# Vertical coordinate

IFS uses a hybrid sigma coordinate vertical coordinate, η,  in which the lowest layers of the model are pure so-called 'sigma' levels, whilst the topmost model levels are pure pressure levels. The hybrid scheme provides for a smooth transition between the two.  The vertical resolution varies with geometric height.  The vertical resolution is greatest (most fine) in the planetary boundary layer while more coarse near the model top.  Pure sigma levels follow the surface topography in the lower layers of the troposphere and ensure no levels intersect the surface.

A characteristic of the hybrid scheme is that the spacing between levels is less over steep orography than at the surface.

The vertical coordinate, η, is monotonic function of the pressure, p, and surface pressure, p s, such that:

η(0,p s) = 0    and    η(p s, p s) = 1

The atmosphere in IFS is divided into layers. The pressure at the interfaces between these layers are known as 'half-levels' and are defined by:

p k+½ = A k+½ + p s.B k+½

where p s is the surface pressure.

The A k+1/2 and B k+1/2 coefficients are constants that determine the vertical coordinate. They are stored in the GRIB header of all the fields output from IFS and can be found in the tables listed below for each of the supported vertical configurations of IFS.

The 'full-level' pressure, p k, associated with each model layer (i.e. the middle of the layer) is defined as:

p k = 0.5 ( p k-½ + p k+½ )

The IFS prognostic variables are represented by their values at the 'full-level' pressures p k.

## Vertical discretization

IFS uses a vertical finite-element scheme for improved accuracy and reducing numerical noise from the vertical discretization. In the finite element scheme, all variables (including pressure) are stored on the full model levels.

For more details of the vertical scheme, please refer to the references at the bottom of this page.

# Vertical configurations

IFS supports a number of vertical configurations, though the mostly commonly used are the 60, 91 and 137 level configurations. Note that the top model pressure level varies between these configurations.

Below the current L137 Model level definition

The following is the list of a(n) and b(n) coefficients defining the model levels, accompanied by the corresponding half-level, ph, and full-level, pf, values of pressure for a surface pressure of 1013.250 hPa. Also provided are the Geopotential and Geometric heights, the temperature and density of the level based on the 1976 version of the International Civil Aviation Organization (ICAO) Standard Atmosphere as described at:

For a description of how model levels should be interpreted see IFS Documentation Part III - Chapter 2, Section 2.2.1.

