GEOS-Chem vertical grids

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On this page we provide information about the various vertical grids used in GEOS-Chem.

Vertical grid for GEOS-5, GEOS-FP, MERRA, and MERRA-2

72-layer vertical grid

Used by
Number of layers
  • 72 centers
  • 73 edges
Indexing
  • Surface upwards (in GEOS-Chem "Classic"); L=1 is the surface
  • Surface upwards (in met field files read in by GEOS-Chem); L=1 is the surface
  • Top down (in GMAO "raw" data files); L=1 is the atmosphere top
Type of grid
Hybrid A parameter [hPa] 
(surface)
0.000000d+00, 4.804826d-02, 6.593752d+00, 1.313480d+01, 1.961311d+01, 2.609201d+01,
3.257081d+01, 3.898201d+01, 4.533901d+01, 5.169611d+01, 5.805321d+01, 6.436264d+01,
7.062198d+01, 7.883422d+01, 8.909992d+01, 9.936521d+01, 1.091817d+02, 1.189586d+02,
1.286959d+02, 1.429100d+02, 1.562600d+02, 1.696090d+02, 1.816190d+02, 1.930970d+02,
2.032590d+02, 2.121500d+02, 2.187760d+02, 2.238980d+02, 2.243630d+02, 2.168650d+02,
2.011920d+02, 1.769300d+02, 1.503930d+02, 1.278370d+02, 1.086630d+02, 9.236572d+01,
7.851231d+01, 6.660341d+01, 5.638791d+01, 4.764391d+01, 4.017541d+01, 3.381001d+01,
2.836781d+01, 2.373041d+01, 1.979160d+01, 1.645710d+01, 1.364340d+01, 1.127690d+01,
9.292942d+00, 7.619842d+00, 6.216801d+00, 5.046801d+00, 4.076571d+00, 3.276431d+00,
2.620211d+00, 2.084970d+00, 1.650790d+00, 1.300510d+00, 1.019440d+00, 7.951341d-01,
6.167791d-01, 4.758061d-01, 3.650411d-01, 2.785261d-01, 2.113490d-01, 1.594950d-01,
1.197030d-01, 8.934502d-02, 6.600001d-02, 4.758501d-02, 3.270000d-02, 2.000000d-02,
1.000000d-02
(atm top)
Hybrid B parameter [1] 
(surface)
1.000000d+00, 9.849520d-01, 9.634060d-01, 9.418650d-01, 9.203870d-01, 8.989080d-01,
8.774290d-01, 8.560180d-01, 8.346609d-01, 8.133039d-01, 7.919469d-01, 7.706375d-01,
7.493782d-01, 7.211660d-01, 6.858999d-01, 6.506349d-01, 6.158184d-01, 5.810415d-01,
5.463042d-01, 4.945902d-01, 4.437402d-01, 3.928911d-01, 3.433811d-01, 2.944031d-01,
2.467411d-01, 2.003501d-01, 1.562241d-01, 1.136021d-01, 6.372006d-02, 2.801004d-02,
6.960025d-03, 8.175413d-09, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00,
0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00,
0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00,
0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00,
0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00,
0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00,
0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00,
0.000000d+00
(atm top)
Pressures and altitudes for a column at atmospheric sea level, from surface upwards 
 L     Eta Edge      Eta Mid     Altitude     Pressure 
      (unitless)   (unitless)        (km)        (hPa) 
========================================================
       0.000000                    80.581        0.010
72                  0.000005       78.146        0.015
       0.000010                    76.357        0.020
71                  0.000016       74.594        0.026
       0.000022                    73.180        0.033
70                  0.000030       71.812        0.040
       0.000037                    70.657        0.048
69                  0.000046       69.440        0.057
       0.000055                    68.392        0.066
68                  0.000067       67.243        0.078
       0.000078                    66.245        0.089
67                  0.000093       65.115        0.105
       0.000108                    64.130        0.120
66                  0.000128       63.004        0.140
       0.000148                    62.021        0.159
65                  0.000173       60.902        0.185
       0.000199                    59.924        0.211
64                  0.000232       58.816        0.245
       0.000265                    57.846        0.279
63                  0.000308       56.752        0.322
       0.000350                    55.794        0.365
62                  0.000405       54.717        0.420
       0.000460                    53.773        0.476
61                  0.000529       52.716        0.546
       0.000599                    51.788        0.617
60                  0.000687       50.754        0.706
       0.000775                    49.844        0.795
59                  0.000886       48.835        0.907
       0.000996                    47.946        1.019
58                  0.001135       46.962        1.160
       0.001274                    46.092        1.301
57                  0.001446       45.134        1.476
       0.001619                    44.286        1.651
56                  0.001834       43.355        1.868
       0.002048                    42.529        2.085
55                  0.002312       41.627        2.353
       0.002576                    40.825        2.620
54                  0.002900       39.951        2.948
       0.003224                    39.173        3.276
53                  0.003619       38.328        3.677
       0.004013                    37.574        4.077
52                  0.004492       36.759        4.562
       0.004971                    36.030        5.047
51                  0.005548       35.244        5.632
       0.006126                    34.539        6.217
50                  0.006818       33.782        6.918
       0.007510                    33.101        7.620
