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diagnostics.f90
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diagnostics.f90
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module diagnostics
implicit none
save
private
public :: vint, hydro_interp, mix_ratio_to_spec_hum, temp_from_theta_p, &
surface_pres, density, sea_pres, lifted_index, mean_rh, &
unstag_hght, cape, sbcape, mlcape, lcl_lfc, storm_motion, &
storm_rel_hel, calcdbz, calcgust
public :: Grav
! Some meteorological constants (set to the values used by WRF)
real, parameter :: RGas = 287., Grav = 9.81, KappaR = 3.5, &
SpecHeatPresDry = KappaR * RGas, &
Kappa = RGas / SpecHeatPresDry, Gamma = .0065, &
LatHeatVap = 2.5e6, RVap = 461.6, Eps = RGas / RVap, &
EpsR = RVap / RGas, Missing = -9999., EpsRM1 = EpsR - 1
interface mix_ratio_to_spec_hum
module procedure mrtsh3d
module procedure mrtsh4d
end interface
interface temp_from_theta_p
module procedure tftp0d
module procedure tftp1d
module procedure tftp2d
module procedure tftp3d
module procedure tftp4d
end interface
interface density
module procedure dens3d
module procedure dens4d
end interface
contains ! Public Functions ==================================================
! vint takes a vertical profile (prof) and interpolates it to regular levels
! starting at first with an interval of delta using a profile of values for
! the interpolating vertical coordinate variable (vCoordVals) defined at the
! same points as prof. The interpolated output is returned as interpProf.
! interpType = 1 --> linear interpolation, interpType = 2 --> interpolate
! with respect to -ln(vertical coordinate value).
subroutine vint(prof, vCoordVals, first, delta, interpType, interpProf)
real, dimension(:), intent(in) :: prof, vCoordVals
integer, intent(in) :: first, delta, interpType
real, dimension(:), intent(out) :: interpProf
real, dimension(2) :: vCoordBounds, profBounds
real :: level
integer :: nz, np, k
nz = size(prof)
np = size(interpProf)
! Validate input
if (nz /= size(vCoordVals)) then
print *, "Error: Array extent mismatch in vint!"
stop
end if
! Initialize output
interpProf = Missing
! Interpolate
do k = 1, np
level = first + (k-1) * delta
! Skip this level if we don't have data for it
if (level < minval(vCoordVals) .or. level > maxval(vCoordVals)) cycle
call find_bounds(vCoordVals, prof, level, vCoordBounds, profBounds)
if (interpType == 2) then ! Handle logarithmic interpolation case
vCoordBounds = -log(vCoordBounds)
level = -log(level)
end if
interpProf(k) = lin_int(vCoordBounds(1), vCoordBounds(2), &
profBounds(1), profBounds(2), level)
end do
end subroutine vint
! ===========================================================================
! hydro_interp hydrostatically interpolates geopotential heights on pressure
! surfaces underground. Provided as input are the height (zs; m), pressure
! (ps; hPa), and temperature (ts; K) in the lowest WRF model layer, as well
! as the lowest (in altitude) pressure surface desired (pBot) and the
! pressure level spacing (dp). The routine takes the currently computed
! geopotential heights on pressure surfaces (z), and interpolates to those
! grid points determined to be underground.
subroutine hydro_interp(zs, ps, ts, pBot, dp, z)
real, dimension(:,:,:), intent(in) :: zs, ps, ts
integer, intent(in) :: pBot, dp
real, dimension(:,:,:,:), intent(inout) :: z
real, parameter :: LapseRate = .0065, Expo = RGas * LapseRate / Grav
integer :: nz, k, p
nz = size(z,3)
! Validate
if (any(shape(zs) /= shape(ps)) .or. any(shape(zs) /= shape(ts)) .or. &
size(z,1) /= size(zs,1) .or. size(z,2) /= size(zs,2) .or. &
size(z,4) /= size(zs,3)) stop "Array mismatch in hydro_interp!"
do k = 1, nz
if (all(z /= Missing)) exit ! Are we above the highest terrain?
p = pBot + (k-1) * dp
where (z(:,:,k,:) == Missing)
z(:,:,k,:) = zs - ts / LapseRate * ((p/ps)**Expo - 1)
end where
end do
end subroutine hydro_interp
! ===========================================================================
! Both mrtsh3d and mrtsh4d convert mixing ratio (kg/kg) to specific
! humidity (kg/kg).
function mrtsh3d(w) result (q)
real, dimension(:,:,:), intent(in) :: w
real, dimension(size(w,1),size(w,2),size(w,3)) :: q
q = w / (1 + w)
end function mrtsh3d
! ...........................................................................
