Modal view of atmospheric circulation

representation of  the atmosphere

MODES applies three-dimensional linear wave theory for the decomposition of global circulation in terms of normal-mode functions (NMFs). NMFs used by MODES are eigensolutions of the linearized primitive equations in the terrain-following sigma coordinates and were derived by Kasahara and Puri (1981, Mon. Wea. Rev). The horizontal structure functions are the Hough harmonics while the vertical structure equation is solved numerically using realistic stratification profiles of the troposphere+stratosphere. The top boundary condition is applied near the zero pressure level. For details, see

MODES outputs quantify spatial and temporal variability associated with the two main circulation regimes, the Rossby wave (or balanced) regime and the inertia-gravity wave (or unbalanced) regime. The approach is most useful in the tropics where the two special NMF solutions, the Kelvin wave and the mixed Rossby-gravity wave, account for a significant part of tropical variability.

Recently published book describes theory and applications of normal-mode functions in weather and climate dynamics and numerical weather prediction research:

MODES pages provide real-time and archive results of modal decomposition of the operational deterministic ECMWF 10-day forecasts. Selected outputs of modal analysis of reanalysis and interesting datasets are also here.

Modal decomposition of ECMWF deterministic forecasts


Energy spectra

Distribution of atmospheric balanced and inertio-gravity energy as a function of the zonal wavenumber.

Circulation maps

Regional circulation maps at 850 hPa and 200 hPa.

Tropical winds

Tropical zonal winds associated with balanced and unbalanced circulation.

Kelvin waves

Kelvin waves in the ECMWF model.

Mixed Rossby-gravity waves

Mixed Rossby-gravity waves in the ECMWF model.

Polar vortex

Polar view of midlatitude circulation in the stratosphere.