Statistical properties of random CO₂ flux measurement uncertainty inferred from model residuals

Information about the uncertainties associated with eddy covariance measurements of surface-atmosphere CO₂ exchange is needed for data assimilation and inverse analyses to estimate model parameters, validation of ecosystem models against flux data, as well as multi-site synthesis activities (e.g., regional to continental integration) and policy decision-making. While model residuals (mismatch between fitted model predictions and measured fluxes) can potentially be analyzed to infer data uncertainties, the resulting uncertainty estimates may be sensitive to the particular model chosen. Here we use 10 site-years of data from the CarboEurope program, and compare the statistical properties of the inferred random flux measurement error calculated first using residuals from five different models, and secondly using paired observations made under similar environmental conditions. Spectral analysis of the model predictions indicated greater persistence (i.e., autocorrelation or "memory") compared to the measured values. Model residuals exhibited weaker temporal correlation, but were not uncorrelated white noise. Random flux measurement uncertainty, expressed as a standard deviation, was found to vary predictably in relation to the expected magnitude of the flux, in a manner that was nearly identical (for negative, but not positive, fluxes) to that reported previously for forested sites. Uncertainty estimates were generally comparable whether the uncertainty was inferred from model residuals or paired observations, although the latter approach resulted in somewhat smaller estimates. Higher order moments (e.g., skewness and kurtosis) suggested that for fluxes close to zero, the measurement error is commonly skewed and leptokurtic. Skewness could not be evaluated using the paired observation approach, because differencing of paired measurements resulted in a symmetric distribution of the inferred error. Patterns were robust and not especially sensitive to the model used, although more flexible models, which did not impose a particular functional form on relationships between environmental drivers and modeled fluxes, appeared to give the best results. We conclude that evaluation of flux measurement errors from model residuals is a viable alternative to the standard paired observation approach.