What is the Probability of a Powder Day?

While some are hoping for Patrick to do his TR from Chile now that the northern season is winding down, I've used some of my time on the DL to crunch a few new numbers.

Riverc0il once defined 6+ inches new snow as "a powder day," so I searched the data for a few areas where I have daily info:
1) 7 years of the Jay Peak "snow tracker," both upper and lower
2) 10 years from Squaw Valley's similar web pages, also both upper and lower
3) 23 years from Steamboat mid-mountain

The objective was to find if there was a consistent relationship between monthly snowfall (where I have tons of data) and number of 6+ inch snowfall days (I also tested 12+ inch days) per month. If this works for the West Coast, Rockies and East Coast examples, then it could be applied to my entire data set.

The known high volatility in the Sierra was most likely to cause a problem I thought. But I was pleasantly surprised to find that Squaw and Jay Peak produced almost identical best fit lines for 6+ inch powder days. These days were somewhat more likely at Steamboat for average or better levels of snowfall, but the numbers for 6+ inches are so close overall that modelling that blended blue line in the graph below to other areas should be very reasonable.

The 12+ inch data conformed to my expectation, quite a bit more likely at Squaw than the other places. The other impression that was reinforced was the greater likelihood of small consistent snows in Colorado. Steamboat's lowest month in the entire data set was 16.5 inches. 16% of Jay's months and 18% of Squaw's were lower than that.

A couple of examples of expected powder days to illustrate:

A month with 105 inches snowfall expects:
7.4 days of 6+ including 2.6 days of 12+ at Jay
7.3 days of 6+ including 3.9 days of 12+ at Squaw
8.0 days of 6+ including 2.0 days of 12+ at Steamboat
7.5 days of 6+ including 2.8 days of 12+ blending all 3 areas as shown in the graph below.

A month with 51 inches snowfall expects:
3.5 days of 6+ including 0.7 days of 12+ at Jay
3.5 days of 6+ including 1.3 days of 12+ at Squaw
3.5 days of 6+ including 0.6 days of 12+ at Steamboat
3.5 days of 6+ including 0.9 days of 12+ blending all 3 areas as shown in the graph below.

I also used the daily data to assemble weekly data, to answer that perennial question, "How likely am I to get some good powder on my one week vacation." I scaled up the Steamboat and Jay daily data to fit Alta's (the consensus powder icon) December-March monthly average of 92.56 inches. I did not use Squaw in this exercise because its volatility is much higher than the other 3 areas.

So what is the expectation of a 7-day advance-booked trip to Alta between Dec. 1 and Mar. 31?

About 1/4 of weeks (0-23rd percentile) will have no days of 6+ inches.
Another 1/4 of weeks (24-51st percentile) will have one day of 6-11 inches.
The third quartile (52-74th percentile) will have 2 days of 6+ inches. From the 60th-74th percentile one of those days will be 12+.
Now for the lucky people:
The top quarter will have at least 3 days of 6+
The top eighth will have at least 2 days of 12+
The top 10% will have at least 4 days of 6+
The top 5% will have at least 5 days of 6+ including 3 days of 12+.

I'm sure you all know that Alta is a best case scenario. At Jay, Squaw and Steamboat (all well above average snowfall areas) the probability of a 7-day trip having no 6+ inch days is around 40%. For a more typical resort averaging 250 inches a year, I'll bet it's more like 60%.

So for most of you who think you're unlucky on advance-booked destination trips, the reality is you're probably not.

Comments are welcome, so fire away!

There appears to be significant variation in the actual data points even if the best fit regression works generally well. What are the confidence intervals used, std deviation for each resort, etc...?

Thread hijack warning - Unrelated, but numerically driven: I forget what thread it was back during the season that brought up the analysis/statistical concept of which areas ski bigger or smaller and could you define it based on acreage, vert, etc... I took data for several 'key' stats from about 30 areas and played with it for a bit and the best answer I can come up with is to ADD vert to acreage.

It gives nearly the same answer as any other combination of multiple stats (snowfall, lifts, % expert, etc..), weighting the importance of the stats, dividing stats, multiplying stats, etc... I tried a bunch of methods and stats and the end results I got showed that the two stats added provided nearly the same answers. If you wanted you could divide by 1000 or another factor to get numbers in a smaller scale, etc... but still the same relative scaling by going as simple as possible...

