Conservative Regridding#
First order conservative regridding between rectilinear grids: each target cell receives the mean of the source values weighted by the area of their overlap with the cell, which preserves the integral of the field. Unlike the interpolators, which sample a field at points, it averages the field: use it to coarsen a grid, or to regrid fluxes and budgets. See Conservative Regridding.
The cells of a dimension are given by their centers, a 1D array, or by their bounds, an array of shape (n, 2) as the CF bounds variables. The bounds of cells given by their centers are the midpoints between consecutive centers, latitudes being clamped to ±90°; a dimension of a single cell must therefore be given by its bounds. Longitudes are periodic: the source and target grids can use different conventions, such as [0, 360) and [-180, 180).
Undefined source values (NaN) are ignored by default: a target cell receives
the mean of the defined values it overlaps (conservative_normed in
xESMF). min_valid_fraction sets the fraction of the area of the target
cell that the defined values must cover, and normalize=False counts the
undefined values as zero (conservative in xESMF).
Sphere and ellipsoid#
The area of the cell \([\lambda_1, \lambda_2] \times [\varphi_1, \varphi_2]\) is \(R^2 (\lambda_2 - \lambda_1)(\sin\beta_2 - \sin\beta_1)\), with \(\beta\) the authalic latitude and \(R\) the authalic radius. The overlap of two cells is therefore the product of the overlaps of their sides, and the regridding is applied along each axis in turn, without building a 2D weight matrix.
The areas are computed on a sphere by default, where \(\beta =
\varphi\), as ESMF and xESMF do. Pass spheroid=Spheroid()
(pyinterp.geometry.geographic.Spheroid, WGS-84 by default) to compute
them exactly on the ellipsoid: coarsening a global field to 1°, the results
change by about \(10^{-6}\) of the field.
Differences with xESMF#
The cells are longitude/latitude boxes, bounded by meridians and parallels. ESMF draws the edges of the cells as great circles, which bulge towards the poles by an amount proportional to the square of the width of the cell and to \(\sin 2\varphi\): the results differ most at mid-latitudes, and least at the equator and at the poles. Largest differences between pyinterp and xESMF, in fraction of the amplitude of a smooth global field coarsened from 0.25°, by band of latitude:
Target grid |
0°–15° |
15°–45° |
45°–75° |
75°–85° |
85°–90° |
|---|---|---|---|---|---|
1° |
\(7 \times 10^{-6}\) |
\(2 \times 10^{-5}\) |
\(2 \times 10^{-5}\) |
\(3 \times 10^{-6}\) |
\(3 \times 10^{-7}\) |
5° |
\(2 \times 10^{-4}\) |
\(4 \times 10^{-4}\) |
\(4 \times 10^{-4}\) |
\(7 \times 10^{-5}\) |
\(5 \times 10^{-6}\) |
Next to undefined values, the slivers of the great circles reach defined values that the boxes do not: some target cells get a value from xESMF and NaN from pyinterp (96 of the 64,800 cells of the 1° grid with the mask tested), and the means of partly undefined cells differ more, up to \(3 \times 10^{-3}\) of the field at 5°. pyinterp preserves the integral of the boxes to \(10^{-12}\), xESMF to about \(10^{-5}\). Curvilinear and unstructured grids are not supported.
xarray accessor#
|
Regrid the data array onto new cells, conserving its integral. |
|
Regrid the variables of the dataset, conserving their integrals. |
NumPy functions#
|
Regrid a field between rectilinear grids, conserving its integral. |
|
Compute the bounds of the cells of an axis from their centers. |
|
Return the centers and the bounds of the cells of an axis. |
Low-level functions#
|
First order conservative regridding between rectilinear grids. |
|
Transform latitude bounds into the sines of the authalic latitudes. |
|
Compute the overlaps between the cells of two axes. |