Atmos 5530/6530: Upper-Level Waves Lab

Objectives:

An important characteristic of the upper-level flow is that waves with relatively low wave numbers tend to move more slowly than waves with high wave numbers. In some cases,low wave number features, commonly refered to as long waves, can remain quasistationary or even retrogress. Higher wave-number features, which we call short waves, tend to propagate through the long waves. This characteristic of upper-level waves arises from the variation of the Coriolis parameter with latitude (i.e., the beta effect) and is commonly explained using barotropic Rossby-wave dynamics. The objectives of this lab are:

To provide a basic introduction to the relationship between zonal wavelength, nondimensional wave number, and Rossby-wave phase speed.
To examine the applicability of the Rossby-wave propagation equation to a real-world case.
To examine and validate how the planetary-scale flow evolves in medium-range global forecast models.

Problem 1:

Determine the wavelength and wave number of a stationary Rossby wave at 45 N if the mean zonal wind speed is 35 m/s. and the meridional wavelength is infinite (i.e., l=0).

Problem 2:

Using the Rossby-wave propagation equation, produce a 12-h forecast of the position of an upper-level trough that was observed over the United States at 1200 UTC 18 October 1996. Assume an infinite meridional wavelength (i.e., l=0), follow the guidelines below, and remember that to estimate the zonal wavelength, 1 degree longitude at 40N equals 85 km.

On the 500 mb geopotential height analysis for 1200 UTC 18 October 1996, mark with a dashed line the axis of the upper-level trough that is located over the midwest United States.
Estimate the propagation speed of the this trough using the Rossby-wave propagation equation (Lackmann 2011, eq. 1.56). Wavelength can be estimated using the ridge axes that are located immediately upwind and downwind of the upper-level trough. Make a reasonable guess for the zonal wind speed using the 500 mb zonal wind analysis. Focus on values around 40 N. In addition to your calculations, be sure to briefly explain your selection of zonal wavelength and zonal wind speed values.
Forecast the position of the trough at 0000 UTC 19 October based on the estimated Rossby wave phase speed.
Plot this position on the 12 h ETA model 500 mb forecast. Is your estimate reasonable? What are some of the assumptions used to derive the Rossby wave propagation equation that may limit the accuracy of your estimate?