Try it and let me know what you think (or I might someday re-find the spreadsheet I was playing with it in from back a few weeks ago...).

I appreciate measuring snow quantity in terms of powder days rather than total snowfall. For example, Jay got 10" more this year than last year but last year's season at Jay was far superior to this season, IMO. Total snow fall doesn't tell half the story, especially in the East where snow melt and consolidation can occur within a day or two of a storm. Frequency of powder days and refreshed conditions can not be overlooked. While I put my personal measurement at 6", I could see why many folks would put the measurement at 12" so having both measurements is solid and shows so frequency differences. Also shows that Jay measures up pretty well to some western destinations. And what goes for Jay pretty much goes for all the larger mountains north of I-89.

The standard error for the individual areas is a bit over 3%, which is one day out of a month. For the chart blending the 3 areas it's more like 1.5 days. As long as that function is linear, my application of it isn't that dependent upon the error. I'm only going to use it to say, "Alta's 92.56 inch December-March average implies that 22% of those days will have 6 inches or more new snow."

My current thinking on area size is to use acreage but adjust it based mainly upon average pitch (lift ratios of 4 length to 1 vertical are typical), but also for lots of unusable terrain.

Conceptually, acreage represents horizontal variety and what we skiers want is vertical variety. So I think that's what EMSC and I are both trying to accomplish.

I don't know if EMSC applied his method outside Colorado, but most measures work well inside Colorado due to similarities among the areas.

A likely overstatement of ESMC's method: Snowmass 4,406 vertical + 3,128 acres = 7,536. Over half that acreage is much flatter than average, at least 5 to 1 length to vert.

Compare to average overall steepness Mammoth 3,500 acres + 3,100 vertical = 6,600 or steeper than average Snowbird 2,700 acres + 3,100 vertical = 5,800. Or Alta 2,000 acres + 2,000 vertical = 4,000.

Anyone who says Snowmass has nearly twice the ski/vertical terrain variety of Alta ... I'm not buying that. Criticism is intended as constructive; I obviously tried to select a specific example where it didn't look so good. Better to put together a spreadsheet of 30-50 areas and maybe only a handful look unreasonable, so fix those.

Riverc0il's observations make total sense. Jay season snowfall was similar last year to this year. But this year was spread somewhat over the whole season while last year almost 2/3 of the snow fell in a 2-month+ period (Feb. 14 - Apr. 18). So no surprise there were more big powder days in 2006-07.

Colorado's snowfall also tends to be spread over more months as a rule. November and April averages are closer to the winter months than in other regions. Therefore a winter month (Dec.-Mar.) average is typically something like 46 inches. Put 46 inches into the Steamboat model (Steamboat itself is a high snow area averaging 64 inches) and here are the results for a 7-day trip:

60% of weeks will have no days of 6+ inches.
26% of weeks will have one day of 6-11 inches.
9% of weeks will have 2 days of 6-11 inches.
Only the top 5% of weeks will have a day with 12+ inches or more than 2 with 6+.

For those of you who travel, here's a list of popular destinations with winter monthly snowfall averages between 42 and 50 inches and similar variability of snowfall: A-Basin, Breckenridge, Copper Mt., the 3 major Aspen areas, Crested Butte, Monarch, Purgatory, Telluride, Taos, Killington, Sugarbush, the Park City group, Big Sky, Big White, Kicking Horse, Sunshine Village. And anyone listed on my website with an annual average less than about 240 inches is probably under 42 inches per winter month.

What is going on here is that there are a lot of days at these places with some new snow but less than 6 inches. So if the area is remote with good stashes and low skier density you can get some good powder after a few days of small accumulations.

I should also mention that 240 inches is typical annual snowfall in the Alps or high Andes resorts. Volatility is higher, so there would be more 12+ days than in the above model. You also might get a month with practically nothing, like I saw in La Grave and Chile in seasons that were considered above average overall. It is fortunate there is a lot of lift accessible off-piste in these places where powder can preserve for a week or more.

