.. _gchp-vgrids: ################### GCHP vertical grids ################### On this page we provide information about the vertical grid used by GCHP. .. _gchp-grids-hybrid: ====================== Hybrid grid definition ====================== A hybrid sigma-pressure grid (aka :math:`\eta` grid) uses a terrain-following coordinate near the surface, which then transitions to a purely fixed-pressure coordinate. The pressure at the bottom edge of grid box :math:`(I,J,L)` of a hybrid grid may be defined as: .. math:: P_{edge}(I,J,L) = A_p(L) + B_p(L) \times P_{surface}(I,J) where - :math:`(I,J,L)` are the lon, lat, and level indices of the grid box; - :math:`P_{surface}(I,J)` is the "true" surface pressure at lon,lat location :math:`(I,J)`; - :math:`A_p(L)` are constants in surface pressure units (Pa or hPa), defined at level edges; - :math:`B_p(L)` are unitless constants, defined at level edges. The values of :math:`A_p(L)` and :math:`B_p(L)` specify the vertical properties of the grid. In GEOS-Chem, you may find these values in source code file :file:`GeosUtil/pressure_mod.F90`. The pressure at the vertical midpoint of grid box :math:`(I,J,L)` is computed as the average of the pressures at successive vertical edges: .. math:: P_{midpoint}(I,J,L) = \frac{P_{edge}(I,J,L) + P_{edge}(I,J,L+1)}{2} An :math:`\eta` coordinate can be constructed from :math:`P_{edge}(I,J,L)` and :math:`P_{midpoint}(I,J,L)` as follows: .. math:: \eta_{edge}(I,J,L) = \frac{P_{edge}(I,J,L) - P_{top}}{P_{surface}(I,J) - P_{top}} .. math:: \eta_{midpoint}(I,J,L) = \frac{P_{midpoint}(I,J,L) - P_{top}}{P_{surface}(I,J) - P_{top}} where :math:`P_{top}` is pressure at the top level of the vertical grid. Specifics for GMAO vertical grids --------------------------------- The the :math:`P_{edge}(I,J,L)` and :math:`P_{midpoint}(I,J,L)` values in GMAO meteorological products vary with the topography up to 170 hPa. Skyward of 170 hPa, :math:`P_{edge}(I,J,L)` and :math:`P_{midpoint}(I,J,L)` remain constant for all longitudes and latitudes :math:`(I,J)`. GMAO meteorological products use a model top of 0.01 hPa. .. _gchp-vgrids_gmao: =================================== Vertical grids for GMAO meteorology =================================== .. _gchp-vgrids-gmao-72: 72-level vertical grid ---------------------- This grid is used by the `GEOS-FP `_, `GEOS-IT `_, and `MERRA-2 `_ meteorological field products from NASA GMAO. It has 72 vertical levels and 73 edges. .. _gchp-vgrids-gmao-72-ind: Indexing ~~~~~~~~ GCHP assumes :literal:`positive:down` indexing, where the surface is denoted as level 72 and top-of-atmosphere is denoted as level 1. The GCHP infrastructure flips input data in the vertical dimension before passing it to the GEOS-Chem science routines (which assume :literal:`positive:up` indexing). .. _gchp-vgrids-gmao-72-ab: :math:`A_p` and :math:`B_p` ~~~~~~~~~~~~~~~~~~~~~~~~~~~ The table below lists the :math:`A_p` and :math:`B_p` parameters that define the 72-level vertical grid. .. list-table:: :header-rows: 1 * - :literal:`positive:down` level edge index - :literal:`positive:up` level edge index - :math:`A_p` (hPa) - :math:`B_p` (unitless) * - 