tag:blogger.com,1999:blog-7729093380675162051.post2045252201751322579..comments2023-09-11T18:23:19.496+10:00Comments on moyhu: Cell weighting schemes for the Earth.Nick Stokeshttp://www.blogger.com/profile/06377413236983002873noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-7729093380675162051.post-70664924849333094232011-08-03T20:16:18.523+10:002011-08-03T20:16:18.523+10:00I've been thinking more about the advice of pe...I've been thinking more about the advice of penguindreams and James about interpolation methods. A basic problem here is that we don't have, at any useful stage of this LS method, anomalies to interpolate, and on land at least (where the main problem is), one can't interpolate raw temperatures from different stations.<br /> <br /> So I have to work through the weighting, and I can't easily use optimal interpolation based on the data. We don't have interpolable data, at least until the LS is done. Maybe I could compute the local offset L and then interpolate an effective anomaly as an iterative process.<br /> <br /> My inclination continues to be to work through the weights. I can invert an interpolation formula, as I described in my response to James. Maybe I can work out an optimal interpolation after calculation of L and use the coefficients<br /> <br />I still haven't really figured out what GISS does, but for the same reason I doubt that I can use it. GISS has gone to a lot of trouble to create grid-based anomalies. The LS method avoids this pesky stage.<br /><br />The simplest method may well be iterative. Do once as is, interpolate the empty cells using the resulting G (anomalies) and L, and do it again.Nick Stokeshttps://www.blogger.com/profile/06377413236983002873noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-68848690411531487672011-08-02T22:22:40.165+10:002011-08-02T22:22:40.165+10:00Thanks, PD. I have actually blogged (briefly) on k...Thanks, PD. I have actually blogged (briefly) on kriging <a href="http://moyhu.blogspot.com/2010/05/scale-of-spatial-correlation.html" rel="nofollow">previously</a>. It seems though that in practice krigers use empirical variograms, which seem to have their own homeliness.<br /><br />At first sight, what I'm looking for doesn't seem statistical. I have a known distribution of stations, and I want to partition the surface to reproduce a spatial integration formula. I've looked at ways of doing that with <a href="http://moyhu.blogspot.com/2011/03/area-weighting-and-60-stations-global.html" rel="nofollow">triangulation</a>.<br /><br />But there is an underlying notion of localness that gives a spatial scale, and depends on spatial correlation. So that's where the variogram comes in. I have the feeling that if I did get a kriging method working, the logical thing to do would be to throw away the cells and derive the weights directly from the variogram.<br /><br />I've obviously missed what GISS does - I'll try to track that down.Nick Stokeshttps://www.blogger.com/profile/06377413236983002873noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-90310209904075937612011-08-02T21:18:55.559+10:002011-08-02T21:18:55.559+10:00Kriging, OI, and Cressman are all used to fill in ...Kriging, OI, and Cressman are all used to fill in the empty cells in the first place. There's no need to fill them in first. Indeed, doing so by some other method renders these moot.<br /><br />I'm fond of homely methods myself. But since Cressman is exactly a method to assign weights to data you do have in order to fill in areas where you don't have data, and it proceeds iteratively in a diffusive-like manner, it seems worth some time of yours to see what has already been done in the area. OI is superior, but more removed from what you're brewing at home.<br /><br />GISS uses something more akin to OI. UKMO ignores the empty cells.Robert Grumbinehttps://www.blogger.com/profile/10783453972811796911noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-80732159729699558992011-08-02T20:41:39.143+10:002011-08-02T20:41:39.143+10:00Thanks, James, it's an interesting suggestion....Thanks, James, it's an interesting suggestion. It wasn't at first clear what to make of it, since I'm thinking of the problem as one of reassigning weights. But another way of solving the empty cell issue would be to put an interpolated value in the cell, and proceed with unchanged weights. Then I could use kriging or OI.<br /><br />Turning that around, since the interpolant is a linear combination of surrounding values, I could take the coefficients and use them as weight increments. That would have the same effect.<br /><br />I'd defend the homeliness of my earlier remedy, though. The default, as I think in GISS, is to do nothing, which means in effect interpolating the global average. Anything local is better than that.Nick Stokeshttps://www.blogger.com/profile/06377413236983002873noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-36267720803501642602011-08-02T18:33:29.481+10:002011-08-02T18:33:29.481+10:00There are standard, well established interpolation...There are standard, well established interpolation methods for doing this sort of thing - kriging and optimal interpolation are key terms. I'd be wary of an ad-hoc invention.James Annanhttps://www.blogger.com/profile/04318741813895533700noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-30092742220002859032011-08-02T07:00:33.420+10:002011-08-02T07:00:33.420+10:00Robert,
Yes, in the previous post I showed plots w...Robert,<br />Yes, in the previous post I showed plots with the two methods (<a href="https://sites.google.com/site/moyhudocs/pics/ju/CruLSsm5.png" rel="nofollow">eg this one</a>. What I should have done, and will add as an update, is to calculate the improvement the second scheme makes to empty cell area over a long calc.Nick Stokeshttps://www.blogger.com/profile/06377413236983002873noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-83040545768871936192011-08-02T06:56:39.227+10:002011-08-02T06:56:39.227+10:00Penguin,
Thanks for the references. The Cressman s...Penguin,<br />Thanks for the references. The Cressman scheme is for interpolating a field variable - here I'm looking at weights. Cressman requires fitting a polynomial or equivalent. Then the lat/lon information would be essential.Nick Stokeshttps://www.blogger.com/profile/06377413236983002873noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-29599927906612165642011-08-02T06:42:40.718+10:002011-08-02T06:42:40.718+10:00This new scheme you are using looks very promising...This new scheme you are using looks very promising. Have you calculated yet the difference in using it would have on a reconstruction?Robert Waynoreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-59641307866283430422011-08-02T00:35:31.999+10:002011-08-02T00:35:31.999+10:00In meteorological analysis history, what you'r...In meteorological analysis history, what you're doing here is in the vein of Cressman analysis.<br /><br />http://onlinelibrary.wiley.com/doi/10.1111/j.2153-3490.1954.tb01126.x/abstract<br /><br />http://journals.ametsoc.org/doi/abs/10.1175/1520-0493%281959%29087%3C0367%3AAOOAS%3E2.0.CO%3B2Robert Grumbinehttps://www.blogger.com/profile/10783453972811796911noreply@blogger.com