International Mass Loading Service: Atmospheric Pressure Loading


The Earth as a whole responses to external forces as an elastic body. As it was shown by Darwin in 1882, changes of the weight of the column of atmosphere due to variations of pressure result in crustal deformations called atmospheric pressure loading. These variations on average have the rms of 2.6 mm for the vertical component and 0.6 mm for the horizontal component, but peak to peak variations can reach 40 mm for the vertical component and 7 mm for the horizontal one. Pressure loading should be taken into account in a reduction of astronomical and space geodesy observations when the accuracy better than 2 nrad or 1 cm is required.

Service for the atmospheric pressure loading

On 2002.12.12 the service of atmospheric pressure loading was established by Leonid Petrov and Jean-Paul Boy. The service provides

Time series of displacements are computed from 2 models developed by Global Modeling and Assimilation Office at NASA Goddard Space Flight Center:

  1. Reanalysis numerical weather model MERRA-2 (Gelaro et al, 2017). MERRA2 model has resolution 0.50° × 0.625° × 72 layers × 6 hours and it is updated monthly. The model covers range since 1980.01.01 though present. It is updated on a monthly basis and it has latency 15–50 days. This model is recommended for applications that require long-term stability.
  2. Operational semi-frozen numerical weather model GEOS-FPIT. It covers time range since 2000.01.01 to present and it is updated several times a day. Model resolution: 0.50° × 0.625° × 72 layers × 3 hours. It is updated 4 times day and it has latency 6–15 hours. This model is recommended for applications that requires low latencies.

Download pre-computed time series

Download pre-computed harmonic variations of displacements

Compute displacements caused by atmospheric pressure loading on-demand  

You can order computation of the time series for the stations of your interest. You need to prepare a station file in plain ascii that has four columns separated by one or more blanks:

Station_name    X-coordinate    Y-coordinate    Z-coordinate   

Station name should have no more than 8 characters. X,Y,Z are Cartesian coordinates of the station of interest in a crust-fixed coordinates system. Units are meters. Here is an example.

  MERRA2     from 19800101_0000     through 20240501_1800
  GEOSFPIT     from 20000101_0000     through 20240618_2100
  Time series       harmonics coefficients
  Center of mass Center of figure
Start date:     Format: YYYY.MM.DD_hh:mm:ss
Stop date:     Format: YYYY.MM.DD_hh:mm:ss
Station file:
E-mail address: Optional

Results of on-demand computations are accessible from here.

Plots of displacements caused by harmonic variations of atmospheric pressure

Plots of global displacements caused by atmospheric tides at 0.25° × 0.25° grid
Wave Frequency (rad/s) Phase (rad) Up displacement component East displacement component North displacement component
      Ampl Phase cos sin Ampl Phase cos sin Ampl Phase cos sin
SA 1.990968752920D-07 3.098467 ampl_up_sa phase_up_sa cos_up_sa sin_up_sa ampl_east_sa phase_east_sa cos_east_sa sin_east_sa ampl_north_sa phase_north_sa cos_north_sa sin_north_sa
SSA 3.982127698995D-07 0.365348 ampl_up_ssa phase_up_ssa cos_up_ssa sin_up_ssa ampl_east_ssa phase_east_ssa cos_east_ssa sin_east_ssa ampl_north_ssa phase_north_ssa cos_north_ssa sin_north_ssa

