A Predictive Uncertainty Model for Field-Based Survey Maps Using Generalized Linear Models

In this paper we present an approach for predictive uncertainty modeling in field-based survey maps using Generalized Linear Models (GLM). Frequently, inherent uncertainty, especially in historical maps, makes the interpretation of objects very difficult. Such maps are of great value, but usually only few reference data are available. Consequently, the process of map interpretation could be greatly improved by the knowledge of uncertainty and its variation in space. To predict inherent uncertainty in forest cover information of the Swiss topographic map series from the 19th century we formulate rules from several predictors. These are topography-dependent variables and distance measures from old road networks. It is hypothesized that these rules best describe the errors of historical field work and hence the mapping quality. The uncertainty measure, the dependent variable, was derived from local map comparisons within moving windows of different sizes using a local community map as a reference map. The derivation of local Kappacoefficient and percent correctlyclassified from these enlarged sample plots takes the local distortion of the map into account. This allows an objective and spatially oriented comparison. Models fitted with uncertainty measures from 100m windows best described the relationship to the explanatory variables. A significant prediction potential for local uncertainty could thus be observed. The explained deviance by the Kappa-based model reached more than 40 percent. The correlation between predictions by the model and independent observations was ρ=0.76. Consequently, an improvement of the model to 47 percent, indicated by the G-value, was calculated. The model allows the spatial-oriented prediction of inherent uncertainty within different regions of comparable conditions. The integration of more study areas will result in more general rules for objective evaluation of the entire topographic map. The method can be applied for the evaluation of any field-based map which is used for subsequent applications such as land cover change assessments.

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