Bayesian Methods for Quantifying and Reducing Uncertainty and Error in Forest Models
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Purpose of review
Forest models are tools for analysis and prediction of productivity and other services. Model outputs can only be useful if possible errors in inputs and model structure are recognized. However, errors cannot be quantified directly, making uncertainty inevitable. In this paper, we aim to clarify terminological confusion around the concepts of error and uncertainty and review current methods for addressing uncertainty in forest modelling.
Modellers increasingly recognize that all uncertainties—in data, model inputs and model structure—can be represented using probability distributions. This has stimulated the use of Bayesian methods for quantifying and reducing uncertainty and error in models of forests and other vegetation. The Achilles’ heel of Bayesian methods has always been their computational demand, but solutions are being found.
We conclude that future work will likely include (1) more use of Bayesian methods, (2) more use of hierarchical modelling, (3) replacement of model spin-up by Bayesian calibration, (4) more use of ensemble modelling and Bayesian model averaging, (5) new ways to account for model structural error in calibration, (6) better software for Bayesian calibration of complex models, (7) faster Markov chain Monte Carlo algorithms, (8) more use of model emulators, (9) novel uncertainty visualization techniques, (10) more use of graphical modelling and (11) more use of risk analysis.
KeywordsCalibration Discrepancy Ensemble modelling Hierarchical modelling Risk analysis Visualization
I thank Peter Levy (CEH-Edinburgh) for his comments on this paper.
Compliance with Ethical Standards
Conflict of Interest
Dr. Van Oijen states that there are no conflicts of interests to declare.
Human and Animal Rights
This article does not contain any studies with human or animal subjects performed by any of the authors.
Papers of particular interest, published recently, have been highlighted as: • Of importance •• Of major importance
- 3.• Reyer C. Forest productivity under environmental change—a review of stand-scale modeling studies. Current Forestry Reports. 2015;1:53–68. This paper is useful for forest modellers aiming to provide global assessments of the impacts of environmental change: it identifies those forest types and parts of the globe for which data are at present lacking. CrossRefGoogle Scholar
- 6.Jaynes ET. Probability theory: The logic of science. Cambridge: Cambridge University Press; 2003.Google Scholar
- 7.Sivia D, Skilling J. Data analysis: a Bayesian tutorial. 2nd ed. Oxford: Oxford University Press, U.S.A; 2006.Google Scholar
- 10.• Van Oijen M, Cameron D, Levy PE, Preston R. Correcting errors from spatial upscaling of nonlinear greenhouse gas flux models. Environ Model Softw. 2017;94:157–65. This paper reviews and revives the powerful yet neglected idea that errors caused by spatial aggregation of the inputs of nonlinear models can be estimated well using a Taylor-expansion of the model, together with information on spatial variability of the inputs. CrossRefGoogle Scholar
- 12.Van Oijen M, Ågren GI, Chertov O, Kellomäki S, Komarov A, Mobbs D, et al. Evaluation of past and future changes in European forest growth by means of four process-based models. In: Kahle H-P, Karjalainen T, Schuck A, Ågren GI, Kellomäki S, Mellert K, Prietzel J, Rehfuess K-E, Spiecker H, editors. Causes and consequences of forest growth trends in Europe: results of the recognition project. Leiden: Brill; 2008. p. 183–99.Google Scholar
- 16.Hyvönen R, Ågren GI, Linder S, Persson T, Cotrufo MF, Ekblad A, et al. The likely impact of elevated [CO2], nitrogen deposition, increased temperature and management on carbon sequestration in temperate and boreal forest ecosystems: a literature review. New Phytol. 2007;173:463–80.CrossRefGoogle Scholar
