pvetc() computes potential vorticity, etc. More...

Functions/Subroutines
subroutine	mptgen (mpirank, mpisize, nd, jt1, jt2, j1, j2, jx, jm, jn)
	mptgen() generates grid decomposition dimensions.

subroutine	mptranr4 (mpicomm, mpisize, im, ida, idb, jm, jma, jmb, jda, km, kma, kmb, kdb, a, b, ta, tb)
	mptranr4() transposes grid decompositions.

subroutine	mxwind (km, p, u, v, t, h, pmw, umw, vmw, tmw, hmw)
	mxwind() computes maximum wind level fields.

subroutine	p2pv (km, pvu, h, t, p, u, v, kpv, pv, pvpt, pvpb, lpv, upv, vpv, hpv, tpv, ppv, spv)
	p2pv() interpolates to potential vorticity level.

subroutine	p2th (km, theta, u, v, h, t, pvu, sigma, rh, omga, kth, th, lth, uth, vth, hth, tth, zth, sigmath, rhth, oth)
	p2th() interpolates from pressure level to isentropic (theta) level.

subroutine	pvetc (km, p, px, py, t, tx, ty, h, u, v, av, hm, s, bvf2, pvn, theta, sigma, pvu)
	pvetc() computes potential vorticity, etc.

subroutine	rsearch1 (km1, z1, km2, z2, l2)
	rsearch1() searches for a surrounding real interval.

subroutine	tpause (km, p, u, v, t, h, ptp, utp, vtp, ttp, htp, shrtp)
	tpause() computes tropopause level fields.

Detailed Description

pvetc() computes potential vorticity, etc.

This subprogram computes

computation	equation
Montgomery streamfunction	hm=cpt+gz
Specific entropy	s=cplog(t/t0)-rlog(p/p0)
Brunt-Vaisala frequency squared	bvf2=g/cp*ds/dz
Potential vorticity	pvn=(avds/dz-dv/dzds/dx+du/dz*ds/dy)/rho/cp
Potential temperature	theta=t0*exp(s/cp)
Static stability	sigma=t/g*bvf2
Potential vorticity in PV units	pvu=10*-6theta*pvn

Parameters

[in]	km	integer number of levels.
[in]	p	real (km) pressure (Pa).
[in]	px	real (km) pressure x-gradient (Pa/m).
[in]	py	real (km) pressure y-gradient (Pa/m).
[in]	t	real (km) (virtual) temperature (K).
[in]	tx	real (km) (virtual) temperature x-gradient (K/m).
[in]	ty	real (km) (virtual) temperature y-gradient (K/m).
[in]	h	real (km) height (m).
[in]	u	real (km) x-component wind (m/s).
[in]	v	real (km) y-component wind (m/s).
[in]	av	real (km) absolute vorticity (1/s).
[out]	hm	real (km) Montgomery streamfunction (m2/s2).
[out]	s	real (km) specific entropy (J/K/kg).
[out]	bvf2	real (km) Brunt-Vaisala frequency squared (1/s**2).
[out]	pvn	real (km) potential vorticity (m**2/kg/s).
[out]	theta	real (km) (virtual) potential temperature (K).
[out]	sigma	real (km) static stability (K/m).
[out]	pvu	real (km) potential vorticity (10*-6Km*2/kg/s).

Program History Log

Date	Programmer	Comments
1999-10-18	Mark Iredell	Initial

Author: Mark Iredell np23

Date: 1999-10-18

Definition in file GFSPOST.F.

Function/Subroutine Documentation

◆ mptgen()

subroutine mptgen	(	integer(kint_mpi), intent(in)	mpirank,
		integer(kint_mpi), intent(in)	mpisize,
		integer(kint_mpi), intent(in)	nd,
		integer(kint_mpi), dimension(nd), intent(in)	jt1,
		integer(kint_mpi), dimension(nd), intent(in)	jt2,
		integer(kint_mpi), dimension(nd), intent(out)	j1,
		integer(kint_mpi), dimension(nd), intent(out)	j2,
		integer(kint_mpi), dimension(nd), intent(out)	jx,
		integer(kint_mpi), dimension(nd), intent(out)	jm,
		integer(kint_mpi), dimension(nd), intent(out)	jn
	)

mptgen() generates grid decomposition dimensions.

