| | 1 | = PDAF-OMI Observation Operators = |
| | 2 | |
| | 3 | [[PageOutline(2-3,Contents of this page)]] |
| | 4 | |
| | 5 | The observation operator is called for each observation type in the routine `obs_op_pdafomi` in the file `callback_obs_pdafomi.F90`. |
| | 6 | |
| | 7 | OMI currently provides 3 observation operators: |
| | 8 | - '''PDAFomi_obs_op_gridpoint'''[[br]] |
| | 9 | This observation operator is used for the case that observations are model variables located at grid points. Thus, the operation is to select single element from the state vector according to the index array `thisobs%id_obs_p` initialized in `init_dim_obs_f_TYPE`. |
| | 10 | - '''PDAFomi_obs_op_gridavg'''[[br]] |
| | 11 | This observation operator is used for the case that observations are the average of model variables at grid points. The averages are computed according to the number of rows in the index array `thisobs%id_obs_p` initialized in `init_dim_obs_f_TYPE`. |
| | 12 | - '''PDAFomi_obs_op_interp_lin'''[[br]] |
| | 13 | This observation operator computes the observation by linear interpolation. It uses the index array `thisobs%id_obs_p` and the array `thisobs%icoeff_p` holding interpolation coefficients initialized in `init_dim_obs_f_TYPE`. To use this observation operator, one has to allocate and initialize `thisobs%icoeff_p` as described below. |
| | 14 | |
| | 15 | The arguments of the observation operators are |
| | 16 | {{{ |
| | 17 | CALL PDAFomi_obs_op_X (thisobs,[nrows,] state_p, ostate) |
| | 18 | }}} |
| | 19 | Where `thisobs` is the observation type variable, `state_p` is the input state vector provided by PDAF and `ostate` is the observed state that will be returned to PDAF. `nrows` only exists for the observation operators X=gridavg and X=interp_lin and specifies the number of grid points involved in the observation operation. For X=gridpoint, this argument does not exist. |
| | 20 | |
| | 21 | |
| | 22 | == Initializing interpolation coefficients == |
| | 23 | |
| | 24 | The observation operator `PDAFomi_obs_op_interp_lin` requires that the interpolation coefficients have been initialized in the array `thisobs%icoeff_p`. This initialization is performed in `init_dim_obs_TYPE`. PDAF-OMI provides three routines for this task: |
| | 25 | - '''PDAFomi_get_interp_coeff_lin1D'''[[br]] |
| | 26 | Simplified initialization for 1-dimensional models |
| | 27 | - '''PDAFomi_get_interp_coeff_lin'''[[br]] |
| | 28 | Determine interpolation coefficients based on the coordinates of grid points and the observation for a rectangular grid in 1, 2, or 3 dimensions. |
| | 29 | - '''PDAFomi_get_interp_coeff_tri'''[[br]] |
| | 30 | Determine barycentric interpolation coefficients for triangular grids based on the coordinates of grid points and the observation |
| | 31 | |
| | 32 | An example of initializing interpolation coefficients with PDAFomi_get_interp_coeff_lin and of using PDAFomi_obs_op_interp_lin is provided in `tutorial/online_2D_serialmodel_omi/obs_C_pdafomi.F90`. |
| | 33 | |
| | 34 | === PDAFomi_get_interp_coeff_lin === |
| | 35 | |
| | 36 | |
| | 37 | The call to this routine is |
| | 38 | {{{ |
| | 39 | CALL PDAFomi_get_interp_coeff_lin(num_gp, n_dim, gcoords, ocoord, icoeff) |
| | 40 | |
| | 41 | INTEGER, INTENT(in) :: num_gp !< Length of thisobs%icoeff_p(:,i) |
| | 42 | INTEGER, INTENT(in) :: n_dim !< Number of dimensions in interpolation |
| | 43 | REAL, INTENT(in) :: gcoords(:,:) !< Coordinates of grid points |
| | 44 | REAL, INTENT(in) :: ocoord(:) !< Coordinates of observation (one column ocoord_p(:,i)) |
| | 45 | REAL, INTENT(inout) :: icoeff(:) !< Interpolation coefficients (one column thisobs%icoeff_p(:,i)) |
| | 46 | |
| | 47 | }}} |
| | 48 | Here it is required that num_gp=2 for n_dim=1; num_gp=4 for n_dim=2; num_gp=8 for n_dim=3. |
| | 49 | |
| | 50 | In the array `gcoords` in init_dim_obs_TYPE, the first index specifies the grid point while the second specifies the coordinate, thus gcoords(j,:) is the list of coordinates for grid point j. The coordinates need to be consistent with the indices specified in `thisobs%id_obs_p` since these specify the elements of the state vector that are interpolated. Only the first `n_dim` entries of ocoord will be used for the interpolation. |
| | 51 | |
| | 52 | `ocoord_p(:,i)` holds the list of the coordinates for the observation with index i. |
| | 53 | |
| | 54 | The order of the coordinates and coefficients is the following: |
| | 55 | {{{ |
| | 56 | (7)------(8) |
| | 57 | /| /| with |
| | 58 | (5)+-----(6)| - column 1 |
| | 59 | | | | | / column 2 |
| | 60 | |(3)-----+(4) | column 3 |
| | 61 | |/ |/ |
| | 62 | (1) ---- (2) |
| | 63 | |
| | 64 | thus gcoords(1,1)/=gcoords(2,1), but gcoords(1,1)=gcoords(3,1)=gcoords(5,1), |
| | 65 | gcoords(1,2)/=gcoords(3,2), gcoords(1,2)=gcoords(2,2)=gcoords(5,2), |
| | 66 | gcoords(1,3)/=gcoords(5,3) gcoords(1,3)=gcoords(2,3)=gcoords(3,3) |
| | 67 | }}} |
| | 68 | |
| | 69 | '''Notes:''' |
| | 70 | - For 1D linear interpolation (n_dim=1) only the coordinates for grid points 1 and 2 are used to compute the coefficients |
| | 71 | - For bi-linear interpolation (n_dim=2) only the coordinates for grid points 1, 2, and 3 are used to compute the coefficients |
| | 72 | - For tri-linear interpolation (n_dim=3) only the coordinates for grid points 1, 2, 3, and 5 are used to compute the coefficients |
| | 73 | |
| | 74 | |
