The role of Bayesian decision theory in hydrologic design problems is presented both in theory and by example. The theory is applied to an actual flood levee design problem on the Rillito Creek floodplain in Tucson, Arizona. Computer solutions provide a basis for judging the costs of overdesign in the face of uncertainty in the parameters of the flood frequency model (log normal) and for determining the worth of hydrologic data. One conclusion is that decision theoretic analysis looks at the decision situation from the standpoint of the engineer: how can one best decide in the face of limited data and the present knowledge about system behavior?

Multiple-objective problems are ubiquitous in human affairs and are commonly attacked in a subjective way. Semops, a sequential multiobjective problem solving technique, allows the decision maker to trade off one objective versus another in an interactive manner. Semops cyclically uses a surrogate objective function based on goals and the decision maker's aspirations about achieving these goals. The algorithm, applied to a synthetic case study of regional water quality management, demonstrates that (1) a complex situation can be handled, (2) the individuality of the deckion maker's preference structure is preserved, (3) the feasible alternatives do not need to be specified a priori, (4) the concept of a satisfactory solution rather than an optimum solution is more realistic in situations involving conflicting goals. SEMOPS: AN OVERVIEWSemops is an interactive programing technique that dynamically involves the decision maker (DM) in a search process that attempts to locate a satisfactory course of action, that is, a 'satisfacturn.' The concept of a satisfactum expresses the idea that we cannot define precisely a multi-objective optimum because we may not know how to trade off one objective versus another except in a subjective way.Our research is predicated on a series of assumptions concerning the decision-making process. Specifically, we assume the following. 1. Perception is influenced by the total set of elements in a situation and the environment in which the situation is imbedded. This assumption is basically the Gestalt philosophy [KOhler, 1947]. 2. Individual preference functions or value structures cannot be expressed analytically, although it is assumed that the DM does subscribe to a set of beliefs. 3. Value structures change over time, and different 'parts' (i.e., religious convictions versus automobile preferences) may change at different rates. 4. Aspirations or desires change as a result of learning and experience. 5. The number of goals in a decision situation is usually < 7 [Johnsen, 1968]. 6. The DM normally satisfices rather than optimizes [Doffman, 1960, p. 608]. 7. A solution to a decision problem is any acceptable course of action. 837 d= A2 A1/z + z/•A: Except for the first transformation these transformations are all nonlinear functions of a criterion function that may itself be nonlinear. The critical fact in this construction is that the direction of any change in d has a consistent interpretation for all T goals. Goals and Criterion Functions Goal 1: DO level at Bowville (z• •_ A• --6 mg•l) z• = 6.5 •-(5.0.3)] r(z) = Goal 3: DO level at Plympton (zs •_ As = 6 mg/1) za = 5.2 •-[(4.42.10 -6) -(4.0.104) ß (xx --0.3) -{-(7.71.10 -•) ß (2.s. •o •).(w• -o.a)] -{-[(7.64.10 -•) .(1.28-105) ß (x2 --0.a) -{-(1.60.10 -5) ß (4.8.104 ).(w2 -0.3)] = (0-s.5) i•ONARCHI ET AL.: I•ULTIOBJECTIYE PROGRAI•IING Goal 4: percent return on equity at Pierce-Hall Cannery (z, •_ •i, = 6.5%) 102 z, -5:•-06 [(3.75.105 ) --0.6 ß 1.09-x• •'--59 Goal 5: addition to the tax rate at Bowville (z5 _• A•-1.5) r(z) = 532 ) (2...

A linear model that permits calculation of recharge to the water table from a source of finite width and infinite length uses water level measurements made in an observation well near the source and independently estimated aquifer constants. The method requires determination of the input given the output (water level measurements) and the impulse response as a function of space and time. The latter is derived from the linear equations of groundwater motion for the particular geometry of this study. The input is obtained from the discrete form of the convolution integral by using the synthetic division method and is then summed over the appropriate time period to obtain total recharge. For the particular recharge event studies, results agree satisfactorily with an independent estimate of recharge and demonstrate that the convolution relation has practical application to groundwater flow problems.

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Modification of watersheds occurs either through natural processes, such as erosion, or human influences, such as urbanization. In either case the rainfall input must be properly modeled before the runoff output can be predicted as the modifications take place. The paper considers runoff‐producing summer precipitation of short duration and high spatial variability as an intermittent stochastic phenomenon. The probability distribution of seasonal total point or areal rainfall is obtained by convoluting a Poisson number of events with a geometric or negative binomial probability of rainfall amount. Close agreement with the experimental data is found. Next the probability of various combinations of rainfall amounts, given the seasonal total and the number of events, is computed. With these results, the theoretical seasonal water yield distribution can be obtained by using a simple rainfall‐runoff relationship, such as the Soil Conservation Service formula. The possibility of using regional input parameters to study the distribution of the output of poorly gaged small watersheds is discussed. In particular, extreme total flows can be computed.