetae_check2 = Thetae ( tguess_2, pres/100., 100., smixr2 )
!~ Whew doggies - that there is some accuracy...
!IF ( ABS (tparcel-tcheck) < .05) THEN
IF ( ABS (thetaeK-thetae_check) < .001) THEN
found = .true.
flag = .true.
EXIT
END IF
!~ Old
!tparcel = tparcel + (tcheck - tparcel)*.3
!~ New
correction = ( thetaeK-thetae_check ) / ( thetae_check2-thetae_check )
tparcel = tparcel + correction
iter = iter + 1
END DO
!IF ( .not. found ) THEN
! print*, "Warning! Thetae to temperature calculation did not converge!"
! print*, "Thetae ", thetaeK, "Pressure ", pres
!END IF
END FUNCTION The2T
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
!~
!~ Name:
!~ VirtualTemperature
!~
!~ Description:
!~ This function returns virtual temperature given temperature ( K )
!~ and mixing ratio.
!~
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
FUNCTION VirtualTemperature ( tK, w ) result ( Tv )
IMPLICIT NONE
!~ Variable declaration
real, intent ( in ) :: tK !~ Temperature
real, intent ( in ) :: w !~ Mixing ratio ( kg kg^-1 )
real :: Tv !~ Virtual temperature
Tv = tK * ( 1.0 + (w/0.622) ) / ( 1.0 + w )
END FUNCTION VirtualTemperature
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
!~
!~ Name:
!~ SaturationMixingRatio
!~
!~ Description:
!~ This function calculates saturation mixing ratio given the
!~ temperature ( K ) and the ambient pressure ( Pa ). Uses
!~ approximation of saturation vapor pressure.
!~
!~ References:
!~ Bolton (1980), Monthly Weather Review, pg. 1047, Eq. 10
!~
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
FUNCTION SaturationMixingRatio ( tK, p ) result ( ws )
IMPLICIT NONE
REAL, INTENT ( IN ) :: tK
REAL, INTENT ( IN ) :: p
REAL :: ws
REAL :: es
es = 6.122 * exp ( (17.67*(tK-273.15))/ (tK-29.66) )
ws = ( 0.622*es ) / ( (p/100.0)-es )
END FUNCTION SaturationMixingRatio
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
!~
!~ Name:
!~ tlcl
!~
!~ Description:
!~ This function calculates the temperature of a parcel of air would have
!~ if lifed dry adiabatically to it's lifting condensation level (lcl).
!~
!~ References:
!~ Bolton (1980), Monthly Weather Review, pg. 1048, Eq. 22
!~
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
FUNCTION TLCL ( tk, rh )
IMPLICIT NONE
REAL, INTENT ( IN ) :: tK !~ Temperature ( K )
REAL, INTENT ( IN ) :: rh !~ Relative Humidity ( % )
REAL :: tlcl
REAL :: denom, term1, term2
term1 = 1.0 / ( tK - 55.0 )
IF ( rh > REAL (0) ) THEN
term2 = ( LOG (rh/100.0) / 2840.0 )
ELSE
term2 = ( LOG (0.001/1.0) / 2840.0 )
END IF
denom = term1 - term2
tlcl = ( 1.0 / denom ) + REAL ( 55 )
END FUNCTION TLCL
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
!~
!~ Name:
!~ PWat
!~
!~ Description:
!~ This function calculates precipitable water by summing up the
!~ water vapor in a column from the first eta layer to model top
!~
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
FUNCTION Pwat ( nz, qv, qc, dz8w, rho )
IMPLICIT NONE
!~ Variable declaration
! --------------------
INTEGER, INTENT ( IN ) :: nz !~ Number of vertical levels
REAL, INTENT ( IN ) :: qv ( nz ) !~ Specific humidity in layer (kg/kg)
REAL, INTENT ( IN ) :: qc ( nz ) !~ Cloud water in layer (kg/kg)
REAL, INTENT ( IN ) :: dz8w ( nz ) !~ Dist between vertical levels (m)
REAL, INTENT ( IN ) :: rho ( nz ) !~ Air density (kg/m^3)
REAL :: Pwat !~ Precipitable water (kg/m^2)
INTEGER :: k !~ Vertical index
!~ Precipitable water (kg/m^2)
! ---------------------------
Pwat=0
DO k = 1, nz
!Based on AMS PWAT defination (https://glossary.ametsoc.org/wiki/Precipitable_water)
!PWAT is corrected as the column accumulated water vapor rather than water vapor + cloud water.
