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MWFM 2.0 |
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MWFM 2.0 |
| We are currently working on improvements in our
parameterization of mountain waves, which will be built into a next generation version of
MWFM, which we are referring to at present as MWFM 2.0. The work is
developmental. Nevertheless,
several key extensions have already been implemented in a working research version of MWFM
2.0, and we have begun using and testing the new code in operational
forecasting scenarios (e.g., USA forecasts and SOLVE
forecasts). We have also used MWFM
2.0 to model stratospheric mountain waves over the southern Andes observed
from space by the CRISTA instrument in November, 1994 [Eckermann and
Preusse, 1999] The overall MWFM 2.0 initiative aims to divest MWFM of some of its grosser simplifications, such as two dimensionality, hydrostatic wave equations, simplified descriptions of the Earth's topography, and so on. Many possible extensions and additions could be made. We are focusing on those that we believe can make significant improvements to its predictive capabilities - those that do not do so will not be incorporated operationally. Much of this work has also been motivated by new applications for MWFM that were not envisaged when the model was first developed. Examples include the forecasting of mountain wave-induced production of polar stratospheric clouds in the Arctic stratosphere, and detailed comparisons of MWFM predictions with the characteristics of measured mountain-waves. Some of our main avenues of current research are discussed briefly below. 1. Nonhydrostatic Rotational Wave Equations and Saturation Criteria MWFM uses hydrostatic irrotational wave equations, which omit processes that can be important in mountain wave dynamics. Examples include vertical reflection (so-called "turning levels"), downstream penetration of wave perturbations, dynamical wave-induced instabilities, to name just a few. We have developed a new test version of MWFM which incorporates a ray-based extension of the model's wave equations, simplified from the general ray formulation used in GROGRAT. Wave group velocities are calculated using a rotating nonhydrostatic dispersion relation. Wave amplitudes are calculated using conservation of vertical flux of wave action, with rotational and nonhydrostatic terms retained. Wave breaking is accomodated through both convective and dynamical instability criteria. Tests of these extensions are in progress. 2. Three Dimensionality
Generalization to flow over three-dimensional obstacles follows somewhat from the extensions discussed in section 1. Specifically, we have been investigating how the ray methods cited above might be used to describe the complex three-dimensional mountain wave patterns that radiate from three-dimensional mountains. A range of examples from orbital cloud imagery are shown in Figure 1. The first row of images (left) show banded cloud structures over Jan Mayen, a small island dominated by a large quasi-circular volcanic mountain called Mount Beerenberg (click here for a longer discussion on wave clouds from Jan Mayen). The bottom-left photo shows similar patterns streaming from an isolated mountain peak on South Georges Island, a long mountainous island chain in the Atlantic north of Antarctica. The final photo shows a number of banded structures over the Falkland Islands. Note in each case the characteristic "ship wave" patterns of radiated waves evident in the cloud banding, rather than regular linear cloud banding produced by mountain waves that emanate from two-dimensional topography (e.g., see some of the linear cloud bands produced by mountain waves over The Appalachians and The Colorado Rockies; for other sources of quasi-plane wave trains, see Figures 1-2 of Erickson and Whitney [1973] and Figure 3 of Reeder and Christie [1998]). Note too that observations over complex topography reveal wave patterns which appear to differ from either plane-wave or simple ship-wave patterns [e.g., Worthington, 1999].
Figure 2 shows some of our preliminary attempts to model these sort of mountain wave patterns using a ray-based methodology. The pattern in Figure 2 was synthesized by tracing a spectrum of waves launched at all possible azimuth angles from the circular Gaussian mountain at the origin. The wind was constant and directed along the dotted blue line. Each ray was assigned a horizontal wavelength and packet width based on the circular Gaussian mountain shape. We see that a radiating ship wave pattern, qualitatively similar to those seen in Figure 1, is produced. We are working currently on better ways to describe the amplitude evolution and dispersion of wave action from isolated three-dimensional obstacles such as these. We have made significant recent progress recently in using ray-based methods to parameterize accurately mountain wave patterns emanating from complex height-varying flow over three-dimensional mountains [Broutman et al., 1999] 3. Wavelet Decomposition of Digital Elevation Data The algorithms used to compile the current list of ridges in MWFM was based on locating long quasi-two dimensional ridge features over the Earth. We have been looking at developing better ways of compiling accurate lists of dominant topographic features over the Earth from the improved higher resolution maps of digital elevation data that are now available. Wavelet methods appear to offer promising possibilities and we have been testing ways of constructing new ridge databases from wavelet decomposition methods. REFERENCES
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