AMIP II Diagnostic Subproject No. 15:

Atmospheric angular momentum and the planetary momentum balance
Project coordinators:
David A. Salstein1, Richard D. Rosen1
Jean O. Dickey2 and Steven L. Marcus2
1Atmospheric and Environmental Research, Inc., USA
2 Jet Propulsion Laboratory, California Institute of Technology, USA


The behavior of atmospheric angular momentum (AAM) is important for any global circulation model to simulate because of its fundamental relationship to global climate variations on many time scales.  Fluctuations in AAM are also important to the angular momentum balance of the whole planet and are reflected in measurable planetary motions.  In AMIP-1, we examined the mean, seasonal, and interannual fluctuations of AAM relative to the Earth's mean rotation (Hide et al. 1997).  The annual cycle was captured very well by the models, and interannual fluctuations were reasonably well simulated, notably the global peaks and latitudinal anomalies associated with the El Nino/Southern Oscillation (Marcus and Dickey 1994). Nevertheless, not all features related to the ENSO cycle were successfully simulated; for example, the relative amplitudes of the ENSO peaks were generally not correct.

The AMIP-1 simulations of AAM were verified against data that extended up to the lower stratosphere.  Because the new NCEP reanalyses now incorporate the upper stratosphere, we will now be able to assess the simulation of important signals there, including elements of the quasi-biennial and semiannual oscillations (Salstein and Rosen 1997). In addition, the longer AMIP-2 period includes ENSO variability beyond that covered by AMIP-1, so that a larger number of ENSO-related AAM signals can be examined.  Newly available from analysis systems, too, are values of angular momentum exchanges between the atmosphere and other Earth components.  We can now assess how AMIP-2 models produce the friction and mountain torques that effect such exchanges (White 1991; Salstein and Rosen 1994; Madden and Speth 1995).

Besides the relative angular momentum highlighted in our AMIP-1 work, AMIP-2 allows us to assess the planetary portion of angular momentum, calculated from the surface pressure field.  Related as well are low-order harmonics of surface pressure (Chao and Au 1991; Dong et al. 1996), measures of the planetary mass distribution; interestingly, gravity anomalies from fluctuations in these harmonics can significantly perturb the orbits of Earth satellites, and observations are sensitive enough to detect such perturbations.

Changes in axial angular momentum, in particular, are mirrored by variations in the momentum of the solid Earth as measured independently by changes in length of day (Hide et al. 1997), while equatorial components of the AAM vector are associated with polar motion excitation. A full exposition of the AAM framework and its application to the global momentum balance is derived in Barnes et al.(1983); details of AAM calculations in an operational setting are given by Salstein et al. (1993).

The primary verification data that we intend to use for AMIP-2 are the relative and planetary atmospheric angular momentum values produced from the wind and surface pressure fields of the NCEP reanalysis system and other reanalyses and analysis systems (Salstein and Rosen 1997).  Although we will focus on monthly mean fields, we will also consider limited sets of daily values for the purpose of verifying statistics of high-frequency fluctuations.  We also plan to use other datasets to supplement reanalyses, such as satellite-based observations of the stresses over the ocean and of upper atmosphere winds, and geodetically-inferred variations in both the axial and equatorial components of global AAM.


We will diagnose the mean climate and variability of the angular momentum of the atmosphere, and assess errors on mean, seasonal, and interannual time scales in the ensemble of AMIP-2 models.  To identify the sources of errors we will examine fields of the zonal wind and surface pressure simulations.  We will extend our diagnoses into the upper stratosphere to determine the ability of models to simulate signals in that layer, such as the quasi-biennial oscillation.  We will also determine the planetary component of angular momentum as well as torque mechanisms driving momentum changes in the atmosphere.