!Modified by Zhixiao
Pwat = Pwat + qv(k) * dz8w(k) * rho(k)
ENDDO
END FUNCTION Pwat
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
!~ ~!
!~ Name: ~!
!~ Buoyancy ~!
!~ ~!
!~ Description: ~!
!~ This function computes Convective Available Potential Energy (CAPE) ~!
!~ with inhibition as a result of water loading given the data required ~!
!~ to run up a sounding. ~!
!~ ~!
!~ Additionally, since we are running up a sounding anyways, this ~!
!~ function returns the height of the Level of Free Convection (LFC) and ~!
!~ the pressure at the LFC. That-a-ways, we don't have to run up a ~!
!~ sounding later, saving a relatively computationally expensive ~!
!~ routine. ~!
!~ ~!
!~ Usage: ~!
!~ ostat = Buoyancy ( tK, rh, p, hgt, sfc, CAPE, ZLFC, PLFC, parcel ) ~!
!~ ~!
!~ Where: ~!
!~ ~!
!~ IN ~!
!~ -- ~!
!~ tK = Temperature ( K ) ~!
!~ rh = Relative Humidity ( % ) ~!
!~ p = Pressure ( Pa ) ~!
!~ hgt = Geopotential heights ( m ) ~!
!~ sfc = integer rank within submitted arrays that represents the ~!
!~ surface ~!
!~ ~!
!~ OUT ~!
!~ --- ~!
!~ ostat INTEGER return status. Nonzero is bad. ~!
!~ CAPE ( J/kg ) Convective Available Potential Energy ~!
!~ ZLFC ( gpm ) Height at the LFC ~!
!~ PLFC ( Pa ) Pressure at the LFC ~!
!~ ~!
!~ tK, rh, p, and hgt are all REAL arrays, arranged from lower levels ~!
!~ to higher levels. ~!
!~ ~!
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
FUNCTION Buoyancy ( nz, tk, rh, p, hgt, sfc, cape, cin, zlfc, plfc, lidx, &
parcel ) result (ostat)
IMPLICIT NONE
INTEGER, INTENT ( IN ) :: nz !~ Number of vertical levels
INTEGER, INTENT ( IN ) :: sfc !~ Surface level in the profile
REAL, INTENT ( IN ) :: tk ( nz ) !~ Temperature profile ( K )
REAL, INTENT ( IN ) :: rh ( nz ) !~ Relative Humidity profile ( % )
REAL, INTENT ( IN ) :: p ( nz ) !~ Pressure profile ( Pa )
REAL, INTENT ( IN ) :: hgt ( nz ) !~ Height profile ( gpm )
REAL, INTENT ( OUT ) :: cape !~ CAPE ( J kg^-1 )
REAL, INTENT ( OUT ) :: cin !~ CIN ( J kg^-1 )
REAL, INTENT ( OUT ) :: zlfc !~ LFC Height ( gpm )
REAL, INTENT ( OUT ) :: plfc !~ LFC Pressure ( Pa )
REAL, INTENT ( OUT ) :: lidx !~ Lifted index
INTEGER :: ostat !~ Function return status
!~ Nonzero is bad.
INTEGER, INTENT ( IN ) :: parcel !~ Most Unstable = 1 (default)
!~ Mean layer = 2
!~ Surface based = 3
!~ Derived profile variables
! -------------------------
REAL :: ws ( nz ) !~ Saturation mixing ratio
REAL :: w ( nz ) !~ Mixing ratio
REAL :: etheta( nz )!~ Equivalent potential temperature. Modified by Zhixiao.