function mrtsh4d(w) result (q)
real, dimension(:,:,:,:), intent(in) :: w
real, dimension(size(w,1),size(w,2),size(w,3),size(w,4)) :: q
q = w / (1 + w)
end function mrtsh4d
! ===========================================================================
! tftp0d, tftp1d, tftp2d, tftp3d, and tftp4d calculate the temperature (K)
! given the potential temperature (th; K) and pressure (p; Pa or hPa
! depending on si flag).
function tftp0d(th, p, si) result (t)
real, intent(in) :: th, p
logical, intent(in), optional :: si
real :: t
real :: p0r
! Set appropriate p0
p0r = 1e-5 ! Default is SI units (p0 = 100000)
if (present(si)) then
if (.not. si) p0r = .001 ! (p0 = 1000)
end if
! Calculate temperature (exp and log faster than ** on my machine)
t = th * exp(Kappa * log(p * p0r))
end function tftp0d
! ...........................................................................
function tftp1d(th, p, si) result (t)
real, dimension(:), intent(in) :: th, p
logical, intent(in), optional :: si
real, dimension(size(p,1)) :: t
real :: p0r
! Make sure arrays match up
if (any(shape(th) /= shape(p))) stop "Array extent mismatch in tftp2d!"
! Set appropriate p0
p0r = 1e-5 ! Default is SI units (p0 = 100000)
if (present(si)) then
if (.not. si) p0r = .001 ! (p0 = 1000)
end if
! Calculate temperature
t = th * (p * p0r) ** Kappa
end function tftp1d
! ...........................................................................
function tftp2d(th, p, si) result (t)
real, dimension(:,:), intent(in) :: th, p
logical, intent(in), optional :: si
real, dimension(size(p,1),size(p,2)) :: t
real :: p0r
! Make sure arrays match up
if (any(shape(th) /= shape(p))) stop "Array extent mismatch in tftp2d!"
! Set appropriate p0
p0r = 1e-5 ! Default is SI units (p0 = 100000)
if (present(si)) then
if (.not. si) p0r = .001 ! (p0 = 1000)
end if
! Calculate temperature
t = th * (p * p0r) ** Kappa
end function tftp2d
! ...........................................................................
function tftp3d(th, p, si) result (t)
real, dimension(:,:,:), intent(in) :: th, p
logical, intent(in), optional :: si
real, dimension(size(p,1),size(p,2),size(p,3)) :: t
real :: p0r
! Make sure arrays match up
if (any(shape(th) /= shape(p))) stop "Array extent mismatch in tftp3d!"
! Set appropriate p0
p0r = 1e-5 ! Default is SI units (p0 = 100000)
if (present(si)) then
if (.not. si) p0r = .001 ! (p0 = 1000)
end if
! Calculate temperature
t = th * (p * p0r) ** Kappa
end function tftp3d
! ...........................................................................
function tftp4d(th, p, si) result (t)
real, dimension(:,:,:,:), intent(in) :: th, p
logical, intent(in), optional :: si
real, dimension(size(p,1),size(p,2),size(p,3),size(p,4)) :: t
real :: p0r
! Make sure arrays match up
if (any(shape(th) /= shape(p))) stop "Array extent mismatch in tftp4d!"
! Set appropriate p0
p0r = 1e-5 ! Default is SI units (p0 = 100000)
if (present(si)) then
if (.not. si) p0r = .001 ! (p0 = 1000)
end if
! Calculate temperature
t = th * (p * p0r) ** Kappa
end function tftp4d
! ===========================================================================
! surface_pres calculates the surface pressure (Pa) given the following data:
! ht- Geopotential height (m) at lowest two w (full) levels (x,y,z,t)
! p1- Pressure (Pa) at lowest mass (half) level (x,y,t)
! q1- Specific humidity (kg/kg) at lowest mass level (x,y,t)
! t1- Temperature (K) at lowest mass level (x,y,t)
! sfcq- Specific humidity (kq/kq) at surface/2-m above ground (x,y,t)
! It is assumed that the array extents match appropriately.
function surface_pres(ht, p1, q1, t1, sfcq)
real, dimension(:,:,:,:), intent(in) :: ht
real, dimension(:,:,:), intent(in) :: p1, q1, t1, sfcq
real, dimension(size(p1,1),size(p1,2),size(p1,3)) :: surface_pres
real, dimension(size(t1,1),size(t1,2),size(t1,3)) :: tvirt
tvirt = (1 + .608 * .5 * (sfcq + q1)) * t1
surface_pres = p1 * exp((Grav / (RGas * tvirt)) &
* .5 * (ht(:,:,2,:) - ht(:,:,1,:)))
end function surface_pres
! ===========================================================================
! dens3d and dens4d calculate the density (kg/m**3) using the ideal gas law
! given:
! p- Pressure (Pa)
! t- Temperature (K)
! q- Water vapor mixing ratio (kg/kg)
! It is assumed that the array extents match appropriately.
