Comparison of statistical estimates of potential seasonal predictability



[1] Four methods for estimating potential seasonal predictability from a single time series are compared. The methods are: an analysis of variance procedure proposed by Shukla and Gutzler (SG), a spectral method proposed by Madden (MN), a bootstrap method proposed by the authors, and an analysis of covariance (ANOCOVA) method proposed by the authors. The time series used for comparison are taken from Monte Carlo simulations, an atmospheric general circulation model (AGCM), and reanalysis data. The comparison clearly reveals that SG systematically underestimates weather noise variance more strongly than the other methods and is therefore not a generally useful method. MN produces the least biased estimates of weather noise variance, but it tends to have a higher probability of identifying insignificant predictability than the other methods. Unfortunately, no simple, universally corrected statements can be made regarding the relative performances of MN, ANOCOVA, and bootstrap based on the AGCM output. Overall, the reanalysis-based estimates of potential predictability of seasonal mean temperature derived from these methods is generally in accord with previous estimates, both in spatial structure and in magnitude. Omitting SG, the other three methods consistently identify about 80% of the globe as significantly predictable, and about 5% of the globe as insignificantly predictable. The remaining 15% of the globe, mostly over extratropical land, yields inconsistent assessments of potential predictability, indicating sensitivity to the assumptions underlying each of the methods. Interestingly, winter mean temperature over most of North America is found to be insignificantly predictable by all three methods.