REAL :: dTvK ( nz ) !~ Parcel / ambient Tv difference
REAL :: buoy ( nz ) !~ Buoyancy
REAL :: tlclK !~ LCL temperature ( K )
REAL :: plcl !~ LCL pressure ( Pa )
REAL :: pel !~ Equilibrium pressure ( Pa ). Modified by Zhixiao.
REAL :: nbuoy !~ Negative buoyancy
REAL :: pbuoy !~ Positive buoyancy
!~ Source parcel information
! -------------------------
REAL :: srctK !~ Source parcel temperature ( K )
REAL :: srcrh !~ Source parcel rh ( % )
REAL :: srcws !~ Source parcel sat. mixing ratio
REAL :: srcw !~ Source parcel mixing ratio
REAL :: srcp !~ Source parcel pressure ( Pa )
REAL :: srctheta !~ Source parcel theta ( K )
REAL :: srcthetaeK !~ Source parcel theta-e ( K )
INTEGER :: srclev !~ Level of the source parcel
REAL :: spdiff !~ Pressure difference
REAL :: srce !~ Equivalent potential temperature ( K ). Modified by Zhixiao.
!~ Parcel variables
! ----------------
REAL :: ptK !~ Parcel temperature ( K )
REAL :: ptvK !~ Parcel virtual temperature ( K )
REAL :: tvK !~ Ambient virtual temperature ( K )
REAL :: pw !~ Parcel mixing ratio
!~ Other utility variables
! -----------------------
INTEGER :: i, j, k !~ Dummy iterator
INTEGER :: lfclev !~ Level of LFC
INTEGER :: ellev !~ Level of EL. Modified by Zhixiao.
INTEGER :: prcl !~ Internal parcel type indicator
INTEGER :: mlev !~ Level for ML calculation
INTEGER :: lyrcnt !~ Number of layers in mean layer
LOGICAL :: flag !~ Dummy flag
LOGICAL :: wflag !~ Saturation flag
REAL :: freeze !~ Water loading multiplier
REAL :: pdiff !~ Pressure difference between levs
REAL :: pm, pu, pd !~ Middle, upper, lower pressures
REAL :: lidxu !~ Lifted index at upper level
REAL :: lidxd !~ Lifted index at lower level
!~ Thermo / dynamical constants
! ----------------------------
REAL :: Rd !~ Dry gas constant
PARAMETER ( Rd = 287.058 ) !~ J deg^-1 kg^-1
REAL :: Cp !~ Specific heat constant pressure
PARAMETER ( Cp = 1004.67 ) !~ J deg^-1 kg^-1
REAL :: g !~ Acceleration due to gravity
PARAMETER ( g = 9.80665 ) !~ m s^-2
REAL :: RUNDEF
PARAMETER ( RUNDEF = -9.999E30 )
!~ Initialize variables
! --------------------
ostat = 0
CAPE = REAL ( 0 )
CIN = RUNDEF !Change CIN filling values from 0 to default filling. CIN should not initially be filled by 0, because 0 means no inhibition energy. Modified by Zhixiao
ZLFC = RUNDEF
PLFC = RUNDEF
!~ Look for submitted parcel definition
!~ 1 = Most unstable
!~ 2 = Mean layer
!~ 3 = Surface based
! -------------------------------------
IF ( parcel > 3 .or. parcel < 1 ) THEN
prcl = 1
ELSE
prcl = parcel
END IF
!~ Initalize our parcel to be (sort of) surface based. Because of
!~ issues we've been observing in the WRF model, specifically with
!~ excessive surface moisture values at the surface, using a true
!~ surface based parcel is resulting a more unstable environment
!~ than is actually occuring. To address this, our surface parcel
!~ is now going to be defined as the parcel between 25-50 hPa
!~ above the surface. UPDATE - now that this routine is in WRF,
!~ going to trust surface info. GAC 20140415
! ----------------------------------------------------------------
!~ Compute mixing ratio values for the layer
! -----------------------------------------
DO k = sfc, nz
ws ( k ) = SaturationMixingRatio ( tK(k), p(k) )
w ( k ) = ( rh(k)/100.0 ) * ws ( k )
!Removed by Zhixiao. Water vapor mixing ratio (w) is not conserved during parcel lifting processes. We should not use w to define MU layer.
