SUBROUTINE prsgrd (ng, tile) ! !svn $Id: prsgrd32.h 774 2008-10-01 22:27:10Z kate $ !*********************************************************************** ! Copyright (c) 2002-2008 The ROMS/TOMS Group ! ! Licensed under a MIT/X style license ! ! See License_ROMS.txt Hernan G. Arango ! !****************************************** Alexander F. Shchepetkin *** ! ! ! This subroutine evaluates the nonlinear baroclinic, hydrostatic ! ! pressure gradient term using a nonconservative Density-Jacobian ! ! scheme, based on cubic polynomial fits for "rho" and "z_r" as ! ! functions of nondimensional coordinates (XI,ETA,s), that is, its ! ! respective array indices. The cubic polynomials are monotonized ! ! by using harmonic mean instead of linear averages to interpolate ! ! slopes. This scheme retains exact anti-symmetry: ! ! ! ! J(rho,z_r)=-J(z_r,rho). ! ! ! ! If parameter OneFifth (below) is set to zero, the scheme becomes ! ! identical to standard Jacobian. ! ! ! ! Reference: ! ! ! ! Shchepetkin A.F and J.C. McWilliams, 2003: A method for ! ! computing horizontal pressure gradient force in an ocean ! ! model with non-aligned vertical coordinate, JGR, 108, ! ! 1-34. ! ! ! !*********************************************************************** ! USE mod_param #ifdef POT_TIDES USE mod_tides #endif #ifdef ATM_PRESS USE mod_forces #endif #ifdef DIAGNOSTICS USE mod_diags #endif USE mod_grid USE mod_ocean USE mod_stepping ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile ! ! Local variable declarations. ! #include "tile.h" ! #ifdef PROFILE CALL wclock_on (ng, iNLM, 23) #endif CALL prsgrd_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs(ng), & #ifdef MASKING & GRID(ng) % umask, & & GRID(ng) % vmask, & #endif & GRID(ng) % om_v, & & GRID(ng) % on_u, & & GRID(ng) % Hz, & & GRID(ng) % z_r, & & GRID(ng) % z_w, & #ifdef ICESHELF & GRID(ng) % zice, & #endif & OCEAN(ng) % rho, & #ifdef DIAGNOSTICS_UV & DIAGS(ng) % DiaRU, & & DIAGS(ng) % DiaRV, & #endif #ifdef POT_TIDES & TIDES(ng) % Ptide, & #endif #ifdef ATM_PRESS & FORCES(ng) % Pair, & #endif & OCEAN(ng) % ru, & & OCEAN(ng) % rv) #ifdef PROFILE CALL wclock_off (ng, iNLM, 23) #endif RETURN END SUBROUTINE prsgrd ! !*********************************************************************** SUBROUTINE prsgrd_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs, & #ifdef MASKING & umask, vmask, & #endif & om_v, on_u, & & Hz, z_r, z_w, & # ifdef ICESHELF & zice, & # endif & rho, & #ifdef DIAGNOSTICS_UV & DiaRU, DiaRV, & #endif #ifdef POT_TIDES & Ptide, & #endif #ifdef ATM_PRESS & Pair, & #endif & ru, rv) !*********************************************************************** ! USE mod_param USE mod_scalars ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile integer, intent(in) :: LBi, UBi, LBj, UBj integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: nrhs #ifdef ASSUMED_SHAPE # ifdef MASKING real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: vmask(LBi:,LBj:) # endif real(r8), intent(in) :: om_v(LBi:,LBj:) real(r8), intent(in) :: on_u(LBi:,LBj:) real(r8), intent(in) :: Hz(LBi:,LBj:,:) real(r8), intent(in) :: z_r(LBi:,LBj:,:) real(r8), intent(in) :: z_w(LBi:,LBj:,0:) # ifdef