This paper reviews the role of uncertainty in the identification of mathematical models of water quality and in the application of these models to problems of prediction. More specifically, four problem areas are examined in detail: uncertainty about model structure, uncertainty in the estimated model parameter values, the propagation of prediction errors, and the design of experiments in order to reduce the critical uncertainties associated with a model. The review is rather lengthy, and it has therefore been prepared in effect as two papers. There is a shorter, largely nontechnical version, which gives a quick impression of the current and future issues in the analysis of uncertainty in water quality modeling. Enclosed by this shorter discussion is the main body of the review dealing in turn with (1) identifiability and experimental design, (2) the generation of preliminary model hypotheses under conditions of sparse, grossly uncertain field data, (3) the selection and evaluation of model structure, (4) parameter estimation (model calibration), (5) checks and balances on the identified model, i.e., model “verification” and model discrimination, and (6) prediction error propagation. Much time is spent in discussing the algorithms of system identification, in particular, the methods of recursive estimation, and in relating these algorithms and the subject of identification to the problems of prediction uncertainty and first‐order error analysis. There are two obvious omissions from the review. It is not concerned primarily with either the development and solution of stochastic differential equations or the issue of decision making under uncertainty, although clearly some reference must be made to these topics. In brief, the review concludes (not surprisingly) that much work has been done on the analysis of uncertainty in the development of mathematical models of water quality, and much remains to be done. A lack of model identifiability has been an outstanding difficulty in the interpretation and explanation of past observed system behavior, and there is ample evidence to show that the “larger,” more “comprehensive” models are easily capable of generating highly uncertain predictions of future behavior. For the future of the subject, it is speculated that there is the possibility of progress in the development of novel algorithms for model structure identification, a need for new questions to be posed in the problem of prediction, and a distinct challenge to the conventional views of this review in the new forms of knowledge representation and manipulation now emerging from the field of artificial intelligence.

To employ technologies that sustainably harvest resources from wastewater (for example struvite granules shown here), new perceptions and infrastructure planning and design processes are required.Water and wastewater system decisions have been traditionally driven by considerations of function, safety, and cost-benefit analysis. The emphasis on costs and benefits would be acceptable if all relevant factors could be included in the analysis, but unfortunately many relevant factors are routinely excluded. Coupled with failures to fully engage the public in decision-making processes, this can impede progress toward achieving sustainable solutions. Ignoring broader social issues that impact the adoption of sustainable solutions prolongs not only global environmental and ecological problems, but also unjust public health and social conditions in the developing world.Within the water and wastewater management industry, discussions of sustainable development have often focused on water stress (1, 2): a hazard that is exacerbated by other global stressors such as climate change, demographic and land use changes, increasing population, and urbanization (2). In addition to water stress, water and wastewater management practices contribute to nutrient imbalances and a host of environmental detriments such as eutrophication (3), discharge of pharmaceuticals and other emerging contaminants (4), and a loss of biodiversity in receiving streams (5). Efforts to address these issues across regional and global scales are hindered by the historical disconnect between the water quality and water quantity factions of the water profession. Although our understanding of sustainability is constantly evolving, the water and wastewater design process retains its foundation in engineering traditions established in the early 20th century (6). As we chart a path in the 21st century, we contend that wastewater contains resources worthy of recovering and that the development of

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The development and use of models for predicting exposures are increasingly common and are essential for many risk assessments of the United States Environmental Protection Agency (EPA). Exposure assessments conducted by the EPA to assist regulatory or policy decisions are often challenged to demonstrate their "scientific validity". Model validation has thus inevitably become a major concern of both EPA officiMs and the regulated community, sufficiently so that the EPA's Risk Assessment Forum is considering guidance for model validation. The present paper seeks to codify the issues and extensive foregoing discussion of validation with special reference to the development and use of models for predicting the impact of novel chemicals on the environment. Its preparation has been part of the process in formulating a White Paper for the EPA's Risk Assessment Forum. Its subject matter has been drawn from a variety of fields, including ecosystem analysis, surface water quality management, the contamination of groundwaters from high-level nuclear waste, and the control of air quality. The philosophical and conceptual bases of model validation are reviewed, from which it is apparent that validation should be understood as a task of product (or tool) design, for which some form of protocol for quality assurance will ultimately be needed. The commonly used procedures and methods of model validation are also reviewed, including the analysis of uncertainty. Following a survey of pe~st attempts at resolving the issue of modeI validation, we close by introducing the notion of a model having maximum relevance to the performance of a specific task, such as, for example, a predictive exposure assessment.Key words. Model validation; analysis of uncertainty; model verification; quality assurance; system identification; model calibration. I n t r o d u c t i o nThe construction and use of m a t h e m a t i c a l models are essential in predicting the possible consequences of releasing chemicals, some of which m a y be quite novel, into new environments. Substantial costs, and substantial damages to the environment, m a y attach to the regulatory decisions that are informed and thus guided by the predictions derived from a model. T h e risk of making a wrong decision will be strongly dependent on the reliability of these predictions, in just the same way as it

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