Index: /CONFIG/UNIFORM/v7/ICOLMDZOR_LAM_v7/SOURCES/DYNAMICO/arch/arch-X64_JEANZAY.fcm
===================================================================
--- /CONFIG/UNIFORM/v7/ICOLMDZOR_LAM_v7/SOURCES/DYNAMICO/arch/arch-X64_JEANZAY.fcm	(revision 6196)
+++ /CONFIG/UNIFORM/v7/ICOLMDZOR_LAM_v7/SOURCES/DYNAMICO/arch/arch-X64_JEANZAY.fcm	(revision 6197)
@@ -7,5 +7,5 @@
 %FPP_DEF             KEY_NONE CPP_NETCDF4
 %BASE_FFLAGS         -i4 -r8 -auto -align all -fp-model strict
-%PROD_FFLAGS         -g -traceback -O1
+%PROD_FFLAGS         -g -traceback -O3 -xHost -qopt-zmm-usage=high
 %DEV_FFLAGS          -g -O1 -traceback
 %DEBUG_FFLAGS        -g -traceback -check bounds 
Index: /CONFIG/UNIFORM/v7/ICOLMDZOR_LAM_v7/SOURCES/DYNAMICO/src/transport/advect.F90
===================================================================
--- /CONFIG/UNIFORM/v7/ICOLMDZOR_LAM_v7/SOURCES/DYNAMICO/src/transport/advect.F90	(revision 6197)
+++ /CONFIG/UNIFORM/v7/ICOLMDZOR_LAM_v7/SOURCES/DYNAMICO/src/transport/advect.F90	(revision 6197)
@@ -0,0 +1,464 @@
+MODULE advect_mod
+  USE icosa
+  IMPLICIT NONE 
+
+  PRIVATE
+  
+  PUBLIC :: init_advect, compute_backward_traj, compute_gradq3d, compute_advect_horiz
+
+CONTAINS
+
+  !==========================================================================
+
+  SUBROUTINE init_advect(normal,tangent,sqrt_leng)
+    IMPLICIT NONE
+    REAL(rstd),INTENT(OUT) :: normal(3*iim*jjm,3)
+    REAL(rstd),INTENT(OUT) :: tangent(3*iim*jjm,3)
+    REAL(rstd),INTENT(OUT) :: sqrt_leng(iim*jjm)
+
+    INTEGER :: ij
+
+!DIR$ SIMD
+      DO ij=ij_begin,ij_end
+
+          CALL cross_product2(xyz_v(ij+z_rdown,:),xyz_v(ij+z_rup,:),normal(ij+u_right,:))
+          normal(ij+u_right,:)=normal(ij+u_right,:)/sqrt(sum(normal(ij+u_right,:)**2)+1e-50)*ne(ij,right)
+
+          CALL cross_product2(xyz_v(ij+z_up,:),xyz_v(ij+z_lup,:),normal(ij+u_lup,:))
+          normal(ij+u_lup,:)=normal(ij+u_lup,:)/sqrt(sum(normal(ij+u_lup,:)**2)+1e-50)*ne(ij,lup)
+
+          CALL cross_product2(xyz_v(ij+z_ldown,:),xyz_v(ij+z_down,:),normal(ij+u_ldown,:))	 
+          normal(ij+u_ldown,:)=normal(ij+u_ldown,:)/sqrt(sum(normal(ij+u_ldown,:)**2)+1e-50)*ne(ij,ldown)
+
+          tangent(ij+u_right,:)=xyz_v(ij+z_rup,:)-xyz_v(ij+z_rdown,:) 
+          tangent(ij+u_right,:)=tangent(ij+u_right,:)/sqrt(sum(tangent(ij+u_right,:)**2)+1e-50)
+
+          tangent(ij+u_lup,:)=xyz_v(ij+z_lup,:)-xyz_v(ij+z_up,:) 
+          tangent(ij+u_lup,:)=tangent(ij+u_lup,:)/sqrt(sum(tangent(ij+u_lup,:)**2)+1e-50)
+
+          tangent(ij+u_ldown,:)=xyz_v(ij+z_down,:)-xyz_v(ij+z_ldown,:)
+          tangent(ij+u_ldown,:)=tangent(ij+u_ldown,:)/sqrt(sum(tangent(ij+u_ldown,:)**2)+1e-50)
+
