Conditional inversion to estimate parameters from eddy flux observations

Data-model assimilation provides a great tool to extract information from large datasets of the net ecosystem exchange (NEE) 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. 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 (MLE) of the constrained parameters were then used as prior to fix parameter values in the next step of inversion. The conditional inversion is repeated until there are no more parameters that can be further constrained. We applied the conditional inversion to hourly NEE data at Harvard forest with a physiologically based ecosystem model. Results showed that the conventional inversion method constrained 6 out of 16 parameters in the model while the conditional inversion method constrained 13 parameters after 6 steps. The cost function that indicates mismatch between the modeled and observed data decreased with each step of conditional Bayesian inversion. Bayesian information criterion (BIC) 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. In addition, our analysis also demonstrates that parameter convergence at each step of the conditional inversion does not depend on its correlations with other parameters. Overall, the conditional Bayesian inversion substantially increases the number of parameters to be constrained by NEE data and can be a powerful tool to be used in data-model assimilation in ecology.