REMORA_bulk_flux.cpp

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#include <REMORA.H>
 
using namespace amrex;
 
/**
 * @param[in   ] lev            level to operate on
 * @param[in   ] mf_cons        scalar data: temperature, salinity, passsive scalar, etc
 * @param[in   ] mf_uwind       u-direction wind dvelocity
 * @param[in   ] mf_vwind       v-direction wind dvelocity
 * @param[inout] mf_evap        evaporation rate
 * @param[  out] mf_sustr       u-direction surface momentum stress
 * @param[  out] mf_svstr       v-direction surface momentum stress
 * @param[  out] mf_stflux      surface scalar flux (temperature, salinity)
 * @param[  out] mf_lrflx       longwave radiation flux
 * @param[inout] mf_lhflx       latent heat flux
 * @param[inout] mf_shflx       sensible heat flux
 * @param[in   ] N              number of vertical levels
 */
void
REMORA::bulk_fluxes (int lev, MultiFab* mf_cons, MultiFab* mf_uwind, MultiFab* mf_vwind,
                     MultiFab* mf_evap, MultiFab* mf_sustr, MultiFab* mf_svstr,
                     MultiFab* mf_stflux, MultiFab* mf_lrflx, MultiFab* mf_lhflx,
                     MultiFab* mf_shflx,
                     const int N)
{
    const int IterMax = 3;
    const BoxArray& ba = mf_cons->boxArray();
    const DistributionMapping& dm = mf_cons->DistributionMap();
    MultiFab mf_Taux(ba, dm, 1, IntVect(NGROW,NGROW,0));
    MultiFab mf_Tauy(ba, dm, 1, IntVect(NGROW,NGROW,0));
    // temps: Taux, Tauy,
    for ( MFIter mfi(*mf_cons, TilingIfNotGPU()); mfi.isValid(); ++mfi) {
        Array4<Real const> const& uwind = mf_uwind->const_array(mfi);
        Array4<Real const> const& vwind = mf_vwind->const_array(mfi);
        Array4<Real const> const& cons = mf_cons->const_array(mfi);
        Array4<Real> const& sustr = mf_sustr->array(mfi);
        Array4<Real> const& svstr = mf_svstr->array(mfi);
        Array4<Real> const& stflux = mf_stflux->array(mfi);
        Array4<Real> const& lrflx = mf_lrflx->array(mfi);
        Array4<Real> const& lhflx = mf_lhflx->array(mfi);
        Array4<Real> const& shflx = mf_shflx->array(mfi);
        Array4<Real> const& evap  = mf_evap->array(mfi);
        Array4<Real> const& Taux = mf_Taux.array(mfi);
        Array4<Real> const& Tauy = mf_Tauy.array(mfi);
 
        Array4<const Real> const& mskr = vec_mskr[lev]->const_array(mfi);
        Array4<const Real> const& msku  = vec_msku[lev]->const_array(mfi);
        Array4<const Real> const& mskv  = vec_mskv[lev]->const_array(mfi);
        Array4<const Real> const& rain  = vec_rain[lev]->const_array(mfi);
 
        Real Hscale = solverChoice.rho0 * Cp;
        Real Hscale2 = 1.0_rt / (solverChoice.rho0 * Cp);
        Real srflux = solverChoice.srflux;
        Real PairM = solverChoice.Pair;
        Real TairC = solverChoice.Tair;
        Real TairK = solverChoice.Tair + 273.16_rt;
        Real Hair = solverChoice.Hair;
        Real cloud = solverChoice.cloud;
        Real blk_ZQ = solverChoice.blk_ZQ;
        Real blk_ZT = solverChoice.blk_ZT;
        Real blk_ZW = solverChoice.blk_ZW;
 
        Real eps = 1e-20_rt;
 
        Box bx = mfi.tilebox();
        Box ubx = mfi.grownnodaltilebox(0,IntVect(NGROW-1,NGROW-1,0));
        Box vbx = mfi.grownnodaltilebox(1,IntVect(NGROW-1,NGROW-1,0));
        Box gbx1 = bx; gbx1.grow(IntVect(NGROW,NGROW,0));
 
