      SUBROUTINE biology (ng,tile)
!
!svn $Id$
!************************************************** Hernan G. Arango ***
!  Copyright (c) 2002-2020 The ROMS/TOMS Group        Craig V. Lewis   !
!    Licensed under a MIT/X style license                              !
!    See License_ROMS.txt                                              !
!***********************************************************************
!                                                                      !
!  Nutrient-Phytoplankton-Zooplankton-Detritus Model.                  !
!                                                                      !
!  This routine computes the biological sources and sinks and adds     !
!  then the global biological fields.                                  !
!                                                                      !
!  Reference:                                                          !
!                                                                      !
!    Franks et al, 1986: Behavior of simple plankton model with        !
!      food-level acclimation by herbivores, Marine Biology, 91,       !
!      121-129.                                                        !
!                                                                      !
!  Adapted from code written originally by Craig V. Lewis.             !
!                                                                      !
!***********************************************************************
!
      USE mod_param
      USE mod_grid
      USE mod_ncparam
      USE mod_ocean
      USE mod_stepping
!
!  Imported variable declarations.
!
      integer, intent(in) :: ng, tile
!
!  Local variable declarations.
!
#include "tile.h"
!
!  Set header file name.
!
#ifdef DISTRIBUTE
      IF (Lbiofile(iNLM)) THEN
#else
      IF (Lbiofile(iNLM).and.(tile.eq.0)) THEN
#endif
        Lbiofile(iNLM)=.FALSE.
        BIONAME(iNLM)=__FILE__
      END IF
!
#ifdef PROFILE
      CALL wclock_on (ng, iNLM, 15, __LINE__, __FILE__)
#endif
      CALL biology_tile (ng, tile,                                      &
     &                   LBi, UBi, LBj, UBj, N(ng), NT(ng),             &
     &                   IminS, ImaxS, JminS, JmaxS,                    &
     &                   nstp(ng), nnew(ng),                            &
#ifdef MASKING
     &                   GRID(ng) % rmask,                              &
#endif
     &                   GRID(ng) % Hz,                                 &
     &                   GRID(ng) % z_r,                                &
     &                   GRID(ng) % z_w,                                &
     &                   OCEAN(ng) % t)

#ifdef PROFILE
      CALL wclock_off (ng, iNLM, 15, __LINE__, __FILE__)
#endif
      RETURN
      END SUBROUTINE biology
!
!-----------------------------------------------------------------------
      SUBROUTINE biology_tile (ng, tile,                                &
     &                         LBi, UBi, LBj, UBj, UBk, UBt,            &
     &                         IminS, ImaxS, JminS, JmaxS,              &
     &                         nstp, nnew,                              &
#ifdef MASKING
     &                         rmask,                                   &
#endif
     &                         Hz, z_r, z_w,                            &
     &                         t)
!-----------------------------------------------------------------------
!
      USE mod_param
      USE mod_biology
      USE mod_ncparam
      USE mod_scalars
!
!  Imported variable declarations.
!
      integer, intent(in) :: ng, tile
      integer, intent(in) :: LBi, UBi, LBj, UBj, UBk, UBt
      integer, intent(in) :: IminS, ImaxS, JminS, JmaxS
      integer, intent(in) :: nstp, nnew

#ifdef ASSUMED_SHAPE
# ifdef MASKING
      real(r8), intent(in) :: rmask(LBi:,LBj:)
# endif
      real(r8), intent(in) :: Hz(LBi:,LBj:,:)
      real(r8), intent(in) :: z_r(LBi:,LBj:,:)
      real(r8), intent(in) :: z_w(LBi:,LBj:,0:)
      real(r8), intent(inout) :: t(LBi:,LBj:,:,:,:)
#else
# ifdef MASKING
      real(r8), intent(in) :: rmask(LBi:UBi,LBj:UBj)
# endif
      real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,UBk)
      real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,UBk)
      real(r8), intent(in) :: z_w(LBi:UBi,LBj:UBj,0:UBk)
      real(r8), intent(inout) :: t(LBi:UBi,LBj:UBj,UBk,3,UBt)
#endif
!
!  Local variable declarations.
!
      integer, parameter :: Nsink = 1

