Quantification of Uncertainty in Mathematical Models: The Statistical Relationship between Field and Laboratory pH Measurements

Abstract

The measurement of soil pH using a field portable test kit represents a fast and inexpensive method to assess pH. Field based pH methods have been used extensively for agricultural advisory services and soil survey and now for citizen soil science projects. In the absence of laboratory measurements, there is a practical need to model the laboratory pH as a function of the field pH to increase the density of data for soil research studies and Digital Soil Mapping. The accuracy and uncertainty in pH field measurements were investigated for soil samples from regional Victoria in Australia using both linear and sigmoidal models. For samples in water and CaCl2 at 1 : 5 dilutions, sigmoidal models provided improved accuracy over the full range of field pH values in comparison to linear models (i.e., pH < 5 or pH > 9). The uncertainty in the field results was quantified by the 95% confidence interval (CI) and 95% prediction interval (PI) for the models, with 95% CI < 0.25 pH units and 95% PI = ±1.3 pH units, respectively. It was found that the Pearson criterion for robust regression analysis can be considered as an alternative to the orthodox least-squares modelling approach because it is more effective in addressing outliers in legacy data.