pcmdi_metrics.effective_resolution.compute_power_spectrum

pcmdi_metrics.effective_resolution.compute_power_spectrum(field, lat, ntrunc=None, gridtype='auto', rsphere=6371000.0)[source]

Compute power spectrum of a 2D scalar field via spherical harmonics.

Parameters:

field (ndarray, shape (nlat, nlon)) – 2D scalar field (e.g., temperature, geopotential height, precipitation).
lat (ndarray, shape (nlat,)) – Latitude in degrees.
ntrunc (int or None, optional) – Triangular truncation wavenumber. Default None is nlat - 1.
gridtype ({"auto", "regular", "gaussian"}, optional) – Grid type for selecting quadrature weights.
rsphere (float, optional) – Earth radius in meters. Default is EARTH_RADIUS.

Returns:

ds (xarray.Dataset) – Dataset containing: - power_spectrum (wavenumber,): Power \(E(l) = \sum_m |C_{l,m}|^2\) - wavenumber (wavenumber,): Total wavenumber \(l\) - eddy_scale (wavenumber,): Half-wavelength scale in km

Notes

For a scalar field \(\phi\) with spherical harmonic expansion \(\phi = \sum_l \sum_m C_{l,m} Y_{l,m}\), the power spectrum is:

\[E(l) = \sum_{m=-l}^{l} |C_{l,m}|^2\]

This represents the variance of the field at each total wavenumber \(l\).

Physical Interpretation:

\(E(l)\) = variance of field at wavenumber \(l\)
Steepening = loss of variance at small scales
Effective resolution = scale below which variance is artificially damped

Differences from Kinetic Energy Spectra:

Wind fields: KE spectrum from vorticity/divergence decomposition
Scalar fields: Direct power spectrum from field variance
Both use same methodology for detecting spectral steepening

Examples

>>> # Temperature field
>>> temp = np.random.randn(96, 192)
>>> lat = np.linspace(-89.0, 89.0, 96)
>>> ds = compute_power_spectrum(temp, lat)
>>> ds['power_spectrum']
<xarray.DataArray 'power_spectrum' (wavenumber: 96)>