SYSTEM IDENTIFICATION
(FOR THE ENVIRONMENTAL SCIENTIST)Purpose
Conceiving of an appropriate representation of an environmental system's behavior and selecting a reasonable procedure for numerical solution of the resulting equations, are these days much less of a problem than previously. Indeed, in many areas of application, standardized packages of software are readily available for such purposes. As a result, users of software for environmental simulation are swiftly catapulted into confronting the far more difficult problem of reconciling their models with the observed field data. The objective of the class is to give students a working knowledge of some of the principal methods of model calibration, with special reference to the role of mathematical filtering theory as a conceptual framework for defining and thinking about these problems of system identification. Understanding how a filter can perform its several functions of signal processing and data assimilation will be a more immediate goal than a detailed appreciation of the associated algorithms. Such a qualitative understanding is especially important, because the conceptual foundations of these algorithms are just the same as those underlying adaptive environmental assessment and management.The Environmental Process Control Laboratory (EPCL) and supporting ancillary equipment provide our program with a capacity for accumulating high-volume, high-quality data bases. It has thrown into sharp contrast the critical need for Environmental Science to avoid the pitfall of being "Data rich, Information poor". This class provides a point of departure for students to acquire the necessary skills of data interpretation and signal processing.
Outline
Hitherto, most sets of field data in environmental systems analysis have been sparse and highly uncertain. Randomness, the possibility of not locating the "best" combination of values for the model's parameters (a lack of model identifiability), and therefore ambiguity of interpretation of the observed record, are the norm. Above all, robust methods of model calibration are required. Among the simplest, most powerful, and most widely used such methods is that called the Regionalized Sensitivity Analysis (RSA). It combines Monte Carlo simulation with a binary classification procedure, in which the randomly generated, candidate combinations of parameter estimates are separated into those giving, and those not giving, an acceptable match of the model's response with the field data. Another popular algorithm, which provides an insight into the use of genetic and evolutionary ideas in optimization, is the Controlled Random Search (CRS). In this Class the principles of operation of the CRS are developed and illustrated with two case studies, one in hydrological modeling, the other (set as a tutorial) dealing with solute transport in a small stream. As it happens, the data from this latter are of unusually high quality, so that they can be used to introduce and demonstrate some more sophisticated algorithms of optimal parameter estimation, specifically the Newton-Raphson and Gauss-Newton algorithms.Recursive estimation of the parameters in a model is a core concept in process control, in particular, in adaptive tracking of a system's evolving dynamics in real time. This part of the class proceeds, therefore, on two parallel paths. The one, covering mathematical development of the Recursive Least Squares (RLS) estimator, begins with the elementary problem of estimating the mean of a time series of data, and works upwards towards the estimation of parameters in simple input-output models. The other presents a pictorial development of the Kalman filter, at the heart of which is an especially elegant procedure for reconciling observations with predictions.
Armed thus with these tools and concepts, the student could then contemplate branching out in a number of directions: of embarking upon solving problems of data assimilation in oceanography; or imagining an automated technique for estimating the metabolism of an aquatic ecosystem, in real time; or, just as easily, of solving signal processing problems in the on-line control of biotechnical engineering systems.