Mathematical models are key components of scientific research as they both represent the current state of the art of science and can function as a tool to explore both the process behaviour as well as generate new hypotheses for future experimentation. Temporal or spatial scales at which observations have been collected are often different from the scale required by the modellers or model end users such as policy makers. As a result, the data must either be transferred from a smaller to a larger scale (upscaling or aggregation) or from a larger scale to a smaller scale (downscaling or disaggregation). The aim of this project is to understand the upscaling behaviour of a mechanistic soil ammonia volatilization model. The generalized scaling procedure in this project consists of a decision system, supported by information on the model behaviour at specific spatial scales. The decision process observes key points such as effective model linearity (or non-linearity) within and between scales, model congruency or scale dependency (dissimilarity in model properties) across scales and overall model parsimony.

In order to explore the spatially explicit model behaviour, we implemented a nested sampling design to study variation at different scales across three contrasting soil landscapes in Bedfordshire, United Kingdom. The advantage of this design is that it allows for the estimation of both the variance and covariance components of the model variables, parameters and outcomes, which are needed to understand its behaviour across scales. Producing a general framework to upscale models, this research provides both efficiencies in (future) sampling and a universal approach to handling process models and model outcomes over multiple scale and constitutes a significant contribution to soil management options for policy makers.