Talk:Yamartino method

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in the process of editing, but need to leave Hwestbrook 23:09, 10 November 2006 (UTC)

Significant additions to this wiki over the last two days. Added actual algorithm and link to original journal article by Yamartino. Also added links to this article on the wiki for wind direction and standard deviation. Gouveia2 17:28, 16 March 2007 (UTC)

Comment[edit]

There seems to be no link or reference for exactly what quantity this method is trying to find an approximation for. That is, define what the "true" value of σθ should be. The link to standard deviation does not mention angular variables, and the wind direction link does not mention standard deviation. Melcombe (talk) 09:43, 17 April 2008 (UTC)

Yamartino's original article uses the two-pass method (his Eq. 1) as "the correctly determined value of σθ". Are you saying this isn't enough of a reference? Maybe you're right.
The wiki article does link to standard deviation. Isn't this enough?
Wind direction does have a link to Yamartino method. Maybe this should be expanded? Gouveia2 (talk) 16:39, 17 April 2008 (UTC)

Two pass not an issue[edit]

For standard deviations (or variances), a single-pass method involving the sum of x, and the sum of the squares of x is well-known and just as avaialable to data loggers with limited memory. The real problem is the attempt to average angles due to the 0°/360° transition. The scheme presented could be rephrased in terms of complex numbers, as it amounts to the average position of unit vectors. (That's another point - the vectors could have a length given by the wind speed, thus a different sort of average) The real question remains: what is the "true" standard deviation that is being approximated? The supplied link is defunct, alas, and some other articles are making my head hurt. Enough! I'm off for lunch. NickyMcLean (talk) 01:04, 30 March 2011 (UTC)

Complete Incomprehension[edit]

I don't understand this calculation at all. Suppose that every wind direction was equal, then, the standard deviation of the direction should be zero, yet the result of this calculation will not be zero except for particular wind directions. It depends only on Sa and Ca, not on any variation around the average direction.

By contrast, the scheme for computing a SD from a set of values Xi in a single pass requires the accumulation of two sums, of X and of X**2, and the deviation from the average shows up in these two parameters. Whereas my understanding of the description here has only one accumulation - though there are two parameters Sa and Ca, they are two parts of one complex number, Z = (Ca,Sa) and there is the sum of Z only (whence the average), with nothing corresponding to a sum of Z**2 or similar to calculate a SD as well. NickyMcLean (talk) 01:19, 31 March 2011 (UTC)

Aha. On looking afresh, the key is to remember that sin2θ + cos2θ = 1, so that in the case where all angles are equal, \varepsilon=\sqrt{1-(s^2_a+c^2_a)} will be zero, leading to a zero value for the standard deviation. NickyMcLean (talk) 22:14, 21 August 2011 (UTC)