FIGURE 3. Difference of zonally averaged brightness temperatures at two latitudes versus time.

The planetographic latitudes are 3.6° and 15.5° north and south, and the plot is given for spectral regions representing methane emission (7.8 m) and ethane emission (12.2 m), showing one-s.d. uncertainties. Peak values represent brightness temperatures higher at latitude 3.6° than at latitude 15.5°. Open circles represent data taken at the IRTF or the Bok Telescope and filled circles represent data taken at Palomar Observatory (1995), at the W. M. Keck Observatory (1998, 2004) or using the Subaru Telescope (2005, 2007). Methane brightness temperature differences between 3.6° N and 15.5° N are denoted by blue symbols, and those between 3.6° S and 15.5° S, by green symbols. Ethane brightness temperature differences between 3.6° N and 15.5° N are denoted by orange symbols, and those between 3.6° S and 15.5° S, by red symbols. Despite evidence for the non-uniform distribution of ethane with latitude⁷, a high correlation between the variations in brightness temperature differences at 7.8 m and 12.2 m exists for all years (except 1993 and 1995); we find that T_b[ 12.2 m] = 2.5T_b[ 7.8 m]  + 2.71 K, allowing us to plot the two sets of data as shown. The difference in T_b values can be attributed to the different vertical regions sampled by the two different wavelengths. A sinusoidal function that best fits the individual data (solid line) yields a period of 15.6 yr; a similar sinusoidal function that best fits an annual average of the data (dashed line) yields a period of 15.0 yr. The true time dependence is clearly not a simple sinusoid, and a correlation between the 1985–1992 12.2-m data and 1997–2007 data yields a period of 13.9 yr. The mean of the three calculated periods is 14.8  1.2 yr, which we take as our fitted value. The 1980 points, taken from convolutions of appropriate filter functions over Voyager-1 Infrared Radiometer Interferometer Spectrometer spectra from a north–south mapping sequence, were not considered in the fit of the sinusoidal function, although they are consistent with it.