na [Pa]bph [hPa]pf [hPa]Geopotential Altitude [m]Geometric Altitude [m]Temperature [K]Density [kg/m^3]
00.0000000.0000000.000000-----
12.0003650.0000000.02000.010079301.7980301.65198.050.000018
23.1022410.0000000.03100.025573721.5874584.91209.210.000042
34.6660840.0000000.04670.038871115.7571918.79214.420.000063
46.8279770.0000000.06830.057568618.4369365.77221.320.000090
59.7469660.0000000.09750.082966210.9966906.53228.060.000127
613.6054240.0000000.13610.116863890.0364537.43234.560.000173
718.6089310.0000000.18610.161161651.7762254.39240.830.000233
824.9857180.0000000.24990.218059492.5060053.46246.870.000308
932.9857100.0000000.32990.289957408.6157930.78252.710.000400
1042.8792420.0000000.42880.379355396.6255882.68258.340.000512
1154.9554630.0000000.54960.489253453.2053905.62263.780.000646
1269.5205760.0000000.69520.622451575.1551996.21269.040.000806
1386.8958820.0000000.86900.782149767.4150159.36270.650.001007
14107.4157410.0000001.07420.971648048.7048413.94270.650.001251
15131.4255070.0000001.31431.194246416.2246756.98269.020.001546
16159.2794040.0000001.59281.453544881.1745199.69264.720.001913
17191.3385620.0000001.91341.753143440.2343738.55260.680.002343
18227.9689480.0000002.27972.096542085.0042364.93256.890.002843
19269.5395810.0000002.69542.487540808.0541071.20253.310.003421
20316.4207460.0000003.16422.929839602.7639850.56249.940.004084
21368.9823610.0000003.68983.427038463.2538696.94246.750.004838
22427.5924990.0000004.27593.982937384.2237604.95243.730.005693
23492.6160280.0000004.92624.601036360.9436569.72240.860.006655
24564.4134520.0000005.64415.285135389.1535586.89238.140.007731
25643.3399050.0000006.43346.038834465.0034652.52235.550.008931
26729.7441410.0000007.29746.865433585.0233763.05233.090.010261
27823.9678340.0000008.23977.768632746.0432915.27230.740.011729
28926.3449100.0000009.26348.751631945.5332106.57228.600.013337
291037.2011720.00000010.37209.817731177.5931330.96227.830.015012
301156.8536380.00000011.568510.970330438.5430584.71227.090.016829
311285.6103520.00000012.856112.212329726.6929866.09226.380.018793
321423.7701420.00000014.237713.546929040.4829173.50225.690.020910
331571.6229250.00000015.716214.977028378.4628505.47225.030.023186
341729.4489750.00000017.294516.505427739.2927860.64224.390.025624
351897.5192870.00000018.975218.134827121.7427237.73223.770.028232
362076.0959470.00000020.761019.868126524.6326635.56223.170.031013
372265.4316410.00000022.654321.707625946.9026053.04222.600.033972
382465.7705080.00000024.657723.656025387.5525489.15222.040.037115
392677.3481450.00000026.773525.715624845.6324942.93221.500.040445
402900.3913570.00000029.003927.888724320.2824413.50220.970.043967
413135.1193850.00000031.351230.177623810.6723900.02220.460.047685
423381.7436520.00000033.817432.584323316.0423401.71219.970.051604
433640.4682620.00000036.404735.111122835.6822917.85219.490.055727
443911.4904790.00000039.114937.759822368.9122447.75219.020.060059
454194.9306640.00000041.949340.532121915.1621990.82218.570.064602
464490.8173830.00000044.908243.428721473.9821546.62218.120.069359
474799.1494140.00000047.991546.449821045.0021114.77217.700.074330
485119.8950200.00000051.199049.595220627.8720694.90217.280.079516
495452.9907230.00000054.529952.864420222.2420286.66216.870.084916
505798.3447270.00000057.983456.256719827.9519889.88216.650.090458
516156.0742190.00000061.560759.772119443.5519503.09216.650.096110
526526.9467770.00000065.269563.415119068.3519125.61216.650.101968
536911.8706050.00000069.118767.194118701.2718756.34216.650.108045
547311.8691410.00000073.118771.118718341.2718394.25216.650.114355
557727.4121090.00000777.281075.199917987.4118038.35216.650.120917
568159.3540040.00002481.618279.449617638.7817687.77216.650.127751
578608.5253910.00005986.145083.881617294.5317341.62216.650.134877
589076.4003910.00011290.877488.511216953.8316999.08216.650.142321
599562.6826170.00019995.828093.352716616.0916659.55216.650.150106
6010065.9785160.000340101.004798.416416281.1016322.83216.650.158248
6110584.6318360.000562106.4153103.710015948.8515988.88216.650.166760
6211116.6621090.000890112.0681109.241715619.3015657.70216.650.175655
6311660.0673830.001353117.9714115.019815292.4415329.24216.650.184946
6412211.5478520.001992124.1337121.052614968.2415003.50216.650.194646
6512766.8730470.002857130.5637127.348714646.6814680.44216.650.204770
6613324.6689450.003971137.2703133.917014327.7514360.05216.650.215331
6713881.3310550.005378144.2624140.766314011.4114042.30216.650.226345
6814432.1396480.007133151.5493147.905813697.6513727.18216.650.237825
6914975.6152340.009261159.1403155.344813386.4513414.65216.650.249786
7015508.2568360.011806167.0450163.092713077.7913104.70216.650.262244
7116026.1152340.014816175.2731171.159112771.6412797.30216.650.275215
7216527.3222660.018318183.8344179.553712467.9912492.44216.650.288713
