## Development of Second Moment Statistics, EOFs, and Time-lag Covariance

Second moment statistics constitute a powerful tool to test predicted response between climate variables in the unperturbed (unforced) state. The development of covariances, Principal Component analysis and time-lag covariance studies (fluctuation/dissipation theory) underpins an analysis approach that promises to rapidly test the fundamentals of climate forecast models as soon as observational data become available. For the signal detection studies (first moment statistical analysis) the natural variability is “noise” that must be eliminated. However, as originally pointed out by Leith (1975), natural variability expresses the way forcing is transmitted through the climate system that leads to a response. A good model must have the same variability statistics as the real atmosphere. In all cases for which statistics from existing GCMs have been compared with observations, large discrepancies have been demonstrated. Model improvements will be based upon minimizing such differences.