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C $Header: /u/gcmpack/MITgcm/pkg/bulk_force/bulkf_formula_lay.F,v 1.1 2006/05/25 17:32:29 jmc Exp $ |
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C $Name: $ |
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|
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#include "BULK_FORCE_OPTIONS.h" |
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|
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CBOP |
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C !ROUTINE: BULKF_FORMULA_LAY |
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C !INTERFACE: |
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SUBROUTINE BULKF_FORMULA_LAY( |
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I uw, vw, ws, Ta, Qa, tsfCel, |
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O flwupa, flha, fsha, df0dT, |
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O ust, vst, evp, ssq, dEvdT, |
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I iceornot, i,j,bi,bj,myThid ) |
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|
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | SUBROUTINE BULKF_FORMULA_LAY |
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C | o Calculate bulk formula fluxes over open ocean or seaice |
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C | Large and Yeager, 2004, NCAR/TN-460+STR. |
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C *==========================================================* |
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C \ev |
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C |
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C === Turbulent Fluxes : |
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C * use the approach "B": shift coeff to height & stability of the |
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C atmosphere state (instead of "C": shift temp & humid to the height |
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C of wind, then shift the coeff to this height & stability of the atmos). |
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C * similar to EXF (except over sea-ice) ; default parameter values |
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C taken from Large & Yeager. |
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C * assume that Qair & Tair inputs are from the same height (zq=zt) |
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C * formulae in short: |
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C wind stress = (ust,vst) = rhoA * Cd * Ws * (del.u,del.v) |
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C Sensib Heat flux = fsha = rhoA * Ch * Ws * del.T * CpAir |
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C Latent Heat flux = flha = rhoA * Ce * Ws * del.Q * Lvap |
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C = -Evap * Lvap |
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C with Ws = wind speed = sqrt(del.u^2 +del.v^2) ; |
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C del.T = Tair - Tsurf ; del.Q = Qair - Qsurf ; |
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C Cd,Ch,Ce = drag coefficient, Stanton number and Dalton number |
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C respectively [no-units], function of height & stability |
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|
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C !USES: |
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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 "BULKF_PARAMS.h" |
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|
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C !INPUT/OUTPUT PARAMETERS: |
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C input: |
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_RL uw ! zonal wind speed (at grid center) [m/s] |
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_RL vw ! meridional wind speed (at grid center) [m/s] |
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_RL ws ! wind speed [m/s] at height zwd |
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_RL Ta ! air temperature [K] at height zth |
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_RL Qa ! specific humidity [kg/kg] at heigth zth |
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_RL tsfCel ! sea-ice or sea surface temperature [oC] |
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INTEGER iceornot ! 0=open water, 1=sea-ice, 2=sea-ice with snow |
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INTEGER i,j, bi,bj !current grid point indices |
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INTEGER myThid ! my Thread Id number |
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C output: |
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_RL flwupa ! upward long wave radiation (>0 upward) [W/m2] |
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_RL flha ! latent heat flux (>0 downward) [W/m2] |
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_RL fsha ! sensible heat flux (>0 downward) [W/m2] |
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_RL df0dT ! derivative of heat flux with respect to Tsf [W/m2/K] |
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_RL ust ! zonal wind stress (at grid center) [N/m2] |
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_RL vst ! meridional wind stress (at grid center)[N/m2] |
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_RL evp ! evaporation rate (over open water) [kg/m2/s] |
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_RL ssq ! surface specific humidity [kg/kg] |
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_RL dEvdT ! derivative of evap. with respect to Tsf [kg/m2/s/K] |
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CEOP |
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|
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#ifdef ALLOW_BULK_FORCE |
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|
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C == Local variables == |
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_RL dflhdT ! derivative of latent heat with respect to T |
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_RL dfshdT ! derivative of sensible heat with respect to T |
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_RL dflwupdT ! derivative of long wave with respect to T |
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|
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_RL Tsf ! surface temperature [K] |
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_RL Ts2 ! surface temperature square [K^2] |
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c _RL ht ! height for air temperature [m] |
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c _RL hq ! height for humidity [m] |
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c _RL hu ! height for wind speed [m] |
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c _RL zref ! reference height [m] |
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_RL wsm ! limited wind speed [m/s] (> umin) |