49                  0.008336       32.372        8.456
       0.009162                    31.716        9.293
48                  0.010141       31.015       10.285
       0.011120                    30.382       11.277
47                  0.012287       29.701       12.460
       0.013455                    29.085       13.643
46                  0.014844       28.423       15.050
       0.016232                    27.824       16.457
45                  0.017878       27.180       18.124
       0.019523                    26.596       19.792
44                  0.021467       25.971       21.761
       0.023410                    25.402       23.730
43                  0.025699       24.794       26.049
       0.027987                    24.240       28.368
42                  0.030673       23.648       31.089
       0.033358                    23.108       33.810
41                  0.036499       22.531       36.993
       0.039641                    22.004       40.175
40                  0.043326       21.438       43.910
       0.047011                    20.920       47.644
39                  0.051326       20.364       52.016
       0.055641                    19.855       56.388
38                  0.060682       19.309       61.496
       0.065723                    18.807       66.603
37                  0.071600       18.269       72.558
       0.077477                    17.773       78.512
36                  0.084313       17.243       85.439
       0.091149                    16.753       92.366
35                  0.099191       16.222      100.514
       0.107233                    15.731      108.663
34                  0.116695       15.198      118.250
       0.126157                    14.706      127.837
33                  0.137287       14.170      139.115
       0.148418                    13.674      150.393
32                  0.161513       13.134      163.661
       0.174608                    12.633      176.930
31                  0.190061       12.086      192.587
       0.205513                    11.578      208.244
30                  0.223772       11.021      226.745
       0.242032                    10.504      245.246
29                  0.263587        9.936      267.087
       0.285142                     9.409      288.927
28                  0.309854        8.846      313.966
       0.334566                     8.320      339.005
27                  0.353349        7.943      358.038
       0.372133                     7.582      377.070
26                  0.390927        7.237      396.112
       0.409720                     6.905      415.155
25                  0.428528        6.585      434.212
       0.447337                     6.277      453.269
24                  0.466153        5.980      472.335
       0.484970                     5.692      491.401
23                  0.503795        5.413      510.475
       0.522620                     5.142      529.550
22                  0.541449        4.879      548.628
       0.560278                     4.623      567.706
21                  0.579115        4.375      586.793
       0.597953                     4.132      605.880
20                  0.616790        3.896      624.967
       0.635628                     3.665      644.054
19                  0.654471        3.439      663.146
       0.673314                     3.219      682.239
18                  0.685878        3.074      694.969
       0.698442                     2.932      707.699
17                  0.711006        2.792      720.429
       0.723570                     2.654      733.160
16                  0.736134        2.517      745.890
       0.748698                     2.382      758.621
15                  0.761265        2.249      771.354
       0.773832                     2.118      784.088
14                  0.786400        1.988      796.822
       0.798967                     1.860      809.556
13                  0.809021        1.759      819.743
       0.819075                     1.659      829.929
12                  0.826616        1.584      837.570
       0.834157                     1.510      845.211
11                  0.841698        1.436      852.852
       0.849239                     1.363      860.493
10                  0.856781        1.290      868.135
       0.864323                     1.218      875.776
 9                  0.871864        1.146      883.418
       0.879406                     1.075      891.059
 8                  0.886948        1.004      898.701
       0.894489                     0.934      906.342
 7                  0.902031        0.864      913.984
       0.909573                     0.795      921.626
 6                  0.917116        0.726      929.268
       0.924658                     0.657      936.911
 5                  0.932200        0.589      944.553
       0.939743                     0.521      952.195
 4                  0.947285        0.454      959.837
       0.954828                     0.387      967.480
 3                  0.962370        0.320      975.122
       0.969913                     0.254      982.765
 2                  0.977456        0.189      990.408
       0.984999                     0.123      998.051
 1                  0.992500        0.058     1005.650
       1.000000                    -0.006     1013.250