This subprogram decomposes total dimensions of a problem into smaller domains to be managed on a distributed memory system. The last dimension given is decomposed first. If more decompositions are possible, the next to last dimension is decomposed next, and so on. The transpositions between decompositions should be done by mptran*.

Parameters

[in]	mpirank	integer(kint_mpi) rank of the process (from mpi_comm_rank).
[in]	mpisize	integer(kint_mpi) size of the process (from mpi_comm_size).
[in]	nd	integer(kint_mpi) number of dimensions to decompose.
[in]	jt1	integer(kint_mpi) (nd) lower bounds of total dimensions.
[in]	jt2	integer(kint_mpi) (nd) upper bounds of total dimensions.
[out]	j1	integer(kint_mpi) (nd) lower bounds of local decompositions.
[out]	j2	integer(kint_mpi) (nd) upper bounds of local decompositions.
[out]	jx	integer(kint_mpi) (nd) local size of decompositions.
[out]	jm	integer(kint_mpi) (nd) maximum size of decompositions.
[out]	jn	integer(kint_mpi) (nd) number of decompositions.

Program History Log

Date	Programmer	Comments
1999-02-12	Mark Iredell	Initial

Author: Mark Iredell np23

Date: 1999-02-12

Definition at line 547 of file GFSPOST.F.

◆ mptranr4()

subroutine mptranr4	(	integer(kint_mpi), intent(in)	mpicomm,
		integer(kint_mpi), intent(in)	mpisize,
		integer(kint_mpi), intent(in)	im,
		integer(kint_mpi), intent(in)	ida,
		integer(kint_mpi), intent(in)	idb,
		integer(kint_mpi), intent(in)	jm,
		integer(kint_mpi), intent(in)	jma,
		integer(kint_mpi), intent(in)	jmb,
		integer(kint_mpi), intent(in)	jda,
		integer(kint_mpi), intent(in)	km,
		integer(kint_mpi), intent(in)	kma,
		integer(kint_mpi), intent(in)	kmb,
		integer(kint_mpi), intent(in)	kdb,
		real(4), dimension(ida,jda,kma), intent(in)	a,
		real(4), dimension(idb,kdb,jmb), intent(out)	b,
		real(4), dimension(im,jm,km,mpisize), intent(inout)	ta,
		real(4), dimension(im,jm,km,mpisize), intent(inout)	tb
	)

mptranr4() transposes grid decompositions.

This subprogram transposes an array of data from one grid decomposition to another by using message passing. The grid decompositions should be generated by mptgen.

Parameters

[in]	mpicomm	integer(kint_mpi) mpi communicator.
[in]	mpisize	integer(kint_mpi) size of the process (from mpi_comm_size).
[in]	im	integer(kint_mpi) undecomposed range.
[in]	ida	integer(kint_mpi) undecomposed input dimension.
[in]	idb	integer(kint_mpi) undecomposed output dimension.
[in]	jm	integer(kint_mpi) output grid decomposition size.
[in]	jma	integer(kint_mpi) input grid undecomposed range.
[in]	jmb	integer(kint_mpi) output grid decomposed range.
[in]	jda	integer(kint_mpi) input grid undecomposed dimension.
[in]	km	integer(kint_mpi) input grid decomposition size.
[in]	kma	integer(kint_mpi) input grid decomposed range.
[in]	kmb	integer(kint_mpi) output grid undecomposed range.
[in]	kdb	integer(kint_mpi) output grid undecomposed dimension.
[in]	a	real(4) (ida,jda,kma) input array.
[out]	b	real(4) (idb,kdb,jmb) output array.
[out]	ta,tb	real(4) (im,jm,km,mpisize) work arrays.

