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Here are the pieces:

1. Ice "RETREAT" means the ice edge is shrinking.

2. Ice "ADVANCE" means the ice edge is expanding.

3. Wind direction and magnitude can affect whether the ice RETREATS or ADVANCES

4. In the summer, there is a thermodynamic component driving overall RETREAT

Here's what I'm trying to do:

I want to determine (statistically) the wind directions and magnitudes for which wind does affect the movement of the ice edge. For example, if the wind is blowing exactly normal to the ice edge (towards the ice), the ice is pushed back and we get retreat. If it's blowing the other direction, we get advance. Physics comes into play in other directions leading to somewhat unintuitive results.

Here are the basics of my strategy:

I've defined the ice edge as a set of x, y coordinates. For each x,y point, I have the distance that it moved since the previous day. For this analysis, I classify this distance as either a RETREAT, or an ADVANCE. There is one ice edge per day over the summer, and of course multiple points for each day. (the correlation between these points is part of "twist"). But ignoring that for now, here's what I did:

Find the fraction of RETREATS across all points (I've unbiased the data so that all wind directions are equally represented) The answer incidentally comes out to be about 0.6. Call this p.

Treating this like a binomial distribution with a "success" being a retreat, and a "failure" being an advance,

if I draw n samples randomly from this data set, the expected number of retreats should be:

E(R) = np

And the Standard Deviation is given by:

std = sqrt(np*(1-p))

If AR = Actual number of retreats that I did get in the sample, then I can compare to E(R):

# of stds away from E(R) = (AR - E(R)) / std

So, if my "random Sample" is not actually random, but instead selected based on wind direction and magnitude, and I find that "# of stds away from E(R)" is greater than 2, I can be pretty sure that wind is significantly affecting the movement of the ice edge.

Complications:

So, some other complications are:

1. the ice edge doesn't retreat at the same rate over the whole summer. I broke it down into months, and it varies from like p=.58 to p=.62

2. I can't treat each point in the ice edge as a separate observation. It makes more sense to think of the retreat as a percentage of the total ice edge.

I've taken these things into consideration, but I'm not sure if what I did is correct. But before I get into that, are there any other general problems with this technique? Am I so far off in left field that it's not worth considering the rest? If so, do you have any suggestions, by chance?

I hope I've made the problem clear enough. Let me know if more detail is required!!

Thanks for reading, and I much appreciate any advice!

Wendy