Comparison of different objective functions for parameterization of simple respiration models

[1] The eddy covariance measurements of carbon dioxide fluxes collected around the world offer a rich source for detailed data analysis. Simple, aggregated models are attractive tools for gap filling, budget calculation, and upscaling in space and time. Key in the application of these models is their parameterization and a robust estimate of the uncertainty and reliability of their predictions. In this study we compared the use of ordinary least squares (OLS) and weighted absolute deviations (WAD, which is the objective function yielding maximum likelihood parameter estimates with a double exponential error distribution) as objective functions within the annual parameterization of two respiration models: the Q10 model and the Lloyd and Taylor model. We introduce a new parameterization method based on two nonparametric tests in which model deviation (Wilcoxon test) and residual trend analyses (Spearman test) are combined. A data set of 9 years of flux measurements was used for this study. The analysis showed that the choice of the objective function is crucial, resulting in differences in the estimated annual respiration budget of up to 40%. The objective function should be tested thoroughly to determine whether it is appropriate for the application for which the model will be used. If simple models are used to estimate a respiration budget, a trend test is essential to achieve unbiased estimates over the year. The analyses also showed that the parameters of the Lloyd and Taylor model are highly correlated and difficult to determine precisely, thereby limiting the physiological interpretability of the parameters.