diffusion_mod

link to source code

Dependency Diagrams:

Direct Dependency Diagram

Reverse Dependency Diagram

Description

MODULE diffusion_mod (prefix=’diff’ category=’4. Data Object transformations’)

Purpose

Diffusion operator and storage of related diffusion configuration used to model background-error horizontal correlations. Both explicit and implicit formulations are included, with implicit being preferred when using large correlation length scales relative to the grid spacing. For implicit the MPI topology must have npex=1, i.e. 1xNPEYxNUMTHREADS. A 2D MPI topology can be used for the explicit formulation.

Reference

Weaver, A. T., and P. Courtier, 2001: Correlation modelling on the sphere using a generalized diffusion equation. Q. J. R. Meteorol. Soc., 127, 1815-1846.

Basic equations

• Lcorr^2 = 2*k*dt*numt (1)

• stab = k*dt/dx^2 (2)

Quick access

Types

struct_diff

Routines

diff_csqrt(), diff_csqrtadj(), diff_finalize(), diff_setup(), diffusion1x_implicit(), diffusion1y_implicit(), diffusion_explicit(), transposelattolonbands(), transposelontolatbands()

Needed modules

• midasmpi_mod: MODULE midasMpi_mod (prefix=’mmpi’ category=’8. Low-level utilities and constants’)

• horizontalcoord_mod: MODULE horizontalCoord_mod (prefix=’hco’ category=’7. Low-level data objects’)

• verticalcoord_mod: MODULE verticalCoord_mod (prefix=’vco’ category=’7. Low-level data objects’)

• oceanmask_mod: MODULE oceanMask_mod (prefix=’ocm’ category=’7. Low-level data objects’)

• earthconstants_mod: MODULE earthConstants_mod (prefix=’ec’ category=’8. Low-level utilities and constants’)

• randomnumber_mod: MODULE randomNumber_mod (prefix=’rng’ category=’8. Low-level utilities and constants’)

• utilities_mod: MODULE utilities_mod (prefix=’utl’ category=’8. Low-level utilities and constants’)

• gridstatevector_mod: MODULE gridStateVector_mod (prefix=’gsv’ category=’6. High-level data objects’)

• gridstatevectorfileio_mod: MODULE gridStateVectorFileIO_mod (prefix=’gio’ category=’4. Data Object transformations’)

Types

• type  diffusion_mod/struct_diff

  number of grid points in x and y directions (includes perimeter of land points)

  Type fields

  • % cosyhalf (*) [real ,allocatable]

  • % cosyinv (*) [real ,allocatable]

  • % cosyinvsq (*) [real ,allocatable]

  • % diff1x_ap (*,*) [real ,allocatable]

  • % diff1x_bp_inv (*,*) [real ,allocatable]

  • % diff1x_c (*,*) [real ,allocatable]

  • % diff1y_ap (*,*) [real ,allocatable]

  • % diff1y_bp_inv (*,*) [real ,allocatable]

  • % diff1y_c (*,*) [real ,allocatable]

  • % dlat [real ] :: grid spacing in radians

  • % dlon [real ]

  • % dt [real ]

  • % khalfx (*,*) [real ,allocatable]

  • % khalfy (*,*) [real ,allocatable]

  • % lambda (*,*) [real ,allocatable]

  • % latindexignore [integer ]

  • % latperpe [integer ]

  • % latperpemax [integer ]

  • % lonperpe [integer ]

  • % lonperpe_transpose [integer ]

  • % lonperpemax [integer ]

  • % lonperpemax_transpose [integer ]

  • % mhalfx (*,*) [real ,allocatable]

  • % mhalfy (*,*) [real ,allocatable]

  • % mylatbeg [integer ]

  • % mylatend [integer ]

  • % mylonbeg [integer ]

  • % mylonbeg_transpose [integer ]

  • % mylonend [integer ]

  • % mylonend_transpose [integer ]

  • % ni [integer ]

  • % nj [integer ]

  • % numiterimp [integer ]

  • % numt [integer ]

  • % useimplicit [logical ]

  • % winv (*,*) [real ,allocatable]

  • % winvsqrt (*,*) [real ,allocatable]

  • % wsqrt (*,*) [real ,allocatable]

Variables

Subroutines and functions

function  diffusion_mod/diff_setup(variableindex, bdiff_varnamelist, hco, vco, corr_len, stab, numbersamples, useimplicit, latindexignore)

Purpose

set up diffusion operator

Arguments

• variableindex [integer ,in] :: Variable index in bdiff_varNameList(:)

• bdiff_varnamelist (*) [character ,in] :: list of 2D analysis variables

• hco [struct_hco ,in,pointer] :: Horizontal grid structure

• vco [struct_vco ,in,pointer] :: Vertical grid structure

• corr_len [real ,in] :: Horizontal corr. length scale (km); if -1, read 2D field from file

• stab [real ,in] :: Stability criteria (definitely < 0.5)

• numbersamples [integer ,in] :: Number of samples to estimate normalization factors by randomization