        ParallelFor(makeSlab(gbx1,2,0), [=] AMREX_GPU_DEVICE (int i, int j, int ) {
            // Input bulk parametrization fields
            Real wind_mag = std::sqrt(uwind(i,j,0)*uwind(i,j,0) + vwind(i,j,0) * vwind(i,j,0)) + eps;
            Real TseaK = cons(i,j,N,Temp_comp) + 273.16_rt;
 
            // Initialize
            Real delTc = 0.0_rt;
            Real delQc = 0.0_rt;
 
            Real LHeat = lhflx(i,j,0) * Hscale;
            Real SHeat = shflx(i,j,0) * Hscale;
            Real Taur = 0.0_rt;
            Taux(i,j,0) = 0.0_rt;
            Tauy(i,j,0) = 0.0_rt;
 
 
            /*-----------------------------------------------------------------------
               Compute net longwave radiation (W/m2), LRad.
             -----------------------------------------------------------------------
 
               Use Berliand (1952) formula to calculate net longwave radiation.
               The equation for saturation vapor pressure is from Gill (Atmosphere-
               Ocean Dynamics, pp 606). Here the coefficient in the cloud term
               is assumed constant, but it is a function of latitude varying from
               1.0 at poles to 0.5 at the Equator).
 
            */
            Real RH = Hair;
            Real cff=(0.7859_rt+0.03477_rt*TairC)/(1.0_rt+0.00412_rt*TairC);
            Real e_sat=std::pow(10.0_rt,cff);   // saturation vapor pressure (hPa or mbar)
            Real vap_p=e_sat*RH;       // water vapor pressure (hPa or mbar)
            Real cff2=TairK*TairK*TairK;
            Real cff1=cff2*TairK;
            Real LRad=-emmiss*StefBo*
                               (cff1*(0.39_rt-0.05_rt*std::sqrt(vap_p))*
                                     (1.0_rt-0.6823_rt*cloud*cloud)+
                                cff2*4.0_rt*(TseaK-TairK));
 
           /*
            -----------------------------------------------------------------------
              Compute specific humidities (kg/kg).
 
                note that Qair is the saturation specific humidity at Tair
                             Q is the actual specific humidity
                          Qsea is the saturation specific humidity at Tsea
 
                      Saturation vapor pressure in mb is first computed and then
                      converted to specific humidity in kg/kg
 
                      The saturation vapor pressure is computed from Teten formula
                      using the approach of Buck (1981):
 
                      Esat(mb) = (1.0007_rt+3.46E-6_rt*PairM(mb))*6.1121_rt*
                              EXP(17.502_rt*TairC(C)/(240.97_rt+TairC(C)))
 
                      The ambient vapor is found from the definition of the
                      Relative humidity:
 
                      RH = W/Ws*100 ~ E/Esat*100   E = RH/100*Esat if RH is in %
                                                   E = RH*Esat     if RH fractional
 
                      The specific humidity is then found using the relationship:
 
                      Q = 0.622 E/(P + (0.622-1)e)
 
                      Q(kg/kg) = 0.62197_rt*(E(mb)/(PairM(mb)-0.378_rt*E(mb)))
 
            -----------------------------------------------------------------------
            */
 
            //  Compute air saturation vapor pressure (mb), using Teten formula.
 
            Real cff_saturation_air=(1.0007_rt+3.46E-6_rt*PairM)*6.1121_rt*
                                std::exp(17.502_rt*TairC/(240.97_rt+TairC));
 
            //  Compute specific humidity at Saturation, Qair (kg/kg).
 
