The motivation for this paper is to understand better the means available for testing climate models. Statistics of observed, outgoing, thermal spectra are compared with those predicted from a climate model, on the basis of data collected over a period of approximately 1 year. This is a powerful approach to testing a model with respect to processes internal to the atmosphere. These processes, which have characteristic timescales of less than a year, define the atmosphere's response to external forcing. Second-moment statistics are particularly important for testing model variability, which is key to predicting the results of forcing the atmosphere, for example, by ocean surface temperature changes, increase of greenhouse gases, etc. Comparisons are presented between statistical data from the infrared interferometer spectrometer (IRIS), an orbiting fourier transform spectrometer, and spectra calculated using the medium-resolution spectral code, MODTRAN, applied to the temperature and humidity profiles from a well-known climate model. Ten months of IRIS data are available, and we have compared means, standard deviations, skew, and kurtosis of its spectrally resolved brightness temperature in three tropical regions for individual months and for a range of timescales. Also presented are comparisons of covariances using Empirical Orthogonal Functions (EOFs) calculated in frequency space. All data that are presented are based on radiance differences from two like spectra, which eliminates many of the errors generated by the use of MODTRAN and most of the errors due to calibration uncertainties in IRIS. Important differences (i.e., residuals) between the IRIS and the GCM statistics are found in comparisons, demonstrating that the spectral data can provide a severe test of many aspects of the variability of a general circulation model. We discuss some of the residuals and how they may be used to improve model performance in the context of an adjoint formalism. In the long run the only way to have confidence in the performance of a model is to subject it to as many discriminating comparisons with data as are practicable, and we present a good candidate.¿ 1997 American Geophysical Union