Explore the vast range of titles available.

The Total Operating Characteristic (TOC) measures how the ranks of an index variable distinguish between presence and absence in a binary reference variable. Previous methods to generate the TOC required the reference data to derive from a census or a simple random sample. However, many researchers apply stratified random sampling to collect reference data because stratified random sampling is more efficient than simple random sampling for many applications. Our manuscript derives a new methodology that uses stratified random sampling to generate the TOC. An application to flood mapping illustrates how the TOC compares the abilities of three indices to diagnose water. The TOC shows visually and quantitatively each index’s diagnostic ability relative to baselines. Results show that the Modified Normalized Difference Water Index has the greatest diagnostic ability, while the Normalized Difference Vegetation Index has diagnostic ability greater than the Normalized Difference Water Index at the threshold where the Diagnosed Presence equals the Abundance of water. Some researchers consider only one accuracy metric at only one threshold, whereas the TOC allows visualization of several metrics at all thresholds. The TOC gives more information and clearer interpretation compared to the popular Relative Operating Characteristic. Our software generates the TOC from a census, simple random sample, or stratified random sample. The TOC Curve Generator is free as an executable file at a website that our manuscript gives.

The Total Operating Characteristic (TOC) is an improvement on the quantitative method called the Relative Operating Characteristic (ROC), both of which plot the association between a binary variable and a rank variable. TOC curves reveal the sizes of the four entries in the confusion matrix at each threshold, which make TOC curves more easily interpretable than ROC curves. The TOC has become popular, especially to assess the fit of simulation models to predict land change. However, the literature has shown variation in how authors apply and interpret the TOC, creating some misleading conclusions. Our manuscript lists best practices when applying and interpreting the TOC to help scientists learn from TOC curves. An example illustrates these practices by applying the TOC to measure the ability to predict the gain of crop in Western Bahia, Brazil. The application compares four ways to design the rank variable based on the distance to either pixels or patches of either the presence or change of crop. The results show that the gain of crop during the validation time interval is more strongly associated with the distance to patches rather than pixels of crop. The Discussion Section reveals that if authors show the TOC curves, then readers can interpret the results in ways that the authors might have missed. The Conclusion encourages scientists to follow best practices to learn the wealth of information that the TOC reveals.

ContextValidation of models of Land Use and Cover Change often involves comparing maps of simulated and reference change. The interpretation of differences between simulated and reference change depends on the characteristics of the process being studied. Our paper focuses on validation of models of one-way land change processes that spread in space.ObjectivesOur objective is to develop a method for validation of one-way land change models, such that the method provides objective information about the spatial distribution of errors.MethodsUsing distance analysis on reference data, we build a baseline model for comparison with simulations. We then simultaneously compare the four maps of reference at initial time, reference at final time, simulation at final time, and baseline at final time. We also use Total Operating Characteristic curves and multiple-resolution map comparison. We illustrate the methods with a simulation of forest insect infestations.ResultsThe methods give insights concerning the reference data and the spatial distribution of misses, hits, and false alarms with respect to initial points of infestations. The new methods reveal that the simulations underestimated change near initial points of spread.ConclusionsThe spatial distribution of errors is a topic of land change models that deserves attention. For models of one-way, geographically-spreading processes, we recommend that validation should distinguish between near and far allocation errors with respect to initial points of spread.

Conventional methods to analyze a transition matrix do not offer in-depth signals concerning land changes. The land change community needs an effective approach to visualize both the size and intensity of land transitions while considering possible map errors. We propose a framework that integrates error analysis, intensity analysis, and difference components, and then uses the framework to analyze land change in Nanchang, the capital city of Jiangxi province, China. We used remotely sensed data for six categories at four time points: 1989, 2000, 2008, and 2016. We had a confusion matrix for only 2016, which estimated that the map of 2016 had a 12% error, while the temporal difference during 2008–2016 was 22% of the spatial extent. Our tools revealed suspected errors at other years by analyzing the patterns of temporal difference. For example, the largest component of temporal difference was exchange, which could indicate map errors. Our framework identified categories that gained during one time interval then lost during the subsequent time interval, which raised the suspicion of map error. This proposed framework facilitated visualization of the size and intensity of land transitions while illustrating possible map errors that the profession routinely ignores.

Geospatial analysis and statistical analysis are coupled in this study to determine the dynamic linkage between landscape characteristics and water quality for the years 1996, 2002, and 2007 in a subtropical coastal watershed of Southeast China. The landscape characteristics include Percent of Built (%BL), Percent of Agriculture, Percent of Natural, Patch Density and Shannon’s Diversity Index (SHDI), with water quality expressed in terms of COD Mn and NH 4 + –N. The %BL was consistently positively correlated with NH 4 + –N and COD Mn at time three points. SHDI is significantly positively correlated with COD Mn in 2002. The relationship between NH 4 + –N, COD Mn and landscape variables in the wet precipitation year 2007 is stronger, with R 2  = 0.892, than that in the dry precipitation years 1996 and 2002, which had R 2 values of 0.712 and 0.455, respectively. Two empirical regression models constructed in this study proved more suitable for predicting COD Mn than for predicting NH 4 + –N concentration in the unmonitored watersheds that do not have wastewater treatment plants. The calibrated regression equations have a better predictive ability over space within the wet precipitation year of 2007 than over time during the dry precipitation years from 1996 to 2002. Results show clearly that climatic variability influences the linkage of water quality-landscape characteristics and the fit of empirical regression models.