function dens3d(p, t, q)
real, dimension(:,:,:), intent(in) :: p, t, q
real, dimension(size(p,1),size(p,2),size(p,3)) :: dens3d
dens3d = p / (t * (RGas + q * RVap))
dens3d = dens3d * (1 + q)
end function dens3d
! ...........................................................................
function dens4d(p, t, q)
real, dimension(:,:,:,:), intent(in) :: p, t, q
real, dimension(size(p,1),size(p,2),size(p,3),size(p,4)) :: dens4d
dens4d = p / (t * (RGas + q * RVap))
dens4d = dens4d * (1 + q)
end function dens4d
! ===========================================================================
! sea_pres is taken from the WRF NCL tools. The inputs are:
! zs- Geopotential height (m) on w (full) levels (x,y,z,t)
! theta- Potential temperature (K) on mass (half) levels (x,y,z,t)
! p- Pressure (Pa) on mass levels (x,y,z,t)
! q- Specific humidity (kg/kg) on mass levels (x,y,z,t)
! It is assumed that the array extents match appropriately.
function sea_pres(zs, theta, p, q)
! Estimate sea level pressure.
real, dimension(:,:,:,:), intent(in) :: zs, theta, p, q
real, dimension(size(p,1),size(p,2),size(p,4)) :: sea_pres
real, dimension(size(p,1),size(p,2),size(p,3),size(p,4)) :: t, z
real, dimension(size(p,1),size(p,2)) :: tSurf, tSeaLevel
integer, dimension(size(p,1),size(p,2)) :: level
! Specific constants for assumptions made in this routine:
real, parameter :: Tc = 273.16+17.5, PConst = 10000
! Local variables:
real :: plo, phi, tlo, thi, zlo, zhi, pAtPConst, tAtPConst, zAtPConst
integer :: nx, ny, nz, nt
integer :: i, j, k, klo, khi, l
logical :: l1, l2, l3, found
nx = size(p,1)
ny = size(p,2)
nz = size(p,3)
nt = size(p,4)
! Convert potential temperature to temperature
t = temp_from_theta_p(theta, p)
! Unstagger z
z(:,:,1:nz,:) = .5 * (zs(:,:,1:nz,:) + zs(:,:,2:nz+1,:))
! Grand loop over all times
do l = 1, nt
! Find least zeta level that is PConst Pa above the surface. We later
! use this level to extrapolate a surface pressure and temperature,
! which is supposed to reduce the effect of the diurnal heating cycle in
! the pressure field.
do j = 1 , ny
do i = 1 , nx
level(i,j) = -1
k = 1
found = .false.
do while( (.not. found) .and. (k <= nz))
if ( p(i,j,k,l) < p(i,j,1,l)-PConst ) then
level(i,j) = k
found = .true.
end if
k = k+1
end do
if ( level(i,j) == -1 ) then
print '(A,I4,A)','Troubles finding level ', &
nint(PConst)/100,' above ground.'
print '(A,I4,A,I4,A)', &
'Problems first occur at (',i,',',j,')'
print '(A,F6.1,A)', &
'Surface pressure = ',p(i,j,1,l)/100,' hPa.'
stop 'Error_in_finding_100_hPa_up'
end if
end do
end do
! Get temperature PConst Pa above surface. Use this to extrapolate
! the temperature at the surface and down to sea level.
do j = 1 , ny
do i = 1 , nx
klo = max ( level(i,j) - 1 , 1 )
khi = min ( klo + 1 , nz - 1 )
if ( klo == khi ) then
print '(A)','Trapping levels are weird.'
print '(A,I3,A,I3,A)','klo = ',klo,', khi = ',khi, &
': and they should not be equal.'
stop 'Error_trapping_levels'
end if
plo = p(i,j,klo,l)
phi = p(i,j,khi,l)
tlo = t(i,j,klo,l) * (1. + 0.608 * q(i,j,klo,l) )
thi = t(i,j,khi,l) * (1. + 0.608 * q(i,j,khi,l) )
zlo = z(i,j,klo,l)
zhi = z(i,j,khi,l)
pAtPConst = p(i,j,1,l) - PConst
TAtPConst = thi - (thi-tlo) * log(pAtPConst/phi) * log(plo/phi)
zAtPConst = zhi - (zhi-zlo) * log(pAtPConst/phi) * log(plo/phi)
tSurf(i,j) = tAtPConst * (p(i,j,1,l)/pAtPConst)**(Gamma*RGas/Grav)
tSeaLevel(i,j) = tAtPConst + Gamma * zAtPConst
end do
end do
! If we follow a traditional computation, there is a correction to the
! sea level temperature if both the surface and sea level temnperatures
! are *too* hot.
do j = 1 , ny
do i = 1 , nx
l1 = tSeaLevel(i,j) < Tc
l2 = tSurf (i,j) <= Tc
l3 = .not. l1
if ( l2 .and. l3 ) then
tSeaLevel(i,j) = Tc
else
tSeaLevel(i,j) = Tc - 0.005 * (tSurf(i,j) - Tc)**2
end if
end do
end do
! The grand finale: ta da!