!thetav(k) = Theta ( VirtualTemperature ( tK (k), w (k) ), p(k)/100.0 )
!Added by Zhixiao. Critical modification: We use the model level with maximum equivalent potential temperature (etheta) below 500mb to define the MU layer
!Because equivalent potential temperature is conserved in dry and moist adiabatic processes.
etheta(k) = Thetae( tK(k), p(k)/100.0, rh(k), w(k) )
END DO
srclev = sfc
srctK = tK ( sfc )
srcrh = rh ( sfc )
srcp = p ( sfc )
srcws = ws ( sfc )
srcw = w ( sfc )
srctheta = Theta ( tK(sfc), p(sfc)/100.0 )
srce = etheta (sfc) !Modified by Zhixiao
!~ Compute the profile mixing ratio. If the parcel is the MU parcel,
!~ define our parcel to be the most unstable parcel within the lowest
!~ 180 mb.
! -------------------------------------------------------------------
mlev = sfc + 1
!Change initial searching level from the second to first model level. Because we did not compute pdiff, and p(k-1) properties is unnecessary.
!Modified by Zhixiao.
DO k = sfc, nz
!~ Identify the last layer within 100 hPa of the surface
! -----------------------------------------------------
pdiff = ( p (sfc) - p (k) ) / REAL ( 100 )
IF ( pdiff <= REAL (100) ) mlev = k
!~ If we've made it past the lowest 500 hPa, exit the loop. MU layer is assumed below 500 hPa. Modified by Zhixiao.
! -------------------------------------------------------
IF ( p(k) <= REAL (50000) ) EXIT
IF ( prcl == 1 ) THEN
! Removed by Zhixiao, w can not used for defining MU layer
!IF ( (p(k) > 70000.0) .and. (w(k) > srcw) ) THEN
! Modified by Zhixiao, MU layer is featured by the max etheta
IF (etheta(k) > srce) THEN !Modified by Zhixiao.
srctheta = Theta ( tK(k), p(k)/100.0 )
srcw = w ( k )
srclev = k
srctK = tK ( k )
srcrh = rh ( k )
srcp = p ( k )
srce = etheta(k) !Modified by Zhixiao
END IF
END IF
END DO
!~ If we want the mean layer parcel, compute the mean values in the
!~ lowest 100 hPa.
! ----------------------------------------------------------------
lyrcnt = mlev - sfc + 1
IF ( prcl == 2 ) THEN
srclev = sfc
srctK = SUM ( tK (sfc:mlev) ) / REAL ( lyrcnt )
srcw = SUM ( w (sfc:mlev) ) / REAL ( lyrcnt )
srcrh = SUM ( rh (sfc:mlev) ) / REAL ( lyrcnt )
srcp = SUM ( p (sfc:mlev) ) / REAL ( lyrcnt )
srctheta = Theta ( srctK, srcp/100. )
END IF
srcthetaeK = Thetae ( srctK, srcp/100.0, srcrh, srcw )
!~ Calculate temperature and pressure of the LCL
! ---------------------------------------------
tlclK = TLCL ( tK(srclev), rh(srclev) )
plcl = p(srclev) * ( (tlclK/tK(srclev))**(Cp/Rd) )
!~ Now lift the parcel
! -------------------
buoy = REAL ( 0 )
pw = srcw
wflag = .false.
DO k = srclev, nz
IF ( p (k) <= plcl ) THEN
!~ The first level after we pass the LCL, we're still going to
!~ lift the parcel dry adiabatically, as we haven't added the
!~ the required code to switch between the dry adiabatic and moist
!~ adiabatic cooling. Since the dry version results in a greater
!~ temperature loss, doing that for the first step so we don't over
!~ guesstimate the instability.
