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The millennial climate cycles are an important factor of global environmental changes. These cycles change the polar ice thickness during ice ages, what results in the Mean Sea Level (MSL) changes. The main cause of ice age periods are the so called Milankovich orbital cycles, generated by variations of climatic precession, eccentricity of the Earth's orbit and Earth's axial tilt with respect to its orbital plane with main periods of about 23 ka 1 , 40 ka and 100 ka, respectively. The common millennial cycles of MSL and Earth's orbit variations are studied by means of reconstructed MSL time series for the last 800 ka and insolation data of the latest orbital solution of Laskar et al. (2011). The models of the common millennial cycles of MSL and insolation variations are based on partial Fourier approximations with different period bands around 23 ka, 18ka, 11.5 ka, 7.5 ka, 6 ka and 2.3 ka, respectively. These models may help to analyze the Earth's rotation cycles caused by millennial solar activity cycles, such as Hallstatt cycles, and to point out new possible millennial cycles of the solar activity.

The solar activity affects all surface geosystems, including weather and climate indices, winds, rains, snow covers, mean sea level, river streamflows and other hydrological cycles. The mean sea level and polar ice changes cause common variations of the principal moments of inertia and Earth rotation with decadal, centennial and millennial periods. The mean sea level, Earth rotation and climate indices have also some oscillations with periods below 40 years, whose origin is not connected with the known tidal and solar effects. The shape of solar cycles is rather different from sinusoidal form, so they affect geosystems by many short-term harmonics. A possible solar origin of decadal variations of Earth rotation, mean sea level and climate indices is investigated by the harmonics of Jose, de Vries and Suess cycles with centennial periods of 178.7, 208 and 231 years. The common decadal cycles of solar-terrestrial influences are investigated by long time series of Length of Day (LOD), Mean Sea Level (MSL) variations at Stockholm, El-Niño/Southern Oscillation (ENSO), temperature and precipitation over Eastern Europe, Total Solar Irradiance (TSI), Wolf's Numbers W n and North-South solar asymmetry. A good agreement exists between the decadal cycles of LOD, MSL, climate and solar indices whose periods are between 12-13, 14-16, 16-18 and 28-33 years. The new linear models of the decadal common Earth and solar cycles may help for long term forecasts of many global and local changes.

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