Distributions whose inverse forms are explicitly defined, such as Tukey's lambda, may present problems in deriving their parameters by more conventional means. Probability weighted moments are introduced and shown to be potentially useful in expressing the parameters of these distributions.

To generate multivariate synthetic sequences that will resemble multivariate historic sequences in terms of means, standard deviations, skewnesses, lag‐one serial correlation, and lag‐zero cross‐correlations, a multivariate, weakly stationary process is used. Techniques of regionalization and maximum likelihood estimates may be used to minimize the biases associated with the estimates of the parameters that characterize the historic sequences.

Estimates of the parameters and quantiles of the Gumbel distribution by the methods of probability weighted moments, (conventional) moments, and maximum likelihood were compared. Results were derived from Monte Carlo experiments by using both independent and serially correlated Gumbel numbers. The method of probability weighted moments was seen to compare favorably with the other two techniques.

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 Earth's 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.

This paper considers the distribution of flood flows in the Upper Mississippi, Lower Missouri, and Illinois Rivers and their relationship to climatic indices. Global climate patterns including El Niño/Southern Oscillation, the Pacific Decadal Oscillation, and the North Atlantic Oscillation explained very little of the variations in flow peaks. However, large and statistically significant upward trends were found in many gauge records along the Upper Mississippi and Missouri Rivers: at Hermann on the Missouri River above the confluence with the Mississippi (p = 2 percent), at Hannibal on the Mississippi River (p < 0.1 percent), at Meredosia on the Illinois River (p = 0.7 percent), and at St. Louis on the Mississippi below the confluence of all three rivers (p = 1 percent). This challenges the traditional assumption that flood series are independent and identically distributed random variables and suggests that flood risk changes over time.