Water availability on the continents is important for human health, economic activity, ecosystem function and geophysical processes. Because the saturation vapour pressure of water in air is highly sensitive to temperature, perturbations in the global water cycle are expected to accompany climate warming. Regional patterns of warming-induced changes in surface hydroclimate are complex and less certain than those in temperature, however, with both regional increases and decreases expected in precipitation and runoff. Here we show that an ensemble of 12 climate models exhibits qualitative and statistically significant skill in simulating observed regional patterns of twentieth-century multidecadal changes in streamflow. These models project 10-40% increases in runoff in eastern equatorial Africa, the La Plata basin and high-latitude North America and Eurasia, and 10-30% decreases in runoff in southern Africa, southern Europe, the Middle East and mid-latitude western North America by the year 2050. Such changes in sustainable water availability would have considerable regional-scale consequences for economies as well as ecosystems.

Formal parameter estimation and model identification procedures for continuous domain spatial processes are introduced. The processes are assumed to be adequately described by a linear model with residuals that follow a second-order stationary Gaussian random field and data are assumed to consist of noisy observations of the process at arbitrary sampling locations. A general class of two-dimensional rational spectral density functions with elliptic contours is used to model the spatial covariance function. An iterative estimation procedure alleviates many of the computational difficulties of conventional maximum likelihood estimation for non-lattice data. The procedure is applied to several generated data sets and to an actual ground-water data set.

Weather and climate extremes have been varying and changing on many different time scales. In recent decades, heat waves have generally become more frequent across the United States, while cold waves have been decreasing. While this is in keeping with expectations in a warming climate, it turns out that decadal variations in the number of U.S. heat and cold waves do not correlate well with the observed U.S. warming during the last century. Annual peak flow data reveal that river flooding trends on the century scale do not show uniform changes across the country. While flood magnitudes in the Southwest have been decreasing, flood magnitudes in the Northeast and north-central United States have been increasing. Confounding the analysis of trends in river flooding is multiyear and even multidecadal variability likely caused by both large-scale atmospheric circulation changes and basin-scale “memory” in the form of soil moisture. Droughts also have long-term trends as well as multiyear and decadal variability. Instrumental data indicate that the Dust Bowl of the 1930s and the drought in the 1950s were the most significant twentieth-century droughts in the United States, while tree ring data indicate that the megadroughts over the twelfth century exceeded anything in the twentieth century in both spatial extent and duration. The state of knowledge of the factors that cause heat waves, cold waves, floods, and drought to change is fairly good with heat waves being the best understood.

Results involving correlation properties and parameter estimation for autoregressive‐moving average models with periodic parameters are presented. A multivariate representation of the PARMA model is used to derive parameter space restrictions and difference equations for the periodic autocorrelations. Close approximation to the likelihood function for Gaussian PARMA processes results in efficient maximum‐likelihood estimation procedures. Terms in the Fourier expansion of the parameters are sequentially included, and a selection criterion is given for determining the optimal number of harmonics to be included. Application of the techniques is demonstrated through analysis of a monthly streamflow time series.