Solar cycle warming at the Earth's surface in NCEP and ERA-40 data: A linear discriminant analysis

The total solar irradiance (TSI) has been measured by orbiting satellites since 1978 to vary on an 11-year cycle by about 0.08%. Because of previous controversies on the reality of solar cycle response at the surface, in this work we discuss the robustness of the solar response with respect to analysis methods, data sets and periods used. Furthermore we concentrate on the globally coherent signal. Two reanalysis data sets are used: one is from National Centers for Environmental Prediction and National Center for Atmospheric Research (NCEP for short) and the other is the European Centre for Medium-Range Weather Forecasts (ECMWF)'s most recent reanalysis denoted by ERA-40. Three analysis methods are considered, with increasing sophistication. Within each data set the analysis results are consistent with each other (i.e., each within the other's error bars), with the method of linear discriminant analysis (LDA) yielding the smallest error bar and the unfiltered global mean data yielding the largest error bar in the temperature amplitude. All three methods and both data sets are able to demonstrate that the 11-year signal is statistically significant and attributable (i.e., related) to the solar cycle. We deduce the spatial surface pattern over the globe which best distinguishes the solar maximum years from the solar minimum years using the LDA method. The resulting warming pattern shows clearly the polar amplification of warming and the preference for continents over oceans. We propose that the magnitude of the surface warming is consistent with direct solar radiative forcing if positive feedback processes such as ice albedo, water vapor/lapse rate and cloud feedbacks, similar to some of those studied for the greenhouse warming problem, are incorporated. It does not appear to be necessary to invoke some previously proposed exotic indirect mechanisms for an explanation of the observed solar signal.