Outline

1. Estimation and Extrapolation of Climatic Trends for Evaluation and Prediction of Climatic Anomalies Robert E. Livezey Climate Services/Office of Services/NWS/NOAA 31st Climate Diagnostics and Prediction Workshop Boulder CO, October 2006

2. Outline • Introduction: The Importance of Trends to Seasonal Prediction and Associated Challenges • Take-Away Messages • Existing Empirical Approaches and their Relative Accuracies (using contributions by Konstantine Vinnikov, Marina Timofeyeva, and Richard Tinker) • The Role of Models • Concluding Remarks

3. Using Trends in Prediction and Extrapolating Them: Context • As a practical matter, we don’t know with sufficient accuracy or confidence what regional or local climates are today! • This is because • the climate is changing rapidly, • we don’t have dynamical models that can credibly replicate the statistics of the current climate at spatial and seasonal resolutions important to operational prediction because they can’t credibly replicate past climates at these resolutions, and • we have put minimal effort into improving the inadequate empirical approaches currently used to estimate trend-related anomalies. The last include linear-trend fits and the Optimum Climate Normal (OCN).

4. Take-Away Messages • The United States has undergone dramatic climate change over the last 30 years or so and change is likely to continue. • Accounting for these changes, i.e. the estimation of the underlying climate and extrapolation of its change, is a critical component of seasonal to interannual prediction. • Little has been done over the last eight years to substantively improve and institutionalize operational approaches for estimation and extrapolation of trend. • There is considerable reason to believe that alternative empirical approaches are available that can provide these improvements now. In the near term this is our best opportunity for improvements to seasonal forecasts from any source. • Perhaps models can also be leveraged directly for this, but at the minimum they can probably usefully inform us about the nature of trend and used to test empirical approaches.

5. U.S. Trends

6. JFM

7. JFM

8. Common Methods for Estimating and Extrapolating Climate Normals • 30-year normal, updated every 10 years, available in 3rd year, persistence constitutes the forecast. • Optimum climate normal (OCN), average of previous 10-years (temp) and 15-years (precip), updated annually, persistence constitutes the forecast (CPC operational methodology). • Least-squares linear trend fit, extrapolation of fitted trend constitutes the forecast. • Intuition suggests that if the climate is changing rapidly and the change is dominantly linear, each successive method above will outperform the others. Vinnikov, et. al. have attempted to quantify this relative performance.

9. Theoretical Error in Estimates of Extrapolated Normals • Assume the time series of a particular monthly or seasonal average can be well represented by trend plus red noise, y(t) = Y(t) + y’(t) = a + bt + y’(t), where Y is the climate normal, σ the standard deviation of the stationary red noise with zero mean, g the one-year lag correlation, τ years from the end of the averaging or estimation period, i.e. the forecast lead, and β = b/σ the scaled trend (per year). • Let η(t) be the expected mean squared scaled (by σ) error of Y(t). As a reference, let an acceptable RMSE be 0.5σ, or η(t) = 0.25

10. Error in Estimates of 30-Year Normals • For β≥ 0.03, τ > 0, and all g, error exceeds acceptable limit. • Error insensitive to redness. • Except for weak trends error is already unacceptable at release.

11. Error in Estimates of OCN • For β≥ 0.10, τ > 0, and all g, error exceeds acceptable limit. • For β≥ 0.05, τ > 0, and all g ≥ 0.3, error exceeds acceptable limit. • Error still relatively insensitive to redness. • Error may be acceptable for moderate trends with small g.

12. Error in Estimates of Linear Fits • For any β, the error threshold expressed as the maximum τ is

13. Notes on Fitting Linear Trends • A linear trend fit should never be fit to a whole time series or a segment arbitrarily. • At a minimum the scatter diagram should be examined to confirm that the trend is not obviously non-linear. • Optimally the functional form of the trend should be based on additional considerations. • Very large-scale trends associated with global warming are approximately linear over the last 30-years but decidedly not over the last 40 to 70 years.

14. Notes on Fitting Linear Trends From Trenberth (2004) Presentation

15. A Hinge Fit for U.S. Trends • Piecewise continuous with no change from 1940-1976 and linear change thereafter. • An appropriate trend model with the reasonable assumption that the strong trends since the mid-1970s are related to global warming. • Livezey and Tinker (unpublished) demonstrated that the sampling variability of the hinge fit is substantially smaller than a linear fit to the last three decades. • Thus it will outperform the linear fit (Slide 12) if the underlying trend is dominantly linear.

16. A Hinge Fit for U.S. Trends • Recently redone by Timofeyeva, Tinker and Hollingshead (unpublished) with an additional 8 years of data and 10-year shift in the hinge point. • Results exceptionally robust.

17. Other Hinge Fits for U.S. Trends • Parabolic, cubical parabolic, or steeper. • Conclusions about relative (to non-hinge) performance the same.

18. Role of Models • IPCC ensembles spanning the last 50 years or so and the next decade or two: • To guide choices of empirical trend models. • To use for testing competing empirical approaches, because trends in model climate normals are known more accurately than in the real world. CFS hindcasts cannot be used for this purpose. • Possibly mixed statistical/model approach, i.e. diagnosed model Δ errors used to correct forecast trends • CFS hindcasts can contribute here. • Eventually fine-mesh, global coupled land-ocean-atmosphere models will be good enough to generate multiple realizations for close estimation of today’s climate.

19. Take-Away Messages • The United States has undergone dramatic climate change over the last 30 years or so and change is likely to continue. • Accounting for these changes, i.e. the estimation of the underlying climate and extrapolation of its change, is a critical component of seasonal to interannual prediction. • Little has been done over the last eight years to substantively improve and institutionalize operational approaches for estimation and extrapolation of trend. • There is considerable reason to believe that alternative empirical approaches are available that can provide these improvements now. In the near term this is our best opportunity for improvements to seasonal forecasts from any source. • Perhaps models can also be leveraged directly for this, but at the minimum they can probably usefully inform us about the nature of trend and used to test empirical approaches.