Information Theory and Predictability Lecture 8: Statistical Predictability
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چکیده
In the following lectures we shall develop and explore a general theoretical framework derived from information theory to study practical dynamical prediction from the viewpoint of analyzing the time flow of uncertainty. Here we review the practical aspects of this problem. There are two important dynamical systems which have convincingly demonstrated practical predictability. The first is the Solar System while the second is the mid-latitude atmosphere. Here we shall focus primarily on the second application because it is possible to study empirically for this system why predictions are limited in their accuracy. On practical time scales predictions of the solar system are extremely accurate while those of the atmosphere less so. It is this inaccuracy which shall interest us here since the focus of this course is uncertainty. Thus we focus primarily on the second case. Practical (and useful) weather predictions have been possible for around fifty years now mainly because of the existence of powerful computers. One of the first to use computers to predict the weather was the mathematician John von Neumann at IAS in Princeton. The accuracy of weather predictions has tended to increase noticeably in the last few decades as a result partly of the availability of increasingly more powerful systems1 consistent with Moore’s Law. In addition to the computer aspect, the MIT meteorologist Edward Lorenz was the first to clearly recognize that atmospheric prediction was very sensitive to initial conditions. This awareness was one of the factors that drove the extensive study of chaotic dynamical systems during the 1960s and 1970s. Our primary focus in these lectures will be on this particular dynamical system and we shall study later a simple dynamical model advocated by Lorenz and others as a crude representation of the atmosphere. Predictions made using a dynamical model typically suffer from two deficiencies: Firstly the model used may have certain inadequacies as a representation of reality and secondly initial conditions for a prediction may not be known exactly. Such problems are known as model errors and initial condition errors respectively. Progress can be made in improving predictions either by improving physical depictions within models or by improving the observational network and thereby reducing errors in the initial conditions. There is considerable evidence for the atmosphere however that no practical observational network will ever eliminate significant prediction errors due to initial condition errors. Even if one was
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تاریخ انتشار 2012