sea_pres(:,:,l) = p(:,:,1,l) * &
exp((2.*Grav*z(:,:,1,l)) / (RGas*(tSeaLevel + tSurf)))
end do
end function sea_pres
! ===========================================================================
! lifted_index calculates the lifted index (K) based on the supplied profiles
! of potential temperature (theta; K), pressure (p; hPa), and mixing ratio
! (w; kg/kg). Array indices are ordered from the ground up. The lowest 4
! model levels are mixed to produce the hypothetical parcel, which is then
! lifted adiabatically to saturation, and pseudoadiabatically thereafter.
function lifted_index(theta, p, w) result (li)
real, dimension(:), intent(in) :: theta, p, w
real :: li
real, dimension(2) :: pBounds, thBounds
real :: dens, thMix, wMix, sm, tk, pLCL, thes, tParcel, tEnv
integer :: nz, k
nz = size(theta)
! Check that array extents match
if (nz /= size(p) .or. nz /= size(w)) &
stop "Array mismatch in lifted_index."
! Set lifted index to 0 if we don't have enough data
if (nz < 4 .or. p(1) < 500.) then
li = 0
else
! Determine temperature of pseudoadiabatically lifted parcel at 500 mb
! Step 1: Mix the lowest 4 model levels
thMix = 0; wMix = 0; sm = 0
do k = 1, 4
dens = density_thp(theta(k), p(k)) ! Effect of water vapor ignored
thMix = thMix + dens * theta(k)
wMix = wMix + dens * w(k)
sm = sm + dens
end do
thMix = thMix / sm
wMix = wMix / sm
! Step 2: Lift parcel to LCL
tk = temp_from_theta_p(thMix, p(1), si=.false.)
! This equation is derived from Curry & Webster (1999, p. 174)
pLCL = 1000 * (temp_lcl(tk, rh(wMix, p(1), tk)) / thMix)**KappaR
! Step 3: Lift parcel to 500 mb
thes = theta_es(thMix, pLCL)
tParcel = temp_from_theta_p(theta_es_to_theta_fast(thes, 500.), 500., &
si=.false.)
! Get environmental temperature at 500 mb
call find_bounds(p, theta, 500., pBounds, thBounds)
tEnv = temp_from_theta_p(lin_int(pBounds(1), pBounds(2), thBounds(1), &
thBounds(2), 500.), 500., si=.false.)
li = tEnv - tParcel
end if
end function lifted_index
! ===========================================================================
! mean_rh computes the mean relative humidity (%) between pBot hPa and pTop
! hPa based on the supplied profiles of potential temperature (theta; K),
! pressure (p; hPa), and mixing ratio (w; kg/kg). Also provided is the
! surface pressure (pSfc; hPa). Array indices are ordered from the ground
! up. The mean is weighted by the thickness of each layer.
function mean_rh(theta, p, w, pSfc, pBot, pTop) result (mrh)
real, dimension(:), intent(in) :: theta, p, w
real, intent(in) :: pSfc, pBot, pTop
real :: mrh
real, dimension(0:size(theta)-1) :: pMid
real :: pThick, relHum, totPresThick, totRH
integer :: nz, k
nz = size(theta)
! Check that array extents match
if (nz /= size(p) .or. nz /= size(w)) stop "Array mismatch in mean_rh."
! Calculate pressure at midpoints
pMid(0) = pSfc
pMid(1:nz-1) = .5 * (p(1:nz-1) + p(2:nz))
! Calculate mean RH
totPresThick = 0; totRH = 0
do k = 1, nz-1
if (pMid(k) > pBot) cycle
if (pMid(k-1) < pTop) exit
! Calculate layer thickness
if (pMid(k-1) > pBot) then
pThick = pBot - pMid(k)
else if (pMid(k) < pTop) then
pThick = pMid(k-1) - pTop
else
pThick = pMid(k-1) - pMid(k)
end if
relHum = rh(w(k), p(k), temp_from_theta_p(theta(k), p(k), si=.false.))
totRH = totRH + pThick * relHum
totPresThick = totPresThick + pThick
end do
if (totPresThick > .01) then
mrh = 100 * totRH / totPresThick
else
mrh = 0
end if
end function mean_rh
! ===========================================================================
! unstag_hght unstaggers the geopotential height from w levels (zs) given
! by znw to u levels (z) given by znu. mu and pt provide additional
! information needed to do an interpolation based on ln p.
function unstag_hght(zs, znw, znu, mu, pt) result (z)
real, dimension(:), intent(in) :: zs, znw, znu
real, intent(in) :: mu, pt
real, dimension(size(znu)) :: z
real, dimension(size(znw)) :: pw
real, dimension(size(znu)) :: pu
integer :: k
! Validate input
if (size(zs) /= size(znw) .or. size(znw) /= size(znu) + 1) &
print *, "Warning: Array extent mismatch in unstag_hght!"
