!--------------------------------------------------------------------------
   !---------------------------- compute_geopot ----------------------------------
   SELECT CASE(caldyn_thermo)
   CASE(thermo_boussinesq)
      ! use hydrostatic balance with theta*rhodz to find pk (=Lagrange multiplier=pressure)
      DO ij=ij_omp_begin_ext,ij_omp_end_ext
         pk(ij,llm) = ptop + .5*g* theta(ij,llm,1)*rhodz(ij,llm)
      END DO
      DO l = llm-1,1,-1
         DO ij=ij_omp_begin_ext,ij_omp_end_ext
            pk(ij,l) = pk(ij,l+1) + (.5*g)*( theta(ij,l,1)*rhodz(ij,l) + theta(ij,l+1,1)*rhodz(ij,l+1) )
         END DO
      END DO
      IF(caldyn_eta == eta_lag) THEN
         DO ij=ij_omp_begin_ext,ij_omp_end_ext
            ps(ij) = pk(ij,1) + .5*g* theta(ij,1,1)*rhodz(ij,1)
         END DO
      END IF
      ! now pk contains the Lagrange multiplier (pressure)
      ! specific volume 1 = dphi/g/rhodz
      DO l = 1,llm
         DO ij=ij_omp_begin_ext,ij_omp_end_ext
            geopot(ij,l+1) = geopot(ij,l) + g*rhodz(ij,l)
         END DO
      END DO
   CASE(thermo_theta)
      DO ij=ij_omp_begin_ext,ij_omp_end_ext
         pk(ij,llm) = ptop + .5*g* rhodz(ij,llm)
      END DO
      DO l = llm-1,1,-1
         DO ij=ij_omp_begin_ext,ij_omp_end_ext
            pk(ij,l) = pk(ij,l+1) + (.5*g)*( rhodz(ij,l) + rhodz(ij,l+1) )
         END DO
      END DO
      IF(caldyn_eta == eta_lag) THEN
         DO ij=ij_omp_begin_ext,ij_omp_end_ext
            ps(ij) = pk(ij,1) + .5*g* rhodz(ij,1)
         END DO
      END IF
      DO l = 1,llm
         DO ij=ij_omp_begin_ext,ij_omp_end_ext
            p_ik = pk(ij,l)
            exner_ik = cpp * (p_ik/preff) ** kappa
            gv = (g*kappa)*theta(ij,l,1)*exner_ik/p_ik
            pk(ij,l) = exner_ik
            geopot(ij,l+1) = geopot(ij,l) + gv*rhodz(ij,l)
         END DO
      END DO
   CASE(thermo_entropy)
      DO ij=ij_omp_begin_ext,ij_omp_end_ext
         pk(ij,llm) = ptop + .5*g* rhodz(ij,llm)
      END DO
      DO l = llm-1,1,-1
         DO ij=ij_omp_begin_ext,ij_omp_end_ext
            pk(ij,l) = pk(ij,l+1) + (.5*g)*( rhodz(ij,l) + rhodz(ij,l+1) )
         END DO
      END DO
      IF(caldyn_eta == eta_lag) THEN
         DO ij=ij_omp_begin_ext,ij_omp_end_ext
            ps(ij) = pk(ij,1) + .5*g* rhodz(ij,1)
         END DO
      END IF
      DO l = 1,llm
         DO ij=ij_omp_begin_ext,ij_omp_end_ext
            p_ik = pk(ij,l)
            temp_ik = Treff*exp((theta(ij,l,1) + Rd*log(p_ik/preff))/cpp)
            gv = (g*Rd)*temp_ik/p_ik ! specific volume v = Rd*T/p
            pk(ij,l) = temp_ik
            geopot(ij,l+1) = geopot(ij,l) + gv*rhodz(ij,l)
         END DO
      END DO
   CASE(thermo_moist)
      DO ij=ij_omp_begin_ext,ij_omp_end_ext
         pk(ij,llm) = ptop + .5*g* rhodz(ij,llm)*(1.+theta(ij,llm,2))
      END DO
      DO l = llm-1,1,-1
         DO ij=ij_omp_begin_ext,ij_omp_end_ext
            pk(ij,l) = pk(ij,l+1) + (.5*g)*( rhodz(ij,l)*(1.+theta(ij,l,2)) + rhodz(ij,l+1)*(1.+theta(ij,l+1,2)) )
         END DO
      END DO
      IF(caldyn_eta == eta_lag) THEN
         DO ij=ij_omp_begin_ext,ij_omp_end_ext
            ps(ij) = pk(ij,1) + .5*g* rhodz(ij,1)*(1.+theta(ij,1,2))
         END DO
      END IF
      DO l = 1,llm
         DO ij=ij_omp_begin_ext,ij_omp_end_ext
            p_ik = pk(ij,l)
            qv = theta(ij,l,2) ! water vaper mixing ratio = mv/md
            Rmix = Rd+qv*Rv
            chi = ( theta(ij,l,1) + Rmix*log(p_ik/preff) ) / (cpp + qv*cppv) ! log(T/Treff)
            temp_ik = Treff*exp(chi)
            ! specific volume v = R*T/p
            ! R = (Rd + qv.Rv)/(1+qv)
            gv = g*Rmix*temp_ik/(p_ik*(1+qv))
            pk(ij,l) = temp_ik
            geopot(ij,l+1) = geopot(ij,l) + gv*rhodz(ij,l)
         END DO
      END DO
   END SELECT
   !---------------------------- compute_geopot ----------------------------------
   !--------------------------------------------------------------------------