- 18.Van Oijen M, Cannell MGR, Levy PE. Modelling biogeochemical cycles in forests: state of the art and perspectives. In: Andersson F, Birot Y, Päivinen R, editors. Towards the sustainable use of European forests-Forest ecosystem and landscape research: scientific challenges and opportunities. Joensuu: European Forest Institute; 2004. p. 157–69.Google Scholar
- 22.•• Medlyn BE, Zaehle S, De Kauwe MG, Walker AP, Dietze MC, Hanson PJ, et al. Using ecosystem experiments to improve vegetation models. Nat Clim Chang. 2015;5:528–34. This very clear paper can be seen as a counterpoint to the present one in that it does not mention probability theory as a tool to reduce uncertainty, but instead focuses on consistency with mechanistic understanding. CrossRefGoogle Scholar
- 27.Minunno F, van Oijen M, Cameron D, Cerasoli S, Pereira J, Tomé M. Using a Bayesian framework and global sensitivity analysis to identify strengths and weaknesses of two process-based models differing in representation of autotrophic respiration. Environ Model Softw. 2013;42:99–115.CrossRefGoogle Scholar
- 29.Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB. Bayesian data analysis, third edition. 3rd ed. Boca Raton: Chapman and Hall/CRC; 2013.Google Scholar
- 30.• McElreath R. Statistical rethinking: A Bayesian course with examples in R and Stan. Boca Raton: CRC Press; 2016. Perhaps the best introduction to Bayesian methods for absolute beginners, explaining both concepts and methods with impressive clarity. Google Scholar
- 32.Levy PE, Cowan N, Van Oijen M, Famulari D, Drewer J, Skiba U. Estimation of cumulative fluxes of nitrous oxide: Uncertainty in temporal upscaling and emission factors. Eur J Soil Sci. 2017;68:400–11.Google Scholar
- 36.Van Oijen M. Bayesian Calibration (BC) and Bayesian Model Comparison (BMC) of process-based models: Theory, implementation and guidelines. Edinburgh: Centre for Ecology and Hydrology; 2008. http://nora.nerc.ac.uk/6087/. Accessed 4 Sept 2017.
- 37.•• Hartig F, Minunno F, Paul S, Cameron D, Ott T. Package ‘BayesianTools’. The Comprehensive R Archive Network; 2017. https://cran.r-project.org/web/packages/BayesianTools/BayesianTools.pdf. Accessed 4 Sept 2017. This document introduces a major software development: an R-package that facilitates the use of Bayesian calibration by means of MCMC for complex process-based models of forests and other vegetation.
- 44.Cressie N, Wikle CK. Statistics for spatio-temporal data. Hoboken: Wiley; 2011.Google Scholar
- 47.Chandler RE. Exploiting strength, discounting weakness: Combining information from multiple climate simulators. Phil Trans R Soc A 2013;371:20120388. https://doi.org/10.1098/rsta.2012.0388.
- 48.Kavetski D, Kuczera G, Franks SW. Bayesian analysis of input uncertainty in hydrological modeling: 1. Theory. Water Resour Res 2006;42:W03407. https://doi.org/10.1029/2005WR004368.
- 51.• Milne AE, Glendining MJ, Lark RM, Perryman SAM, Gordon T, Whitmore AP. Communicating the uncertainty in estimated greenhouse gas emissions from agriculture. J Environ Manag. 2015;160:139–53. A thorough assessment of six different ways of communicating uncertainty, both verbal and visual. CrossRefGoogle Scholar
- 52.•• Van Oijen M, Balkovič J, Beer C, Cameron DR, Ciais P, Cramer W, et al. Impact of droughts on the carbon cycle in European vegetation: a probabilistic risk analysis using six vegetation models. Biogeosciences. 2014;11:6357–75. This paper shows how risk can be formally decomposed as the product of two terms: hazard probability and ecosystem vulnerability. The method is applied to the results of six vegetation models, and predicts future drought risk to increase mainly in Mediterranean vegetation because of changes in hazard probability. CrossRefGoogle Scholar
- 53.Smith R, Dick J, Trench H, Van Oijen M. Extending a Bayesian belief network for ecosystem evaluation. In: Proceedings of the 2012 Berlin Conference on the Human Dimensions of Global Environmental Change, 5-6 October 2012, Berlin, Germany. 2012. http://www.berlinconference.org/2012/wpcontent/uploads/2013/01/Smith-Extending_a_Bayesian_Belief_Network_for_ecosystem_evaluation-266.pdf. Accessed 4 Sept 2017.