• useimplicit [logical ,in] :: Indicate to use the implicit formulation

• latindexignore [integer ,in] :: Number of grid points to ignore near poles

Return

diff_setup [integer ]

Called from

bdiff_setup()

Call to

utl_abort(), mmpi_setup_latbands(), mmpi_setup_lonbands(), ocm_readmaskfromfile(), ocm_deallocate(), gsv_allocate(), gsv_zero(), gio_readfromfile(), gsv_deallocate(), utl_fstlir_r4(), rng_setup(), rng_gaussian(), diffusion1x_implicit(), transposelattolonbands(), diffusion1y_implicit(), transposelontolatbands(), diffusion_explicit()

subroutine  diffusion_mod/diff_finalize(diffid)

Purpose

To finalize the diffusion operator module, and to free up memory.

Arguments

diffid [integer ,in]

subroutine  diffusion_mod/diffusion_explicit(diffid, xin, xout)

Purpose

To compute Lsqrt*xin (diffusion over numt/2 timesteps), and to specify initial conditions

Arguments

• diffid [integer ,in]

• xin (*,*) [real ,in]

• xout (*,*) [real ,out]

Called from

diff_setup(), diff_csqrt(), diff_csqrtadj()

subroutine  diffusion_mod/diff_csqrt(diffid, xin, xout)

Arguments

• diffid [integer ,in]

• xin (diff(diffid)%mylonend-(diff(diffid)%mylonbeg)+1,diff(diffid)%mylatend-(diff(diffid)%mylatbeg)+1) [real ,in]

• xout (diff(diffid)%mylonend-(diff(diffid)%mylonbeg)+1,diff(diffid)%mylatend-(diff(diffid)%mylatbeg)+1) [real ,out]

Called from

bdiff_bsqrt()

Call to

diffusion1x_implicit(), transposelattolonbands(), diffusion1y_implicit(), transposelontolatbands(), diffusion_explicit()

subroutine  diffusion_mod/diff_csqrtadj(diffid, xin, xout)

Arguments

• diffid [integer ,in]

• xin (diff(diffid)%mylonend-(diff(diffid)%mylonbeg)+1,diff(diffid)%mylatend-(diff(diffid)%mylatbeg)+1) [real ,in]

• xout (diff(diffid)%mylonend-(diff(diffid)%mylonbeg)+1,diff(diffid)%mylatend-(diff(diffid)%mylatbeg)+1) [real ,out]

Called from

bdiff_bsqrtad()

Call to

transposelattolonbands(), diffusion1y_implicit(), transposelontolatbands(), diffusion1x_implicit(), diffusion_explicit()

subroutine  diffusion_mod/transposelattolonbands(diffid, xin, xout)

Purpose

Perform an MPI transposition for a 2D array between latitude bands and longitude bands.

Arguments

• diffid [integer ,in]

• xin (diff(diffid)%ni,diff(diffid)%mylatend-(diff(diffid)%mylatbeg)+1) [real ,in]

• xout (diff(diffid)%mylonend_transpose-(diff(diffid)%mylonbeg_transpose)+1,diff(diffid)%nj) [real ,out]

Called from

diff_setup(), diff_csqrt(), diff_csqrtadj()

subroutine  diffusion_mod/transposelontolatbands(diffid, xin, xout)

Purpose

Perform an MPI transposition for a 2D array between longitude bands and latitude bands.

Arguments

• diffid [integer ,in]

• xin (diff(diffid)%mylonend_transpose-(diff(diffid)%mylonbeg_transpose)+1,diff(diffid)%nj) [real ,in]

• xout (diff(diffid)%ni,diff(diffid)%mylatend-(diff(diffid)%mylatbeg)+1) [real ,out]

Called from

diff_setup(), diff_csqrt(), diff_csqrtadj()

subroutine  diffusion_mod/diffusion1x_implicit(diffid, xin, xout)

Purpose

To compute Lsqrt*xin (diffusion over 1 timestep, loop over timesteps is external to the subroutine).

Arguments

• diffid [integer ,in]

• xin (diff(diffid)%ni,diff(diffid)%mylatend-(diff(diffid)%mylatbeg)+1) [real ,in]

• xout (diff(diffid)%ni,diff(diffid)%mylatend-(diff(diffid)%mylatbeg)+1) [real ,out]

Called from

diff_setup(), diff_csqrt(), diff_csqrtadj()

subroutine  diffusion_mod/diffusion1y_implicit(diffid, xin, xout)

Purpose

To compute Lsqrt*xin (diffusion over 1 timestep, loop over timesteps is external to the subroutine).

Arguments

• diffid [integer ,in]

• xin (diff(diffid)%mylonend_transpose-(diff(diffid)%mylonbeg_transpose)+1,diff(diffid)%nj) [real ,in]

• xout (diff(diffid)%mylonend_transpose-(diff(diffid)%mylonbeg_transpose)+1,diff(diffid)%nj) [real ,out]

Called from

diff_setup(), diff_csqrt(), diff_csqrtadj()