Class Project: Spectral Analysis of Reanalysis Data

This is an alternative to the standard spectral analysis homework, in which you work on synthetic data. In this case you use real data, but of course it is messier. The data are taken from reanalysis products, so there are not missing values, though.

The data are stored in vT_195709_200208.mat in my public directory.

It contains time series of v and T for 45N at 5 longitude locations (300, 302.5, 305, 307.5, 310) from 1 Sept 1957 – 31 Aug 2002 (the entire time series from the ERA-40 reanalysis). The data are every 6 hours (4x daily).

There are two time vectors. 'time' is in hours since 1800-01-01. 'year' is decimal year.

The objective is to see if there are any periodicities near 4-5 days or so, as suggested in Hartmann(1974). He focused on the winter season. There are several challenges.

1) Probably need to remove the annual cycle.

2) 4x daily is much more frequent that needed. Probably should smooth a bit and resample at 12 or 24 hour intervals.

3) The period will be broad at best and might depend on season. Since we have 45 years of data we could focus on only the winter season, picking a Hamming window that centers on winter and averaging 45 of those.

4) There is a lot of low frequency noise/variance in addition to the annual cycle. We probably want to remove the mean and trend from each of these chunks.

5) If these time series show nothing, we can pick another point where there might be more periodicity.

6) If you cannot show a peak, you can at least show the coherence between v and T at 850mb and its dependence on frequency.

Also available in my pub directory is a program to do some spectral analysis that I was developing mspecvt.m, plus a crude program to remove the annual cycle from the 4x daily data, removeAC.m.

Good Luck.