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dimitri |
1.7 |
c $Header: /u/gcmpack/MITgcm/pkg/exf/exf_bulkformulae.F,v 1.6 2004/07/02 00:48:23 heimbach Exp $ |
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heimbach |
1.2 |
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edhill |
1.4 |
#include "EXF_OPTIONS.h" |
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heimbach |
1.2 |
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subroutine exf_bulkformulae(mycurrenttime, mycurrentiter, mythid) |
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c ================================================================== |
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c SUBROUTINE exf_bulkformulae |
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c ================================================================== |
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c |
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c o Read-in atmospheric state and/or surface fluxes from files. |
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c |
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c o Use bulk formulae to estimate turbulent and/or radiative |
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c fluxes at the surface. |
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c |
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c NOTES: |
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c ====== |
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c |
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edhill |
1.4 |
c See EXF_OPTIONS.h for a description of the various possible |
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heimbach |
1.2 |
c ocean-model forcing configurations. |
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c |
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c The bulk formulae of pkg/exf are not valid for sea-ice covered |
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c oceans but they can be used in combination with a sea-ice model, |
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c for example, pkg/seaice, to specify open water flux contributions. |
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c |
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c ================================================================== |
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c |
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c The calculation of the bulk surface fluxes has been adapted from |
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c the NCOM model which uses the formulae given in Large and Pond |
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c (1981 & 1982 ) |
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c |
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c |
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c Header taken from NCOM version: ncom1.4.1 |
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c ----------------------------------------- |
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c |
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c Following procedures and coefficients in Large and Pond |
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c (1981 ; 1982) |
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c |
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c Output: Bulk estimates of the turbulent surface fluxes. |
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c ------- |
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c |
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c hs - sensible heat flux (W/m^2), into ocean |
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c hl - latent heat flux (W/m^2), into ocean |
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c |
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c Input: |
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c ------ |
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c |
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c us - mean wind speed (m/s) at height hu (m) |
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c th - mean air temperature (K) at height ht (m) |
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c qh - mean air humidity (kg/kg) at height hq (m) |
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c sst - sea surface temperature (K) |
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c tk0 - Kelvin temperature at 0 Celsius (K) |
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c |
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c Assume 1) a neutral 10m drag coefficient = |
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c |
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c cdn = .0027/u10 + .000142 + .0000764 u10 |
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c |
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c 2) a neutral 10m stanton number = |
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c |
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c ctn = .0327 sqrt(cdn), unstable |
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c ctn = .0180 sqrt(cdn), stable |
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c |
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c 3) a neutral 10m dalton number = |
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c |
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c cen = .0346 sqrt(cdn) |
