cal problems to be developed virtually than direct experimentation allows with the real system, especially for the systems discussed below.

Models have become indispensable for managing complex systems ranging from transportation systems (including most airline scheduling) to large building structures, as well as routine wholesaling, retailing, and commercial systems by engineers, business managers, and economists. In the physical and environmental sciences, conceptual and quantitative models have been central to the development of new theories and practices, especially in attempts to understand cause-and-effect relations in managed river systems, as well as in predictions of how natural systems will behave.

Historically, the scientific use of quantitative models began as early as the 1600s in Galileo’s time, and engineering applications became established in France before the the beginning of the French Revolution in 1789. Modeling now is the accepted approach for improving the efficiency and effectiveness of efforts to understand and manage complex problems. To improve the likelihood that modeling will deliver on such promises, model development and use commonly follows a fairly standardized process, described in this chapter. Scientific progress results when the hypothetical understanding of the system represented by the model diverges from field observations, leading to improvements in the model, field data, understanding of the modeled system, and the model’s predictive powers.

Conceptual Versus Simulation Models

The science of river restoration is still in its infancy. In most river or wetland systems, there is only a partial understanding of the relation between flows, people, and ecosystems (Castleberry et al. 1996), and therefore science cannot yet provide certain predictions about the consequences of policy and management decisions. For this reason, the concept of “learning by doing” has become an accepted part of management activities in many river basins. A key part of the learning-by-doing process is the development of models that can be tested and refined through monitoring and research programs. Examples where modeling plays a prominent role in ecosystem restoration include the CALFED Bay-Delta Ecological Restoration Program (Healey et al. 2007), the Glen Canyon Adaptive Management Program (Walters et al. 2000), the Comprehensive Everglades Restoration Plan (Ogden et al. 2005), and the Trinity River Restoration Program (USFWS/HVT 1999, Schleusner 2006).

For the purposes of this discussion, the committee distinguishes between conceptual models and simulation models. Conceptual models serve to organize knowledge and information in the most general way, whereas simulation models attempt to describe system behavior quantitatively, using a series of deterministic or stochastic relations that link processes together

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