Capturing site-to-site variability through Hierarchical Bayesian calibration of a process-based dynamic vegetation model

Process-based ecosystem models help us understand and predict ecosystem processes, but using them has long involved a difficult choice between performing data- and labor-intensive site-level calibrations or relying on general parameters that may not reflect local conditions. Hierarchical Bayesian (HB) calibration provides a third option that frees modelers from assuming model parameters to be completely generic or completely site-specific and allows a formal distinction between prediction at known calibration sites and "out-of-sample" prediction to new sites. Here, we compare calibrations of a process-based dynamic vegetation model to eddy-covariance data across 12 temperate deciduous Ameriflux sites fit using either site-specific, joint cross-site, or HB approaches. To be able to apply HB to computationally demanding process-based models we introduce a novel emulator-based HB calibration tool, which we make available through the PEcAn community cyberinfrastructure. Using these calibrations to make predictions at held-out tower sites, we show that the joint cross-site calibration is falsely over-confident because it neglects parameter variability across sites and therefore underestimates variance in parameter distributions. By showing which parameters show high site-to-site variability, HB calibration also formally gives us a structure that can detect which process representations are missing from the models and prioritize errors based on the magnitude of the associated uncertainty. For example, in our case-study, we were able to identify large site-to-site variability in the parameters related to the temperature responses of respiration and photosynthesis, associated with a lack of thermal acclimation and adaptation in the model. Moving forward, HB approaches present important new opportunities for statistical modeling of the spatiotemporal variability in modeled parameters and processes that yields both new insights and improved predictions.