Abstract There are increasing demands in assessing the impacts of change on environmental systems to couple different model components together in a cascade, the outputs from one component providing the inputs to another with or without feedbacks in the coupling. Each model component will necessarily involve some uncertainty in its specification and simulations that can be conditioned using some observational data. Taking account of this uncertainty should result in more robust decision making and may change the nature of the decision made. The difficulty in environmental decision making is in making proper estimates of uncertainties when so many of the sources of uncertainty result from lack of knowledge (epistemic uncertainties) rather than uncertainty that can be treated as random variability (aleatory uncertainty). This is particularly the case for problems that involve cascades of model components. Examples are the use of UKCP09 climate scenarios in impact studies, flood risk assessment involving models of runoff generation and their impact on hydraulic models of flood plains, and integrated catchment management involving upstream to downstream surface and subsurface routing of water quality variables. The uncertainties are such that, even for relatively simple problems, they can result in wide ranges of potential outputs. This poses the questions that will be considered in this paper: how to take account of knowledge uncertainties in cascades of model components; and how to constrain the potential uncertainties for use in making decisions. In particular we highlight the difficulties of defining statistical likelihood functions that properly reflect the non-stationary uncertainty characteristics expected of epistemic sources of uncertainty.