GERALD R. NORTH AND KWANG-YUL KIM1
A method of signal detection used in communication theory can be applied to the problem of detecting forced climate signals. This method calls for the construction of an optimal filter (averaging procedure) which is then applied to a data stream that varies in both space and time such that the natural variability is suppressed to the maximum extent possible. The construction of such filters requires a good knowledge of the waveform of the signal and the frequency-dependent empirical orthogonal functions for the natural variability. Although we cannot yet supply reliable estimates of either of these from data or from coupled general-circulation-model simulations, we present some samples that are based on simple stochastic models. These exercises suggest that the signal due to sunspot forcing, while quite weak, can be considerably enhanced by using optimal filters. Greenhouse warming, modeled with a ramp increase of temperature, presents a large signal-to-noise ratio. Either the observed warming signal is highly significant, or the surface climate has experienced a very rare natural fluctuation over the last century.
To detect a faint signal that is superimposed on random fluctuations, it is helpful to know as much as possible about the characteristics of the fluctuations and the form of the signal. In the detection and attribution of forced climate signals we are faced with this generic problem. But precisely in what form do we need variability statistics? And how can we objectively employ variability statistics in our detection strategy? Can sensible statistical tests be applied using this information? Is there an optimal procedure that will assist us in formulating our questions clearly? Some of the answers lie in a class of techniques known to signal-processing engineers for over half a century, dating to the work of Wiener (e.g., as summarized in his 1949 book) and Kolmogorov (1941). Such techniques were first connected with the climate problem by Hasselmann (1979) and Bell (1982, 1986). Other approaches to the climate-change detection problem have been taken by Barnett and colleagues (e.g., Barnett, 1986, 1991). Several others are summarized in a recent book edited by Schlesinger (1991). Here I summarize the signal-processing approach as detailed by North et al. (1992).