Quantitative measures for the local similarity of hydrological spatial patterns

The task of assessing similarity between data sets is common in hydrological modelling. While this has been widely researched for temporal data sets, the similarity between spatial patterns has been largely ignored. This has been due to a lack of spatial pattern data. Today there is widespread use of distributed hydrological models and increasing availability of observed spatial patterns. These observed spatial patterns are useful for model calibration and optimisation, though at present there is limited use of the spatial information contained in them, other than through visual comparison. This is mostly due to a lack of understanding of methods to make optimal use of this information-rich data. The work in this paper investigates quantitative measures for judging the similarity between observed and simulated spatial patterns, with a particular emphasis on local similarity techniques. Three methods — fuzzy comparison, importance maps and image segmentation — are introduced, with a detailed demonstration using fuzzy comparison. Fuzzy comparison allows users to specify their tolerance for errors in value and location when comparing spatial patterns. The different measures presented here can be used to assess many aspects of similarity, which is important for automated model calibration and/or evaluation.