colored topo maps

[montoya 0]

http://net.jmc.or.jp/saishiki/index.asp

http://net.jmc.or.jp/saishiki/MF_SearchSampleDigitalMap_k.asp

[soubriquet 0]

Thanks for the links

[jgraves 0]

Now if only I had a half-decent printer and a laminating machine.

[dizzy 0]

good link, montoya

 

you don't need a laminating machine once you have maps in hand. ziplocks work great.

[sock_monkey 0]

great link.

i have a decent printer and ziplocks!

[keba 0]

I won't say I'm a hard-core backcountry skier, 'cause I'm not (ducking under ropes is my limit). But as good as those maps look, they don't have gridlines for reference, so won't that make getting your bearings difficult, using GPS? Or do you guys use the old-fashioned way, picking out landmarks and triangulating?

[damian 0]

Hello Keba,

 

I don't use the above maps, but generally, grid references are only useful if you are writing out a detailed multi-leg navigational data sheet for a long hike the following day and even then I just use land marks and features for each leg. Some grids can be nice to exactly describe the start and end of each leg, but once on the ground the avalanche conditions tend to dictate your movements along a general route and you seldom take a direct line for 1200m heading Mag 274 degrees from GR 352753 to GR 270992, even if that's what you has written on you navigational plan.

 

Also, GR's aren't usually much use for GPS as depending on the country, the GPS grids are different to the 'normal' map grids. Many national topo maps have both grid systems marked and numbered in different colours.

 

As for knowing where you are: [unless you're using GPS] you don't need a grid system to know where you are on a map, in fact, a grid system can't tell you where you are, it can only describe in numbers where you are once you know where on that map that is. All you need to know is where Grid North is on the map. If I printed out a map on A4 like these guys are suggesting then I would take pencil and draw one north-south line on the map to use with my compass.

 

It helps to have a grid reference for your location if you want to tell other people exactly where you are for calling in artillery fire support, or a hit from an F16. Not something we will be doing in the back country. More likely is if you are calling a helicopter rescue and they want your exact location but even then, tell them what mountain you are on and what feature/aspect you are at and they will find you no worries.

[keba 0]

Thanks for clearing that up DB... I might try staying in-bounds, all that talk about avalanches and helicopter rescue has dampened my enthusiasm.

[damian 0]

 Quote:

Originally posted by keba:
I might try staying in-bounds, all that talk about avalanches and helicopter rescue has dampened my enthusiasm.

That is actually a very good call! (I'm not being a smart arse).

And I am not trying to compound your fears, just trying to prove for yours and others benefit that they are perfectly founded in reality. Here is a small quote taken from the following article, credits go to the dude at pistehors.com. His discussion in this piece is a good service to back country users.

Analyses of 2005/06 French Avalanche Deaths

check out Figure 3 in the above article. Doesn't look like much, does it? A small gully with thin cross loading due to the wind that blew from the picture's left to right. After getting off the lift 100's of skiers traverse this slope every day at Tignes. In Japan it would be roped off as it is not a groomed run. If this innocent picture doesn't scare you...

 Quote:

a British student was caught at the edge of the ski slopes in Tignes. The man was snowboarding with his brother when they decided to take a run which was closed due to poor snow cover. There had been 20cm of fresh snow coupled with strong westerly winds the day before. This had cross-loaded some dips with just enough snow to prove fatal. The man was not wearing an avalanche beacon and the delay of 30 minutes before rescue by members of the ski patrol was possibly fatal. His brother, who avoided the slide, was unable to believe that with so little snow the conditions were so dangerous despite the resort flying the black and yellow checkerboard flags

Also have a look at Figure 6, a classic example. Tracks all over the low angle powder, then one guy drops into a small slightly steeper bowl and is killed.

[keba 0]

Great article, DB, with some sobering anecdotes... I would not have thought twice about taking on the gully in figure 6 on a good weather day.

 

We take a risk every time we clip in. You go out of bounds, the risk increases. Experience and attention to conditions can mitigate the risk, but luck factors into it too. Doug Coombs was one of the best, and he didn't see it coming.

 

If we could guarantee our safety, would we be having as much fun?

[montoya 0]

timely post keba. Lately I've been thinking about this more, as we are in the mountains alot and unfortunately there are alot of accidents out there:

 

*do statistical odds accumulate?

