I have a problem concerning interpolation of compositional data of grain sizes. I need to interpolate the content of each component (clay, silt, sand in percent) to a raster. There are compositional variables — the values are connected by definition. In the case of the three texture fractions, a value of any variable equals 100 less sum of the other two.
As I am reading into this topic I get into more and more problems. For kriging there compositional data do not meet the constrains of stationarity and known mean value. On the other hand my results do not satisfy the constant sum and nonnegativity constrains of the data.
Walvoort and de Gruijter (2001) for example, already developed a compositional solution for ordinary kriging that will enforce estimated values to sum to unity at all locations. (Walvoort, D. J. J., de Gruijter, J. J., 2001. Compositional Kriging: A Spatial Interpolation Method forCompositional Data. Mathematical Geology 33 (8): 951–966)
I would like to use ArcGIS and its geostatistical capacities - what would be your method of choice for such a interpolation? (There has been developed an R package for such cases: http://www.inside-r.org/packages/cran/compositions/docs/compOKriging - but I am not into this program yet to be able to generate meaningful results quickly)