Causal modelling applied to the risk assessment of a wastewater discharge

  • Warren L. PaulEmail author
  • Pat A. Rokahr
  • Jeff M. Webb
  • Gavin N. Rees
  • Tim S. Clune


Bayesian networks (BNs), or causal Bayesian networks, have become quite popular in ecological risk assessment and natural resource management because of their utility as a communication and decision-support tool. Since their development in the field of artificial intelligence in the 1980s, however, Bayesian networks have evolved and merged with structural equation modelling (SEM). Unlike BNs, which are constrained to encode causal knowledge in conditional probability tables, SEMs encode this knowledge in structural equations, which is thought to be a more natural language for expressing causal information. This merger has clarified the causal content of SEMs and generalised the method such that it can now be performed using standard statistical techniques. As it was with BNs, the utility of this new generation of SEM in ecological risk assessment will need to be demonstrated with examples to foster an understanding and acceptance of the method. Here, we applied SEM to the risk assessment of a wastewater discharge to a stream, with a particular focus on the process of translating a causal diagram (conceptual model) into a statistical model which might then be used in the decision-making and evaluation stages of the risk assessment. The process of building and testing a spatial causal model is demonstrated using data from a spatial sampling design, and the implications of the resulting model are discussed in terms of the risk assessment. It is argued that a spatiotemporal causal model would have greater external validity than the spatial model, enabling broader generalisations to be made regarding the impact of a discharge, and greater value as a tool for evaluating the effects of potential treatment plant upgrades. Suggestions are made on how the causal model could be augmented to include temporal as well as spatial information, including suggestions for appropriate statistical models and analyses.


Causal modelling Graph theoretical structural equation modelling Ecological risk assessment Wastewater Environmental impact study Spatiotemporal causal model 



The authors would like to express their thanks to Bill Shipley for his helpful discussions on the subject of testable conditional independencies in the presence of deterministic variables. Any flaws in the ideas that were stimulated by these discussions are, however, the responsibility of the authors.

Compliance with ethical standards

Conflict of interest

TS Clune is affiliated with North East Water, as the Manager of Risk and Business Sustainability, and La Trobe University, as the Adjunct Professor in the Centre for Water Policy and Management. All other authors declare that they have no conflict of interest.

Supplementary material

10661_2015_5074_MOESM1_ESM.docx (39 kb)
Online Resource 1 R code for the Wangaratta analyses (DOCX 39 kb)
10661_2015_5074_MOESM2_ESM.xlsx (15 kb)
Online Resource 2 Wangaratta macroinvertebrate data (XLSX 15 kb)
10661_2015_5074_MOESM3_ESM.xlsx (12 kb)
Online Resource 3 Wangaratta environmental data (XLSX 12 kb)


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Warren L. Paul
    • 1
    Email author
  • Pat A. Rokahr
    • 1
  • Jeff M. Webb
    • 2
  • Gavin N. Rees
    • 3
  • Tim S. Clune
    • 4
  1. 1.Department of Ecology, Environment and EvolutionLa Trobe University (Albury-Wodonga campus)WodongaAustralia
  2. 2.Rhithron Associates, Inc.MissoulaUSA
  3. 3.Murray-Darling Freshwater Research Centre and CSIRO Land and Water FlagshipWodongaAustralia
  4. 4.North East WaterWodongaAustralia

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