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c |
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c 4) the saturation humidity of air at |
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c |
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c t(k) = exf_BulkqSat(t) (kg/m^3) |
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c |
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c Note: 1) here, tstar = <wt>/u*, and qstar = <wq>/u*. |
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c 2) wind speeds should all be above a minimum speed, |
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c say 0.5 m/s. |
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c 3) with optional iteration loop, niter=3, should suffice. |
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c 4) this version is for analyses inputs with hu = 10m and |
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c ht = hq. |
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c 5) sst enters in Celsius. |
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c |
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c ================================================================== |
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c |
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c started: Christian Eckert eckert@mit.edu 27-Aug-1999 |
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c |
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c changed: Christian Eckert eckert@mit.edu 14-Jan-2000 |
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c - restructured the original version in order to have a |
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c better interface to the MITgcmUV. |
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c |
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c Christian Eckert eckert@mit.edu 12-Feb-2000 |
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c - Changed Routine names (package prefix: exf_) |
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c |
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c Patrick Heimbach, heimbach@mit.edu 04-May-2000 |
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c - changed the handling of precip and sflux with respect |
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c to CPP options ALLOW_BULKFORMULAE and ALLOW_ATM_TEMP |
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c - included some CPP flags ALLOW_BULKFORMULAE to make |
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c sure ALLOW_ATM_TEMP, ALLOW_ATM_WIND are used only in |
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c conjunction with defined ALLOW_BULKFORMULAE |
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c - statement functions discarded |
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c |
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c Ralf.Giering@FastOpt.de 25-Mai-2000 |
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c - total rewrite using new subroutines |
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c |
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c Detlef Stammer: include river run-off. Nov. 21, 2001 |
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c |
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c heimbach@mit.edu, 10-Jan-2002 |
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c - changes to enable field swapping |
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c |
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c mods for pkg/seaice: menemenlis@jpl.nasa.gov 20-Dec-2002 |
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c |
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c ================================================================== |
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c SUBROUTINE exf_bulkformulae |
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c ================================================================== |
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implicit none |
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c == global variables == |
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#include "EEPARAMS.h" |
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#include "SIZE.h" |
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#include "PARAMS.h" |
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#include "DYNVARS.h" |
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#include "GRID.h" |
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#include "exf_param.h" |
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#include "exf_fields.h" |
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#include "exf_constants.h" |
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#ifdef ALLOW_AUTODIFF_TAMC |
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#include "tamc.h" |
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#endif |
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c == routine arguments == |
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integer mythid |
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integer mycurrentiter |
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_RL mycurrenttime |
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heimbach |
1.3 |
#ifdef ALLOW_BULKFORMULAE |
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heimbach |
1.2 |
c == local variables == |
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integer bi,bj |
