Abstract
Scale interaction is examined in the limited-area PSU/NCAR mesoscale model, with emphasis on the forcing of small scales by the small-scale fields themselves. Output data from the model are filtered by expanding fields at each level in two-dimensional Fourier series and eliminating all contributions outside a particular band of vector wavenumber. A trend defined by boundary values is removed prior to spectral analysis to reduce misrepresentation of scales larger than the domain. After the fields are filtered, time tendencies are computed from them using the model's finite difference equations. Spectral analysis of these tendencies is then employed to determine the scale interaction present.
Results indicate that there is significant forcing of small-scale tendencies by the small scales themselves. This forcing is primarily due to topography, and appears mainly in the pressure gradient terms in the momentum equations and in the vertical motion-dependent terms in the thermodynamic equation. The effect of the large scales alone (excluding trends) on the small-scale tendencies is relatively unimportant. Additionally, the small-scale fields do not produce noticeable amplitude in the large-scale tendencies; thus, little interaction between large and small scales is evident, except for interactions with the trend field. Groups of interactions with and without the trend nearly cancel each other to yield a much smaller total tendency. All of the above conclusions are insensitive to the particular synoptic situations we have examined.
The main implication with regard to predictability is that, since the small scales are so strongly influenced by topography, which is fixed in time and space, one might expect low sensitivity to small-scale (e.g., mesoscale) initial conditions in cases where topographic forcing is dominant. Although this conclusion is based on examination of instantaneous tendencies only, the fact that the above scale relationships are observed at all times suggests that the conclusion should be valid for some longer-period (mean) tendencies as well.
