Bayesian calibration, comparison and averaging of six forest models, using data from Scots pine stands across Europe

Abstract

We used six models, ranging from simple parameter-sparse models to complex process-based 7 models: 3PG, 4C, ANAFORE, BASFOR, BRIDGING and FORMIND. For each model, the initial 8 degree of uncertainty about parameter values was expressed in a prior probability distribution. 9Inventory data for Scots pine on tree height and diameter, with estimates of measurement 10 uncertainty, were assembled for twelve sites, from four countries: Austria, Belgium, Estonia and 11Finland. From each country, we used data from two sites of the National Forest Inventories (NFI), 12 and one Permanent Sample Plot (PSP). The models were calibrated using the NFI-data and tested 13 against the PSP-data. Calibration was done both per country and for all countries simultaneously, 14 thus yielding country-specific and generic parameter distributions. We assessed model 15 performance by sampling from prior and posterior distributions and comparing the growth 16 predictions of these samples to the observations at the PSP"s. 17We found that BC reduced uncertainties strongly in all but the most complex model. 18 Surprisingly, country-specific BC did not lead to clearly better within-country predictions than 19 generic BC. BMC identified the BRIDGING model, which is of intermediate complexity, as the 20 most plausible model before calibration, with 4C taking its place after calibration. In this BMC, 21 model plausibility was quantified as the relative probability of a model being correct given the 22 information in the PSP-data. We discuss how the method of model initialisation affects model 23 performance. Finally, we show how BMA affords a robust way of predicting forest growth that 24 accounts for both parametric and model structural uncertainty. 25 26 27

Growth decline assessment in Pinus sylvestris L. and Pinus nigra Arnold. forest by using 3-PG model.

“…Using 3PG model to assess growth decline processes to forest decline (McDowell et al, 2008). On decline trees, values of stem partitioning ratio (pFS 20 ), maximum litterfall rate (γ Fx ), maximum canopy conductance (g Cx ), specific leaf area for mature aged stands (σ 1 ), age at which specific leaf area = ½ (σ 0 + σ 1 ), age at full canopy cover (t c ), and canopy boundary layer conductance (g B ) were different from those used on other simulations for pine species (Landsberg et al, 2005;Patenaude et al, 2008;van Oijen et al, 2013), and they were important for DBH and BAI predictions under drought stress (Esprey et al, 2004 for Black pine were within the lower range of those measured in England (Mencuccini & Bonosi, 2001;Patenaude et al, 2008). More restrictive physiological values (i.e., maximum canopy conductance (g Cx ) and canopy boundary layer conductance (g B ) affecting water photosynthetic status) led to a different biomass allocation to the stem or to foliage, resulting in lower DBH and BAI estimates.…”

Managing forests in a changing world: the need for a systemic approach. A review

“…Bayesian model averaging (e.g. van Oijen et al, 2013), have been developed to better assess the uncertainty of model predictions.…”

Bayesian calibration of a soil organic carbon model using Δ<sup>14</sup>C measurements of soil organic carbon and heterotrophic respiration as joint constraints

“…Process-based models in geosciences tend to be overparameterized with regard to data availability (van Oijen et al, 2005). Hence, it does not make sense to apply parameter finetuning, i.e., looking for one best parameter set, but rather to show how well we can constrain the uncertainty about model parameters with the data at hand.…”