Title: Is climate variability the result of frequency modulation by the solar cycle? Evidence from the El Nino Southern Oscillation, Australian climate, Central England Temperature, and reconstructed solar activity and climate records

Abstract: Oceanic atmospheric oscillations and climate variability are tightly linked and both exhibit broad band spectral content that ranges, with roughly equal strength, from annual to centennial periodicity. The explanation for variability based on the integration of weather noise leads to a spectral content heavily weighted to low frequencies; explaining the variability as resulting from solar forcing leads to a narrow band, approximately eleven year period, spectral content. In both cases the spectral content is incompatible with the observed spectrum. It is known that the Southern Oscillation is frequency modulated, i.e. the time interval between successive events varies on an approximately centenary scale. In this paper we develop a model of the Southern Oscillation responding to the slowly changing frequency of the solar cycle. This results in a frequency modulated oscillation, the spectrum of which is intrinsically broad and flat and therefore compatible with the observed spectrum. Fortunately, the change in frequency of the solar cycle with time has been reconstructed from tree ring data for the last millennium. It is possible to identify time intervals when the frequency was dominated by a single frequency in which case the model oscillation is relatively simple. The 11 year period component of the model time variation was shown to correlate closely with the 11 year period components of observed Southern Oscillation and climate variability. A characteristic of a frequency modulated variable, the equal spacing of spectral peaks, was utilized via a double Fourier transform method to recover solar cycle periodicity from instrumental and reconstructed climate records, with the recovered periodicity and the known periodicity of the solar cycle in good agreement. The concept outlined provides a new way of viewing and assessing the Sun climate connection.