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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.

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-12 - Cartographic Modeling

Cartographic modeling is an integrated sequence of data processing tasks that organize, combine, analyze and display information to answer a question. Cartographic modeling is effective in GIS environments because they rely heavily upon visualization, making it easy to show input and output layers in map form. In many GIS platforms, the sequence of tasks can be created and modified graphically as well. The modeling is visual, intuitive, and requires some knowledge of GIS commands and data preparation, along with curiosity to answer a particular question about the environment. It does not require programming skill. Cartographic modeling has been used in applications to delineate habitats, to solve network routing problems, to assess risk of storm runoff across digital terrain, and to conserve fragile landscapes. Historical roots emphasize manual and later automated map overlay. Cartographic models can take three forms (descriptive, prescriptive and normative). Stages in cartographic modeling identify criteria that meet an overarching goal; collect data describing each criterion in map form; design a flowchart showing data, GIS operations and parameters; implement the model; and evaluate the solution. A scenario to find a suitable site for biogas energy production walks through each stage in a simple demonstration of mechanics.

AM-23 - Local Measures of Spatial Association

Local measures of spatial association are statistics used to detect variations of a variable of interest across space when the spatial relationship of the variable is not constant across the study region, known as spatial non-stationarity or spatial heterogeneity. Unlike global measures that summarize the overall spatial autocorrelation of the study area in one single value, local measures of spatial association identify local clusters (observations nearby have similar attribute values) or spatial outliers (observations nearby have different attribute values). Like global measures, local indicators of spatial association (LISA), including local Moran’s I and local Geary’s C, incorporate both spatial proximity and attribute similarity. Getis-Ord Gi*another popular local statistic, identifies spatial clusters at various significance levels, known as hot spots (unusually high values) and cold spots (unusually low values). This so-called “hot spot analysis” has been extended to examine spatiotemporal trends in data. Bivariate local Moran’s I describes the statistical relationship between one variable at a location and a spatially lagged second variable at neighboring locations, and geographically weighted regression (GWR) allows regression coefficients to vary at each observation location. Visualization of local measures of spatial association is critical, allowing researchers of various disciplines to easily identify local pockets of interest for future examination.

AM-66 - Watersheds and Drainage Networks

This topic is an overview of basic concepts about how the distribution of water on the Earth, with specific regard to watersheds, stream and river networks, and waterbodies are represented by geographic data. The flowing and non-flowing bodies of water on the earth’s surface vary in extent largely due to seasonal and annual changes in climate and precipitation. Consequently, modeling the detailed representation of surface water using geographic information is important. The area of land that collects surface runoff and other flowing water and drains to a common outlet location defines a watershed. Terrain and surface features can be naturally divided into watersheds of various sizes. Drainage networks are important data structures for modeling the distribution and movement of surface water over the terrain.  Numerous tools and methods exist to extract drainage networks and watersheds from digital elevation models (DEMs). The cartographic representations of surface water are referred to as hydrographic features and consist of a snapshot at a specific time. Hydrographic features can be assigned general feature types, such as lake, pond, river, and ocean. Hydrographic features can be stored, maintained, and distributed for use through vector geospatial databases, such as the National Hydrography Dataset (NHD) for the United States.

AM-34 - The Geographically Weighted Regression Framework

Local multivariate statistical models are increasingly encountered in geographical research to estimate spatially varying relationships between a response variable and its associated predictor variables. In geography and many other disciplines, such models have been largely embedded within the framework of regression and can reveal significantly more information about the determinants of observed spatial distribution of the dependent variable than their global regression model counterparts. This section introduces one type of local statistical modeling framework: Geographically Weighted Regression (GWR). Models within this framework estimate location-specific parameter estimates for each covariate, local diagnostic statistics, and bandwidth parameters as indicators of the spatial scales at which the modeled processes operate. These models provide an effective means to estimate how the same factors may evoke different responses across locations and by so doing, bring to the fore the role of geographical context on human preferences and behavior.

AM-20 - Geospatial Analysis and Model Building

Spatial modeling is an important instrument to conduct geospatial analysis to understand the world and guide decision-making. In GIS, spatial models are formal languages to express mechanisms of geographic processes and design analytical workflows to understand these processes. With the development of GIS and computer science, various types of spatial models and modeling techniques have become available, which endows the term of “spatial model” with different meanings. This entry provides an overview of common types of spatial models, modeling techniques, and related applications.

AM-10 - Spatial Interaction

Spatial interaction (SI) is a fundamental concept in the GIScience literature, and may be defined in numerous ways. SI often describes the "flow" of individuals, commodities, capital, and information over (geographic) space resulting from a decision process. Alternatively, SI is sometimes used to refer to the influence of spatial proximity of places on the intensity of relations between those places. SI modeling as a separate research endeavor developed out of a need to mathematically model and understand the underlying determinants of these flows/influences. Proponents of SI modeling include economic geographers, regional scientists, and regional planners, as well as climate scientists, physicists, animal ecologists, and even some biophysical/environmental researchers. Originally developed from theories of interacting particles and gravitational forces in physics, SI modeling has developed through a series of refinements in terms of functional form, conceptual representations of distances, as well as a range of analytically rigorous technical improvements.
 

AM-42 - The Classic Transportation Problem

The classic transportation problem concerns minimizing the cost of transporting a product from sources/supplies to destinations/demands. It is a network-flow problem that arises in industrial logistics and is often solved by linear programming (LP). The three inputs of the model are total units produced at each source, total units needed at each destination, and the cost to transport one unit from each source to each destination. And the objective is to minimize the total cost of transporting all units produced at sources to meet the demands at destinations. The problem solution includes three basic steps: 1) finding an initial basic feasible solution, 2) checking if the current solution is optimal (with the lowest costs), and improving the current solution through iteration. Solving such a problem relies strongly on the network data models, least-cost path algorithms, other functionalities in GIS. And an integrated framework is often adopted to utilize both GIS and non-GIS linear programming solvers to search for the optimal solution.

AM-86 - Theory of error propagation
  • Describe stochastic error models
  • Exemplify stochastic error models used in GIScience