easyclimate.core.spec.tool¶

Tools for spherical harmonics analysis

This is the top layer of packaging for the Pyspharm package.

Functions¶

`calc_gaussian_latitudes`(nlat)	Calculate the gaussian latitudes (in degrees) and quadrature weights.
`calc_gaussian_latitudes_rs`(nlat)	Calculate the gaussian latitudes (in degrees) and quadrature weights by Rust backend.
`calc_geodesic_points`(m)	Calculate the lat/lon values of the points on the surface of the sphere
`calc_geodesic_points_rs`(m)	Calculate the lat/lon values of the points on the surface of the sphere
`calc_spherical_harmonic_coefficients`(ntrunc)	Calculate indices of zonal wavenumber (indxm) and degree (indxn) for complex spherical harmonic coefficients.
`calc_spherical_harmonic_coefficients_rs`(ntrunc)	Calculate indices of zonal wavenumber (indxm) and degree (indxn) for complex spherical harmonic coefficients by Rust backend.
`calc_legendre_functions`(→ xarray.DataArray)	Calculate associated legendre functions for triangular truncation T(ntrunc), at a given latitude.
`calc_legendre_functions_rs`(→ xarray.DataArray)	Calculate associated legendre functions for triangular truncation T(ntrunc), at a given latitude by Rust backend.
`transfer_grid2spectral_transform`(→ xarray.DataArray)	Transform grid data to spectral representation (spherical harmonic analysis).
`transfer_grid2spectral_transform_rs`(→ xarray.DataArray)	Transform grid data to spectral representation (spherical harmonic analysis) by Rust backend.
`transfer_spectral_transform2grid`(→ xarray.DataArray)	Transform spectral data back to grid space representation (spherical harmonic synthesis)
`transfer_spectral_transform2grid_rs`(→ xarray.DataArray)	Transform spectral data back to grid space representation (spherical harmonic synthesis) by Rust backend.

Module Contents¶

easyclimate.core.spec.tool.calc_gaussian_latitudes(nlat: int)¶

Calculate the gaussian latitudes (in degrees) and quadrature weights.

Parameters¶

nlat: int.: Number of gaussian latitudes desired.

Returns¶

The gaussian latitudes (in degrees north) and gaussian quadrature weights (xarray.Dataset).

Parameters¶

nlat: int.: Number of gaussian latitudes desired.

Returns¶

The gaussian latitudes (in degrees north) and gaussian quadrature weights (xarray.Dataset).

Parameters¶

m: int.: The number of points on the edge of a single geodesic triangle. There are \(10(m-1)^2+2\) total geodesic points, including the poles.

Returns¶

The latitudes and longitudes of the geodesic points (in degrees). These points are nearly evenly distributed on the surface of the sphere. (xarray.Dataset).

Tools for Spherical Harmonics

easyclimate.core.spec.tool.calc_geodesic_points_rs(m: int)¶

Calculate the lat/lon values of the points on the surface of the sphere corresponding to a twenty-sided (icosahedral) geodesic by Rust backend.

Parameters¶

m: int.: The number of points on the edge of a single geodesic triangle. There are \(10(m-1)^2+2\) total geodesic points, including the poles.

Returns¶

The latitudes and longitudes of the geodesic points (in degrees). These points are nearly evenly distributed on the surface of the sphere. (xarray.Dataset).

Tools for Spherical Harmonics

easyclimate.core.spec.tool.calc_spherical_harmonic_coefficients(ntrunc: int)¶

Calculate indices of zonal wavenumber (indxm) and degree (indxn) for complex spherical harmonic coefficients.

Parameters¶

ntrunc: int.: The spherical harmonic triangular truncation limit, i.e, truncation wavenumber (e.g., T42).

Returns¶

The latitudes and longitudes of the geodesic points (in degrees). These points are nearly evenly distributed on the surface of the sphere. (xarray.Dataset).

Tools for Spherical Harmonics

easyclimate.core.spec.tool.calc_spherical_harmonic_coefficients_rs(ntrunc: int)¶

Calculate indices of zonal wavenumber (indxm) and degree (indxn) for complex spherical harmonic coefficients by Rust backend.

Parameters¶

ntrunc: int.: The spherical harmonic triangular truncation limit, i.e, truncation wavenumber (e.g., T42).

Returns¶

The latitudes and longitudes of the geodesic points (in degrees). These points are nearly evenly distributed on the surface of the sphere. (xarray.Dataset).

Tools for Spherical Harmonics

easyclimate.core.spec.tool.calc_legendre_functions(lat: float, ntrunc: int) → xarray.DataArray¶

Calculate associated legendre functions for triangular truncation T(ntrunc), at a given latitude.

Parameters¶

lat: float.: The latitude (in degrees) to compute the associate legendre functions.
ntrunc: int.: The spherical harmonic triangular truncation limit, i.e, truncation wavenumber (e.g., T42).