PI1 7.232384890619D-05 3.002044 ampl_up_pi1 phase_up_pi1 cos_up_pi1 sin_up_pi1 ampl_east_pi1 phase_east_pi1 cos_east_pi1 sin_east_pi1 ampl_north_pi1 phase_north_pi1 cos_north_pi1 sin_north_pi1
P1 7.252294578148D-05 2.958919 ampl_up_p1 phase_up_p1 cos_up_p1 sin_up_p1 ampl_east_p1 phase_east_p1 cos_east_p1 sin_east_p1 ampl_north_p1 phase_north_p1 cos_north_p1 sin_north_p1
S1 7.272206167609D-05 3.367392 ampl_up_s1 phase_up_s1 cos_up_s1 sin_up_s1 ampl_east_s1 phase_east_s1 cos_east_s1 sin_east_s1 ampl_north_s1 phase_north_s1 cos_north_s1 sin_north_s1
K1 7.292115855138D-05 3.324267 ampl_up_k1 phase_up_k1 cos_up_k1 sin_up_k1 ampl_east_k1 phase_east_k1 cos_east_k1 sin_east_k1 ampl_north_k1 phase_north_k1 cos_north_k1 sin_north_k1
PSI1 7.312025542667D-05 3.281141 ampl_up_psi1 phase_up_psi1 cos_up_psi1 sin_up_psi1 ampl_east_psi1 phase_east_psi1 cos_east_psi1 sin_east_psi1 ampl_north_psi1 phase_north_psi1 cos_north_psi1 sin_north_psi1
2T2 1.450459105823D-04 0.086250 ampl_up_2t2 phase_up_2t2 cos_up_2t2 sin_up_2t2 ampl_east_2t2 phase_east_2t2 cos_east_2t2 sin_east_2t2 ampl_north_2t2 phase_north_2t2 cos_north_2t2 sin_north_2t2
T2 1.452450074576D-04 0.043125 ampl_up_t2 phase_up_t2 cos_up_t2 sin_up_t2 ampl_east_t2 phase_east_t2 cos_east_t2 sin_east_t2 ampl_north_t2 phase_north_t2 cos_north_t2 sin_north_t2
S2 1.454441043329D-04 0.0 ampl_up_s2 phase_up_s2 cos_up_s2 sin_up_s2 ampl_east_s2 phase_east_s2 cos_east_s2 sin_east_s2 ampl_north_s2 phase_north_s2 cos_north_s2 sin_north_s2
R2 1.456432012082D-04 3.098467 ampl_up_r2 phase_up_r2 cos_up_r2 sin_up_r2 ampl_east_r2 phase_east_r2 cos_east_r2 sin_east_r2 ampl_north_r2 phase_north_r2 cos_north_r2 sin_north_r2
K2 1.458423171028D-04 3.506941 ampl_up_k2 phase_up_k2 cos_up_k2 sin_up_k2 ampl_east_k2 phase_east_k2 cos_east_k2 sin_east_k2 ampl_north_k2 phase_north_k2 cos_north_k2 sin_north_k2

U3 2.177679627494D-04 0.0 ampl_up_u3 phase_up_u3 cos_up_u3 sin_up_u3 ampl_east_u3 phase_east_u3 cos_east_u3 sin_east_u3 ampl_north_u3 phase_north_u3 cos_north_u3 sin_north_u3
T3 2.179670596247D-04 0.0 ampl_up_t3 phase_up_t3 cos_up_t3 sin_up_t3 ampl_east_t3 phase_east_t3 cos_east_t3 sin_east_t3 ampl_north_t3 phase_north_t3 cos_north_t3 sin_north_t3
S3 2.181661850283D-04 0.0 ampl_up_s3 phase_up_s3 cos_up_s3 sin_up_s3 ampl_east_s3 phase_east_s3 cos_east_s3 sin_east_s3 ampl_north_s3 phase_north_s3 cos_north_s3 sin_north_s3
R3 2.183652533752D-04 0.0 ampl_up_r3 phase_up_r3 cos_up_r3 sin_up_r3 ampl_east_r3 phase_east_r3 cos_east_r3 sin_east_r3 ampl_north_r3 phase_north_r3 cos_north_r3 sin_north_r3
K3 2.185643502505D-04 0.0 ampl_up_k3 phase_up_k3 cos_up_k3 sin_up_k3 ampl_east_k3 phase_east_k3 cos_east_k3 sin_east_k3 ampl_north_k3 phase_north_k3 cos_north_k3 sin_north_k3

