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

[Andreas Philipp]

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


Am Freitag, den 25.07.2008, 23:35 -0700 schrieb Dimos: 
> Searching at the Grass online manual, I have found two
> modules that are relevant to my question:
> 
> 1)v.surf.rst 
> 2)v.vol.rst
> 
> So, maybe these could be used to create a 1km climate
> surface with independent variables of Lat, Long and
> Elev? (v.vol.rst needs similar input on the 3D x,y,z
> files)
> 
> Thanks, Dimos
> 
> 
> --- Dimos <dimos_anastasiou at yahoo.com> wrote:
> 
> > Dear Grass Users,
> > 
> > How to do thin plate spline interpolation with Grass
> > GIS (ex. Anusplin
> >
> http://fennerschool.anu.edu.au/publications/software/anusplin.php)
> > using:
> > 
> > -Lat, long and elevation as the 3 independent
> > variables
> > -Temperature or precipitation as dependent variable
> > -1 KM elevation grid 
> > -Irregularly spaced 30 year climate records (POINT
> > DATA)
> > 
> > To create a: 1 KM resolution climate surface for
> > each
> > dependent variable
> > 
> > Thanks,
> > 
> > Dimos
> > 
> 
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