a.  Relative angular momentum and zonal winds

    We will calculate global mean angular momentum in the troposphere, stratosphere, and the entire atmosphere on a monthly mean basis, to determine how low-frequency signals of AAM are being simulated in the models.  We plan to verify these quantities over the 180 months of AMIP-2 with the NCEP and other reanalyses.  We will assess the agreement among the models, and we will try to relate errors in theseasonal and/or interannual signals to model attributes.  Because in AMIP-1 the source of model errors in global AAM of similar characterwere sometimes caused by very different zonal wind error patterns, we will also carefully diagnose regional characteristics of the relative angular momentum for all the AMIP-2 models.
b.  Planetary angular momentum and mass field
    We plan to calculate the planetary angular momentum component based on the surface pressure distribution from AMIP models.  This term, when added to the relative momentum, forms a more complete calculation of the global AAM.  At the same time, low-order harmonics of the surface pressure field will be calculated.  We will consider comparisons of the modeled atmospheric mass field with observations of this parameter from reanalyses, and from gravity field anomalies determined by satellite.
c. Torques
    The mountain torque, derived from the normal component of pressure-gradient forces against mountainous topography, and the friction torque, derived from the tangential force against the underlying land or ocean, including that due to gravity wave drag, can be determined on both high and low frequencies with AMIP-2 output.  We  intend to verify these torque components using values from both the NCEP system and some direct satellite-based data, and on a global basis using geodetically-inferred changes in LOD.
Data Requirements
    Table 1
    Eastward wind speed
    Northward wind speed
    Geopotential height

    Table 2
    Surface pressure
    Surface eastward wind
    Surface northward wind
    Eastward surface wind stress
    Northward surface wind stress
    Eastward surface gravity wave drag-induced stress
    Northward surface gravity wave drag-induced stress

    Table 3
    Eastward wind speed
    Northward wind speed

    Table 4
    Total relative angular momentum
    Global average surface pressure
    Total kinetic energy

    Table 5
    Model topography

    Table 6
    Geopotential height
    Surface eastward wind
    Surface northward wind
    Eastward wind stress on surface
    Northward wind stress on surface
    Eastward gravity wave drag-induced stress on surface
    Northward gravity wave drag-induced stress on surface
    Surface pressure

    Barnes, R.T.H., R. Hide, A.A. White, and C.A. Wilson, 1983: Atmospheric angular momentum fluctuations, length of day changes and polar motion.  Proc. R. Soc. Lon., A387, 31-73.

    Chao, B.F., and A. Y. Au, 1991: Temporal variation of the earth's low-degree zonal gravitation field caused by atmospheric mass redistribution: 1980-1988. J. Geophys. Res., 96, 6569-6575.

    Dong, D., R. S. Gross, and J. O. Dickey, 1996: Seasonal variations of the Earth's gravitationalfField: an analysis of atmospheric and ocean tidal excitation," Geophys. Res. Lett., 23, 725-728.

    Hide, R.H., J.O. Dickey, S.L. Marcus, R.D. Rosen, and D.A. Salstein, 1997: Atmospheric angular momentum fluctuations during 1979-1988 simulated by global circulation models, J. Geophys. Res., 102,16,423-16438.

    Madden, R.A., and P. Speth, 1995: Estimates of atmospheric angular momentum, friction, and mountain torques during 1987-1988. J. Atmos. Sci., 52, 3681-3694.

    Marcus, S. L., and J. O. Dickey, 1994: Coupled poleward propagation of sea surface temperature and atmospheric angular momentum anomalies: results from AMIP, Sixth Conference on Climate Variations, American Meteorological Society, 70-74.

    Salstein, D.A., D.M. Kann, A.J. Miller, and R.D. Rosen, 1993: The sub-bureau for Atmospheric Angular Momentum of the International Earth Rotation Service (IERS): A meteorological data center with geodetic applications, Bull. Am. Met. Soc., 74, 67-80.

    Salstein, D.A., and R.D. Rosen, 1994: Topographic forcing of the atmosphere and a rapid change in the length-of-day.  Science, 264, 407-409.

    Salstein, D.A., and R.D. Rosen, 1997: Global momentum and energy signals from reanalysis systems. Reprint, 7th Conference on Climate Variations, American Meteorological Society, 344-348.

    White, G.H., 1991: Mountain and surface stress torques in NMC analyses.  Proceedings of the AGU Chapman Conference on Geodetic VLBI: Monitoring Global Change, U.S. Department of Commerce/NOAA/NOS, NOAA Technical Report NOS 137 NGS 49, Washington, DC, 262-269.

For further information, contact David A. Salstein (, Richard D. Rosen  ( or the AMIP Project Office (

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