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Polarimetric radar systems are commonly used to study the microphysics of precipitation. While they offer continuous measurements with a large spatial coverage, retrieving information about the microphysical processes that govern the evolution of snowfall from the polarimetric signal is challenging. The present study develops a new method, called Process Identification based on Vertical gradient Signs (PIVS), to spatially identify the occurrence of the main microphysical processes (aggregation and riming, crystal growth by vapor deposition, and sublimation) in snowfall from dual-polarization Doppler radar scans. We first derive an analytical framework to assess in which meteorological conditions the local vertical gradients of radar variables reliably inform about microphysical processes. In such conditions, we then identify regions dominated by (i) vapor deposition, (ii) aggregation and riming and (iii) snowflake sublimation and possibly snowflake breakup based on the sign of the local vertical gradients of the reflectivity ZH and the differential reflectivity ZDR. The method is then applied to data from two frontal snowfall events: one in coastal Adélie Land, Antarctica and one in the Taebaeck mountains in South Korea. The validity of the method is assessed by comparing its outcome with snowflake observations using a Multi-Angle Snowflake Camera and with the output of a hydrometeor classification based on polarimetric radar signal. The application of the method further makes it possible to better characterize and understand how snowfall forms, grows and decays in two different geographical and meteorological contexts. For the Antarctic case study, we show that crystal growth by vapor deposition dominates above 2500 m a.g.l., aggregation and riming prevail between 1500 and 2500 m a.g.l. and snowflake sublimation by low-level katabatic winds occurs below 1500 m a.g.l.. For the event in South Korea, aggregation and riming dominate between 4000 and 4800 m a.g.l., with local sublimation below and vapor deposition above. We infer some microphysical characteristics in terms of radar variables from statistical analysis of the method output (e.g. ZH and ZDR distribution for each process). We finally highlight the potential for extensive application to cold precipitation events in different meteorological contexts. [ABSTRACT FROM AUTHOR]