How vulnerable is a region or location to having a good or bad snow year relative to its "average" year?
For many, these few plots will simply confirm what you already know about snow but sometimes it's nice to see it in the data. The question was addressed using 551 SNOTEL stations which have 25 or more years of Snow Water Equivalent (SWE) data (many extend to 35 years of data). SWE is used as it is a more robust measurement (compared to snow depth), however, SWE does not tell you if snowfall was heavy cement or blower pow. Most skiers know that there's a gradient from the slightly heavier snow of the maritime regions (Cascades, Sierra) through to the lighter snow of continental Colorado. Also, a couple of quick notes:
Figure 1:Snowfall regime cumlative distribution functions (CDF's) for all 551 stations. The dashed line and annotated text indicate the value of the CDF Index as used in the section near the bottom of the page.
To make describing this problem easier, the CDF's are placed into five representative groups (C1, C2, C3, C4, C5). The average CDF for each of these CDF's is shown in the below plot (Figure 2). There are 128 stations in C1, 237 in C2, 137 in C3, 27 in C4 and 22 in C5.
Figure 2:Average of the grouped snowfall regime cumlative distribution functions (CDF's)
We can now use this characterization to see how these different snowfall regimes are distributed across the Western US. Is the usual snowpack the result of several (relatively) larger events or is it composed of numerous smaller events? We can see that there is a general gradient from the north-east to the south-west in the type of snowfall regime. The mountains of Arizona and New Mexico rely on fewer larger storms for their snow, as does the Lake Tahoe region. The quality of skiing can be erratic in these locations; those in California who sufferered through the rather poor 2013/2014 ski season will no doubt be well aware of this. Most of the stations in Utah fall into C2 and C3. The San Juan mountains of Colorado are similarly in categories C2 and C3. In contrast, the spine of the Cascades is mostly in C1, as is Northern Idaho. Central Idaho contains many categories.
Figure 3:Spatial distribution of snowfall regimes. The categories C1 (light) to C5 (dark) relate directly to the different colors on the map.
The map above is relative to the average snowpack of a given location. While many stations in the Lake Tahoe area and New Mexico are in the same category of snowfall regime, the average snowpack in Tahoe is considerable larger so even the relatively small storms can make for some good skiing. The map below shows the average annual maximum SWE for each station.
Figure 4:Map of mean annual maximum Snow Water Equivalent (SWE) for each station.
So far we have looked at the snowfall regime, but this hasn't actually told us about the reliability of the average snowpack for a given location.
A simple metric that can inform us about the reliability is the Coefficient of Variation (CoV) of SWE.
To obtain the CoV, gather a timeseries of the SWE for each year, compute the standard deviation of this series (which is a measure of variability) and divide it by the mean of the timeseries so as to "normalize" the data and allow us to compare all the stations on a equal footing. i.e.
Figure 5: The distribution of the coefficient of variation (CoV) for all stations within each of the groups.
The CoV was calculated on the first of each month (Jan-April) so as to assess its progression through the
main portion of the ski season. The red line passes through the median value of each group. Note that the Y-axis for April is twice
that of the other months.
... but isn't the snowfall regime just a function of mean annual SWE?
An index has been created to help describe this matter - we'll call it the CDF Index. The CDF index is defined as the Percentage of Annual SWE per Snowfall Event that is found at the 85th percentile of all snowfall events. This value is shown by the dashed line in Figure 1; a lower value suggests many storms are needed to create the snowpack, while a higher CDF Index value suggests that a fewer (but larger, % wise) snowfall events make the seasonal snowpack. If we look at the relationship between mean annual maximum SWE and the CDF Index, we can see that in general, the lower the SWE, the higher the Index, meaning that places with lower SWE are subject to getting their snow from occasional storms. However, the important item to note in this graph is that there is a rather large spread in annual maximum SWE for a given CDF Index value, so it's not just a down to this single factor.
Figure 6: X-Y plot of Mean Annual Maximum SWE vs. CDF Index. A large spread in values exists along with a general inverse relationship between the two variables. The light blue line is a 2nd order polynomial fit.
Lastly, remember that we are talking about general statistics here. Any location can be subject to an epic storm or a lack of quality snowfall that is enough to make the locals restless. Additionally, SNOTEL stations are not necessarily located at ski areas and as we know, snow distribution can be highly heterogeneous.