The impact of wave number selection and spin‐up time in spectral nudging

Numerous studies have been presented describing the benefits of using Nudging to constrain the evolution of a numerical model. Recently, a variation of this approach called Spectral Nudging has gained popularity for its ability to maintain the higher temporal and spatial variability of the model results, while forcing the large scales in the solution with a coarser‐resolution field. Here, we focus on a not‐much‐explored aspect of this technique: the impact of selecting different cut‐off wave numbers and spin‐up times. We perform 4‐day‐long simulations with the WRF model, daily for three different 1‐month periods including a free run and several Spectral Nudging experiments with cut‐off wave numbers ranging from the smallest to the largest possible (Grid Nudging). Results show that Spectral Nudging is very effective at imposing the selected synoptic scales onto the solution, while allowing the limited‐area model to incorporate finer‐scale features. The model error diminishes rapidly as the nudging expands over broader parts of the spectrum, but this decreasing trend ceases sharply at cut‐off wave numbers equivalent to a length‐scale of about 1000 km, and the error magnitude changes minimally thereafter. This scale corresponds to the Rossby radius of deformation, separating synoptic from convective scales in the flow. When nudging is applied for scales larger than the Rossby radius of deformation, a shifting of the synoptic patterns can occur in the solution, yielding large model corrections towards the analysis. However, when selecting smaller scales, the fine‐scale contribution of the model is damped, thus making 1000 km the appropriate scale threshold to nudge in order to balance both effects. Finally, we note that longer spin‐up times are needed for model errors to stabilize when using Spectral Nudging than with Grid Nudging. Results suggest that this time is between 36 and 48 h.