7317008.7890630.022355192.7389188.286712166.8112190.10216.650.302755
7417467.6132810.026964201.9969197.367911868.0811890.24216.650.317357
7517901.6210940.032176211.6186206.807811571.7911592.86216.650.332536
7618308.4335940.038026221.6146216.616611277.9211297.93216.650.348308
7718685.7187500.044548231.9954226.805010986.7011005.69216.740.364545
7819031.2890630.051773242.7719237.383710696.2210714.22218.620.378253
7919343.5117190.059728253.9549248.363410405.6110422.64220.510.392358
8019620.0429690.068448265.5556259.755310114.8910130.98222.400.406868
8119859.3906250.077958277.5852271.57049824.089839.26224.290.421790
8220059.9316410.088286290.0548283.82009533.209547.49226.180.437130
8320219.6640630.099462302.9762296.51559242.269255.70228.080.452897
8420337.8632810.111505316.3607309.66848951.308963.90229.970.469097
8520412.3085940.124448330.2202323.29048660.328672.11231.860.485737
8620442.0781250.138313344.5663337.39328369.358380.36233.750.502825
8720425.7187500.153125359.4111351.98878078.418088.67235.640.520367
8820361.8164060.168910374.7666367.08897787.517797.04237.530.538370
8920249.5117190.185689390.6450382.70587496.687505.51239.420.556842
9020087.0859380.203491407.0583398.85167205.937214.09241.310.575790
9119874.0253910.222333424.0190415.53876915.296922.80243.200.595219
9219608.5722660.242244441.5395432.77926624.766631.66245.090.615138
9319290.2265630.263242459.6321450.58586334.386340.68246.980.635553
9418917.4609380.285354478.3096468.97086044.156049.89248.860.656471
9518489.7070310.308598497.5845487.94705754.105759.30250.750.677899
9618006.9257810.332939517.4198507.50215464.605469.30252.630.699815
9717471.8398440.358254537.7195527.56965176.775180.98254.500.722139
9816888.6875000.384363558.3430548.03124892.264896.02256.350.744735
9916262.0468750.411125579.1926568.76784612.584615.92258.170.767472
10015596.6953130.438391600.1668589.67974338.774341.73259.950.790242
10114898.4531250.466003621.1624610.66464071.804074.41261.680.812937
10214173.3242190.493800642.0764631.61943812.533814.82263.370.835453
10313427.7695310.521619662.8084652.44243561.703563.69265.000.857686
10412668.2578130.549301683.2620673.03523319.943321.67266.570.879541
10511901.3398440.576692703.3467693.30433087.753089.25268.080.900929
10611133.3046880.603648722.9795713.16312865.542866.83269.520.921768
10710370.1757810.630036742.0855732.53252653.582654.69270.900.941988
1089617.5156250.655736760.5996751.34262452.042452.99272.210.961527
1098880.4531250.680643778.4661769.53292260.992261.80273.450.980334
1108163.3750000.704669795.6396787.05282080.412081.09274.630.998368
1117470.3437500.727739812.0847803.86221910.191910.76275.731.015598
1126804.4218750.749797827.7756819.93021750.141750.63276.771.032005
1136168.5312500.770798842.6959835.23581600.041600.44277.751.047576
1145564.3828130.790717856.8376849.76681459.581459.91278.661.062310
1154993.7968750.809536870.2004863.51901328.431328.70279.521.076209
1164457.3750000.827256882.7910876.49571206.211206.44280.311.089286
1173955.9609380.843881894.6222888.70661092.541092.73281.051.101558
1183489.2343750.859432905.7116900.1669987.00987.15281.731.113047
1193057.2656250.873929916.0815910.8965889.17889.29282.371.123777
1202659.1406250.887408925.7571920.9193798.62798.72282.961.133779
1212294.2421880.899900934.7666930.2618714.94715.02283.501.143084
1221961.5000000.911448943.1399938.9532637.70637.76284.001.151724
1231659.4765630.922096950.9082947.0240566.49566.54284.471.159733
1241387.5468750.931881958.1037954.5059500.91500.95284.891.167147
1251143.2500000.940860964.7584961.4311440.58440.61285.291.173999
126926.5078130.949064970.9046967.8315385.14385.16285.651.180323
127734.9921880.956550976.5737973.7392334.22334.24285.981.186154
128568.0625000.963352981.7968979.1852287.51287.52286.281.191523
129424.4140630.969513986.6036984.2002244.68244.69286.561.196462
130302.4765630.975078991.0230988.8133205.44205.44286.811.201001
131202.4843750.980072995.0824993.0527169.50169.51287.051.205168
132122.1015630.984542998.8081996.9452136.62136.62287.261.208992
13362.7812500.9885001002.22501000.5165106.54106.54287.461.212498
13422.8359380.9919841005.35621003.790679.0479.04287.641.215710
1353.7578130.9950031008.22391006.790053.9253.92287.801.218650
1360.0000000.9976301010.84871009.536330.9630.96287.951.221341
1370.0000001.0000001013.25001012.049410.0010.00288.091.223803

# References

See IFS Documentation,  Part III: Dynamics for more details of horizontal and vertical grids.

Simmons A.J., and D.M. Burridge, 1981, An energy and angular momentum conversing vertical finite difference scheme and hybrid vertical coordinates, Mon. Wea. Rev., 109, 758-766.

Untch, A. and Hortal, M., 2004. A finite-element scheme for the vertical discretization of the semi-Lagrangian version of the ECMWF forecast model. Q. J. R. Meteorol. Soc., 130, 1505–1530.