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 (CO 2 ) emissions from soil. The soil (Dystric and Typic Eutrudepts) was sampled on a 1024‐m transect at Silsoe, UK. Observed CO 2 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 CO 2 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 CO 2 emissions on the transect was 10 to 20 m.