ALBERT

Description / Table of Contents: PREFACE Following the economical and social development of the local communities, mountain regions of temperate climates are increasingly becoming the site of valuable infrastructures and important urban and industrial settlements. As the catastrophic events of last years in the European Alps have clearly shown, the vulnerability of these territories has correspondingly increased, in terms of both property damage and losses of human life. Until recently, the hydraulic scientific community has paid little attention to mountain watersheds, except perhaps during the period if the hydropower development. Nevertheless attention was then focused on problems and methodologies somewhat different from the issues of actual environmental concern. More recently, however, hydraulic engineers have joined their colleagues from forest and rural engineering, who have traditionally dealt with erosion control in mountain areas, to bring in their own methodology, already experienced in lowland rivers. At the same time, academic people focused an interest in some phenomena, like massive transport, which is typical of mountain environment. To bring together all these contributions and to make the state of the art of the mountain river science (oropotamology) and technology, an International Workshop was called at the University of Trent (Italy), on October 1989, under the sponsorship of Fluvial Hydraulic Section of the IAHR. Three main topics have been recognized as particularly relevant from the point of view of both research and professivnal people: a) Hydrodynamics of steep channels and local scale process; b) Sediment movement and sediment training, with special emphasis on massive transport; c) Particular features of sediment transport related to non-uniform grain-size. However, as it is the case in these circumstances, the contest of several contributions often spread over more than one topic. In the following Introduction to papers, the three topics were split into 11 Sections, each one devoted to a more particular aspect recurrently addressed during the discussion. The same paper, thus, may be mentioned in different Sections of the Introduction.

Description / Table of Contents: PREFACE There are problems, when applying statistical inference to the analysis of data, which are not readily solved by the inferential methods of the standard statistical techniques. One example is the computation of confidence intervals for variance components or for functions of variance components. Another example is the statistical inference on the random parameters of the mixed model of the standard statistical techniques or the inference on parameters of nonlinear models. Bayesian analysis gives answers to these problems. The advantage of the Bayesian approach is its conceptual simplicity. It is based on Bayes' theorem only. In general, the posterior distribution for the unknown parameters following from Bayes' theorem can be readily written down. The statistical inference is then solved by this distribution. Often the posterior distribution cannot be integrated analytically. However, this is not a serious drawback, since efficient methods exist for the numerical integration. The results of the standard statistical techniques concerning the linear models can also be derived by the Bayesian inference. These techniques may therefore be considered as special cases of the Bayesian analysis. Thus, the Bayesian inference is more general. Linear models and models closely related to linear models will be assumed for the analysis of the observations which contain the information on the unknown parameters of the models. The models, which are presented, are well suited for a variety of tasks connected with the evaluation of data. When applications are considered, data will be analyzed which have been taken to solve problems of surveying engineering. This does not mean, of course, that the applications are restricted to geodesy. Bayesian statistics may be applied wherever data need to be evaluated, for instance in geophysics. After an introduction the basic concepts of Bayesian inference are presented in Chapter 2. Bayes' theorem is derived and the introduction of prior information for the unknown parameters is discussed. Estimates of the unknown parameters, of confidence regions and the testing of hypotheses are derived and the predictive analysis is treated. Finally techniques for the numerical integration of the integrals are presented which have to be solved for the statistical inference. Chapter 3 introduces models to analyze data for the statistical inference on the unknown parameters and deals with special applications. First the linear model is presented with noninformative and informative priors for the unknown parameters. The agreement with the results of the standard statistical techniques is pointed out. Furthermore, the prediction of data and the linear model not of full rank are discussed. A method for identifying a model is presented and a less sensitive hypothesis test for the standard statistical techniques is derived. The Kalman-Bucy filter for estimating unknown parameters of linear dynamic systems is also given. Nonlinear models are introduced and as an example the fit of a straight line is treated. The resulting posterior distribution for the unknown parameters is analytically not tractable, so that numerical methods have to be applied for the statistical inference. In contrast to the standard statistical techniques, the Bayesian analysis for mixed models does not discriminate between fixed and random parameters, it distinguishes the parameters according to their prior information. The Bayesian inference on the parameters, which correspond to the random parameters of the mixed model of the standard statistical techniques, is therefore readily accomplished. Noninformafive priors of the variance and covariance components are derived for the linear model with unknown variance and covariance components. In addition, informative priors are given. Again, the resulting posterior distributions are analytically not tractable, so that numerical methods have to be applied for the Bayesian inference. The problem of classification is solved by applying the Bayes rule, i.e. the posterior expected loss computed by the predictive density function of the observations is minimized. Robust estimates of the standard statistical techniques, which are maximum likelihood type estimates, the so-called M-estimates, may also be derived by Bayesian inference. But this approach not only leads to the M-estimates, but also any inferential problem for the parameters may be solved. Finally, the reconstruction of digital images is discussed. Numerous methods exist for the analysis of digital images. The Bayesian approach unites some of them and gives them a common theoretical foundation. This is due to the flexibility by which prior information for the unknown parameters can be introduced. It is assumed that the reader has a basic knowledge of the standard statistical techniques. Whenever these results are needed, for easy reference the appropriate page of the book "Parameter Estimation and Hypothesis Testing in Linear Models" by the author (Koch 1988a) is cited. Of course, any other textbook on statistical techniques can serve this purpose. To easily recognize the end of an example or a proof, it is marked by a A or a t~, respectively. I want to thank all colleagues and students who contributed to this book. In particular, I thank Mr. Andreas Busch, Dipl.-Ing., for his suggestions. I also convey my thanks to Mrs. Karin Bauer, who prepared the copy of the book. The assistance of the Springer- Verlag in checking the English text is gratefully acknowledged. The responsibility of errors, of course, remains with the author.

