We have developed a robust seasonality detector that uses singular spectrum analysis (SSA) and a chi-squared red noise test to extract statistically-significant frequencies from smoothed spectra computed with the discrete Fourier transform (DFT). SSA is found to provide a useful time-series decomposition into a low frequency trend, the total noise and periodicity, but is unable to extract individual cyclical components. We show that it is possible to identify these cycles in the frequency domain by applying a statistical-significance test to the smoothed spectrum such that: (i) spectral estimates at peak frequencies account for the largest proportion of the total variance and (ii) that the peaks are distinct from an equivalent auto-regression AR(1) red noise continuum. We apply this seasonality detector to 141 noisy and often fairly discontinuous time series of monthly mean anthropogenic SO2 loads over major cities and power plants in China extracted from ten years of OMI/Aura satellite observations between 2005 and 2015. We routinely observed the presence of an annual cycle (99 cases) but also a bi-annual cycle (60 cases) in the satellite data. This strong annual and inter-annual variability observed from space is also detected in co-located ground-based SO2 concentrations at the Xinglong observational station in Hebei Province, China.