*if the law of large numbers dictates that probabilities will be borne out if an event occurs often enough, is there anything you can do to lessen exposure?

*does individual choice mitigate the odds or frequency?

*is risk random or not?

*are random events governed by probability?

*can you reduce exposure to random statistical averages, for example by good skills?

 

probably someone with a stronger background in math or risk management will know more..

[keba 0]

Statistical odds do not accumulate. If you have a 1% chance of a bad outcome, then every single time you undertake the risk it is 1%. If you have 1000 people undertaking the same risk though, then about 10 people (give or take) will suffer that bad outcome. Who will be in that 10, and who will be in the 990? That is where the luck comes into it. Individual choice, skill level and experience do alter the risk, but there are factors that you won't be able to control. They are not strictly random though. Mathematicians would prefer the term "chaotic".

 

 

But I don't think skiing out of bounds with a calculator makes it any safer...

[montoya 0]

I also don't think statistical odds accumulate per se.

 

Still, that leaves me with law of large numbers, which your second example alludes to. Since the principle is that the probability of any possible event occurring at least once in a series increases with the number of events in the series, we can rephrase the example as 1 person (me) going out into avie terrain 100 days a season.

 

But, probably the observed frequency of an avie-accident will also vary on the type of risk as well (eg 25 degree slope vs 35 degree slope, timing of new snowfall, heavily forested area vs bowl terrain, etc).

[keba 0]

So many factors, and what is the baseline risk? Is it 1%, 5%, 10% or 0.001%? Considering the number of skiers/riders who put themselves in harm's way each season, the odds are pretty good that you will be fine.

 

Still, don't come crying to me when it all goes pear-shaped. You control your own destiny, and you don't want to be filling your head up with statistics and probability theory right before you take a cornice onto a 50 degree couloir 6 feet wide.

[damian 0]

Montoya... have you been lurking in my thoughts? Risk is my hobby and profession

 

Quoting yourself and keba:

 

Q. Do statistical odds accumulate?

A. If you have a 1% chance of a bad outcome, then every single time you undertake the risk it is 1%

 

Thats it.

 

Basically think of Roulette or Backgammon: neither the ball nor die has memory. Every event is independent, there is no serial correlation between events (Autocorrelation). Throwing a 1 doesn't change the probabilities if throwing another 1, or a 4. It is random sampling with replacement.

 

Veronica used to ask about her iPod and why the random setting would sometimes play the same song twice: that's because after that marble (song) had been randomly drawn from the bag, it was returned to the bag. V expected vPod to randomly sample and not replace, thus depleting the pool of songs and increasing the probability of that song by Bananarama eventually being played.

 

That is not the case with avalanche risk per se. If you are safe for 100 BC days in a row, the 101th does not carry a higher probability of death.

 

BUT:

 

1. The more you sample (roll a die), the more the distribution of probability will reveal itself, be that Gaussian (bell curve, normal...) or otherwise. So an event on that distribution will happen eventually.

 

2. For an avalanche death you need: slope, snow and people. It is the inclusion of people that causes the issue. Suddenly you have emotion (read into Behavioural Finance and decision heuristics) and you have very difficult to measure type of serial correlation between events. What happened last time nearly always influences your actions and thus what happens next time. Because of emotion, events are no longer independent and depending on your behaviour, statistical odds will accumulate.

 

So don't let your guard drop or you will be Walking Like an Egyptian sooner or later

[keba 0]

Who is Veronica, and why in the blue blazes does she want to hear a song by Bananarama?!?!

 

I'd rather take my chances with the avalanche...

 

[Rag-Doll 0]

Good thread guys and that is a great article. So many of those slides seem to take place on ground that we rope duckers seek out -scary stuff.

 

The whole probability thing did my head in at school - I understand the independance of one outcome to the next, but is there also a way of looking at the risk from a collective point of view? For example, the chance of getting heads in any particular coin toss is 50% but the chance of getting heads for 10 or 50 or 100 tosses in a row are much much lower. Hence a 1 in a 100 chance on any given day is very good, but the chance of avoiding avies over a life time of extended BC touring is probably quite low - or have I got that completely arse about?

[montoya 0]

we probably need to agree on some definitions before we can develop this further.