+          sqrt_leng(ij) = sqrt(max(sum((xyz_v(ij+z_up,:) - xyz_i(ij,:))**2),sum((xyz_v(ij+z_down,:) - xyz_i(ij,:))**2), &
+                                   sum((xyz_v(ij+z_rup,:) - xyz_i(ij,:))**2),sum((xyz_v(ij+z_rdown,:) - xyz_i(ij,:))**2),  &
+                                   sum((xyz_v(ij+z_lup,:) - xyz_i(ij,:))**2),sum((xyz_v(ij+z_ldown,:) - xyz_i(ij,:))**2)) )
+    ENDDO
+
+  END SUBROUTINE init_advect
+
+  !=======================================================================================
+
+  SUBROUTINE compute_gradq3d(qi,sqrt_leng,gradq3d,xyz_i,xyz_v)
+    USE trace
+    USE omp_para
+    IMPLICIT NONE
+    REAL(rstd),INTENT(IN)  :: qi(iim*jjm,llm)
+    REAL(rstd),INTENT(IN)  :: sqrt_leng(iim*jjm)
+    REAL(rstd),INTENT(IN)  :: xyz_i(iim*jjm,3)
+    REAL(rstd),INTENT(IN)  :: xyz_v(2*iim*jjm,3)
+    REAL(rstd),INTENT(OUT) :: gradq3d(iim*jjm,llm,3)
+    REAL(rstd) :: maxq,minq,minq_c,maxq_c 
+    REAL(rstd) :: alphamx,alphami,alpha,maggrd
+    REAL(rstd) :: arr(2*iim*jjm)
+    REAL(rstd) :: ar(iim*jjm)
+    REAL(rstd) :: gradtri(2*iim*jjm,llm,3) 
+    INTEGER :: ij,k,l
+    REAL(rstd) :: detx,dety,detz,det
+    REAL(rstd) :: A(3,3), a11,a12,a13,a21,a22,a23,a31,a32,a33
+    REAL(rstd) :: x1,x2,x3
+    REAL(rstd) :: dq(3)
+    
+    CALL trace_start("compute_gradq3d1")
+
+    ! TODO : precompute ar, drop arr as output argument of gradq ?
+
+    !========================================================================================== GRADIENT 
+    ! Compute gradient at triangles solving a linear system
+    ! arr = area of triangle joining centroids of hexagons
+!     DO l = ll_begin,ll_end 
+!!DIR$ SIMD
+!      DO ij=ij_begin_ext,ij_end_ext
+!!             CALL gradq(ij,l,ij+t_rup,ij+t_lup,ij+z_up,qi,gradtri(ij+z_up,l,:),arr(ij+z_up))
+!!             CALL gradq(ij,l,ij+t_ldown,ij+t_rdown,ij+z_down,qi,gradtri(ij+z_down,l,:),arr(ij+z_down))
+!             CALL gradq(ij,l,ij+t_rup,ij+t_lup,ij+z_up,qi,gradtri(ij+z_up,l,1),gradtri(ij+z_up,l,2),gradtri(ij+z_up,l,3),arr(ij+z_up))
+!             CALL gradq(ij,l,ij+t_ldown,ij+t_rdown,ij+z_down,qi,gradtri(ij+z_down,l,1),gradtri(ij+z_down,l,2),gradtri(ij+z_down,l,3),arr(ij+z_down))
+!       END DO
+!    END DO
+
+     !$acc data create(gradtri(:,:,:), arr(:), ar(:)) present(sqrt_leng(:), xyz_i(:,:), xyz_v(:,:), qi(:,:), gradq3d(:,:,:)) async
+
+     !$acc parallel loop collapse(2) async private(A, dq)
+     DO l = ll_begin,ll_end
+!DIR$ SIMD
+      DO ij=ij_begin_ext,ij_end_ext
+!       CALL gradq(ij,l,ij+t_rup,ij+t_lup,ij+z_up,qi,gradtri(ij+z_up,l,1),gradtri(ij+z_up,l,2),gradtri(ij+z_up,l,3),arr(ij+z_up))
+
+        
+        A(1,1)=xyz_i(ij+t_rup,1)-xyz_i(ij,1);  A(1,2)=xyz_i(ij+t_rup,2)-xyz_i(ij,2); A(1,3)=xyz_i(ij+t_rup,3)-xyz_i(ij,3) 
