A simplified annular mode index based on zonal-mean data

This paper suggests a simplified method of calculating annular modes from data and models. The new method is more robust, simpler, relies on fewer subjective choices, and requires less data.

The Northern and Southern Hemisphere annular modes are most commonly defined as the leading empirical orthogonal functions (EOFs) of monthly-mean, hemispheric, wintertime geopotential height. In the lower troposphere, the structure of the annular modes is defined as the leading EOF of the near-surface geopotential height field. At pressure levels above the surface, the structure of the annular modes is typically found by either: 1) regressing geopotential height data onto the leading Principal Component time series of near-surface geopotential height; or 2) calculating the leading EOF of the geopotential height field at the respective pressure level. Daily resolution indices of the annular modes are found not by performing EOF analysis on daily geopotential, but rather by “projecting” daily-mean geopotential height data onto the monthly-mean EOF patterns.

The methodologies used to identify the three dimensional time/space structure of the annular modes are problematic in several ways. For example: 1) in the Northern Hemisphere, the leading EOF of upper tropospheric geopotential is a mix of the first two EOFs of surface geopotential, and hence represents a mix of annular and non-annular variability; 2) the structure of the annular modes varies from season-to-season, but the choice of the seasons used to defined the annular modes is often arbitrary; and 3) the extension of annular mode indices to daily resolution requires daily horizontal fields of geopotential, which may not be archived (e.g., as in the models used in the fourth IPCC assessment). Furthermore, the variety of methods and subjective choices used for defining the annular modes inevitably makes difficult the comparison of results from different studies, particularly the annular mode response to anthropogenic forcing or stratospheric variability in numerical simulations.

Here we provide a simplified recipe for calculating annular modes and their daily indices from zonally-averaged, daily, year-round geopotential. The method yields results that are physically consistent with our current understanding of the annular modes, but unlike existing methods requires few subjective choices and requires only zonally-averaged data and so is feasible for archived model output. We therefore suggest that zonal-mean daily geopotential be routinely archived from climate model runs.