Note

While this routine serves a wide variety of scalable transpose functions for multidimensional grids,

It does not work with nonrectanguloid grids;
It does not do any load balancing;
It does not do any communication hiding.

This subprogram must be used rather than mpi_alltoall in any of the following cases:
The undecomposed range is less than the respective dimension (either im<ida or im<idb)
The decomposition size is greater than one (either km>1 or jm>1)
The decomposed range is ever zero (either kma==0 or jmb==0 for any process)
The output grid range is not the full extent (either kmb<mpisize or kmb<kda or jma<mpisize or jma<jda)

If none of these conditions apply, mpi_alltoall could be used directly rather than this subprogram and would be more efficient.

Example 1. Transpose a 1000 x 10000 matrix.

  include 'mpif.h'                                     ! use mpi
  parameter(jt=1000,kt=10000)                          ! set problem size
  real,allocatable:: a(:,:),b(:,:)                     ! declare arrays
  call mpi_init(ierr)                                  ! initialize mpi
  call mpi_comm_rank(MPI_COMM_WORLD,mpirank,ierr)      ! get mpi rank
  call mpi_comm_size(MPI_COMM_WORLD,mpisize,ierr)      ! get mpi size
  call mptgen(mpirank,mpisize,1,1,jt,j1,j2,jx,jm,jn)   ! decompose output
  call mptgen(mpirank,mpisize,1,1,kt,k1,k2,kx,km,kn)   ! decompose input
  allocate(a(jt,k1:k2),b(kt,j1:j2))                    ! allocate arrays
  a=reshape((/((j+k,j=1,jt),k=k1,k2)/),(/jt,k2-k1+1/)) ! initialize input
  call mptranr4(MPI_COMM_WORLD,mpisize,1,1,1,          ! transpose arrays
  &              jm,jt,j2-j1+1,jt,km,k2-k1+1,kt,kt,a,b)
  print '(2i8,f16.1)',((k,j,b(k,j),k=2000,kt,2000),    ! print some values
  &                    j=((j1-1)/200+1)*200,j2,200)
  call mpi_finalize(ierr)                              ! finalize mpi
  end

This transpose took 0.6 seconds on 4 2-way winterhawk nodes.

A 20000x10000 transpose took 3.4 seconds on 16 2-way winterhawk nodes.

Thus a transpose may take about 1 second for every 16 Mb per node.

Program History Log

Date	Programmer	Comments
1999-02-12	Mark Iredell	Initial

Author: Mark Iredell np23

Date: 1999-02-12

Definition at line 649 of file GFSPOST.F.

◆ mxwind()

subroutine mxwind	(	integer, intent(in)	km,
		real, dimension(km), intent(in)	p,
		real, dimension(km), intent(in)	u,
		real, dimension(km), intent(in)	v,
		real, dimension(km), intent(in)	t,
		real, dimension(km), intent(in)	h,
		real, intent(out)	pmw,
		real, intent(out)	umw,
		real, intent(out)	vmw,
		real, intent(out)	tmw,
		real, intent(out)	hmw
	)

mxwind() computes maximum wind level fields.

This subprogram finds the maximum wind level and computes fields at the maximum wind level. The maximum wind level is searched for between 500 mb and 100 mb. The height and wind speed at the maximum wind speed level is calculated by assuming the wind speed varies quadratically in height in the neighborhood of the maximum wind level. The other fields are interpolated linearly in height to the maximum wind level. The maximum wind level pressure is found hydrostatically.

Parameters

[in]	km	integer number of levels.
[in]	p	real (km) pressure (Pa).
[in]	u	real (km) x-component wind (m/s).
[in]	v	real (km) y-component wind (m/s).
[in]	t	real (km) temperature (K).
[in]	h	real (km) height (m).
[out]	pmw	real maximum wind level pressure (Pa).
[out]	umw	real maximum wind level x-component wind (m/s).
[out]	vmw	real maximum wind level y-component wind (m/s).
[out]	tmw	maximum wind level temperature (K).
[out]	hmw	real maximum wind level height (m).