ICESHELF real(r8), intent(in) :: zice(LBi:,LBj:) # endif real(r8), intent(in) :: rho(LBi:,LBj:,:) # ifdef DIAGNOSTICS_UV real(r8), intent(inout) :: DiaRU(LBi:,LBj:,:,:,:) real(r8), intent(inout) :: DiaRV(LBi:,LBj:,:,:,:) # endif # ifdef POT_TIDES real(r8), intent(in) :: Ptide(LBi:,LBj:) # endif # ifdef ATM_PRESS real(r8), intent(in) :: Pair(LBi:,LBj:) # endif real(r8), intent(inout) :: ru(LBi:,LBj:,0:,:) real(r8), intent(inout) :: rv(LBi:,LBj:,0:,:) #else # ifdef MASKING real(r8), intent(in) :: umask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: vmask(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: om_v(LBi:UBi,LBj:UBj) real(r8), intent(in) :: on_u(LBi:UBi,LBj:UBj) real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: z_w(LBi:UBi,LBj:UBj,0:N(ng)) # ifdef ICESHELF real(r8), intent(in) :: zice(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: rho(LBi:UBi,LBj:UBj,N(ng)) # ifdef DIAGNOSTICS_UV real(r8), intent(inout) :: DiaRU(LBi:UBi,LBj:UBj,N(ng),2,NDrhs) real(r8), intent(inout) :: DiaRV(LBi:UBi,LBj:UBj,N(ng),2,NDrhs) # endif # ifdef POT_TIDES real(r8), intent(in) :: Ptide(LBi:UBi,LBj:UBj) # endif # ifdef ATM_PRESS real(r8), intent(in) :: Pair(LBi:UBi,LBj:UBj) # endif real(r8), intent(inout) :: ru(LBi:UBi,LBj:UBj,0:N(ng),2) real(r8), intent(inout) :: rv(LBi:UBi,LBj:UBj,0:N(ng),2) #endif ! ! Local variable declarations. ! integer :: i, j, k real(r8), parameter :: OneFifth = 0.2_r8 real(r8), parameter :: OneTwelfth = 1.0_r8/12.0_r8 real(r8), parameter :: eps = 1.0E-10_r8 #ifdef ICESHELF real(r8), parameter :: drhodz = 0.00478_r8 #endif real(r8) :: GRho, GRho0, HalfGRho real(r8) :: cff, cff1, cff2 real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: P real(r8), dimension(IminS:ImaxS,0:N(ng)) :: dR real(r8), dimension(IminS:ImaxS,0:N(ng)) :: dZ real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FC real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: aux real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: dRx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: dZx ! #include "set_bounds.h" ! !----------------------------------------------------------------------- ! Preliminary step (same for XI- and ETA-components: !----------------------------------------------------------------------- ! GRho=g/rho0 GRho0=1000.0_r8*GRho HalfGRho=0.5_r8*GRho ! DO j=JstrV-1,Jend DO k=1,N(ng)-1 DO i=IstrU-1,Iend dR(i,k)=rho(i,j,k+1)-rho(i,j,k) dZ(i,k)=z_r(i,j,k+1)-z_r(i,j,k) END DO END DO DO i=IstrU-1,Iend dR(i,N(ng))=dR(i,N(ng)-1) dZ(i,N(ng))=dZ(i,N(ng)-1) dR(i,0)=dR(i,1) dZ(i,0)=dZ(i,1) END DO DO k=N(ng),1,-1 DO i=IstrU-1,Iend cff=2.0_r8*dR(i,k)*dR(i,k-1) IF (cff.gt.eps) THEN dR(i,k)=cff/(dR(i,k)+dR(i,k-1)) ELSE dR(i,k)=0.0_r8 END IF dZ(i,k)=2.0_r8*dZ(i,k)*dZ(i,k-1)/(dZ(i,k)+dZ(i,k-1)) END DO END DO DO i=IstrU-1,Iend cff1=1.0_r8/(z_r(i,j,N(ng))-z_r(i,j,N(ng)-1)) cff2=0.5_r8*(rho(i,j,N(ng))-rho(i,j,N(ng)-1))* & & (z_w(i,j,N(ng))-z_r(i,j,N(ng)))*cff1 #ifdef ICESHELF P(i,j,N(ng))=GRho0*(z_w(i,j,N(ng))-zice(i,j))- & & GRho*(rho(i,j,N(ng))+0.5_r8*drhodz*zice(i,j))* & & zice(i,j)+ & & GRho*(rho(i,j,N(ng))+cff2)* & & (z_w(i,j,N(ng))-z_r(i,j,N(ng))) #else