            Real Qair = 0.62197_rt*(cff_saturation_air/(PairM-0.378_rt*cff_saturation_air+eps));
 
            //  Compute specific humidity, Q (kg/kg).
            Real Q;
            if (RH < 2.0) {
                Real cff_Q = cff_saturation_air*RH;                  //Vapor pressure (mb)
                Q=0.62197_rt*(cff_Q/(PairM-0.378_rt*cff_Q+eps)); //Spec hum (kg/kg)
            } else { // RH input was actually specific humidity in g/kg
                Q=RH/1000.0_rt;                          //!Spec Hum (kg/kg)
            }
 
            //  Compute water saturation vapor pressure (mb), using Teten formula.
 
            Real cff_saturation_water=(1.0007_rt+3.46E-6_rt*PairM)*6.1121_rt*
                                std::exp(17.502_rt*cons(i,j,N,Temp_comp)/(240.97_rt+cons(i,j,N,Temp_comp)));
 
            //  Compute water saturation vapor pressure (mb), using Teten formula.
            //   Vapor Pressure reduced for salinity (Kraus and Businger, 1994, pp42).
            Real cff_vp=cff_saturation_water*0.98_rt;
 
            //   Compute Qsea (kg/kg) from vapor pressure.
 
            Real Qsea=0.62197_rt*(cff_vp/(PairM-0.378_rt*cff_vp));
            //
            // -----------------------------------------------------------------------
            //   Compute Monin-Obukhov similarity parameters for wind (Wstar),
            //   heat (Tstar), and moisture (Qstar), Liu et al. (1979).
            // -----------------------------------------------------------------------
            //
            //   Moist air density (kg/m3).
 
            Real rhoAir=PairM*100.0_rt/(blk_Rgas*TairK*(1.0_rt+0.61_rt*Q));
 
            //  Kinematic viscosity of dry air (m2/s), Andreas (1989).
 
            Real VisAir=1.326E-5_rt*(1.0_rt+TairC*(6.542E-3_rt+TairC*
                                     (8.301E-6_rt-4.84E-9_rt*TairC)));
 
            //  Compute latent heat of vaporization (J/kg) at sea surface, Hlv.
 
            Real Hlv = (2.501_rt-0.00237_rt*cons(i,j,N,Temp_comp))*1.0e6_rt;
 
            //  Assume that wind is measured relative to sea surface and include
            //  gustiness.
 
            Real Wgus=0.5_rt;
            Real delW=std::sqrt(wind_mag*wind_mag+Wgus*Wgus);
            Real delQ=Qsea-Q;
            Real delT=cons(i,j,N,Temp_comp)-TairC;
 
            // Neutral coefficients.
            Real ZoW=0.0001_rt;
            Real u10=delW*std::log(10.0_rt/ZoW)/std::log(blk_ZW/ZoW);
            Real Wstar=0.035_rt * u10;
            Real Zo10=0.011_rt*Wstar*Wstar/g+0.11_rt*VisAir/Wstar;
            Real Cd10 =(vonKar/std::log(10.0_rt/Zo10));
            Cd10 = Cd10 * Cd10;
            Real Ch10 =0.00115_rt;
            Real Ct10 = Ch10/std::sqrt(Cd10);
            Real ZoT10=10.0_rt/std::exp(vonKar/Ct10);
            Real Cd=(vonKar/std::log(blk_ZW/Zo10));
            Cd = Cd * Cd;
 
            //  Compute Richardson number.
            Real Ct=vonKar/std::log(blk_ZT/ZoT10);  // T transfer coefficient
            Real CC=vonKar*Ct/Cd;
 
            Real Ribcu = -blk_ZW/(blk_Zabl*0.004_rt*blk_beta*blk_beta*blk_beta);
            Real Ri = -g*blk_ZW*((delT-delTc)+0.61_rt*TairK*delQ)/
                                 (TairK*delW*delW+eps);
            Real Zetu;
            if (Ri < 0.0) {
                Zetu=CC*Ri/(1.0_rt+Ri/Ribcu);       // Unstable
            } else {
                Zetu=CC*Ri/(1.0_rt+3.0_rt*Ri/CC);   // Stable
            }
            Real L10 = blk_ZW/Zetu;
 
            // First guesses for Monon-Obukhov similarity scales.
            Wstar=delW*vonKar/(std::log(blk_ZW/Zo10)-
                                bulk_psiu(blk_ZW/L10));
            Real Tstar=-(delT-delTc)*vonKar/(std::log(blk_ZT/ZoT10)-
                                         bulk_psit(blk_ZT/L10));
            Real Qstar=-(delQ-delQc)*vonKar/(std::log(blk_ZQ/ZoT10)-
                                         bulk_psit(blk_ZQ/L10));
 
            //  Modify Charnock for high wind speeds. The 0.125 factor below is for
            //  1.0/(18.0-10.0).
 
