Thundersnow is a snowstorm event in which thunder and lightning occur. An example is the classic 2011 thundersnow in Chicago that surprised Jim Cantore.
Thunderstorms accompanied by snow are usually of a different character than the "normal" thunderstorm. The latter are usually rather tall, narrow storms containing a rising updraft of warm, moist air that has risen in a layer from near the surface that may go upward to 40,000 feet or more. Temperatures at the surface are usually well above freezing.
Snowstorms, by contrast, are mostly associated with rather extensive layers of flat, relatively shallow cloud. Precipitation in the clouds is usually formed below 20,000 feet, as sketched in the first diagram on the right. Upward and downward motions in ordinary snowstorms are rather gentle. The exception is lake-effect snow, where the clouds are created by heating of air moving over relatively warm lakes. Lake effect snowstorms have narrow clouds shaped more like ordinary thunderstorms, and actually sometimes develop thunder and lightning.
Most thundersnow events develop when "ordinary" flat, layered snow clouds develop upward bumps or "turrets", as illustrated in the second diagram. They rise upward above the rest of the flat snow cloud by about 5,000 feet. These turrets can develop when there is some strong lifting mechanism around the 20,000 foot level, such as an approaching strong mid- and upper-level trough. Winds with the upper trough bring in colder air aloft, and the lifting also cools the layer. Air cools as it rises.
When the air above the initial cloud layer is relatively cool and dry, and when the added cooling and lifting is strong, a shallow layer just above the original flat cloud can become unstable. This makes it favorable for "elevated convection" – showers or thunderstorms. The rising turret is the result, containing vigorous upward and also some downward motions. There is usually more than one turret that forms in these conditions. There can be bands or a checkerboard pattern of turrets present.
When the unstable layer develops where the temperature is about -10 to -20 degrees Celsius (+14 to -4 degrees Fahrenheit), conditions are favorable for both snowflakes and small hailstones (called graupel) to form. As these different particles interact, electrical charges can develop. It's a similar process to developing static electricity when you slide your leather shoes across a wool rug. Stick out a pointing finger and watch the spark fly when you touch a metal object or another person! In the cloud case, that spark is lightning. Sometimes it's cloud-to-ground (as depicted in the third diagram) and often it's quasi-horizontal within the cloud.
That deeper cloud creates a deeper layer in which snow can form, and those stronger upward motions inside the cloud turret can condense snowflakes from the rising moist air at very high rates. So the same process that creates the electrification can also create a burst of heavy snow and sometimes small hail pellets (graupel) resembling sleet.
Thundersnow develops when the air is below freezing near the ground, and unlike most summer thunderstorms, it isn't near-ground air that rises all the way into the tall thunderstorm top. The instability is in only a shallow layer aloft. In thundersnow, the "action" mainly takes place in a rather shallow layer that is usually near 20,000 feet and only around 5,000 feet thick.
In the case of the Chicago thundersnow, a colleague (Tom Warner) tells me that most of the lightning bolts went upward between the tall buildings and the charge centers inside the cloud turrets.
MORE: Stunning Thunderstorm Photos
Lightning strikes over Zirje, southwest Slovenia, on May 24, 2012. (Marko Korosec/Caters News Agency)