This paper reformulates the two-phase solidification problem (i.e., the Stefan problem) as an inverse problem in which a cost functional is minimized with respect to the position of the interface and subject to PDE constraints. An advantage of this formulation is that it allows for a thermodynamical
What makes a fish (hydrologically) happy? A case for inverse modelling
โ Scribed by Stuart N. Lane
- Publisher
- John Wiley and Sons
- Year
- 2008
- Tongue
- English
- Weight
- 78 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0885-6087
- DOI
- 10.1002/hyp.7145
No coin nor oath required. For personal study only.
โฆ Synopsis
Prediction in hydrology is replete with the concept of a process cascade. Such cascades are encoded in conceptual analyses such as the driver, pressure state, impact and response framework recommended by the OECD (1993), now being modified to explore issues such as flood risk (e.g. Evans et al., 2004) and soil erosion (e.g. Gobin et al., 2004). Informed by an army of laboratory-and field-based studies, the process cascade sits with our basic assumption that any system can be broken down into its constituent parts and then rebuilt, using process relationships, to create a mathematical model. It has an implicit reductionism that is self-sustaining; the exposure of models to scrutiny by field data encourages us to look for more complex model formulations; these more complex formulations require new forms of field data and their assimilation into models.
As a community, we periodically expose this way of working to scrutiny. This has included concerns that we are not paying enough attention to data collection (e.g. Harris and Heathwaite, 2005), and the observation that as the complexity and scale of the process cascade grow, components of the cascade (e.g. model processes, model parameters) become less resolvable by available data whether because there are no data, not enough data or the data are simply wrong (e.g. Beven, 2006). Herein, I want to raise a new sort of discomfort for the hydrological modellers, myself included, one that derives from a growing interest in the linkages between hydrology and instream ecology.
Research has demonstrated that landscape or watershed scale processes can influence instream aquatic ecosystems, associated with the delivery of fine sediment, solutes and organic matter (e.g.
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