Program History Log

Date	Programmer	Comments
1999-10-18	Mark Iredell	Initial
2005-02-02	Mark Iredell	Changed upper limit to 100 mb

Author: Mark Iredell np23

Date: 1999-10-18

Definition at line 459 of file GFSPOST.F.

References rsearch1().

Referenced by miscln().

◆ p2pv()

subroutine p2pv	(	integer, intent(in)	km,
		real, dimension(km), intent(in)	pvu,
		real, dimension(km), intent(in)	h,
		real, dimension(km), intent(in)	t,
		real, dimension(km), intent(in)	p,
		real, dimension(km), intent(in)	u,
		real, dimension(km), intent(in)	v,
		integer, intent(in)	kpv,
		real, dimension(kpv), intent(in)	pv,
		real, dimension(kpv), intent(in)	pvpt,
		real, dimension(kpv), intent(in)	pvpb,
		logical*1, dimension(kpv), intent(out)	lpv,
		real, dimension(kpv), intent(out)	upv,
		real, dimension(kpv), intent(out)	vpv,
		real, dimension(kpv), intent(out)	hpv,
		real, dimension(kpv), intent(out)	tpv,
		real, dimension(kpv), intent(out)	ppv,
		real, dimension(kpv), intent(out)	spv
	)

p2pv() interpolates to potential vorticity level.

This subprogram interpolates fields to given potential vorticity levels within given pressure limits. The output level is the first encountered from the top pressure limit. If the given potential vorticity level is not found, the outputs are zero and the bitmap is false. The interpolation is linear in potential vorticity.

Parameters

[in]	km	integer number of levels.
[in]	pvu	real (km) potential vorticity in PV units (10*-6Km*2/kg/s).
[in]	h	real (km) height (m).
[in]	t	real (km) temperature (K).
[in]	p	real (km) pressure (Pa).
[in]	u	real (km) x-component wind (m/s).
[in]	v	real (km) y-component wind (m/s).
[in]	kpv	integer number of potential vorticity levels.
[in]	pv	real (kpv) potential vorticity levels (10*-6Km*2/kg/s).
[in]	pvpt	real (kpv) top pressures for PV search (Pa).
[in]	pvpb	real (kpv) bottom pressures for PV search (Pa).
[out]	lpv	logical*1 (kpv) bitmap.
[out]	upv	real (kpv) x-component wind (m/s).
[out]	vpv	real (kpv) y-component wind (m/s).
[out]	hpv	real (kpv) temperature (K).
[out]	tpv	real (kpv) temperature (K).
[out]	ppv	real (kpv) pressure (Pa).
[out]	spv	real (kpv) wind speed shear (1/s).

Program History Log

Date	Programmer	Comments
1999-10-18	Mark Iredell	Initial
2021-08-31	Hui-ya Chuang	Increase depth criteria for identifying PV layer from 25 to 50 to avoid finding shallow high level PV layer in high latitudes

Author: Mark Iredell np23

Date: 1999-10-18

Definition at line 203 of file GFSPOST.F.

References rsearch1().

Referenced by mdl2thandpv().

◆ p2th()

subroutine p2th	(	integer, intent(in)	km,
		real, dimension(km), intent(in)	theta,
		real, dimension(km), intent(in)	u,
		real, dimension(km), intent(in)	v,
		real, dimension(km), intent(in)	h,
		real, dimension(km), intent(in)	t,
		real, dimension(km), intent(in)	pvu,
		real, dimension(km), intent(in)	sigma,
		real, dimension(km), intent(in)	rh,
		real, dimension(km), intent(in)	omga,
		integer, intent(in)	kth,
		real, dimension(kth), intent(in)	th,
		logical*1, dimension(kth), intent(out)	lth,
		real, dimension(kth), intent(out)	uth,
		real, dimension(kth), intent(out)	vth,
		real, dimension(kth), intent(out)	hth,
		real, dimension(kth), intent(out)	tth,
		real, dimension(kth), intent(out)	zth,
		real, dimension(kth), intent(out)	sigmath,
		real, dimension(kth), intent(out)	rhth,
		real, dimension(kth), intent(out)	oth
	)

p2th() interpolates from pressure level to isentropic (theta) level.

