Abstract. in this paper a kriging method is reviewed and a way of its application in numerical weather prediction is proposed. The basic principles of the kriging are shown; the main advantage is its accuracy, but at the same time a disadvantage is its large computational complexity. The construction stage of the variographical model is highlighted, as it is the most important stage and has a significant impact on the accuracy of interpolation. The algorithm for the construction of the variographical model is described. special attention is paid to averaging an experimental variogram by introducing a special interval, called "lag". precisely this issue, according to the authors has a significant impact on the effectiveness of the practical application of kriging for the interpolation of meteorological parameters.The advantages of averaging an experimental variogram by the administration of lag are presented, and the error that arises in this case is estimated. a theoretical study for the determination of the optimal lag was conducted. The lag proposed for the determination is guided by the criteria of accuracy and the economy of computer time. The twocriteria problem is solved, and the formula, which makes it possible to determine the optimal lag on these criteria, is received. an example shown here is the application of the obtained results for solving the applied task associated with meteorological parameters forecast by the cosMo model.
In the late 20 th century, warming on the Antarctic Peninsula was most pronounced compared to other parts of Antarctica. However, air temperature showed a significant variability, which has become especially evident in recent decades. Thus, the investigation of air temperature trends on the Antarctic Peninsula is important. This study examines the extreme air temperature at the Ukrainian Antarctic Akademik Vernadsky station, located on Galindez Island, Argentine Islands Archipelago, near the Antarctic Peninsula. For 1951 to 2020, based on the daily air temperature data, the temporal trends of extreme air temperature were analyzed, using 11 extreme temperature indices. Based on linear trend analysis and the Mann-Kendall trend test, the TXn, TNn, TN90p, and TN90p indices showed an upward trend, whereas theFD0, ID0, TN10p, TX10p, and DTR indices showed a downward trend. Among them, annually, FD0, ID0, and TN10p significantly decreased by -0.427 days, -0.452 days, and -0.465%, respectively, whereas TXn and TNn increased by 0.164℃ and 0.201℃, respectively. The indices TXx and TNn showed no statistically significant trends. The average annual difference between TX and TN (index DTR) showed a nonsignificant decreasing trend at -0.029℃ year -1 . Thus, for the period of 1951-2020, the Ukrainian Antarctic Akademik Vernadsky station was subjected to warming.
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.
The distribution of drop effective radius on cloud upper level was defined and analyzed for main cloud forms over Ukraine during two years (2014-2015) using satellite observations. The effective radius values of isolated cumulonimbus on cloud top and its dependency on optical thickness was estimated in measurements during April-September 2014 over Kyiv area. For cumulonimbus clouds with precipitation the dependence of effective radius on the type, precipitation intensity and liquid water path was defined. The distribution of drop effective radius on cloud top in the strength frontal systems with heavy showers area over all territory of Ukraine was defined for two systems and it dependence on the cloud height and the precipitation type, their intensity and the liquid water path was estimated. For all types of clouds the size of effective radius of the droplets was 6 μm. In St and As cloud system droplets with this size of effective radius were observed in 100%, in Sc and As cloud system – 91-92%. The values of effective radius in Ns and Cb cloud system was close to 6 μm (71 and 89% respectively). Larger droplets (8 μm) in Ns were observed in 29% and in Cb in 9%. However, in Cb, accompanied by rainfalls and powerful thunderstorms, the values of effective radius were 10-15 μm (1.5%) and 25-45 μm (0.5%). In 75% of moderate precipitation cases were formed by drops with an effective radius of 6 μm and in 25% with an effective radius of 8 μm. For the heavy precipitated clouds, the drops with an effective radius of 8 μm (62%) had the highest frequency, in 33% the effective radius of 6 μm were observed. The larger droplets (≥10 μm) had a small frequency (5%). The drop effective radius for cases of heavy rainfalls was 8 μm in 75%, in 25% larger droplets were observed (10, 15 and 30 μm). More intense rainfall was accompanied by greater values of cloud water content and, accordingly, greater effective radius values. The cases with large values of microphysical parameters and precipitation were observed as streaks in frontal cloud systems.
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