Expanding the conceptual, mathematical and practical methods for map comparison

Conventional methods of map comparison frequently produce unhelpful results for a variety of reasons. In particular, conventional methods usually analyze pixels at a single default scale and frequently insist that each pixel belongs to exactly one category. The purpose of this paper is to offer improved methods so that scientists can obtain more helpful results by performing multiple resolution analysis on pixels that belong simultaneously to several categories. This paper examines the fundamentals of map comparison beginning from the elementary comparison between two pixels that have partial membership to multiple categories. We examine the conceptual foundation of three methods to create a crosstabulation matrix for a single pair of pixels, and then show how to extend those concepts to compare entire maps at multiple spatial resolutions. This approach is important because the crosstabulation matrix is the basis for numerous popular measurements of spatial accuracy. The three methods show the range of possibilities for constructing a crosstabulation matrix based on possible variations in the spatial arrangement of the categories within a single pixel. A smaller range in the possible spatial distribution of categories within the pixel corresponds to more certainty in the crosstabulation matrix. The quantity of each category within each pixel constrains the range for possible arrangements in subpixel mapping, since there is more certainty for pixels that are dominated by a single category. In this respect, the proposed approach is placed in the context of a philosophy of map comparison that focuses on two separable components of information in a map: 1) information concerning the proportional distribution of the quantity of categories, and 2) information concerning the spatial distribution of the location of categories. The methods apply to cases where a scientist needs to compare two maps that show categories, even when the categories in one map are different from the categories in the other map. We offer a fourth method that is designed for the common case where a scientist needs to compare two maps that show the same set of categories. Results show that the methods can produce extremely different measurements, and that it is possible to interpret the differences at multiple resolutions in a manner that reveals patterns in the maps. The method is designed to present the results graphically in order to facilitate communication. We describe the concepts using simplified examples, and then apply the methods to characterize the change in land cover between 1971 and 1999 in Massachusetts

The Flow Matrix Offers a Straightforward Alternative to the Problematic Markov Matrix

The Flow matrix is a novel method to describe and extrapolate transitions among categories. The Flow matrix extrapolates a constant transition size per unit of time on a time continuum with a maximum of one incident per observation during the extrapolation. The Flow matrix extrapolates linearly until the persistence of a category shrinks to zero. The Flow matrix has concepts and mathematics that are more straightforward than the Markov matrix. However, many scientists apply the Markov matrix by default because popular software packages offer no alternative to the Markov matrix, despite the conceptual and mathematical challenges that the Markov matrix poses. The Markov matrix extrapolates a constant transition proportion per time interval during whole-number multiples of the duration of the calibration time interval. The Markov extrapolation allows at most one incident per observation during each time interval but allows repeated incidents per observation through sequential time intervals. Many Markov extrapolations approach a steady state asymptotically through time as each category size approaches a constant. We use case studies concerning land change to illustrate the characteristics of the Flow and Markov matrices. The Flow and Markov extrapolations both deviate from the reference data during a validation time interval, implying there is no reason to prefer one matrix to the other in terms of correspondence with the processes that we analyzed. The two matrices differ substantially in terms of their underlying concepts and mathematical behaviors. Scientists should consider the ease of use and interpretation for each matrix when extrapolating transitions among categories. © 2023 by the authors

Effects of Category Aggregation on Land Change Simulation Based on Corine Land Cover Data

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Spatial distribution of land type in regression models of pollutant loading

This paper proposes a method to improve landscape-pollution interaction regression models through the inclusion of a variable that describes the spatial distribution of a land type with respect to the pattern of runoff within a drainage catchment. The proposed index is used as an independent variable to enhance the strength, as quantified by R² values, of regression relationships between empirical observations of in-stream pollutant concentrations and land type by considering the spatial distribution of key land-type categories within the sample point’s drainage area. We present an index that adds a new dimension of explanatory power when used in conjunction with a variable describing the proportion of the land type. We demonstrate the usefulness of this index by exploring the relationship between nitrate ( - 3 NO ) and land type within 40 drainage sub-catchments in the Ipswich River watershed, Massachusetts. Nutrient loads associated with non-point source pollution paths are related to land type within the up-stream drainage catchments of sample sites. Past studies have focused on the quantity of particular land type within a sample point’s drainage catchment. Quantifying the spatial distribution of key land-type categories in terms of location on a runoff surface can improve our understanding of the relationship between sampled - 3 NO concentrations and land type. Regressions that employ the proportion of residential and agricultural land type within catchments provide a fair fit (R² = 0.67). However, we find that a regression adding a variable that indicates the spatial distribution of residential land improves the overall relationship between instream - 3 NO measurements and associated land types (R² = 0.712). We test the sensitivity of the results with respect to variations in the surface definition in order to determine the conditions under which the spatial index variable is useful

