w3sic1md Module Reference

Calculate ice source term S_{ice} according to simple methods. More...

Functions/Subroutines
subroutine, public	w3sic1 (A, DEPTH, CG, IX, IY, S, D)
	S_{ice} source term using 5 parameters read from input files. More...

Detailed Description

Calculate ice source term S_{ice} according to simple methods.

Author

E. Rogers

S. Zieger

Date

11-Oct-2013

Copyright

Copyright 2009-2022 National Weather Service (NWS), National Oceanic and Atmospheric Administration. All rights reserved. WAVEWATCH III is a trademark of the NWS. No unauthorized use without permission.

Function/Subroutine Documentation

w3sic1()

subroutine, public w3sic1md::w3sic1	(	real, dimension(nspec), intent(in)	A,
		real, intent(in)	DEPTH,
		real, dimension(nk), intent(in)	CG,
		integer, intent(in)	IX,
		integer, intent(in)	IY,
		real, dimension(nspec), intent(out)	S,
		real, dimension(nspec), intent(out)	D
	)

S_{ice} source term using 5 parameters read from input files.

Parameters

[in]	A	Action density spectrum (1-D).
[in]	DEPTH	Local water depth.
[in]	CG	Group velocities.
[in]	IX	Grid index.
[in]	IY	Grid index.
[out]	S	Source term (1-D version).
[out]	D	Diagonal term of derivative (1-D version).

Author

E. Rogers

S. Zieger

Date

11-Oct-2013

Definition at line 94 of file w3sic1md.F90.

