Bayesian networks (BNs), also known as Bayesian belief networks or Bayes nets, are a kind of probabilistic graphical model that has become very popular to practitioners mainly due to the powerful probability theory involved, which makes them able to deal with a wide range of problems. The goal of this review is to show how BNs are being used in environmental modelling. We are interested in the application of BNs, from January 1990 to December 2010, in the areas of the ISI Web of Knowledge related to Environmental Sciences. It is noted that only the 4.2% of the papers have been published under this item. The different steps that configure modelling via BNs have been revised: aim of the model, data pre-processing, model learning, validation and software. Our literature review indicates that BNs have barely been used for Environmental Science and their potential is, as yet, largely unexploited.

Review: Bayesian networks in environmental modelling

The inevitable though frequently informal use of expert opinion in modelling, the increasing number of models that incorporate formally expert opinion from a diverse range of experience and stakeholders, arguments for participatory modelling and analytic-deliberative-adaptive approaches to managing complex environmental problems, and an expanding but uneven literature prompt this critical review and analysis. Aims are to propose common definitions, identify and categorise existing concepts and practice, and provide a frame of reference and guidance for future environmental modelling. The extensive literature review and classification conducted demonstrate that a broad and inclusive definition of experts and expert opinion is both required and part of current practice. Thus an expert can be anyone with relevant and extensive or in-depth experience in relation to a topic of interest. The literature review also exposes informal model assumptions and modeller subjectivity, examines in detail the formal uses of expert opinion and expert systems, and critically analyses the main concepts of, and issues arising in, expert elicitation and the modelling of associated uncertainty. It is noted that model scrutiny and use of expert opinion in modelling will benefit from formal, systematic and transparent procedures that include as wide a range of stakeholders as possible. Enhanced awareness and utilisation of expert opinion is required for modelling that meets the informational needs of deliberative fora. These conclusions in no way diminish the importance of conventional science and scientific opinion but recognise the need for a paradigmatic shift from traditional ideals of unbiased and impartial experts towards unbiased processes of expert contestation and a plurality of expertise and eventually models. Priority must be given to the quality of the enquiry for those responsible for environmental management and policy formulation, and this review emphasises the role for science to maintain and enhance the rigour and formality of the information that informs decision making.

Position Paper: The role of expert opinion in environmental modelling

A wide range of quantitative and qualitative modelling research on ecosystem services (ESS) has recently been conducted. The available models range between elementary, indicator-based models and complex process-based systems. A semi-quantitative modelling approach that has recently gained importance in ecological modelling is Bayesian belief networks (BBNs). Due to their high transparency, the possibility to combine empirical data with expert knowledge and their explicit treatment of uncertainties, BBNs can make a considerable contribution to the ESS modelling research. However, the number of applications of BBNs in ESS modelling is still limited. This review discusses a number of BBN-based ESS models developed in the last decade. A SWOT analysis highlights the advantages and disadvantages of BBNs in ESS modelling and pinpoints remaining challenges for future research. The existing BBN models are suited to describe, analyse, predict and value ESS. Nevertheless, some weaknesses have to be considered, including poor flexibility of frequently applied software packages, difficulties in eliciting expert knowledge and the inability to model feedback loops. BBNs are increasingly used to analyse, predict and value ecosystem services (ESS).Most BBN applications in ESS modelling target only a single service.Numerous advantages of BBNs in ESS modelling are demonstrated in current applications.Model drawbacks are absence of feedback loops and obligatory variable discretization.Spatially explicit modelling and modelling of ESS bundles are future opportunities.

A review of Bayesian belief networks in ecosystem service modelling

A soil change-based methodology for the quantification and valuation of ecosystem services from agro-ecosystems: A case study of pastoral agriculture in New Zealand

Bayesian belief networks (BBNs) are probabilistic graphical models that can capture and integrate both quantitative and qualitative data, thus accommodating data-limited conditions. This paper systematically reviews applications of BBNs with respect to spatial factors, water domains, and the consideration of climate change impacts. The methods used for constructing and validating BBN models, and their applications in different forms of decision-making support are examined. Most reviewed publications originate from developed countries (70%), in temperate climate zones (42%), and focus mainly on water quality (42%). In 60% of the reviewed applications model validation was based on the expert or stakeholder evaluation and sensitivity analysis, and whilst in 27% model performance was not discussed. Most reviewed articles applied BBNs in strategic decision-making contexts (52%). Integrated modelling tools for addressing challenges of dynamically complex systems were also reviewed by analysing the strengths and weaknesses of BBNs, and integration of BBNs with other modelling tools. The application of BBNs to water resource management was rarely applied in developing countries and in tropical regions.Only 8% reviewed papers explored potential impacts of climate change on water resources.Only 11% and 6% of reviewed articles applied influence diagrams and Object-Oriented Bayesian Networks respectively.Most reviewed articles applied BBNs in strategic decision-making contexts (52%) for water resource management.Results from BBN models were rarely compared or tested against other modelling approaches to validate their performance.

Applications of Bayesian belief networks in water resource management

Quantifying and managing diffuse P losses from small catchments or at the farm scale requires detailed knowledge of farming practices and their interaction with catchment processes. However, detailed knowledge may not be available and hence modeling is required. This paper demonstrates two approaches to developing tools that assist P losses from New Zealand or Australian dairy farms. The first is largely empirical and separates sources of P within a paddock into soil, fertilizer, dung, and treading impacts (including damage to grazed pasture). This information is combined with expert knowledge of hydrological processes and potential point sources (e.g., stream crossings) to create a deterministic model that can be used to evaluate the most cost and labor efficient method of mitigating P losses. For instance, in one example, 45% of annual P lost was attributed to the application of superphosphate just before a runoff event for which a mitigation strategy could be to use a less water soluble P fertilizer. The second approach uses a combination of interviews, expert knowledge and relationships to develop a Bayesian Network that describes P exports. The knowledge integration process helped stakeholders develop a comprehensive understanding of the problem. The Network, presented in the form of a "cause and effect", diagram provided a simple, visual representation of current knowledge that could be easily applied to individual circumstances and isolate factors having the greatest influence on P loss. Both approaches demonstrate that modeling P losses and mitigation strategies does not have to cover every process or permutation and that a degree of uncertainty can be handled to create a working model of P losses at a farm or small catchment scale.

Approaches for quantifying and managing diffuse phosphorus exports at the farm/small catchment scale.

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Approaches for quantifying and managing diffuse phosphorus exports at the farm/small catchment scale.