Bayesian calibration of a growth-dependent tree mortality model to simulate the dynamics of European temperate forests
Abstract
Dynamic vegetation models (DVMs) are important tools to understand and predict the functioning and dynamics of terrestrial ecosystems under changing environmental conditions. In these models, uncertainty in the description of demographic processes, in particular tree mortality, is a persistent problem. Current mortality formulations lack realism and are insufficiently constrained by empirical evidence. It has been suggested that empirically estimated mortality submodels would enhance DVM performance, but due to the many processes and interactions within a DVM, the claim has rarely been tested. Here, we compare the performance of three alternative growth‐dependent tree mortality submodels in the DVM ForClim: (1) a mortality function with theoretical foundation (ForClim v3.3); (2) a mortality function with parameters directly estimated based on forest inventory data; and (3) the same function, but with parameters estimated using an inverse approach through Bayesian calibration (BC). Time series of inventory data from 30 ecologically distinct Swiss natural forest reserves collected over 35+ yr, including the main tree species of Central Europe, were used for the calibration and subsequent validation of the mortality functions and the DVM. The recalibration resulted in mortality parameters that differed from the direct empirical estimates, particularly for the relationship between tree size and mortality. The calibrated parameters outperformed the direct estimates, and to a lesser extent the original mortality function, for predicting decadal‐scale forest dynamics at both calibration and validation sites. The same pattern was observed regarding the plausibility of their long‐term projections under contrasting environmental conditions. Our results demonstrate that inverse calibration may be useful even when direct empirical estimates of DVM parameters are available, as structural model deficiencies or data problems can result in discrepancies between direct and inverse estimates. Thus, we interpret the good performance of the inversely calibrated model for long‐term projections (which were not a calibration target) as evidence that the calibration did not compensate for model errors. Rather, we surmise that the discrepancy was mainly caused by a lack of representativeness of the mortality data. Our results underline the potential for learning more about elusive processes, such as tree mortality or recruitment, through data integration in DVMs.
What the paper shows and why it matters
(AI-generated)
Dynamic vegetation models project how ecosystems respond to environmental change, but their projections remain uncertain, partly because demographic processes, tree mortality above all, are weakly constrained by empirical evidence. Submodels built on empirical estimates have been suggested as a remedy. Earlier studies in the forest model ForClim tested this with parameters taken directly from field data (for example Bircher et al. 2015; Hülsmann et al. 2018). The paper reads these studies as showing that, contrary to general expectations, direct estimates did not substantially improve the model’s reliability. It questions the assumption behind that expectation: that parameters estimated directly from field data are the best ones to put into a complex process-based model.
The study argues that, for forest models with a poorly known process such as tree mortality, calibrating parameters inversely, by adjusting them until the model’s outputs match observed data, can be worthwhile even where direct field estimates exist, because direct estimates need not make the whole model behave well. It tests this in ForClim with a growth-dependent mortality function, comparing the original theoretically founded version, one with parameters estimated directly from forest inventory data, and one calibrated by Bayesian methods, using inventories from Swiss natural forest reserves. The calibration changed the parameters relative to the direct estimates, notably for the link between tree size and mortality. The calibrated version predicted decadal-scale forest dynamics better on average than the direct estimates, and to a lesser extent better than the original function, at calibration and validation sites alike, and its long-term projections under contrasting environmental conditions were more plausible than those of the direct estimates. The paper suspects that the mismatch arose mainly because the mortality data under-represent large trees.
The paper concludes that direct measurements are not always ideal for constraining a complex model so that it produces satisfactory patterns as a whole, and that tree mortality crucially determines simulated forest development. Comparing direct and inverse estimates is therefore informative: the paper argues that a mismatch can reveal structural problems in the model or biases in the data. It notes that generalising from a single case is difficult and that Bayesian calibration is computationally costly.
References
- Bircher et al. (2015). The agony of choice: different empirical mortality models lead to sharply different future forest dynamics. Ecological Applications 25, 1303–1318. doi:10.1890/14-1462.1
- Hülsmann et al. (2018). How to kill a tree: empirical mortality models for 18 species and their performance in a dynamic forest model. Ecological Applications 28, 522–540. doi:10.1002/eap.1668