Assessing Error Effects in Critical Application Areas
Important economic and environmental decisions are routinely based on spatial/temporal models. This thesis studies the uncertainty in the predictions of three such models caused by uncertainty propagation. This is considered important as it quantifies the sensitivity of a model’s prediction to uncertainty in other components of the model, such as the model’s inputs. Furthermore, many software packages that implement these models do not permit users to easily visualize either the uncertainty in the data inputs, the effects of the model on the magnitude of that uncertainty, or the sensitivity of the uncertainty to individual data layers. In this thesis, emphasis has been placed on demonstrating the methods used to quantify and then, to a lesser extent, visualize the sensitivity of the models. Also, the key questions required to be resolved with regards to the source of the uncertainty and the structure of the model is investigated. For all models investigated, the propagation paths that most influence the uncertainty in the prediction were determined. How the influence of these paths can be minimised, or removed, is also discussed.
Two different methods commonly used to analyse uncertainty propagation were investigated. The first is the analytical Taylor series method, which can be applied to models with continuous functions. The second is the Monte Carlo simulation method which can be used on most types of models. Also, the later can be used to investigate how the uncertainty propagation changes when the distribution of model uncertainty is non Gaussian. This is not possible with the Taylor method.
The models tested were two continuous Precision Agriculture models and one ecological niche statistical model. The Precision Agriculture models studied were the nitrogen (N) availability component of the SPLAT model and the Mitscherlich precision agricultural model. The third, called BIOCLIM, is a probabilistic model that can be used to investigate and predict species distributions for both native and agricultural species.
It was generally expected that, for a specific model, the results from the Taylor method and the Monte Carlo will agree. However, it was found that the structure of the model in fact influences this agreement, especially in the Mitscherlich Model which has more complex non linear functions. Several nonnormal input uncertainty distributions were investigated to see if they could improve the agreement between these methods. The uncertainty and skew of the Monte Carlo results relative to the prediction of the model was also useful in highlighting how the distribution of model inputs and the models structure itself, may bias the results.
The version of BIOCLIM used in this study uses three basic spatial climatic input layers (monthly maximum and minimum temperature and precipitation layers) and a dataset describing the current spatial distribution of the species of interest. The thesis investigated how uncertainty in the input data propagates through to the estimated spatial distribution for Field Peas (Pisum sativum) in the agriculturally significant region of south west Western Australia. The results clearly show the effect of uncertainty in the input layers on the predicted specie’s distribution map. In places the uncertainty significantly influences the final validity of the result and the spatial distribution of the validity also varies significantly.