    !/
    !/                  +-----------------------------------+
    !/                  | WAVEWATCH III           NOAA/NCEP |
    !/                  |           E. Rogers               |
    !/                  |           S. Zieger               |
    !/                  |                        FORTRAN 90 |
    !/                  | Last update :         11-Oct-2013 |
    !/                  +-----------------------------------+
    !/
    !/    16-Oct-2012 : Origination.                        ( version 4.04 )
    !/                                                        (E. Rogers)
    !/    09-Oct-2013 : W3SIC1 SUBTYPE=2 outsourced to W3SIC2 (S. Zieger)
    !/
    !/        FIXME   : Move field input to W3SRCE and provide
    !/     (S.Zieger)   input parameter to W3SIC1 to make the subroutine
    !/                : versatile for point output processors ww3_outp
    !/                  and ww3_ounp.
    !/
    !/    Copyright 2009 National Weather Service (NWS),
    !/       National Oceanic and Atmospheric Administration.  All rights
    !/       reserved.  WAVEWATCH III is a trademark of the NWS.
    !/       No unauthorized use without permission.
    !/
    !  1. Purpose :
    !
    !     S_{ice} source term using 5 parameters read from input files.
    !     These parameters are allowed to vary in space and time.
    !     The parameters control the exponential decay rate k_i
    !     Since there are 5 parameters, this permits description of
    !     dependence of k_i on frequency or wavenumber.
    !
    !/ ------------------------------------------------------------------- /
    !
    !  2. Method :
    !
    !     Regarding i/o (general to all Sice modules): S_{ice} source term
    !     is calculated using up to 5 parameters read from input files.
    !     These parameters are allowed to vary in space and time.
    !     The parameters control the exponential decay rate k_i
    !     Since there are 5 parameters, this permits description of
    !     dependence of k_i on frequency or wavenumber.
    !
    !     Sea ice affects the wavenumber k of wind-generated ocean waves.
    !     The ice-modified wavenumber can be expressed as a complex number
    !     k = k_r + i*k_i, with the real part k_r representing impact of
    !     the sea ice on the physical wavelength and propagation speeds,
    !     producing something analogous to shoaling and refraction by
    !     bathymetry, whereas the imaginary part of the complex
    !     wavenumber, k_i, is an exponential decay coefficient
    !     k_i(x,y,t,sigma) (depending on location, time and frequency,
    !     respectively), representing wave attenuation, and can be
    !     introduced in a wave model such as WW3 as S_ice/E=-2*Cg*k_i,
    !     where S_ice is one of several dissipation mechanisms, along
    !     with whitecapping, for example, S_ds=S_wc+S_ice+⋯. The k_r -
    !     modified by ice would enter the model via the C calculations
    !     on the left-hand side of the governing equation.The fundamentals
    !     are straightforward, e.g. Rogers and Holland (2009 and
    !     subsequent unpublished work) modified a similar model, SWAN
    !     (Booij et al. 1999) to include the effects of a viscous mud
    !     layer using the same approach (k = k_r + i*k_i) previously.
    !
    !     General approach is analogous to Rogers and Holland (2009)
    !         approach for mud.
    !     See text near their eq. 1 :
    !       k        = k_r  +  i * k_i
    !       eta(x,t) = Real( a * exp( i * ( k * x - sigma * t ) ) )
    !       a        = a0 * exp( -k_i * x )
    !       S / E    = -2 * Cg * k_i (see also Komen et al. (1994, pg. 170)
    !
    !     Following W3SBT1 as a guide, equation 1 of W3SBT1 says:
    !         S = D * E
    !     However, the code of W3SBT1 has
    !         S = D * A
    !     This leads me to believe that the calling routine is
    !         expecting "S/sigma" not "S"
    !     Thus we will use D = S/E = -2 * Cg * k_i
    !
    !     Notes regarding numerics:
    !     Experiments with constant k_i values suggest that :
    !       for dx=20.0 km, k_i should not exceed 3.5e-6
    !      (assumes 2.7% Hs error in my particular test case is intolerable)
    !       for dx=5.0 km,  k_i should not exceed 2.0e-5
    !       for dx=2.5 km,  k_i should not exceed 5.0e-5
    !       for dx=1.0 km,  k_i should not exceed 2.0e-4
    !       for dx=0.35 km, error is less than 2.1% for all k_i tested
    !       for dx=0.10 km, error is less than 1.3% for all k_i tested
    !     "Ground truth" used for this is an exponential decay profile.
    !
    !      For reference, ACNFS is 1/12th deg, so delta_latitude=9.25 km.
    !
    !     {put more equations here}
    !
    !  3. Parameters :
    !
    !     Parameter list
    !     ----------------------------------------------------------------
    !       A       R.A.  I   Action density spectrum (1-D)
    !       DEPTH   Real  I   Local water depth
    !       CG      R.A.  I   Group velocities.
    !       IX,IY   I.S.  I   Grid indices.
    !       S       R.A.  O   Source term (1-D version).
    !       D       R.A.  O   Diagonal term of derivative (1-D version).
    !     ----------------------------------------------------------------
    !
    !  4. Subroutines used :
    !
    !      Name      Type  Module   Description
    !     ----------------------------------------------------------------
    !      STRACE    Subr. W3SERVMD Subroutine tracing (!/S switch).
    !      PRT2DS    Subr. W3ARRYMD Print plot output (!/T1 switch).
    !      OUTMAT    Subr. W3ARRYMD Matrix output (!/T2 switch).
    !     ----------------------------------------------------------------
    !
    !  5. Called by :
    !
    !      Name      Type  Module   Description
    !     ----------------------------------------------------------------
    !      W3SRCE    Subr. W3SRCEMD Source term integration.
    !      W3EXPO    Subr.   N/A    ASCII Point output post-processor.
    !      W3EXNC    Subr.   N/A    NetCDF Point output post-processor.
    !      GXEXPO    Subr.   N/A    GrADS point output post-processor.
    !     ----------------------------------------------------------------
    !
    !  6. Error messages :
    !
    !     None.
    !
    !  7. Remarks :
    !
    !     If ice parameter 1 is zero, no calculations are made.
    !
    !  8. Structure :
    !
    !     See source code.
    !
    !  9. Switches :
    !
    !     !/S  Enable subroutine tracing.
    !     !/T   Enable general test output.
    !     !/T0  2-D print plot of source term.
    !     !/T1  Print arrays.
    !
    ! 10. Source code :
    !
    !/ ------------------------------------------------------------------- /
    USE constants, ONLY: tpi
    USE w3odatmd, ONLY: ndse
    USE w3servmd, ONLY: extcde
    USE w3gdatmd, ONLY: nk, nth, nspec, sig, mapwn
    USE w3idatmd, ONLY: icep1, icep2, icep3, icep4, icep5, inflags2
#ifdef W3_T
    USE w3odatmd, ONLY: ndst
#endif
#ifdef W3_S
    USE w3servmd, ONLY: strace
#endif
#ifdef W3_T0
    USE w3arrymd, ONLY: prt2ds
#endif
#ifdef W3_T1
    USE w3arrymd, ONLY: outmat
#endif
    !
    IMPLICIT NONE
    !/
    !/ ------------------------------------------------------------------- /
    !/ Parameter list
    REAL, INTENT(IN)        :: CG(NK),   A(NSPEC), DEPTH
    REAL, INTENT(OUT)       :: S(NSPEC), D(NSPEC)
    INTEGER, INTENT(IN)     :: IX, IY
    !/
    !/ ------------------------------------------------------------------- /
    !/ Local parameters
    !/
#ifdef W3_S
    INTEGER, SAVE           :: IENT = 0
#endif
#ifdef W3_T0
    INTEGER                 :: ITH
    REAL                    :: DOUT(NK,NTH)
#endif
    INTEGER                 :: IKTH, IK
    REAL                    :: D1D(NK) !In SBT1: D1D was named "CBETA"
    REAL                    :: ICECOEF1, ICECOEF2, ICECOEF3, &
         ICECOEF4, ICECOEF5
    REAL, ALLOCATABLE       :: WN_I(:)  ! exponential decay rate for amplitude
    !/
    !/ ------------------------------------------------------------------- /
    !/
#ifdef W3_S
    CALL strace (ient, 'W3SIC1')
#endif
    !
    ! 0.  Initializations ------------------------------------------------ *
    !
    d        = 0.0
    !
    ALLOCATE(wn_i(nk))
    wn_i     = 0.0
    icecoef1 = 0.0
    icecoef2 = 0.0
    icecoef3 = 0.0
    icecoef4 = 0.0
    icecoef5 = 0.0
    !
    IF (.NOT.inflags2(-7))THEN
      WRITE (ndse,1001) 'ICE PARAMETER 1'
      CALL extcde(2)
    ENDIF
    !
    icecoef1 = icep1(ix,iy)
 
