I have a question concerning the appropriateness of using standard deviation in a particular circumstance.
I have a dataset that represents the movement of a glacier from one side to the other (a cross-glacier transect). Because it wasn't feasible to measure every spot across the glacier, the measured points were spaced approximately 300 meters apart, for a total of 18 measured points. At each of the points, GPS was used to find the position at each of two periods in time. The difference in position between Time 2 and Time 1 gives the velocity at each of the 18 measured points.
Glaciers move faster in the center and slower along the edges. This is reflected by the velocities of the measured points. Those points along the sides have a lower velocity than those in the center. So if I want to report some descriptive statistics of the flow, is it appropriate to use standard deviation as an indicator of the variability of the flow across the glacier?
I've been told that this is not appropriate because the velocity of each of the 18 measured points is, of course, going to be different from the other points. In other words, what I'm hearing is that it is appropriate to calculate a standard deviation for each of the 18 points individually (assuming each point was measured numerous times), rather than calculating the standard deviation of all 18 points collectively.
Calculating the std dev of the 18 points would give you a measure of the "roughness" of the velocity across the glacier, but would, of course, have measurement error roughness included. The std dev of multiple measurement of each location would better define the measurement error, but would also reflect change in velocity over time or season. I don't know what the magnitude of the measurement error is compared to the velocity change across the glacier or the potential velocity change across the time span of your measurements. You might consider best-fitting a quadratic or cubic polynomial to your points. The constant term would be the average glacier velocity, the linear term would be a measure of one side vs the other, and the quadratic term would be a measure of the bulge in the middle. Whether the terms would mean much without something to compare them to is another story.
I don't see why you need to use descriptive stats for the problem at hand. Supposed you're asked to measure the width of a spoon, how will you describe it by stats ? This is analogous to situation you have.
You have 18 points measured across the glacier. If you really need to have "std dev" for each data point, then you have to calculate it from the measurement error. Get the error from GPS accuracy, error from stop watch, etc. Calculate your "std dev" by propagation of error.
Point jth: (measured value +/- error) m/s
Point 1: (0.5 +/- 0.02) m/s Point 2: (0.6 +/- 0.02) m/s ... Point 18: (0.5 +/- 0.02) m/s
Most likely the measurement error for each point is the same for all, unless they were measured with different tools, different day, different GPS,..got it?
If you really insist on using descriptive stats, there's another way. You can categorize your 18 into 3 groups.
L: Left side of glacier (6 points) M: Middle of glacier (6 points) R: Right side of glacier (6 points)
Now you can do stats from your data. Calculate the average and stdev for each category. Next you make story of you results, you know.. make comparisons between L&M, R&M, L&R. Then draw your conclusions. Of course you need to report on experimental methods and data reduction as well to be complete.
Experimental methods -- this describes how you make your measurements.
Data reduction-- this describes how you categorize and analyze you data.
I agree. "descriptive statistics of the flow" would be descriptions of the aggrigate details of the flow NOT a means by which to estimate the flow. For instance, average speed along the glacier, average speed" during the year, maximum speed during the year and so on.
You will be wanting to research hydrolics/hydrology (I don't know the term - my partner is the engineer). There are nice mathematical models for understanding and measuring the flow of liquid.
The dynamics of the liquid speeds along the side versus the centre of a tube, tunnel, creek and so on. Although slow moving, a glacier does have liquid flow, albeit very viscous. On the bright side, glaciers normally have very smoth sides, so calculation should be simplified.
Measuring at multiple points across the glacier should be enough to calculate flow. This would be an accurate measurement of the flow at the point you measured.
Philip ___________________ Correct answers don't require correct spelling.
> The velocity estimate, being derived from GPS position estimates have inherent errors, caused by both systematic and random sources. Unless you're using differential GPS, the velocity uncertainties are probably quite large.
> Each individual point on the glacier presumably does not move at a constant velocity, and is subject to external factors such as weather and temperature, and terrain.
Your report should have estimates of the GPS errors, which then determines your ability to discern differences in velocities between points, and the differences in velocities of the same point.
I would have thought that the velocity and direction at any point would be affected by the velocity and direction of all the points around and below it and therefore not necessarily independent and identically distributed. Sort of like describing the velocity profile of a viscous fluid in laminar flow but in Scott�s case much more complicated. I don�t recall seeing any probability measures used to describe the laminar flow case. OT: Scott first logged on September 05, 2000 and last logged in on September 08, 2000 so it would be interesting to see what Scott finally ended up reporting. - Mike
>I don�t recall seeing any probability measures used to describe the laminar flow case.<<br> ____________________________
I have recollection of the laminar flow profile in the "Hydraulics Bible", the Russian ICELDICK [available in french, but don't know if the english version ever existed]. In Process Control & Instrumentation, for small circular pipe we use laminar flow meters, and in larger pipe sizes we use the ordinary orifice plate [typical] and other flow meters not sensitive to viscosity.
I Understand it has nothing to do with your glacier. You could probably do a "traverse" like in non circular air duct and the "Pitot tube".
There is a bit too much yet with no data at all. In the averaging "Pitot tube" and circular pipes the pressure points are distributed on the Chebyshev zero error grid.