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:

\[P_{edge}(I,J,L) = A_p(L) + B_p(L) \times P_{surface}(I,J)\]

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:

\[P_{midpoint}(I,J,L) = \frac{P_{edge}(I,J,L) + P_{edge}(I,J,L+1)}{2}\]

An \(\eta\) coordinate can be constructed from \(P_{edge}(I,J,L)\) and \(P_{midpoint}(I,J,L)\) as follows:

\[\eta_{edge}(I,J,L) = \frac{P_{edge}(I,J,L) - P_{top}}{P_{surface}(I,J) - P_{top}}\]
\[\eta_{midpoint}(I,J,L) = \frac{P_{midpoint}(I,J,L) - P_{top}}{P_{surface}(I,J) - P_{top}}\]

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.

positive:down level edge index

positive:up level edge index

\(A_p\) (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