P(i,j,N(ng))=GRho0*z_w(i,j,N(ng))+ & & GRho*(rho(i,j,N(ng))+cff2)* & & (z_w(i,j,N(ng))-z_r(i,j,N(ng))) #endif #ifdef POT_TIDES P(i,j,N(ng)) = P(i,j,N(ng)) - g*Ptide(i,j) #endif #ifdef ATM_PRESS P(i,j,N(ng)) = P(i,j,N(ng)) + 100._r8*Pair(i,j)/rho0 #endif END DO DO k=N(ng)-1,1,-1 DO i=IstrU-1,Iend P(i,j,k)=P(i,j,k+1)+ & & HalfGRho*((rho(i,j,k+1)+rho(i,j,k))* & & (z_r(i,j,k+1)-z_r(i,j,k))- & & OneFifth* & & ((dR(i,k+1)-dR(i,k))* & & (z_r(i,j,k+1)-z_r(i,j,k)- & & OneTwelfth* & & (dZ(i,k+1)+dZ(i,k)))- & & (dZ(i,k+1)-dZ(i,k))* & & (rho(i,j,k+1)-rho(i,j,k)- & & OneTwelfth* & & (dR(i,k+1)+dR(i,k))))) END DO END DO END DO ! !----------------------------------------------------------------------- ! Compute XI-component pressure gradient term. !----------------------------------------------------------------------- ! DO k=N(ng),1,-1 DO j=Jstr,Jend DO i=IstrU-1,Iend+1 aux(i,j)=z_r(i,j,k)-z_r(i-1,j,k) #ifdef MASKING aux(i,j)=aux(i,j)*umask(i,j) #endif FC(i,j)=rho(i,j,k)-rho(i-1,j,k) #ifdef MASKING FC(i,j)=FC(i,j)*umask(i,j) #endif END DO END DO ! DO j=Jstr,Jend DO i=IstrU-1,Iend cff=2.0_r8*aux(i,j)*aux(i+1,j) IF (cff.gt.eps) THEN cff1=1.0_r8/(aux(i,j)+aux(i+1,j)) dZx(i,j)=cff*cff1 ELSE dZx(i,j)=0.0_r8 END IF cff1=2.0_r8*FC(i,j)*FC(i+1,j) IF (cff1.gt.eps) THEN cff2=1.0_r8/(FC(i,j)+FC(i+1,j)) dRx(i,j)=cff1*cff2 ELSE dRx(i,j)=0.0_r8 END IF END DO END DO ! DO j=Jstr,Jend DO i=IstrU,Iend ru(i,j,k,nrhs)=on_u(i,j)*0.5_r8* & & (Hz(i,j,k)+Hz(i-1,j,k))* & & (P(i-1,j,k)-P(i,j,k)- & & HalfGRho* & & ((rho(i,j,k)+rho(i-1,j,k))* & & (z_r(i,j,k)-z_r(i-1,j,k))- & & OneFifth* & & ((dRx(i,j)-dRx(i-1,j))* & & (z_r(i,j,k)-z_r(i-1,j,k)- & & OneTwelfth* & & (dZx(i,j)+dZx(i-1,j)))- & & (dZx(i,j)-dZx(i-1,j))* & & (rho(i,j,k)-rho(i-1,j,k)- & & OneTwelfth* & & (dRx(i,j)+dRx(i-1,j)))))) #ifdef DIAGNOSTICS_UV DiaRU(i,j,k,nrhs,M3pgrd)=ru(i,j,k,nrhs) #endif END DO END DO END DO ! !----------------------------------------------------------------------- ! ETA-component pressure gradient term. !----------------------------------------------------------------------- ! DO k=N(ng),1,-1 DO j=JstrV-1,Jend+1 DO i=Istr,Iend aux(i,j)=z_r(i,j,k)-z_r(i,j-1,k) #ifdef MASKING aux(i,j)=aux(i,j)*vmask(i,j) #endif FC(i,j)=rho(i,j,k)-rho(i,j-1,k) #ifdef MASKING FC(i,j)=FC(i,j)*vmask(i,j) #endif END DO END DO ! DO j=JstrV-1,Jend DO i=Istr,Iend cff=2.0_r8*aux(i,j)*aux(i,j+1) IF (cff.gt.eps) THEN cff1=1.0_r8/(aux(i,j)+aux(i,j+1)) dZx(i,j)=cff*cff1 ELSE dZx(i,j)=0.0_r8 END IF cff1=2.0_r8*FC(i,j)*FC(i,j+1) IF (cff1.gt.eps) THEN cff2=1.0_r8/(FC(i,j)+FC(i,j+1)) dRx(i,j)=cff1*cff2 ELSE dRx(i,j)=0.0_r8 END IF END DO END DO ! DO j=JstrV,Jend DO i=Istr,Iend rv(i,j,k,nrhs)=om_v(i,j)*0.5_r8* & & (Hz(i,j,k)+Hz(i,j-1,k))* & & (P(i,j-1,k)-P(i,j,k)- & & HalfGRho* & & ((rho(i,j,k)+rho(i,j-1,k))* & & (z_r(i,j,k)-z_r(i,j-1,k))- & & OneFifth* & & ((dRx(i,j)-dRx(i,j-1))* & & (z_r(i,j,k)-z_r(i,j-1,k)- & & OneTwelfth* & & (dZx(i,j)+dZx(i,j-1)))- & & (dZx(i,j)-dZx(i,j-1))* & & (rho(i,j,k)-rho(i,j-1,k)- & & OneTwelfth* & & (dRx(i,j)+dRx(i,j-1)))))) #ifdef DIAGNOSTICS_UV DiaRV(i,j,k,nrhs,M3pgrd)=rv(i,j,k,nrhs) #endif END DO END DO END DO RETURN END SUBROUTINE prsgrd_tile