A.R. Rao

Conventionally, time series have been studied either in the time domain or the frequency domain. The representation of a signal in the time domain is localized in time, i.e . the value of the signal at each instant in time is well defined . However, the time representation of a signal is poorly localized in frequency , i.e. little information about the frequency content of the signal at a certain frequency can be known by looking at the signal in the time domain . On the other hand, the representation of a signal in the frequency domain is well localized in frequency, but is poorly localized in time, and as a consequence it is impossible to tell when certain events occurred in time. In studying stationary or conditionally stationary processes with mixed spectra , the separate use of time domain and frequency domain analyses is sufficient to reveal the structure of the process . Results discussed in the previous chapters suggest that the time series analyzed in this book are conditionally stationary processes with mixed spectra. Additionally, there is some indication of nonstationarity, especially in longer time series.

To accommodate the inherent non-linearity and non-stationarity of many natural time series, empirical mode decomposition (EMD) and Hilbert-Huang transform (HHT) provide an adaptive and efficient method. The HHT is based on the local characteristic time scale of the data. The HHT method provides not only a precise definition in time-frequency representation than the other conventional signal processing methods, but also more physically meaningful interpretation of the underlying dynamic processes. The EMD also works as a filter to extract the variability of signals with different scales and is applicable to non-linear and n- stationary processes. This promising algorithm has been applied in many fields since it was developed, but it has not been applied to hydrological and climatic time series. The discussion in this book starts with several simulated data sets in order to investigate the capability of this method and to compare it to other conventional frequency-domain analysis methods that assume stationarity. Rainfall, streamflow, temperature, wind speed time series and lake temperature data are investigated in this study. The aim of the work is to investigate periodicity, long term oscillations and trends embedded in these data by using HHT. The analysis is performed in both the time and frequency domains. The results from HHT are compared to those from the multi-taper method (MTM) which is based on Fourier Transform of the data.

Written by a sociologist, a graph theorist, and a statistician, this title provides social network analysts and students with a solid statistical foundation from which to analyze network data. Clearly demonstrates how graph-theoretic and statistical techniques can be employed to study some important parameters of global social networks. The authors uses real life village-level social networks to illustrate the practicalities, potentials, and constraints of social network analysis ("SNA"). They also offer relevant sampling and inferential aspects of the techniques while dealing with potentially large networks. Intended Audience This supplemental text is ideal for a variety of graduate and doctoral level courses in social network analysis in the social, behavioral, and health sciences

Design of water control structures, reservoir management, economic evaluation of flood protection projects, land use planning and management, flood insurance assessment, and other projects rely on knowledge of magnitude and frequency of floods. Often, estimation of floods is not easy because of lack of flood records at the target sites. Regional flood frequency analysis (RFFA) alleviates this problem by utilizing flood records pooled from other watersheds, which are similar to the watershed of the target site in flood characteristics. Clustering techniques are used to identify group(s) of watersheds which have similar flood characteristics. This book is a comprehensive reference on how to use these techniques for RFFA and is the first of its kind. It provides a detailed account of several recently developed clustering techniques, including those based on fuzzy set theory and artificial neural networks. It also documents research findings on application of clustering techniques to RFFA that remain scattered in various hydrology and water resources journals. The optimal number of groups defined in an area is based on cluster validation measures and L-moment based homogeneity tests. These form the bases to check the regions for homogeneity. The subjectivity involved and the effort needed to identify homogeneous groups of watersheds with conventional approaches are greatly reduced by using efficient clustering techniques discussed in this book. Furthermore, better flood estimates with smaller confidence intervals are obtained by analysis of data from homogeneous watersheds. Consequently, the problem of over- or under-designing by using these flood estimates is reduced. This leads to optimal economic design of structures. The advantages of better regionalization of watersheds and their utility are entering into hydrologic practice. Audience:This book will be of interest to researchers in stochastic hydrology, practitioners in hydrology and graduate students.

To accommodate the inherent non-linearity and non-stationarity of many natural time series, empirical mode decomposition (EMD) and Hilbert-Huang transform (HHT) provide an adaptive and efficient method. The HHT is based on the local characteristic time scale of the data. The HHT method provides not only a precise definition in time-frequency representation than the other conventional signal processing methods, but also more physically meaningful interpretation of the underlying dynamic processes. The EMD also works as a filter to extract the variability of signals with different scales and is applicable to non-linear and n- stationary processes. This promising algorithm has been applied in many fields since it was developed, but it has not been applied to hydrological and climatic time series. The discussion in this book starts with several simulated data sets in order to investigate the capability of this method and to compare it to other conventional frequency-domain analysis methods that assume stationarity. Rainfall, streamflow, temperature, wind speed time series and lake temperature data are investigated in this study. The aim of the work is to investigate periodicity, long term oscillations and trends embedded in these data by using HHT. The analysis is performed in both the time and frequency domains. The results from HHT are compared to those from the multi-taper method (MTM) which is based on Fourier Transform of the data.

Conventionally, time series have been studied either in the time domain or the frequency domain. The representation of a signal in the time domain is localized in time, i.e . the value of the signal at each instant in time is well defined . However, the time representation of a signal is poorly localized in frequency , i.e. little information about the frequency content of the signal at a certain frequency can be known by looking at the signal in the time domain . On the other hand, the representation of a signal in the frequency domain is well localized in frequency, but is poorly localized in time, and as a consequence it is impossible to tell when certain events occurred in time. In studying stationary or conditionally stationary processes with mixed spectra , the separate use of time domain and frequency domain analyses is sufficient to reveal the structure of the process . Results discussed in the previous chapters suggest that the time series analyzed in this book are conditionally stationary processes with mixed spectra. Additionally, there is some indication of nonstationarity, especially in longer time series.