Solar-cycle related variation of differential rotation is investigated through analyzing the rotation rates of magnetic fields, distributed along latitudes and varying with time at the time interval of August 1976 to April 2008. More pronounced diffe
rentiation of rotation rates is found to appear at the ascending part of a Schwabe cycle than at the descending part on an average. The coefficient $B$ in the standard form of differential rotation, which represents the latitudinal gradient of rotation, may be divided into three parts within a Schwabe cycle. Part one spans from the start to the $4^{th}$ year of a Schwabe cycle, within which the absolute $B$ is approximately a constant or slightly fluctuates. Part two spans from the $4^{th}$ to the $7^{th}$ year, within which the absolute $B$ decreases. Part three spans from the $7^{th}$ year to the end, within which the absolute $B$ increases. Strong magnetic fields repress differentiation of rotation rates, so that rotation rates show less pronounced differentiation, but weak magnetic fields seem to just reflect differentiation of rotation rates. The solar-cycle related variation of solar differential rotation is inferred to the result of both the latitudinal migration of the surface torsional pattern and the repression of strong magnetic activity to differentiation of rotation rates.
The latitudinal distributions of the yearly mean rotation rates measured respectively by Suzuki in 1998 and 2012 and Pulkkinen $&$ Tuominen in 1998 are utilized to investigate internal-cycle variation of solar differential rotation. The rotation rate
at the solar Equator seems to decrease since cycle 10 onwards. The coefficient $B$ of solar differential rotation, which represents the latitudinal gradient of rotation, is found smaller in the several years after the minimum of a solar cycle than in the several years after the maximum time of the cycle, and it peaks several years after the maximum time of the solar cycle. The internal-cycle variation of the solar rotation rates looks similar in profile to that of the coefficient $B$. A new explanation is proposed to address such a solar-cycle related variation of the solar rotation rates. Weak magnetic fields may more effectively reflect differentiation at low latitudes with high rotation rates than at high latitudes with low rotation rates, and strong magnetic fields may more effectively repress differentiation at relatively low latitudes than at high latitudes. The internal-cycle variation is inferred to the result of both the latitudinal migration of the surface torsional pattern and the repression of strong magnetic activity to differentiation.
In order to probe the mechanism of variations of the Solar Constant on the inter-solar-cycle scale, total solar irradiance (TSI, the so-called Solar Constant) in the time interval of 7 November 1978 to 20 September 2010 is decomposed into three compo
nents through the empirical mode decomposition and time-frequency analyses. The first component is the rotation signal, counting up to 42.31% of the total variation of TSI, which is understood to be mainly caused by large magnetic structures, including sunspot groups. The second is an annual-variation signal, counting up to 15.17% of the total variation, the origin of which is not known at this point in time. Finally, the third is the inter-solar-cycle signal, counting up to 42.52%, which are inferred to be caused by the network magnetic elements in quiet regions, whose magnetic flux ranges from $(4.27-38.01)times10^{19}$ Mx.
