Final answer:
Bombogenesis and snowfall duration are unrelated; bombogenesis is defined by rapid atmospheric pressure drop, not snow accumulation. The persistence of snow depends on the temperature, atmospheric conditions, and energy absorption.
Step-by-step explanation:
The concept of bombogenesis refers to a rapid drop in atmospheric pressure in a storm system, leading to intense strengthening of the storm. This meteorological phenomenon is not measured by the duration or amount of snowfall, so the question of how long snow needs to fall for a storm to be considered a bombogenesis is fundamentally misstated. Instead, bombogenesis is defined by a pressure drop of at least 24 millibars within 24 hours.
When snow does fall, the conditions that allow it to accumulate and persist involve a complex interplay between temperature and the heat energy available in the environment. Snow forms from ice crystals and is the solid phase of water. The transition between phases of matter involves significant energy exchange. A colder atmosphere slows down melting, while a warmer atmosphere accelerates it, contributing to how quickly snow might accumulate or melt after a snowstorm.
If it is warm enough that the sun can deliver 500 W/m² to the ground, but the snow reflects most of the energy, and only 5% is absorbed, that energy can still contribute to the melting of the snowpack. For example, this energy absorption would lead to some amount of snow melting over the course of an hour, depending on its density and mass.