+        A(2,1)=xyz_i(ij+t_lup,1)-xyz_i(ij,1);  A(2,2)=xyz_i(ij+t_lup,2)-xyz_i(ij,2); A(2,3)=xyz_i(ij+t_lup,3)-xyz_i(ij,3) 
+        A(3,1)=xyz_v(ij+z_up,1);               A(3,2)= xyz_v(ij+z_up,2);             A(3,3)=xyz_v(ij+z_up,3)
+    
+        dq(1) = qi(ij+t_rup,l)-qi(ij,l)
+        dq(2) = qi(ij+t_lup,l)-qi(ij,l)
+        dq(3) = 0.0
+
+
+!        CALL determinant(A(1,1),A(2,1),A(3,1),A(1,2),A(2,2),A(3,2),A(1,3),A(2,3),A(3,3),det)
+
+         a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1)
+         a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2)
+         a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3)
+
+         x1 =  a11 * (a22 * a33 - a23 * a32)
+         x2 =  a12 * (a21 * a33 - a23 * a31)
+         x3 =  a13 * (a21 * a32 - a22 * a31)
+         det =  x1 - x2 + x3
+                 
+!        CALL determinant(dq(1),dq(2),dq(3),A(1,2),A(2,2),A(3,2),A(1,3),A(2,3),A(3,3),detx)
+
+         a11=dq(1)  ; a12=dq(2)  ; a13=dq(3)
+         a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2)
+         a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3)
+
+         x1 =  a11 * (a22 * a33 - a23 * a32)
+         x2 =  a12 * (a21 * a33 - a23 * a31)
+         x3 =  a13 * (a21 * a32 - a22 * a31)
+         detx =  x1 - x2 + x3
+        
+!        CALL determinant(A(1,1),A(2,1),A(3,1),dq(1),dq(2),dq(3),A(1,3),A(2,3),A(3,3),dety)
+
+         a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1)
+         a21=dq(1)  ; a22=dq(2)  ; a23=dq(3)
+         a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3)
+
+         x1 =  a11 * (a22 * a33 - a23 * a32)
+         x2 =  a12 * (a21 * a33 - a23 * a31)
+         x3 =  a13 * (a21 * a32 - a22 * a31)
+         dety =  x1 - x2 + x3
+
+!        CALL determinant(A(1,1),A(2,1),A(3,1),A(1,2),A(2,2),A(3,2),dq(1),dq(2),dq(3),detz)
+
+         a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1)
+         a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2)
+         a31=dq(1)  ; a32=dq(2)  ; a33=dq(3)
+
+         x1 =  a11 * (a22 * a33 - a23 * a32)
+         x2 =  a12 * (a21 * a33 - a23 * a31)
+         x3 =  a13 * (a21 * a32 - a22 * a31)
+         detz =  x1 - x2 + x3
+
+        gradtri(ij+z_up,l,1) = detx
+        gradtri(ij+z_up,l,2) = dety
+        gradtri(ij+z_up,l,3) = detz
+        arr(ij+z_up) = det
+        
+      ENDDO
+     ENDDO
+      
+     !$acc parallel loop collapse(2) async private(A, dq)
+     DO l = ll_begin,ll_end
+      DO ij=ij_begin_ext,ij_end_ext
+
+
+!        CALL gradq(ij,l,ij+t_ldown,ij+t_rdown,ij+z_down,qi,gradtri(ij+z_down,l,1),gradtri(ij+z_down,l,2),gradtri(ij+z_down,l,3),arr(ij+z_down))
+
+        A(1,1)=xyz_i(ij+t_ldown,1)-xyz_i(ij,1);  A(1,2)=xyz_i(ij+t_ldown,2)-xyz_i(ij,2); A(1,3)=xyz_i(ij+t_ldown,3)-xyz_i(ij,3) 
