The research objective is the analysis of the appropriation of space in urban public parks. For this purpose, extensive field observations were conducted in several parks in Zurich, Switzerland, over the span of three years, with records made of the location, assumed age, gender and activity of park visitors. Based on research in environmental psychology and anthropology, a model was developed building on the two concepts of «personal space» and «activity footprints» to represent space appropriation. In line with the view that quantitative spatial analysis methods remain a valid tool for critical, non-positivist research, the model was implemented using kernel density estimations for the spatio-temporal analysis of the observed park use. It is argued that the probability surfaces generated by kernel density estimations are an adequate representation of the specific vagueness of human space appropriation as they remain sensitive to the presence of individual park visitors.