! Initialize pressures
do k = 1, size(znw)
if (k < size(znw)) pu(k) = pd(znu(k))
pw(k) = pd(znw(k))
end do
! Interpolate to half levels
do k = 1, size(znu)
!orig z(k) = lin_int(-log(pw(k)), -log(pw(k+1)), zs(k), zs(k+1), -log(pu(k)))
z(k) = lin_int(pw(k), pw(k+1), zs(k), zs(k+1), pu(k))
end do
contains
real function pd(eta)
real, intent(in) :: eta
pd = pt + mu * eta
end function pd
end function unstag_hght
! ===========================================================================
! cape calculates the convective available potential energy (J/kg) given
! profiles of potential temperature (theta; K), pressure (p; hPa),
! mixing ratio (w; kg/kg), and height (z; m). By default, it returns the
! most unstable CAPE, but if lplOutI is set to .true., the height above
! ground level of the parcel whose CAPE is most unstable is returned instead.
! In that case, the terrain height at the profile location (ter) is also
! required.
real function cape(theta, p, w, z, ter, lplOutI)
real, dimension(:), intent(in) :: theta, p, w, z
real, optional, intent(in) :: ter
logical, optional, intent(in) :: lplOutI
real, dimension(size(z)) :: tProf
real, dimension(2) :: pBounds, zBounds
real :: lpl, tk, pLCL, thes, zLCL, parcelCape
integer :: nz, i
logical :: lplOut
! Initialize
cape = 0; lpl = 0
nz = size(z)
lplOut = .false.
if (present(lplOutI)) then
lplOut = lplOutI
if (.not. present(ter)) stop "For LPL, need terrain height!"
end if
! Validate
if (nz /= size(theta) .or. nz /= size(p) .or. nz /= size(w)) &
stop "Error: Array extent mismatch in cape!"
! Compute environmental profile with virtual temperature correction.
! Note that applying the correction here doesn't affect LCL values below.
tProf = temp_from_theta_p(theta, p, si=.false.) * (1 + EpsRM1 * w)
! We loop over all parcels originating in the lowest 300 hPa
do i = 1, nz-1
if (p(i) < p(1) - 300) exit
! Find LCL for this parcel
tk = temp_from_theta_p(theta(i), p(i), si=.false.)
pLCL = 1000 * (temp_lcl(tk, rh(w(i), p(i), tk)) / theta(i))**KappaR
if (pLCL > p(i)) pLCL = p(i)
if (pLCL < 200.) cycle
thes = theta_es(theta(i), pLCL)
call find_bounds(p, z, pLCL, pBounds, zBounds)
zLCL = lin_int(pBounds(1), pBounds(2), zBounds(1), zBounds(2), pLCL)
parcelCape = calc_cape(tProf(i:nz), p(i:nz), z(i:nz), theta(i), w(i), &
thes, pLCL, zLCL)
! Check if largest CAPE so far
if (parcelCape > cape) then
cape = parcelCape
if (lplOut) lpl = z(i) - ter
end if
end do
if (lplOut) cape = lpl
end function cape
! ===========================================================================
! sbcape calculates the convective available potential energy (J/kg) of the
! parcel lifted from the lowest model layer given profiles of potential
! temperature (theta; K), pressure (p; hPa), mixing ratio (w; kg/kg), and
! height (z; m). By default, it returns the CAPE, but if cinOutI is set to
! .true., the convective inhibition (J/kg) is returned instead.
real function sbcape(theta, p, w, z, cinOutI)
real, dimension(:), intent(in) :: theta, p, w, z
logical, optional, intent(in) :: cinOutI
real, dimension(size(z)) :: tProf
real, dimension(2) :: pBounds, zBounds
real :: tk, pLCL, zLCL, thes
integer :: nz
logical :: cinOut
! Initialize
sbcape = 0
nz = size(z)
cinOut = .false.
if (present(cinOutI)) cinOut = cinOutI
! Validate
if (nz /= size(theta) .or. nz /= size(p) .or. nz /= size(w)) &
stop "Error: Array extent mismatch in sbcape!"
! Compute environmental profile with virtual temperature correction.
