We introduce two methods to detect short-period variation in solar activity. These are called amplitude of low frequency fluctuation （ALFF） and fractional am- plitude of low frequency fluctuation （FALFF）. We find a positive correlation between short-period variation and 11-year variation of solar activity using these two methods. Through ALFF, we find that solar activity over a short period becomes intensive when the 11-year solar activity is intensive. The ALFF value of the short period activity varies with the peak in sunspot number as a quadratic function. Through FALFF we find that the ratio of short-period spectral intensity to intensity over the whole period of solar activity will increase when the 11-year period of solar activity is intensive. The short-period FALFF value varies with the peak in sunspot number according to a cubic function. Using ALFF, we obtain a yearly series of solar activity that varies over a short period of 1-5 yr from 1860 to 2003, which shows an obvious periodicity of about 22 yr, 33 yr, 11 yr and a century. These short period variations show good correlations with long term variations in solar activity.
In order to uncover a possible influence on the Earth's climate, we need a much longer time series, i.e., the total solar irradiance (TSI) which is also an interesting issue in its own right in solar physics. By comparing different solar indices associated with TSI during the period 1979 to 2009, several empirical models in the TSI are presented. We verify that the reconstruction model based on the three variables: sunspot number, sunspot area, and solar 10.7 cm radio flux, is the best one. As demonstrated by model calculations, the history of TSI was reconstructed back to 1947 based on 3-indices and to 1874 based on 2-indices, respectively. The reason that the reduced irradiance on the trough during 2006 to 2009 lasts long may be due to the about 85-year cycle of solar activity, which modulates the intensity of the 11-year cycle (Schwabe cycles), possesses a considerable potential to produce an effective reducing, and holds on a steadily lower level of irradiance.