47-layer reduced vertical grid

The GEOS-5.2.0, MERRA, MERRA-2, and GEOS-FP native 72-layer grids are all identical. GEOS-Chem collapses this down to a 47-level grid, as follows. Groups of 2 and 4 layers are lumped together starting at ~70 hPa. 

GEOS-5.2.0 / MERRA / MERRA-2 / GEOS-FP  47-level reduced vertical grid
 
 Bottom   Bottom    # levels
 edge of  edge prs  lumped 
 level    (hPa)     together

  PTOP       0.010   
   47        0.066     4
   46        0.211     4
   45        0.617     4
   44        1.651     4
   43        4.077     4
   42        9.293     4
   41       19.792     4
   40       28.368     2
   39       40.175     2
   38       56.388     2
   37       78.512     2
%%%% START LUMPING LEVELS ABOVE HERE %%%%%
   36       92.366       
   35      108.663
   34      127.837
   33      150.393
   32      176.930
%%%% FIXED-PRESSURE LEVELS BEGIN HERE %%%%
Used by
Number of layers
  • 72 centers
  • 73 edges
Indexing
  • Surface upwards (in GEOS-Chem "Classic"); L=1 is the surface
  • Surface upwards (in met field files read in by GEOS-Chem); L=1 is the surface
  • Top down (in GMAO "raw" data files); L=1 is the atmosphere top
Type of grid
Hybrid A parameter [hPa] 
(surface)
0.000000d+00, 4.804826d-02, 6.593752d+00, 1.313480d+01, 1.961311d+01, 2.609201d+01,
3.257081d+01, 3.898201d+01, 4.533901d+01, 5.169611d+01, 5.805321d+01, 6.436264d+01,
7.062198d+01, 7.883422d+01, 8.909992d+01, 9.936521d+01, 1.091817d+02, 1.189586d+02,
1.286959d+02, 1.429100d+02, 1.562600d+02, 1.696090d+02, 1.816190d+02, 1.930970d+02,
2.032590d+02, 2.121500d+02, 2.187760d+02, 2.238980d+02, 2.243630d+02, 2.168650d+02,
2.011920d+02, 1.769300d+02, 1.503930d+02, 1.278370d+02, 1.086630d+02, 9.236572d+01,
7.851231d+01, 5.638791d+01, 4.017541d+01, 2.836781d+01, 1.979160d+01, 9.292942d+00,
4.076571d+00, 1.650790d+00, 6.167791d-01, 2.113490d-01, 6.600001d-02, 1.000000d-02
(atm top)
Hybrid B parameter [1] 
(surface)
1.000000d+00, 9.849520d-01, 9.634060d-01, 9.418650d-01, 9.203870d-01, 8.989080d-01,
8.774290d-01, 8.560180d-01, 8.346609d-01, 8.133039d-01, 7.919469d-01, 7.706375d-01,
7.493782d-01, 7.211660d-01, 6.858999d-01, 6.506349d-01, 6.158184d-01, 5.810415d-01,
5.463042d-01, 4.945902d-01, 4.437402d-01, 3.928911d-01, 3.433811d-01, 2.944031d-01,
2.467411d-01, 2.003501d-01, 1.562241d-01, 1.136021d-01, 6.372006d-02, 2.801004d-02,
6.960025d-03, 8.175413d-09, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00,
0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00,
0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00, 0.000000d+00
(atm top)
Pressures and altitudes for a column at atmospheric sea level, from surface upwards 
 L     Eta Edge     Eta Mid     Altitude     Pressure
     (unitless)   (unitless)        (km)        (hPa)
========================================================
       0.000000                    80.581        0.010
47                  0.000028       72.180        0.038
       0.000055                    68.392        0.066
46                  0.000127       63.053        0.139
       0.000199                    59.924        0.211
45                  0.000399       54.834        0.414
       0.000599                    51.788        0.617
44                  0.001109       47.135        1.134
       0.001619                    44.286        1.651
43                  0.002816       40.166        2.864
       0.004013                    37.574        4.077
42                  0.006588       34.024        6.685
       0.009162                    31.716        9.293
41                  0.014342       28.654       14.542
       0.019523                    26.596       19.792
40                  0.023755       25.307       24.080
       0.027987                    24.240       28.368
39                  0.033814       23.020       34.272
       0.039641                    22.004       40.175
38                  0.047641       20.836       48.282
       0.055641                    19.855       56.388
37                  0.066559       18.727       67.450
