Geostatistical prediction of nitrous oxide emissions from soil using data, process models and expert opinion

Abstract

Geostatistical techniques can be used to predict spatially correlated variables at unsampled locations. We can incorporate information from soil process models in the geostatistical methodology via regression kriging (RK), which we consider in a Bayesian statistical framework (BRK). The resulting predictions are better than those obtained from the process model alone or by ordinary kriging. We consider approaches to predict the nitrous oxide emissions from soil along a transect in Bedfordshire in the UK. In this case study, there exists uncertainty about the most appropriate model to represent the denitrification process. We account for this uncertainty by model averaging (MA); the MA predictions are a weighted average of the BRK predictions based on the individual models. We consider several approaches to calculate weights for MA. We use Bayesian model averaging (BMA) to investigate whether the local data from the neighbourhood of a prediction location can provide useful information for calculating the model weights. We use the opinions of an expert on the relevant soil processes to define probabilities for the candidate models, and investigate how this information benefits the MA and BMA predictions. If we would prefer not to base analysis on the opinions of a single expert, we could use a linear opinion pool to merge the opinions of multiple experts, which we demonstrate through a simple example. We show the conditions under which MA and BMA improve predictions in this case study, and suggest reasons for these improvements. We use the BMA model weights, which are calculated from local data, to provide information about the ability of the models to represent the spatial variability of the data along the transect.

The North Wyke Farm Platform: effect of temperate grassland farming systems on soil moisture contents, runoff and associated water quality dynamics

“…Opportunities also exist for the application and development of a wide range of statistical methodologies to the NWFP data; including the possibility of mechanistic and statistical model hybrids (e.g. Orton et al , ; Clifford et al , ) that examine the complexity of processes whilst at the same time account for data and model uncertainty. The NWFP also enables the development of biodiversity statistical models that indicate field‐scale distributions of pests, diseases and pathogens and how these distributions interact with livestock production.…”

Burgess, T.M. & Webster, R. 1980. Optimal interpolation and isarithmic mapping of soil properties. I. The semi‐variogram and punctual kriging. Journal of Soil Science, 31, 315–331.

“…An example is provided by Orton et al . (), who used a Bayesian approach to deal with both the uncertainty arising from the spatial variation of observations, and the uncertainty about the appropriate form of a model to express the relationship between the target variable and a set of covariates.…”

“…In many circumstances this has little effect, but a Bayesian approach, in which the parameters are treated as random variables and the process of estimation from data entails obtaining posterior distributions for these parameters, can be useful for dealing with the uncertainty in the parameters, particularly when data are sparse. An example is provided by Orton et al (2011), who used a Bayesian approach to deal with both the uncertainty arising from the spatial variation of observations, and the uncertainty about the appropriate form of a model to express the relationship between the target variable and a set of covariates.…”

Pedometrics

“…We are shown how some long‐standing issues in geostatistics can now be tackled: block kriging of log‐normal data (Paul & Cressie, 2011) and prediction of complex variables resulting from a mixture of diffuse and point contamination (Marchant et al , 2011). We are reminded that geostatistics does not require us to ignore our understanding of soil processes or the information presented in conventional soil maps (Orton et al , 2011; Goovaerts, 2011). Allard et al (2011) present a significant advance in the spatial prediction of categorical data, showing how, among other classifications, those of soil can be predicted at unsampled sites.…”