easyclimate.core.spec.wind¶

Wind-related analysis for spherical harmonics

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

Functions¶

`calc_wind_speed`(→ xarray.DataArray)	Calculate the wind speed (magnitude of vector wind).
`calc_wind_speed_rs`(→ xarray.DataArray)	Calculate the wind speed (magnitude of vector wind) by Rust backend.
`calc_relative_vorticity_and_horizontal_divergence`(...)	Calculate relative vorticity and horizontal divergence.
`calc_relative_vorticity_and_horizontal_divergence_rs`(...)	Calculate relative vorticity and horizontal divergence by Rust backend.
`calc_relative_vorticity`(→ xarray.DataArray)	Calculate relative vorticity.
`calc_relative_vorticity_rs`(→ xarray.DataArray)	Calculate relative vorticity by Rust backend.
`calc_divergence`(→ xarray.DataArray)	Calculate horizontal divergence.
`calc_divergence_rs`(→ xarray.DataArray)	Calculate horizontal divergence by Rust backend.
`calc_planetary_vorticity`(→ xarray.DataArray)	Calculate planetary vorticity (Coriolis parameter).
`calc_planetary_vorticity_rs`(→ xarray.DataArray)	Calculate planetary vorticity (Coriolis parameter) by Rust backend.
`calc_absolute_vorticity`(→ xarray.DataArray)	Calculate absolute vorticity (sum of relative and planetary vorticity).
`calc_absolute_vorticity_rs`(→ xarray.DataArray)	Calculate absolute vorticity (sum of relative and planetary vorticity) by Rust backend.
`calc_streamfunction_and_velocity_potential`(...)	Calculate stream function and velocity potential.
`calc_streamfunction_and_velocity_potential_rs`(...)	Calculate stream function and velocity potential by Rust backend.
`calc_streamfunction`(→ xarray.DataArray)	Calculate stream function.
`calc_streamfunction_rs`(→ xarray.DataArray)	Calculate stream function by Rust backend.
`calc_velocity_potential`(→ xarray.DataArray)	Calculate velocity potential.
`calc_velocity_potential_rs`(→ xarray.DataArray)	Calculate velocity potential by Rust backend.
`calc_helmholtz`(→ xarray.Dataset)	Calculate irrotational and non-divergent components of the vector wind.
`calc_helmholtz_rs`(→ xarray.Dataset)	Calculate irrotational and non-divergent components of the vector wind by Rust backend.
`calc_irrotational_component`(→ xarray.Dataset)	Calculate irrotational (divergent) component of the vector wind.
`calc_irrotational_component_rs`(→ xarray.Dataset)	Calculate irrotational (divergent) component of the vector wind by Rust backend.
`calc_nondivergent_component`(→ xarray.Dataset)	Calculate non-divergent (rotational) component of the vector wind.
`calc_nondivergent_component_rs`(→ xarray.Dataset)	Calculate non-divergent (rotational) component of the vector wind by Rust backend.
`calc_rossby_wave_source`(→ xarray.DataArray)	Calculate Rossby wave sources (RWS).
`calc_rossby_wave_source_rs`(→ xarray.DataArray)	Calculate Rossby wave sources (RWS) by Rust backend.
`calc_gradient`(→ xarray.Dataset)	Computes the vector gradient of a scalar field on the sphere.
`calc_gradient_rs`(→ xarray.Dataset)	Computes the vector gradient of a scalar field on the sphere by Rust backend.

Module Contents¶

easyclimate.core.spec.wind.calc_wind_speed(u_data: xarray.DataArray, v_data: xarray.DataArray, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat') → xarray.DataArray¶

Calculate the wind speed (magnitude of vector wind).

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

The wind speed (xarray.DataArray).

easyclimate.core.spec.wind.calc_wind_speed_rs(u_data: xarray.DataArray, v_data: xarray.DataArray, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat', transform_backend: Literal['standard', 'nogil', 'latpar'] = 'latpar') → xarray.DataArray¶

Calculate the wind speed (magnitude of vector wind) by Rust backend.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

The wind speed (xarray.DataArray).

easyclimate.core.spec.wind.calc_relative_vorticity_and_horizontal_divergence(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat') → xarray.Dataset¶

Calculate relative vorticity and horizontal divergence.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Relative vorticity and horizontal divergence (xarray.Dataset).

Geographic Finite Difference

Divergence (Spherical Harmonics)

Relative Vorticity (Spherical Harmonics)

easyclimate.core.spec.wind.calc_relative_vorticity_and_horizontal_divergence_rs(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat', transform_backend: Literal['standard', 'nogil', 'latpar'] = 'latpar') → xarray.Dataset¶

Calculate relative vorticity and horizontal divergence by Rust backend.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Relative vorticity and horizontal divergence (xarray.Dataset).

