Kernel density estimation is a technique for estimation of probability density function that is a must-have enabling the user to better analyse the studied probability distribution than when using a traditional histogram. Unlike the histogram, the kernel technique produces smooth estimate of the pdf, uses all sample points' locations and more convincingly suggest multimodality. In its two-dimensional applications, kernel estimation is even better as the 2D histogram requires additionally to define the orientation of 2D bins. Two concepts play fundamental role in kernel estimation: kernel function shape and coefficient of smoothness, of which the latter is crucial to the method. Several real-life examples, both for univariate and bivariate applications, are shown.

No abstract

No abstract

This study aims to characterize temporal and spatial trends of sunshine duration in Poland based on data from the years 1971-2018 and to make an attempt to explain their causes. Daily sunshine duration came from 31 Polish meteorological stations. Data from 10 stations came only from a traditional Campbell-Stokes heliograph, while in the other 21 synoptic stations Campbell-Stokes heliograph was replaced with an automatic sensor in 2014 and since then only such data are available. The smallest sunshine duration occurs in December (average areal total-39.7 hr), and the highest in July (average areal total-230.1 hr). The spatial distribution of sunshine duration in Poland shows great diversity associated with different day lengths depending on latitude. In the cool part of the year (November, December, January, and February) the isolines of totals of sunshine duration run from the highest values in the south to the lowest in the north of the country, while in the months of the warm part of the year (March to September) the system is reversed. The multi-annual trends in sunshine duration in Poland are similar to the changes taking place in other parts of the world. The years 1971-1980 mark the end of "global dimming," which was manifested in very low values of actual and relative sunshine duration. "Global brightening" confirms a statistically significant growing trend in sunshine duration at all the analysed meteorological stations in Poland from April to September. There is a strong statistically significant relationship between the areal totals of sunshine duration and the type of pressure system, average monthly cloud cover, and atmospheric optical depth.

The article demonstrates the impact of atmospheric circulation on the long‐term variability of cloudiness (amount and certain cloud genera) in Kraków based on midday observations of the amount and genera of clouds in the period from 1 January 1906 to 31 December 2015. There was found statistically significant (although rather moderate) correlation between circulation indices and the frequency of cloud cover consisting of a single cloud genus or a group of clouds. The 11‐year moving averages of frequency of occurrence of one‐genus cloud cover show periods of alternating increasing/decreasing trends, some of which are multi‐decadal. Decreasing trends, lasting till now, are shown for Cirrostratus, Nimbostratus and Stratus beginning from the 1920s to 1930s and for Altostratus from the 1970s. The Cirrus, Stratocumulus and Cumulus trends are generally increasing from the 1920s, 1950s and 1950s, respectively.