This subprogram interpolates fields to given isentropic levels. The interpolation is linear in entropy. Outside the domain the bitmap is set to false.

Parameters

[in]	km	integer number of levels.
[in]	theta	real (km) potential temperature (K).
[in]	u	real (km) x-component wind (m/s).
[in]	v	real (km) y-component wind (m/s).
[in]	h	real (km) height (m).
[in]	t	real (km) temperature (K).
[in]	pvu	real (km) potential vorticity in PV units (10*-6Km*2/kg/s).
[in]	sigma	real (km) static stability (K/m).
[in]	rh	real (km) relative humidity.
[in]	omga	real (km) vertical velocity in pressure coordinates (Pa/s).
[in]	kth	integer number of isentropic levels.
[in]	th	real (kth) isentropic levels (K).
[in]	lth	logical*1 (kth) bitmap.
[out]	uth	real (kth) x-component wind (m/s).
[out]	vth	real (kth) y-component wind (m/s).
[out]	hth	real (kth) height (m).
[out]	tth	real (kth) temperature (K).
[out]	zth	real (kth) potential vorticity in PV units (10*-6Km*2/kg/s).
[out]	sigmath	(kth) real static stability (K/m).
[out]	rhth	(kth) real relative humidity.
[out]	oth	(kth) real vertical velocity in pressure coordinates (Pa/s).

Program History Log

Date	Programmer	Comments
1999-10-18	Mark Iredell	Initial

Author: Mark Iredell np23

Date: 1999-10-18

Definition at line 137 of file GFSPOST.F.

References rsearch1().

Referenced by mdl2thandpv().

◆ pvetc()

subroutine pvetc	(	integer, intent(in)	km,
		real, dimension(km), intent(in)	p,
		real, dimension(km), intent(in)	px,
		real, dimension(km), intent(in)	py,
		real, dimension(km), intent(in)	t,
		real, dimension(km), intent(in)	tx,
		real, dimension(km), intent(in)	ty,
		real, dimension(km), intent(in)	h,
		real, dimension(km), intent(in)	u,
		real, dimension(km), intent(in)	v,
		real, dimension(km), intent(in)	av,
		real, dimension(km), intent(out)	hm,
		real, dimension(km), intent(out)	s,
		real, dimension(km), intent(out)	bvf2,
		real, dimension(km), intent(out)	pvn,
		real, dimension(km), intent(out)	theta,
		real, dimension(km), intent(out)	sigma,
		real, dimension(km), intent(out)	pvu
	)

pvetc() computes potential vorticity, etc.

Parameters

[in]	km	integer number of levels.
[in]	p	real (km) pressure (Pa).
[in]	px	real (km) pressure x-gradient (Pa/m).
[in]	py	real (km) pressure y-gradient (Pa/m).
[in]	t	real (km) (virtual) temperature (K).
[in]	tx	real (km) (virtual) temperature x-gradient (K/m).
[in]	ty	real (km) (virtual) temperature y-gradient (K/m).
[in]	h	real (km) height (m).
[in]	u	real (km) x-component wind (m/s).
[in]	v	real (km) y-component wind (m/s).
[in]	av	real (km) absolute vorticity (1/s).
[out]	hm	real (km) Montgomery streamfunction (m2/s2).
[out]	s	real (km) specific entropy (J/K/kg).
[out]	bvf2	real (km) Brunt-Vaisala frequency squared (1/s**2).
[out]	pvn	real (km) potential vorticity (m**2/kg/s).
[out]	theta	real (km) (virtual) potential temperature (K).
[out]	sigma	real (km) static stability (K/m).
[out]	pvu	real (km) potential vorticity (10*-6Km*2/kg/s).

Definition at line 62 of file GFSPOST.F.

References rsearch1().

Referenced by mdl2thandpv().