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_RL usn ! neutral, zref (=10m) wind speed [m/s] |
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_RL usm ! usn but limited [m/s] (> umin) |
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c _RL umin ! minimum wind speed used for drag-coeff [m/s] |
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_RL lath ! latent heat of vaporization or sublimation [J/kg] |
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_RL t0 ! virtual temperature [K] |
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_RL delth ! potential temperature diff [K] |
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_RL delq ! specific humidity difference [kg/kg] |
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_RL ustar ! friction velocity [m/s] |
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_RL tstar ! temperature scale [K] |
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_RL qstar ! humidity scale [kg/kg] |
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_RL rd ! = sqrt(Cd) [-] |
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_RL re ! = Ce / sqrt(Cd) [-] |
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_RL rh ! = Ch / sqrt(Cd) [-] |
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_RL rdn, ren, rhn ! neutral, zref (=10m) values of rd, re, rh |
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_RL stable ! = 1 if stable ; = 0 if unstable |
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_RL huol ! stability parameter at zwd [-] (=z/Monin-Obuklov length) |
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_RL htol ! stability parameter at zth [-] |
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_RL x ! stability function [-] |
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_RL xsq ! = x^2 [-] |
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_RL psimh ! momentum stability function |
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_RL psixh ! latent & sensib. stability function |
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_RL czol ! = zref*Karman_cst*gravity |
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_RL zwln ! = log(zwd/zref) |
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_RL ztln ! = log(zth/zref) |
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c _RL cdalton ! coeff to evaluate Dalton Number |
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c _RL mixratio |
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c _RL ea |
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c _RL psim_fac |
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_RL tau ! surface stress coef = rhoA * Ws * Cd |
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_RL csha ! sensib.heat flx coef = rhoA * Ws * Ch * CpAir |
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_RL clha ! latent heat flx coef = rhoA * Ws * Ce * Lvap |
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c _RL zice |
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c _RL ssq0, ssq1, ssq2 ! constant used in saturated specific humidity |
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c _RL p0 ! reference sea-level atmospheric pressure [mb] |
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_RL qs1w, qs2w ! above freezing saturated specific humidity |
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_RL qs1i, qs2i ! below freezing saturated specific humidity |
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_RL tmpBlk |
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_RL half, one, two |
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INTEGER iter |
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|
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C == external Functions |
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|
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C-- Constant |
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DATA half, one, two |
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& / 0.5 _d 0 , 1. _d 0 , 2. _d 0 / |
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c DATA ssq0, ssq1, ssq2 |
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c & / 3.797915 _d 0 , 7.93252 _d -6 , 2.166847 _d -3 / |
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c DATA p0 / 1013. _d 0 / |
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DATA qs1w, qs2w |
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& / 640.38 _d 3 , 5107.0 _d -0 / |
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DATA qs1i, qs2i |
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& / 11637.80 _d 3 , 5897.8 _d -0 / |
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|
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C-- Set surface parameters : |
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c zice = 0.0005 _d 0 |
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zwln = LOG(zwd/zref) |
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ztln = LOG(zth/zref) |
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czol = zref*xkar*gravity |
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C- Surface Temp. |
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Tsf = tsfCel+Tf0kel |
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Ts2 = Tsf*Tsf |
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C- Wind speed |
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IF (ws.EQ.0. _d 0) THEN |
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ws = SQRT(uw*uw + vw*vw) |
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ENDIF |
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wsm = MAX(ws,umin) |
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|
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C--- Compute turbulent surface fluxes |
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C- Pot. Temp and saturated specific humidity |
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t0 = Ta*(one + humid_fac*Qa) |
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IF ( iceornot.EQ.0 ) THEN |
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lath=Lvap |
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ssq = saltQsFac*qs1w*EXP( -qs2w/Tsf ) / rhoA |
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dEvdT = qs2w |
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ELSE |
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lath = Lvap+Lfresh |
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ssq = qs1i*EXP( -qs2i/Tsf ) / rhoA |
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dEvdT = qs2i |
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ENDIF |
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c ssq = ssq0*EXP( lath*(ssq1-ssq2/Tsf) ) / p0 |
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c dEvdT = lath*ssq2 |
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|
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delth = Ta + gamma_blk*zth - Tsf |
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delq = Qa - ssq |
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|
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C-- initial guess for exchange coefficients: |