! Note that applying the correction here doesn't affect LCL values below.
tProf = temp_from_theta_p(theta, p, si=.false.) * (1 + EpsRM1 * w)
! Find LCL for lowest parcel
tk = temp_from_theta_p(theta(1), p(1), si=.false.)
pLCL = 1000 * (temp_lcl(tk, rh(w(1), p(1), tk)) / theta(1))**KappaR
if (pLCL > p(1)) pLCL = p(1)
thes = theta_es(theta(1), pLCL)
! Calculate what we want
if (cinOut) then
sbcape = calc_cin(tProf, p, z, theta(1), w(1), thes, pLCL)
else
call find_bounds(p, z, pLCL, pBounds, zBounds)
zLCL = lin_int(pBounds(1), pBounds(2), zBounds(1), zBounds(2), pLCL)
sbcape = calc_cape(tProf, p, z, theta(1), w(1), thes, pLCL, zLCL)
end if
end function sbcape
! ===========================================================================
! mlcape calculates the convective available potential energy (J/kg) of the
! parcel mixed from the lowest 4 model layers given profiles of potential
! temperature (theta; K), pressure (p; hPa), mixing ratio (w; kg/kg), and
! height (z; m). By default, it returns the CAPE, but if cinOutI is set to
! .true., the convective inhibition (J/kg) is returned instead.
real function mlcape(theta, p, w, z, cinOutI)
real, dimension(:), intent(in) :: theta, p, w, z
logical, optional, intent(in) :: cinOutI
real, dimension(size(z)) :: tProf
real, dimension(2) :: pBounds, zBounds
real :: thMix, wMix, total, dens, tk, pLCL, zLCL, thes
integer :: nz, k
logical :: cinOut
! Initialize
mlcape = 0
nz = size(z)
cinOut = .false.
if (present(cinOutI)) cinOut = cinOutI
! Validate
if (nz /= size(theta) .or. nz /= size(p) .or. nz /= size(w)) &
stop "Error: Array extent mismatch in mlcape!"
! Set result to 0 if we don't have enough data
if (nz < 4) then
mlcape = 0
return
end if
! Mix the lowest 4 model levels
thMix = 0; wMix = 0; total = 0
do k = 1, 4
dens = density_thp(theta(k), p(k)) ! Effect of water vapor ignored
thMix = thMix + dens * theta(k)
wMix = wMix + dens * w(k)
total = total + dens
end do
thMix = thMix / total
wMix = wMix / total
! Compute environmental profile with virtual temperature correction.
! Note that applying the correction here doesn't affect LCL values below.
tProf = temp_from_theta_p(theta, p, si=.false.) * (1 + EpsRM1 * w)
! Find LCL for mixed parcel
tk = temp_from_theta_p(thMix, p(1), si=.false.)
pLCL = 1000 * (temp_lcl(tk, rh(wMix, p(1), tk)) / thMix)**KappaR
if (pLCL > p(1)) pLCL = p(1)
thes = theta_es(thMix, pLCL)
! Calculate what we want
if (cinOut) then
mlcape = calc_cin(tProf, p, z, thMix, wMix, thes, pLCL)
else
call find_bounds(p, z, pLCL, pBounds, zBounds)
zLCL = lin_int(pBounds(1), pBounds(2), zBounds(1), zBounds(2), pLCL)
mlcape = calc_cape(tProf, p, z, thMix, wMix, thes, pLCL, zLCL)
end if
end function mlcape
! ===========================================================================
! lcl_lfc returns the lifting condensation level or level of free convection.
! If lclFlag is true (false), the former (latter) is returned. Provided as
! input are profiles of potential temperature (theta; K), pressure (p; hPa),
! mixing ratio (w; kg/kg), and geopotential height (z; m). The terrain
! height (ter; m) is also provided as input.
real function lcl_lfc(theta, p, w, z, ter, lclFlag)
real, dimension(:), intent(in) :: theta, p, w, z
real, intent(in) :: ter
logical, intent(in) :: lclFlag
real, dimension(size(z)) :: tProf, tTraj
real, dimension(2) :: pBounds, zBounds
real :: thMix, wMix, total, dens, tk, pLCL, zLCL, thes
integer :: nz, k
! Initialize
lcl_lfc = -9999 ! The GEMPAK missing value
nz = size(z)
! Validate
if (nz /= size(theta) .or. nz /= size(p) .or. nz /= size(w)) &
stop "Error: Array extent mismatch in lcl_lfc!"
! Return immediately if we don't have enough data
if (nz < 4) return
! Mix the lowest 4 model levels
thMix = 0; wMix = 0; total = 0
do k = 1, 4
dens = density_thp(theta(k), p(k)) ! Effect of water vapor ignored
thMix = thMix + dens * theta(k)
wMix = wMix + dens * w(k)
total = total + dens
end do
thMix = thMix / total
wMix = wMix / total
! Find LCL for mixed parcel
tk = temp_from_theta_p(thMix, p(1), si=.false.)
pLCL = 1000 * (temp_lcl(tk, rh(wMix, p(1), tk)) / thMix)**KappaR
if (pLCL > p(1)) pLCL = p(1)
call find_bounds(p, z, pLCL, pBounds, zBounds)
zLCL = lin_int(pBounds(1), pBounds(2), zBounds(1), zBounds(2), pLCL)
! Calculate what we want
if (lclFlag) then
lcl_lfc = zLCL - ter
else
thes = theta_es(thMix, pLCL)
! Compute environmental profile and ascent trajectory using the
! virtual temperature correction.