    !
    ! 1.  No ice --------------------------------------------------------- /
    !
    IF ( icecoef1==0. ) THEN
      d = 0.
      !
      ! 2.  Ice ------------------------------------------------------------ /
    ELSE
      !
      ! 2.a Set constant(s) and write test output -------------------------- /
      !
      !         (none)
      !
#ifdef W3_T38
      WRITE (ndst,9000) depth,icecoef1,icecoef2,icecoef3,icecoef4
#endif
      !
      ! 2.b Make calculations ---------------------------------------------- /
      wn_i = icecoef1 ! uniform in k
 
      DO ik=1, nk
        !   SBT1 has: D1D(IK) = FACTOR *  MAX(0., (CG(IK)*WN(IK)/SIG(IK)-0.5) )
        !             recall that D=S/E=-2*Cg*k_i
        d1d(ik) = -2. * cg(ik) * wn_i(ik)
      END DO
      !
      ! 2.c Fill diagional matrix
      !
      DO ikth=1, nspec
        d(ikth) = d1d(mapwn(ikth))
      END DO
      !
    END IF
    !
    s = d * a
    !
    ! ... Test output of arrays
    !
#ifdef W3_T0
    DO ik=1, nk
      DO ith=1, nth
        dout(ik,ith) = d(ith+(ik-1)*nth)
      END DO
    END DO
    CALL prt2ds (ndst, nk, nk, nth, dout, sig(1:), '  ', 1.,    &
         0.0, 0.001, 'Diag Sice', ' ', 'NONAME')
#endif
    !
#ifdef W3_T1
    CALL outmat (ndst, d, nth, nth, nk, 'diag Sice')
#endif
    !
    ! Formats
    !
1001 FORMAT (/' *** WAVEWATCH III ERROR IN W3SIC1 : '/               &
         '     ',a,' REQUIRED BUT NOT SELECTED'/)
    !
#ifdef W3_T
9000 FORMAT (' TEST W3SIC1 : DEPTH,ICECOEF1  : ',2e10.3)
#endif
    !/
    !/ End of W3SIC1 ----------------------------------------------------- /
    !/

References w3servmd::extcde(), w3idatmd::inflags2, w3gdatmd::mapwn, w3odatmd::ndse, w3odatmd::ndst, w3gdatmd::nk, w3gdatmd::nspec, w3gdatmd::nth, w3arrymd::outmat(), w3arrymd::prt2ds(), w3gdatmd::sig, w3servmd::strace(), and constants::tpi.

Referenced by gxexpo(), and w3srcemd::w3srce().