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integer i,j,k |
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_RL aln |
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#ifdef ALLOW_ATM_TEMP |
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integer iter |
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_RL delq |
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_RL deltap |
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_RL hqol |
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_RL htol |
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_RL huol |
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_RL psimh |
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_RL psixh |
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_RL qstar |
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_RL rd |
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_RL re |
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_RL rdn |
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_RL rh |
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_RL ssttmp |
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_RL ssq |
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_RL stable |
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_RL tstar |
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_RL t0 |
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_RL ustar |
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_RL uzn |
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_RL shn |
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_RL xsq |
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_RL x |
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_RL tau |
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#ifdef ALLOW_AUTODIFF_TAMC |
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integer ikey_1 |
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integer ikey_2 |
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#endif |
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#endif /* ALLOW_ATM_TEMP */ |
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_RL ustmp |
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_RL us |
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_RL cw |
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_RL sw |
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_RL sh |
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_RL hs(1-olx:snx+olx,1-oly:sny+oly,nsx,nsy) |
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_RL hl(1-olx:snx+olx,1-oly:sny+oly,nsx,nsy) |
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_RL hfl |
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heimbach |
1.6 |
_RL tmpbulk |
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heimbach |
1.2 |
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c == external functions == |
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integer ilnblnk |
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external ilnblnk |
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_RL exf_BulkqSat |
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external exf_BulkqSat |
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_RL exf_BulkCdn |
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external exf_BulkCdn |
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_RL exf_BulkRhn |
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external exf_BulkRhn |
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#ifndef ALLOW_ATM_WIND |
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_RL TMP1 |
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_RL TMP2 |
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_RL TMP3 |
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_RL TMP4 |
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_RL TMP5 |
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#endif |
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c == end of interface == |
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cph This statement cannot be a PARAMETER statement in the header, |
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cph but must come here; it's not fortran77 standard |
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aln = log(ht/zref) |
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c-- Use atmospheric state to compute surface fluxes. |
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c Loop over tiles. |
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#ifdef ALLOW_AUTODIFF_TAMC |
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C-- HPF directive to help TAMC |
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CHPF$ INDEPENDENT |
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#endif |
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do bj = mybylo(mythid),mybyhi(mythid) |
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#ifdef ALLOW_AUTODIFF_TAMC |
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C-- HPF directive to help TAMC |
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CHPF$ INDEPENDENT |
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#endif |
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do bi = mybxlo(mythid),mybxhi(mythid) |
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k = 1 |
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do j = 1,sny |
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do i = 1,snx |
