A Systems Engineering Methodology for Structuring and Calibrating Lake Ecosystem Models

Roberts, Glenn F.; Cesare, Frank Di

doi:10.1109/tsmc.1982.4308770

Cited by 2 publications

(2 citation statements)

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“…There are two matters arising from this discussion that may cause confusion. First, there is the method of quasilinearization [Bellman and Kalaba, 1965], which has both attracted considerable interest in the analysis of water quality/ecological systems [Bellman et al, 1966;Lee and Hwang, 1971;Stehfest, 1977;Roberts and DiCesare, 1982] and has also (mistakenly) attracted the interpretation of being a fifth type of estimator uniquely different from the four types already identified. The basis of the method is to linearize the nonlinear system equations, such as those of our class II model (equation (6)) so that e{xJ becomes a linear function of x 0 • Then, as stated earlier, (26) leads to a set of (n + p) linear algebraic equations in the (n + p) unknowns, i.e., the elements of the augmented state-parameter vector x 0 • Here n is the order of the state vector and p the order of the parameter vector.…”

Section: Algorithms For the Implementation Of Batch Estimation Schemesmentioning

confidence: 99%

“…A second, but rather different, pair of case studies can be found in Halfon's [1976] analysis of the dynamics of selenium in an aquatic microcosm and Roberts and DiCesare's [1982] work with a simple model for nutrient dynamics in Lake George, New York. The common theme of these studies is the transformation of the basic system description of a class II model, i.e., (32), into the discrete-time form of the multipleinput/ multiple-output class III model of (3).…”

Section: Prudent Transformations Of Ill-posed Problemsmentioning

confidence: 99%

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Water quality modeling: A review of the analysis of uncertainty

Beck¹

1987

Water Resources Research

863

431

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This paper reviews the role of uncertainty in the identification of mathematical models of water quality and in the application of these models to problems of prediction. More specifically, four problem areas are examined in detail: uncertainty about model structure, uncertainty in the estimated model parameter values, the propagation of prediction errors, and the design of experiments in order to reduce the critical uncertainties associated with a model. The review is rather lengthy, and it has therefore been prepared in effect as two papers. There is a shorter, largely nontechnical version, which gives a quick impression of the current and future issues in the analysis of uncertainty in water quality modeling. Enclosed by this shorter discussion is the main body of the review dealing in turn with (1) identifiability and experimental design, (2) the generation of preliminary model hypotheses under conditions of sparse, grossly uncertain field data, (3) the selection and evaluation of model structure, (4) parameter estimation (model calibration), (5) checks and balances on the identified model, i.e., model “verification” and model discrimination, and (6) prediction error propagation. Much time is spent in discussing the algorithms of system identification, in particular, the methods of recursive estimation, and in relating these algorithms and the subject of identification to the problems of prediction uncertainty and first‐order error analysis. There are two obvious omissions from the review. It is not concerned primarily with either the development and solution of stochastic differential equations or the issue of decision making under uncertainty, although clearly some reference must be made to these topics. In brief, the review concludes (not surprisingly) that much work has been done on the analysis of uncertainty in the development of mathematical models of water quality, and much remains to be done. A lack of model identifiability has been an outstanding difficulty in the interpretation and explanation of past observed system behavior, and there is ample evidence to show that the “larger,” more “comprehensive” models are easily capable of generating highly uncertain predictions of future behavior. For the future of the subject, it is speculated that there is the possibility of progress in the development of novel algorithms for model structure identification, a need for new questions to be posed in the problem of prediction, and a distinct challenge to the conventional views of this review in the new forms of knowledge representation and manipulation now emerging from the field of artificial intelligence.

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Section: Algorithms For the Implementation Of Batch Estimation Schemesmentioning

confidence: 99%

Section: Prudent Transformations Of Ill-posed Problemsmentioning

confidence: 99%