73 - 1 - 0.0 - 1.0 * - 72 - 2 - 0.04804826 - 0.984952 * - 71 - 3 - 6.593752 - 0.963406 * - 70 - 4 - 13.1348 - 0.941865 * - 69 - 5 - 19.61311 - 0.920387 * - 68 - 6 - 26.09201 - 0.898908 * - 67 - 7 - 32.57081 - 0.877429 * - 66 - 8 - 38.98201 - 0.856018 * - 65 - 9 - 45.33901 - 0.8346609 * - 64 - 10 - 51.69611 - 0.8133039 * - 63 - 11 - 58.05321 - 0.7919469 * - 62 - 12 - 64.36264 - 0.7706375 * - 61 - 13 - 70.62198 - 0.7493782 * - 60 - 14 - 78.83422 - 0.721166 * - 59 - 15 - 89.09992 - 0.6858999 * - 58 - 16 - 99.36521 - 0.6506349 * - 57 - 17 - 109.1817 - 0.6158184 * - 56 - 18 - 118.9586 - 0.5810415 * - 55 - 19 - 128.6959 - 0.5463042 * - 54 - 20 - 142.91 - 0.4945902 * - 53 - 21 - 156.26 - 0.4437402 * - 52 - 22 - 169.609 - 0.3928911 * - 51 - 23 - 181.619 - 0.3433811 * - 50 - 24 - 193.097 - 0.2944031 * - 49 - 25 - 203.259 - 0.2467411 * - 48 - 26 - 212.15 - 0.2003501 * - 47 - 27 - 218.776 - 0.1562241 * - 46 - 28 - 223.898 - 0.1136021 * - 45 - 29 - 224.363 - 0.06372006 * - 44 - 30 - 216.865 - 0.02801004 * - 43 - 31 - 201.192 - 0.006960025 * - 42 - 32 - 176.93 - 8.175413e-09 * - 41 - 33 - 150.393 - 0.0 * - 40 - 34 - 127.837 - 0.0 * - 39 - 35 - 108.663 - 0.0 * - 38 - 36 - 92.36572 - 0.0 * - 37 - 37 - 78.51231 - 0.0 * - 36 - 38 - 66.60341 - 0.0 * - 35 - 39 - 56.38791 - 0.0 * - 34 - 40 - 47.64391 - 0.0 * - 33 - 41 - 40.17541 - 0.0 * - 32 - 42 - 33.81001 - 0.0 * - 31 - 43 - 28.36781 - 0.0 * - 30 - 44 - 23.73041 - 0.0 * - 29 - 45 - 19.7916 - 0.0 * - 28 - 46 - 16.4571 - 0.0 * - 27 - 47 - 13.6434 - 0.0 * - 26 - 48 - 11.2769 - 0.0 * - 25 - 49 - 9.292942 - 0.0 * - 24 - 50 - 7.619842 - 0.0 * - 23 - 51 - 6.216801 - 0.0 * - 22 - 52 - 5.046801 - 0.0 * - 21 - 53 - 4.076571 - 0.0 * - 20 - 54 - 3.276431 - 0.0 * - 19 - 55 - 2.620211 - 0.0 * - 18 - 56 - 2.08497 - 0.0 * - 17 - 57 - 1.65079 - 0.0 * - 16 - 58 - 1.30051 - 0.0 * - 15 - 59 - 1.01944 - 0.0 * - 14 - 60 - 0.7951341 - 0.0 * - 13 - 61 - 0.6167791 - 0.0 * - 12 - 62 - 0.4758061 - 0.0 * - 11 - 63 - 0.3650411 - 0.0 * - 10 - 64 - 0.2785261 - 0.0 * - 9 - 65 - 0.211349 - 0.0 * - 8 - 66 - 0.159495 - 0.0 * - 7 - 67 - 0.119703 - 0.0 * - 6 - 68 - 0.08934502 - 0.0 * - 5 - 69 - 0.06600001 - 0.0 * - 4 - 70 - 0.04758501 - 0.0 * - 3 - 71 - 0.0327 - 0.0 * - 2 - 72 - 0.02 - 0.0 * - 1 - 73 - 0.01 - 0.0 .. _gchp-vgrids-gmao-72-prs-alt: Pressures and altitudes ~~~~~~~~~~~~~~~~~~~~~~~ The table below lists pressures and altitudes of the 72 layer grid for a column at atmospheric sea level. .. code-block:: text L L Eta Edge Eta Mid Altitude Pressure down up (unitless) (unitless) (km) (hPa) =================================================================== 0.000000 80.581 0.010 1 72 0.000005 78.146 0.015 0.000010 76.357 0.020 2 71 0.000016 74.594 0.026 0.000022 73.180 0.033 3 70 0.000030 71.812 0.040 0.000037 70.657 0.048 4 69 0.000046 69.440 0.057 0.000055 68.392 0.066 5 68 0.000067 67.243 0.078 0.000078 66.245 0.089 6 67 0.000093 65.115 0.105 0.000108 64.130 0.120 7 66 0.000128 63.004 0.140 0.000148 62.021 0.159 8 65 0.000173 60.902 0.185 0.000199 59.924 0.211 9 64 0.000232 58.816 0.245 0.000265 57.846 0.279 10 63 0.000308 56.752 0.322 0.000350 55.794 0.365 11 62 0.000405 54.717 0.420 0.000460 