! ----------------------------------------------------------------
IF ( wflag ) THEN
flag = .false.
!~ Above the LCL, our parcel is now undergoing moist adiabatic
!~ cooling. Because of the latent heating being undergone as
!~ the parcel rises above the LFC, must iterative solve for the
!~ parcel temperature using equivalant potential temperature,
!~ which is conserved during both dry adiabatic and
!~ pseudoadiabatic displacements.
! --------------------------------------------------------------
ptK = The2T ( srcthetaeK, p(k), flag )
!~ Calculate the parcel mixing ratio, which is now changing
!~ as we condense moisture out of the parcel, and is equivalent
!~ to the saturation mixing ratio, since we are, in theory, at
!~ saturation.
! ------------------------------------------------------------
pw = SaturationMixingRatio ( ptK, p(k) )
!~ Now we can calculate the virtual temperature of the parcel
!~ and the surrounding environment to assess the buoyancy.
! ----------------------------------------------------------
ptvK = VirtualTemperature ( ptK, pw )
tvK = VirtualTemperature ( tK (k), w (k) )
!~ Modification to account for water loading
! -----------------------------------------
freeze = 0.033 * ( 263.15 - pTvK )
IF ( freeze > 1.0 ) freeze = 1.0
IF ( freeze < 0.0 ) freeze = 0.0
!~ Approximate how much of the water vapor has condensed out
!~ of the parcel at this level
! ---------------------------------------------------------
freeze = freeze * 333700.0 * ( srcw - pw ) / 1005.7
pTvK = pTvK - pTvK * ( srcw - pw ) + freeze
dTvK ( k ) = ptvK - tvK
buoy ( k ) = g * ( dTvK ( k ) / tvK )
ELSE
!~ Since the theta remains constant whilst undergoing dry
!~ adiabatic processes, can back out the parcel temperature
!~ from potential temperature below the LCL
! --------------------------------------------------------
ptK = srctheta / ( 100000.0/p(k) )**(Rd/Cp)
!~ Grab the parcel virtual temperture, can use the source
!~ mixing ratio since we are undergoing dry adiabatic cooling
! ----------------------------------------------------------
ptvK = VirtualTemperature ( ptK, srcw )
!~ Virtual temperature of the environment
! --------------------------------------
tvK = VirtualTemperature ( tK (k), w (k) )
!~ Buoyancy at this level
! ----------------------
dTvK ( k ) = ptvK - tvK
buoy ( k ) = g * ( dtvK ( k ) / tvK )
wflag = .true.
END IF
ELSE
!~ Since the theta remains constant whilst undergoing dry
!~ adiabatic processes, can back out the parcel temperature
!~ from potential temperature below the LCL
! --------------------------------------------------------
ptK = srctheta / ( 100000.0/p(k) )**(Rd/Cp)
!~ Grab the parcel virtual temperture, can use the source
!~ mixing ratio since we are undergoing dry adiabatic cooling
! ----------------------------------------------------------
ptvK = VirtualTemperature ( ptK, srcw )
!~ Virtual temperature of the environment
! --------------------------------------
tvK = VirtualTemperature ( tK (k), w (k) )
!~ Buoyancy at this level
! ---------------------
dTvK ( k ) = ptvK - tvK
buoy ( k ) = g * ( dtvK ( k ) / tvK )
END IF
!~ Chirp
! -----
! WRITE ( *,'(I15,6F15.3)' )k,p(k)/100.,ptK,pw*1000.,ptvK,tvK,buoy(k)
END DO
!~ Add up the buoyancies, find the LFC
! -----------------------------------
flag = .false.
lfclev = -1
ellev = -1 !Modified by Zhixiao
DO k = sfc, nz !Modified by Zhixiao
!~ LFC is defiend as the highest level when negative buyancy turns postive.