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#ifdef ALLOW_AUTODIFF_TAMC |
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act1 = bi - myBxLo(myThid) |
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max1 = myBxHi(myThid) - myBxLo(myThid) + 1 |
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act2 = bj - myByLo(myThid) |
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max2 = myByHi(myThid) - myByLo(myThid) + 1 |
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act3 = myThid - 1 |
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max3 = nTx*nTy |
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act4 = ikey_dynamics - 1 |
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ikey_1 = i |
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& + sNx*(j-1) |
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& + sNx*sNy*act1 |
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& + sNx*sNy*max1*act2 |
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& + sNx*sNy*max1*max2*act3 |
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& + sNx*sNy*max1*max2*max3*act4 |
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#endif |
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#ifdef ALLOW_DOWNWARD_RADIATION |
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c-- Compute net from downward and downward from net longwave and |
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c shortwave radiation, if needed. |
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c lwflux = Stefan-Boltzman constant * emissivity * SST - lwdown |
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c swflux = - ( 1 - albedo ) * swdown |
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#ifdef ALLOW_ATM_TEMP |
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if ( lwfluxfile .EQ. ' ' .AND. lwdownfile .NE. ' ' ) |
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& lwflux(i,j,bi,bj) = 5.5 _d -08 * |
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& ((theta(i,j,k,bi,bj)+cen2kel)**4) |
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& - lwdown(i,j,bi,bj) |
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if ( lwfluxfile .NE. ' ' .AND. lwdownfile .EQ. ' ' ) |
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& lwdown(i,j,bi,bj) = 5.5 _d -08 * |
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& ((theta(i,j,k,bi,bj)+cen2kel)**4) |
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& - lwflux(i,j,bi,bj) |
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#endif |
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#if defined(ALLOW_ATM_TEMP) || defined(SHORTWAVE_HEATING) |
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if ( swfluxfile .EQ. ' ' .AND. swdownfile .NE. ' ' ) |
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dimitri |
1.5 |
& swflux(i,j,bi,bj) = -(1.0-exf_albedo) * swdown(i,j,bi,bj) |
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heimbach |
1.2 |
if ( swfluxfile .NE. ' ' .AND. swdownfile .EQ. ' ' ) |
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dimitri |
1.5 |
& swdown(i,j,bi,bj) = -swflux(i,j,bi,bj) / (1.0-exf_albedo) |
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heimbach |
1.2 |
#endif |
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| 272 |
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#endif /* ALLOW_DOWNWARD_RADIATION */ |
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c-- Compute the turbulent surface fluxes. |
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#ifdef ALLOW_ATM_WIND |
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c Wind speed and direction. |
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ustmp = uwind(i,j,bi,bj)*uwind(i,j,bi,bj) + |
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& vwind(i,j,bi,bj)*vwind(i,j,bi,bj) |
| 280 |
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if ( ustmp .ne. 0. _d 0 ) then |
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us = sqrt(ustmp) |
| 282 |
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cw = uwind(i,j,bi,bj)/us |
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sw = vwind(i,j,bi,bj)/us |
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else |
| 285 |
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us = 0. _d 0 |
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cw = 0. _d 0 |
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sw = 0. _d 0 |
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endif |
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sh = max(us,umin) |
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#else /* ifndef ALLOW_ATM_WIND */ |
| 291 |
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#ifdef ALLOW_ATM_TEMP |
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c The variables us, sh and rdn have to be computed from |
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c given wind stresses inverting relationship for neutral |
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c drag coeff. cdn. |
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c The inversion is based on linear and quadratic form of |
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c cdn(umps); ustar can be directly computed from stress; |
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ustmp = ustress(i,j,bi,bj)*ustress(i,j,bi,bj) + |
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& vstress(i,j,bi,bj)*vstress(i,j,bi,bj) |
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if ( ustmp .ne. 0. _d 0 ) then |
