easyclimate.field.teleconnection.index_ao_nam

The Arctic Oscillation (AO)/ Monthly Northern Hemisphere Annular Mode (NAM) Index

The Arctic Oscillation (AO) Index (or Monthly Northern Hemisphere Annular Mode (NAM) Index) is a key metric used to describe large-scale atmospheric variability in the Northern Hemisphere, particularly influencing mid-to-high latitude weather patterns. It is defined by the leading mode of Empirical Orthogonal Function (EOF) analysis of sea-level pressure (SLP) anomalies north of 20°N. The AO Index quantifies fluctuations in atmospheric pressure between the Arctic and mid-latitudes, with positive and negative phases reflecting distinct circulation patterns. In the positive phase, lower Arctic pressure and higher mid-latitude pressure strengthen westerly winds, confining cold air to polar regions, often leading to milder winters in North America and Europe. The negative phase, with higher Arctic pressure and weaker winds, allows cold air to move southward, causing colder, stormier weather in these regions.

The AO’s role in climate variability is significant, as it modulates temperature and precipitation, especially in winter. The AO Index, typically derived from monthly or seasonal SLP data, reflects the strength of the polar vortex, with positive values indicating a stronger vortex and negative values a weaker one. It is closely linked to the North Atlantic Oscillation (NAO) due to shared variability patterns.

The AO’s fluctuations are driven by internal atmospheric dynamics, stratospheric processes, and external forcings like sea surface temperatures. Its teleconnections make it a critical factor in seasonal weather predictions and long-term climate modeling. In a warming climate, Arctic amplification may alter AO dynamics, making its study essential for understanding future climate trends.

See also

  • Thompson, D. W. J., & Wallace, J. M. (1998). The Arctic oscillation signature in the wintertime geopotential height and temperature fields. Geophysical Research Letters, 25(9), 1297–1300. https://doi.org/10.1029/98gl00950

  • Fang, Z., Sun, X., Yang, X.-Q., & Zhu, Z. (2024). Interdecadal variations in the spatial pattern of the Arctic Oscillation Arctic center in wintertime. Geophysical Research Letters, 51, e2024GL111380. https://doi.org/10.1029/2024GL111380

  • Li, J., and J. X. L. Wang (2003), A modified zonal index and its physical sense, Geophys. Res. Lett., 30, 1632, doi: https://doi.org/10.1029/2003GL017441, 12.

  • Thompson, D. W. J. , & Wallace, J. M. . (1944). The Arctic oscillation signature in the wintertime geopotential height and temperature fields. Geophys. Res. Lett., doi: https://10.1029/98GL00950

Functions

calc_index_AO_EOF_Thompson_Wallace_1998(, lon_dim, ...)

The calculation of monthly mean Arctic Oscillation (AO) index using empirical orthogonal functions (EOFs) method over the entire Northern Hemisphere:

calc_index_NAH_zonal_lat_Li_Wang_2003(, lon_dim, ...)

The calculation of Monthly Northern Hemisphere Annular Mode (NAM) Index using normalized monthly zonal-mean sea level pressure (SLP) between 35°N and 65°N.

Module Contents

easyclimate.field.teleconnection.index_ao_nam.calc_index_AO_EOF_Thompson_Wallace_1998(slp_monthly_data: xarray.DataArray, time_range: slice = slice(None, None), lon_dim: str = 'lon', lat_dim: str = 'lat', lat_range: slice = slice(20, 90), time_dim: str = 'time', random_state: int | None = None, solver: Literal['auto', 'full', 'randomized'] = 'auto', solver_kwargs: dict = {}, normalized: bool = True) → xarray.DataArray

The calculation of monthly mean Arctic Oscillation (AO) index using empirical orthogonal functions (EOFs) method over the entire Northern Hemisphere:

Tip

EOF analysis on SLP anomalies poleward of 20°N to obtain the winter AO pattern and AO index, which is used in Thompson and Wallace (1998)

Parameters

slp_monthly_data: xarray.DataArray.

The monthly data of sea level pressure (SLP).

time_range: slice, default: slice(None, None).

The time range of seasonal cycle means to be calculated. The default value is the entire time range.

lon_dim: str, default: lon.

Longitude coordinate dimension name. By default extracting is applied over the lon dimension.

lat_dim: str, default: lat.

Latitude coordinate dimension name. By default extracting is applied over the lat dimension.

lat_range: slice, default: slice(20, 90).

The latitude range of computation using EOFs over the Northern Hemisphere. The default value is from \(\mathrm{20^{\circ}N}\) to \(\mathrm{90^{\circ}N}\).

time_dim: str, default: time.

The time coordinate dimension name.

random_state: int, default None.

Seed for the random number generator.

solver: {“auto”, “full”, “randomized”}, default: “auto”.

Solver to use for the EOFs computation.

solver_kwargs: dict, default {}.

Additional keyword arguments to be passed to the EOFs solver.

normalized: bool, default True, optional.

Whether to standardize the index based on standard deviation over time_range.

Returns

The monthly mean AO index (xarray.DataArray).

Reference

  • Thompson, D. W. J., & Wallace, J. M. (1998). The Arctic oscillation signature in the wintertime geopotential height and temperature fields. Geophysical Research Letters, 25(9), 1297–1300. https://doi.org/10.1029/98gl00950

  • Fang, Z., Sun, X., Yang, X.-Q., & Zhu, Z. (2024). Interdecadal variations in the spatial pattern of the Arctic Oscillation Arctic center in wintertime. Geophysical Research Letters, 51, e2024GL111380. https://doi.org/10.1029/2024GL111380

  • Li, J., and J. X. L. Wang (2003), A modified zonal index and its physical sense, Geophys. Res. Lett., 30, 1632, doi: https://doi.org/10.1029/2003GL017441, 12.

  • Thompson, D. W. J. , & Wallace, J. M. . (1944). The Arctic oscillation signature in the wintertime geopotential height and temperature fields. Geophys. Res. Lett., doi: https://doi.org/10.1029/98GL00950, 12.

See also

get_EOF_model

easyclimate.field.teleconnection.index_ao_nam.calc_index_NAH_zonal_lat_Li_Wang_2003(slp_monthly_data: xarray.DataArray, time_range: slice = slice(None, None), lon_dim: str = 'lon', lat_dim: str = 'lat', time_dim: str = 'time', normalized: bool = True) → xarray.DataArray

The calculation of Monthly Northern Hemisphere Annular Mode (NAM) Index using normalized monthly zonal-mean sea level pressure (SLP) between 35°N and 65°N.

Tip

The monthly NAM index (NAMI) or AO index (AOI) is defined as the idfference in the normalized monthly zonal-mean sea level pressure (SLP) between 35°N and 65°N (Li and Wang, 2003)

Parameters

slp_monthly_data: xarray.DataArray.

The monthly data of sea level pressure (SLP).

time_range: slice, default: slice(None, None).

The time range of seasonal cycle means to be calculated. The default value is the entire time range.

lon_dim: str, default: lon.

Longitude coordinate dimension name. By default extracting is applied over the lon dimension.

lat_dim: str, default: lat.

Latitude coordinate dimension name. By default extracting is applied over the lat dimension.

time_dim: str, default: time.

The time coordinate dimension name.

normalized: bool, default True, optional.

Whether to standardize the index based on standard deviation over time_range.

Returns

The monthly mean NAH/AO index (xarray.DataArray).

Reference