      integer :: Iter, i, ibio, isink, itrc, itrmx, j, k, ks

      integer, dimension(Nsink) :: idsink

      real(r8), parameter :: eps = 1.0e-16_r8

      real(r8) :: cff, cff1, cff2, cff3, dtdays
      real(r8) :: cffL, cffR, cu, dltL, dltR

      real(r8), dimension(Nsink) :: Wbio

      integer, dimension(IminS:ImaxS,N(ng)) :: ksource

      real(r8), dimension(IminS:ImaxS,N(ng),NT(ng)) :: Bio

      real(r8), dimension(IminS:ImaxS,N(ng),NT(ng)) :: Bio_old

      real(r8), dimension(IminS:ImaxS,0:N(ng)) :: FC

      real(r8), dimension(IminS:ImaxS,N(ng)) :: Hz_inv
      real(r8), dimension(IminS:ImaxS,N(ng)) :: Hz_inv2
      real(r8), dimension(IminS:ImaxS,N(ng)) :: Hz_inv3
      real(r8), dimension(IminS:ImaxS,N(ng)) :: WL
      real(r8), dimension(IminS:ImaxS,N(ng)) :: WR
      real(r8), dimension(IminS:ImaxS,N(ng)) :: bL
      real(r8), dimension(IminS:ImaxS,N(ng)) :: bR
      real(r8), dimension(IminS:ImaxS,N(ng)) :: qc

