Analyzing the Losses and Gains of a Land Category: Insights from the Total Operating Characteristic

Abstract This manuscript provides guidance concerning how to use the Total Operating Characteristic (TOC) when 1) analyzing change through time, 2) ranking a categorical independent variable, and 3) constraining the extent for a gaining category. The illustrative variable is the marsh land cover category in the Plum Island Ecosystems of northeastern Massachusetts, USA. The data are an elevation map and maps showing land categories water, marsh, and upland at 1938, 1971, and 2013. Marsh lost and gained during 1938 − 1972 and 1972 − 2013 near the edge of marsh. TOC curves show that marsh gained most intensively at intermediate elevations during the first time interval and then had a weaker association with elevation during the second time interval. Marsh gains more intensively from water than from upland during both time intervals. The TOC curves also demonstrate that marsh gains occur where marsh previously lost, a phenomenon called Alternation. Furthermore, eliminating far distances and extreme elevations from the spatial extent decreased the area under the curve (AUC) for distance and increased the AUC for elevation. We invite scientists to use the TOC because TOC is easier to interpret and shows more information than the Relative Operative Characteristic.