U4 2.904900529562D-04 0.0 ampl_up_u4 phase_up_u4 cos_up_u4 sin_up_u4 ampl_east_u4 phase_east_u4 cos_east_u4 sin_east_u4 ampl_north_u4 phase_north_u4 cos_north_u4 sin_north_u4
T4 2.906891498303D-04 0.0 ampl_up_t4 phase_up_t4 cos_up_t4 sin_up_t4 ampl_east_t4 phase_east_t4 cos_east_t4 sin_east_t4 ampl_north_t4 phase_north_t4 cos_north_t4 sin_north_t4
S4 2.908882467044D-04 0.0     cos_up_t4       cos_east_s4       cos_north_s4  

Movie of vertical displacements

Movie of vertical displacements from MERRA2 model at 0.25 ° ×& 0.25 ° × 6h grid for 2012 is available here (2:30 duration, mpg format, 15MB).


  1. Darwin, G.H., On variations in the vertical due to elasticity of the Earth's surface, Phil. Mag., Ser. 5, col. 14, N. 90, 409--427, 1882.
  2. Farrell, W.E, Deformation of the Earth by Surface Loads, Rev. Geophys. and Spac. Phys., vol. 10(3), pp. 751--797, 1972.
  3. Rienecker, M.M., M.J. Suarez, R. Gelaro, R. Todling, J. Bacmeister, E. Liu, M.G. Bosilovich, S.D. Schubert, L. Takacs, G.-K. Kim, S. Bloom, J. Chen, D. Collins, A. Conaty, A. da Silva, et al., 2011. MERRA: NASA's Modern-Era Retrospective Analysis for Research and Applications. J. Climate, 24, 3624-3648, doi:10.1175/JCLI-D-11-00015.1.
  4. Lefevre, F., F.H. Lyard, C. Le Provost and E.J.O. Schrama, FES99: a global tide finite element solution assimilating tide gauge and altimetric information, J. Atmos. Oceanic Technol., vol. 19, pp.1345--1356, 2002.
  5. Manabe, S., T. Sato, S. Sakai, K. Yokoyama, Atmospheric load effect on VLBI observations, Proc. of the AGU Chapman conference on geodetic VLBI: Monitoring global change, NOAA TR NOS 437, NGS 49, Washington D.C., pp.111--122, 1991.
  6. MacMillan, D.S. and J.M. Gipson, Atmospheric pressure loading parameters from very long baseline interferometric observations, J. Geophys. Res., vol. 99(B9), pp. 18,081--18,087, 1994.
  7. Ponte, R.M. and Ray, R.D., Atmospheric pressure correction in geodesy and oceanography: A strategy for handling air tides, Geophys. Res. Let., vol. 29, (24), 2153, doi:10.1029/2002GL016340, 2002.
  8. van Dam, T.M. and T.A. Herring, Detection of atmospheric pressure loading using Very Long Baseline Interferometry measurements, J. Geophys. Res. 99(B3), pp. 4505--4518, 1994.
  9. van Dam, T.M., G. Blewitt, and M. Heflin, Detection of atmospheric pressure loading using the Global Positioning System, J. Geophys. Res., vol. 99(B12), pp. 23,939--23,950, 1994.
  10. van Dam, T.M. and J. Wahr, Displacements of the Earth's surface due to atmospheric loading: Effects on gravity and baseline measurements, J. Geophys. Res., vol. 92, pp. 1281--1286, 1987.
  11. Wunsch, C. and D. Stammer, Atmospheric loading and the "inverted barometer" effect, Rev. Geophys., vol. 35, pp. 117--135, 1997.


This work was supported by NASA Earth Surface & Interior program, grant NNX12AQ29G.

Back to the International Mass Loading Service.
This page was prepared by Leonid Petrov ()
Last update: 2021.02.23_15:58:34