Good year/bad year correlation

Tony, or anyone else who might know,

Historically, how much correlation in snowfall is there between one year and the next? What I mean is, if one year is particularly below average, what are the chances the next year will be as bad, vs. average, vs. above average?

I know the answer doesn't give us any predictions, but hey, last year in Tahoe was SO bad that it makes me wonder, what are the chances this year will be better.

TIA!

user":1zbwdk64 said:

Tony, or anyone else who might know,

Historically, how much correlation in snowfall is there between one year and the next? What I mean is, if one year is particularly below average, what are the chances the next year will be as bad, vs. average, vs. above average?

I know the answer doesn't give us any predictions, but hey, last year in Tahoe was SO bad that it makes me wonder, what are the chances this year will be better.

TIA!

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I am sure it is quite variable like about everything else in life. I don't think it varies by a static number each year. My desire to make the season a great one does not seem to vary much or translate to the snowfall amounts!

I am wondering about a website that I found that claims that Heavenly Valley Ski Resort is the largest Ski Resort in the United States? Anyone know, care to know, or have a clue? Not that I really care one way or another about it; but, I dreamed of larger areas existing somewhere in the United States! Carol

Thanks for the reply. I'm not trying to imply that there's a "static number" - I realize in many ways weather is a random process that's difficult to predict. Otherwise, our weather forecasters would have an easy job! What I'm trying to get at is, if you do indeed look at snowfall amounts, number of storms, or length of season, if any patterns emerge from year to year.

For example in Tahoe, 2000-2001 was a horrible season, and then 2001-2002 was so-so. 1991-1992 was a disaster, and I can't remember what 1992-1993 was like, to be honest. I guess the root of the question is, do winter weather patterns generally follow a year-to-year variation, or are there multi-year patterns that play out when you look at the data? I'm sure this varies from region to region, and Tahoe is probably especially dicey, as it gets huge swings in snowfall totals from season to season.

Historically, how much correlation in snowfall is there between one year and the next?

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ZERO. Well, since you asked I calculated 40 years in California of season to next season correlation as -.04, which certainly means we can assume there is none. In California the 3rd (1975-76) and 1st (1976-77) worst seasons of the past 41 were consecutive. Last year was 5th worst. 1992-93 was 3rd best.

Some of the anecdotal impression of good years following bad comes from the instances when ocean temperature El Nino anomalies swing to La Nina by the next season. 1997-98 (El Nino) and 1998-99 (La Nina), both strong episodes come to mind. Also, the string of La Nina years in the early 1970's was interrupted by one strong El Nino (which produced record snow in Arizona and New Mexico) in 1972-73.

I've spent some time analyzing correlations from one month to the next within the same season. Not much correlation there either. There's a bit of a tendency for weather to persist, particularly in the early season and on the West Coast. When I updated my website this year I recalculated season standard deviations. I used to scale up them based upon monthly deviations. I now use season deviations directly and index areas with less data to nearby areas with complete data, as I've been doing all along for averages. The season deviations are thus slightly higher under the new method. The old method of scaling up monthly deviations assumed that month-to-month is completely independent.

Acreage sometime works as a good measure of size and sometimes not. Heavenly is a good example of not IMHO. There's a lot of flat unusable acreage between layers. I don't think anyone who has skied all 3 areas would think that Heavenly is even close to Squaw or Mammoth in usable ski terrain.

Big Sky/Moonlight also has a fair amount of unusable terrain, for the opposite reason of sheer cliffs that are never covered. I don't think there's much argument against Vail having the most usable terrain within a single area in the U.S. But Whistler alone is close to that size, and with Blackcomb included has far more.

The rest of the ski area size discussion is here: http://www.firsttracksonline.com/boards ... php?t=5799 .

Tony Crocker":21ptw1ak said:

Historically, how much correlation in snowfall is there between one year and the next?

Click to expand...

ZERO. Well, since you asked I calculated 40 years in California of season to next season correlation as -.04, which certainly means we can assume there is none. In California the 3rd (1975-76) and 1st (1976-77) worst seasons of the past 41 were consecutive. Last year was 5th worst. 1992-93 was 3rd best.

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I've only done some intro stats, but help me understand.

If things were close +1.0, does it mean one good year would be followd by another --- or one bad year followed by another?

And if things were close to -1.0, does it mean one good year is followed by a bad one and vice versa.

Correct. There is much uncertainty in snowfall stats.

The highest correlations are between snowfall at areas within the same region and/or sharing weather patterns. Squaw Valley and Donner Summit snowfall are 93% correlated. Portillo and Las Lenas are 69% correlated even though they are 200+ miles apart. Perhaps the most interesting example is that Mt. Rainier and Fernie are 80% correlated.

When you go to my El Nino/La Nina chart you see that effects are less predictable, with the most sensitive areas being +50% or -50% correlated on a seasonal basis and only +20% or -20% on a monthly basis.