! -----------------------------------
IF ( .not. flag .and. buoy (k) > REAL (0) .and. p (k) <= plcl ) THEN !Modified by Zhixiao
flag = .true.
lfclev = k
END IF
!~ Take the Highest EL as final result. Modified by Zhixiao
! ----------------------------------------------------------------
IF (k >= 2) THEN !Modified by Zhixiao
IF ( flag .and. buoy (k) < REAL (0) .and. buoy (k-1) >= REAL (0)) THEN !Modified by Zhixiao
ellev = k !Modified by Zhixiao
END IF
END IF
! When buoy turns negative again, reset LFC flag and keep the highest LFC as the effective output
IF (buoy (k) < REAL (0) .and. flag) THEN
flag = .false.
END IF
END DO
IF ((ellev >= 0) .and. (lfclev >= 0)) THEN !Modified by Zhixiao
plfc = p (lfclev)
pel = p (ellev)
CIN = REAL ( 0 )
DO k = sfc+1, nz
! Make CAPE and CIN consistent with AMS definition
! https://glossary.ametsoc.org/wiki/Convective_available_potential_energy
! https://glossary.ametsoc.org/wiki/Convective_inhibition
IF ( p (k) <= plcl .and. p (k) > plfc) THEN !Modified by Zhixiao
! CIN is the vertically integrated negative buoyant energy between LCL and LFC
CIN = CIN + MIN ( buoy (k), 0.0 ) * ( hgt (k) - hgt (k-1) )
END IF
IF ( p (k) <= plfc .and. p (k) > pel) THEN !Modified by Zhixiao
! CAPE is the vertically integrated positive buoyant energy between LFC and EL
CAPE = CAPE + MAX ( buoy (k), 0.0 ) * ( hgt (k) - hgt (k-1) )
END IF !Modified by Zhixiao
END DO !Modified by Zhixiao
END IF !Modified by Zhixiao
!~ Calculate lifted index by interpolating difference between
!~ parcel and ambient Tv to 500mb.
! ----------------------------------------------------------
DO k = sfc + 1, nz
pm = 50000.
pu = p ( k )
pd = p ( k - 1 )
!~ If we're already above 500mb just set lifted index to 0.
!~ --------------------------------------------------------
IF ( pd .le. pm ) THEN
lidx = 0.
EXIT
ELSEIF ( pu .le. pm .and. pd .gt. pm) THEN
!~ Found trapping pressure: up, middle, down.
!~ We are doing first order interpolation.
! ------------------------------------------
lidxu = -dTvK ( k ) * ( pu / 100000. ) ** (Rd/Cp)
lidxd = -dTvK ( k-1 ) * ( pd / 100000. ) ** (Rd/Cp)
lidx = ( lidxu * (pm-pd) + lidxd * (pu-pm) ) / (pu-pd)
EXIT
ENDIF
END DO
!~ Assuming the the LFC is at a pressure level for now
! ---------------------------------------------------
IF ( lfclev > 0 ) THEN
PLFC = p ( lfclev )
ZLFC = hgt ( lfclev )
END IF
IF ( PLFC /= PLFC .OR. PLFC < REAL (0) ) THEN
PLFC = REAL ( -1 )
ZLFC = REAL ( -1 )
END IF
IF ( CAPE /= CAPE ) cape = REAL ( 0 )
IF ( CIN /= CIN ) cin = RUNDEF
!~ Chirp
! -----
! WRITE ( *,* ) ' CAPE: ', cape, ' CIN: ', cin
! WRITE ( *,* ) ' LFC: ', ZLFC, ' PLFC: ', PLFC
! WRITE ( *,* ) ''
! WRITE ( *,* ) ' Exiting buoyancy.'
! WRITE ( *,* ) ' ==================================== '
! WRITE ( *,* ) ''
END FUNCTION Buoyancy
!$$$ SUBPROGRAM DOCUMENTATION BLOCK
! . . .
! SUBPROGRAM: NGMSLP NMC SEA LEVEL PRESSURE REDUCTION
! PRGRMMR: TREADON ORG: W/NP2 DATE: 93-02-02
!
! ABSTRACT:
!
