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, <[EMAIL PROTECTED]> <[EMAIL PROTECTED]
> wrote:
Date: Sat, 26 Jul 2008 16:30:53 +0200
From: Andreas Philipp <[EMAIL PROTECTED]>
Subject: Re: [GRASS-user] Re: Thin plate spline for climate point
record interpollation?
To: grass-user <[email protected]>
Message-ID: <[EMAIL PROTECTED]>
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
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