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Re: GRIDDATA woes [message #59094 is a reply to message #59031]

Wed, 05 March 2008 06:14

Kenneth Bowman
Messages: 86
Registered: November 2006

Member

In article <MPG.223755c5d615d3ab98a2aa@news.frii.com>,
David Fanning <news@dfanning.com> wrote:

> Do you have a way of handling this situation? I mention
> this because in the perverse CCCMA climate model I am
> using, the longitude vector is evenly spaced, *except*
> for the two values at either end of the vector. (Don't
> ask me, I have no idea.) My "regularly spaced" interpolation
> vector blows up on me at either end.

I forgot to add that global spectral models, of which the CCCMA
is an example, use a Gaussian grid in the latitudinal direction.
This allows the use of Gaussian quadrature to compute the
Legendre transforms that are essential to the way a spectral
model works.

The Gaussian grid does not have points at the poles. Sometimes
it is desirable to interpolate to a regular grid that does have
points at the poles. In this case, I think the best approach is
to treat the pole points as special. They can be calculated by
*averaging* all of the points in the northernmost and southernmost
rows of the Gaussian grid. That is, to estimate the value at
90 deg N, average the last row of points, which might be at
89.5 deg N. This makes good physical sense, because the
northernmost row of points actually lie in a circle surrounding
the pole.

If you chose your regular grid wisely ( ;-) ), then the row of points
closest to, but not at, the poles, will lie equatorward of the
highest latitude points of the Gaussian grid.

If you need to interpolate to a row of points poleward of the
highest latitude Gaussian points, then use your interpolated
(averaged) value at the poles to extend the Gaussian grid to
+/- 90 deg and do bilinear interpolation as usual.

If that isn't clear, I can draw some pictures.

Cheers, Ken

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[Message index]

		Re: GRIDDATA woes By: David Fanning on Tue, 04 March 2008 13:14
		Re: GRIDDATA woes By: David Fanning on Tue, 04 March 2008 11:49
		Re: GRIDDATA woes By: David Fanning on Tue, 04 March 2008 09:54
		Re: GRIDDATA woes By: wgallery on Tue, 04 March 2008 09:43
		Re: GRIDDATA woes By: David Fanning on Tue, 04 March 2008 09:14
		Re: GRIDDATA woes By: David Fanning on Tue, 04 March 2008 09:05
		Re: GRIDDATA woes By: Brian Larsen on Tue, 04 March 2008 08:23
		Re: GRIDDATA woes By: ben.bighair on Tue, 04 March 2008 08:05
		Re: GRIDDATA woes By: David Fanning on Tue, 04 March 2008 08:03
		Re: GRIDDATA woes By: David Fanning on Tue, 04 March 2008 07:35
		Re: GRIDDATA woes By: Kenneth P. Bowman on Mon, 03 March 2008 06:24
		Re: GRIDDATA woes By: wgallery on Mon, 03 March 2008 11:00
		Re: GRIDDATA woes By: Kenneth P. Bowman on Tue, 04 March 2008 19:04
		Re: GRIDDATA woes By: Kenneth P. Bowman on Tue, 04 March 2008 19:02
		Re: GRIDDATA woes By: wgallery on Tue, 04 March 2008 14:17
		Re: GRIDDATA woes By: Kenneth Bowman on Wed, 05 March 2008 06:14
		Re: GRIDDATA woes By: Kenneth P. Bowman on Tue, 04 March 2008 18:55
		Re: GRIDDATA woes By: ben.bighair on Tue, 04 March 2008 14:46
		Re: GRIDDATA woes By: pgrigis on Tue, 04 March 2008 14:39

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