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Narrow bands of snow can occur anywhere in the United States.  An excellent example of a narrow snowband occurred on November 20, 2015.  Below is a plot of the snowfall across southeastern South Dakota and northern Iowa.

Preliminary snowfall on November 20, 2015

Notice the large difference (or gradient) in snowfall from south of Interstate 90 to north of Interstate 90.  To the south of I-90, there was 12 to 18 inches of snow from the south side of Sioux Falls into far northwestern Iowa. North of Interstate 90, snowfall rapidly decreased to less than 6 inches, with no snowfall farther north toward Brookings and Marshall.  In fact, over a distance of approximately 20 miles, snowfall increased from 2 to 4 inches, to 16 to 18 inches.  

So why do the bands of heavy snowfall form?  And how can such an extreme gradient in snowfall form?  

There are three basic ingredients that are needed in the atmosphere to produce narrow bands of snow.  They are:

1.) Moisture

This first ingredient is rather obvious.  The atmosphere has to have enough moisture in the air to produce clouds and snow.  If there is not enough moisture, then snow will not develop.  For heavier snowfall, the atmosphere needs to continously bring moisture into the clouds so that snow continues to be produced and fall to the ground.  The more effectively the atmosphere is able to bring moisture to the clouds, the heavier the snow may be. 

2.) Front

A front is needed so that air is forced to rise in the atmosphere to produce clouds and snowfall.  In summer, we typically look for fronts near the surface to produce thunderstorms.  For narrow bands of snowfall, we are no longer looking at the surface for the front.  Instead we look for fronts located between 3000 and 15000 feet above the ground.  This forces air to be lifted in an area where the production of snow is most efficient.  Near the surface, the atmosphere typically does a poor job forming snowflakes, but as one rises in the atmosphere and temperatures fall to 0ºF to -10ºF, snowfall production can occur more rapidly.  So having a front located in the area where temperatures are in that range can force moist air to rise and quickly form snowflakes.

3.) Atmospheric instability

Atmospheric instability is needed to make the air rise even more quickly.  The quicker the air rises, the more quickly snow forms in the clouds and the heavier the snowfall is at the surface.  In summer, meteorologists talk about instability when looking for the development of thunderstorms.  The instability associated with bands of heavy snow in winter is much less than in summer, so it is rare to see thunderstorms.  For comparison, the typical thunderstorm has air rising well over 10 mph and in severe storms this can approach 100 mph.  For the most intense snowbands, the air is rising around 2 mph.  While much slower than a thunderstorm, this is still much higher than is typically seen in the atmosphere, and that speed is able to produce very heavy snowfall.  

Atmospheric instability impacts bands of heavy snow in two ways.  First, the less stable the atmosphere is, the faster the air rises and the heavier the snowfall.  Second, the less stable the atmosphere is, the more narrow the band of snow is.  Here are some examples.

 

Example of snow bands with high stability

For the first example, there is the same atmospheric stability.  The difference is that there is a weak front above the surface on the left and a strong front above the surface on the right.   On the left, with both a weak front and high stability, there is a broad area of 2 to 4" of snow and as one goes from north to south, the amount of snow changes very slowly.  Also the rate of snowfall is rather slow - typically much less than a half inch an hour.  Looking at the right figure, there is a stronger front but also high stability.  The stronger front will increase the lift so that there may be 6 inches in 12 hours and perhaps a half inch of snow per hour snowfall rate. But while there is a larger difference in snowfall from north to south, the change is still relatively little.  For example, looking near Brookings, the snow fall ranges from 1 inch north of Brookings to around 4 inches south of Brookings.  And the area of 4 to 6 inches covers a large area from Brookings to Sioux Falls.

Now let's look at what happens when we change the stability.

In both of these cases, there is a strong front present.  In the example on the left, there is also some instability.  With more instability than in the previous example, the strong front will produce much more snowfall perhaps as much as 10" in 12 hours.  The area that receives snow is a little bit smaller than in the previous two examples.  Notice also that to the north of the heavy snowfall, the amount of snow rapidly decreases from 10" near Sioux Falls, to less than an inch south of Brookings.  In this example, we show that the gradient in snowfall is larger to the north than to the south.  This is not always the case - there are events where there can also be a large difference (or gradient) in snowfall south of the heaviest snow.  In addition to getting more snow, notice that the snowfall rate is also higher.  In many of these cases, snowfall of an inch per hour for several hours is common.  This will make travel much more difficult since snow can quickly cover roads - even well travelled roads such as interstates. This example is most typical for bands of heavy snow over South Dakota, Minnesota, Iowa and Nebraska.  
 
The last example, on the right, is the most extreme example.  In this case, we have a strong front and a very unstable atmosphere (for winter).  In this case, the band of heavy snow is even more narrow.  In the example above, the heaviest snowfall - 10 to 15 inches - is only 10 to 20 miles wide and even the area that receives over 6 inches is relatively narrow.  In these cases, extreme snowfall rates can occur.  It is not unusual to see snow fall at the rate of 3 inches per hour or more for a few hours.  These events typically have a large difference (or very tight gradient) either to the north or to the south of the heaviest snow. In the example above, snowfall ranges from over 10 inches just south of the Iowa and Minnesota border to less than 4 inches north of Interstate 90.  In a few cases, there can be enough instability that thunderstorms can develop within the band of heavy snowfall.  This is the most rare type of snow band observed.
 
One final note - in these examples, we have assumed the band of snow is stationary.  In other words, once the band of snow forms, it stays in the same place until it ends 12 hours later.  The real atmosphere is much more complex.  In many cases, these bands of heavy snow may move.  How fast they move and in what direction they move will impact both the amount of snow in a particular location and the gradient in snow fall to the north, or south of the heaviest snowfall.  For example, if band of snow were stationary for 6 hours and then slowly moved south the last 6 hours, there would still be a large gradient in snowfall on the north of the heaviest snowfall, however, the gradient in snowfall will be less than what is shown in the example above.