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ustar = sqrt(ustmp/atmrho) |
| 303 |
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cw = ustress(i,j,bi,bj)/sqrt(ustmp) |
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sw = vstress(i,j,bi,bj)/sqrt(ustmp) |
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else |
| 306 |
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ustar = 0. _d 0 |
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cw = 0. _d 0 |
| 308 |
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sw = 0. _d 0 |
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endif |
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| 311 |
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if ( ustar .eq. 0. _d 0 ) then |
| 312 |
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us = 0. _d 0 |
| 313 |
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else if ( ustar .lt. ustofu11 ) then |
| 314 |
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tmp1 = -cquadrag_2/cquadrag_1/2 |
| 315 |
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tmp2 = sqrt(tmp1*tmp1 + ustar*ustar/cquadrag_1) |
| 316 |
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us = sqrt(tmp1 + tmp2) |
| 317 |
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else |
| 318 |
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tmp3 = clindrag_2/clindrag_1/3 |
| 319 |
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tmp4 = ustar*ustar/clindrag_1/2 - tmp3**3 |
| 320 |
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tmp5 = sqrt(ustar*ustar/clindrag_1* |
| 321 |
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& (ustar*ustar/clindrag_1/4 - tmp3**3)) |
| 322 |
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us = (tmp4 + tmp5)**(1/3) + |
| 323 |
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& tmp3**2 * (tmp4 + tmp5)**(-1/3) - tmp3 |
| 324 |
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endif |
| 325 |
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| 326 |
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if ( us .ne. 0 ) then |
| 327 |
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rdn = ustar/us |
| 328 |
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else |
| 329 |
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rdn = 0. _d 0 |
| 330 |
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end if |
| 331 |
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| 332 |
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sh = max(us,umin) |
| 333 |
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#endif /* ALLOW_ATM_TEMP */ |
| 334 |
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#endif /* ifndef ALLOW_ATM_WIND */ |
| 335 |
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| 336 |
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#ifdef ALLOW_ATM_TEMP |
| 337 |
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| 338 |
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c Initial guess: z/l=0.0; hu=ht=hq=z |
| 339 |
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c Iterations: converge on z/l and hence the fluxes. |
| 340 |
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c t0 : virtual temperature (K) |
| 341 |
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c ssq : sea surface humidity (kg/kg) |
| 342 |
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c deltap : potential temperature diff (K) |
| 343 |
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| 344 |
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if ( atemp(i,j,bi,bj) .ne. 0. _d 0 ) then |
| 345 |
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t0 = atemp(i,j,bi,bj)* |
| 346 |
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& (exf_one + humid_fac*aqh(i,j,bi,bj)) |
| 347 |
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ssttmp = theta(i,j,k,bi,bj) |
| 348 |
heimbach |
1.6 |
tmpbulk= exf_BulkqSat(ssttmp + cen2kel) |
| 349 |
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ssq = saltsat*tmpbulk/atmrho |
| 350 |
heimbach |
1.2 |
deltap = atemp(i,j,bi,bj) + gamma_blk*ht - |
| 351 |
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& ssttmp - cen2kel |
| 352 |
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delq = aqh(i,j,bi,bj) - ssq |
| 353 |
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stable = exf_half + sign(exf_half, deltap) |
| 354 |
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#ifdef ALLOW_AUTODIFF_TAMC |
| 355 |
|
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CADJ STORE sh = comlev1_exf_1, key = ikey_1 |
| 356 |
|
|
#endif |
| 357 |
heimbach |
1.6 |
tmpbulk= exf_BulkCdn(sh) |
| 358 |
|
|
rdn = sqrt(tmpbulk) |
| 359 |
heimbach |
1.2 |
ustar = rdn*sh |
| 360 |
heimbach |
1.6 |
tmpbulk= exf_BulkRhn(stable) |
| 361 |
|
|
tstar = tmpbulk*deltap |
| 362 |
heimbach |
1.2 |
qstar = cdalton*delq |
| 363 |
|
|
|
| 364 |
|
|
do iter = 1,niter_bulk |
| 365 |
|
|
|
| 366 |
|
|
#ifdef ALLOW_AUTODIFF_TAMC |
| 367 |
|
|
ikey_2 = iter |
| 368 |
|
|
& + niter_bulk*(i-1) |
| 369 |
heimbach |
1.6 |
& + niter_bulk*sNx*(j-1) |
| 370 |
|
|
& + niter_bulk*sNx*sNy*act1 |
| 371 |
|
|
& + niter_bulk*sNx*sNy*max1*act2 |
| 372 |
|
|
& + niter_bulk*sNx*sNy*max1*max2*act3 |
| 373 |
|
|
& + niter_bulk*sNx*sNy*max1*max2*max3*act4 |
| 374 |
heimbach |
1.2 |
|
| 375 |
|
|
CADJ STORE rdn = comlev1_exf_2, key = ikey_2 |
| 376 |
|
|
CADJ STORE ustar = comlev1_exf_2, key = ikey_2 |
| 377 |
|
|
CADJ STORE qstar = comlev1_exf_2, key = ikey_2 |
| 378 |
|