       0.077477                    17.773       78.512
36                  0.084313       17.243       85.439
       0.091149                    16.753       92.366
35                  0.099191       16.222      100.514
       0.107233                    15.731      108.663
34                  0.116695       15.198      118.250
       0.126157                    14.706      127.837
33                  0.137287       14.170      139.115
       0.148418                    13.674      150.393
32                  0.161513       13.134      163.661
       0.174608                    12.633      176.930
31                  0.190061       12.086      192.587
       0.205513                    11.578      208.244
30                  0.223772       11.021      226.745
       0.242032                    10.504      245.246
29                  0.263587        9.936      267.087
       0.285142                     9.409      288.927
28                  0.309854        8.846      313.966
       0.334566                     8.320      339.005
27                  0.353349        7.943      358.038
       0.372133                     7.582      377.070
26                  0.390927        7.237      396.112
       0.409720                     6.905      415.155
25                  0.428528        6.585      434.212
       0.447337                     6.277      453.269
24                  0.466153        5.980      472.335
       0.484970                     5.692      491.401
23                  0.503795        5.413      510.475
       0.522620                     5.142      529.550
22                  0.541449        4.879      548.628
       0.560278                     4.623      567.706
21                  0.579115        4.375      586.793
       0.597953                     4.132      605.880
20                  0.616790        3.896      624.967
       0.635628                     3.665      644.054
19                  0.654471        3.439      663.146
       0.673314                     3.219      682.239
18                  0.685878        3.074      694.969
       0.698442                     2.932      707.699
17                  0.711006        2.792      720.429
       0.723570                     2.654      733.160
16                  0.736134        2.517      745.890
       0.748698                     2.382      758.621
15                  0.761265        2.249      771.354
       0.773832                     2.118      784.088
14                  0.786400        1.988      796.822
       0.798967                     1.860      809.556
13                  0.809021        1.759      819.743
       0.819075                     1.659      829.929
12                  0.826616        1.584      837.570
       0.834157                     1.510      845.211
11                  0.841698        1.436      852.852
       0.849239                     1.363      860.493
10                  0.856781        1.290      868.135
       0.864323                     1.218      875.776
 9                  0.871864        1.146      883.418
       0.879406                     1.075      891.059
 8                  0.886948        1.004      898.701
       0.894489                     0.934      906.342
 7                  0.902031        0.864      913.984
       0.909573                     0.795      921.626
 6                  0.917116        0.726      929.268
       0.924658                     0.657      936.911
 5                  0.932200        0.589      944.553
       0.939743                     0.521      952.195
 4                  0.947285        0.454      959.837
       0.954828                     0.387      967.480
 3                  0.962370        0.320      975.122
       0.969913                     0.254      982.765
 2                  0.977456        0.189      990.408
       0.984999                     0.123      998.051
 1                  0.992500        0.058     1005.650
       1.000000                    -0.006     1013.250

