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This paper is devoted to the analysis of air temperature and humidity changes during the two solar eclipses of 26 December 2019 and 21 June 2020 in Saudi Arabia based on data we collected from two different sites. We highlight the complexity of humidity's response to a solar eclipse, which is quite different from temperature's response. During the December event, the Sun rose already partially eclipsed, while for the June eclipse, it was only partial at Riyadh. This difference apparently affected the observed response on the recorded variables: temperature, relative humidity (RH), and vapor pressure (VP) in the two events. Changes in these variables went unnoticed for the first eclipse since they were within the natural variability of the day; yet for the other, they showed evident alterations in the slopes of the major parameters, which we analyze and discuss. A decrease in temperature of 3.2 °C was detected in Riyadh. However, RH and VP showed an oscillation that we explain taking into account a similar effect reported in other eclipses. We measured a time lag of about 15 min from the eclipse central phase in the city. Related fluctuations and dynamics from the computed rates of the temporal variation of temperature and RH are scrutinized. Furthermore, an overdue significant review of terrestrial atmospheric parameters is also offered in the context of the eclipse meteorology, particularly related to desert atmospheres. We also try to identify the influence of solar eclipses in similar environments doing a broad inter-comparison with other observations of these variables in the Near East, northern Africa, and in the United States. These inter-comparisons reveal how complex and dissimilar the response of the lower atmosphere to a solar eclipse can be within a desert environment and other similar environments. [ABSTRACT FROM AUTHOR]