tProf = temp_from_theta_p(theta, p, si=.false.) * (1 + EpsRM1 * w)
tTraj = calc_traj(p, tProf(1), theta(1), w(1), thes, pLCL)
! Find LFC height (from bottom up)
do k = 2, nz-1
if (p(k) >= pLCL .or. tTraj(k) <= tProf(k)) cycle
! We just passed through LFC, but we need to allow for case where the
! LCL is in a region of positive area already due to a superadiabatic
! environmental lapse rate.
if (tTraj(k-1) - tProf(k-1) >= 0) then
lcl_lfc = zLCL
else
lcl_lfc = lin_int(tTraj(k-1)-tProf(k-1), tTraj(k)-tProf(k), &
z(k-1), z(k), 0.)
end if
exit
end do
if (lcl_lfc /= -9999) lcl_lfc = lcl_lfc - ter
end if
end function lcl_lfc
! ===========================================================================
! storm_motion computes either the u or v component of the supercell storm
! motion vector derived by Bunkers et al. (2000). uComp = true (false)
! means the u (v) component will be output. Provided for input are the u and
! v components of the wind (m), the 10-m winds (u and v; m), and the
! terrain height (ter; m).
function storm_motion(u, v, z, u10m, v10m, ter, uComp)
real, dimension(:,:,:,:), intent(in) :: u, v, z
real, dimension(:,:,:), intent(in) :: u10m, v10m
real, dimension(:,:), intent(in) :: ter
logical, intent(in) :: uComp
real, dimension(size(u,1),size(u,2),size(u,4)) :: storm_motion
integer :: k
real, parameter :: D = 7.5
integer, parameter :: NumLevs = 13, Dz = 500 ! 0 to 6 km
real, dimension(NumLevs), parameter :: Heights = (/ (Dz * k, &
k = 0, NumLevs-1) /)
real, dimension(3), parameter :: HeadHeights = (/ 5500, 5750, 6000 /), &
TailHeights = (/ 0, 250, 500 /)
real, dimension(size(u,1),size(u,2),size(u,4)) :: uShear, vShear, magShear
integer :: nx, ny, nt
nx = size(u,1); ny = size(u,2); nt = size(u,4)
! Validate
if (any(shape(u) /= shape(z)) .or. any(shape(v) /= shape(z)) .or. &
nx /= size(u10m,1) .or. ny /= size(u10m,2) .or. &
nt /= size(u10m,3) .or. nx /= size(v10m,1) .or. &
ny /= size(v10m,2) .or. nt /= size(v10m,3) .or. &
nx /= size(ter,1) .or. ny /= size(ter,2)) &
stop "Array mismatch in storm_motion!"
! Calculate Bunkers wind shear and its magnitude
uShear = mean_wind(u, z, u10m, ter, HeadHeights) - &
mean_wind(u, z, u10m, ter, TailHeights)
vShear = mean_wind(v, z, v10m, ter, HeadHeights) - &
mean_wind(v, z, v10m, ter, TailHeights)
magShear = sqrt(uShear**2 + vShear**2)
! Calculate appropriate storm motion vector.
if (uComp) then
storm_motion = mean_wind(u, z, u10m, ter, Heights) + &
D * VShear / MagShear
else
storm_motion = mean_wind(v, z, v10m, ter, Heights) - &
D * UShear / MagShear
end if
end function storm_motion
! ===========================================================================
! storm_rel_hel computes the storm relative helicity (m2/s2) for the layer
! defined by heights (m), given as input the u and v components of the wind
! (m), the geopotential height (z; m), the u and v components of the wind at
! 10m (u10m, v10m; m), and the terrain height (ter; m).
function storm_rel_hel(u, v, z, u10m, v10m, ter, heights) result (srh)
real, dimension(:,:,:,:), intent(in) :: u, v, z
real, dimension(:,:,:), intent(in) :: u10m, v10m
real, dimension(:,:), intent(in) :: ter
real, dimension(:), intent(in) :: heights
real, dimension(size(u,1),size(u,2),size(u,4)) :: srh
real, dimension(size(z,1),size(z,2),size(z,3),size(z,4)) :: hagl
real, dimension(size(u,1),size(u,2),size(heights),size(u,4)) :: uInt, &
vInt, &
xVort, &
yVort, &
srhs
real, dimension(size(u,1),size(u,2),size(u,4)) :: uStorm, vStorm
real, dimension(2) :: haglBounds, windBounds
integer :: nx, ny, nz, nt, numLevs, i, j, k, t
nx = size(u,1); ny = size(u,2); nz = size(u,3); nt = size(u,4)
numLevs = size(heights)
! Validate
if (any(shape(u) /= shape(z)) .or. any(shape(v) /= shape(z)) .or. &
nx /= size(u10m,1) .or. ny /= size(u10m,2) .or. &
nt /= size(u10m,3) .or. nx /= size(v10m,1) .or. &
ny /= size(v10m,2) .or. nt /= size(v10m,3) .or. &
nx /= size(ter,1) .or. ny /= size(ter,2)) &
stop "Array mismatch in storm_motion!"