#include "set_bounds.h"
!
!-----------------------------------------------------------------------
!  Add biological Source/Sink terms.
!-----------------------------------------------------------------------
!
!  Avoid computing source/sink terms if no biological iterations.
!
      IF (BioIter(ng).le.0) RETURN
!
!  Set time-stepping according to the number of iterations.
!
      dtdays=dt(ng)*sec2day/REAL(BioIter(ng),r8)
!
!  Set vertical sinking indentification vector.
!
      idsink(1)=iSDet                 ! Small detritus
!
!  Set vertical sinking velocity vector in the same order as the
!  identification vector, IDSINK.
!
      Wbio(1)=wDet(ng)                ! Small detritus
!
!  Compute inverse thickness to avoid repeated divisions.
!
      J_LOOP : DO j=Jstr,Jend
        DO k=1,N(ng)
          DO i=Istr,Iend
            Hz_inv(i,k)=1.0_r8/Hz(i,j,k)
          END DO
        END DO
        DO k=1,N(ng)-1
          DO i=Istr,Iend
            Hz_inv2(i,k)=1.0_r8/(Hz(i,j,k)+Hz(i,j,k+1))
          END DO
        END DO
        DO k=2,N(ng)-1
          DO i=Istr,Iend
            Hz_inv3(i,k)=1.0_r8/(Hz(i,j,k-1)+Hz(i,j,k)+Hz(i,j,k+1))
          END DO
        END DO
!
!  Extract biological variables from tracer arrays, place them into
!  scratch arrays, and restrict their values to be positive definite.
!  At input, all tracers (index nnew) from predictor step have
!  transport units (m Tunits) since we do not have yet the new
!  values for zeta and Hz. These are known after the 2D barotropic
!  time-stepping.
!
        DO itrc=1,NBT
          ibio=idbio(itrc)
          DO k=1,N(ng)
            DO i=Istr,Iend
              Bio_old(i,k,ibio)=t(i,j,k,nstp,ibio)
            END DO
          END DO
        END DO
!
!  Determine Correction for negativity.
!
        DO k=1,N(ng)
          DO i=Istr,Iend
            cff1=MAX(0.0_r8,eps-Bio_old(i,k,iNO3_))+                    &
     &           MAX(0.0_r8,eps-Bio_old(i,k,iPhyt))+                    &
     &           MAX(0.0_r8,eps-Bio_old(i,k,iZoop))+                    &
     &           MAX(0.0_r8,eps-Bio_old(i,k,iSDet))
!
!  If correction needed, determine the largest pool to debit.
!
            IF (cff1.gt.0.0) THEN
              itrmx=idbio(1)
              cff=t(i,j,k,nstp,itrmx)
              DO ibio=idbio(2),idbio(NBT)
                IF (t(i,j,k,nstp,ibio).gt.cff) THEN
                  itrmx=ibio
                  cff=t(i,j,k,nstp,ibio)
                END IF
              END DO
!
!  Update new values.
!
              DO itrc=1,NBT
                ibio=idbio(itrc)
                Bio(i,k,ibio)=MAX(eps,Bio_old(i,k,ibio))-               &
     &                        cff1*(SIGN(0.5_r8,                        &
     &                                   REAL(itrmx-ibio,r8)**2)+       &
     &                              SIGN(0.5_r8,                        &
     &                                  -REAL(itrmx-ibio,r8)**2))
              END DO
            ELSE
              DO itrc=1,NBT
                ibio=idbio(itrc)
                Bio(i,k,ibio)=Bio_old(i,k,ibio)
              END DO
            END IF
          END DO
        END DO
!
!=======================================================================
!  Start internal iterations to achieve convergence of the nonlinear
!  backward-implicit solution.
!=======================================================================
!
!  During the iterative procedure a series of fractional time steps are
!  performed in a chained mode (splitting by different biological
!  conversion processes) in sequence of the main food chain.  In all
!  stages the concentration of the component being consumed is treated
!  in fully implicit manner, so the algorithm guarantees non-negative
!  values, no matter how strong s the concentration of active consuming
!  component (Phytoplankton or Zooplankton).  The overall algorithm,
!  as well as any stage of it, is formulated in conservative form
!  (except explicit sinking) in sense that the sum of concentration of
!  all components is conserved.
!
!  In the implicit algorithm, we have for example (N: nutrient,
!                                                  P: phytoplankton),
!
!     N(new) = N(old) - uptake * P(old)     uptake = mu * N / (Kn + N)
!                                                    {Michaelis-Menten}
!  below, we set
!                                           The N in the numerator of
!     cff = mu * P(old) / (Kn + N(old))     uptake is treated implicitly
!                                           as N(new)
!
!  so the time-stepping of the equations becomes:
!
!     N(new) = N(old) / (1 + cff)     (1) when substracting a sink term,
!                                         consuming, divide by (1 + cff)
!  and
!
!     P(new) = P(old) + cff * N(new)  (2) when adding a source term,
!                                         growing, add (cff * source)
!
!  Notice that if you substitute (1) in (2), you will get:
!
!     P(new) = P(old) + cff * N(old) / (1 + cff)    (3)
