Environmental research has focused on monitoring, assessing and predicting the impact of environmental agents on human beings and animals. The study of spatial distribution of the environmental agents requires the use of geospatial analysis and modelling. The outputs from the geospatial analysis and modelling are prone to possible errors in the model inputs and model parameters. The uncertainty in the outputs of the geospatial analysis and modelling should be quantified and provided for decision makers to effectively make choices or decisions related to, for example, mitigation or treatment that can have strong effects on human and animals.

In the context of this research, uncertainty is defined as an interval around a value such that any repetition of estimating this value will produce a new result that mainly lies within this interval. Different sources of uncertainties in geospatial modelling can be categorized into four main sources: (1) Input uncertainty; (2) Model parameter uncertainty; (3) Model structure uncertainty and (4) Model solution uncertainty. In this research, the questions of how to quantify model input, model parameter uncertainties and their propagation through environmental models were addressed.

The Monte Carlo uncertainty analysis method was used in this research. The idea of the Monte Carlo method is to repeatedly compute results of the model, with inputs that are randomly sampled from their probability distributions. These inputs can be the model input and/or the model parameter and/or error in the model structure. The model outputs form a random sample of the output probability distribution. Analysing this sample distribution by computing its mean and its variance represents the level of uncertainty about model output, provided that the sample is large enough.

A case study of using a spatial linear regression model to predict the emission of air pollutant, i.e. soil nitrous oxide was used to illustrate the application of the Monte Carlo method to quantify uncertainty propagation to the prediction outcomes. The linear regression model calculates soil nitrous oxide emission as a function of many factors, including climate variables (e.g. monthly precipitation, minimum temperature), water-pH, soil organic carbon content, nitrogen deposition and vegetation types. The main results of this case study indicate that: (1) The developed statistical models are sufficient to quantify uncertainty about the model inputs and model parameters; (2) Uncertainty about nitrous oxide estimate is expressed by the standard deviation of the prediction outcomes that has a high variation over the study area; (3) Uncertainty in the regression coefficients is the most important source of error that propagates to the uncertainty in the prediction of soil nitrous oxide emission.