Empirical And Mechanistic Approaches To Forecast Forest Growth Dynamics Under A Bayesian Framework

Forest growth modelling and ecological forecasting commonly rely on the observations from an uncontrolled environment.Multiple uncontrolled environmental drivers or mechanistic lead to complex interactions between data and forecasting,which make the simulation and interpretation unquantifiable.Under a Bayesian framework of information fusion,we analyzed the relations between data and models.Treating all the terms in a forecast as probability distributions results in two advantages: 1)the ability to update predictions as new data becomes available,and 2)flexible and robust for dealing with the complexity of real-world data and to build,fit and forecast with relatively complex models.Inverse modelling approaches,such as Bayesian calibration(BC),adjust model parameters and processes according to their ability to reproduce stand-level field observations,which bridges the gap between models and various databases.The main content and results are as follows:(1)This study focused on the data-model updating loop in continuous forest inventories.The aim was to compare different sources of data,with respect to their impacts on forest dynamic forecasting.The patterns of parametric uncertainty and predictive uncertainty were analyzed and quantified,to illustrate the process of information fusion.Multi-period and multi-type of inventory data of Pinus tabuliformis were collected in Qinling Mountains.A simple variable-density stand-level model with low data requirement was selected.On one hand,the changes in the probability distributions of both parameters and predictions were compared for multi-period inventory data;on the other hand,the multi-type data that includes observations from temporary plots,permanent plots and stem analysis were tested considering their impacts on model performances.to quantify the uncertainty in the forecasts of forest dynamics.The data-model updating loop was achieved by the relation between the priori and the posteriori,which means that the joint posterior parametric distribution in the former experiment was continuously used as the prior information for the latter experiment.The integration of multiple source data was based on the assumptions of the independent likelihood for sampling and observing error in each dataset.To avoid the biases from erratic observations and outliers,the likelihood of error structure applied a heavy-tailed normal distribution.The heteroscedasticity of errors was considered using an automatically changing variance in likelihood during iterations.With new dataset continuously obtained,the marginal and joint parametric distributions kept changing.In general,the parametric uncertainty decreased along with the increase of the kurtosis in probability distribution,resulting in decreasing predictive uncertainty.In comparison with parameterization from inventory in 1990,the model being calibrated with data from 2005 and 2012 showed obvious lower predictive uncertainty during mature stage,while the asymptotic parameter was shifting to higher values.The distinctions of predictions among various datasets revealed the advantages and drawbacks of different inventory datasets.The information from stem analysis tended a higher prediction of average height for mature stand,when compared with plot sampling.Temporary plots and permanent plots differed in sampling method and the observation quantity,which made the forecasts of stand basal area distinctive.The model based on continuously updating and multi-source data performed highest precision and accuracy.One challenge of forest growth and yield modeling is that sampling and observing errors vary with datasets.Even with the same set of optimal parameters,the advantages and drawbacks in different datasets will lead to distinctive pattern of uncertainty.The probabilistic information demonstrates both the accuracy of model and the lacking information of data,which reveal the further direction of model development and data collection.The case study chose specific Bayesian approach to demonstrate the complete logic of data-model loop and processes of information fusion.(2)We propose a methodology to develop a preliminary version of a growth model when tree-level growth data are unavailable.This modelling approach predicts individual tree growth using only one-time observations from temporary plots.A virtual dataset was generated by linking the whole stand and diameter distribution models.The individual tree model was parameterized using Bayesian calibration and a likelihood of diameter distributions.A key component of tree-level growth and yield prediction is the diameter increment model that requires at least two different points in time with individual-tree measurements.In some cases,however,sufficient inventory data from remeasured permanent or semi-temporary plots are unavailable or difficult to access.The purpose of this study was to propose a three-stage approach for modelling individual-tree diameter growth based on temporary plots.The first stage is to predict stand dynamics at 5-year intervals based on stand-level resource inventory data.The second stage is to simulate diameter distribution at 5-year intervals using a Weibull function based on tree-level research inventory data.The final stage is to improve the reliability of individual-tree diameter estimates by updating parameters with Bayesian calibration based on a likelihood of diameter distributions.The virtual-data-based diameter increment model provided logicalpatterns and reliable performances in both tree-and stand-level predictions.Although it underestimated the growth of suppressed trees compared to tree cores and remeasurements,this bias was negligible when aggregating tree-level simulations into stand-level growth predictions.Our virtual-data-based modelling approach only requires one-time observations from temporary plots,but provide reliable predictions of stand-and tree-level growth when validated with tree cores and whole-stand models.This preliminary model can be updated in a Bayesian framework when growth data from tree cores or remeasurements were obtained.