Fig. 1: Schematic depiction of the forcing by MWFM of two-dimensional plane hydrostatic gravity waves from a ridge. Waves are aligned orthogonal to the ridge axis (shown in red) and propagate hydrostatically through a height varying background wind profile (shown in yellow). The entire problem is "two dimensionalized" along a plane defined by the white mountain wave axes.

The mountain wave vector is aligned at right angles to the ridge axis (i.e. the alignment of the "long axis" of the ridge), as shown in red in Figure 1. The entire problem is two-dimensionalized along the white axes in Figure 1. Background flow (shown in yellow) occurs at arbitrary angles to the ridge, but only the component along the white axes is "felt" by the forced mountain wave. The vertical variation of the winds along the white axis affects the propagation and amplitude development of the mountain wave.

The model is clearly very simple. Our experience is that these simplifications lead to the model being "overactive," in the sense that, when the approximations fail, it tends to overestimate levels of mountain wave activity. For many applications, this is a somehat desirable property, as it gives a maximum or "upper limit" measure of possible mountain wave activity (for instance, it is always best to overestimate rather than underestimate possible mountain wave-induced turbulence when planning aircraft flights).

We are working at improving weaknesses in the model in the next generation model MWFM 2.0.

The major approximations and limitations of the current approach are summarized below, in order of their ``suspectness.''

1) Linear Wave Saturation: This assumes that each individual gravity wave behaves in a linear fashion (i.e. as a small-amplitude plane wave), until the wave produces instabilities. At this point, linear saturation theory assumes that the instabilities drain exactly enough energy from the wave to maintain it on the verge of instability. A related assumption is made at the lower boundary, to determine the initial amplitude of the mountain wave. Here saturation is used to limit the amplitudes of mountain waves from larger scale ridge features (in practice, those higher than 1000 meters). Nonlinear processes are assumed to force some portion of the flow to go around, rather than over, large mountains, or to simply bring the low-level flow to a complete stop in the case of tall, very long ridges (so-called "blocking").

2) The Hydrostatic Approximation: This amounts to assuming that each ridge is broad compared to an intrinsic, flow-related vertical wavelength. While this length scale may vary from day to day at any location, in practice the hydrostatic approximation is only good for ridges with widths much greater than about 10km. Thus, for a large number of ridges on earth (e.g., The Appalachians) this approximation is suspect. The end result of making this approximation inappropriately is to confine the predicted wave activity too narrowly over the forcing topography. This results in wave amplitudes that are too large immediately over the ridge and too small downstream of the ridge. In certain cases nonhydrostatic effects can prevent vertical propagation. Thus, a hydrostatic model would predict penetration of the wave to higher altitudes than actually occurs.

3) Two-dimensionality: This amounts to assuming that each ridge is very long compared to its width. While this may seem like a very bad approximation in many cases, evidence suggests that as long as the ridge aspect-ratio is greater than 3:1 2-D may not be a bad description of the wave forcing by the ridge. Nevertheless, many mountain wave features have a more three-dimensional structure, which gives rise to three-dimensional radiated mountain patterns (e.g., "ship wave" patterns).