!
!  If you add (1) and (3), you get
!
!     N(new) + P(new) = N(old) + P(old)
!
!  implying conservation regardless how "cff" is computed. Therefore,
!  this scheme is unconditionally stable regardless of the conversion
!  rate. It does not generate negative values since the constituent
!  to be consumed is always treated implicitly. It is also biased
!  toward damping oscillations.
!
!  The iterative loop below is to iterate toward an universal Backward-
!  Euler treatment of all terms. So if there are oscillations in the
!  system, they are only physical oscillations. These iterations,
!  however, do not improve the accuaracy of the solution.
!
        ITER_LOOP: DO Iter=1,BioIter(ng)
!
!  Nutrient uptake by phytoplankton.
!
          cff1=dtdays*Vm_NO3(ng)
          DO k=1,N(ng)
            DO i=Istr,Iend
              cff=Bio(i,k,iPhyt)*                                       &
     &            cff1*EXP(K_ext(ng)*z_r(i,j,k))/                       &
     &            (K_NO3(ng)+Bio(i,k,iNO3_))
              Bio(i,k,iNO3_)=Bio(i,k,iNO3_)/                            &
     &                       (1.0_r8+cff)
              Bio(i,k,iPhyt)=Bio(i,k,iPhyt)+                            &
     &                       Bio(i,k,iNO3_)*cff
            END DO
          END DO
!
!  Phytoplankton grazing by Zooplankton and mortality to Detritus
!  (rate: PhyMR).
!
          cff1=dtdays*ZooGR(ng)
          cff2=dtdays*PhyMR(ng)
          cff3=K_phy(ng)*K_phy(ng)
          DO k=1,N(ng)
            DO i=Istr,Iend
              cff=Bio(i,k,iZoop)*Bio(i,k,iPhyt)*cff1/                   &
     &            (cff3+Bio(i,k,iPhyt)*Bio(i,k,iPhyt))
              Bio(i,k,iPhyt)=Bio(i,k,iPhyt)/                            &
     &                       (1.0_r8+cff+cff2)
              Bio(i,k,iZoop)=Bio(i,k,iZoop)+                            &
     &                       Bio(i,k,iPhyt)*cff*(1.0_r8-ZooGA(ng))
              Bio(i,k,iSDet)=Bio(i,k,iSDet)+                            &
     &                       Bio(i,k,iPhyt)*                            &
     &                       (cff2+cff*(ZooGA(ng)-ZooEC(ng)))
              Bio(i,k,iNO3_)=Bio(i,k,iNO3_)+                            &
     &                       Bio(i,k,iPhyt)*cff*ZooEC(ng)
            END DO
          END DO
!
!  Zooplankton excretion to nutrients and mortality to Detritus.
!
          cff1=1.0_r8/(1.0_r8+dtdays*(ZooMR(ng)+ZooMD(ng)))
          cff2=dtdays*ZooMR(ng)
          cff3=dtdays*ZooMD(ng)
          DO k=1,N(ng)
            DO i=Istr,Iend
              Bio(i,k,iZoop)=Bio(i,k,iZoop)*cff1
              Bio(i,k,iNO3_)=Bio(i,k,iNO3_)+                            &
     &                       Bio(i,k,iZoop)*cff2
              Bio(i,k,iSDet)=Bio(i,k,iSDet)+                            &
     &                       Bio(i,k,iZoop)*cff3
            END DO
          END DO
!
!  Detritus breakdown to nutrients.
!
          cff1=dtdays*DetRR(ng)
          cff2=1.0_r8/(1.0_r8+cff1)
           DO k=1,N(ng)
             DO i=Istr,Iend
               Bio(i,k,iSDet)=Bio(i,k,iSDet)*cff2
               Bio(i,k,iNO3_)=Bio(i,k,iNO3_)+                           &
     &                        Bio(i,k,iSDet)*cff1
            END DO
          END DO
!
!-----------------------------------------------------------------------
!  Vertical sinking terms.
!-----------------------------------------------------------------------
!
!  Reconstruct vertical profile of selected biological constituents
!  "Bio(:,:,isink)" in terms of a set of parabolic segments within each
!  grid box. Then, compute semi-Lagrangian flux due to sinking.
!
          SINK_LOOP: DO isink=1,Nsink
            ibio=idsink(isink)
!
!  Copy concentration of biological particulates into scratch array
!  "qc" (q-central, restrict it to be positive) which is hereafter
!  interpreted as a set of grid-box averaged values for biogeochemical
!  constituent concentration.
!
            DO k=1,N(ng)
              DO i=Istr,Iend
                qc(i,k)=Bio(i,k,ibio)
              END DO
            END DO
!
            DO k=N(ng)-1,1,-1
              DO i=Istr,Iend
                FC(i,k)=(qc(i,k+1)-qc(i,k))*Hz_inv2(i,k)
              END DO
            END DO
            DO k=2,N(ng)-1
              DO i=Istr,Iend
                dltR=Hz(i,j,k)*FC(i,k)
                dltL=Hz(i,j,k)*FC(i,k-1)
                cff=Hz(i,j,k-1)+2.0_r8*Hz(i,j,k)+Hz(i,j,k+1)
                cffR=cff*FC(i,k)
                cffL=cff*FC(i,k-1)
!
!  Apply PPM monotonicity constraint to prevent oscillations within the
!  grid box.
!
                IF ((dltR*dltL).le.0.0_r8) THEN
                  dltR=0.0_r8
                  dltL=0.0_r8
                ELSE IF (ABS(dltR).gt.ABS(cffL)) THEN
                  dltR=cffL
                ELSE IF (ABS(dltL).gt.ABS(cffR)) THEN
                  dltL=cffR
                END IF
!
!  Compute right and left side values (bR,bL) of parabolic segments
!  within grid box Hz(k); (WR,WL) are measures of quadratic variations.