+        A(2,1)=xyz_i(ij+t_rdown,1)-xyz_i(ij,1);  A(2,2)=xyz_i(ij+t_rdown,2)-xyz_i(ij,2); A(2,3)=xyz_i(ij+t_rdown,3)-xyz_i(ij,3) 
+        A(3,1)=xyz_v(ij+z_down,1);               A(3,2)= xyz_v(ij+z_down,2);             A(3,3)=xyz_v(ij+z_down,3)
+ 
+        dq(1) = qi(ij+t_ldown,l)-qi(ij,l)
+        dq(2) = qi(ij+t_rdown,l)-qi(ij,l)
+        dq(3) = 0.0
+
+
+!        CALL determinant(A(1,1),A(2,1),A(3,1),A(1,2),A(2,2),A(3,2),A(1,3),A(2,3),A(3,3),det)
+
+         a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1)
+         a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2)
+         a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3)
+
+         x1 =  a11 * (a22 * a33 - a23 * a32)
+         x2 =  a12 * (a21 * a33 - a23 * a31)
+         x3 =  a13 * (a21 * a32 - a22 * a31)
+         det =  x1 - x2 + x3
+                 
+!        CALL determinant(dq(1),dq(2),dq(3),A(1,2),A(2,2),A(3,2),A(1,3),A(2,3),A(3,3),detx)
+
+         a11=dq(1)  ; a12=dq(2)  ; a13=dq(3)
+         a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2)
+         a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3)
+
+         x1 =  a11 * (a22 * a33 - a23 * a32)
+         x2 =  a12 * (a21 * a33 - a23 * a31)
+         x3 =  a13 * (a21 * a32 - a22 * a31)
+         detx =  x1 - x2 + x3
+        
+!        CALL determinant(A(1,1),A(2,1),A(3,1),dq(1),dq(2),dq(3),A(1,3),A(2,3),A(3,3),dety)
+
+         a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1)
+         a21=dq(1)  ; a22=dq(2)  ; a23=dq(3)
+         a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3)
+
+         x1 =  a11 * (a22 * a33 - a23 * a32)
+         x2 =  a12 * (a21 * a33 - a23 * a31)
+         x3 =  a13 * (a21 * a32 - a22 * a31)
+         dety =  x1 - x2 + x3
+
+!        CALL determinant(A(1,1),A(2,1),A(3,1),A(1,2),A(2,2),A(3,2),dq(1),dq(2),dq(3),detz)
+
+         a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1)
+         a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2)
+         a31=dq(1)  ; a32=dq(2)  ; a33=dq(3)
+
+         x1 =  a11 * (a22 * a33 - a23 * a32)
+         x2 =  a12 * (a21 * a33 - a23 * a31)
+         x3 =  a13 * (a21 * a32 - a22 * a31)
+         detz =  x1 - x2 + x3
+
+         gradtri(ij+z_down,l,1) = detx
+         gradtri(ij+z_down,l,2) = dety
+         gradtri(ij+z_down,l,3) = detz
+         arr(ij+z_down) = det
+
+      END DO
+    END DO
+
+!DIR$ SIMD
+    !$acc parallel loop async
+    DO ij=ij_begin,ij_end
+       ar(ij) = arr(ij+z_up)+arr(ij+z_lup)+arr(ij+z_ldown)+arr(ij+z_down)+arr(ij+z_rdown)+arr(ij+z_rup)+1.e-50
+    ENDDO
+    CALL trace_end("compute_gradq3d1")
+    CALL trace_start2("compute_gradq3d2")
+      
+    !$acc parallel loop collapse(3) async
+    DO k=1,3
+      DO l =ll_begin,ll_end
