February 6th, 2009 | | By Ken Mankoff
Current Location: lat:-73.1986, lon:-114.9596
Sailing south toward the Getz Ice Shelf
Weather: Gray skies, gray sea, -0.5C (Air), -0.01C (Water)
Moods: Excited to finally leave Pine Island Bay and do something new (although new really just means more CTDs and more mooring deployments).
Note about last image: Photo of me taking sextant reading by Katie Leonard (I hear multiple of her friends and family might be reading this).
I was asked to provide more info about the sextant reading. We took 18 samples across the front of the ice shelf. By “we” I mean Katie Leonard and Chris Little (author of the other NBP09-01 blog). I helped with the first few and then went to bed, most of the transect happened on their shift. An example one went something like this:
* Date: …
* Time: …
* Lat: …
* Lon: …
* Radar dist: 0.18 nautical miles
* Sextant: 8 deg 8.6 min
* Note: Caves just north of ship, elephant seals spotted nearby.
After we were done, we began the analysis. The math is pretty basic trigonometry:
1) Convert the distance from nautical miles to meters (333)
2) Convert the angle to degrees (8.1)
3) Convert degrees to radians (0.14)
Draw a triangle, knowing one angle and side:
__—-|
__– |
__— |
__— | h = ?
o) theta = 0.14 |
-|- ——————-|
^ d = 333
I’m not sure how that looks to you readers but as I write it I have drawn a person on the left, and a vertical line on the right.
In general, tangent = opposite/adjacent
So tan(theta) = h/d
we want to solve for h so multiply both sides by d and you get
h = d * tan(theta)
= 320 * tan( 0.14 )
= 45.1 m high
We took a additional steps to make sure things were more accurate. For example, the radar measured 333m but we corrected for the distance between where the radar took its measurement and where we took our measurement, which was not directly under the radar, and about 10 meters closer to the ice shelf.
As you can see by plugging in 310 instead of 320, we were close enough that a 10 m error makes a significant difference in the height of the ice shelf.
310 * tan( 0.14 ) = 43.7 m
Further analysis will refine the equation to take into account the height of the radar and the height of the average observer eye above sea level. We could even take into account the difference in eye height between Chris, Katie, and I, but I do not think that will make much of a difference.
Tags:
Antarctica,
NBP09-01,
Pine Island Glacier