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C take U_N = del.U ; stability from del.Theta ; |
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stable = half + SIGN(half, delth) |
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tmpBlk = cdrag_1/wsm + cdrag_2 + cdrag_3*wsm |
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rdn = SQRT(tmpBlk) |
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rhn = stable*cStantonS + (one-stable)*cStantonU |
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ren = cDalton |
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c rdn=xkar/(LOG(zref/zice)) |
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c rhn=rdn |
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c ren=rdn |
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C-- calculate turbulent scales |
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ustar=rdn*wsm |
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tstar=rhn*delth |
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qstar=ren*delq |
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C--- iterate with psi-functions to find transfer coefficients |
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DO iter=1,blk_nIter |
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huol = ( tstar/t0 |
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& +qstar/(Qa + one/humid_fac) |
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& )*czol/(ustar*ustar) |
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huol = SIGN( MIN(abs(huol),10. _d 0), huol) |
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stable = half + SIGN(half, huol) |
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xsq = SQRT( ABS(one - huol*16. _d 0) ) |
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x = SQRT(xsq) |
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psimh = -5. _d 0*huol*stable |
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& + (one-stable)* |
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& ( LOG( (one + two*x + xsq)*(one+xsq)*.125 ) |
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& -two*ATAN(x) + half*pi ) |
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htol = huol*zth/zwd |
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xsq = SQRT( ABS(one - htol*16. _d 0) ) |
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psixh = -5. _d 0*htol*stable |
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& + (one-stable)*( two*LOG(half*(one+xsq)) ) |
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|
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C- Shift wind speed using old coefficient |
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usn = ws/(one + rdn/xkar*(zwln-psimh) ) |
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usm = MAX(usn, umin) |
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|
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C- Update the 10m, neutral stability transfer coefficients |
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tmpBlk = cdrag_1/usm + cdrag_2 + cdrag_3*usm |
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rdn = SQRT(tmpBlk) |
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rhn = stable*cStantonS + (one-stable)*cStantonU |
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ren = cDalton |
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C- Shift all coefficients to the measurement height and stability. |
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rd = rdn/(1. _d 0 + rdn*(zwln-psimh)/xkar) |
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rh = rhn/(1. _d 0 + rhn*(ztln-psixh)/xkar) |
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re = ren/(1. _d 0 + ren*(ztln-psixh)/xkar) |
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|
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C-- Update ustar, tstar, qstar using updated, shifted coefficients. |
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ustar = rd*wsm |
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qstar = re*delq |
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tstar = rh*delth |
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|
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ENDDO |
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|
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C- Coeff: |
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tau = rhoA*rd*ws |
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csha = cpAir*tau*rh |
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clha = lath*tau*re |
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|
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C- Turbulent Fluxes |
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fsha = csha*delth |
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flha = clha*delq |
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evp = -flha/lath |
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ust = tau*rd*uw |
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vst = tau*rd*vw |
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|
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C- surf.Temp derivative of turbulent Fluxes |
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dEvdT = tau*re*ssq*dEvdT/Ts2 |
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dflhdT = -lath*dEvdT |
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dfshdT = -csha |
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|
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C--- Upward long wave radiation |
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IF ( iceornot.EQ.0 ) THEN |
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flwupa = ocean_emissivity*stefan*Ts2*Ts2 |
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dflwupdT= ocean_emissivity*stefan*Ts2*Tsf*4. _d 0 |
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ELSEIF (iceornot.EQ.2) THEN |
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flwupa = snow_emissivity*stefan*Ts2*Ts2 |
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dflwupdT = snow_emissivity*stefan*Ts2*Tsf*4. _d 0 |
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ELSE |
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flwupa = ice_emissivity*stefan*Ts2*Ts2 |
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dflwupdT = ice_emissivity*stefan*Ts2*Tsf*4. _d 0 |
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ENDIF |
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|
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C- Total derivative with respect to surface temperature |
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df0dT = -dflwupdT+dfshdT+dflhdT |
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|
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#endif /*ALLOW_BULK_FORCE*/ |
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|
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RETURN |
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END |
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