Bayesian methods for quantifying and reducing uncertainty and error in forest models

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. Recent findings: 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. Summary: 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

Effects of climate change on grassland biodiversity and productivity: the need for a diversity of models

There is increasing evidence that the impact of climate change on the productivity of grasslands will at least partly depend on their biodiversity. A high level of biodiversity may confer stability to grassland ecosystems against environmental change, but there are also direct effects of biodiversity on the quantity and quality of grassland productivity. To explain the manifold interactions, and to predict future climatic responses, models may be used. However, models designed for studying the interaction between biodiversity and productivity tend to be structurally different from models for studying the effects of climatic impacts. Here we review the literature on the impacts of climate change on biodiversity and productivity of grasslands. We first discuss the availability of data for model development. Then we analyse strengths and weaknesses of three types of model: ecological, process-based and integrated. We discuss the merits of this model diversity and the scope for merging different model types

Identifying Target Traits for Forage Grass Breeding under a Changing Climate in Norway Using the BASGRA Model

Grass-based dairy and livestock production constitutes the most important agricultural sector in Norway in economic terms, and 60% of the agricultural land in Norway is used for grass production. Climate change may have consider-able impact on the survival and productivity of grasslands, with consequences for the local supply of forage to live-stock, farmers’ income and the supply of dairy- and livestock-based food products to the global market. Farmers can adapt to climate change by choosing different grass species or cultivars or by changing management practices such as the timing and frequency of harvests. Plant breeders select new cultivars of grasses that are better suited to a specific environment and management practices by utilizing available resources in the most optimal way. A key characteristic for grass cultivars grown in Norway is their ability to survive the winter, a characteristic that will re-main important also in the future (Thorsen and Höglind 2010). Winter hardy cultivars contribute to high and stable yields, and minimize the need for costly reseeding. Other desired traits for grass cultivars in Norway are high nutritive value of the herbage, high tolerance of the plants to frequent cutting and grazing, and good suitability for conservation through ensiling. Breeding for a new grass cultivar usually takes 15-20 years. It is difficult to predict which trait combinations will be important in the future, especially under climate change conditions. However, it is important to define breeding targets and investigate the underlying genetic and physiological mechanisms of important traits. Process-based simulation models for grass can be used to evaluate the effects of altered plant traits under projected climate change conditions. Here we show an example with preliminary results from a study where the BASGRA model was used to evaluate the effect of modified plant characteristics on grass winter survival and yield under projected climate change conditions for Norway

Estimation of gross land-use change and its uncertainty using a Bayesian data assimilation approach

We present a method for estimating land-use change using a Bayesian data assimilation approach. The approach provides a general framework for combining multiple disparate data sources with a simple model. This allows us to constrain estimates of gross land-use change with reliable national-scale census data, whilst retaining the detailed information available from several other sources. Eight different data sources, with three different data structures, were combined in our posterior estimate of land use and land-use change, and other data sources could easily be added in future. The tendency for observations to underestimate gross land-use change is accounted for by allowing for a skewed distribution in the likelihood function. The data structure produced has high temporal and spatial resolution, and is appropriate for dynamic process-based modelling. Uncertainty is propagated appropriately into the output, so we have a full posterior distribution of output and parameters. The data are available in the widely used netCDF file format from http://eidc.ceh.ac.uk/

Process-based simulation of growth and overwintering of grassland using the BASGRA model

