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##### AM-06 - Grid Operations and Map Algebra

Grid operations are manipulation and analytical computations performed on raster data. Map Algebra is a language for organizing and implementing grid operations in Geographic Information Systems (GIS) software, and is typically categorized into Local, Focal, and Zonal functions, where each function typically ingests one or more grids and outputs a new grid. The value of a specific grid cell in the output grid for Local functions is determined from the value(s) of the analogous cell position(s) in the input grid(s), for Focal functions from the grid cell values drawn from a neighborhood around the specific output grid cell, and for Zonal functions from a set of grid cells specified in a separate zone grid. Individual functions within a category vary by applying a different arithmetic, statistical, or other type of operator to the function. Map Algebra also includes Global and Block function categories. Grid operations can be categorized as data manipulation procedures or within domain-specific applications, such as terrain analysis or image processing. Grid operations are employed in a variety of GIS-based analyses, but are particularly widely used for suitability modeling and environmental analyses.

##### AM-40 - Areal Interpolation

Areal interpolation is the process of transforming spatial data from source zones with known values or attributes to target zones with unknown attributes. It generates estimates of source zone attributes over target zone areas. It aligns areal spatial data attributes over a single spatial framework (target zones) to overcome differences in areal reporting units due to historical boundary changes of reporting areas, integrating data from domains with different reporting conventions or in situations when spatially detailed information is not available. Fundamentally, it requires assumptions about how the target zone attribute relates to the source zones. Areal interpolation approaches can be grouped into two broad categories: methods that link target and source zones by their spatial properties (area to point, pycnophylactic and areal weighed interpolation) and methods that use ancillary or auxiliary information to control, inform, guide, and constrain the interpolation process (dasymetric, statistical, streetweighted and point-based interpolation). Additionally, there are new opportunities to use novel data sources to inform areal interpolation arising from the many new forms of spatial data supported by ubiquitous web- and GPS-enabled technologies including social media, PoI check-ins, spatial data portals (e.g for crime, house sales, microblogging sites) and collaborative mapping activities (e.g. OpenStreetMap).

##### AM-09 - Classification and Clustering

Classification and clustering are often confused with each other, or used interchangeably. Clustering and classification are distinguished by whether the number and type of classes are known beforehand (classification), or if they are learned from the data (clustering). The overarching goal of classification and clustering is to place observations into groups that share similar characteristics while maximizing the separation of the groups that are dissimilar to each other. Clusters are found in environmental and social applications, and classification is a common way of organizing information. Both are used in many areas of GIS including spatial cluster detection, remote sensing classification, cartography, and spatial analysis. Cartographic classification methods present a simplified way to examine some classification and clustering methods, and these will be explored in more depth with example applications.

##### FC-27 - Thematic Accuracy Assessment

Geographic Information System (GIS) applications often involve various analytical techniques and geographic data to produce thematic maps for gaining a better understanding of geospatial situations to support spatial decisions. Accuracy assessment of a thematic map is necessary for evaluating the quality of the research results and ensuring appropriate use of the geographic data. Thematic accuracy deals with evaluating the accuracy of the attributes or labels of mapped features by comparing them to a reference that is assumed to be true. The fundamental practice presents the remote sensing approach to thematic accuracy assessment as a good guidance. For instance, the accuracy of a remote sensing image can be represented as an error matrix when the map and reference classification are conducted based on categories. This entry introduces basic concepts and techniques used in conducting thematic accuracy with an emphasis on land cover classification based on remote sensing images. The entry first introduces concepts of spatial uncertainty and spatial data quality standards and further gives an example of how spatial data quality affects thematic accuracy. Additionally, the entry illustrates the techniques that can be used to access thematic accuracy as well as using spatial autocorrelation in thematic accuracy sampling design.