◆ rsearch1()

subroutine rsearch1	(	integer, intent(in)	km1,
		real, dimension(km1), intent(in)	z1,
		integer, intent(in)	km2,
		real, dimension(km2), intent(in)	z2,
		integer, dimension(km2), intent(out)	l2
	)

rsearch1() searches for a surrounding real interval.

This subprogram searches a monotonic sequences of real numbers for intervals that surround a given search set of real numbers. the sequences may be monotonic in either direction; the real numbers may be single or double precision.

Parameters

[in]	km1	integer number of points in the sequence.
[in]	z1	real (km1) sequence values to search. (z1 must be monotonic in either direction)
[in]	km2	integer number of points to search for.
[in]	z2	real (km2) set of values to search for. (z2 need not be monotonic)
[out]	l2	integer (km2) interval locations from 0 to km1. (z2 will be between z1(l2) and z1(l2+1))

Note

Returned values of 0 or km1 indicate that the given search value is outside the range of the sequence.
If a search value is identical to one of the sequence values then the location returned points to the identical value.
If the sequence is not strictly monotonic and a search value is identical to more than one of the sequence values, then the location returned may point to any of the identical values.
If l2(k)=0, then z2(k) is less than the start point z1(1) for ascending sequences (or greater than for descending sequences).
If l2(k)=km1, then z2(k) is greater than or equal to the end point z1(km1) for ascending sequences (or less than or equal to for descending sequences). Otherwise z2(k) is between the values z1(l2(k)) and z1(l2(k+1)) and may equal the former.

Program History Log

Date	Programmer	Comments
1998-05-01	Mark Iredell	Initial

Author: Mark Iredell w/nmc23

Date: 1998-05-01

Definition at line 297 of file GFSPOST.F.

Referenced by mxwind(), p2pv(), p2th(), pvetc(), and tpause().

◆ tpause()

subroutine tpause	(	integer, intent(in)	km,
		real, dimension(km), intent(in)	p,
		real, dimension(km), intent(in)	u,
		real, dimension(km), intent(in)	v,
		real, dimension(km), intent(in)	t,
		real, dimension(km), intent(in)	h,
		real, intent(out)	ptp,
		real, intent(out)	utp,
		real, intent(out)	vtp,
		real, intent(out)	ttp,
		real, intent(out)	htp,
		real, intent(out)	shrtp
	)

tpause() computes tropopause level fields.

This subprogram finds the tropopause level and computes fields at the tropopause level. The tropopause is defined as the lowest level above 500 mb which has a temperature lapse rate of less than 2 K/km. The lapse rate must average less than 2 K/km over a 2 km depth. If no such level is found below 50 mb, the tropopause is set to 50 mb. The tropopause fields are interpolated linearly in lapse rate. The tropopause pressure is found hydrostatically. The tropopause wind shear is computed as the partial derivative of wind speed with respect to height at the tropopause level.

Parameters

[in]	km	integer number of levels.
[in]	p	real (km) pressure (Pa).
[in]	u	real (km) x-component wind (m/s).
[in]	v	real (km) y-component wind (m/s).
[in]	t	real (km) temperature (K).
[in]	h	real (km) height (m).
[out]	ptp	real tropopause pressure (Pa).
[out]	utp	real tropopause x-component wind (m/s).
[out]	vtp	real tropopause y-component wind (m/s).
[out]	ttp	real tropopause temperature (K).
[out]	htp	real tropopause height (m).
[out]	shrtp	real tropopause wind shear (1/s).

Program History Log

Date	Programmer	Comments
1999-10-18	Mark Iredell	Initial

Author: Mark Iredell np23

Date: 1999-10-18

Definition at line 372 of file GFSPOST.F.

References rsearch1().

Referenced by miscln().

Functions/Subroutines

Detailed Description

Program History Log

Function/Subroutine Documentation

◆ mptgen()

Program History Log

◆ mptranr4()

Program History Log

◆ mxwind()

Program History Log

◆ p2pv()

Program History Log

◆ p2th()

Program History Log

◆ pvetc()

◆ rsearch1()

Program History Log

◆ tpause()

Program History Log