[GRASS-user] Re: Thin plate spline for climate point, record interpolation?

[Michael Barton]

Andreas and Dimos,

In my NSF project, we are doing the kind of climate spatial modeling  
that you are discussing below. As you note, Andreas, this is not  
really interpolation, but multiple regression in that it takes into  
account topographic parameters that can affect the weather. We've been  
using external software--some initial work in ArcGIS (which could also  
be done in GRASS) and primarily Excel and OpenOffice for the  
regressions, but may do something more sophisticated in the very near  
future--to calculate the regression coefficients that best account for  
variance in, say precipitation, among known weather stations. Then we  
apply those coefficients to a raster landscape in GRASS, using the map  
calculator, to create climate landscapes.

A couple of examples can be seen in this conference paper:
Barton, Michael, H. Sarjoughian, S. Falconer, H. Mitasova, R.  
Arrowsmith, & P. Fall (2006) Modeling Long-Term Landscape Dynamics and  
the Emergence of Intensification. Invited symposium paper presented at  
the 71st Annual Meeting of the Society for American Archaeology, San  
Juan. Link to PDF (2 Mb): http://www.asu.edu/clas/shesc/projects/medland/files/barton_etal_SAA2006.pdf

More on our methodology can be found here:
Hill, J. Brett, Alexandra Miller, Elizabeth Wentz. & C. Michael Barton  
(2008). Archaeoclimatology and Ancient Mediterranean Landscape  
Dynamics. Invited symposium paper presented at the 73rd Annual Meeting  
of the Society for American Archaeology, Vancouver, BC. Link to PDF  
(1.3 Mb): http://www.asu.edu/clas/shesc/projects/medland/files/Hill_etal_SAA2008.pdf

Hope this helps.

Michael


On Jul 26, 2008, at 7:48 AM, <grass-user-request at lists.osgeo.org> <grass-user-request at lists.osgeo.org 
 > wrote:

> Date: Sat, 26 Jul 2008 16:30:53 +0200
> From: Andreas Philipp <andreas.philipp at geo.uni-augsburg.de>
> Subject: Re: [GRASS-user] Re: Thin plate spline for climate point
> 	record	interpollation?
> To: grass-user <grass-user at lists.osgeo.org>
> Message-ID: <1217082653.9125.19.camel at geo>
> Content-Type: text/plain
>
>
> I think Dimos does not look just for "normal" interpolation of a
> variable just using the spatial information of the variable itself,  
> but
> for a procedure using additionally a multiple regression scheme of a  
> set
> of "independent" variables. As far as I know there is no tool yet to  
> do
> that easily within GRASS at the moment (please correct me if it is  
> there
> already).
>
> Because I was also thinking how to realise a regression based
> interpolation scheme in GRASS and might be not the only one, I try to
> describe the problem:
>
> Those independent variables can be elevation, lat and lon of the  
> station
> or relief parameters which have a stable average influence on the
> spatial distribution of the target variable.
> E.g. in order to interpolate temperature accurately you
> calculate a regression coefficient from height-above-sea-level-values
> onto the temperature-values (over the whole space and time domain).  
> Then
> you subtract the fitted temperature values from the observed
> temperatures and receive a temperature anomaly field (the residuals)
> which would be realised if no height differences would be given but  
> only
> the spatial temperature variation due to meteorological reasons. Then
> these anomalies (residuals) are interpolated in space with splines or
> whatever onto a regular grid. Afterwards this grid is scaled to height
> again by using the regression coefficients, et voila. This takes into
> account that the target variable is not only dependend of spatial
> autocorrelation (interpolated temperature of a mountain is then not as
> high as the station record in the nearby valley). This is a procedure
> which is commonly recommended in climatology.
> However, in order to calculate the regression coefficients, longer  
> time
> series should be used (not only the time slice or map which is  
> intended
> to be interpolated) in order to get the pure average dependence of
> temperature to elevation. Further it might be necessary to do the  
> whole
> analysis for each month of the year separately in order to account for
> effects of large scale climatological differences in the annual cycle.
>
> Instead of elevation only also latitude, longitude and other  
> parameters
> can be used in a multiple regression scheme. An especially interesting
> independent parameter is a typical relief type of the surrounding of
> each gridpoint (achieved by principal component analysis of the
> neighbour grid point heights in a moving window. May be to be  
> plugged in
> into r.li?).
>
> If I'm right this is not easy to do within GRASS at this time. May  
> be R
> can be used as a work around? Anyone has an idea?
> I think it would be great to have such a tool originally in GRASS (I'm
> sure a lot of climatologists would grep for GRASS just for that  
> feature)
> but it is a bit of work to program it (I think the main problem  
> would be
> the multiple regression, if only there was a fortran90 interface ...).
>
> However to use a single independent variable may be r.mapcalc could be
> used if the vector point observations are transformed to raster maps
> (bivariate regression is rather simple even if quite a few raster maps
> are neccessary).
>
> Hm, quite a long mail, but may be some others are interested and  
> willing
> to solve ...
> Please correct me if I'm missing something.
>
> Andreas