dubfi.fluxes.localization¶

Localization utilities.

Added in version 0.1.1.

Changed in version 0.1.2: (renamed some methods)

Attributes¶

`GASPARI_COHN_CUTOFF`	Cutoff scale of `gaspari_cohn()`.
`GASPARI_COHN_GAUSS_CUTOFF`	Cutoff scale of `gaspari_cohn_gauss()`.
`LOCALIZATION_FUNCTIONS`	Access localization functions by (lower case) name.

Localization class for in-situ observations.

`gaspari_cohn`(→ numpy.ndarray)	Gaspari-Cohn function.
`gaspari_cohn_gauss`(→ numpy.ndarray)	Gaspari-Cohn with scale adjusted to match Gaussian.
`gauss`(→ numpy.ndarray)	Gaussian, \(\exp(-\tfrac{1}{2} x^2)\).

dubfi.fluxes.localization.gaspari_cohn(x: numpy.ndarray) → numpy.ndarray¶

Gaspari-Cohn function.

This function has compact support on [-2, 2].

See also

dubfi.fluxes.localization.GASPARI_COHN_GAUSS_CUTOFF = 3.6514837167011076¶

gaspari_cohn_gauss(x) == 0 for abs(x) > GASPARI_COHN_GAUSS_CUTOFF.

dubfi.fluxes.localization.gauss(x: numpy.ndarray) → numpy.ndarray¶: Gaussian, \(\exp(-\tfrac{1}{2} x^2)\).

dubfi.fluxes.localization.LOCALIZATION_FUNCTIONS¶: Access localization functions by (lower case) name.

class dubfi.fluxes.localization.Localization(func: Callable | str, hscale: float, vscale: float, tscale: numpy.timedelta64)¶

Localization class for in-situ observations.

Localization object allows creating localization matrices.

Parameters:

func (callable | {"Gauss", "Gaspari-Cohn", "Gaspari-Cohn-scaled"}) – localization function. This must take an array as argument and describe a positive, symmetric function f(x) that decreases monotonically from |x| from f(0)=1 to f(x)=0 (at least asymptotically) for large x. Names for known localization functions are allowed. Note that “Gaspari-Cohn-scaled” is an approximation of a Gaussian with compact support, see gaspari_cohn_gauss().
hscale (float) – horizontal scale in meters
vscale (float) – vertical scale in meters
tscale (np.timedelta64) – temporal scale

classmethod from_config(config: dict)¶: Construct Localization from configuration.

rel_dist_horizontal(lon: numpy.ndarray, lat: numpy.ndarray, lon2: numpy.ndarray | None = None, lat2: numpy.ndarray | None = None) → numpy.ndarray¶: Matrix of normalized horizontal distances.

Changed in version 0.1.2: (renamed, added optional variables)

weights_spatial(lon: numpy.ndarray, lat: numpy.ndarray, height: numpy.ndarray, lon2: numpy.ndarray | None = None, lat2: numpy.ndarray | None = None, height2: numpy.ndarray | None = None) → numpy.ndarray¶: Spatial weights (localization) matrix.

Changed in version 0.1.2: (added optional variables)

weights_time(time: numpy.ndarray, time2: numpy.ndarray | numpy.datetime64 | None = None) → numpy.ndarray¶: Temporal weights (localization) matrix.

Changed in version 0.1.2: (added optional variables)

rel_dist_horizontal_unique(lon: numpy.ndarray, lat: numpy.ndarray) → tuple[numpy.ndarray, numpy.ndarray]¶

Return normalized horizontal distance matrix for unique coordinates.

Returns:

matrix(lon: numpy.ndarray, lat: numpy.ndarray, height: numpy.ndarray, time: numpy.ndarray) → numpy.ndarray¶

Construct localization matrix based on coordinates.

All input arrays must be one-dimensional and aligned.

Parameters:

lon (np.ndarray) – longitude (degrees east)
lat (np.ndarray) – latitude (degrees east)
height (np.ndarray) – vertical coordinate in meters
time (np.ndarray) – time relative to localization time scale with arbitrary offset

Returns:

localization_weights – localization matrix specifying weights between each combination of coordiniates

Return type:

np.ndarray

matrix_sparse(lon: numpy.ndarray, lat: numpy.ndarray, height: numpy.ndarray, time: numpy.ndarray, threshold: float = 1e-05, chunk: int = 500) → scipy.sparse.csc_array¶: Construct localization matrix based on coordinates, see matrix().