+!DIR$ SIMD
+      DO ij=ij_begin,ij_end
+              gradq3d(ij,l,k) = ( gradtri(ij+z_up,l,k) + gradtri(ij+z_down,l,k)   +   &
+                                 gradtri(ij+z_rup,l,k) +  gradtri(ij+z_ldown,l,k)   +   & 
+                                 gradtri(ij+z_lup,l,k)+    gradtri(ij+z_rdown,l,k) ) / ar(ij)  
+        END DO
+      END DO
+    ENDDO
+    CALL trace_end2("compute_gradq3d2")
+    CALL trace_start("compute_gradq3d3")
+
+    !============================================================================================= LIMITING 
+    !$acc parallel loop collapse(2) async
+    DO l =ll_begin,ll_end
+!DIR$ SIMD
+      DO ij=ij_begin,ij_end
+!             maggrd =  dot_product_3d(gradq3d(ij,l,:),gradq3d(ij,l,:))
+             maggrd = gradq3d(ij,l,1)*gradq3d(ij,l,1) + gradq3d(ij,l,2)*gradq3d(ij,l,2) + gradq3d(ij,l,3)*gradq3d(ij,l,3) 
+             maggrd = sqrt(maggrd) 
+             maxq_c = qi(ij,l) + maggrd*sqrt_leng(ij)
+             minq_c = qi(ij,l) - maggrd*sqrt_leng(ij)
+             maxq = max(qi(ij,l),qi(ij+t_right,l),qi(ij+t_lup,l),qi(ij+t_rup,l),qi(ij+t_left,l), &
+                  qi(ij+t_rdown,l),qi(ij+t_ldown,l))
+             minq = min(qi(ij,l),qi(ij+t_right,l),qi(ij+t_lup,l),qi(ij+t_rup,l),qi(ij+t_left,l), &
+                  qi(ij+t_rdown,l),qi(ij+t_ldown,l))
+             IF ((maxq_c - qi(ij,l)) /= 0.0) THEN
+               alphamx = (maxq - qi(ij,l)) ; alphamx = alphamx/(maxq_c - qi(ij,l) )
+               alphamx = max(alphamx,0.0)
+             ELSE
+               alphamx = 0.0
+             ENDIF
+             IF ((minq_c - qi(ij,l)) /= 0.0) THEN
+               alphami = (minq - qi(ij,l)); alphami = alphami/(minq_c - qi(ij,l))
+               alphami = max(alphami,0.0)
+             ELSE
+               alphami = 0.0
+             ENDIF
+             alpha   = min(alphamx,alphami,1.0)
+!             gradq3d(ij,l,:) = alpha*gradq3d(ij,l,:)
+             gradq3d(ij,l,1) = alpha*gradq3d(ij,l,1)
+             gradq3d(ij,l,2) = alpha*gradq3d(ij,l,2)
+             gradq3d(ij,l,3) = alpha*gradq3d(ij,l,3)
+       END DO
+    END DO
+
+  CALL trace_end("compute_gradq3d3")
+
+  !$acc end data
+  
+  CONTAINS
+
+    SUBROUTINE gradq(n0,l,n1,n2,n3,q,dq1,dq2,dq3,det)
+    IMPLICIT NONE
+    INTEGER, INTENT(IN) :: n0,l,n1,n2,n3
+    REAL(rstd), INTENT(IN)     :: q(iim*jjm,llm)
+!    REAL(rstd), INTENT(OUT)    :: dq(3), det
+    REAL(rstd), INTENT(OUT)    :: dq1,dq2,dq3,det
+    REAL(rstd)    :: dq(3)
+
+    REAL(rstd) :: A(3,3)
+    
+    ! TODO : replace A by A1,A2,A3
+    A(1,1)=xyz_i(n1,1)-xyz_i(n0,1);  A(1,2)=xyz_i(n1,2)-xyz_i(n0,2); A(1,3)=xyz_i(n1,3)-xyz_i(n0,3) 
+    A(2,1)=xyz_i(n2,1)-xyz_i(n0,1);  A(2,2)=xyz_i(n2,2)-xyz_i(n0,2); A(2,3)=xyz_i(n2,3)-xyz_i(n0,3) 