GEOS-4 vertical grid

GEOS-3 vertical grid

GCAP vertical grid

Reference

Sigma grid

The sigma grid is a purely terrain-following coordinate. The following met data products are defined on the sigma grid:

  1. GMAO GEOS-3 (NOTE: Now obsolete)
  2. GCAP/GISS meteroloogy
    • NOTE: GCAP met is really a hybrid grid, but it is defined as if it were a pure sigma grid (i.e. PTOP=150 hPa, and negative sigma edges at higher levels.

The sigma grid is defined as follows: 

           P(I,J,L)     - PTOP
   σ(L)= ------------------------
           Psurface(I,J) - PTOP

where: 

   I,J,L         are the longitude, latitude, level indices of the grid box
   P(I,J,L)      is the pressure at a level edge or level center at grid box (I,J,L)
   Psurface(I,J)  is the surface pressure at grid box (I,J)
   PTOP          is the pressure at the top of the atmosphere

σ(L) always varies between 0 and 1, with 1 being the surface and 0 being the atmosphere top. Therefore you can think of σ(L) as the "fraction" of the atmosphere (measured from the top down) at which you are located.

The σ(L) therefore are independent of (I,J). The sigma values are typically fixed for a given met field type. Knowing the sigma value allows you to compute the center or edge pressures as follows: 

   Pedge(I,J,L)   = σedge(L) * [ Psurface(I,J) - PTOP ] + PTOP

   Pcenter(I,J,L) = σcenter(L) * [ Psurface(I,J) - PTOP ] + PTOP

Any sigma grid can also be computed with the hybrid grid equation: 

   Pedge(I,J,L)   = Ap(L) + [ Bp(L) * ( Psurface(I,J) - PTOP ) ]

   Pcenter(I,J,L) = [ Pedge(I,J,L) + Pedge(I,J,L+1) ] / 2

where 

   Psurface(I,J) = the "true" surface pressure at lon,lat (I,J)
   Ap(L)        = PTOP    = model top pressure
   Bp(L)        = σedge(L) = bottom sigma edge of level L

Hybrid grid definition

Earlier versions of the GMAO met data products used a pure-sigma grid definition. The problem with a sigma-grid is that you still see the signature of the mountains at the very top of the atmosphere. This was the case in GEOS-3 and this caused a lot of noise in the stratospheric winds, which led to poor STE.

The improvement on the sigma grid is the hybrid (or η) grid. This grid is defined with A and B coefficients, which are specified by the makers of the met data products (e.g. GMAO).

The following met data products use the hybrid grid formulation:

  1. GMAO GEOS-4
  2. GMAO GEOS-5
  3. GMAO MERRA
  4. GMAO MERRA-2
  5. GMAO GEOS-FP

The pressure at the bottom edge of grid box (I,J,L) is defined as follows: 

    Pedge(I,J,L) = Ap(L) + [ Bp(L) * Psurface(I,J) ]

    Pcenter(I,J,L) = [ Pedge(I,J,L) + Pedge(I,J,L) ] / 2

where 

    I,J,L        are the lon, lat, level indices of the grid box
    Psurface(I,J) is  the "true" surface pressure at lon,lat (I,J)
    Ap(L)        has the same units as surface pressure [hPa]
    Bp(L)        is  a unitless constant given at level edges

The Ap(L) and Bp(L) for each met field type are listed in the GEOS-Chem source code file pressure_mod.f.

