Rainfall on Earth is most intense in the intertropical convergence zone (ITCZ), a narrow belt of clouds centred on average around six degrees north of the Equator. The mean position of the ITCZ north of the Equator arises primarily because the Atlantic Ocean transports energy northward across the Equator, rendering the Northern Hemisphere warmer than the Southern Hemisphere. On seasonal and longer timescales, the ITCZ migrates, typically towards a warming hemisphere but with exceptions, such as during El Niño events. An emerging framework links the ITCZ to the atmospheric energy balance and may account for ITCZ variations on timescales from years to geological epochs.

Global warming is expected to lead to a large increase in atmospheric water vapor content and to changes in the hydrological cycle, which include an intensification of precipitation extremes. The intensity of precipitation extremes is widely held to increase proportionately to the increase in atmospheric water vapor content. Here, we show that this is not the case in 21st-century climate change scenarios simulated with climate models. In the tropics, precipitation extremes are not simulated reliably and do not change consistently among climate models; in the extratropics, they consistently increase more slowly than atmospheric water vapor content. We give a physical basis for how precipitation extremes change with climate and show that their changes depend on changes in the moist-adiabatic temperature lapse rate, in the upward velocity, and in the temperature when precipitation extremes occur. For the tropics, the theory suggests that improving the simulation of upward velocities in climate models is essential for improving predictions of precipitation extremes; for the extratropics, agreement with theory and the consistency among climate models increase confidence in the robustness of predictions of precipitation extremes under climate change.global warming ͉ hydrological cycle ͉ rainfall ͉ extreme events I n simulations of 21st century climate change scenarios, mean precipitation generally increases in the deep tropics and extratropics and decreases in the subtropics (1-3). However, precipitation extremes (defined, for example, as a high percentile of daily precipitation) increase almost across the globe (2, 3), with expected societal impacts such as increased flooding and soil erosion (4). Precipitation extremes are widely held to increase proportionately to the mean atmospheric water vapor content (5, 6), or to the amount of water vapor converging at the base of storms (7). Global-mean water vapor content increases strongly in global warming simulations, at a rate of ϳ7.5% K Ϫ1 with respect to surface temperature, approximately consistent with a constant effective relative humidity (1). Precipitation extremes are thought to increase at a similar rate, or maybe even more rapidly if the strength of the updrafts associated with extreme precipitation events increases as the climate warms (5, 6).However, although precipitation extremes in simulations increase as the climate warms, their rate of increase varies with latitude and is generally not equal to the rate of increase in atmospheric water vapor content (6). Simulations of a wide range of climates with an idealized general circulation model show that precipitation extremes outside the subtropics scale more similarly to mean precipitation than to water vapor content (8). In simulations with comprehensive climate models, the rate of increase in precipitation extremes varies widely among models, particularly in the tropics (2). The variations among models in the tropics indicate that simulated precipitation extremes may depend sensitively on the parameterizatio...

Estimating the mean and the covariance matrix of an incomplete dataset and filling in missing values with imputed values is generally a nonlinear problem, which must be solved iteratively. The expectation maximization (EM) algorithm for Gaussian data, an iterative method both for the estimation of mean values and covariance matrices from incomplete datasets and for the imputation of missing values, is taken as the point of departure for the development of a regularized EM algorithm. In contrast to the conventional EM algorithm, the regularized EM algorithm is applicable to sets of climate data, in which the number of variables typically exceeds the sample size. The regularized EM algorithm is based on iterated analyses of linear regressions of variables with missing values on variables with available values, with regression coefficients estimated by ridge regression, a regularized regression method in which a continuous regularization parameter controls the filtering of the noise in the data. The regularization parameter is determined by generalized cross-validation, such as to minimize, approximately, the expected mean-squared error of the imputed values. The regularized EM algorithm can estimate, and exploit for the imputation of missing values, both synchronic and diachronic covariance matrices, which may contain information on spatial covariability, stationary temporal covariability, or cyclostationary temporal covariability. A test of the regularized EM algorithm with simulated surface temperature data demonstrates that the algorithm is applicable to typical sets of climate data and that it leads to more accurate estimates of the missing values than a conventional noniterative imputation technique.

[1] Water vapor is not only Earth's dominant greenhouse gas. Through the release of latent heat when it condenses, it also plays an active role in dynamic processes that shape the global circulation of the atmosphere and thus climate. Here we present an overview of how latent heat release affects atmosphere dynamics in a broad range of climates, ranging from extremely cold to extremely warm. Contrary to widely held beliefs, atmospheric circulation statistics can change nonmonotonically with global-mean surface temperature, in part because of dynamic effects of water vapor. For example, the strengths of the tropical Hadley circulation and of zonally asymmetric tropical circulations, as well as the kinetic energy of extratropical baroclinic eddies, can be lower than they presently are both in much warmer climates and in much colder climates. We discuss how latent heat release is implicated in such circulation changes, particularly through its effect on the atmospheric static stability, and we illustrate the circulation changes through simulations with an idealized general circulation model. This allows us to explore a continuum of climates, to constrain macroscopic laws governing this climatic continuum, and to place past and possible future climate changes in a broader context. Citation: Schneider, T., P. A. O'Gorman, and X. J. Levine (2010), Water vapor and the dynamics of climate changes, Rev. Geophys., 48, RG3001,