Dynamic environmental modelling in GIS: 2. Modelling error propagation

Environmental modelling languages provide the possibility to construct models in two or three spatial dimensions. These models can be static models, without a time component, or dynamic models. Dynamic models are simulations run forward in time, where the state of the model at time t is defined as a function of its state in a period or time step preceding t. Since inputs and parameters of environmental models are associated with errors, environmental modelling languages need to provide techniques to calculate how these errors propagate to the output(s) of the model. Since these techniques are not yet available, the paper describes concepts for extending an environmental‐modelling language with functionality for error‐propagation modelling. The approach models errors in inputs and parameters as stochastic variables, while the error in the model outputs is approximated with a Monte Carlo simulation. A modelling language is proposed which combines standard functions in a structured script (program) for building environmental models, and calculation of error propagation in these models. A prototype implementation of the language is used in three example models to illustrate the concepts.

[1]  K. Thapa,et al.  Accuracy of spatial data used in geographic information systems , 1992 .

[2]  Gerard B. M. Heuvelink,et al.  Developments in statistical approaches to spatial uncertainty and its propagation , 2002, Int. J. Geogr. Inf. Sci..

[3]  Edzer Pebesma,et al.  The stochastic dimension in a dynamic GIS , 2000 .

[4]  William H. Press,et al.  Numerical Recipes in FORTRAN - The Art of Scientific Computing, 2nd Edition , 1987 .

[5]  William Ribarsky,et al.  Next-Generation Data Visualization Tools , 1994 .

[6]  Edzer Pebesma,et al.  GSTAT: a program for geostatistical modelling, prediction and simulation , 1998 .

[7]  Derek Karssenberg,et al.  Dynamic environmental modelling in GIS: 1. Modelling in three spatial dimensions , 2005, Int. J. Geogr. Inf. Sci..

[8]  Michael F. Goodchild,et al.  Development and test of an error model for categorical data , 1992, Int. J. Geogr. Inf. Sci..

[9]  P. Burrough,et al.  The indicator approach to categorical soil data: I. Theory , 1993 .

[10]  P. Burrough,et al.  The indicator approach to categorical soil data. II: Application to mapping and land use suitability analysis , 1993 .

[11]  Mary P. Anderson,et al.  Introduction to Groundwater Modeling: Finite Difference and Finite Element Methods , 1982 .

[12]  Howard Veregin,et al.  Developing and Testing of an Error Propagation Model for GIS Overlay Operations , 1995, Int. J. Geogr. Inf. Sci..

[13]  Clayton V. Deutsch,et al.  GSLIB: Geostatistical Software Library and User's Guide , 1993 .

[14]  H. Veregin.  Integration of simulation modeling and error propagation for the buffer operation in GIS , 1994 .

[15]  Harold Moellering,et al.  A draft proposed standard for digital cartographic data , 1987 .

[16]  Harri T. Kiiveri,et al.  Assessing, Representing and Transmitting Positional Uncertainty in Maps , 1997, Int. J. Geogr. Inf. Sci..

[17]  Gerard B. M. Heuvelink,et al.  Error Propagation in Environmental Modelling with GIS , 1998 .

[18]  Trevor J. Davis,et al.  Modelling Uncertainty in Natural Resource Analysis Using Fuzzy Sets and Monte Carlo Simulation: Slope Stability Prediction , 1997, Int. J. Geogr. Inf. Sci..

[19]  J. Hammersley,et al.  Monte Carlo Methods , 1965 .

[20]  D. Lanter,et al.  A research paradigm for propagating error in layer-based GIS , 1992 .

[21]  Peter F. Fisher,et al.  Modelling soil map-unit inclusions by Monte Carlo simulation , 1991, Int. J. Geogr. Inf. Sci..

[22]  Stefano Tarantola,et al.  Uncertainty and sensitivity analysis: tools for GIS-based model implementation , 2001, Int. J. Geogr. Inf. Sci..

[23]  Yee Leung,et al.  A Locational Error Model for Spatial Features , 1998, Int. J. Geogr. Inf. Sci..