+    A(3,1)=xyz_v(n3,1);              A(3,2)= xyz_v(n3,2);            A(3,3)=xyz_v(n3,3)
+
+    dq(1) = q(n1,l)-q(n0,l)
+    dq(2) = q(n2,l)-q(n0,l)
+    dq(3) = 0.0
+
+    !    CALL DGESV(3,1,A,3,IPIV,dq(:),3,info)
+!    CALL determinant(A(:,1),A(:,2),A(:,3),det)
+!    CALL determinant(dq,A(:,2),A(:,3),detx)
+!    CALL determinant(A(:,1),dq,A(:,3),dety)
+!    CALL determinant(A(:,1),A(:,2),dq,detz)
+!    dq(1) = detx
+!    dq(2) = dety
+!    dq(3) = detz 
+
+    CALL determinant(A(1,1),A(2,1),A(3,1),A(1,2),A(2,2),A(3,2),A(1,3),A(2,3),A(3,3),det)
+    CALL determinant(dq(1),dq(2),dq(3),A(1,2),A(2,2),A(3,2),A(1,3),A(2,3),A(3,3),dq1)
+    CALL determinant(A(1,1),A(2,1),A(3,1),dq(1),dq(2),dq(3),A(1,3),A(2,3),A(3,3),dq2)
+    CALL determinant(A(1,1),A(2,1),A(3,1),A(1,2),A(2,2),A(3,2),dq(1),dq(2),dq(3),dq3)
+
+  END SUBROUTINE gradq
+
+  !==========================================================================
+!  PURE SUBROUTINE determinant(a1,a2,a3,det)
+!    IMPLICIT NONE
+!    REAL(rstd), DIMENSION(3), INTENT(IN) :: a1,a2,a3
+!    REAL(rstd), INTENT(OUT) :: det
+!    REAL(rstd) ::  x1,x2,x3
+!    x1 =  a1(1) * (a2(2) * a3(3) - a2(3) * a3(2))
+!    x2 =  a1(2) * (a2(1) * a3(3) - a2(3) * a3(1))
+!    x3 =  a1(3) * (a2(1) * a3(2) - a2(2) * a3(1))
+!    det =  x1 - x2 + x3
+!  END SUBROUTINE determinant
+
+   SUBROUTINE determinant(a11,a12,a13,a21,a22,a23,a31,a32,a33,det)
+    IMPLICIT NONE
+    REAL(rstd), INTENT(IN) :: a11,a12,a13,a21,a22,a23,a31,a32,a33
+    REAL(rstd), INTENT(OUT) :: det
+    REAL(rstd) ::  x1,x2,x3
+    x1 =  a11 * (a22 * a33 - a23 * a32)
+    x2 =  a12 * (a21 * a33 - a23 * a31)
+    x3 =  a13 * (a21 * a32 - a22 * a31)
+    det =  x1 - x2 + x3
+  END SUBROUTINE determinant
+
+
+  END SUBROUTINE compute_gradq3d
+
+  ! Backward trajectories, for use with Miura approach
+  SUBROUTINE compute_backward_traj(normal,tangent,ue,tau, cc, &
+                                   xyz_e, de, wee, le         ) ! metrics terms
+    USE trace
+    USE omp_para
+    IMPLICIT NONE
+    REAL(rstd),INTENT(IN)    :: normal(3*iim*jjm,3)
+    REAL(rstd),INTENT(IN)    :: tangent(3*iim*jjm,3)
+    REAL(rstd),INTENT(IN)    :: ue(iim*3*jjm,llm)
+    REAL(rstd),INTENT(OUT)   :: cc(3*iim*jjm,llm,3) ! start of backward trajectory
+    REAL(rstd),INTENT(IN)    :: tau
+! metrics terms
+    REAL(rstd),INTENT(IN)    :: xyz_e(iim*3*jjm,3)
+    REAL(rstd),INTENT(IN)    :: de(iim*3*jjm)
+    REAL(rstd),INTENT(IN)    :: wee(iim*3*jjm,5,2)
+    REAL(rstd),INTENT(IN)    :: le(iim*3*jjm)
+
+    REAL(rstd) :: v_e(3), up_e   
+    INTEGER :: ij,l
+
+    CALL trace_start("compute_backward_traj")
+
+    ! TODO : compute normal displacement ue*tau as hfluxt / mass(upwind) then reconstruct tangential displacement
