Climatology is, to a large degree, the study of the statistics of our climate. The powerful tools of mathematical statistics therefore find wide application in climatological research. The purpose of this book is to help the climatologist understand the basic precepts of the statistician's art and to provide some of the background needed to apply statistical methodology correctly and usefully. The book is self contained: introductory material, standard advanced techniques, and the specialised techniques used specifically by climatologists are all contained within this one source. There are a wealth of real-world examples drawn from the climate literature to demonstrate the need, power and pitfalls of statistical analysis in climate research. Suitable for graduate courses on statistics for climatic, atmospheric and oceanic science, this book will also be valuable as a reference source for researchers in climatology, meteorology, atmospheric science, and oceanography.

Extremes of weather and climate can have devastating effects on human society and the environment. Understanding past changes in the characteristics of such events, including recent increases in the intensity of heavy precipitation events over a large part of the Northern Hemisphere land area, is critical for reliable projections of future changes. Given that atmospheric water-holding capacity is expected to increase roughly exponentially with temperature--and that atmospheric water content is increasing in accord with this theoretical expectation--it has been suggested that human-influenced global warming may be partly responsible for increases in heavy precipitation. Because of the limited availability of daily observations, however, most previous studies have examined only the potential detectability of changes in extreme precipitation through model-model comparisons. Here we show that human-induced increases in greenhouse gases have contributed to the observed intensification of heavy precipitation events found over approximately two-thirds of data-covered parts of Northern Hemisphere land areas. These results are based on a comparison of observed and multi-model simulated changes in extreme precipitation over the latter half of the twentieth century analysed with an optimal fingerprinting technique. Changes in extreme precipitation projected by models, and thus the impacts of future changes in extreme precipitation, may be underestimated because models seem to underestimate the observed increase in heavy precipitation with warming.

Indices for climate variability and extremes have been used for a long time, often by assessing days with temperature or precipitation observations above or below specific physically-based thresholds. While these indices provided insight into local conditions, few physically based thresholds have relevance in all parts of the world. Therefore, indices of extremes evolved over time and now often focus on relative thresholds that describe features in the tails of the distributions of meteorological variables. In order to help understand how extremes are changing globally, a subset of the wide range of possible indices is now being coordinated internationally which allows the results of studies from different parts of the world to fit together seamlessly. This paper reviews these as well as other indices of extremes and documents the obstacles to robustly calculating and analyzing indices and the methods developed to overcome these obstacles. Gridding indices are necessary in order to compare observations with climate model output. However, gridding indices from daily data are not always straightforward because averaging daily information from many stations tends to dampen gridded extremes. The paper describes recent progress in attribution of the changes in gridded indices of extremes that demonstrates human influence on the probability of extremes. The paper also describes model projections of the future and wraps up with a discussion of ongoing efforts to refine indices of extremes as they are being readied to contribute to the IPCC's Fifth Assessment Report.

[1] This paper provides a first overview of the performance of state-of-the-art global climate models participating in the Coupled Model Intercomparison Project Phase 5 (CMIP5) in simulating climate extremes indices defined by the Expert Team on Climate Change Detection and Indices (ETCCDI), and compares it to that in the previous model generation (CMIP3). For the first time, the indices based on daily temperature and precipitation are calculated with a consistent methodology across multimodel simulations and four reanalysis data sets (ERA40, ERA-Interim, NCEP/NCAR, and NCEP-DOE) and are made available at the ETCCDI indices archive website. Our analyses show that the CMIP5 models are generally able to simulate climate extremes and their trend patterns as represented by the indices in comparison to a gridded observational indices data set (HadEX2). The spread amongst CMIP5 models for several temperature indices is reduced compared to CMIP3 models, despite the larger number of models participating in CMIP5. Some improvements in the CMIP5 ensemble relative to CMIP3 are also found in the representation of the magnitude of precipitation indices. We find substantial discrepancies between the reanalyses, indicating considerable uncertainties regarding their simulation of extremes. The overall performance of individual models is summarized by a "portrait" diagram based on root-mean-square errors of model climatologies for each index and model relative to four reanalyses. This metric analysis shows that the median model climatology outperforms individual models for all indices, but the uncertainties related to the underlying reference data sets are reflected in the individual model performance metrics.

[1] This study provides an overview of projected changes in climate extremes indices defined by the Expert Team on Climate Change Detection and Indices (ETCCDI). The temperature-and precipitation-based indices are computed with a consistent methodology for climate change simulations using different emission scenarios in the Coupled Model Intercomparison Project Phase 3 (CMIP3) and Phase 5 (CMIP5) multimodel ensembles. We analyze changes in the indices on global and regional scales over the 21st century relative to the reference period 1981-2000. In general, changes in indices based on daily minimum temperatures are found to be more pronounced than in indices based on daily maximum temperatures. Extreme precipitation generally increases faster than total wet-day precipitation. In regions, such as Australia, Central America, South Africa, and the Mediterranean, increases in consecutive dry days coincide with decreases in heavy precipitation days and maximum consecutive 5 day precipitation, which indicates future intensification of dry conditions. Particularly for the precipitation-based indices, there can be a wide disagreement about the sign of change between the models in some regions. Changes in temperature and precipitation indices are most pronounced under RCP8.5, with projected changes exceeding those discussed in previous studies based on SRES scenarios. The complete set of indices is made available via the ETCCDI indices archive to encourage further studies on the various aspects of changes in extremes.

Overall, the climate models simulate present-day warm extremes reasonably well on the global scale, as compared to estimates from reanalyses. The model discrepancies in simulating cold extremes are generally larger than those for warm extremes, especially in sea ice-covered areas. Simulated present-day precipitation extremes are plausible in the extratropics, but uncertainties in extreme precipitation in the Tropics are very large, both in the models and the available observationally based datasets.Changes in warm extremes generally follow changes in the mean summertime temperature. Cold extremes warm faster than warm extremes by about 30%-40%, globally averaged. The excessive warming of cold extremes is generally confined to regions where snow and sea ice retreat with global warming. With the exception of northern polar latitudes, relative changes in the intensity of precipitation extremes generally exceed relative changes in annual mean precipitation, particularly in tropical and subtropical regions. Consistent with the increased intensity of precipitation extremes, waiting times for late-twentieth-century extreme precipitation events are reduced almost everywhere, with the exception of a few subtropical regions. The multimodel multiscenario consensus on the projected change in the globally averaged 20-yr return values of annual extremes of 24-h precipitation amounts is that there will be an increase of about 6% with each kelvin of global warming, with the bulk of models simulating values in the range of 4%-10% K Ϫ1. The very large intermodel disagreements in the Tropics suggest that some physical processes associated with extreme precipitation are not well represented in models. This reduces confidence in the projected changes in extreme precipitation.

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