            Real charn;
            if (delW > 18.0_rt) {
                charn=0.018_rt;
            } else if ((10.0_rt < delW) and (delW <= 18.0_rt)) {
                charn=0.011_rt+0.125_rt*(0.018_rt-0.011_rt)*(delW-10.0_rt);
            } else {
                charn=0.011_rt;
            }
 
            //  Iterate until convergence. It usually converges within 3 iterations.
            for (int it=0; it<IterMax; it++) {
                ZoW=charn*Wstar*Wstar/g+0.11_rt*VisAir/(Wstar+eps);
                Real Rr=ZoW*Wstar/VisAir;
                //  Compute Monin-Obukhov stability parameter, Z/L.
                Real ZoQ=std::min(1.15e-4_rt,5.5e-5_rt/std::pow(Rr,0.6_rt));
                Real ZoT=ZoQ;
                Real ZoL=vonKar*g*blk_ZW*(Tstar*(1.0_rt+0.61_rt*Q)+
                             0.61_rt*TairK*Qstar)/
                            (TairK*Wstar*Wstar*(1.0_rt+0.61_rt*Q)+eps);
                Real L=blk_ZW/(ZoL+eps);
 
                //  Evaluate stability functions at Z/L.
                Real Wpsi=bulk_psiu(ZoL);
                Real Tpsi=bulk_psit(blk_ZT/L);
                Real Qpsi=bulk_psit(blk_ZQ/L);
 
                //  Compute wind scaling parameters, Wstar.
                Wstar=std::max(eps,delW*vonKar/(std::log(blk_ZW/ZoW)-Wpsi));
                Tstar=-(delT-delTc)*vonKar/(std::log(blk_ZT/ZoT)-Tpsi);
                Qstar=-(delQ-delQc)*vonKar/(std::log(blk_ZQ/ZoQ)-Qpsi);
 
                //  Compute gustiness in wind speed.
                Real Bf=-g/TairK*Wstar*(Tstar+0.61_rt*TairK*Qstar);
                if (Bf>0.0_rt) {
                    Wgus=blk_beta*std::pow(Bf*blk_Zabl,1.0_rt/3.0_rt);
                } else {
                    Wgus=0.2_rt;
                }
                delW=std::sqrt(wind_mag*wind_mag+Wgus*Wgus);
            }
 
            // Compute transfer coefficients for momentum (Cd).
            Real Wspeed=std::sqrt(wind_mag*wind_mag+Wgus*Wgus);
            Cd=Wstar*Wstar/(Wspeed*Wspeed+eps);
 
            // Compute turbulent sensible heat flux (W/m2), Hs.
            Real Hs=-blk_Cpa*rhoAir*Wstar*Tstar;
 
            //  Compute sensible heat flux (W/m2) due to rainfall (kg/m2/s), Hsr.
            Real diffw=2.11E-5_rt*std::pow(TairK/273.16_rt,1.94_rt);
            Real diffh=0.02411_rt*(1.0_rt+TairC*
                               (3.309E-3_rt-1.44E-6_rt*TairC))/
                               (rhoAir*blk_Cpa+eps);
            cff=Qair*Hlv/(blk_Rgas*TairK*TairK);
            Real wet_bulb=1.0_rt/(1.0_rt+0.622_rt*(cff*Hlv*diffw)/
                                                  (blk_Cpa*diffh));
            Real Hsr=rain(i,j,0)*wet_bulb*blk_Cpw*
                              ((cons(i,j,N,Temp_comp)-TairC)+(Qsea-Q)*Hlv/blk_Cpa);
            SHeat=(Hs+Hsr) * mskr(i,j,0);
 
            // Compute turbulent latent heat flux (W/m2), Hl.
 