|
CADJ STORE tstar = comlev1_exf_2, key = ikey_2 |
| 379 |
|
|
CADJ STORE sh = comlev1_exf_2, key = ikey_2 |
| 380 |
|
|
CADJ STORE us = comlev1_exf_2, key = ikey_2 |
| 381 |
|
|
#endif |
| 382 |
|
|
|
| 383 |
|
|
huol = czol*(tstar/t0 + |
| 384 |
|
|
& qstar/(exf_one/humid_fac+aqh(i,j,bi,bj)))/ |
| 385 |
|
|
& ustar**2 |
| 386 |
|
|
huol = max(huol,zolmin) |
| 387 |
|
|
stable = exf_half + sign(exf_half, huol) |
| 388 |
|
|
htol = huol*ht/hu |
| 389 |
|
|
hqol = huol*hq/hu |
| 390 |
|
|
|
| 391 |
|
|
c Evaluate all stability functions assuming hq = ht. |
| 392 |
|
|
xsq = max(sqrt(abs(exf_one - 16.*huol)),exf_one) |
| 393 |
|
|
x = sqrt(xsq) |
| 394 |
|
|
psimh = -psim_fac*huol*stable + |
| 395 |
|
|
& (exf_one - stable)* |
| 396 |
|
|
& log((exf_one + x*(exf_two + x))* |
| 397 |
|
|
& (exf_one + xsq)/8.) - exf_two*atan(x) + |
| 398 |
|
|
& pi*exf_half |
| 399 |
|
|
xsq = max(sqrt(abs(exf_one - 16.*htol)),exf_one) |
| 400 |
|
|
psixh = -psim_fac*htol*stable + (exf_one - stable)* |
| 401 |
|
|
& exf_two*log((exf_one + xsq)/exf_two) |
| 402 |
|
|
|
| 403 |
|
|
c Shift wind speed using old coefficient |
| 404 |
|
|
ccc rd = rdn/(exf_one + rdn/karman* |
| 405 |
|
|
ccc & (log(hu/zref) - psimh) ) |
| 406 |
heimbach |
1.6 |
rd = rdn/(exf_one - rdn/karman*psimh ) |
| 407 |
|
|
shn = sh*rd/rdn |
| 408 |
|
|
uzn = max(shn, umin) |
| 409 |
heimbach |
1.2 |
|
| 410 |
|
|
c Update the transfer coefficients at 10 meters |
| 411 |
|
|
c and neutral stability. |
| 412 |
|
|
|
| 413 |
heimbach |
1.6 |
tmpbulk= exf_BulkCdn(uzn) |
| 414 |
|
|
rdn = sqrt(tmpbulk) |
| 415 |
heimbach |
1.2 |
|
| 416 |
|
|
c Shift all coefficients to the measurement height |
| 417 |
|
|
c and stability. |
| 418 |
|
|
c rd = rdn/(exf_one + rdn/karman*(log(hu/zref) - psimh)) |
| 419 |
heimbach |
1.6 |
rd = rdn/(exf_one - rdn/karman*psimh) |
| 420 |
|
|
tmpbulk= exf_BulkRhn(stable) |
| 421 |
|
|
rh = tmpbulk/( exf_one + |
| 422 |
|
|
& tmpbulk/karman*(aln - psixh) ) |
| 423 |
|
|
re = cdalton/( exf_one + |
| 424 |
|
|
& cdalton/karman*(aln - psixh) ) |
| 425 |
heimbach |
1.2 |
|
| 426 |
|
|
c Update ustar, tstar, qstar using updated, shifted |
| 427 |
|
|
c coefficients. |
| 428 |
heimbach |
1.6 |
ustar = rd*sh |
| 429 |
|
|
qstar = re*delq |
| 430 |
|
|
tstar = rh*deltap |
| 431 |
|
|
tau = atmrho*ustar**2 |
| 432 |
|
|
tau = tau*us/sh |
| 433 |
heimbach |
1.2 |
|
| 434 |
|
|
enddo |
| 435 |
|
|
|
| 436 |
|
|
#ifdef ALLOW_AUTODIFF_TAMC |
| 437 |
|
|
CADJ STORE ustar = comlev1_exf_1, key = ikey_1 |
| 438 |
|
|
CADJ STORE qstar = comlev1_exf_1, key = ikey_1 |
| 439 |
|
|
CADJ STORE tstar = comlev1_exf_1, key = ikey_1 |
| 440 |
|
|
CADJ STORE tau = comlev1_exf_1, key = ikey_1 |
| 441 |
|
|
CADJ STORE cw = comlev1_exf_1, key = ikey_1 |
| 442 |
|
|
CADJ STORE sw = comlev1_exf_1, key = ikey_1 |
| 443 |
|
|
#endif |
| 444 |
|
|
|
| 445 |
|
|
hs(i,j,bi,bj) = atmcp*tau*tstar/ustar |
| 446 |
|
|
hl(i,j,bi,bj) = flamb*tau*qstar/ustar |
| 447 |
|
|
#ifndef EXF_READ_EVAP |
| 448 |
|
|
cdm evap(i,j,bi,bj) = tau*qstar/ustar |
| 449 |
|
|
cdm !!! need to change sign and to convert from kg/m^2/s to m/s !!! |
| 450 |
|
|
evap(i,j,bi,bj) = -recip_rhonil*tau*qstar/ustar |
| 451 |
|
|
#endif |
| 452 |
|
|
ustress(i,j,bi,bj) = tau*cw |
| 453 |
|
|
vstress(i,j,bi,bj) = tau*sw |
| 454 |
|
|
else |
| 455 |
|
|
ustress(i,j,bi,bj) = 0. _d 0 |
| 456 |
|
|
vstress(i,j,bi,bj) = 0. _d 0 |
| 457 |
|
|
hflux (i,j,bi,bj) = 0. _d 0 |
| 458 |
|
|
hs(i,j,bi,bj) = 0. _d 0 |
| 459 |
|
|
hl(i,j,bi,bj) = 0. _d 0 |
| 460 |
|
|
endif |
| 461 |
|
|
|
| 462 |
|
|
#else /* ifndef ALLOW_ATM_TEMP */ |
| 463 |
|
|
#ifdef ALLOW_ATM_WIND |
| 464 |
heimbach |
1.6 |
tmpbulk= exf_BulkCdn(sh) |
| 465 |
|
|
ustress(i,j,bi,bj) = atmrho*tmpbulk*us* |
| 466 |
heimbach |
1.2 |
& uwind(i,j,bi,bj) |
| 467 |
heimbach |
1.6 |
vstress(i,j,bi,bj) = atmrho*tmpbulk*us* |
| 468 |
heimbach |
1.2 |
& vwind(i,j,bi,bj) |
| 469 |
|
|
#endif |
| 470 |
|
|
#endif /* ifndef ALLOW_ATM_TEMP */ |
| 471 |
|
|
enddo |
| 472 |
|
|
enddo |
| 473 |
|
|
enddo |
| 474 |
|
|
enddo |
| 475 |
|
|
|
| 476 |
|
|
c Add all contributions. |
| 477 |
|
|
do bj = mybylo(mythid),mybyhi(mythid) |
| 478 |
|
|
do bi = mybxlo(mythid),mybxhi(mythid) |
| 479 |
|
|
do j = 1,sny |
| 480 |
|
|
do i = 1,snx |
| 481 |
|
|
c Net surface heat flux. |
| 482 |
|
|
#ifdef ALLOW_ATM_TEMP |
| 483 |
|
|
hfl = 0. _d 0 |
| 484 |
|
|
hfl = hfl - hs(i,j,bi,bj) |
| 485 |
|
|
hfl = hfl - hl(i,j,bi,bj) |
| 486 |
|
|
hfl = hfl + lwflux(i,j,bi,bj) |
| 487 |
|
|
#ifndef SHORTWAVE_HEATING |
| 488 |
|
|
hfl = hfl + swflux(i,j,bi,bj) |
| 489 |
|
|
#endif |
| 490 |
|
|
c Heat flux: |
| 491 |
|
|
hflux(i,j,bi,bj) = hfl |
| 492 |
|
|
c Salt flux from Precipitation and Evaporation. |
| 493 |
|
|
sflux(i,j,bi,bj) = evap(i,j,bi,bj) - precip(i,j,bi,bj) |
| 494 |
|
|
#endif /* ALLOW_ATM_TEMP */ |
| 495 |
|
|
|
| 496 |
|
|
enddo |
| 497 |
|
|
enddo |
| 498 |
|
|
enddo |
| 499 |
|
|
enddo |
| 500 |
heimbach |
1.3 |
|
| 501 |
dimitri |
1.7 |
#ifdef ALLOW_DIAGNOSTICS |
| 502 |
|
|
IF ( useDiagnostics ) THEN |
| 503 |
|
|
CALL DIAGNOSTICS_FILL(hs ,'EXFhs ',0,1,0,1,1,myThid) |
| 504 |
|
|
CALL DIAGNOSTICS_FILL(hl ,'EXFhs ',0,1,0,1,1,myThid) |
| 505 |
|
|
CALL DIAGNOSTICS_FILL(lwflux,'EXFhs ',0,1,0,1,1,myThid) |
| 506 |
|
|
CALL DIAGNOSTICS_FILL(swflux,'EXFhs ',0,1,0,1,1,myThid) |
| 507 |
|
|
ENDIF |
| 508 |
|
|
#endif /* ALLOW_DIAGNOSTICS */ |
| 509 |
|
|
|
| 510 |
heimbach |
1.3 |
#endif /* ALLOW_BULKFORMULAE */ |
| 511 |
heimbach |
1.2 |
|
| 512 |
|
|
end |
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