K. de Jong

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.

Modelling landscape dynamics with Python

A new tool for construction of models is presented that allows earth scientists without specialist knowledge in programming to convert theories to numerical computer models simulating landscape change through time. This tool, referred to as the PCRaster Python library, consists of: (1) the standard Python programming language, which is a generic, interpreted scripting language, supporting object oriented programming; (2) a large set of spatial and temporal functions on raster maps that are embedded in the Python language as an extension; (3) a framework provided as a Python class to construct and run iterative temporal models and to calculate error propagation with Monte Carlo simulation; and (4) visualization routines to display spatio‐temporal data read and written by this framework. Python is a high‐level programming language, and users of the tool do not have to be specialist computer programmers. Users of the PCRaster Python library can take advantage of several other Python libraries, such as extensions for matrix algebra and for modelling in three spatial dimensions.

Dynamic environmental modelling in GIS: 1. Modelling in three spatial dimensions

Environmental modelling languages are programming languages developed for building computer models simulating environmental processes. They come with database and visualization routines for the data used in the models. Environmental modelling languages provide the possibility to construct dynamic models, also called forward models, which 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 time step preceding t. Nowadays, these modelling languages can deal with simulations in two spatial dimensions, but existing software does not support the construction of models in three dimensions. We describe concepts of an environmental modelling language supporting dynamic model construction in two and three spatial dimensions. The lateral dimension is represented by gridded maps, with a regular discretization, while the vertical dimension is represented by an irregular discretization in voxels. Universal spatial functions are described with these entities of the modelling language as input. Dynamic modelling through time is possible by combining these functions in structured script sections, providing a section, which is executed repetitively, representing the time steps. The concepts of the language are illustrated with two example models, built with a prototype of the language.