Kriging is a statistical technique used to interpolate spatial sparse data and obtain a field of measures. Interpolation of data (Mitas and Mitasova, 1999) is ubiquitous i hydrology and, in fact, the GEOframe system contains a solid Kriging interpolator.

In fact, in literature there exist some trials to get a version of Kriging constrained to such values. Mainly three are the relevant contributions.

My preferred one is Szidarovszky et al., 1987 which takes the problem directly by definitions and solve it. However also Deutsch, 1996 use an iterative (trial and error method to obtain the same result). A more restrictive condition which impose the conservation of the total "mass" of the quantity modeled is pursued in Walvoort and de Gruiter (2001).

Other suggest, especially for the case of precipitation of using an indicator Kriging to detect locations where rain is falling from locations where it is not (e.g. Atkinson, 1998) or cokriging techniques.

References

Adhikary, Sajal Kumar, Nitin Muttil, and Abdullah Gokhan Yilmaz. 2017. “Cokriging for Enhanced Spatial Interpolation of Rainfall in Two Australian Catchments.” *Hydrological Processes* 31 (12): 2143–61.

Atkinson, Peter M. 1998. “Mapping Precipitation in Switzerland with Ordinary and Indicator Kriging.” *Journal of Geographic Information and Deci Sion Analysis* 2 (2): 65–76.

Deutsch, Clayton V. 1996. “Correcting for Negative Weights in Ordinary Kriging.”

*Computers & Geosciences*.

https://doi.org/10.1016/0098-3004(96)00005-2.

Mitas, Lubos, and Helena Mitasova. 1999. “Spatial Interpolation.”

*Geographical Information Systems: Principles, Techniques, Management and Applications* 1 (2).

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.224.5959&rep=rep1&type=pdf.

Myers, Donald E. 1991. “Pseudo-Cross Variograms, Positive-Definiteness, and Cokriging.” *Mathematical Geology*. https://doi.org/10.1007/bf02068776.

Walvoort, Dennis J. J., and Jaap J. de Gruijter. 2001. “Compositional Kriging: A Spatial Interpolation Method for Compositional Data.” *Mathematical Geology* 33 (8): 951–66.