##### FC-21 - Resolution

Resolution in the spatial domain refers to the size of the smallest measurement unit observed or recorded for an object, such as pixels in a remote sensing image or line segments used to record a curve. Resolution, also called the measurement scale, is considered one of the four major dimensions of scale, along with the operational scale, observational scale, and cartographic scale. Like the broader concept of scale, resolution is a fundamental consideration in GIScience because it affects the reliability of a study and contributes to the uncertainties of the findings and conclusions. While resolution effects may never be eliminated, techniques such as fractals could be used to reveal the multi-resolution property of a phenomenon and help guide the selection of resolution level for a study.

##### AM-21 - The Evolution of Geospatial Reasoning, Analytics, and Modeling

The field of geospatial analytics and modeling has a long history coinciding with the physical and cultural evolution of humans. This history is analyzed relative to the four scientific paradigms: (1) empirical analysis through description, (2) theoretical explorations using models and generalizations, (3) simulating complex phenomena and (4) data exploration. Correlations among developments in general science and those of the geospatial sciences are explored. Trends identify areas ripe for growth and improvement in the fourth and current paradigm that has been spawned by the big data explosion, such as exposing the ‘black box’ of GeoAI training and generating big geospatial training datasets. Future research should focus on integrating both theory- and data-driven knowledge discovery.

##### FC-11 - Set Theory

Basic mathematical set theory is presented and illustrated with a few examples from GIS. The focus is on set theory first, with subsequent interpretation in some GIS contexts ranging from story maps to municipal planning to language use. The breadth of interpretation represents not only the foundational universality of set theory within the broad realm of GIS but is also reflective of set theory's fundamental role in mathematics and its numerous applications. Beyond the conventional, the reader is taken to see glimpses of set theory not commonly experienced in the world of GIS and asked to imagine where else they might apply. Initial broad exposure leaves room for the mind to grow into deep and rich fields flung far across the globe of academia. Direction toward such paths is offered within the text and in additional resources, all designed to broaden the horizons of the open-minded reader.

##### AM-106 - Error-based Uncertainty

The largest contributing factor to spatial data uncertainty is error. Error is defined as the departure of a measure from its true value. Uncertainty results from: (1) a lack of knowledge of the extent and of the expression of errors and  (2) their propagation through analyses. Understanding error and its sources is key to addressing error-based uncertainty in geospatial practice. This entry presents a sample of issues related to error and error based uncertainty in spatial data. These consist of (1) types of error in spatial data, (2) the special case of scale and its relationship to error and (3) approaches to quantifying error in spatial data.

##### AM-84 - Simulation Modeling

Advances in computational capacity have enabled dynamic simulation modeling to become increasingly widespread in scientific research. As opposed to conceptual or physical models, simulation models enable numerical experimentation with alternative parametric assumptions for a given model design. Numerous design choices are made in model development that involve continuous or discrete representations of time and space. Simulation modeling approaches include system dynamics, discrete event simulation, agent-based modeling, and multi-method modeling. The model development process involves a shift from qualitative design to quantitative analysis upon implementation of a model in a computer program or software platform. Upon implementation, model analysis is performed through rigorous experimentation to test how model structure produces simulated patterns of behavior over time and space. Validation of a model through correspondence of simulated results with observed behavior facilitates its use as an analytical tool for evaluating strategies and policies that would alter system behavior.

##### AM-04 - Overlay

Overlay operation is a critical and powerful tool in GIS that superimposes spatial and attribute information from various thematic map layers to produce new information. Overlay operations facilitate spatial analysis and modeling processes when being used with other spatial operations (e.g. buffer, dissolve, merge) to solve real-world problems. For both vector and raster data models, the input layers need to be spatially aligned precisely with each other to ensure a correct overlay operation. In general, vector overlay is geometrically and computationally complex. Some most used vector overlay operations include intersection, union, erase, and clip. Raster overlay combines multiple raster layers cell by cell through Boolean, arithmetic, or comparison operators. This article provides an overview of the fundamentals of overlay operations, how they are implemented in vector and raster data, and how suitability analysis is conducted.