Derivatives (rojak.core.derivatives)

Coordinate-aware spatial derivatives on a latitude/longitude grid

This module computes gradients, divergence, and the Laplacian of fields defined on a geographic (latitude/ longitude) grid, accounting for the physical (geodesic) distance between grid points and, where relevant, the distortion introduced by a map projection. It underlies the derivative-based turbulence diagnostics in rojak.turbulence.calculations and rojak.turbulence.diagnostic.

Grid spacing between adjacent points can be computed either from the true geodesic distance at every grid point (grid_spacing()) or, more cheaply, from a nominal spacing measured along the equator and prime meridian (nominal_grid_spacing()). get_projection_correction_factors() computes the map projection scale factors used to correct raw Cartesian derivatives (spatial_gradient(), in GradientMode.GEOSPATIAL mode) for projection distortion, and vector_derivatives() computes the full set of horizontal velocity derivatives (du/dx, du/dy, dv/dx, dv/dy) with this correction applied. divergence() and spatial_laplacian() build on spatial_gradient().

Functions

divergence(u, v, *, units[, geod, crs])	Horizontal divergence of a 2D vector field
first_derivative(array, ...)	First derivative of array along axis, with respect to physical distance
get_dimension_number(name, data_array)	Get the axis position of a named dimension in a DataArray
get_projection_correction_factors(latitude, ...)	Compute the map projection scale factors at each point of a latitude/longitude grid
grid_spacing(latitude, longitude, units[, geod])	Compute the geodesic distance between adjacent points of a 2D latitude/longitude grid
nominal_grid_spacing(latitude, longitude, units)	Estimate the grid spacing of a regular latitude/longitude grid from a single row and column
spatial_gradient(array, units, gradient_mode)	Spatial gradient of a scalar field on a latitude/longitude grid
spatial_laplacian(array, units, gradient_mode)	Laplacian of a scalar field on a latitude/longitude grid
vector_derivatives(u, v, units[, ...])	Horizontal derivatives of a 2D velocity field, corrected for map projection distortion

Classes

CartesianDimension(*values)	Cartesian x/y direction, and the corresponding geographic coordinate/grid spacing/scale factor
GradientMode(*values)	How spatial_gradient() should compute the gradient
GridSpacing(dx, dy)	Grid spacing (in meters) along the x and y Cartesian directions, e.g. as computed by grid_spacing().
LatLonUnits(*values)	Units latitude/longitude coordinates are expressed in
ProjectionCorrectionFactors(parallel_scale, ...)	Map projection scale factors, as computed by get_projection_correction_factors()
SpatialGradient(dfdx, dfdy)	x and y components of a spatial gradient, as computed by spatial_gradient()
VelocityDerivative(*values)	The four horizontal derivatives of a 2D velocity field, as computed by vector_derivatives()