Geographic Finite Difference

Divergence (Spherical Harmonics)

Relative Vorticity (Spherical Harmonics)

easyclimate.core.spec.wind.calc_relative_vorticity(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat') → xarray.DataArray¶

Calculate relative vorticity.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Relative vorticity (xarray.DataArray).

Geographic Finite Difference

Relative Vorticity (Spherical Harmonics)

easyclimate.core.spec.wind.calc_relative_vorticity_rs(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat', transform_backend: Literal['standard', 'nogil', 'latpar'] = 'latpar') → xarray.DataArray¶

Calculate relative vorticity by Rust backend.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Relative vorticity (xarray.DataArray).

Geographic Finite Difference

Relative Vorticity (Spherical Harmonics)

easyclimate.core.spec.wind.calc_divergence(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat') → xarray.DataArray¶

Calculate horizontal divergence.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Horizontal divergence (xarray.DataArray).

Divergence (Spherical Harmonics)

easyclimate.core.spec.wind.calc_divergence_rs(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat', transform_backend: Literal['standard', 'nogil', 'latpar'] = 'latpar') → xarray.DataArray¶

Calculate horizontal divergence by Rust backend.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Horizontal divergence (xarray.DataArray).

Divergence (Spherical Harmonics)

easyclimate.core.spec.wind.calc_planetary_vorticity(u_data: xarray.DataArray, v_data: xarray.DataArray, omega: float = 7.292e-05, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat') → xarray.DataArray¶

Calculate planetary vorticity (Coriolis parameter).

Parameters¶

u_data: xarray.DataArray.: The zonal component of the wind.
v_data: xarray.DataArray.: The meridional component of vector wind.
omega: float.: Earth’s angular velocity. The default value if not specified is \(7.292 \times 10^{-5} \mathrm{s^{-1}}\).
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Planetary vorticity (xarray.DataArray).

Planetary Vorticity (Spherical Harmonics)

easyclimate.core.spec.wind.calc_planetary_vorticity_rs(u_data: xarray.DataArray, v_data: xarray.DataArray, omega: float = 7.292e-05, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat', transform_backend: Literal['standard', 'nogil', 'latpar'] = 'latpar') → xarray.DataArray¶

Calculate planetary vorticity (Coriolis parameter) by Rust backend.

Parameters¶

u_data: xarray.DataArray.: The zonal component of the wind.
v_data: xarray.DataArray.: The meridional component of vector wind.
omega: float.: Earth’s angular velocity. The default value if not specified is \(7.292 \times 10^{-5} \mathrm{s^{-1}}\).
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Planetary vorticity (xarray.DataArray).

Planetary Vorticity (Spherical Harmonics)

easyclimate.core.spec.wind.calc_absolute_vorticity(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, omega: float = 7.292e-05, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat') → xarray.DataArray¶

Calculate absolute vorticity (sum of relative and planetary vorticity).

Parameters¶

u_data: xarray.DataArray.: The zonal component of the wind.
v_data: xarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
omega: float.: Earth’s angular velocity. The default value if not specified is \(7.292 \times 10^{-5} \mathrm{s^{-1}}\).
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Absolute vorticity (xarray.DataArray).

Absolute Vorticity (Spherical Harmonics)

easyclimate.core.spec.wind.calc_absolute_vorticity_rs(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, omega: float = 7.292e-05, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat', transform_backend: Literal['standard', 'nogil', 'latpar'] = 'latpar') → xarray.DataArray¶

Calculate absolute vorticity (sum of relative and planetary vorticity) by Rust backend.

Parameters¶

u_data: xarray.DataArray.: The zonal component of the wind.
v_data: xarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
omega: float.: Earth’s angular velocity. The default value if not specified is \(7.292 \times 10^{-5} \mathrm{s^{-1}}\).
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Absolute vorticity (xarray.DataArray).

Absolute Vorticity (Spherical Harmonics)

easyclimate.core.spec.wind.calc_streamfunction_and_velocity_potential(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat') → xarray.Dataset¶

Calculate stream function and velocity potential.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Stream function and velocity potential (xarray.Dataset).

Streamfunction (Spherical Harmonics)

Velocity Potential (Spherical Harmonics)

easyclimate.core.spec.wind.calc_streamfunction_and_velocity_potential_rs(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat', transform_backend: Literal['standard', 'nogil', 'latpar'] = 'latpar') → xarray.Dataset¶

Calculate stream function and velocity potential by Rust backend.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Stream function and velocity potential (xarray.Dataset).

