[R-sig-Geo] Projection of a large spherical surface on to a plane [SEC=UNCLASSIFIED]

[Jin.Li at ga.gov.au]

Thank you all for your kind help.

Following examples from the link provided by Edzer, I tested the difference between:
1. projection specified
coordinates(data.file.dev) = ~LON+LAT
proj4string(data.file.dev)=CRS("+proj=longlat")
vgm1 <- variogram(sqrt(mud)~1, data.file.dev)
model.1 <- fit.variogram(vgm1,vgm(1,"Exp",5,1))
coordinates(data.file.pred) = ~LON+LAT
proj4string(data.file.pred)=CRS("+proj=longlat")
mud.ok <- krige(sqrt(mud)~1, data.file.dev, data.file.pred, model = model.1)
mud.pred<- as.data.frame(mud.ok)

2. projection not specified
coordinates(data.file.dev) = ~LON+LAT
vgm1 <- variogram(sqrt(mud)~1, data.file.dev)
model.1 <- fit.variogram(vgm1,vgm(1,"Exp",5,1))
coordinates(data.file.pred) = ~LON+LAT
mud.ok <- krige(sqrt(mud)~1, data.file.dev, data.file.pred, model = model.1)
mud.pred<- as.data.frame(mud.ok)

The above code was applied to 50 datasets from an area spanning ca. 20 degrees in terms of longitude from 9 to 18 degrees south in latitude. Kriging with projection specified gave 'Warning: singular model in variogram fit' for three datasets and the consequent predictions are poor. After removing the results for these datasets, the average MAE and RMSE for the remaining 47 datasets are:
Projection specified    MAE             RMSE
Yes                             12.986  18.335
No                              12.977  18.326
It seems that the difference in terms of MAE and RMSE is really marginal. Is there any thing wrong with the code or we can really ignore the specification of projection?

To Paul, the impression was based on the comparison of the results from a few equal distance projection methods with utm projection that was used as a control.

To Martin, the projection used for the map you mentioned is Lambert conformal conic. The hexagons method seems doing a good job at pole area, while for regions between 0 to 50 degrees in latitude the effect is not so obvious.

Cheers,
Jin

-----Original Message-----
From: Edzer Pebesma [mailto:edzer.pebesma at uni-muenster.de]
Sent: Tuesday, 28 April 2009 9:23 PM
To: Paul Hiemstra
Cc: Li Jin; r-sig-geo at stat.math.ethz.ch
Subject: Re: [R-sig-Geo] Projection of a large spherical surface on to a plane [SEC=UNCLASSIFIED]

Paul, as mentioned here:

https://stat.ethz.ch/pipermail/r-sig-geo/2008-October/004456.html

gstat does use spherical distances when data are in geographical
coordinates, however the usual variogram models are typically not
non-negative definite on the sphere, and no appropriate models are
available. Some people use it despite this, but it would surely worry
me. In experiments with random points and an exponential variogram
without nugget, I've found very weird results.

To be honest I dislike it so much that I'm thinking about making it as
hard as cokriging without a valid LMC: break with an error message that
you could override, as for experimenting, and so protecting people who
don't understand what positive definite means.
--
Edzer

Paul Hiemstra wrote:
> Hi Jin Li,
>
> I seem to remember that gstat can deal with Great circle distances,
> but I could be wrong as I have never used them before. You say that a
> certain projection does not produce satisfactory results, how have you
> defined satisfactory?
>
> cheers,
> Paul
>
> Jin.Li at ga.gov.au wrote:
>> Dear all,
>>
>> We are going to interpolate biophysical variables into continuous
>> surface data using point samples in Australian EEZ that covers an
>> area of 10 utm zones and ca. 44 degrees in terms of latitude. Our
>> data is in lat and long (i.e., WGS84). We intend to apply kriging
>> methods to such a big area. Of course, we can divide the whole EEZ
>> into some subregions and actually we are going to divide it into some
>> subregions based on a number of factors, but these sub-regions are
>> still quite large and can cover 2 to 3 utms and 7-15 degrees in terms
>> of latitude. Obviously it is not quite appropriate to treat a
>> spherical surface as a plane. Given that kriging can not handle a
>> spherical surface (hope this assumption is still valid), perhaps an
>> alternative is project such spherical surface on to a plane. We have
>> tried some equal distance projections to convert our data for
>> Australian EEZ, but it seems that none of them can produce
>> satisfactory projections, although sinusoidal gave slightly bet!
> te!
>>  r results in comparison with utm projection. Any suggestions? Thanks
>> in advance.
>>
>> Cheers,
>>
>> Jin
>> _______________________________________
>> Jin Li, PhD
>> Spatial Modeller/Computational Statistician
>> Marine & Coastal Environment
>> Geoscience Australia
>> GPO Box 378, Canberra, ACT 2601, Australia
>>
>> Ph: 61 (02) 6249 9899; email: jin.li at ga.gov.au<mailto:jin.li at ga.gov.au>
>> _______________________________________
>>
>>
>>
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>>
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>
>

--
Edzer Pebesma
Institute for Geoinformatics (ifgi), University of Münster
Weseler Straße 253, 48151 Münster, Germany. Phone: +49 251
8333081, Fax: +49 251 8339763 http://ifgi.uni-muenster.de/
http://www.springer.com/978-0-387-78170-9 e.pebesma at wwu.de