# Meteorology 454 - Wave Analysis Procedures

Because we are working with real data and because our observations recorded from the web site are not perfect, we will have some noise in our results. It is best to consider the data you recorded as a collective whole and attempt to discern patterns of behavior that emerge, rather than focus on individual observations. Plots similar to examples I show below will help bring out collective behavior in your data.

Analysis focuses on the questions raised at the beginning of this exercise. You should attempt to answer each of the questions posed, as well as give any further assessment yourself. Construct answers for the Southern and Northern Hemispheres.

Ultimately, you need to submit a report on your work, guided by the questions below. You should pay attention to some pointers for a good report that I have assembled. You might also find this example of a good report to be a useful guide for your analysis and report.

1. How rapidly to wave patterns move?

and

5. Is there a relationship between zonal wind speed and wave propagation?

• (a) Compute the overall average of your recorded wave speed [deg/d], separately for each hemisphere. Which way are waves moving in each hemisphere? Is travel much faster in one than the other? How many days would it take one wave crest/trough to go around a latitude circle if it remained intact?

• (b) How much does wave speed vary with zonal wind speeds you recorded, especially your U(500 hPa)? It helps to have the speeds in the same units. To do this, convert the [m/s] speed you recorded for U(500 hPa) and convert it to [deg/d] recognizing that we are looking at speeds at 50 degrees latitude. Thus, take the length of a latitude circle at 50 degrees latitude, then divide it by the wind speed to find how many days it would take to travel 360 degrees at that speed.

Make a plot of wave speed versus U(500 hPa) where both are in [deg/d]. Here is an example. Does Rossby wave theory help us here? (Think about the dispersion relationship we derived for phase speed.) Compute the overall average of the U(500 hPa) you recorded. Is the wave speed larger or smaller than the U(500 hPa) on average? Does this make sense in terms of Rossby wave theory?

Plot wave speed vs. upper atmosphere Uupper. Does a dependence on Uupper appear? Why do you think this is the case?

• (c) Rossby wave theory tells us that wave speed varies with wave number. Remove the dependence of wave speed on zonal wind by plotting (wave speed - U500) versus wavenumber (example), again making sure that both are in the same units. How does wave speed vary with wavenumber in your observations? Is the relationship consistent (even if approximate) with how Rossby wave theory tells us wave speed should change with wavenumber?

2. How long does one identifiable pattern last?

• (a) Plot wavenumber versus day in your series of observations (example). Are there persistent periods where the dominant wavenumber remains the same or shifts only by +/- 1? How long are they versus typical synoptic time scale?

• (b) Plot amplitude versus wavenumber (example). Do longer or shorter waves tend to have larger amplitude? Why do you think that might be?

3. How rapidly do waves increase or decrease in amplitude?

• Plot amplitude versus date (example). Are there episodes of growth? How long? By what percentage does amplitude increase during this period?

4. How does zonal wind evolve through the period?

and

6. Is there a relationship between zonal wind speed and wave growth/decay?

• Plot U500 versus date. If possible, plot U500 and amplitude versus date on the same graph (example). How does U500 change versus time, especially in relation to how wave amplitude changes? Is there are discernible relationship?

Overall

What does Rossby wave theory as produced by our simple barotropic model tell us about the evolution of atmospheric, large-scale waves? Are there approximate agreements between the theory and your observations? What factors might be missing in our simple barotropic model that (potentially) might improve the relationship between theory and observation if they were included?