Reply — The prediction of hypolimnetic oxygen profiles: a plea for a deductive approach

Abstract

While not agreeing completely with Molotis (1997) comments on our oxygen depletion paper (Livingstone and Imboden 1996), we appreciate having the opportunity to respond to lucid and practical criticism of our plea for a deductive, processbased approach to the prediction of hypolimnetic oxygen profiles. We note with pleasure that an airing of the tacit assumptions and preconceptions underlying various attitudes towards tackling environmental problems is still able to stimulate fruitful and constructive debate. There are many points of convergence between Molotis opinions and our own, especially our common belief that both inductive and deductive approaches are indispensable to the environmental sciences. Where we differ is principally in the way we believe these approaches and their associated models can be best made use of. In our opinion, the decision on which approach to use should not be based merely on personal preference. Inductive and deductive approaches are qualitatively different (although deductive models can and do incorporate inductive elements and vice versa; see below) and have different aims. Our concern is not that a deductive approach be adopted under all circumstances but rather that the approach chosen be appropriate to the problem tackled. We have no objection to an inductive approach with purely empirical curve fitting when this is justified (see Livingstone and Imboden 1993, for instance), and we would, of course, be just as ready to argue against the employment of deductive models in specific cases. Molot interprets our opinion as being that ideductive models should always be the approach of choice when there is sufficient understanding of underlying processes,i and then criticizes this opinion on the grounds that environmental managers need accurate predictive tools with an external independent or driving variable. We believe that neither deductive nor inductive models designed to deal with environmental problems can afford to sacrifice predictive accuracy by ignoring already available knowledge, either of data or of processes. In deductive models, relevant processes that are badly or incompletely understood are not omitted but parameterized empirically (see the comprehensive oxygen model of Stefan and Fang (1994) for a good example of this). In contrast, although inductive models often include some qualitative knowledge of the variables involved in relevant processes, they very rarely include any quantitative knowledge of the processes themselves, the functional forms of the model relationships being more usually constrained by the imagination of the modeller than by any of the preconceptions inherent in established scientific theories or laws. The initial investigation of any natural phenomenon involves the employment of inductive reasoning. Without Kepleris painstaking inductive work in setting down his descriptive, empirical laws of planetary motion, for instance, it is unlikely