(3)Applications of ecosystem flux models on large geographical scales are often limited by model complexity and data availability.Here,we calibrated and evaluated a semi-empirical ecosystem flux model,PRELES,for various forest types and climate conditions,based on eddy covariance data from 55 sites.A Bayesian approach was adopted for model calibration and uncertainty quantification.We applied the site-specific calibrations and multisite calibrations to nine plant functional types(PFTs)to obtain the site-specific and PFT specific parameter vectors for PRELES.A systematically designed cross-validation was implemented to evaluate calibration strategies and the risks in extrapolation.The combination of plant physiological traits and climate patterns generated significant variation in vegetation responses and model parameters across but not within PFTs,implying that applying the model without PFT-specific parameters is risky.But within PFT,the multisite calibrations performed as accurately as the site-specific calibrations in predicting gross primary production(GPP)and evapotranspiration(ET).Moreover,the variations among sites within one PFT could be effectively simulated by simply adjusting the parameter of potential light-use efficiency(LUE),implying significant convergence of simulated vegetation processes within PFT.The hierarchical modelling of PRELES provides a compromise between satellite-driven LUE and physiologically oriented approaches for extrapolating the geographical variation of ecosystem productivity.Although measurement errors of eddy covariance and remotely sensed data propagated a substantial proportion of uncertainty or potential biases,the results illustrated that PRELES could reliably capture daily variations of GPP and ET for contrasting forest types on large geographical scales if PFT-specific parameterizations were applied.(4)The response of canopy photosynthetic production to environmental factors,including light intensity,temperature,vapour pressure deficit(VPD),and soil water status,can be generalised and quantified using the light-use-efficiency(LUE)model PRELES.By partitioning the variability of canopy photosynthetic production,the effect of each environmental stress was respectively detected.We analysed the global variation andseasonal pattern of each environmental restriction,by applying PRELES to forests in tropical,subtropical,temperate,and boreal regions.Besides,Water limitations and drought events were assessed based on both PRELES and meteorological indices on daily,monthly and annual time scales.The results showed that the intensities of restrictions varied with the forest-climate types.Similar seasonal patterns were found for most sites in light saturation,temperature acclimation,and the VPD stress.Limitation from soil water occurred more irregularly.Annual meteorological drought indices strongly correlated with each other,and insufficiently described drought conditions across biomes.For the monthly indicators,in comparison to SPI(standardized precipitation Index),SPEI(standardized precipitation evapotranspiration index)showed a higher correlation with the water restriction modifiers in PRELES.The LUE-based model illustrated that those forests only reached 26%(SD±12%)of the potential productivity,while 56%(SD±17%)of the potential productivity was unachieved due to light saturation,21%(±13%)was temperature limitation,12%(SD ±10%)was soil water stress,and 9%(±9%)was VPD stress.(5)Adding nitrogen to boreal forest ecosystems causes clear increases in gross primary production(GPP).The effect of nitrogen addition on GPP is convoluted due to the impacts of and interactions among photosynthetic productivity,canopy structure,site fertility,and environmental constraints.We used a unique controlled nitrogen fertilisation experiment combined with eddy covariance measurements and the calibration of a LUE-based(light use efficiency)photosynthetic production model in order to reveal differences in photosynthetic capacity due to a nitrogen addition effect.The canopy photosynthetic light responses and environmental constraints were evaluated using an inverse modelling approach.Nitrogen fertilisation elevated ecosystem GPP by 24%.This was caused by elevation of ecosystem light interception(through an increase in leaf area index(LAI))by 7% and LUE by 17%.Nitrogen addition increased canopy LUE on both low and high photosynthetic photon flux density(PPFD)conditions.The calculation of light interception indicated that the understorey(shrubs)contributed 9.1% of ecosystem GPP in the fertilised site and 6.8% in the control site.The constraint arising from atmospheric water demand,instead of soil water stress,was dominating the intra-and inter-annual GPP variation,and even during drought events.The Bayesian framework has shown advantages in both empirical and mechanistic modelling.For the empirical modelling approach,it quantitatively described the parametric and predictive uncertainty,as well as the error distribution of each dataset.Models can be updated iteratively along with obtained new data.The missing information was gap-filled bylinking models of different resolutions.For the mechanistic models,this inverse modelling approach adjusted model parameters and processes according to their ability to reproduce stand-level field observations,which bridges the gap between complex models and various databases.