Quantitative comparison of categorical maps with applications for the analysis of global environmental data

This dissertation reviews the map comparison methodology literature and presents a new technique for comparing categorical grid data. The technique employs a distance approach and results in a statistic, referred to as the "Nomad" (Normalized Minimum Agreement Distance) Index. The Nomad Index is developed as an alternative to the Kappa statistic and other map comparison measures for evaluating interpolation results, classification accuracy, spatial model output, and spatial change over time. The algorithm for calculating the Nomad Index determines an optimal set of grid-cell pairs (one grid cell from the baseline map and one grid cell from the comparison map) for each category, such that overall grid-cell-to-grid-cell distances are minimized. The resulting distances are compared to an overall average distance value, and normalized to determine individual Nomad values for each category. These category-specific Nomad values are averaged to determine an overall Nomad Index measurement that ranges, generally, between 0 and 1 (negative values are theoretically possible). If the Nomad Index equals 1 there is perfect agreement. Nomad Index values approaching 1 indicate a strong level of agreement. Nomad Index values near 0, or less than 0, indicate weak, or only chance, agreement. This approach, though computationally complex, facilitates measurement of error magnitude and spatial-pattern agreement while limiting problems that can arise associated with map or image coregistration. Nomad's utility is demonstrated through two applications. First, interpolation methods for mapping paleovegetation are evaluated and compared. Second, global monthly composite normalized differential vegetation index (NDVI) data are analyzed to detect and measure intermonthly and interannual land cover change.