does appear to be a small oscillation of the solar constant that is consistent with a modulation by the sunspot number. The amplitude of the oscillation appears to be about 0.1 percent. If we use this one cycle as a calibrator and ask what the temporal variation over the last century would have been, we can proceed to compute the climatic response of the earth. Figure 1 shows the curve of the global average temperature as computed by the Kim-North-Huang model. The response is a disturbed 11-year cycle with an amplitude of about 0.02°C, a very faint signal considering that the standard deviation of one-year averages for natural variations is about 10 times larger. This simple exercise suggests a signal-to-noise ratio of about 0.1, implying that the signal is virtually undetectable. On the other hand, if we use more information, which is fortunately at our disposal (at least from the model simulations), we can do much better.
Next we show the results of optimal filtering of the data to detect the surface-temperature response to the sunspot cycle. Figure 2 shows the geographical pattern of response to an 11-year periodic solar forcing in this model. When this pattern is included along with the precise phase and amplitude information represented in Figure 2, the signal-to-noise ratio squared can be plotted as a function of the number of fdTOFs included as shown in Figure 3. A monotonic increase in the signal-to-noise ratio can be seen as more fdTOFs are included. Hence, we have shown that the method is capable of improving signal-to-noise ratio through
the inclusion of geographical, frequency, and phase information in the filter. The signal-to-noise value of the order of unity is still short of acceptable for purposes of detection, but the sunspot cycle is used here mainly for illustration (although we think more can be done with the sunspot problem). Significant degradation will occur when we start to use real data instead of simulated data.
Confirming the existence of greenhouse warming consists of detecting a ramp-like increase of temperature over the last century. Our simulations show that the differences between the 1980 and the 1880 surface temperature fields should look like the map shown in Figure 4, which clearly shows the land-leading effect. If we expand our ramp-like response into sine and cosine harmonics of 100 years and into the fdEOFs at these frequencies, we can estimate the signal-to-noise ratio squared, as we did in the sunspot case. The result is shown in Figure 5. We find that greenhouse-warming detection is not helped as much by the addition of pattern recognition as sunspot-cycle detection, but the signal is large enough to be detected with considerable confidence. Thus, if our assessment of the low-frequency variance in the model is correct, either the greenhouse-warming ramp is real, or a very rare natural fluctuation with a positive slope of 0.5°C per century is occurring. (By a rare natural fluctuation we mean one that is 0.25°C above normal and lasts for a century.)
Signal-processing methods can significantly enhance our ability to detect forced climate response. It is important to