Land change modeling: moving beyond projections

International audienceDuring the last decades, there has been an increasing interest from the academic and policy communities to monitor and model changes of the earth surface. Modeling environmental dynamics helps to understand changes that are taking place currently and to anticipate future evolutions. Prospective simulation supports decision-making for environmental management and land planning. This special issue is dedicated to advances in land change modeling. Land Use / Land Cover Change, also called LUCC, is certainly a prominent interface between natural and social dynamics because anthropogenic LUCC has a profound impact on Earth. LUCC impacts a large amount of highly relevant topics such as resource exploitation, climate change, biodiversity loss, etc. Land change modeling can provide transparent, efficient and sustainable decision support to these current and rising environmental problem

Intensity Analysis and the Figure of Merit’s components for assessment of a Cellular Automata – Markov simulation model

Some popular metrics to evaluate land change simulation models are misleading. Therefore, land change scientists have called for the development of methods to evaluate various aspects of modelling applications. This article answers the call by giving novel methods to compare three types of land change: 1) reference change during the calibration time interval, 2) simulation change during the validation time interval, and 3) reference change during the validation time interval. We compare these changes by using Intensity Analysis’ three levels and the Figure of Merit’s four components: Misses, Hits, Wrong Hits and False Alarms. We illustrate the concepts by applying a Cellular Automata – Markov land change model to a case study in northeast Hungary. We used reference maps of five land categories to calibrate the model during 2000–2006, then to validate the simulation during 2006–2012. Intensity Analysis’ time interval level shows that the simulation change and the reference change decelerated from 2000–2006 to 2006–2012. Intensity Analysis’ category level shows that the simulation losses were less than what a pure Markov chain would have dictated. Intensity Analysis’ transition level shows that the model’s Markov algorithm simulated correctly that the gain of Forest targeted Agriculture and Wetland. The Figure of Merit’s components reveals more allocation error than quantity error. Our collection of metrics show that more error derived from the Cellular Automata algorithm than from the Markov algorithm. We recommend that scientists use Intensity Analysis and the Figure of Merit’s components to reveal various fundamental aspects of modelling applications

Using Fine Resolution Orthoimagery and Spatial Interpolation to Rapidly Map Turf Grass in Suburban Massachusetts

This paper explores the use of spatial interpolative methods in conjunction with object based image analysis to estimate turf grass land cover quantity and allocation in Greater Boston, Massachusetts, USA. The goal is to learn how accurately turf grass can be estimated if only a limited portion of the study area is mapped. First, turf grass land cover is mapped at the 0.5 m resolution across the entire Plum Island Ecosystems (PIE) Long Term Ecological Research (LTER) site, a 1143-km2 area. Second, the turf grass map is aggregated into 120 m cells (N = 84,661). Third, a random sample of these 120 m cells are selected to generate an estimate of the unselected cells using four estimation methods - Inverse Distance Weighting, Kriging, Polygonal Interpolation, and Mean Estimation. The difference between known and estimated values is recorded using 120 m cell and census block group stratifications. This process is repeated 500 times for sample sizes of 2.5%, 5.0%, 7.5% and 10.0% of the study area, for a total of 2000 iterations. The average error statistics are reported by sample size, strata, and estimation method. Inverse distance weighting performed best in terms of total error across all sample sizes. It was found that by mapping only 2.5% of the study area, all four methods outperformed a recently published approach to estimating turf grass in terms of overall error

Land classification and change intensity analysis in a coastal watershed of Southeast China

