Spatial Analysis of Model Error, Illustrated by Soil Carbon Dioxide Emissions

A spatial analysis of model error is required when the observations and model predictions are made at locations in space. This is because: (i) a model may reproduce observed variations better at some spatial scales than others, (ii) the model may be more or less successful at reproducing the relative variability of a process at different spatial scales, and (iii) the spatial pattern of model error may contain information about its possible sources. A geostatistical analysis can address these issues. We developed a model of carbon dioxide (CO2) emissions from soil. The soil (Dystric and Typic Eutrudepts) was sampled on a 1024-m transect at Silsoe, UK. Observed CO2 emissions were compared with model predictions at 156 random locations on the transect. A spatial analysis of the model's error, using a (cross-validated) linear model of coregionalization, revealed details not apparent with a nonspatial analysis. The model could not predict high-frequency fluctuations in CO2 emissions, but could accurately predict lower-frequency fluctuations. Factorial cokriging analysis allowed us to estimate and visualize the low-frequency components. We interpolated model error to unsampled locations, and found bias on soil with relatively large clay contents. Volumetric water content had a weak scale-dependent correlation with model error. We propose the inter-block correlation to quantify the effect of a change of support on the correlation of observations and model predictions; the best pixel size for the prediction of soil CO2 emissions on the transect was 10 to 20 m.