+
+    !$acc data present(ue(:,:), cc(:,:,:), normal(:,:), tangent(:,:), xyz_e(:,:), de(:), wee(:,:,:), le(:)) async
+
+    ! reconstruct tangential wind then 3D wind at edge then cc = edge midpoint - u*tau
+    !$acc parallel loop private(up_e, v_e) collapse(2) gang vector async
+    DO l = ll_begin,ll_end
+!DIR$ IVDEP
+      DO ij=ij_begin,ij_end
+             up_e =1/de(ij+u_right)*(                                                   &
+                  wee(ij+u_right,1,1)*le(ij+u_rup)*ue(ij+u_rup,l)+                        &
+                  wee(ij+u_right,2,1)*le(ij+u_lup)*ue(ij+u_lup,l)+                        &
+                  wee(ij+u_right,3,1)*le(ij+u_left)*ue(ij+u_left,l)+                      &
+                  wee(ij+u_right,4,1)*le(ij+u_ldown)*ue(ij+u_ldown,l)+                    &
+                  wee(ij+u_right,5,1)*le(ij+u_rdown)*ue(ij+u_rdown,l)+                    & 
+                  wee(ij+u_right,1,2)*le(ij+t_right+u_ldown)*ue(ij+t_right+u_ldown,l)+    &
+                  wee(ij+u_right,2,2)*le(ij+t_right+u_rdown)*ue(ij+t_right+u_rdown,l)+    &
+                  wee(ij+u_right,3,2)*le(ij+t_right+u_right)*ue(ij+t_right+u_right,l)+    &
+                  wee(ij+u_right,4,2)*le(ij+t_right+u_rup)*ue(ij+t_right+u_rup,l)+        &
+                  wee(ij+u_right,5,2)*le(ij+t_right+u_lup)*ue(ij+t_right+u_lup,l)         &
+                  )
+             v_e = ue(ij+u_right,l)*normal(ij+u_right,:) + up_e*tangent(ij+u_right,:)
+             cc(ij+u_right,l,:) = xyz_e(ij+u_right,:) - v_e*tau
+
+             up_e=1/de(ij+u_lup)*(                                                      &
+                  wee(ij+u_lup,1,1)*le(ij+u_left)*ue(ij+u_left,l)+                        &
+                  wee(ij+u_lup,2,1)*le(ij+u_ldown)*ue(ij+u_ldown,l)+                      &
+                  wee(ij+u_lup,3,1)*le(ij+u_rdown)*ue(ij+u_rdown,l)+                      &
+                  wee(ij+u_lup,4,1)*le(ij+u_right)*ue(ij+u_right,l)+                      &
+                  wee(ij+u_lup,5,1)*le(ij+u_rup)*ue(ij+u_rup,l)+                          & 
+                  wee(ij+u_lup,1,2)*le(ij+t_lup+u_right)*ue(ij+t_lup+u_right,l)+          &
+                  wee(ij+u_lup,2,2)*le(ij+t_lup+u_rup)*ue(ij+t_lup+u_rup,l)+              &
+                  wee(ij+u_lup,3,2)*le(ij+t_lup+u_lup)*ue(ij+t_lup+u_lup,l)+              &
+                  wee(ij+u_lup,4,2)*le(ij+t_lup+u_left)*ue(ij+t_lup+u_left,l)+            &
+                  wee(ij+u_lup,5,2)*le(ij+t_lup+u_ldown)*ue(ij+t_lup+u_ldown,l)           &
+                  )
+             v_e = ue(ij+u_lup,l)*normal(ij+u_lup,:) + up_e*tangent(ij+u_lup,:)
+             cc(ij+u_lup,l,:) = xyz_e(ij+u_lup,:) - v_e*tau