Description / Table of Contents: This volume contains the proceedings of a symposium held at Freiburg im Breisgau, October 7-11, 1990. The symposium was sponsored mainly by the Deutsche Forschungsgemeinschaft (DFG), by the Geological Institute of the University of Freiburg, and by the International Association of Mathematical Geology. We thank these and all other sponsors of the meeting. The symposium whose participants came from more then twenty countries was the first international meeting dedicated entirely to geological applications of threedimensional computer graphics, a rapidly growing field of scientific visualization in geology. The selection of papers in this volume covers a wide range of methods developed in the last decade.

Description / Table of Contents: Cellular growth is an important crystal growth process and offers an interesting example of natural pattern formation. The present work has been undertaken to study cellular growth, especially its pattern formation, both experimentally and numerically. In situ observations of faceted cellular growth clearly revealed cellular interactions in the array of cells. Cell tip splitting and loss of cells were observed to be the two main mechanisms for the adjustment of cell spacings during growth. For the first time, the true time-dependent faceted cellular growth has been modelled properly. The time evolution of faceted cellular growth has demonstrated the dynamical features of cellular growth processes. It was shown that the pattern formation was determined by cellular interactions in the array, either transient or persistent depending on the growth condition. The cellular structures were irregular when persistent interactions occurred, whereas relatively regular structures could be formed once the transient interactions had stopped. As a result of cellular interactions, a finite range of stable cell spacings was found under a given growth condition. Numerical experiments were carried out for k 〉 1 and k 〈 1 (where k is the solute partition coefficient), under a number of different growth conditions. It was found that these two cases were not symmetric as far as solute distribution is concerned; however the pattern formation behaviours were similar. For k 〉 1 shallow cells were retained, while for k 〈 1, the formation of liquid grooves along the cell boundary depended on the growth condition. The solute effect plays an important role in the cellular interactions in the array. The results were compared with experimental observations in thin film silicon single crystals. It is felt that a general behaviour of pattern formation is found and should be expected for other processes such as non-faceted cellular or eutectic growth. In addition, the solute flow in steady state cellular array growth was studied using the point source technique. Preliminary work was carried out to measure steady state non-faceted cell shapes. Heat flow in zone melting was studied numerically.

Description / Table of Contents: The present interest in sediments which are rich in organic matter results not only from their economic significance as potential oil and gas source rocks, but also from the fact that their deposition is the result of special environments. Subtle changes in the environmental conditions may result in great variations in the geochemical and petrographical characteristics of the organic matter. Therefore, the study of organic matter-rich sediments can provide a key to past sedimentary conditions. In addition, the elucidation of the depositional controls is of importance for oil and gas exploration strategies, for which the knowledge of source rock distribution and quality is critical. Furthermore, organic matter reacts extremely sensitive to changes in temperature during burial. The result of this sensitivity is the generation of volatile products such as carbon dioxide, water, nitrogen, oil and gas and a reorganization of the solid organic residue. Some of these changes are quantified as maturity parameters which can be used as calibration tools in basin modelling, i.e., in the modelling of temperature histories of sedimentary basins. The use of maturity parameters and other organic matter characteristics as indicators for diagenetic conditions and depositional processes is, however, restricted, if analyses are performed on outcrop samples, because weathering also affects organic matter.