The authors systematically investigate two easily computed measures of the effective number of spatial degrees of freedom (ESDOF), or number of independently varying spatial patterns, of a time-varying field of data. The first measure is based on matching the mean and variance of the time series of the spatially integrated squared anomaly of the field to a chi-squared distribution. The second measure, which is equivalent to the first for a long time sample of normally distributed field values, is based on the partitioning of variance between the EOFs. Although these measures were proposed almost 30 years ago, this paper aims to provide a comprehensive discussion of them that may help promote their more widespread use. The authors summarize the theoretical basis of the two measures and considerations when estimating them with a limited time sample or from nonnormally distributed data. It is shown that standard statistical significance tests for the difference or correlation between two realizations of a field (e.g., a forecast and an observation) are approximately valid if the number of degrees of freedom is chosen using an appropriate combination of the two ESDOF measures. Also described is a method involving ESDOF for deciding whether two time-varying fields are significantly correlated to each other. A discussion of the parallels between ESDOF and the effective sample size of an autocorrelated time series is given, and the authors review how an appropriate measure of effective sample size can be computed for assessing the significance of correlations between two time series.

The need to understand differences among general circulation model projections of CO2-induced climatic change has motivated the present study, which provides an intercomparison and interpretation of climate feedback processes in 19 atmospheric general circulation models. This intercomparison uses sea surface temperature change as a surrogate for climate change. The interpretation of cloud-climate interactions is given special attention. A roughly threefold variation in one measure of global climate sensitivity is found among the 19 models. The important conclusion is that most of this variation is attributable to differences in the models' depiction of cloud feedback, a result that emphasizes the need for improvements in the treatment of clouds in these models if they are ultimately to be used as reliable climate predictors. It is further emphasized that cloud feedback is the consequence of all interacting physical and dynamical processes in a general circulation model. The result of these processes is to produce changes in temperature, moisture distribution, and clouds which are integrated into the radiative response termed cloud feedback. INTRODUCTIONProjected increases in the concentration of atmospheric carbon dioxide and other greenhouse gases are expected to have an important impact on climate. The most comprehensive way to infer future climatic change associated with this perturbation of atmospheric composition is by means of three-dimensional general circulation models (GCMs). Schlesinger and Mitchell [1987] have, however, demonstrated that several existing GCMs simulate climate responses to increasing CO2 that differ considerably. Cess and Potter [1988], following a suggestion by Speltnan and Manabe [1984], indicate that differences in global-mean warming, The global-mean direct radiative forcing G of the surfaceatmosphere system is evaluated by holding all other climate parameters fixed. It is this quantity that induces the ensuing climate change, and physically, it represents a change in the net (solar plus infrared) radiative flux at the top of the atmosphere (TOA). For an increase in the CO2 concentration of the atmosphere, to cite one example, G is the reduction in the emitted TOA infrared flux resulting solely from the CO2 increase, and this reduction results in a heating of the surface-atmosphere system. The response process is the change in climate that is then necessary to restore the TOA radiation balance, such that that is either too warm or too cold, then it will respectively produce a climate sensitivity parameter that is too small or too large, and clearly, the intercomparison simulation had to be designed to eliminate this effect. There was also a practical constraint: the CO2 simulations require large amounts of computer time for equilibration of the rather primitive ocean models that have been used in these numerical experiments.An attractive alternative that eliminated both of the above mentioned difficulties was to adopt +_2øK sea surface temperature ( The perpetual July simulation e...

Six years ago, we compared the climate sensitivity of 19 atmospheric general circulation models and found a roughly threefold variation among the models; most of this variation was attributed to differences in the models' depictions of cloud feedback. In an update of this comparison, current models showed considerably smaller differences in net cloud feedback, with most producing modest values. There are, however, substantial differences in the feedback components, indicating that the models still have physical disagreements

Snow feedback is expected to amplify global warming caused by increasing concentrations of atmospheric greenhouse gases. The conventional explanation is that a warmer Earth will have less snow cover, resulting in a darker planet that absorbs more solar radiation. An intercomparison of 17 general circulation models, for which perturbations of sea surface temperature were used as a surrogate climate change, suggests that this explanation is overly simplistic. The results instead indicate that additional amplification or moderation may be caused both by cloud interactions and longwave radiation. One measure of this net effect of snow feedback was found to differ markedly among the 17 climate models, ranging from weak negative feedback in some models to strong positive feedback in others.

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