Bayesian approaches have become increasingly popular in water quality modelling, thanks to their ability to handle uncertainty comprehensively (data, model structure and parameter uncertainty) and as flexible statistical and data mining tools. Furthermore, graphical Bayesian belief networks can be powerful decision support tools that make it relatively easy for stakeholders to engage in the model building process, thus building trust in the modelled outcomes. The aim of this special issue is to review the state-of-the-art in this field in order to consolidate and set new directions for the emerging community of Bayesian water quality modellers.

This special issue invites high-quality contributions from participants in the EGU 2019–2020 special sessions on this topic, as well as the wider scientific community. Relevant contributions may be related to the use of Bayesian approaches to, for example but not exclusively,

• quantify the uncertainty of model predictions;
• quantify especially model structural error through, for example, Bayesian model averaging or structural error terms;
• address the problem of scaling (e.g. disparity of scales between processes, observations, model resolution and predictions) through hierarchical models;
• model water quality in data-sparse environments;
• compare models with different levels of complexity and process representation;
• use statistical emulators to allow probabilistic predictions of complex modelled systems;
• integrate prior knowledge, especially problematizing the choice of Bayesian priors;
• produce user-friendly decision support tools using graphical Bayesian belief networks;
• involve stakeholders in model development and maximize the use of expert knowledge; and
• use machine-learning and data-mining approaches to learn from large, possibly high-resolution data sets.