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