Streamfunction (Spherical Harmonics)

Velocity Potential (Spherical Harmonics)

easyclimate.core.spec.wind.calc_streamfunction(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat') → xarray.DataArray¶

Calculate stream function.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

stream function (xarray.DataArray).

Streamfunction (Spherical Harmonics)

easyclimate.core.spec.wind.calc_streamfunction_rs(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat', transform_backend: Literal['standard', 'nogil', 'latpar'] = 'latpar') → xarray.DataArray¶

Calculate stream function by Rust backend.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

stream function (xarray.DataArray).

Streamfunction (Spherical Harmonics)

easyclimate.core.spec.wind.calc_velocity_potential(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat') → xarray.DataArray¶

Calculate velocity potential.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Velocity potential (xarray.DataArray).

Velocity Potential (Spherical Harmonics)

easyclimate.core.spec.wind.calc_velocity_potential_rs(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat', transform_backend: Literal['standard', 'nogil', 'latpar'] = 'latpar') → xarray.DataArray¶

Calculate velocity potential by Rust backend.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Velocity potential (xarray.DataArray).

Velocity Potential (Spherical Harmonics)

easyclimate.core.spec.wind.calc_helmholtz(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat') → xarray.Dataset¶

Calculate irrotational and non-divergent components of the vector wind.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Irrotational and non-divergent components of the vector wind (xarray.Dataset).

Irrotational Component (Spherical Harmonics)

Nondivergent Component (Spherical Harmonics)

easyclimate.core.spec.wind.calc_helmholtz_rs(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat', transform_backend: Literal['standard', 'nogil', 'latpar'] = 'latpar') → xarray.Dataset¶

Calculate irrotational and non-divergent components of the vector wind by Rust backend.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Irrotational and non-divergent components of the vector wind (xarray.Dataset).

Irrotational Component (Spherical Harmonics)

Nondivergent Component (Spherical Harmonics)

easyclimate.core.spec.wind.calc_irrotational_component(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat') → xarray.Dataset¶

Calculate irrotational (divergent) component of the vector wind.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Irrotational (divergent) component of the vector wind (xarray.Dataset).

Irrotational Component (Spherical Harmonics)

easyclimate.core.spec.wind.calc_irrotational_component_rs(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat', transform_backend: Literal['standard', 'nogil', 'latpar'] = 'latpar') → xarray.Dataset¶

Calculate irrotational (divergent) component of the vector wind by Rust backend.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Irrotational (divergent) component of the vector wind (xarray.Dataset).

Irrotational Component (Spherical Harmonics)

easyclimate.core.spec.wind.calc_nondivergent_component(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat') → xarray.Dataset¶

Calculate non-divergent (rotational) component of the vector wind.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Non-divergent (rotational) component of the vector wind (xarray.Dataset).

Nondivergent Component (Spherical Harmonics)

easyclimate.core.spec.wind.calc_nondivergent_component_rs(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat', transform_backend: Literal['standard', 'nogil', 'latpar'] = 'latpar') → xarray.Dataset¶

Calculate non-divergent (rotational) component of the vector wind by Rust backend.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Non-divergent (rotational) component of the vector wind (xarray.Dataset).

Nondivergent Component (Spherical Harmonics)

easyclimate.core.spec.wind.calc_rossby_wave_source(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat') → xarray.DataArray¶

Calculate Rossby wave sources (RWS).

\[RWS=-\nabla \cdot \left({v}_{x}\zeta \right)=-\left(\zeta \nabla \cdot {v}_{x}+{v}_{x}\cdot \nabla \zeta \right)\]

with \(\zeta\) being the absolute vorticity.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Rossby wave sources (xarray.DataArray).