Process-based models (PBM) for simulation of weather dependent grass growth can assist farmers and plant breeders in addressing the challenges of climate change by simulating alternative roads of adaptation. They can also provide management decision support under current conditions. A drawback of existing grass models is that they do not take into account the effect of winter stresses, limiting their use for full-year simulations in areas where winter survival is a key factor for yield security. Here, we present a novel full-year PBM for grassland named BASGRA. It was developed by combining the LINGRA grassland model (Van Oijen et al., 2005a) with models for cold hardening and soil physical winter processes. We present the model and show how it was parameterized for timothy (Phleum pratense L.), the most important forage grass in Scandinavia and parts of North America and Asia. Uniquely, BASGRA simulates the processes taking place in the sward during the transition from summer to winter, including growth cessation and gradual cold hardening, and functions for simulating plant injury due to low temperatures, snow and ice affecting regrowth in spring. For the calibration, we used detailed data from five different locations in Norway, covering a wide range of agroclimatic regions, day lengths (latitudes from 59◦ to 70◦ N) and soil conditions. The total dataset included 11 variables, notably above-ground dry matter, leaf area index, tiller density, content of C reserves, and frost tolerance. All data were used in the calibration. When BASGRA was run with the maximum a-posteriori (MAP) parameter vector from the single, Bayesian calibration, nearly all measured variables were simulated to an overall normalized root mean squared error (NRMSE) < 0.5. For many site × experiment combinations, NRMSE was <0.3. The temporal dynamics were captured well for most variables, as evaluated by comparing simulated time courses versus data for the individual sites. The results may suggest that BASGRA is a reasonably robust model, allowing for simulation of growth and several important underlying processes with acceptable accuracy for a range of agroclimatic conditions. However, the robustness of the model needs to be tested further using independent data from a wide range of growing conditions. Finally we show an example of application of the model, comparing overwintering risks in two climatically different sites, and discuss future model applications. Further development work should include improved simulation of the dynamics of C reserves, and validation of winter tiller dynamics against independent data

Integrating parameter uncertainty of a process-based model in assessments of climate change effects on forest productivity

The parameter uncertainty of process-based models has received little attention in climate change impact studies. This paper aims to integrate parameter uncertainty into simulations of climate change impacts on forest net primary productivity (NPP). We used either prior (uncalibrated) or posterior (calibrated using Bayesian calibration) parameter variations to express parameter uncertainty, and we assessed the effect of parameter uncertainty on projections of the process-based model 4C in Scots pine (Pinus sylvestris) stands under climate change. We compared the uncertainty induced by differences between climate models with the uncertainty induced by parameter variability and climate models together. The results show that the uncertainty of simulated changes in NPP induced by climate model and parameter uncertainty is substantially higher than the uncertainty of NPP changes induced by climate model uncertainty alone. That said, the direction of NPP change is mostly consistent between the simulations using the standard parameter setting of 4C and the majority of the simulations including parameter uncertainty. Climate change impact studies that do not consider parameter uncertainty may therefore be appropriate for projecting the direction of change, but not for quantifying the exact degree of change, especially if parameter combinations are selected that are particularly climate sensitive. We conclude that if a key objective in climate change impact research is to quantify uncertainty, parameter uncertainty as a major factor driving the degree of uncertainty of projections should be included

Inference of spatial heterogeneity in surface fluxes from eddy covariance data: a case study from a subarctic mire ecosystem

Horizontal heterogeneity causes difficulties in the eddy covariance technique for measuring surface fluxes, related to both advection and the confounding of temporal and spatial variability. Our aim here was to address this problem, using statistical modelling and footprint analysis, applied to a case study of fluxes of sensible heat and methane in a subarctic mire. We applied a new method to infer the spatial heterogeneity in fluxes of sensible heat and methane from a subarctic ecosystem in northern Sweden, where there were clear differences in surface types within the landscape. We inferred the flux from each of these surface types, using a Bayesian approach to estimate the parameters of a hierarchical model which includes coefficients for the different surface types. The approach is based on the variation in the flux observed at a single eddy covariance tower as the footprint changes over time. The method has applications wherever spatial heterogeneity is a concern in the interpretation of eddy covariance fluxes

A novel probabilistic risk analysis to determine the vulnerability of ecosystems to extreme climatic events

We present a simple method of probabilistic risk analysis for ecosystems. The only requirements are time series—modelled or measured—of environment and ecosystem variables. Risk is defined as the product of hazard probability and ecosystem vulnerability. Vulnerability is the expected difference in ecosystem performance between years with and without hazardous conditions. We show an application to drought risk for net primary productivity of coniferous forests across Europe, for both recent and future climatic conditions