Do nudging tendencies depend on the nudging timescale chosen in atmospheric models?

Nudging is a ubiquitous capability of numerical weather and climate models that is widely used in a variety of applications (e.g., crude data assimilation, "intelligent" interpolation between analysis times, constraining flow in tracer advection/diffusion simulations). Here, the focus is on the momentum nudging tendencies themselves, rather than the atmospheric state that results from application of the method. The initial intent was to interpret these tendencies as a quantitative estimate of model error (net parameterization error in particular). However, it was found that nudging tendencies depend strongly on the nudging time scale chosen, which is the primary result presented here. Reducing the nudging time scale reduces the difference between the model state and the target state, but much less so than the reduction in the nudging time scale, resulting in increased nudging tendencies. The dynamical core, in particular, appears to increasingly oppose nudging tendencies as the nudging time scale is reduced. A heuristic analysis suggests such a result should be expected as long as the state the model is trying to achieve differs from the target state, regardless of the type of target state (e.g., a reanalysis, another model). These results suggest nudging tendencies cannot be quantitatively interpreted as model error. Still, two experiments aimed at seeing how nudging can identify a withheld parameterization suggest nudging tendencies do contain some information on model errors and/or missing physical processes and still might be useful in model development and tuning, even if only qualitatively.