Several factors influence the performance of land change simulation models. One potentially important factor is land category aggregation, which reduces the number of categories while having the potential to reduce also the size of apparent land change in the data. Our article compares how four methods to aggregate Corine Land Cover categories influence the size of land changes in various spatial extents and consequently influence the performance of 114 Cellular Automata-Markov simulation model runs. We calculated the reference change during the calibration interval, the reference change during the validation interval and the simulation change during the validation interval, along with five metrics of simulation performance, Figure of Merit and its four components: Misses, Hits, Wrong Hits and False Alarms. The Corine Standard Level 1 category aggregation reduced change more than any of the other aggregation methods. The model runs that used the Corine Standard Level 1 aggregation method tended to return lower sizes of changing areas and lower values of Misses, Hits, Wrong Hits and False Alarms, where Hits are correctly simulated changes. The behavior-based aggregation method maintained the most change while using fewer categories compared to the other aggregation methods. We recommend an aggregation method that maintains the size of the reference change during the calibration and validation intervals while reducing the number of categories, so the model uses the largest size of change while using fewer than the original number of categories.

The profession debates how to encode a categorical variable for input to machine learning algorithms, such as neural networks. A conventional approach is to convert a categorical variable into a collection of binary variables, which causes a burdensome number of correlated variables. TerrSet’s Land Change Modeler proposes encoding a categorical variable onto the continuous closed interval from 0 to 1 based on each category’s Population Evidence Likelihood (PEL) for input to the Multi-Layer Perceptron, which is a type of neural network. We designed examples to test the wisdom of these encodings. The results show that encoding a categorical variable based on each category’s Sample Empirical Probability (SEP) produces results similar to binary encoding and superior to PEL encoding. The Multi-Layer Perceptron’s sigmoidal smoothing function can cause PEL encoding to produce nonsensical results, while SEP encoding produces straightforward results. We reveal the encoding methods by illustrating how a dependent variable gains across an independent variable that has four categories. The results show that PEL can differ substantially from SEP in ways that have important implications for practical extrapolations. If users must encode a categorical variable for input to a neural network, then we recommend SEP encoding, because SEP efficiently produces outputs that make sense.

This paper examines the size and intensity of changes among five land categories during the two time intervals in a region of Indonesia that is pioneering negotiations concerning reducing emissions from deforestation and forest degradation (REDD). Maps at 1973, 1993, and 2005 indicate that land-cover change is accelerating, while carbon loss is decelerating in Jambi Province, Sumatra. Land dynamics have shifted from Forest loss during 1973–1993 to Agroforest loss during 1993–2005. Forest losses account for most reductions in aboveground carbon during the both time intervals, but Agroforest plays an increasingly important role in carbon reductions during the more recent interval. These results provide motivation for future REDD policies to count carbon changes associated with all influential land categories, such as Agroforests.

This article describes a quantitative assessment of the output from the Behavioral Landscape Model (BLM), which has been developed to simulate the spatial pattern of deforestation (i.e. forest fragmentation) in the Amazon basin in a manner consistent with human behavior. The assessment consists of eighteen runs for a section of the Transamazon Highway in the lower basin, where the BLM's simulated deforestation map for each run is compared to a reference map of 1999. The BLM simulates the transition from forest to non-forest in a spatially explicit manner in 20-m × 20-m pixels. The pixels are nested within a hierarchical stratification structure of household lots within larger development rectangles that emanate from the Transamazon Highway. Each of the eighteen runs derives from a unique combination of three model parameters. We have derived novel methods of assessment to consider (1) the nested stratification structure, (2) multiple resolutions, (3) a simpler model that predicts deforestation near the highway, (4) a null model that predicts forest persistence, and (5) a uniform model that has accuracy equal to the expected accuracy of a random spatial allocation. Results show that the model's specification of the overall quantity of non-forest is the most important factor that constrains and correlates with accuracy. A large source of location agreement is the BLM's assumption that deforestation within household lots occurs near roads. A large source of location disagreement is the BLM's less than perfect ability to simulate the proportion of deforestation by household lot. This article discusses implications of these results in the context of land change science and dynamic simulation modeling. Eugenio Arima and Marcellus Caldas were affiliated with Michigan State University during the time the work reported in this article was done.

The relative operating characteristic (ROC) is a widely-used method to measure diagnostic signals including predictions of land changes, species distributions, and ecological niches. The ROC measures the degree to which presence for a Boolean variable is associated with high ranks of an index. The ROC curve plots the rate of true positives versus the rate of false positives obtained from the comparison between the Boolean variable and multiple diagnoses derived from thresholds applied to the index. The area under the ROC curve (AUC) is a summary metric, which is commonly reported and frequently criticized. Our manuscript recommends four improvements in the use and interpretation of the ROC curve and its AUC by: (1) highlighting important threshold points on the ROC curve, (2) interpreting the shape of the ROC curve, (3) defining lower and upper bounds for the AUC, and (4) mapping the density of the presence within each bin of the ROC curve. These recommendations encourage scientists to interpret the rich information that the ROC curve can reveal, in a manner that goes far beyond the potentially misleading AUC. We illustrate the benefit of our recommendations by assessing the prediction of land change in a suburban landscape.