!
!  NOTE: Although each parabolic segment is monotonic within its grid
!        box, monotonicity of the whole profile is not guaranteed,
!        because bL(k+1)-bR(k) may still have different sign than
!        qc(i,k+1)-qc(i,k).  This possibility is excluded,
!        after bL and bR are reconciled using WENO procedure.
!
                cff=(dltR-dltL)*Hz_inv3(i,k)
                dltR=dltR-cff*Hz(i,j,k+1)
                dltL=dltL+cff*Hz(i,j,k-1)
                bR(i,k)=qc(i,k)+dltR
                bL(i,k)=qc(i,k)-dltL
                WR(i,k)=(2.0_r8*dltR-dltL)**2
                WL(i,k)=(dltR-2.0_r8*dltL)**2
              END DO
            END DO
            cff=1.0E-14_r8
            DO k=2,N(ng)-2
              DO i=Istr,Iend
                dltL=MAX(cff,WL(i,k  ))
                dltR=MAX(cff,WR(i,k+1))
                bR(i,k)=(dltR*bR(i,k)+dltL*bL(i,k+1))/(dltR+dltL)
                bL(i,k+1)=bR(i,k)
              END DO
            END DO
            DO i=Istr,Iend
              FC(i,N(ng))=0.0_r8            ! NO-flux boundary condition
#if defined LINEAR_CONTINUATION
              bL(i,N(ng))=bR(i,N(ng)-1)
              bR(i,N(ng))=2.0_r8*qc(i,N(ng))-bL(i,N(ng))
#elif defined NEUMANN
              bL(i,N(ng))=bR(i,N(ng)-1)
              bR(i,N(ng))=1.5_r8*qc(i,N(ng))-0.5_r8*bL(i,N(ng))
#else
              bR(i,N(ng))=qc(i,N(ng))       ! default strictly monotonic
              bL(i,N(ng))=qc(i,N(ng))       ! conditions
              bR(i,N(ng)-1)=qc(i,N(ng))
#endif
#if defined LINEAR_CONTINUATION
              bR(i,1)=bL(i,2)
              bL(i,1)=2.0_r8*qc(i,1)-bR(i,1)
#elif defined NEUMANN
              bR(i,1)=bL(i,2)
              bL(i,1)=1.5_r8*qc(i,1)-0.5_r8*bR(i,1)
#else
              bL(i,2)=qc(i,1)               ! bottom grid boxes are
              bR(i,1)=qc(i,1)               ! re-assumed to be
              bL(i,1)=qc(i,1)               ! piecewise constant.
#endif
            END DO
!
!  Apply monotonicity constraint again, since the reconciled interfacial
!  values may cause a non-monotonic behavior of the parabolic segments
!  inside the grid box.
!
            DO k=1,N(ng)
              DO i=Istr,Iend
                dltR=bR(i,k)-qc(i,k)
                dltL=qc(i,k)-bL(i,k)
                cffR=2.0_r8*dltR
                cffL=2.0_r8*dltL
                IF ((dltR*dltL).lt.0.0_r8) THEN
                  dltR=0.0_r8
                  dltL=0.0_r8
                ELSE IF (ABS(dltR).gt.ABS(cffL)) THEN
                  dltR=cffL
                ELSE IF (ABS(dltL).gt.ABS(cffR)) THEN
                  dltL=cffR
                END IF
                bR(i,k)=qc(i,k)+dltR
                bL(i,k)=qc(i,k)-dltL
              END DO
            END DO
!
!  After this moment reconstruction is considered complete. The next
!  stage is to compute vertical advective fluxes, FC. It is expected
!  that sinking may occurs relatively fast, the algorithm is designed
!  to be free of CFL criterion, which is achieved by allowing
!  integration bounds for semi-Lagrangian advective flux to use as
!  many grid boxes in upstream direction as necessary.
!
!  In the two code segments below, WL is the z-coordinate of the
!  departure point for grid box interface z_w with the same indices;
!  FC is the finite volume flux; ksource(:,k) is index of vertical
!  grid box which contains the departure point (restricted by N(ng)).
!  During the search: also add in content of whole grid boxes
!  participating in FC.
!
            cff=dtdays*ABS(Wbio(isink))
            DO k=1,N(ng)
              DO i=Istr,Iend
                FC(i,k-1)=0.0_r8
                WL(i,k)=z_w(i,j,k-1)+cff
                WR(i,k)=Hz(i,j,k)*qc(i,k)
                ksource(i,k)=k
              END DO
            END DO
            DO k=1,N(ng)
              DO ks=k,N(ng)-1
                DO i=Istr,Iend
                  IF (WL(i,k).gt.z_w(i,j,ks)) THEN
                    ksource(i,k)=ks+1
                    FC(i,k-1)=FC(i,k-1)+WR(i,ks)
                  END IF
                END DO
              END DO
            END DO
!
!  Finalize computation of flux: add fractional part.
!
            DO k=1,N(ng)
              DO i=Istr,Iend
                ks=ksource(i,k)
                cu=MIN(1.0_r8,(WL(i,k)-z_w(i,j,ks-1))*Hz_inv(i,ks))
                FC(i,k-1)=FC(i,k-1)+                                    &
     &                    Hz(i,j,ks)*cu*                                &
     &                    (bL(i,ks)+                                    &
     &                     cu*(0.5_r8*(bR(i,ks)-bL(i,ks))-              &
     &                         (1.5_r8-cu)*                             &
     &                         (bR(i,ks)+bL(i,ks)-                      &
     &                          2.0_r8*qc(i,ks))))
              END DO
            END DO
            DO k=1,N(ng)
              DO i=Istr,Iend
                Bio(i,k,ibio)=qc(i,k)+(FC(i,k)-FC(i,k-1))*Hz_inv(i,k)
              END DO
            END DO

