Map algebra and model algebra for integrated model building

• We develop an integrated modelling framework in a high-level scripting language.
• The framework supports component building and coupling at different temporal discretisations.
• The concepts are demonstrated with the help of a prototype implementation and example models.

Computer models are important tools for the assessment of environmental systems. A seamless workflow of construction and coupling of model components is essential for environmental scientists. However, currently available software packages are often tailored either to the construction of model components, or to the coupling of existing components. Combining both objectives is not straightforward, because it requires merging concepts for model component building and model component coupling. Also, software packages should be usable for domain experts such as hydrologists or ecologists who do not necessarily have expert knowledge in programming.We propose an integrated modelling framework that provides descriptive means to specify (1) model components with conventional map algebra, and (2) interactions between model components with model algebra. A prototype implementation in a high-level scripting language supports the building of integrated spatio-temporal models. For a seamless coupling of model components with different temporal and spatial discretisation, we introduce the use of accumulators. These handle the temporal aggregation of model component outputs. The framework provides templates for the custom construction of model components and accumulators, and a management layer arranges the schedule for the execution of the integrated model. We use the prototype implementation of the framework in an illustrative case study to build an integrated model that couples model components simulating the interaction between biomass growth, wildfire, and human impacts with different temporal discretisations. The high-level Python language is used as model building environment to allow domain experts without in-depth knowledge of software development practices to conduct exploratory model construction and analysis.