hagl = z - &
spread(source=spread(source=ter, dim=3, ncopies=nz), dim=4, ncopies=nt)
! Interpolate winds to constant height grid
do t = 1, nt
do j = 1, ny
do i = 1, nx
do k = 1, numLevs
if (heights(k) < hagl(i,j,1,t)) then
uInt(i,j,k,t) = u10m(i,j,t)
vInt(i,j,k,t) = v10m(i,j,t)
else
call find_bounds(hagl(i,j,:,t), u(i,j,:,t), heights(k), &
haglBounds, windBounds)
uInt(i,j,k,t) = lin_int(haglBounds(1), haglBounds(2), &
windBounds(1), windBounds(2), heights(k))
call find_bounds(hagl(i,j,:,t), v(i,j,:,t), heights(k), &
haglBounds, windBounds)
vInt(i,j,k,t) = lin_int(haglBounds(1), haglBounds(2), &
windBounds(1), windBounds(2), heights(k))
end if
end do
end do
end do
end do
! Neglect vertical motion component of horizontal vorticity, a valid
! approximation on the synoptic and mesoscales.
xVort = -calc_ddz(vInt, heights)
yVort = calc_ddz(uInt, heights)
uStorm = storm_motion(u, v, z, u10m, v10m, ter, .true.)
vStorm = storm_motion(u, v, z, u10m, v10m, ter, .false.)
srhs = (uInt - spread(uStorm, dim=3, ncopies=numLevs)) * xVort + &
(vInt - spread(vStorm, dim=3, ncopies=numLevs)) * yVort
srh = 0
do k = 1, numLevs-1
srh = srh + .5*(heights(k+1)-heights(k))*(srhs(:,:,k,:)+srhs(:,:,k+1,:))
end do
end function storm_rel_hel
! ===========================================================================
! calcdbz diagnoses reflectivity (dBZ) provided inputs of air density
! (rhoair; kg/m^3), temperature (tmk; K), rain water mixing ratio
! (qra; kg/kg), snow mixing ratio (qsn; kg/kg), and graupel mixing ratio
! (qgr; kg/kg). This function is largely taken from that in RIP4. Note that
! to be more accurate the parameters in this function should depend on the
! microphysical scheme being used.
function calcdbz(rhoair, tmk, qra, qsn, qgr) result (dbz)
real, dimension(:,:,:,:), intent(in) :: rhoair, tmk, qra, qsn, qgr
real, dimension(size(tmk,1),size(tmk,2),size(tmk,3),size(tmk,4)) :: dbz
real, parameter :: r1 = 1.e-15, ron2 = 1.e10, gon = 5.e7, ron_min = 8.e6, &
ron_qr0 = 0.00010, ron_delqr0 = 0.25*ron_qr0, &
ron_const1r = (ron2 - ron_min)*0.5, &
ron_const2r = (ron2 + ron_min)*0.5, &
gamma_seven = 720., rhowat = 1000., &
rho_r = rhowat, & ! 1000. kg m^-3
rho_s = 100., & ! kg m^-3
rho_g = 400., & ! kg m^-3
alpha = 0.224, celkel = 273.15
real, dimension(size(tmk,1),size(tmk,2),size(tmk,3),size(tmk,4)) :: ronv, &
sonv, &
gonv
real :: pi, factor_r, factor_s, factor_g
! Constants
pi = 4. * atan(1.)
factor_r = gamma_seven * 1.e18 * (1./(pi*rho_r))**1.75
factor_s = gamma_seven * 1.e18 * (1./(pi*rho_s))**1.75 &
* (rho_s/rhowat)**2 * alpha
factor_g = gamma_seven * 1.e18 * (1./(pi*rho_g))**1.75 &
* (rho_g/rhowat)**2 * alpha
! Validate
if (any(shape(tmk) /= shape(rhoair)) .or. any(shape(tmk) /= shape(qra)) &
.or. any(shape(tmk) /= shape(qsn)) &
.or. any(shape(tmk) /= shape(qgr))) stop "Array mismatch in calcdbz!"
! Calculate variable intercept parameters
sonv = min(2.0e8, 2.0e6 * exp(-0.12 * min(-0.001, tmk-celkel)))
where (qgr <= r1)
gonv = gon
elsewhere
gonv = max(1.e4, min(2.38 * (pi*rho_g / (rhoair*qgr))**0.92, gon))
end where
where (qra <= r1)