          END DO SINK_LOOP
        END DO ITER_LOOP
!
!-----------------------------------------------------------------------
!  Update global tracer variables: Add increment due to BGC processes
!  to tracer array in time index "nnew". Index "nnew" is solution after
!  advection and mixing and has transport units (m Tunits) hence the
!  increment is multiplied by Hz.  Notice that we need to subtract
!  original values "Bio_old" at the top of the routine to just account
!  for the concentractions affected by BGC processes. This also takes
!  into account any constraints (non-negative concentrations, carbon
!  concentration range) specified before entering BGC kernel. If "Bio"
!  were unchanged by BGC processes, the increment would be exactly
!  zero. Notice that final tracer values, t(:,:,:,nnew,:) are not
!  bounded >=0 so that we can preserve total inventory of nutrients
!  when advection causes tracer concentration to go negative.
!-----------------------------------------------------------------------
!
        DO itrc=1,NBT
          ibio=idbio(itrc)
          DO k=1,N(ng)
            DO i=Istr,Iend
              cff=Bio(i,k,ibio)-Bio_old(i,k,ibio)
              t(i,j,k,nnew,ibio)=t(i,j,k,nnew,ibio)+cff*Hz(i,j,k)
            END DO
          END DO
        END DO

      END DO J_LOOP

      RETURN
      END SUBROUTINE biology_tile
