Balancing multiple constraints in model-data integration: Weights and the parameter block approach

Model data integration (MDI) studies are key to parameterize ecosystem models that synthesize our knowledge about ecosystem function. The use of diverse data sets, however, results in strongly imbalanced contributions of data streams with model fits favoring the largest data stream. This imbalance poses new challenges in the identification of model deficiencies. A standard approach for balancing is to attribute weights to different data streams in the cost function. However, this may result in overestimation of posterior uncertainty. In this study, we propose an alternative: the parameter block approach. The proposed method enables joint optimization of different blocks, i.e., subsets of the parameters, against particular data streams. This method is applicable when specific parameter blocks are related to processes that are more strongly associated with specific observations, i.e., data streams. A comparison of different approaches using simple artificial examples and the DALEC ecosystem model is presented. The unweighted inversion of a DALEC model variant, where artificial structural errors in photosynthesis calculation had been introduced, failed to reveal the resulting biases in fast processes (e.g., turnover). The posterior bias emerged only in parameters related to slower processes (e.g., carbon allocation) constrained by fewer data sets. On the other hand, when weighted or blocked approaches were used, the introduced biases were revealed, as expected, in parameters of fast processes. Ultimately, with the parameter block approach, the transfer of model error was diminished and at the same time the overestimation of posterior uncertainty associated with weighting was prevented.