Conditional inversion to estimate parameters from eddy-flux observations

Aims Data assimilation is a useful tool to extract information from large datasets of the net ecosystem exchange (NEE) of CO₂ obtained by eddy-flux measurements. However, the number of parameters in ecosystem models that can be constrained by eddy-flux data is limited by conventional inverse analysis that estimates parameter values based on one-time inversion. This study aimed to improve data assimilation to increase the number of constrained parameters.Methods In this study, we developed conditional Bayesian inversion to maximize the number of parameters to be constrained by NEE data in several steps. In each step, we conducted a Bayesian inversion to constrain parameters. The maximum likelihood estimates of the constrained parameters were then used as prior to fix parameter values in the next step of inversion. The conditional inversion was repeated until there were no more parameters that could be further constrained. We applied the conditional inversion to hourly NEE data from Harvard Forest with a physiologically based ecosystem model.Important findings Results showed that the conventional inversion method constrained 6 of 16 parameters in the model while the conditional inversion method constrained 13 parameters after six steps. The cost function that indicates mismatch between the modeled and observed data decreased with each step of conditional Bayesian inversion. The Bayesian information criterion also decreased, suggesting reduced information loss with each step of conditional Bayesian inversion. A wavelet analysis reflected that model performance under conditional Bayesian inversion was better than that under conventional inversion at multiple time scales, except for seasonal and half-yearly scales. In addition, our analysis also demonstrated that parameter convergence in a subsequent step of the conditional inversion depended on correlations with the parameters constrained in a previous step. Overall, the conditional Bayesian inversion substantially increased the number of parameters to be constrained by NEE data and can be a powerful tool to be used in data assimilation in ecology.