Multi-resolution Nudging#
When the convolution method is used, the nudging increment can optionally be computed on a mesh that is coarser than the one used for the rest of the model. Since the nudging is usually desired only on large scales, this gives similar scientific behaviour but at considerably reduced cost..
The convolution (see Filtering by Convolution) must span the range of scales that are being nudged. Nudging is typically applied at horizontal scales of the order of \(2000\,\text{km}\), which at a global NWP resolution corresponds to a stencil spanning many cells and, in a distributed implementation, many processor partitions. Computing the convolution directly on the model mesh would therefore require a very large halo depth and correspondingly large halo exchanges, which could be as expensive as the global spectral transforms the convolution is intended to avoid.
The cost is greatly reduced by applying the convolution only to a coarse-grained form of the field. If the coarse mesh has of the order of a single cell per partition, then nudging over a given physical distance requires halo exchanges of only a modest depth, which is far more efficient.
Coarse-grained convolution#
To describe this, let \(\mathcal{A}\) be a restriction operator that performs a local averaging to compute a coarse-grained field, and let \(\mathcal{R}\) be the corresponding prolongation operator, which reconstructs a field on the fine mesh from a coarse-grained field using a linear reconstruction. The filter \(\mathcal{L}\) of (208) is then applied as
where \(\overline{\mathcal{C}}\) denotes the convolution computed on the coarse mesh, and \(\overline{c}\) is the corresponding coarse-mesh kernel. In words, the increment field is first restricted to the coarse mesh, the convolution is performed there, and the result is prolongated back onto the model’s mesh, where it is applied to the model’s tendency for \(X\).
When coarse-mesh nudging is not used, no restriction or prolongation takes place, and the convolution is computed directly on the model’s own mesh.
The external reference fields used to compute the increment (see Vertical Treatment) are themselves prepared on the coarse mesh when coarse-mesh nudging is used: in particular, the pressure fields used to construct the model pressure profile are first mapped onto the coarse mesh before being used in the vertical interpolation.
For details of how to enable and configure coarse-mesh nudging, see the Nudging section of the User Guide.