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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 (N-i). This study investigates how combined lidar-radar measurements can be used to provide satellite estimates of N-i, 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 T-c < -30 degrees C.

Theoretical considerations demonstrate the capability for accurate retrievals of N-i, apart from a possible bias in the concentration in small crystals when T-c greater than or similar to - 50 degrees 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 N-i. Following these results, satellite estimates of N-i 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 N-i spatial distribution patterns. Notably, increases in N-i 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 N-i. Part 2 of this series uses this new dataset to examine the controls on N-i.