First decide what hypotheses
you want to test, like what questions you want to answer. Here are some ideas:
- Hypothesis 1 -- Laysan and black-footed albatrosses
fly at the same speed
- Hypothesis 2 -- male and female albatrosses fly to
the same places to find food
- Hypothesis 3 -- albatrosses don't care at all about
the surface temperature of the ocean
Are these hypotheses correct? If
they are, keep 'em. If they're not, chuck 'em.
You can think up lots of other hypotheses to test to advance
albatross science! Do it! Also, check out the details below. You'll need to know them.
Details That You Need
In mid-January 1998 we put small transmitters on six Laysan
albatrosses and six black-footed albatrosses. On Tern Island, Paul Sievert attached each
transmitter with tape to the feathers on the back of each bird. From that point on, for
the next several months, the TIROS satellites used by the Argos System reported any
location data that they collected from those albatrosses. We'll be doing the same thing in
1999. If you are subscribed to The Albatross Project, you will receive the data by
email just like the classes did in 1998. [Ask your teacher if your class is subscribed. If
not, see Join the Project.]
The data deliveries will look like this:
BIRD DATE
TIME LAT
LON
51C 5/5/98 14:39:08 24.435
163.734
Here you have the bird's i.d. (51C), the date and time
that the satellites took the location, and the latitude and longitude of the location.
These particular data came from a bird that travelled the equivalent distance of around the world in less than 80 days! 51C did it 79 days, and this location came in the
middle of that period.
Something that you must understand about the time is that
the 24 hour clock is used, in which 12 noon
is 12:00:00,
and 1:15 PM is 13:15:00, and 10:26:15 PM is 22:26:15. Another thing you need to know
is that the time recorded is the time in Greenwich, England! This is not
as strange as it seems. Greenwich Time is also called Universal Time, and many global
communications use GMT (Greenwich Mean Time) to avoid problems with communications across
time zones. During the first few months of the project, Hawaii time will be 10
hours behind GMT. So the data above were collected when the time in England was
2:39:08 PM, in the afternoon. If those data were collected from a transmitter in the
Hawaiian Islands, then the time of day there (in Hawaii) was 4:39:08 AM, a difference of
10 hours. It’s an important difference. The albatross was doing its nighttime thing
when the data were collected, so you have to be sure to convert the time by ten hours or
you would think the albatross was experiencing afternoon time when the location was taken
by the satellites. The date of the location is also the date in Greenwich.
Plotting
Data on a Map
Latitude and longitude are like the X and Y axes of the Earth.
Lines of latitude run around the Earth east-west. They tell you how far you are from the
Equator. O° latitude is at the Equator, 45° N is about halfway between the Equator and
the North Pole, and 45° S is about halfway between the Equator and the South Pole. Lines
of longitude run from the North Pole to the South Pole. O° longitude is a line between
the Poles that runs through Greenwich, England, and it is called the Prime Meridian. As
you go east and west from the Prime Meridian the longitude numbers get larger, just as the
latitude numbers get larger as you move away from the Equator.
The albatross location data are provided as latitude
and longitude measurements, in degrees. To see where exactly the bird was when the
satellites located it, you can plot it on a map. Back up at the Hawaii Study you can find
maps that you can print to do this. You should have a separate map for each of the
individual birds, and you should plot each point as they come in by email to you. If you
connect the dots then you will have the path taken by
that bird, like we did in the Galápagos Study. When you have those paths, you can
easily compare the travel choices of the birds with climate conditions, chlorophyll
concentrations, and any other factor that you like.
Check Satellite Accuracy
To do a careful study you should verify that the satellites do
a good job of locating the transmitters. You can do this when the bird is at its nest
because the true location is known for sure at that moment. Our scientists on Tern Island
will be checking the nests of our albatrosses throughout the study, keeping track of when
each bird and transmitter is at the nest and when it is not. Whenever they are at the nest
we can compare the location reported by the Argos System with the known location of the
bird, and see if the two are very different. Part way through the tracking period we will
send you a list of satellite locations and true locations of birds at their nests, and you
can check the accuracy of the satellites, like we did in the Galápagos Study.
Figuring Out the Distance
Traveled by the Birds
Let's say you want to know how far a bird travelled between
yesterday and today. You plot the location for yesterday on your map using the lat. and
long. data from the satellites, and then you plot today's location. You COULD
use a ruler to measure the distance, but that would not be very exact nor very elegant.
Instead, you could use the Pythagorean Theorem and make your math teacher really happy!
Pythagoras was a Greek mathematician, and the theorem named for him says that the length
of the long side of a right triangle can be calculated from the lengths of the two shorter
sides. SO WHAT? That plot you made of
yesterday's and today's locations involves a right triangle, and especially the long side
of the triangle! Plot two points on a graph, like the position of a bird yesterday and the
position of the same bird today. Then connect them with a line. That line can be the long
side of an imaginary right triangle, whose right angle is at the corner R. The long side
of a right triangle is also called the hypotenuse.
The Pythagorean Theorem says that a^{2} + b^{2} = c^{2},
where a and b and c are the lengths of sides in a right triangle. From the satellite data
we can know what the lengths of a and b are, and then we can calculate the length of c.
The length of c is the distance that the bird traveled, which is what we want to know. In
this case,
the triangle's vertical side a has the length 25 - 23.9 = 1.1
the triangle's horizontal side b has the
length 166.2 - 163 = 3.2
Pythagoras tells us (get your calculator)
that
1.1^{2} + 3.2^{2} = c^{2},
so c^{2} = 11.45 and c = 3.4
We just showed that the bird traveled 3.4 degrees between
those two contacts with the satellites. (It might have flown more, if fact, if the bird
didn't follow a straight line.) To change the degrees to kilometers, you multiply
the 3.4 degrees times 111.3 (the number of kilometers in a degree). To change the degrees
to miles, you multiply the 3.4 degrees times 69.2. Now we have our result: the bird flew
at least 378.4 kilometers (or 235.3 miles).
There is a slight problem with this method. If you look at
a globe, you see that the lines of latitude and longitude are pretty straight near the
Equator, so this Pythagoras method works well. But as you get away from the Equator, those
lines become more curved and you're dealing more and more with triangles that aren't
really right triangles. The Pythagoras method will still give you a result that is
approximately correct, but you can get a more exact answer using the "Great
Circle Formula:"
Cos D = (Sin L1 x Sin L2) + (CosL1 x Cos
L2 x Cos DLo)
Yeah, right... Make it easy on yourself and use the Flight Distance Calculator on
The Hawaii Study page. It uses the Great Circle Formula and will give you the exact
answer. Compare that answer with what you get from the Pythagorean Theorem. If the two
answers are not very different, then you can calculate the flight distances yourself
using a^{2} + b^{2} = c^{2}, and make
your math teacher so proud.
The Need for Speed
When you have a flight distance calculated, it is easy to
calculate the speed that the bird was moving if you know how much time the bird took to
move that flight distance. You can get that time from the email data, right? Just divide
the distance by the time. How fast do you think an albatross can move?
Does it matter what direction they are moving? |