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

Aug 5, 2026

Upload by Noah

This manuscript guides how to apply the Total Operating Characteristic (TOC) to (1) analyze change over time, (2) rank a categorical independent variable, and (3) constrain the extent for a gaining category. The illustrative case uses marsh landcover in the Plum Island Ecosystems of northeastern Massachusetts, USA, comparing elevation and land-category maps for water, marsh, and upland in 1938, 1971, and 2013. Results show strongest marsh gains at intermediate elevations during the first interval, a weaker elevation association during the second, and intensified gains from water rather than upland. The TOC also reveals alternation and how spatial restriction reduces distance-related AUC while increasing elevation-related AUC.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages12

Reading Time30 min

AccessFree to download

Abstract

Introduction

TOC purpose in land-change analysis

Comparison to related methods (ROC)

Framework: binary vs ranked variables

Methods and application setup (TOC for gains and losses)

Results interpretation (losses, gains, alternation)

Effects of spatial extent constraints

Clark University Clark Digital Commons | Geography | Faculty Works by Department and/or School | | --- | --- | 8-2024 Analyzing the Losses and Gains of a Land Category: Insights from the Total Operating Characteristic Thomas Mumuni Bilintoh Robert Gilmore Pontius Zhen Liu Follow this and additional works at: [https://commons.clarku.edu/faculty_geography](https://commons.clarku.edu/faculty_geography) Part of the Geography Commons land Article Analyzing the Losses and Gains of a Land Category: Insights from the Total Operating Characteristic Thomas Mumuni Bilintoh 1, *, Robert Gilmore Pontius, Jr. 1 and Zhen Liu 2 Citation: Bilintoh, T.M.; Pontius, R.G., Jr.; Liu, Z. Analyzing the Losses and Gains of a Land Category: Insights from the Total Operating Characteristic. Land 2024, 13, 1177. [https://doi.org/](https://doi.org/)[ ](https://doi.org/)[10.3390/land13081177](10.3390/land13081177) Academic Editors: Jingye Li, Wenwu Tang, Jianxin Yang and Minrui Zheng Received: 6 June 2024 Revised: 24 July 2024 Accepted: 25 July 2024 Published: 31 July 2024 Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([https://](https://)[ ](https://)[creativecommons.org/licenses/by/](creativecommons.org/licenses/by/)[ ](creativecommons.org/licenses/by/)[4.0/](4.0/)) . 1 Graduate School of Geography, Clark University, 950 Main Street, Worcester, MA 01610, USA; [rpontius@clarku.edu](rpontius@clarku.edu) 2 Department of Geographical Sciences, University of Maryland, College Park, MD 20742, USA; [zliu1997@terpmail.umd.edu](zliu1997@terpmail.umd.edu) * Correspondence: [tbilintoh@clarku.edu](tbilintoh@clarku.edu); Tel.: +1-517-303-7904 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 landcover category in the Plum Island Ecosystems of northeastern Massachusetts, USA. The data are an elevation map and maps showing the land categories of water, marsh, and upland in 1938, 1971, and 2013. There were losses and gains near the edge of the marsh between 1938 and 1972 and between 1972 and 2013 . The 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 the marsh gains occurred where marsh was 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 the TOC is easier to interpret and shows more information than the Relative Operative Characteristic. Keywords: alternation; land change; marsh; TOC; AUC 1. Introduction The Total Operating Characteristic (TOC) can help researchers understand land change because the TOC analyzes the relationships between a ranked independent variable, such as distance, and a binary variable, such as the presence or absence of a land category. The TOC has gained increasing attention in the field of spatiotemporal analysis. This is because the TOC shows the total information in an error or change matrix, which other popular methods like the Receiver Operating Characteristic (ROC) fail to show. Pontius Jr and Si [1] first proposed the TOC as a modification of the ROC, which has been popular in diverse fields such as genetics [2,3], radiology [4], psychology [5,6], machine learning [7,8], and remote sensing [9,10] . Pontius and Si [1]

FAQs

What does the Total Operating Characteristic (TOC) help researchers do in land-change studies?

The TOC explains relationships between a ranked independent variable (e.g., distance or elevation) and a binary land-category outcome (presence/absence). It summarizes total information in an error/change matrix that other approaches like the ROC do not fully show.

How is alternation identified using the TOC in this study?

The TOC curves show that marsh gains occur in places where marsh was previously lost. This location-by-location pairing of losses and gains across consecutive intervals is called Alternation.

How do spatial constraints affect the TOC results in the study?

Eliminating far distances and extreme elevations from the spatial extent reduces the area under the curve (AUC) for distance, while increasing the AUC for elevation, indicating a shift in which ranked factor shows stronger association.

Aug 5, 2026

Upload by Noah