A model for the propagation of uncertainty from continuous estimates of tree cover to categorical forest cover and change

Rigorous monitoring of Earth's terrestrial surface requires mapping estimates of land cover and of their errors in space and time. Estimation of error in land-cover change detection currently relies heavily on external, post hoc validation-i.e., comparison of estimated cover to independent values that are assumed to be true. However, reference data are themselves uncertain, and acquiring observations coincident with historical data is often impossible. Complementarily, modeling the transmission, or propagation, of error through the processes of classification and change detection provides an internal means to estimate classification and change-detection error at the scale of pixels. Modeling uncertainty around the estimate of fractional, “continuous-field” cover as a standard Normal distribution in each pixel at each of two times, we derive a method for propagating this uncertainty to categorical land cover-classification and change detection. We demonstrate the approach for mapping forest-cover change and its uncertainty based on bi-temporal estimates of percent-tree cover and their associated root-mean-square errors (RMSE). The method described here propagates only the imprecision component of error and not bias, so neither the resulting categorical estimates of cover nor the detection of change (e.g., forest loss) are affected by the transmission of uncertainty. However, propagating the RMSE of input estimates into probabilities of forest cover and change enables mapping and visualization of the spatial distribution of the imprecision resulting from model-based estimation of tree cover and from selection of the threshold of tree cover to define “forest”. When compared to reference data with a fixed definition of forest (e.g., ≥ 30% tree cover) the threshold effect is an importance source of apparent error in forest-cover and -change estimates. The approach described here provides a useful description of classification and change-detection certainty and can accommodate any definition of forest based on tree cover-an especially important consideration given the variety of institutional definitions of forest cover based on remotely sensible structural characteristics.