[R-sig-Geo] are these methods appropriate for four dimensional modeling?

[Dylan Beaudette]

On Monday 08 February 2010, Mark Connolly wrote:
> repeat post - added signature
>
> I am working on a thesis in soil science with four dimensional modeling
> as a major component.  I am using R for the interpolation of data and
> VisIT to render the data as volumes and as volumes changing in time.  I
> am using Applied Spatial Data Analysis with R (Bivand, Pebesma,
> Gomez-Rubio) as a reference.  I've also been using Chatfield's Analysis
> of Time Series, less for time series specifically than for helping to
> understand the statistical concepts.

Hi Mark, nice to see a fellow soil scientist on R-sig-geo.

> My data are soil property data. A purely spatial component comprises
> nine soil physical properties taken across a 12 ha agriculture field.
> There are sixty locations with five measurement depths at each location
> (3D).  The spatial-temporal component is the measure of volumetric soil
> moisture status taken at the same 300 positions.  These data are
> discrete readings taken at unequal intervals.  The readings exist for
> growing seasons over three years.

We have a similar dataset, and have found that RST interpolation to be a 
useful starting point. GRASS has functionality for interpolating volumetric 
data, and numerous export routines for visualization in Paraview. Here are 
some examples:

http://www-pool.math.tu-berlin.de/~soeren/grass/modules/screenshots/

> The observation grid is half regular and half semi-random.  Each of
> thirty regularly placed locations has a satellite location set in random
> proximity but not too far and not too close.  The observation depths are
> at 15 cm intervals starting at -15 cm and extending down to -75 cm.
>
> My first pass through the data was mainly concerned with the mechanics
> of the process.  I used IDW for interpolating each of the soil
> properties through the volume (myriad packages including sp, gstat, and
> others mentioned in Bivand et al), treating each property as independent
> of the others.
>
> I then went after the temporal soil moisture data.  At each of the 300
> positions, I took the set of time-sequenced measures (measurement
> intervals varied from days to weeks during each growing season) and
> interpolated values for days not measured.  I used the Stineman
> algorithm provided by the na.stinterp function from the stinepack R
> package.  Once I had all days for all positions, I used IDW again to
> interpolate volumes for each day.
>
> Each volume was exported as an unstructured point grid for rendering in
> VisIT.  My data analysis was limited to adjusting the IDW weighting
> power such that the density distributions of the interpolated values
> were similar to the density distributions of the observed values
> (eyeballing overlaid plots).
>
> My interpolation grid cell size is defined at 10x10x1, modeling 10 m by
> 10 m by 1 meter.  This is a little misleading.  I treat the depth
> dimension as having the same units as the areal dimension, so -15 cm
> becomes equivalent to -15 m.  Two reasons (the second not necessarily
> defensible): I need the depth to be scaled for reasonable visualization,
> and I want to decrease the influence of the depth measures on the layers
> above and below each depth.

Again RST interpolation to voxels may be useful in this case. There has been 
some talk on the GRASS mailing list about interpolation through time, but I 
haven't seen anything available yet.

Cheers,
Dylan


> In my next iteration through the data, I'd like to use the
> geostatistical techniques presented in Bivand et al.  I have (just)
> started with variograms with the hope of exploring the variogram in the
> context of the volume.  I have run into the problem of dimensionality.
> The plot functions are 2D, so projecting the variogram onto the
> observation spatial volume is not working.  That got me thinking.  If I
> use kriging, will I be using the influence of depth in the interpolation
> model?  Is the variogram created with the influence of depth when the
> spatial structure has three dimensions?  Is a better use to treat each
> depth as a separate layer to be interpolated in two dimensions,
> especially given that soils are often physically layered?  If three
> dimensional kriging is okay, how about four dimensional to move through
> a time series? Or would I be better to stick with the Stineman algorithm
> for the time-series interpolation?
>
> Any feedback on this (including any warnings that I might be abusing
> things with my time series and IDW approaches) would be very much
> appreciated.  I am definitely in learning mode.
>
> Mark



-- 
Dylan Beaudette
Soil Resource Laboratory
http://casoilresource.lawr.ucdavis.edu/
University of California at Davis
530.754.7341