Part I The linear distributed parameter filtering problem is considered for systems of engineering interest. In particular, the boundary conditions and observation processes considered represent those encountered in practice. The intent is to consolidate the theoretical results relevant to engineering applications and to provide a unified structure to facilitate implementation of these results through a complete and consistent set of formal derivations. When necessary, previous results are extended. The types of observation processes considered are - continuous time, discrete space - discrete time, discrete space. The discrete time case includes both instantaneous and limited time average observations. And the discrete space case includes both pointwise and integral observations. Based on the orthogonal projection lemma, the minimum variance estimate is derived. To examine the effect of stochastic boundary conditions, second order systems with mixed and Dirichlet boundary conditions are considered. Part II Aspects of air quality analysis that must be characterized with statistical methods are considered. The evaluation of air quality models is considered in detail . First, an evaluation framework is developed. The significance of evaluations of validity, accuracy and efficiency are discussed. Then, the specific aspect of accuracy assessment is addressed. The emphasis is placed on practical and objective methods. An extensive package of specific methods is set forth for use with air quality models. The package has been coded in FORTRAN. A description of the code is included. In an attempt to increase the understanding of characterizations of long-term data, observed frequency distributions of air pollutant concentration levels are critically analyzed with respect to their statistical description. It is demonstrated that several common distributions can be used to fit observed data, one of which is the popular log-normal distribution. The observation that concentration distributions for all averaging times are approximately log-normal can be explained if the short averaging time data are themselves assumed to be log-normally distributed. The near log-normality of pollutant concentration frequency distributions can be explained on the basis of the near log-normality of wind speed distributions, although this explanation does not establish that wind speed distributions are solely responsible for observed concentration distributions. It is concluded that pollutant concentration frequency distributions are the result of complex phenomena and cannot be predicted exactly, but that the approximate log-normal character of the distributions is useful from a practical point of view and can be understood qualitatively on the basis of the relation between wind speed and concentration.
Kenneth Edward Bencala (Mon,) studied this question.