Property changes in space

In sectionSpatial distribution analysis of change indices we were considering spatial features as permanent during the studied period and were focusing on the description of their property changes. In this section, we will now consider the study area as a whole and then model the spatial distribution of properties of a phenomenon and its change through the considered period of time. With this approach, spatial features are resulting from the spatial distribution of properties at each moment. In order to build up these spatial features, it is necessary to describe space with regular units of observation rather than existing spatial features, such as regular cells in image mode. The objective of this approach is to model the process of spatial property changes in order to describe past changes to the present time, but also to forecast future changes.

As previously discussed and illustrated, one should differentiate between phenomena with a continuous spatial distribution from those with a discontinuous (discrete) spatial distribution. This is important because of the differences in rules pertaining to spatial autocorrelation. Let us differentiate between two general approaches ruled by the nature of the spatial distribution of the considered phenomenon:

• Discontinuous spatial distribution : As the number of possible properties is limited, they are mainly expressed at a nominal level with a categorical content. In this situation we are involved with the analysis of a change of state for each unit of observation. Each cell has a specific state at beginning of the process and the model has to evaluate the probabilities to change to another state according to probabilities or possibilities of occurrence as well as to the neighbourhood properties. In this situation the spatial dependency is limited to a local neighbour. This approach can be modelled with the use of cellular automata. (link to lesson)
• Continuous spatial distribution : In this context the number of possible properties is very large or even infinite. The assumption is that the property at a specific location (a cell) is influenced by the proximity to other cells up to a threshold distance of influence. Throughout time the model should express a change of intensity (quantitative). Such situations assume a high spatial dependency (autocorrelation) and can be modelled by contagious spatial diffusion models (link to lesson).