The aim of this study is to improve the understanding of land changes in the Jiulong River watershed, a coastal watershed of Southeast China. We developed a stratified classification methodology for land mapping, which combines linear stretching, an Iterative Self-Organizing Data Analysis (ISODATA) clustering algorithm, and spatial reclassification. The stratified classification for 2002 generated less overall error than an unstratified classification. The stratified classifications were then used to examine temporal differences at 1986, 1996, 2002, 2007 and 2010. Intensity Analysis was applied to analyze land changes at three levels: time interval, category, and transition. Results showed that land use transformation has been accelerating. Woodland's gains and losses were dormant while the gains and losses of Agriculture, Orchard, Built-up and Bare land were active during all time intervals. Water's losses were active and stationary. The transitions from Agriculture, Orchard, and Water to Built-up were systematically targeting and stationary, while the transition from Woodland to Built-up was systematically avoiding and stationary. ? 2014 by the authors; licensee MDPI, Basel, Switzerland

Meeting reports: Research on Coupled Human and Natural Systems (CHANS): Approach, Challenges, and Strategies

Understanding the complexity of human–nature interactions is central to the quest for both human well-being and global sustainability. To build an understanding of these interactions, scientists, planners, resource managers, policymakers, and communities increasingly are collaborating across wide-ranging disciplines and knowledge domains. Scientists and others are generating new integrated knowledge on top of their requisite specialized knowledge to understand complex systems in order to solve pressing environmental and social problems (e.g., Carpenter et al. 2009). One approach to this sort of integration, bringing together detailed knowledge of various disciplines (e.g., social, economic, biological, and geophysical), has become known as the study of Coupled Human and Natural Systems, or CHANS (Liu et al. 2007a, b). In 2007 a formal standing program in Dynamics of Coupled Natural and Human Systems was created by the U.S. National Science Foundation. Recently, the program supported the launch of an International Network of Research on Coupled Human and Natural Systems (CHANS-Net.org). A major kick-off event of the network was a symposium on Complexity in Human–Nature Interactions across Landscapes, which brought together leading CHANS scientists at the 2009 meeting of the U.S. Regional Association of the International Association for Landscape Ecology in Snowbird, Utah. The symposium highlighted original and innovative research emphasizing reciprocal interactions between human and natural systems at multiple spatial, temporal, and organizational scales. The presentations can be found at ‹http://chans- net.org/Symposium_2009.aspx›. The symposium was accompanied by a workshop on Challenges and Opportunities in CHANS Research. This article provides an overview of the CHANS approach, outlines the primary challenges facing the CHANS research community, and discusses potential strategies to meet these challenges, based upon the presentations and discussions among participants at the Snowbird meeting

Knowledge to Serve the City: Insights from an Emerging Knowledge-Action Network to Address Vulnerability and Sustainability in San Juan, Puerto Rico

This paper presents initial efforts to establish the San Juan Urban Long-Term Research Area Exploratory (ULTRA-Ex), a long-term program aimed at developing transdisciplinary social-ecological system (SES) research to address vulnerability and sustainability for the municipality of San Juan. Transdisciplinary approaches involve the collaborations between researchers, stakeholders, and citizens to produce socially-relevant knowledge and support decision-making. We characterize the transdisciplinary arrangement emerging in San Juan ULTRA-Ex as a knowledge-action network composed of multiple formal and informal actors (e.g., scientists, policymakers, civic organizations and other stakeholders) where knowledge, ideas, and strategies for sustainability are being produced, evaluated, and validated. We describe in this paper the on-the-ground social practices and dynamics that emerged from developing a knowledge-action network in our local context. Specifically, we present six social practices that were crucial to the development of our knowledge-action network: 1) understanding local framings; 2) analyzing existing knowledge-action systems in the city; 3) framing the social-ecological research agenda; 4) collaborative knowledge production and integration; 5) boundary objects and practices; and 6) synthesis, application, and adaptation. We discuss key challenges and ways to move forward in building knowledge-action networks for sustainability. Our hope is that the insights learned from this process will stimulate broader discussions on how to develop knowledge for urban sustainability, especially in tropical cities where these issues are under-explored