Nicholas C. Matalas

A Survey of Approaches for Assessing and Managing the Risk of Extremes

In this paper, we review methods for assessing and managing the risk of extreme events, where “extreme events” are defined to be rare, severe, and outside the normal range of experience of the system in question. First, we discuss several systematic approaches for identifying possible extreme events. We then discuss some issues related to risk assessment of extreme events, including what type of output is needed (e.g., a single probability vs. a probability distribution), and alternatives to the probabilistic approach. Next, we present a number of probabilistic methods. These include: guidelines for eliciting informative probability distributions from experts; maximum entropy distributions; extreme value theory; other approaches for constructing prior distributions (such as reference or noninformative priors); the use of modeling and decomposition to estimate the probability (or distribution) of interest; and bounding methods. Finally, we briefly discuss several approaches for managing the risk of extreme events, and conclude with recommendations and directions for future research.

Hydrology: The interdisciplinary science of water

We live in a world where biophysical and social processes are tightly coupled. Hydrologic systems change in response to a variety of natural and human forces such as climate variability and change, water use and water infrastructure, and land cover change. In turn, changes in hydrologic systems impact socioeconomic, ecological, and climate systems at a number of scales, leading to a coevolution of these interlinked systems. The Harvard Water Program, Hydrosociology, Integrated Water Resources Management, Ecohydrology, Hydromorphology, and Sociohydrology were all introduced to provide distinct, interdisciplinary perspectives on water problems to address the contemporary dynamics of human interaction with the hydrosphere and the evolution of the Earths hydrologic systems. Each of them addresses scientific, social, and engineering challenges related to how humans influence water systems and vice versa. There are now numerous examples in the literature of how holistic approaches can provide a structure and vision of the future of hydrology. We review selected examples, which taken together, describe the type of theoretical and applied integrated hydrologic analyses and associated curricular content required to address the societal issue of water resources sustainability. We describe a modern interdisciplinary science of hydrology needed to develop an in-depth understanding of the dynamics of the connectedness between human and natural systems and to determine effective solutions to resolve the complex water problems that the world faces today. Nearly, every theoretical hydrologic model introduced previously is in need of revision to accommodate how climate, land, vegetation, and socioeconomic factors interact, change, and evolve over time.

Frequency of record-breaking floods in the United States

The theory of record-breaking processes offers a framework for understanding extreme events which is nearly independent of the theory of extremes. The mathematical theory of record-breaking processes is applied to the problem of identifying nonstationarity in hydrological records. A record flood event is simply an event which exceeds all previous events. The probability distribution and first four moments of the number of record events in an n-year period, R, are derived for a serially independent process. The variance of estimates of the mean, standard deviation, and coefficient of variation R is also derived. In addition, approximate confidence intervals are derived for the mean number of record-breaking events in a region with spatially correlated flood series. Using these results, in combination with 1571 flood records in the United States, we document that the average number of record breaking flood events over n-year periods ranging from [10, 80] behaved as if the annual flood series were serially independent for all regions of the United States. However, when spatial correlation of the flood records is ignored, as is the case in many previous studies, it appears as if flood records are not serially independent in the western and Midwestern regions of the United States. These results emphasize the importance of accounting for the spatial correlation structure of hydrologic records when performing regional hypothesis tests.

STATISTICAL PROPERTIES OF TREE RING DATA

Abstract A statistical analysis is made of the sequences of annual tree ring widths and indices. The expected value of growth during any year is shown to be proportional to the standard deviation of the growth, so that the coefficient of variation is a measure of the sensitivity of the growth of a tree. Tree ring data were found to be non-randomly distributed in time. The large values of serial correlation indicated that the non-randomness cannot be attributed entirely to climatic factors. Correlogram and power spectrum analyses applied to a sequence of tree ring indices for a pinyon pine showed that the data were generated by an autoregressive process. The statistical parameter measuring the sensitivity or complacency of growth is used to derive a growth function.

On the nature of persistence in dendrochronologic records with implications for hydrology

Abstract Hydrologic processes are generally held to be persistent and not secularly independent. Impetus for this view was given by Hurst in his work which dealt with properties of the rescaled range of many types of long geophysical records, in particular dendrochronologic records, in addition to hydrologic records. Mandelbrot introduced an infinite memory stationary process, the fractional Gaussian noise process (F), as an explanation for Hursts observations. This is in contrast to other explanations which have been predicated on the implicit non-stationarity of the process underlying the construction of the records. In this work, we introduce a stationary finite memory process which arises naturally from a physical concept and show that it can accommodate the persistence structures observed for dendrochronological records more successfully than an F or any other of a family of related processes examined herein. Further, some question arises as to the empirical plausibility of an F process. Dendrochronologic records are used because they are widely held to be surrogates for records of average hydrologic phenomena and the length of these records allows one to explore questions of stochastic process structure which cannot be explored with great validity in the case of generally much shorter hydrologic records.