Monday, June 5, 2017

Intricacies of Late Season Snowpack Statistics

The snowpack in the central Wasatch is going fast as temperatures sit well above average for this time of year, offering up a good opportunity for lessons in the intricacies of snowpack statistics.  

The graph below shows the snowpack water equivalent at the Snowbird SNOTEL site for this season (green line) compared to last season (red line), average (blue), and median (magenta).  I have added a dashed line during a period of missing data in late May and early June this season.  

Source CBRFC (My dashed line).  
Let's take a closer look at the graph from May through July.  As of midnight today (June 5), the snowpack water equivalent was 22 inches, which is 140% of median.  That sounds remarkably fat.  However, snowpack statistics can be very deceptive in the spring when the melt rates are fast.  Another way to look at it is that 22 inches is only 2 days behind the median.  Basically, we sit at the median for June 3rd, which doesn't sound anywhere near as impressive.  

Also evident in the plot above are important differences between median and average that arise late in the snow season.  The median is the point in the middle of the distribution of past observations.  For example, the median snowpack water equivalent for today is 15.8 inches.  Half of the seasons on record on this date were above that amount, half were below.  Starting yesterday, however, the average exceeds the median and the difference between the two grows with time.  "Average" may represent the mathematical mean, but it does not represent a typical snowpack.  

This is because there are a small number of years with fat snowpacks and many years with scant or non-existent snowpacks in late June.  As a result, the average strongly weighted by a small number of fat years (94/95, 04/05, 10/11 you know who you are).  June 18 represents the date at this site on which at least half of the years have no snow, but July 11 is the first day that the average is zero (no snow in any season at this site).  Saying that July 11 is the "average" date that the snowpack is gone is misleading.  Probably all but one year had no snow on that day. 

Real estate suffers from similar statistical oddities.   The average sale price in a neighborhood can be highly skewed by a small number of homes being sold at very high or very low values.  The median is in the middle of the distribution.  Trends in "average" home sales can be highly deceptive for this reason, especially in smaller neighborhoods that features a wide range of home types and sizes.  

The Snowbird SNOTEL has been losing about 2 inches of water equivalent a day for the past 5 days.  At that rate the site will lose almost half of its remaining snowpack by next Saturday morning.

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