The investigations of connection between the different meteorological processes, for example, the circulation indexes with the quantity of the total and lower cloudiness during 1961-2018 over Ukraine were made. The spatial distributions of the total and lower cloudiness were received for 73 years (1946-2018) at first. The quantity of cloudiness is diminished from west to east and with north to south. The declinations of the annual data of total and lower cloudiness from the historical (1961-1990) and the present (1981-2010) norms were calculated. The great variations were characterized for the lower cloudiness. The linear trends showed that the diminish of the lower cloudiness was on 90 % of the all territory, this changes were important on 70 % of the territory. The trends of the monthly variations were showed on the diminish of the lower cloudiness in during all year only on north, on other territory was the increasing in the separate months, frequently in January and September. The variations of the total cloudiness were insignificant, the increase or decrease were nearly in equal parts. North Atlantic Oscillation (NAO), Arctic Oscillation (AO), East-Atlantic Oscillation (EA), Scandinavian Oscillation (SCAND), Greenlandic Oscillation (GBI) and South Oscillation (El-Niño) were used for the investigation of relationship between the circulation indexes and cloud cover. It was shown that different circulation indexes have influence on climate of Northern Hemisphere and on Ukraine too. The relation with each other and their variations in period of global warming were showed. The quantity estimation of the total and lower cloudiness variations was made by the frequencies of clear, semi clear and overcast sky in the successive decades and by the relative variations of frequencies between decades (1961-1970 and 1971-1980; 1971-1980 and 1981-1990; 1981-1990 and 1991-2000; 1991-2000 and 2001-2010; 2001-2010 and 2011-2018). The parallel analyze of the variations of circulation was estimated in that time. The difference between the circulating processes during 1961-1970 and 1971-1980 contributed to a decrease in the relative frequency of the clear sky (on 5.4%) and a slight increase of the overcast sky (on 1.6%) by total cloud cover and a slight increase of the clear sky (on 0.8 %) and a decrease of the overcast sky (on 5.2%) by lower cloudiness. At the same time, the relative frequency of the semi-clear sky by lower cloudiness almost in three times increased in comparison to total cloudiness (on 10.2% and 3.8%, respectively). In the third decade of 1981-1990 the relative frequency of clear sky by lower cloudiness increased on 5.1% and did not change by total cloudiness (0%). During this decade the relative frequency of overcast sky decreased the most in the whole period under study: by total cloudiness on 6.4% and by lower cloudiness on 13.3%. At the same time, the relative frequency of semi-clear sky had largest increasing: on 22.4% for total cloudiness and 13% for lower cloudiness. Then, during 1991-2000, the frequency of clear sky decreased significantly both for total cloudiness (on 6.5%) and for lower cloudiness (on 3.1%). The frequency of overcast sky decreased also, but less significantly (on 1.3% and 2.3%, respectively), thereby the number of clouds of the middle and upper levels increased. From 2001 to 2010, the frequency of clear sky by total cloudiness and by lower cloudiness continued to decrease (on 5.3 and 3.2%, respectively), but the frequency of overcast sky increased (on 0.9 and 1.7%, respectively), thereby the number of clouds for all levels increased. During 2011-2018 the frequency of clear sky by total cloudiness increased (on 0.9%) and by lower cloudiness did not change. The frequency of overcast sky decreased on 3.6% (by total cloudiness) and on 0.7% (by lower cloudiness). The variations of the relative frequencies of the different state sky between the successive decades are agreed with the changes of the circulation indexes.
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