! THIS ROUTINE COMPUTES SEA LEVEL PRESSURE USING THE
! HYDROSTATIC EQUATION WITH THE SHUELL CORRECTION. THE
! FOLLOWING IS BASED ON DOCUMENTATION IN SUBROUTINE
! OUTHYDRO OF THE NGM:
!
! THE FUNDAMENTAL HYDROSTATIC EQUATION IS
! D(HEIGHT)
! --------- = TAU = VIRTUAL TEMPERATURE * (RGAS/GRAVITY)
! D (Z)
! WHERE
! Z = MINUS LOG OF PRESSURE (-LN(P)).
!
! SEA-LEVEL PRESSURE IS COMPUTED FROM THE FORMULA
! PRESS(MSL) = PRESS(GROUND) * EXP( F)
! WHERE
! F = HEIGHT OF GROUND / MEAN TAU
! MEAN TAU = ( TAU(GRND) + TAU(SL) ) / 2
!
! IN THE NGM TAU(GRND) AND TAU(SL) ARE FIRST SET USING A
! 6.5DEG/KM LAPSE RATE FROM LOWEST MDL LEVEL. THIS IS MODIFIED
! BY A CORRECTION BASED ON THE CRITICAL TAU OF THE SHUELL
! CORRECTION:
! TAUCR=(RGASD/GRAVITY) * 290.66
!
! 1) WHERE ONLY TAU(SL) EXCEEDS TAUCR, CHANGE TAU(SL) TO TAUCR.
!
! 2) WHERE BOTH TAU(SL) AND TAU(GRND) EXCEED TAUCR,
! CHANGE TAU(SL) TO TAUCR-CONST*(TAU(GRND)-TAUCR )**2
! WHERE CONST = .005 (GRAVITY/RGASD)
!
! THE AVERAGE OF TAU(SL) AND TAU(GRND) IS THEN USED TOGETHER
! WITH THE GROUND HEIGHT AND PRESSURE TO DERIVE THE PRESSURE
! AT SEA LEVEL.
!
! HEIGHT OF THE 1000MB SURFACE IS COMPUTED FROM THE MSL PRESSURE
! FIELD USING THE FORMULA:
!
! P(MSL) - P(1000MB) = MEAN DENSITY * GRAVITY * HGT(1000MBS)
!
! WHERE P(MSL) IS THE SEA LEVEL PRESSURE FIELD WE HAVE JUST
! COMPUTED.
!
!
! MEB 6/13/02: THIS CODE HAS BEEN SIMPLIFIED CONSIDERABLY FROM
! THE ONE USED IN ETAPOST. HORIZONTAL SMOOTHING HAS BEEN
! REMOVED AND THE FIRST MODEL LEVEL IS USED RATHER
! THAN THE MEAN OF THE VIRTUAL TEMPERATURES IN
! THE LOWEST 30MB ABOVE GROUND TO COMPUTE TAU(GRND).
!
! .
!
! PROGRAM HISTORY LOG:
! 93-02-02 RUSS TREADON
! 98-06-08 T BLACK - CONVERSION FROM 1-D TO 2-D
! 00-01-04 JIM TUCCILLO - MPI VERSION
! 01-10-25 H CHUANG - MODIFIED TO PROCESS HYBRID MODEL OUTPUT
! 01-11-02 H CHUANG - MODIFIED LINE 234 FOR COMPUTATION OF
! SIGMA/HYBRID SLP
! 01-12-18 H CHUANG - INCLUDED SMOOTHING ALONG BOUNDARIES TO BE
! CONSISTENT WITH MESINGER SLP
! 02-06-13 MIKE BALDWIN - WRF VERSION
! 06-12-18 H CHUANG - BUG FIX TO CORRECT TAU AT SFC
! 14-04-17 G CREIGHTON - MODIFIED TO INSERT INTO AFWA DIAGNOSTICS IN WRF
!
