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Striding and aliasing #1007

Open karlmsmith opened 6 years ago

karlmsmith commented 6 years ago

Reported by @AnsleyManke on 14 Dec 2010 17:41 UTC For a time axis with an annual signal, there are choices of strides that will cause aliasing. Sampling every 10th or 11th month, say, causes a false signal of 10 or 11 years.

Should the striding methods do something to determine the frequency of the original time series and sample so that the decimation does not cause aliasing??

Example:

yes? use coads_air
yes? set view upper
yes? plot/x=300/y=20/t=1-jan-1950:1-jan-1995 air
yes? set view lower
yes? plot/x=300/y=20/\\
title="Sampled: 11 months(black),12 months(red),12 months offset(green)"  \\
air[l=1153:1692:11],air[l=1153:1692:12], air[l=1159:1698:12]

The upper panel shows the full resolution data, the lower one an aliased sample - where the signal gets spread out over 11 years, and two other sampling choices which sample once per the annual cycle and so don't show the aliasing.

Migrated-From: http://dunkel.pmel.noaa.gov/trac/las/ticket/1001

karlmsmith commented 6 years ago

Attachment from @AnsleyManke on 14 Dec 2010 17:43 UTC aliasing a monthly time series alias

karlmsmith commented 6 years ago

Comment by steven.c.hankin on 14 Dec 2010 18:26 UTC This is a very serious concern for the striding approach and calendar axes. Only certain deltas are permissible on monthly data. You have to have at least 2 samples per cycle to avoid aliasing. So deltas of 2, 3, 4, or 6 are ok. (6 is already dangerous, because it is likely to significantly miss the extreme seasonal values.)

On the other hand the extreme errors that we are seeing in the example are a little artificial. A 40 year time series of monthly data is 480 points, which would not reach the threshold to stride, I believe. (yes? allows 800 points?) Strides of 2,3,4,6 would be used for time series of up to (approx) 4800 points.

Lets look at this problem again using the actual algorithm that the plotting scripts use on very long time series. We're after a "visually correct" result. We also need to think about this for Hofmoller plots, where the striding algorithm might get applied differently.

Another question: does the Ferret script "know" that it is looking at a monthly time axis?

karlmsmith commented 6 years ago

Modified by @AnsleyManke on 6 Jan 2011 23:26 UTC