A Revisit to the Prototype Water System

Wood, E.F. (1974). A Revisit to the Prototype Water System. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-74-041

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Abstract

In M. Fiering's paper, "Mathematical Model of a Prototype Water System," he describes a system which has the following properties: (1) Upstream Reservoir with associated benefits (e.g. power). (2) Downstream Levees with benefits from flood damage reductions. (3) Independent inflows known on the first day of the season. (4) One-season model, i.e. yearly. (5) Technical functions between yearly inflow volume and the instantaneous flood peak downstream.

Fiering was aware that many of the assumptions do not hold in real cases. Furthermore, there are other extensions of the described prototype water system that would be useful to explore -- for example, downstream supply by either the upstream reservoir or by an alternate ground water source.

Another set of questions is centered around the upstream/downstream division of costs and benefits. The area of the division of costs and benefits falls under such headings as "game-theory", "conflict resolution", "bargaining", etc. and involves often side-payments from one user to another. In many cases, the role of the analyst is not to find an optimal solution to the bargaining procedure but to display various outcome sets to alternative actions.

In a framework similar to that used by Fiering, this working paper investigates the outcome sets (upstream and downstream benefit positions) in the following cases: (1) A one-season model for upstream water-supply and downstream supply, where the targets may be different; (2) A two-season model for upstream water supply and downstream supply, where the targets may be different; and (3) A two-season extension of upstream supply and flood control downstream.

From these results, further extensions to a real situation, like the Tisza, will be discussed in detail and will include a "where-do-we-go-with-this" section.

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