53.773 0.476 12 61 0.000529 52.716 0.546 0.000599 51.788 0.617 13 60 0.000687 50.754 0.706 0.000775 49.844 0.795 14 59 0.000886 48.835 0.907 0.000996 47.946 1.019 15 58 0.001135 46.962 1.160 0.001274 46.092 1.301 16 57 0.001446 45.134 1.476 0.001619 44.286 1.651 17 56 0.001834 43.355 1.868 0.002048 42.529 2.085 18 55 0.002312 41.627 2.353 0.002576 40.825 2.620 19 54 0.002900 39.951 2.948 0.003224 39.173 3.276 20 53 0.003619 38.328 3.677 0.004013 37.574 4.077 21 52 0.004492 36.759 4.562 0.004971 36.030 5.047 22 51 0.005548 35.244 5.632 0.006126 34.539 6.217 23 50 0.006818 33.782 6.918 0.007510 33.101 7.620 24 49 0.008336 32.372 8.456 0.009162 31.716 9.293 25 48 0.010141 31.015 10.285 0.011120 30.382 11.277 26 47 0.012287 29.701 12.460 0.013455 29.085 13.643 27 46 0.014844 28.423 15.050 0.016232 27.824 16.457 28 45 0.017878 27.180 18.124 0.019523 26.596 19.792 29 44 0.021467 25.971 21.761 0.023410 25.402 23.730 30 43 0.025699 24.794 26.049 0.027987 24.240 28.368 31 42 0.030673 23.648 31.089 0.033358 23.108 33.810 32 41 0.036499 22.531 36.993 0.039641 22.004 40.175 33 40 0.043326 21.438 43.910 0.047011 20.920 47.644 34 39 0.051326 20.364 52.016 0.055641 19.855 56.388 35 38 0.060682 19.309 61.496 0.065723 18.807 66.603 36 37 0.071600 18.269 72.558 0.077477 17.773 78.512 37 36 0.084313 17.243 85.439 0.091149 16.753 92.366 38 35 0.099191 16.222 100.514 0.107233 15.731 108.663 39 34 0.116695 15.198 118.250 0.126157 14.706 127.837 40 33 0.137287 14.170 139.115 0.148418 13.674 150.393 41 32 0.161513 13.134 163.661 0.174608 12.633 176.930 42 31 0.190061 12.086 192.587 0.205513 11.578 208.244 43 30 0.223772 11.021 226.745 0.242032 10.504 245.246 44 29 0.263587 9.936 267.087 0.285142 9.409 288.927 45 28 0.309854 8.846 313.966 0.334566 8.320 339.005 46 27 0.353349 7.943 358.038 0.372133 7.582 377.070 47 26 0.390927 7.237 396.112 0.409720 6.905 415.155 48 25 0.428528 6.585 434.212 0.447337 6.277 453.269 49 24 0.466153 5.980 472.335 0.484970 5.692 491.401 50 23 0.503795 5.413 510.475 0.522620 5.142 529.550 51 22 0.541449 4.879 548.628 0.560278 4.623 567.706 52 21 0.579115 4.375 586.793 0.597953 4.132 605.880 53 20 0.616790 3.896 624.967 0.635628 3.665 644.054 54 19 0.654471 3.439 663.146 0.673314 3.219 682.239 55 18 0.685878 3.074 694.969 0.698442 2.932 707.699 56 17 0.711006 2.792 720.429 0.723570 2.654 733.160 57 16 0.736134 2.517 745.890 0.748698 2.382 758.621 58 15 0.761265 2.249 771.354 0.773832 2.118 784.088 59 14 0.786400 1.988 796.822 0.798967 1.860 809.556 60 13 0.809021 1.759 819.743 0.819075 1.659 829.929 61 12 0.826616 1.584 837.570 0.834157 1.510 845.211 62 11 0.841698 1.436 852.852 0.849239 1.363 860.493 63 10 0.856781 1.290 868.135 0.864323 1.218 875.776 64 9 0.871864 1.146 883.418 0.879406 1.075 891.059 65 8 0.886948 1.004 898.701 0.894489 0.934 906.342 66 7 0.902031 0.864 913.984 0.909573 0.795 921.626 67 6 0.917116 0.726 929.268 0.924658 0.657 936.911 68 5 0.932200 0.589 944.553 0.939743 0.521 952.195 69 4 0.947285 0.454 959.837 0.954828 0.387 967.480 70 3 0.962370 0.320 975.122 0.969913 0.254 982.765 71 2 0.977456 0.189 990.408 0.984999 0.123 998.051 72 1 0.992500 0.058 1005.650 1.000000 -0.006 1013.250