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AM-08 - Kernels and Density Estimation

Kernel density estimation is an important nonparametric technique to estimate density from point-based or line-based data. It has been widely used for various purposes, such as point or line data smoothing, risk mapping, and hot spot detection. It applies a kernel function on each observation (point or line) and spreads the observation over the kernel window. The kernel density estimate at a location will be the sum of the fractions of all observations at that location. In a GIS environment, kernel density estimation usually results in a density surface where each cell is rendered based on the kernel density estimated at the cell center. The result of kernel density estimation could vary substantially depending on the choice of kernel function or kernel bandwidth, with the latter having a greater impact. When applying a fixed kernel bandwidth over all of the observations, undersmoothing of density may occur in areas with only sparse observation while oversmoothing may be found in other areas. To solve this issue, adaptive or variable bandwidth approaches have been suggested.

AM-46 - Location-allocation modeling

Location-allocation models involve two principal elements: 1) multiple facility location; and 2) the allocation of the services or products provided by those facilities to places of demand. Such models are used in the design of logistic systems like supply chains, especially warehouse and factory location, as well as in the location of public services. Public service location models involve objectives that often maximize access and levels of service, while private sector applications usually attempt to minimize cost. Such models are often hard to solve and involve the use of integer-linear programming software or sophisticated heuristics. Some models can be solved with functionality provided in GIS packages and other models are applied, loosely coupled, with GIS. We provide a short description of formulating two different models as well as discuss how they are solved.

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-17 - Intervisibility, Line-of-Sight, and Viewsheds

The visibility of a place refers to whether it can be seen by observers from one or multiple other locations. Modeling the visibility of points has various applications in GIS, such as placement of observation points, military observation, line-of-sight communication, optimal path route planning, and urban design. This chapter provides a brief introduction to visibility analysis, including an overview of basic conceptions in visibility analysis, the methods for computing intervisibility using discrete and continuous approaches based on DEM and TINs, the process of intervisibility analysis, viewshed and reverse viewshed analysis. Several practical applications involving visibility analysis are illustrated for geographical problem-solving. Finally, existing software and toolboxes for visibility analysis are introduced.

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-80 - Capturing Spatiotemporal Dynamics in Computational Modeling

We live in a dynamic world that includes various types of changes at different locations over time in natural environments as well as in human societies. Modern sensing technology, location-aware technology and mobile technology have made it feasible to collect spatiotemporal tracking data at a high spatial and temporal granularity and at affordable costs. Coupled with powerful information and communication technologies, we now have much better data and computing platforms to pursue computational modeling of spatiotemporal dynamics. Researchers have attempted to better understand various kinds of spatiotemporal dynamics in order to predict, or even control, future changes of certain phenomena. A simple approach to representing spatiotemporal dynamics is by adding time (t) to the spatial dimensions (x,y,z) of each feature. However, spatiotemporal dynamics in the real world are more complex than a simple representation of (x,y,z,t) that describes the location of a feature at a given time. This article presents selected concepts, computational modeling approaches, and sample applications that provide a foundation to computational modeling of spatiotemporal dynamics. We also indicate why the research of spatiotemporal dynamics is important to geographic information systems (GIS) and geographic information science (GIScience), especially from a temporal GIS perspective.

AM-44 - Modelling Accessibility

Modelling accessibility involves combining ideas about destinations, distance, time, and impedances to measure the relative difficulty an individual or aggregate region faces when attempting to reach a facility, service, or resource. In its simplest form, modelling accessibility is about quantifying movement opportunity. Crucial to modelling accessibility is the calculation of the distance, time, or cost distance between two (or more) locations, which is an operation that geographic information systems (GIS) have been designed to accomplish. Measures and models of accessibility thus draw heavily on the algorithms embedded in a GIS and represent one of the key applied areas of GIS&T.

AM-32 - Spatial Autoregressive Models

Regression analysis is a statistical technique commonly used in the social and physical sciences to model relationships between variables. To make unbiased, consistent, and efficient inferences about real-world relationships a researcher using regression analysis relies on a set of assumptions about the process generating the data used in the analysis and the errors produced by the model. Several of these assumptions are frequently violated when the real-world process generating the data used in the regression analysis is spatially structured, which creates dependence among the observations and spatial structure in the model errors. To avoid the confounding effects of spatial dependence, spatial autoregression models include spatial structures that specify the relationships between observations and their neighbors. These structures are most commonly specified using a weights matrix that can take many forms and be applied to different components of the spatial autoregressive model. Properly specified, including these structures in the regression analysis can account for the effects of spatial dependence on the estimates of the model and allow researchers to make reliable inferences. While spatial autoregressive models are commonly used in spatial econometric applications, they have wide applicability for modeling spatially dependent data.

AM-07 - Point Pattern Analysis

Point pattern analysis (PPA) focuses on the analysis, modeling, visualization, and interpretation of point data. With the increasing availability of big geo-data, such as mobile phone records and social media check-ins, more and more individual-level point data are generated daily. PPA provides an effective approach to analyzing the distribution of such data. This entry provides an overview of commonly used methods in PPA, as well as demonstrates the utility of these methods for scientific investigation based on a classic case study: the 1854 cholera outbreaks in London.