Wavelet analysis of the scale- and location-dependent correlation of modelled and measured nitrous oxide emissions from soil

Abstract

We used the wavelet transform to quantify the performance of models that predict the rate of emission of nitrous oxide (N2O) from soil. Emissions of N2O and other soil variables that influence emissions were measured on soil cores collected at 256 locations across arable land in Bedfordshire, England. Rate-limiting models of N2O emissions were constructed and fitted to the data by functional analysis. These models were then evaluated by wavelet variance and wavelet correlations, estimated from coefficients of the adapted maximal overlap discrete wavelet transform (AMODWT), of the fitted and measured emission rates. We estimated wavelet variances to assess whether the partition of the variance of modelled rates of N2O emission between scales reflected that of the data. Where the relative distribution of variance in the model is more skewed to coarser scales than is the case for the observation, for example, this indicates that the model predictions are too smooth spatially, and fail adequately to represent some of the variation at finer scales. Scale-dependent wavelet correlations between model and data were used to quantify the model performance at each scale, and in several cases to determine the scale at which the model description of the data broke down. We detected significant changes in correlation between modelled and predicted emissions at each spatial scale, showing that, at some scales, model performance was not uniform in space. This suggested that the influence of a soil variable on N2O emissions, important in one region but not in another, had been omitted from the model or modelled poorly. Change points usually occurred at field boundaries or where soil textural class changed. We show that wavelet analysis can be used to quantify aspects of model performance that other methods cannot. By evaluating model behaviour at several scales and positions wavelet analysis helps us to determine whether a model is suitable for a particular purpose.