Overview

Spectral nudging relaxes the potential temperature, \(\theta\), and the horizontal wind components, \((u,v)\), towards reference fields derived from an external dataset (for example a reanalysis, or the driving model in a regional or limited-area configuration).

At each application of the scheme, an increment is calculated for a given field \(X \in \{\theta, u, v\}\) and added to the model’s prognostic tendencies. Two methods are available for calculating this increment:

• Newtonian relaxation: a pointwise relaxation of the field towards the reference field, described in Newtonian relaxation.

• Convolution: a physical-space convolution that emulates a spectral low-pass (or band-pass) filter, so that only the large scales are nudged. The rationale for this approach, and its derivation on the sphere, are described in Filtering by Convolution.

In both cases the increment is scaled by a set of weights which:

• ramp the nudging increment smoothly up and down with height, targeting nudging at a chosen range of vertical levels, optionally capped by the model’s diagnosed tropopause level (see Vertical Treatment);

• ramp the nudging on gradually at the start of a run, over a configurable spin-up period;

• scale the increment according to the model timestep and a configurable relaxation timescale.

These weights are described fully in Formulation.

The external reference data is supplied on its own set of pressure levels, and must be vertically interpolated onto the model’s levels before it can be used; this process is described in Vertical Treatment.

Finally, when the convolution method is used, nudging can optionally be performed on a coarser mesh than the mesh used for the rest of the model, with the resulting increment prolongated back onto the model’s mesh. This improves efficiency and is described in Multi-resolution Nudging.