Empirical estimates of uncertainty for mapping continuous depth functions of soil attributes

We use an empirical method where model output uncertainties are expressed as a prediction interval (PI) of the underlying distribution of prediction errors. This method obviates the need to identify and determine the contribution of each source of uncertainty to the overall prediction uncertainty. Conceptually, in the context of digital soil mapping, rather than a single point estimate at every prediction location, a PI, characterised by upper and lower prediction limits, encloses the prediction (which lies somewhere on the interval) and ideally the true but unknown value 100(1 − α)% of times on average the target variable (typically 95%). The idea is to partition the environmental covariate feature space into clusters which share similar attributes using fuzzy k-means with extragrades. Model error for predicting a target variable is then estimated from which cluster PIs are constructed on the basis of the empirical distribution of errors associated with the observations belonging to each cluster. PIs for each non-calibration observation are then formulated on the basis of the grade of membership each has to each cluster.We demonstrate how we can apply this method for mapping continuous soil depth functions. First, using soil depth functions and digital soil mapping (DSM) methods, we map the continuous vertical and lateral distribution of organic carbon (OC) and available water capacity (AWC) across the Edgeroi district in north-western NSW, Australia. From those predictions we define a continuous PI for each prediction node, generating upper and lower prediction limits of both attributes. From an external validation dataset, preliminary results are encouraging where 91% and 93% of the OC and AWC observations respectively fall within the bounds of their 95% PIs. Ideally, 95% of instances should fall within these bounds.

Research Highlights
► The empirical uncertainty model presented complements the continuous prediction of soil attributes.
► The empirical uncertainty model explicitly accounts for all sources of uncertainty without the requirement to separate out the contribution of each error source.
► We have demonstrated that this method performed well for both OC and AWC.
► This methodology represents a pragmatic approach to estimating uncertainties both spatially and laterally in a digital soil mapping framework.