Academic journal article Cartography and Geographic Information Science

Error Propagation Modeling in Raster GIS: Adding and Ratioing Operations

Academic journal article Cartography and Geographic Information Science

Error Propagation Modeling in Raster GIS: Adding and Ratioing Operations

Article excerpt

Introduction

The study of map error and map error propagation raises a distinct set of problems that go beyond traditional error analysis (Taylor 1982). Map data consist of attributes recorded at locations and, with the exception of lines of discontinuity such as shorelines and urban/rural boundaries, attribute values at adjacent locations are often similar (spatially correlated) because of the continuity of ground truth. The error processes that can contaminate map data also raise new problems. Attribute measurement error may not be independent between adjacent locations and there may be errors in specifying the locations of attributes. For discussions of different sources and forms of map error see, for example, Goodchild and Gopal (1989), Heuvelink et al. (1989, Lunetta et al. (1991), Amrhein and Griffith (1992), Thapa and Bossler (1992), Haining and Arbia (1993), Heuvelink (1993), and Veregin (1995).

In this paper it is assumed that errors arise only from the measurement of the real world and not from any discrepancy between the form of the GIS data model and the reality it is seeking to capture (Altman 1994). Errors originate in source maps as a result of the measurement processes used to construct those maps and then are propagated as a consequence of map operations. The overlay operations of adding and ratioing maps are used separately and together in deriving vegetation indexes (Curran 1980), in seismic risk assessment (Emmi and Horton 1995), and in map analysis techniques such as principal components and linear discriminant analysis. Map overlay using logical operators and buffering may be applied for the purposes of resource exploitation, factory siting, or environmental risk assessment (Berry 1987; Veregin 1994). There is interest in how the results from multiple as well as single map operations are affected by the presence of error in the source maps (Richards 1986).

The purpose of this paper is to identify the contribution made by different forms of error to final map error as a result of adding or ratioing two maps. Error propagation in the case of overlay using logical operators is analyzed in Arbia et al. (1998). Error properties on maps include both the size of the errors and the spatial structure, or geography, of the errors. Any study of map error needs to consider how errors are distributed in geographic space. Further, there is a practical reason for studying the spatial structure of errors. Isolated or random errors may be more likely to stand out and be detected by the trained eye, particularly if they are large. An analyst familiar with a region or the phenomena under study may be better at spotting this type of error as opposed to the error that possesses spatial continuity and may blend in with the underlying map structure. For this reason short- and long-distance error properties are examined, and it is determined whether there is a tendency for error regions to form.

The approach taken in this paper combines formal mathematical modeling with simulation and is based on an error or corruption process with specified properties. The simulation modeling is based on using artificially generated maps with specified map properties. The error process is defined in the following section. The purpose of adopting this approach using maps and error processes with simple but well defined properties is to understand better how different elements of the situation, individually and together, contribute to the final propagated error. The problem with using real maps (rather than artificially generated maps) is that real maps usually have complex structures so that it may not be clear the extent to which aggregate statistics computed to measure the severity of the error problem are an aggregation across many types of quite different map segments with different structures. Usually, real errors are not known for any data set, and unless their structure is uniform across the map, the same problem for interpreting aggregate statistics could arise. …

Search by... Author
Show... All Results Primary Sources Peer-reviewed

Oops!

An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.