  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.
