Detecting trends and changes in urbanization via statistical modelling of land use maps

Land use maps are a powerful resource to study the dynamics of urban growth. Official land use data, routinely produced by a wide range of institutions, are usually the result of processing remote sensing images. After complex elaborations, maps are provided to the public in two possible spatial formats: vector and raster. Vector maps are a collection of polygons, where each polygon belongs to a land use category. Raster maps result from converting polygons into a regular lattice or grid, where each grid box is assigned a land use category. Visual inspection of raster maps can immediately provide important information on the urban distribution over space, however, formal methods for the detection of spatio-temporal trends in this type of data are required. Modelling the spatial dependencies using the traditional Matern class of covariance functions is problematic because of the high dimensionality of these maps. We discuss efficient P-spline smoothing models for raster maps, which give computational advantages and therefore allows urbanization trends to be investigated, even in relatively large regions such as a city or a metropolitan area. An application of the proposed models is illustrated on urban data on the metropolitan area around Bologna, Italy. One of the most challenging application goals is the detection of regions showing a significant change in the urbanisation process over time.