## 1 Introduction  
Primary cosmic radiations or cosmic rays are composed of highly energetic particles, mainly protons. Those particles can be classified by origin to two main components: galactic cosmic rays (GCRs) that come from outside our solar system and solar energetic particles (SEPs) that originate from an eruptive process on the sun. The high-energy cosmic-ray particles that enter the Earth's atmosphere cause nuclear spallation reactions with atmospheric atoms, mainly oxygen or nitrogen atoms, in the stratosphere and the upper troposphere. The electromagnetic cascades produce various secondary radiations such as electrons, pions, neutrons, etc. These nuclear reactions also produce many cosmogenic nuclides such as \({}^{3}\)H, \({}^{7}\)Be, \({}^{10}\)Be, \({}^{14}\)C, and \({}^{36}\)Cl that fall out onto the ground with almost constant rates. Those nuclides provide useful information related to geoscience, and much research has actively been performed in the relevant field [1; 2; 3; 4; 5]. Particularly, cosmogenic nuclides in snow and ice in polar regions at high geomagnetic latitudes can tell us about the long history of solar activities, including extreme solar particle events that affect cosmic radiation intensities and resultant cosmogenic production rates [6; 7; 8]. Production rates of cosmogenic nuclides in the earth's atmosphere have been estimated by model calculations, and many modelshave been developed for this purpose over the past 70 years. The first models [9; 10; 11] were based on simplified functions expressing the cosmic-ray-induced cascade process. Since the 1980s, Monte Carlo simulation codes were developed to describe the stochastic process of the spallation reactions in more detail [12; 13; 14; 15; 16; 17]. In addition, an analytical model based on comprehensive Monte Carlo simulations has been lately developed [18; 19]. Cosmic radiation can change the physical-chemical properties of the atmosphere, such as ion balance and temperature, and may subsequently affect regional climate variability [20; 21; 22; 23]. It has been considered that ionizations induced by cosmic radiation in the atmosphere contribute to the production of many ions that are followed by various reaction processes that may cause different climate parameters. More accurate prediction of long-term climate change needs a more reliable model that can precisely describe the atmospheric ionization processes in the atmosphere, especially in the polar regions. Aside from the effects on the atmospheric compositions, direct exposure of humans to cosmic radiation at high altitude has become a subject in view of health [24]. According to the fact that the dose level of the cosmic radiation is elevated with altitude and reaches a level about 100 times higher at the cruising altitude of a commercial jet aircraft than that on the ground, the International Commission on Radiological Protection (ICRP) has recommended that exposure to cosmic radiation of aircraft crew should be managed as an occupational exposure [25; 26]. ICRP recommended in a recent publication [27] that frequent flyers also be informed of their dose levels in aviation. Following these recommendations, the individual doses received from cosmic radiation onboard aircraft have been assessed by using numerical models. Several easy-to-use program tools for aviation-dose calculations were developed based on those models and have been provided by different groups. Those are CARI [28], PCAIRE [29], SIEVERT [30], AVIDOS [31], EPCARD [32], JISCARD EX [33], and other models [34]. Periodic verification of the accuracies of those programs including intercomparisons [35; 36] is crucially important for reliable dose assessments of aircraft crew and frequent flyers. Furthermore, there are concerns about possible errors by many avionic electronic systems during a flight due to the hits by cosmic radiation, particularly high-energy neutrons [37; 38].