Point processes and random sets for analyzing patterns of methylene blue coloured soil

Abstract

We consider the problem of quantitatively characterizing horizontal patterns of dye following infiltration. Such patterns display important information on the movement of possibly contaminated solutes from the soil surface to the ground water, which may cause risks for human health. The stains were made visible by means of methylene blue dye tracers. Different spatial statistical techniques are compared. First, a standard point pattern analysis is applied. Since the stains usually have a non-point type appearance, geostatistical techniques were used to account for positive areas. Next, more advanced point pattern techniques have been applied on replicate samples from different land management and land use types, focusing on the hazard rate for spatial patterns. As it turned out, point patterns analysis and geostatistics could be used in a complementary way, the point pattern analysis by considering colouring as basically generated by single points, the geostatistics by taking the spatial extension into account as well. The spatial hazard rate was useful to detect changes in the effects of land use.