 

regarding terrain, "backcountry" in the widest sense can mean just a snow-covered area, regardless of slope angle. if it's flat, then I'm probably not at much risk regardless of how many days I'm out there. on the other hand, if you mean "+30 degree slopes" by avie terrain, that's a different story.

 

you would also need to talk about timing (eg green/yellow/red light days, proximity to storm cycle, etc).

 

experience/skill level, I don't know how you would quantify that. this is also related to the messy area that spud brought up, past behaviour/emotions influencing future actions.

 

there's also the concept of "risk" itself. here's one possible definition, I'm sure you risk management guys will have other variations:

risk = (probability of accident) x (consequences of accident)

[keba 0]

Montoya, I think we'd all agree that "backcountry" refers to non-lift accessed terrain, not "under the ropes" in-bounds. I like your definition of risk. The consequences of a bad outcome have to influence your judgement regarding a particular course of action. Take the choice between a 5% risk of dying, and a 20% chance of non-fatal major injury, or an 70% chance of a minor injury. I'd take option C.

 

Rag-Doll, but if the coin is weighted so that it only lands tails 1% of the time, the chance that you will throw 10 or 50 or 100 heads in a row is very good... If you think there is a 50-50 chance of getting caught in an avalanche though, you'd better take another line.

 

I think we just need to accept that we take a risk, when skiing outside patrolled areas, and we should try as hard as possible to minimise the risk, based on our relative experience and assessment of conditions.

 

Fact is, it can happen to any of us, anytime, regardless of how cautious we have been. Just not this season...

[SerreChe 2]

Spud thanks for the article/link, very interesting. Some of the spots are unfortunately familiar.

 

As for risk, you can only mitigate but never negate (in whatever you do). Your risk/reward ratio will ultimately dictate your behaviour and the people you hang-out with in the BC (hopefully).

 

Good luck and stay safe.

[damian 0]

Damn, I just spent my entire free 2 hours this evening writing this post. Half of it might be wrong, I am not an expert at all in this stuff.

 

 Quote:

Originally posted by Rag-Doll:

The whole probability thing did my head in at school

You might enjoy playing with Pascal's Triangle.

 

 Quote:

Originally posted by Rag-Doll:

the chance of getting heads in any particular coin toss is 50% but the chance of getting heads for 10 or 50 or 100 tosses in a row are much much lower.

The theory of runs. It isn't easy.

 

Assume you toss a coin n times. What is the probability of a run of heads m instances long, that is, in n tosses you throw m heads in a row.

 

The probability of the run occurring at the very start of n throws is:

 

q^2 p^m + p^2 q^m

 

where p is the probability of tossing a head and q = 1-p is the probability of tossing a tail.

 

Example: you start tossing a coin, what is the probability of a starting sequence of m = 3 heads in a row?

 

Definition: the run of m=3 heads is a sequence of 3 heads with a tail at the beginning and end, eg, THHHT. The probability of such an event is:

 

0.5^2 0.5^3 + 0.5^2 0.5^3 = 6.25%

 

Notice that the size of n is irrelevant, so long as n >m

 

There are complicating issues, like where in the n tosses do you want the run of m heads to occur? And of more use in understanding the implications of runs is determining the expected number of runs of length m in n throws of a coin, not just the probability of a run of m occurring.

 

There are n - m - 1 ways of positioning the run of m heads in the sequence of n tosses. And the events of a sequence containing a run of m heads starting at each of the n - m - 1 positions are not mutually exclusive. The probability of each such event is weighted according to the number of runs occurring in the sequence...

 

blah blah blah... some hard stuff required here to explain the weightings...

 

Conclusion: the expected number of runs of length m in n throws of a coin is equal to n/(2^m+1)

 

If you toss a coin n=100 times you can expect a run of m=3 heads in a row to occur 100/(2^3+1) = 6.25 times. And when n is large, the number runs containing a sequence of m becomes normally distributed.

 

Notice the factor of 10 between the probability of starting with run m and the expected number of runs of m in 100 tosses?

 

All this was my troubled interpretation of page 78 from Richard Epstein "The Theory of Gambling and Statistical Logic"

 

And I struggle these days to understand any of it.