!$$$
FUNCTION MSLP ( zsfc, psfc, zlev1, qlev1, tlev1 )
implicit none
! DECLARE VARIABLES
REAL, INTENT ( IN ) :: zsfc !~ Surface height ( m )
REAL, INTENT ( IN ) :: psfc !~ Surface height ( m )
REAL, INTENT ( IN ) :: zlev1 !~ Level 1 height ( m )
REAL, INTENT ( IN ) :: qlev1 !~ Level 1 mixing ratio ( kg/kg )
REAL, INTENT ( IN ) :: tlev1 !~ Level 1 temperature ( K )
real,PARAMETER :: G=9.81
real,PARAMETER :: GI=1./G
real,PARAMETER :: RD=287.0
real,PARAMETER :: ZSL=0.0
real,PARAMETER :: TAUCR=RD*GI*290.66,CONST=0.005*G/RD
real,PARAMETER :: GORD=G/RD,DP=60.E2
real,PARAMETER :: GAMMA=6.5E-3
real MSLP,TVRT,TVRSFC,TAUSFC,TVRSL,TAUSL,TAUAVG
!
!**********************************************************************
! START NGMSLP HERE.
!
MSLP = PSFC
!
! COMPUTE LAYER TAU (VIRTUAL TEMP*RD/G).
TVRT = TLEV1*(1.0+0.608*QLEV1)
!TAU = TVRT*RD*GI
!
! COMPUTE TAU AT THE GROUND (Z=ZSFC) AND SEA LEVEL (Z=0)
! ASSUMING A CONSTANT LAPSE RATE OF GAMMA=6.5DEG/KM.
TVRSFC = TVRT + (ZLEV1 - ZSFC)*GAMMA
TAUSFC = TVRSFC*RD*GI
TVRSL = TVRT + (ZLEV1 - ZSL)*GAMMA
TAUSL = TVRSL*RD*GI
!
! IF NEED BE APPLY SHEULL CORRECTION.
IF ((TAUSL.GT.TAUCR).AND.(TAUSFC.LE.TAUCR)) THEN
TAUSL=TAUCR
ELSEIF ((TAUSL.GT.TAUCR).AND.(TAUSFC.GT.TAUCR)) THEN
TAUSL = TAUCR-CONST*(TAUSFC-TAUCR)**2
ENDIF
!
! COMPUTE MEAN TAU.
TAUAVG = 0.5*(TAUSL+TAUSFC)
!
! COMPUTE SEA LEVEL PRESSURE.
MSLP = PSFC*EXP(ZSFC/TAUAVG)
END FUNCTION MSLP
!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
!~ ~!
!~ Name: ~!
!~ calc_fits ~!
!~ ~!
!~ Description: ~!
!~ This function computes Fighter Index Thermal Stress values given ~!
!~ dry bulb temperature, relative humidity, and pressure. ~!
!~ ~!
!~ Usage: ~!
!~ fitsval = calc_fits ( p, tK, rh ) ~!
!~ ~!
!~ Where: ~!
!~ p = Pressure ( Pa ) ~!
!~ tK = Temperature ( K ) ~!
!~ rh = Relative Humidity ( % ) ~!
!~ ~!
!~ Reference: ~!
!~ Stribley, R.F., S. Nunneley, 1978: Fighter Index of Thermal Stress: ~!
!~ Development of interim guidance for hot-weather USAF operations. ~!
!~ SAM-TR-78-6. Eqn. 9 ~!
!~ ~!
!~ Formula: ~!
!~ FITS = 0.8281*Twb + 0.3549*Tdb + 5.08 (degrees Celsius) ~!
!~ ~!
!~ Where: ~!
!~ Twb = Wet Bulb Temperature ~!
!~ Tdb = Dry Bulb Temperature ~!
!~ ~!
!~ Written: ~!
!~ Scott Rentschler, Software Engineering Services ~!
!~ Fine Scale Models Team ~!
!~ Air Force Weather Agency, 16WS/WXN ~!
!~ DSN: 271-3331 Comm: (402) 294-3331 ~!
!~ scott.rentschler@offutt.af.mil ~!