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The number concentration of cloud particles is a key quantity for understanding aerosol–cloud interactions and describing clouds in climate and numerical weather prediction models. In contrast with recent advances for liquid clouds, few observational constraints exist regarding the ice crystal number concentration (Ni). This study investigates how combined lidar–radar measurements can be used to provide satellite estimates of Ni, using a methodology that constrains moments of a parameterized particle size distribution (PSD). The operational liDAR–raDAR (DARDAR) product serves as an existing base for this method, which focuses on ice clouds with temperatures Tc<-30 ∘C. Theoretical considerations demonstrate the capability for accurate retrievals of Ni, apart from a possible bias in the concentration in small crystals when Tc≳−50 ∘C, due to the assumption of a monomodal PSD shape in the current method. This is verified via a comparison of satellite estimates to coincident in situ measurements, which additionally demonstrates the sufficient sensitivity of lidar–radar observations to Ni. Following these results, satellite estimates of Ni are evaluated in the context of a case study and a preliminary climatological analysis based on 10 years of global data. Despite a lack of other large-scale references, this evaluation shows a reasonable physical consistency in Ni spatial distribution patterns. Notably, increases in Ni are found towards cold temperatures and, more significantly, in the presence of strong updrafts, such as those related to convective or orographic uplifts. Further evaluation and improvement of this method are necessary, although these results already constitute a first encouraging step towards large-scale observational constraints for Ni. Part 2 of this series uses this new dataset to examine the controls on Ni.