GCHP vertical grids
On this page we provide information about the vertical grid used by GCHP.
Hybrid grid definition
A hybrid sigma-pressure grid (aka \(\eta\) 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 \((I,J,L)\) of a hybrid grid may be defined as:
where
\((I,J,L)\) are the lon, lat, and level indices of the grid box;
\(P_{surface}(I,J)\) is the “true” surface pressure at lon,lat location \((I,J)\);
\(A_p(L)\) are constants in surface pressure units (Pa or hPa), defined at level edges;
\(B_p(L)\) are unitless constants, defined at level edges.
The values of \(A_p(L)\) and \(B_p(L)\) specify the vertical
properties of the grid. In GEOS-Chem, you may find these values in
source code file GeosUtil/pressure_mod.F90.
The pressure at the vertical midpoint of grid box \((I,J,L)\) is computed as the average of the pressures at successive vertical edges:
An \(\eta\) coordinate can be constructed from \(P_{edge}(I,J,L)\) and \(P_{midpoint}(I,J,L)\) as follows:
where \(P_{top}\) is pressure at the top level of the vertical grid.
Specifics for GMAO vertical grids
The the \(P_{edge}(I,J,L)\) and \(P_{midpoint}(I,J,L)\) values in GMAO meteorological products vary with the topography up to 170 hPa. Skyward of 170 hPa, \(P_{edge}(I,J,L)\) and \(P_{midpoint}(I,J,L)\) remain constant for all longitudes and latitudes \((I,J)\). GMAO meteorological products use a model top of 0.01 hPa.
Vertical grids for GMAO meteorology
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.
Indexing
GCHP assumes 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
positive:up indexing).
\(A_p\) and \(B_p\)
The table below lists the \(A_p\) and \(B_p\) parameters that define the 72-level vertical grid.
|
|
\(A_p\) (hPa) |
\(B_p\) (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 |
Pressures and altitudes
The table below lists pressures and altitudes of the 72 layer grid for a column at atmospheric sea level.
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