Scale and abstraction : the sensitivity of fire regime simulation to nuisance parameters

Abstract

Fire plays a key role in ecosystem dynamics and its impact on environmental, social and economic assets is increasingly a critical area of research. Fire regime simulation models are one of many approaches that provide insights into the relative importance of factors driving the dynamics of fire-vegetation systems. Fire propagates as a contagious process and simulation is an approach that captures this behaviour explicitly, integrating spatial and temporal data to produce auto-correlated patterns of fire regimes. However, when formulating these models, time and many aspects of space must be made discrete. These parameters are 'nuisance parameters': parameters necessary for the model formulation but not otherwise of interest. Fire growth simulations are therefore discrete approximations of continuous non-linear systems, and it might be expected that the values chosen for these nuisance parameters will be important. While it is well known that discrete geometries have consequences for the shape and area of simulated fires, no research has investigated the consequence this may have for estimates of the relative importance of the various drivers of fire regimes. I argue that nuisance parameters can be demonstrated to be unimportant for this class of model. I use the idea of 'importance' to underline the need for context with such an assertion. With sufficient replication, any parameter can be found statistically significant. A parameter is important, on the other hand, if different values produce qualitatively different outcomes. Models are commonly either re-parameterised to account for changes in resolution or scaling-up methods applied if such exist. I will further argue that such differences as there are in model outputs due to spatial resolution, cannot be accounted for by either re-parameterising or using a common approach that allows resolution to vary over the spatial extent. A set of experiments were devised using a published fire regime simulation model, modified, verified and validated, to isolate just those aspects of the model's sensitivity to resolution and discrete geometries that are unavoidable or intrinsic to these choices. This new model was used to test the above hypotheses, using peer-reviewed treatments that stand as yardsticks by which formal estimates of the importance of nuisance parameters can be made. As estimated by the model, neither spatio-temporal resolution nor any of the various choices available for discrete geometries, altered the model predictions. As expected, it is spatial resolution that has the greatest impact on running times for the model but this study finds that neither calibration, nor taking an approach that allows resolution to vary over the spatial extent, can account for differences in model outputs that arise from running simulations at coarser resolutions. All models are abstractions and a good model should ideally hold over levels of abstraction. This is rarely the case, but this study shows that results obtained through simulation in estimating the drivers of fire frequency in large landscapes, are robust with regard to these aspects of abstraction. This adds considerable confidence to a significant body of work that has used this approach over the last two decades.