GEOS-Chem vertical grids

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	GMAO GEOS-5 GMAO GEOS-5 "forward processing" (aka GEOS-FP) GMAO MERRA reanalysis product GMAO MERRA-2 reanalysis product
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 sigma-pressure
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	GMAO GEOS-5 GMAO GEOS-5 "forward processing" (aka GEOS-FP) GMAO MERRA reanalysis product GMAO MERRA-2 reanalysis product
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 sigma-pressure
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

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. P_TOP=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 A_p(L) and B_p(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)