Identifying trends in climate: an application to the cenozoic

The recent literature on trending in climate has raised several issues, whether trends should be modeled as deterministic or stochastic, whether trends are nonlinear, and the relative merits of statistical models versus models based on physics. This article models trending since the late Cretaceous. This 68 million‐year interval is selected because the reliability of tests for trending is critically dependent on the length of time spanned by the data. Two main hypotheses are tested, that the trend has been caused primarily by CO 2 forcing, and that it reflects a variety of forcing factors which can be approximated by statistical methods. The CO 2 data is obtained from model simulations. Several widely‐used statistical models are found to be inadequate. ARIMA methods parameterize too much of the short‐term variation, and do not identify low frequency movements. Further, the unit root in the ARIMA process does not predict the long‐term path of temperature. Spectral methods also have little ability to predict temperature at long horizons. Instead, the statistical trend is estimated using a nonlinear smoothing filter. Both of these paradigms make it possible to model climate as a cointegrated process, in which temperature can wander quite far from the trend path in the intermediate term, but converges back over longer horizons. Comparing the forecasting properties of the two trend models demonstrates that the optimal forecasting model includes CO 2 forcing and a parametric representation of the nonlinear variability in climate. © 1998 Royal Meteorological Society