Reference¶

Sardeshmukh, P. D., & Hoskins, B. J. (1988). The Generation of Global Rotational Flow by Steady Idealized Tropical Divergence. Journal of Atmospheric Sciences, 45(7), 1228-1251. https://doi.org/10.1175/1520-0469(1988)045<1228:TGOGRF>2.0.CO;2
James IN (1994) Low frequency variability of the circulation. Introduction to Circulating Atmospheres. Cambridge University Press, Cambridge, UK, pp 255–301
Trenberth, K. E., Branstator, G. W., Karoly, D., Kumar, A., Lau, N.-C., and Ropelewski, C. (1998), Progress during TOGA in understanding and modeling global teleconnections associated with tropical sea surface temperatures, J. Geophys. Res., 103(C7), 14291–14324, doi: https://doi.org/10.1029/97JC01444.
Nie, Y., Zhang, Y., Yang, X.-Q., & Ren, H.-L. (2019). Winter and summer Rossby wave sources in the CMIP5 models. Earth and Space Science, 6, 1831–1846. https://doi.org/10.1029/2019EA000674
Fuentes-Franco, R., Koenigk, T., Docquier, D. et al. Exploring the influence of the North Pacific Rossby wave sources on the variability of summer atmospheric circulation and precipitation over the Northern Hemisphere. Clim Dyn 59, 2025–2039 (2022). https://doi.org/10.1007/s00382-022-06194-4

easyclimate.core.spec.wind.calc_rossby_wave_source_rs(u_data: xarray.DataArray, v_data: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat', transform_backend: Literal['standard', 'nogil', 'latpar'] = 'latpar') → xarray.DataArray¶

Calculate Rossby wave sources (RWS) by Rust backend.

\[RWS=-\nabla \cdot \left({v}_{x}\zeta \right)=-\left(\zeta \nabla \cdot {v}_{x}+{v}_{x}\cdot \nabla \zeta \right)\]

with \(\zeta\) being the absolute vorticity.

Parameters¶

u_dataxarray.DataArray.: The zonal component of the wind.
v_dataxarray.DataArray.: The meridional component of vector wind.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

Rossby wave sources (xarray.DataArray).

Reference¶

Sardeshmukh, P. D., & Hoskins, B. J. (1988). The Generation of Global Rotational Flow by Steady Idealized Tropical Divergence. Journal of Atmospheric Sciences, 45(7), 1228-1251. https://doi.org/10.1175/1520-0469(1988)045<1228:TGOGRF>2.0.CO;2
James IN (1994) Low frequency variability of the circulation. Introduction to Circulating Atmospheres. Cambridge University Press, Cambridge, UK, pp 255–301
Trenberth, K. E., Branstator, G. W., Karoly, D., Kumar, A., Lau, N.-C., and Ropelewski, C. (1998), Progress during TOGA in understanding and modeling global teleconnections associated with tropical sea surface temperatures, J. Geophys. Res., 103(C7), 14291–14324, doi: https://doi.org/10.1029/97JC01444.
Nie, Y., Zhang, Y., Yang, X.-Q., & Ren, H.-L. (2019). Winter and summer Rossby wave sources in the CMIP5 models. Earth and Space Science, 6, 1831–1846. https://doi.org/10.1029/2019EA000674
Fuentes-Franco, R., Koenigk, T., Docquier, D. et al. Exploring the influence of the North Pacific Rossby wave sources on the variability of summer atmospheric circulation and precipitation over the Northern Hemisphere. Clim Dyn 59, 2025–2039 (2022). https://doi.org/10.1007/s00382-022-06194-4

easyclimate.core.spec.wind.calc_gradient(data_input: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat') → xarray.Dataset¶

Computes the vector gradient of a scalar field on the sphere.

Parameters¶

data_inputxarray.DataArray: The spatio-temporal data to be calculated.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

The zonal and meridional components of the vector gradient respectively (xarray.Dataset).

Geographical Gradient (Spherical Harmonics)

easyclimate.core.spec.wind.calc_gradient_rs(data_input: xarray.DataArray, truncation: int = None, R: float = 6371200.0, legfunc: str = 'stored', lon_dim: str = 'lon', lat_dim: str = 'lat', transform_backend: Literal['standard', 'nogil', 'latpar'] = 'latpar') → xarray.Dataset¶

Computes the vector gradient of a scalar field on the sphere by Rust backend.

Parameters¶

data_inputxarray.DataArray: The spatio-temporal data to be calculated.
truncation: int.: Truncation limit (triangular truncation) for the spherical harmonic computation.
R: float.: The radius in metres of the sphere used in the spherical harmonic computations. Default is 6371200 m, the approximate mean spherical Earth radius.
legfunc: str, ‘stored’ (default) or ‘computed’.: If ‘stored’, associated legendre functions are precomputed and stored when the class instance is created. This uses \(O(\mathrm{nlat}^3)\) memory, but speeds up the spectral transforms. If ‘computed’, associated legendre functions are computed on the fly when transforms are requested. This uses \(O(\mathrm{nlat}^2)\) memory, but slows down the spectral transforms a bit.
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.

Returns¶

The zonal and meridional components of the vector gradient respectively (xarray.Dataset).

Geographical Gradient (Spherical Harmonics)