Anyone who says Snowmass has nearly twice the ski/vertical terrain variety of Alta ... I'm not buying that. Criticism is intended as constructive; I obviously tried to select a specific example where it didn't look so good. Better to put together a spreadsheet of 30-50 areas and maybe only a handful look unreasonable, so fix those.

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Been out of town for a while. I suppose I shouldn't start up a topic the day before leaving for a couple weeks.

My attempt was more along the lines of your final sentence. Going for a relatively easy method of comparison instead of having to unbury length/vert stats for major lifts, etc... (if they are even published/available for some areas). There will be exceptions in my basic formula, but based on the 30 I had previously looked at there are far fewer exceptions/adjustments needed than I had thought would be the case.

In your specific example, Snowmass would 'feel' like it skied a lot better/steeper if it had better lift layout/more lifts directly into the good terrain. Which is one variable that seems nearly impossible to put an objective numerical factor on (lift layout/efficiency).

Perhaps we should do like Golf courses do. They have a complicated 'slope' rating based on extensive detail of every hole (# & placement of bunkers, # & placement of trees, width of fairways, length, etc... , etc...). Maybe the next answer is to create a complex, but objective tool to apply to ski resorts. I can smell the consulting dollars coming our way already :lol:

My first take on this subject was to construct a "variety index<" where 1 = 1 run of 1,000 vertical. Nice in theory, but you need to actually go out and ski an area fairly extensively to construct this measurement. And if the terrain includes much in the way of high alpine or skiable glades it's still going to be somewhat subjective.

Another problem with vert + acreage is when you go to eastern areas that are nearly all cut trails. An extreme example Whiteface 3,166 lift served vertical, 225 acres (of which 35 are the rarely skiable Slides) plus 28.5 acres glades. Mammoth (same vertical) is 3,500 acres. Do we believe ski variety ratio is really only 2 to 1, or is it closer to the 14 to 1 represented by acreage alone?

I'm still inclined to use acreage, then adjust for average pitch that deviates substantially from the 4 to 1 length to vertical intermediate benchmark. Whiteface's upper lifts are actually about 3 to 1, so its acreage would be adjusted upwards. I suspect variety ratio vs. Mammoth is something like 10 to 1.

Finally found the data and added most of NA just to see how it fares.

My inclination is to go one of two ways... very easy/simple with readily available data such as the vert+ acreage (instead of looking up or figuring out pitch ratios - which can vary wildly across a large resort too) or to go all the way and do a detailed model ala Golf Slope analysis. Not that I have time for such a detailed model right now, but could be an interesting project...

Tony Crocker":2jhmzvbv said:

Riverc0il once defined 6+ inches new snow as "a powder day,"...

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HA! In the Northeast maybe. Here in the intermountain west, "it's not a powder day if you can feel bottom on each turn". In the Wasatch that equates to at minimum, 9", but far more typically, 12" - 18". On a 4% day, it'll be more than 24" on that metric. 6" is the lower limit of when you might consider calling in sick.

That's a long list of 280 areas! But most of us would look at it and see quite a few relationships that don't make sense.

For the big areas, most people have skied them, and a panel of FTO ski junkies could probably reach a consensus on ranking them in size order.

For the smaller areas, pitch ratios are derivable whenever you have a trail map that has vert and length of the lifts. From what I saw in the East, my inclination is that most of the areas would be marked down for having more than the benchmark 4 to 1 length to vertical ratio. Yet I easily found a Whiteface map online, and thus know that its acreage would be adjusted upwards due to mostly 3 to 1 length to vertical ratio.

We also have to examine acreage numbers for credibility/consistency. Does anyone believe that Smuggs 1,000 acres and Stowe 480 acres make any sense?

Yes, the 6 inches is somewhat arbitrary. But we're not counting at all the situations with 4 inches 3 days in a row, so that's somewhat of an offset. I'll remind the Utards as a reality check that Snowbird's average water content (1979-1995) is 8.3%.

I do in principle agree with the definition "it's not a powder day if you can feel bottom on each turn." Lots of variables affect that, notably pitch and water content as well as depth of new snow.

Since I did regressions at both 6 and 12 inches, you could interpolate a linear function for a different benchmark. But coincidentally 6 inches turned out to be a point where daily volatility is quite accurately modeled by monthly volatility.