The effects of bias, drift, and trends in calculating anomalies for evaluating skill of seasonal-to-decadal initialized climate predictions

In initialized seasonal to decadal (S2D) predictions, model hindcasts rapidly drift away from the initial observed state and converge toward a preferred state characterized by systematic error, or bias. Bias and drift are among the greatest challenges facing initialized prediction today. Differences in trends between initial states and drifted states, combined with bias and drift, introduce complexities in calculating anomalies to assess skill of initialized predictions. We examine several methods of calculating anomalies using the Decadal Prediction Large Ensemble (DPLE) using the Community Earth System Model (CESM) initialized hindcasts and focus on Pacific and Atlantic SSTs to illustrate issues with anomaly calculations. Three methods of computing anomalies, one as differences from a long term model climatology, another as bias-adjusted differences from the previous 15 year average from observations, and a third as differences from the previous 15 year average from the model, are contrasted and each is shown to have limitations. For the first, trends in bias and drift introduce higher skill estimates earlier and later in the hindcast period due to the trends that contribute to skill. For the second, higher skill can be introduced in situations where low frequency variability in the observations is large compared to the hindcasts on timescales greater than 15 years, while lower skill can result if the predicted signal is small and the bias-correction itself produces a transition of SST anomalies to the opposite sign of those that are observed. The third method has somewhat lower skill compared to each of the others, but has less difficulties with not only the long term trends in the model climatology, but also with the unrealistic situational skill from using observations as a reference. However, the first 15 years of the hindcast period cannot be evaluated due to having to wait to accumulate the previous 15 year model climatology before the method can be applied. The IPO transition in the 2014-2016 time frame from negative to positive (predicted by Meehl et al. in in Nat Commun, 10.1038/NCOMMS11718, 2016) did indeed verify using all three methods, though each provides somewhat different skill values as a result of the respective limitations. There is no clear best method, as all are roughly comparable, and each has its own set of limitations and caveats. However, all three methods show generally higher overall skill in the AMO region compared to the IPO region.