+            
+
+             up_e=1/de(ij+u_ldown)*(                                                    &
+                  wee(ij+u_ldown,1,1)*le(ij+u_rdown)*ue(ij+u_rdown,l)+                    &
+                  wee(ij+u_ldown,2,1)*le(ij+u_right)*ue(ij+u_right,l)+                    &
+                  wee(ij+u_ldown,3,1)*le(ij+u_rup)*ue(ij+u_rup,l)+                        &
+                  wee(ij+u_ldown,4,1)*le(ij+u_lup)*ue(ij+u_lup,l)+                        &
+                  wee(ij+u_ldown,5,1)*le(ij+u_left)*ue(ij+u_left,l)+                      & 
+                  wee(ij+u_ldown,1,2)*le(ij+t_ldown+u_lup)*ue(ij+t_ldown+u_lup,l)+        &
+                  wee(ij+u_ldown,2,2)*le(ij+t_ldown+u_left)*ue(ij+t_ldown+u_left,l)+      &
+                  wee(ij+u_ldown,3,2)*le(ij+t_ldown+u_ldown)*ue(ij+t_ldown+u_ldown,l)+    &
+                  wee(ij+u_ldown,4,2)*le(ij+t_ldown+u_rdown)*ue(ij+t_ldown+u_rdown,l)+    &
+                  wee(ij+u_ldown,5,2)*le(ij+t_ldown+u_right)*ue(ij+t_ldown+u_right,l)     &
+                  )
+             v_e = ue(ij+u_ldown,l)*normal(ij+u_ldown,:) + up_e*tangent(ij+u_ldown,:)
+             cc(ij+u_ldown,l,:) = xyz_e(ij+u_ldown,:) - v_e*tau
+       ENDDO
+    END DO
+    !$acc end data
+    CALL trace_end("compute_backward_traj")
+
+  END SUBROUTINE compute_backward_traj
+
+  ! Horizontal transport (S. Dubey, T. Dubos)
+  ! Slope-limited van Leer approach with hexagons
+  SUBROUTINE compute_advect_horiz(update_mass,diagflux_on, hfluxt,cc,gradq3d, mass, qi, qfluxt,  &
+                                  Ai, xyz_i)   ! metrics terms 
+    USE trace
+    USE omp_para
+    USE abort_mod
+    IMPLICIT NONE
+    LOGICAL, INTENT(IN)       :: update_mass, diagflux_on
+    REAL(rstd), INTENT(IN)    :: gradq3d(iim*jjm,llm,3) 
+    REAL(rstd), INTENT(IN)    :: hfluxt(3*iim*jjm,llm) ! mass flux
+    REAL(rstd), INTENT(IN)    :: cc(3*iim*jjm,llm,3)   ! barycenter of quadrilateral, where q is evaluated (1-point quadrature)
+    REAL(rstd), INTENT(INOUT) :: mass(iim*jjm,llm)
+    REAL(rstd), INTENT(INOUT) :: qi(iim*jjm,llm)
+    REAL(rstd), INTENT(INOUT) :: qfluxt(3*iim*jjm,MERGE(llm,1,diagflux_on)) ! time-integrated tracer flux
+! metrics terms
+    REAL(rstd), INTENT(IN)    :: Ai(iim*jjm)
+    REAL(rstd), INTENT(IN)    :: xyz_i(iim*jjm,3)
+    
+    REAL(rstd) :: dq,dmass,qe,newmass
+    REAL(rstd) :: qflux(3*iim*jjm,llm)
+    INTEGER :: ij,l,ij_tmp
+
+    IF(diagflux_on) CALL abort_acc("compute_advect_horiz : diagflux_on")
+
+    CALL trace_start("compute_advect_horiz")
+#include "../kernels/advect_horiz.k90"
+    CALL trace_end("compute_advect_horiz")
+
+  END SUBROUTINE compute_advect_horiz
+
+
+END MODULE advect_mod