 

 Quote:

Originally posted by montoya:

we probably need to agree on some definitions before we can develop this further.

 

regarding terrain, "backcountry" in the widest sense can mean just a snow-covered area, regardless of slope angle. if it's flat, then I'm probably not at much risk regardless of how many days I'm out there. on the other hand, if you mean "+30 degree slopes" by avie terrain, that's a different story.

 

you would also need to talk about timing (eg green/yellow/red light days, proximity to storm cycle, etc).

 

experience/skill level, I don't know how you would quantify that. this is also related to the messy area that spud brought up, past behaviour/emotions influencing future actions.

It is almost impossible to define a repeatable event. Every day BC is different. And as I said in my post above and you say again, there is the emotional lack of independence between events. Even if all circumstances are the same between two BC outings, the outcome of the last tour will have a bearing on the outcome of this tour as you will not have the same mentality as you did on the last tour (event).

 

Tossing a coin: the coin has no memory, each toss is independent.

 

Tossing yourself in the BC: you have emotional memory and will always play a different hand as a result, ergo, each toss is not independent. I don't want to go into it here, and at the risk of making enemies.... this is the reason my speculative trading activities are all programmed into code and operated by a computer: it totally removes the human emotional element between events. No matter how good a speculative strategy may be, if I can't express it in code and let my computer run the algorithm and take care of business then I don't touch it in the first place. Humans are appallingly flawed decision makers. We can identify patterns that point to certain things but we can seldom be relied upon to make the correct judgement based on that observation, time after time after time and irrespective of the outcome of the previous judgement.

 

15 long years ago I wrote an AI application (closer to an Expert System) that contained a lot of rules and made human judgement based on those rules. I have thought about creating the same AI tool for avalanche forecasting. The vital and missing element is interpretation of risks based on years of experience. Not every situation is the same and no coded rule set will manage every instance.

 

 Quote:

Originally posted by montoya:

there's also the concept of "risk" itself. here's one possible definition, I'm sure you risk management guys will have other variations:

risk = (probability of accident) x (consequences of accident)

Almost but not quite. What you are getting at is mathematical expectation but you have left out half the equation. Correcting for that I would say:

 

Expected value = (probability of accident) x (consequences of accident) + (probability of no accident) x (consequences of no accident)

 

definitions:

 

probability of no accident = 1 - probability of accident.

consequences of accident = death

consequences of no accident = life

 

Notice I have gone for a death event, not just a broken leg and a nasty experience buried for 5 minutes. The problem here is the pay-off of losing very large. The general expression is:

 

E(X) = x1P(X1) + x2P(X2) + ... + xkP(Xk)

 

That is, the expected value of event X if it is repeated over and over is the sum of each outcome times the outcomes payoff.

 

Risk $10 to make $100 with a 9% chance of winning. Do you take that bet? NO.

 

-10 x .91 + 100 x .09 = -0.10 ie, the expected value of a $10 bet is $9.90. Place that bet 100 times and you will walk away with that amount.

 

Rather than me type it out, check wikipedia for a simple example: http://en.wikipedia.org/wiki/Expected_value

 

Apply it to the BC example above:

 

You have 1 life and risk it all. The death payoff is -1 therefore no matter how low the probability of death, if you do it enough time you will come out with less than you started with. Obviously there is no such thing as having 0.9 of a life, there is no shade of grey.

 

-1 x 0.01% + 1 x 99.99% = .9998 which is less than a 1 life. Even when you chances of dying are only 1 in 9999 (note: they are your odds, and odds are different to probability)

 

No gamble is ever worth repeating many times when the pay out is non-existence.

 

An alternative to this is introducing the utility derived from a BC outing. That is, you go in with 1 and come out with 1 + a bit more. That changes things.

[damian 0]

I'd just like to say I am sorry for the above post.

[SerreChe 2]

Better be

[keba 0]

Long post (yes it took me 8 days to read it), but it was worth it just to see the mathematical equation converting percent slope to degrees. Very elegant.

 

Thanks db

 

I would have to say, though, that on the topic of risk, that we are not rolling dice here, and every conscious decision loads the odds, but not necesarily in your favour. There can be good or bad decisions made in any given situation (see thread "Have you been lost in a white-out?").

 

 

No more math, please.

[SerreChe 2]

bump