            Real Hl=-Hlv*rhoAir*Wstar*Qstar;
 
            // Compute Webb correction (Webb effect) to latent heat flux, Hlw.
            Real upvel=-1.61_rt*Wstar*Qstar-
                        (1.0_rt+1.61_rt*Q)*Wstar*Tstar/TairK;
            Real Hlw=rhoAir*Hlv*upvel*Q;
            LHeat=(Hl+Hlw) * mskr(i,j,0);
 
            // Compute momentum flux (N/m2) due to rainfall (kg/m2/s).
            Taur=0.85_rt*rain(i,j,0)*wind_mag;
 
            // Compute wind stress components (N/m2), Tau.
            cff=rhoAir*Cd*Wspeed;
            Real sign_u = (uwind(i,j,0) >= 0.0_rt) ? 1 : -1;
            Real sign_v = (vwind(i,j,0) >= 0.0_rt) ? 1 : -1;
            Taux(i,j,0)=(cff*uwind(i,j,0)+Taur*sign_u) * mskr(i,j,0);
            Tauy(i,j,0)=(cff*vwind(i,j,0)+Taur*sign_v) * mskr(i,j,0);
 
            //=======================================================================
            //  Compute surface net heat flux and surface wind stress.
            //=======================================================================
            //
            //  Compute kinematic, surface, net heat flux (degC m/s).  Notice that
            //  the signs of latent and sensible fluxes are reversed because fluxes
            //  calculated from the bulk formulations above are positive out of the
            //  ocean.
            //
            //  For EMINUSP option,  EVAP = LHeat (W/m2) / Hlv (J/kg) = kg/m2/s
            //                       PREC = rain = kg/m2/s
            //
            //  To convert these rates to m/s divide by freshwater density, rhow.
            //
            //  Note that when the air is undersaturated in water vapor (Q < Qsea)
            //  the model will evaporate and LHeat > 0:
            //
            //                   LHeat positive out of the ocean
            //                    evap positive out of the ocean
            //
            //  Note that if evaporating, the salt flux is positive
            //        and if     raining, the salt flux is negative
            //
            //  Note that stflux(:,:,isalt) is the E-P flux. The fresh water flux
            //  is positive out of the ocean and the salt flux is positive into the
            //  ocean. It is  multiplied by surface salinity when computing state
            //  variable stflx(:,:,isalt) in "set_vbc.F".
 
//            Real one_over_rhow=1.0_rt/rhow;
            lrflx(i,j,0) = LRad*Hscale2;
            lhflx(i,j,0) = -LHeat*Hscale2;
            shflx(i,j,0) = -SHeat*Hscale2;
            stflux(i,j,0,Temp_comp)=(srflux + lrflx(i,j,0) + lhflx(i,j,0) + shflx(i,j,0)) * mskr(i,j,0);
            evap(i,j,0) = (LHeat / Hlv+eps) * mskr(i,j,0);
            stflux(i,j,0,Salt_comp) = mskr(i,j,0) * (evap(i,j,0)-rain(i,j,0)) / rhow;
        });
 
        Real cff_rho = 0.5_rt / solverChoice.rho0;
        ParallelFor(makeSlab(ubx,2,0), [=] AMREX_GPU_DEVICE (int i, int j, int ) {
            sustr(i,j,0) = cff_rho*(Taux(i-1,j,0) + Taux(i,j,0)) * msku(i,j,0);
        });
        ParallelFor(makeSlab(vbx,2,0), [=] AMREX_GPU_DEVICE (int i, int j, int ) {
            svstr(i,j,0) = cff_rho*(Tauy(i,j-1,0) + Tauy(i,j,0)) * mskv(i,j,0);
        });
    }
 
}