AMIP II Diagnostic Subproject 30

Maintenance Mechanisms of Stationary Waves in General Circulation Models

Project coordinators:
Mingfang Ting and Renu Joseph
University of Illinois at Urbana Champaign

Data Requirements


Atmospheric general circulation models (GCMs) are used extensively in making extended weather forecasts, climate predictions, as well as simulating future climate changes.  Due to differences in model physics and numerical procedures, different GCMs tend to produce differences in atmospheric circulation patterns.  The climatological stationary waves simulated in the GCMs, for example, can have considerable variation amongst themselves and are often different from those in observations.  The complexity of GCMs makes it difficult to isolate the causes for the differences among GCMs.  We propose to use simplified models with the AMIP output to study the differences in the maintenance of stationary waves. The AMIP program provides an ideal opportunity for the proposed study.

Linear stationary wave models have been powerful tools aiding in the diagnostic understanding of the maintenance of stationary waves in both GCMs and observations (e.g., Nigam et al. 1986, 1988; Valdes and Hoskins 1989; Ting, 1994; Wang and Ting, 1999). The linear model allows a separation of different stationary wave forcings, i.e. diabatic heating, orography and transient flux convergences.  Thus the relative roles of the forcings in the maintenance of stationary waves can be isolated. For example, Valdes and Hoskins (1989) studied the northern winter stationary wave maintenance using the ECMWF analysis while Wang and Ting (1999) examined the stationary wave maintenance for the entire seasonal cycle using the NCEP/NCAR reanalysis. Both studies found that diabatic heating played the dominant role in stationary wave maintenance.  Given the complexity of the cumulus parameterization schemes, it is expected that the stationary wave maintenance mechanisms may be rather different in GCMs.  Nigam (1986, 1988) showed that orography and diabatic heating were of equal importance in the maintenance of northern winter stationary waves in the GFDL GCM.

In this study, we plan to investigate the stationary wave maintenance in the AMIP-2 GCMs using a linear and a nonlinear stationary wave model. Specifically, the relative role of diabatic heating and orography will be examined.  Using a linear model in conjunction with a non-linear model will help us better understand the role of non-linearity in the maintenance of stationary waves. Given the availability of the different components of the diabatic heating, i.e. latent, sensible, and radiative heating in AMIP-2, we plan to examine the relative importance of the different components of the heating in the stationary wave maintenance. In most GCMs, latent heating is further parameterized in terms of moist convective, dry convective and large-scale precipitation processes. The relative roles of these diabatic forcings can be further examined in a linear/non-linear model. This should not only shed light into the roles of these diabatic processes in maintaining stationary waves, but also provide insight into the importance of the different parameterizations involved in latent heating in different seasons.


The proposed study will determine:

  • How well are stationary waves simulated in the various AMIP GCMs
  • How are stationary waves maintained in the AMIP GCMs, in particular,
  • the relative roles of diabatic heating and orography
  • the relative contributions of latent, sensible and radiative heating
  • How does different heating parameterization schemes affect the stationary wave simulation and maintenance.

We plan to study stationary waves using the linear and non-linear stationary wave models as tools to examine the maintenance mechanisms of stationary waves during the different seasons.

The linear model to be used here (Ting and Held, 1990) is one that is linearized about the zonal-mean climatological flow and is subjected to the zonally asymmetric forcings. The linear model can be used at a spatial resolution of R30 or R15 with various vertical resolutions and is described in Ting (1994). The basic model equations are the prognostic equations for vorticity, divergence, temperature and log of surface pressure. The forcings of the linear model include orography, diabatic heating, transients and stationary nonlinearity.

The non-linear model developed by Ting and Yu (1998) incorporates the non-linear interaction among the orographic, diabatic and transient forcings among themselves and with each other. This takes into account the necessary but unrealistic forcing of stationary non-linearity in the linear model. A combination of these two models will therefore help us understand the non-linear stationary wave forcings of orography, diabatic heating and transients and the different components of latent heating.

Data Requirements
The data required for the study outlined above are as follows:

Upper-air low frequency (monthly mean) output at all 17-levels

1.Northward wind speed
2.Eastward wind speed
3.Vertical motion
4.Air temperature
5.Geopotential height
6.Temperature tendency due to total diabatic heating
7.Temperature tendency due to SW radiation
8.Temperature tendency due to LW radiation
9.Temperature tendency due to moist convective processes
10.Temperature tendency due to dry convective processes
11.Temperature tendency due to large scale precipitation
12.Eddy kinetic energy
13.Mean product of eastward and northward winds
14.Mean product of northward wind and temperature
Single-level low frequency (monthly mean) output
1.Total precipitation
3.Surface pressure

Model topography

The monthly-mean pressure-surface data are required for constructing the basic states as well as forcings for the linear and nonlinear models.  Surface pressure data is necessary for converting the pressure level data to sigma surfaces in the linear and nonlinear models.  Total precipitation and OLR are requested for comparison of AMIP models with observations.  Model topography is a necessary forcing for the stationary wave models.


Nigam, S., I. M. Held, and S. W. Lyons, 1986: Linear simulation of the stationary eddies in a general circulation model. Part I: The no-mountain model. J. Atmos. Sci., 43, 2944-2961.

Nigam, S., I. M. Held,  and S. W. Lyons,  1988: Linear simulation of stationary eddies in a GCM. Part II: The ?mountain? model. J. Atmos. Sci., 45, 1433-1452.

Ting, M. 1994: Maintenance of northern summer stationary waves in a GCM. J. Atmos. Sci., 51, 3286-3308.

Ting, M., and I. M. Held, 1990: The stationary wave response to a tropical SST anomaly in an idealized GCM. J. Atmos. Sci., 47, 2546-2566.

Ting, M., and L. Yu, 1998: Steady response to tropical heating in wavy linear and non-linear baroclinic models. J. Atmos. Sci., 55, 3565-3581.

Valdes, P. J., and B. J. Hoskins, 1989: Linear stationary wave simulations of the time mean climatological flow. J. Atmos. Sci., 48, 2509-2106.

Wang, H., and M. Ting, 1999: Seasonal Cycle of the Climatological Stationary Waves in the NCEP/NCAR Reanalysis.  J. Atmos. Sci., 56, in press.

For further information, contact the AMIP Project Office (amip@pcmdi.llnl.gov).
Last update: 2 September 1999.  This page is maintained by mccravy@pcmdi.llnl.gov

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