The month-to-month correlations are weaker still. Averaging 24 areas where I have lots of data:
November to December: +19%
December to January: +9%
January to February: +20%
February to March: -1%
March to April: +11%
These numbers really mean little, as is evidenced by some of the individual areas. For example does anyone believe that Alta's -37% historical correlation of February to March snowfall has any predictive value? In fact 35 of the 120 month-to-month correlations are negative. But since the majority are positive, seasonal standard deviations tend to be somewhat higher than one would project based upon the monthly deviations.

Hopefully the above should convince you than a season-to-season correlation of -4% means nothing.

Tony Crocker":25s0szmp said:

Correct. There is much uncertainty in snowfall stats.

The highest correlations are between snowfall at areas within the same region and/or sharing weather patterns. Squaw Valley and Donner Summit snowfall are 93% correlated. Portillo and Las Lenas are 69% correlated even though they are 200+ miles apart. Perhaps the most interesting example is that Mt. Rainier and Fernie are 80% correlated.

When you go to my El Nino/La Nina chart you see that effects are less predictable, with the most sensitive areas being +50% or -50% correlated on a seasonal basis and only +20% or -20% on a monthly basis.

The month-to-month correlations are weaker still. Averaging 24 areas where I have lots of data:
November to December: +19%
December to January: +9%
January to February: +20%
February to March: -1%
March to April: +11%
These numbers really mean little, as is evidenced by some of the individual areas. For example does anyone believe that Alta's -37% historical correlation of February to March snowfall has any predictive value? In fact 35 of the 120 month-to-month correlations are negative. But since the majority are positive, seasonal standard deviations tend to be somewhat higher than one would project based upon the monthly deviations.

Hopefully the above should convince you than a season-to-season correlation of -4% means nothing.

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I operate on the following analysis. (I know it is basic for you), but I just need to bring people with me to make a judgement.

My understanding is the following:

1.0 +/- 0.33 worth nothing for correlation. So -0.04% is nothing, can it get closer to o.o?

1.0 +/- 0.33 to 0.66 a little interesting, but not much

and 0.66 to 1 or -0.66 to -1....very interesting....high correlation


Now to put some statements together, nothing is relevant of your stats but Squaw-Donner (which anyone would expect), but Rainier-Fernie is really interesting! Could you try to make hypothesis for this correlation - like storms from the SW hit Rainier and the Lizard (sp?) Range similarly?

Tony Crocker":2jnpwmlk said:

Hopefully the above should convince you than a season-to-season correlation of -4% means nothing.

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It does mean something...it means that you can't base this year's snowfall on the previous year.

Patrick":wxnukm1g said:

Tony Crocker":wxnukm1g said:

Hopefully the above should convince you than a season-to-season correlation of -4% means nothing.

Click to expand...

It does mean something...it means that you can't base this year's snowfall on the previous year.

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Well yes.

But it is so more interesting when you can find a relationship.

That is where any $$ is.....stats that people do not understand.

The other point to keep in mind with stats is quantity of data. 10 annual observations don't mean much, especially with data as volatile as snowfall. The formal definition is "confidence interval," which is the probability that an observed statistic is not random, and you will hear periodically of 95% confidence intervals, which will be much wider with less data. I have done little of this formal testing, but I'm generally suspicious of sketchy data.

40-50 observations is usually needed for meaningful information. So when some baseball announcer says that batter X is 3 for 5 against pitcher Y (or even that A-Rod was 2 for 29 in his last 2 post-season series) there is no statistical validity to such statements. It is possible that batter X hits the type of pitch pitcher Y throws well, or that the pressure gets to A-Rod in the postseason with the Yankees, but the number of data points in both cases is too low to draw a conclusion from a statistical point of view. The A-Rod example is also a selective use of statistics. His postseason record through 2004 was not that far off his in-season stats. Similarly, when someone draws a ski conclusion based upon the past 5 years, you can often tell that's it BS if you have 20+ years of data.

This is one reason I try to collect monthly stats if possible. For Portillo I was only able to get annual, so that correlation with Las Lenas is based on 22 observations, OK but not great. The Rainier/Fernie correlation is based upon 91 months.

I should refer the meteorological question to Larry Schick, but for weather systems going through Washington State, the area along the U.S. Canadian border is not as mountainous as many of the places farther away on either side of the border. So perhaps much of the moisture is funneled through that gap into the Lizard Range.

We skiers all know of localized snowy microclimates (Cottonwood Canyons, Targhee, Wolf Creek) that get way more snow than other areas close by. The Lizard Range is one of those, but if you read many of Craig Morris' reports you'll soon get the impression that Fernie is a slice of the Pacific Northwest 800 miles inland. Thus the low elevation rain incidence and much more wet and mild climate than Banff/Lake Louise, Panorama/Kicking Horse, or even Castle Mt. on the Alberta side of Crowsnest Pass from Fernie.