1. An Empirical Model of Decadal ENSO Variability Sergey Kravtsov University of Wisconsin-Milwaukee Department of Mathematical Sciences Atmospheric Science Group Collaborators: M. Ghil, ENS & UCLA; D. Kondrashov, UCLA; A. W. Robertson, IRI EGU General Assembly, Vienna, Austria May 2–7, 2010 http://www.uwm.edu/kravtsov/

2. Multidecadal-vs.-interannual climate variability: Are they separable? The simplest way to isolate lowest-frequency variability from the rest is to use temporal filters. Problem: The filtered signal is contaminated by noise. Various spatiotemporal filters may work better! Examples: EOFs (Preisendorfer 1988), M-SSA (Ghil et al. 2002), OPPs (DelSole 2001, 2006), DPs (Schneider and Held 2001), APT (DelSole and Tippett 2009a,b). Despite multidecadal and interannual variability may have different spatial patterns, which vary according to their respective predominant time scales, they may still be dynamically linked!

3. SST discriminants Patterns that maximize ratio of multidecadal to interannual SST variance (Schneider and Held 2001) ; SST data is based on Kaplan (1998). Time series correlated with global Ts This and next pattern ~AMO+PDO

4. Niño-3 decomposition Niño-3 SST is natu- rally dominated by interannual variability (DPs’ contribution is small) Niño-3 variance exhibits multidecadal modulation anti- correlated with the AMO index (cf. Federov and Philander 2000; Dong and Sutton 2005; Dong et al. 2006; Timmermann et al. 2007)

5. Methodology Model Niño-3 index x as a 1-D stochastic process where f is a polynomial function of x with coefficients that depend on time t (seasonal cycle) and external decadal variables y given by leading Canonical Variates (CV) of SST; dw is a random deviate. Study the numerical and algebraic structure of this model and use it to estimate potential predictability of decadal ENSO modulations

6. Properties of the empirical ENSO model-I

7. Properties of the empirical ENSO model-II

8. Properties of the empirical ENSO model-III

9. Algebraic structure of ENSO model F – potential function

10. ENSO Forecasts: Procedure Compute and extrapolate decadal predictors (CVs) Do stochastic-model runs forced by extrapolated CVs Compute probabilistic measures of ENSO events Compare with actual obs.

11. ENSO “decadal” forecast skill

12. Spaghetti-Plot of All Retroactive Forecasts The retroactively forecasts are much less impressive than hindcasts. Why? — CV extrapolation is not skillful!

13. Forecast skill of CV extrapolation One-discriminant based extrapolation is most skillful, and captures an anthropogenically forced warming trend. The inclusion of AMO/PDO related predictors lowers the extrapolation forecast skill. The latter lack of skill limits the predictive capacity of our empirical ENSO model (cf. Wittenberg 2009)

14. Summary These results argue that decadal ENSO modulations are potentially predictable, subject to our ability to forecast AMO-type climate modes. We used statistical SST decomposition into multidecadal and interannual components to define low-frequency predictors ( CVs ). An empirical Niño-3 model trained on the entire 20th- century SST data and forced by CVs captures a variety of observed ENSO characteristics, including multidecadal modulation of ENSO intensity. The retroactive forecast skill of this model is limited chiefly by the lack of skill in CV extrapolation.

15. Selected references DelSole, T., 2006: Low-frequency variations of surface temperature in observations and simulations. J. Climate, 19, 4487–4507. DelSole, T., and M. K. Tippett, 2009b: Average predictability time. Part II: Seamless diagnoses of predictability on multiple time scales. J. Atmos. Sci., 66, 1188–1204. Dong, B. W., R. T. Sutton, and A. A. Scaife, 2006: Multidecadal modulation of El Niño Southern Oscillation (ENSO) variance by Atlantic Ocean sea surface temperatures. Geophys. Res. Lett., 3, L08705, doi:10.1029/2006GL025766. Federov, A., and S. G. Philander, 2000: Is El Niño changing? Science, 288, 1997– 2002. doi: 10.1126/science.288.5473.1997. Ghil M., R. M. Allen, M. D. Dettinger, K. Ide, D. Kondrashov, M. E. Mann, A. Robertson, A. Saunders, Y. Tian, F. Varadi, and P. Yiou, 2002: Advanced spectral methods for climatic time series. Rev. Geophys., 40(1), 1003, doi:10.1029/2000RG000092 Schneider, T., and I. M. Held, 2001: Discriminants of twentieth-century changes in earth surface temperatures. J. Climate, 14, 249–254. Timmermann, A., Y. Okumura, S. I. An, A. Clement, B. Dong, E. Guilyardi, A. Hu, J. H. Jungclaus, M. Renold, T. F. Stocker, R. J. Stouffer, R. Sutton, S. P. Xie, J. Yin, 2007: The influence of a weakening of Atlantic meridional overturning circulation on ENSO. J Climate, 20, 4899–4919, doi:10.1175/JCLI4283.1. Wittenberg, A. T., 2009: Are historical records sufficient to constrain ENSO simulations? Geophys. Res. Lett., 36, L12702, doi:10.1029/2009GL038710..