Returns¶

\((\mathrm{ntrunc} + 1) (\mathrm{ntrunc} + 2) /2\) associated legendre functions at latitude lat.

Tools for Spherical Harmonics

easyclimate.core.spec.tool.calc_legendre_functions_rs(lat: float, ntrunc: int) → xarray.DataArray¶

Calculate associated legendre functions for triangular truncation T(ntrunc), at a given latitude by Rust backend.

Parameters¶

lat: float.: The latitude (in degrees) to compute the associate legendre functions.
ntrunc: int.: The spherical harmonic triangular truncation limit, i.e, truncation wavenumber (e.g., T42).

Returns¶

\((\mathrm{ntrunc} + 1) (\mathrm{ntrunc} + 2) /2\) associated legendre functions at latitude lat.

Tools for Spherical Harmonics

easyclimate.core.spec.tool.transfer_grid2spectral_transform(grid_data: xarray.DataArray, grid_data_type: Literal['regular', 'gaussian'], lon_dim: str = 'lon', lat_dim: str = 'lat', ntrunc: int = None) → xarray.DataArray¶

Transform grid data to spectral representation (spherical harmonic analysis).

Parameters¶

grid_data: xarray.DataArray.: Input grid data, must contain longitude and latitude dimensions
grid_data_type:: Type of grid (‘regular’ or ‘gaussian’)
lon_dim: str.: Name of longitude dimension, default is 'lon'.
lat_dim: str.: Name of latitude dimension, default is 'lat'.
ntrunc: int.: Spectral truncation wavenumber, defaults to nlat-1.

Returns¶

xarray.DataArray containing complex spherical harmonic coefficients with triangular spectral dimension

Visualization for Spherical Harmonics

easyclimate.core.spec.tool.transfer_grid2spectral_transform_rs(grid_data: xarray.DataArray, grid_data_type: Literal['regular', 'gaussian'], lon_dim: str = 'lon', lat_dim: str = 'lat', ntrunc: int = None, transform_backend: Literal['standard', 'nogil', 'latpar'] = 'latpar') → xarray.DataArray¶

Transform grid data to spectral representation (spherical harmonic analysis) by Rust backend.

Parameters¶

grid_data: xarray.DataArray.: Input grid data, must contain longitude and latitude dimensions
grid_data_type:: Type of grid (‘regular’ or ‘gaussian’)
lon_dim: str.: Name of longitude dimension, default is 'lon'.
lat_dim: str.: Name of latitude dimension, default is 'lat'.
ntrunc: int.: Spectral truncation wavenumber, defaults to nlat-1.

Returns¶

xarray.DataArray containing complex spherical harmonic coefficients with triangular spectral dimension

Visualization for Spherical Harmonics

easyclimate.core.spec.tool.transfer_spectral_transform2grid(spec_data: xarray.DataArray, nlon: int, nlat: int, grid_data_type: Literal['regular', 'gaussian'], spec_dim: str = 'spec_dim', lon_dim: str = 'lon', lat_dim: str = 'lat') → xarray.DataArray¶

Transform spectral data back to grid space representation (spherical harmonic synthesis)

Parameters¶

spec_data: xarray.DataArray.: Input spectral coefficient data, must contain the spectral dimension.
nlon: int.: Number of longitude points in output grid.
nlat: int.: Number of latitude points in output grid.
grid_data_type:: Type of output grid ('regular' or 'gaussian').
spec_dim:: Name of spectral dimension, default is 'spec_dim'.
lon_dim: str.: Name for output longitude dimension, default is 'lon'.
lat_dim: str.: Name for output latitude dimension, default is 'lat'.

Returns¶

xarray.DataArray in grid space representation with (lat, lon) dimensions

Visualization for Spherical Harmonics

easyclimate.core.spec.tool.transfer_spectral_transform2grid_rs(spec_data: xarray.DataArray, nlon: int, nlat: int, grid_data_type: Literal['regular', 'gaussian'], spec_dim: str = 'spec_dim', lon_dim: str = 'lon', lat_dim: str = 'lat', transform_backend: Literal['standard', 'nogil', 'latpar'] = 'latpar') → xarray.DataArray¶

Transform spectral data back to grid space representation (spherical harmonic synthesis) by Rust backend.

Parameters¶

spec_data: xarray.DataArray.: Input spectral coefficient data, must contain the spectral dimension.
nlon: int.: Number of longitude points in output grid.
nlat: int.: Number of latitude points in output grid.
grid_data_type:: Type of output grid ('regular' or 'gaussian').
spec_dim:: Name of spectral dimension, default is 'spec_dim'.
lon_dim: str.: Name for output longitude dimension, default is 'lon'.
lat_dim: str.: Name for output latitude dimension, default is 'lat'.

Returns¶

xarray.DataArray in grid space representation with (lat, lon) dimensions

Visualization for Spherical Harmonics