An empirical model of global solar irradiance (EMGSI) under all sky conditions was developed by using solar radiation and meteorological parameters at Sodankylä. The calculated hourly global solar irradiance is in agreement with that observed at the ground during 2008-2011 and at the top of the atmosphere (TOA). Annual losses of global solar irradiance due to absorbing and scattering substances decreased by 0.02% and increased by 0.72%, respectively, and total loss increased by 0.24% per year. The contributions of annual mean absorbing and scattering losses to total loss were 63.32% and 36.68%, respectively, i.e., more energy was lost in the atmosphere by absorption. Global solar irradiance is more sensitive to changes in scattering than to changes in water vapor. The calculated the albedos at the TOA and the surface are in agreement with the satellite-retrieved values. The simulated albedos were smaller at the TOA than at the surface. During 2000-2018, the annual global solar radiation decreased and diffuse radiation increased. They were associated with the increases of the atmospheric substances and water vapor. Simulated and satellite-based annual albedos decreased at the TOA. Annual air temperature increased by 0.07 ℃. This empirical model can be used to calculate the global solar radiation at the ground and the TOA, as well as its attenuation in the atmosphere due to absorbing and scattering substances. Solar energy (including global solar radiation and its losses in the atmosphere, the reflection at the TOA and the surface), the atmospheric constituents (including gases, liquids and particles) and their long-term variations are essential to thoroughly understand the physical and chemical processes in the atmosphere, biological processes, and regional climate and climate change.