The hybrid grid formula in more depth

Rebecca Buchholz wrote:

I'm having trouble conceptualising exactly how GEOS-Chem deals with the vertical grid. I'm using the GEOS-5 reduced vertical resolution of 47 eta levels. I've seen the AMS definition of eta.
I can see the first fraction is the sigma definition (which follows terrain). Is the second fraction essentially a scaling by the pressure at altitude relative to pressure at sea surface? I'm not sure how it fits in with the GEOS-Chem definition, i.e. when rearranging the equation, what becomes A_p and B_p.
The manual and wiki pages indicate GEOS-5 is a hybrid pressure-sigma grid. Are the first 31 levels pure sigma levels in both the reduced vertical 47 and native 72 level GEOS-5 fields? Does this mean GEOS-5 doesn't use the above eta definition of the levels - only sigma definition? Does GEOS-Chem then change the sigma levels to eta levels?

Bob Yantosca replied:

Maybe we have used “eta” as a synonym for “hybrid” grid. Basically it refers to a grid that transitions smoothly from a sigma terrain-following coordinate near the surface to fixed pressure levels in the upper atmosphere.
Older met fields (e.g. GEOS-3) came on pure-sigma grids. However, the problem is that with a pure-sigma grid, you still see some signal of the mountains even at the top of the atmosphere. This makes the upper-atmosphere winds very noisy and it messes up the strat-trop exchange. (Or so GMAO tells us.)
The way I like to think of it is we specify the pressure at the bottom edge of grid box (I,J,L) with this formula:
   Pedge(I,J,L) = Ap(L) + [ Bp(L) * Psurface(I,J) ]
where Ap(L) and Bp(L) are specified by GMAO. Then you specify the pressures at the center of grid box (I,J,L) with this formula:
   Pcenter(I,J,L) = [ Pedge(I,J,L) + Pedge(I,J,L+1) ] / 2
i.e. it’s an average of the pressure at both edges.
Note that the Pedge(I,J,L) and Pcenter(I,J,L) vary w/ the topography up until about 170 hPa. That is where the first fixed-pressure levels occur. Skyward of that, then Pedge(I,J,L) and Pcenter(I,J,L) will be constant for all longitudes and latitudes (I,J).
Once you have computed Pedge(I,J,L) and Pcenter(I,J,L), you can construct an ETA coordinate such as:
   ETAedge(I,J,L)   = [ Pedge(I,J,L)   – Ptop ] / [ Psurface – Ptop ]

   ETAcenter(I,J,L) = [ Pcenter(I,J,L) – Ptop ] / [ Psurface – Ptop ]
but for the purposes of GEOS-Chem, we don’t really use the ETA values. We use the pressures computed from the Ap(L) and Bp(L) values.
The most important thing to note is that the thicknesses of the grid boxes near the surface vary with the surface pressure. When you come to a mountain, the levels all kind of bunch together and get small. When you are over flat land or ocean, the levels widen out.
Also note that a pure-sigma grid (like GEOS-3) can also be expressed using the same type of hybrid formulation:
  Pedge(I,J,L) = Ap(L) + [ Bp(L) * ( Psurface(I,J) – PTOP ) ]

where 

  Ap(L) = PTOP (for all L)
  Bp(L) = Sigma_Edge(L) = the bottom sigma edge for level L
In GeosUtil/pressure_mod.f we use the same hybrid formula but we use the Ap(L) and Bp(L) that pertain to each grid (GEOS-3, GEOS-4, GEOS-5, GCAP, etc). That simplifies the coding.

--Bob Y. 15:58, 6 April 2011 (EDT)

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