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 (PIVSs), 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, namely one in coastal Adélie Land, Antarctica, and one in the Taebaek 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. In particular, we are able to automatically derive and discuss the altitude and thickness of the layers where each process prevails for both case studies. 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.