A data structure with associated algorithms for representing and reconstructing contaminant transport in realistic complex geometries, e.g. in cities and around buildings, is described (160). The data structure has a pair of two-dimensional matrices compressed and extracted from three-dimensional matrices describing the transport and dispersion of contaminants in complex geometries using full-resolution, time-dependent computational fluid dynamics or compete and detailed experimental data (130). A first matrix (220, 320) has numerical values, in which continuous, monotone, gauge-invariant contours of the same value represent an edge of a family of contaminant clouds transported from one edge of the domain. A second matrix (250, 350) contains numerical values, in which continuous, monotone, gauge-invariant contours of the same value represent an opposite edge of a family of contaminant clouds transported from the other edge of the domain. The dual-matrix data structure may be used by overlapping the two matrices (440, 480) within the domain, and reading the areas between the two edge contours crossing at particular locations of interest.