What is looking for dolphins in the ocean really like?

Many people are curious about what it is like to be out on a boat looking for dolphins in Hawaii. Lots of people think it's easy - my job is simply to sit on a boat and watch dolphins. Many people have a hard time believing that you can actually get paid to lounge on a boat and watch dolphins frolic in the surf.  The reality is a lot more complicated.

This is not what I look at all day (photo from FIRMM.org).

Finding dolphins, especially in Hawaii, can be really time consuming and difficult. Especially if you are interested in the types of dolphins that don't generally hang out near shore, which is most Hawaiian species (the exception being spinner dolphins).

Searching for dolphins at sea requires something called a "search image." Visual predators use search image all the time to find food. For example, blue jays look for the color, shape, or pattern of a moth to find their food. Prey can also use a search image to look out for predators: sea lions also use a visual search image to watch out for hungry killer whales.  If a killer whale doesn't match their search image - for example, by having a weird, bent over dorsal fin - sea lions don't always recognize it as a threat.

Biologists also use search images. Bird biologists look for something moving against a still background. Snail biologists look for a round, white spiral in a sea of shaking green leaves. And dolphin biologists look for moving triangles (dorsal fins) in a sea of other moving triangles (waves).

Lots and lots of blue-gray triangles. But which is a dolphin?
Photo by Alexis Rudd, 8/15/12.

Looking at waves is a lot like looking at the ants on a tv screen.  It's kind of like watching random noise (although obviously I am oversimplifying things to give you an idea, waves aren't really random).

So, most of the time, when whale and dolphin observers are  looking at the ocean, it's like looking at this (you might want to adjust your screen so you can only see one of these .gif files at a time - it's making me kind of queasy):

When a large whale comes along, the observer sees a shape in the noise that isn't changing for a little while, like this:

Did you find the "whale?" Hint: it's the blacker spot that appears in the bottom right hand corner for about 3 seconds.

Dolphins are even harder to see, because they move faster. When a scientist is searching for a dolphin, they look for a shape that isn't changing very much, but might be moving across the waves.  Can you spot my "dolphin?"

That one's kind of hard (I am having trouble, and I made the thing!), so I made the "dolphin" pink.  Now can you see it?

This week, I've been out on the water on the big island, helping look for whales and dolphins. We usually get out on the water at about 6:00 am (sometimes a little earlier) and come back in at 3:00 pm (if we're lucky unlucky). For the last two days, we have seen two groups of animals per day. That means that we have effectively been staring at noise for about 8 hours, searching for that tiny little clue that will tell us where the dolphins might be.  Coastal cetaceans are not spread out as much as in the tropics, so there is not always as much time staring at noise.

Isn't the human brain an amazing thing? It can pick up a tiny difference in pattern -

"That bit of the ocean isn't moving as much as the other bits!"

out of an enormous amount of noise. There isn't much on earth that's more enormous than the ocean.


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We Should Have Studied Dolphins in High School Math

When I look back at my educational career, it's really striking how poor of a student I was.  That is, I was a pretty mediocre student in the "hard" sciences until I took Marine Biology class during my senior year of college.  Most of the time, I think I was just really bored.  It wasn't always because the material wasn't challenging or useful (although sometimes this was the case). It was often because I had no idea what the point of it was.  OK, so in physics we could calculate where a ball would land based on the angle and force.  I only played baseball when forced to in gym class, and when I did I had no control over the force and angle of my wild swings.  I didn't have a home catapult, and I just didn't get how this stuff could really matter to ME.

It wasn't until I got really interested in marine biology, and specifically whale and dolphin bioacoustics, that I started seeing how amazing and cool math & physics can be.  If you read my blog, you know that bioacoustics is the study of the sounds of living things.  Whales and dolphins use sound to communicate and find food underwater, so even if you can't see them, you can very often hear them.  Some whales, such as beaked whales, are actually easier to find by listening than by looking with your eyes.  In addition, sound travels further underwater than light, so people at the surface can even hear whales that are thousands of feet underwater, or even hundreds of miles away. We can use these sounds to track the location of the animal, and we can do it using high school math.  Super cool.

Why didn't we do this in my high school trigonometry class?

It's really pretty simple.  First, you need something in the water making a sound.  Let's say... a whale.

Then you'll need a boat and something to record the sound.  We're going to use a hydrophone array, which is made up of three underwater microphones (hydrophones) strung in a line, with 15 meters between each hydrophone.  

When the whale makes a sound, it travels in a straight line through the water* to each hydrophone, arriving at the closer hydrophones sooner and arriving at the further hydrophones last.  Let's say the sound arrives at our recordings at time 0 for hydrophone 1, 0.006 seconds for hydrophone 2, and 0.0007 seconds for hydrophone 3.

How on earth do we figure out the distance to a whale when all we know is the difference between when we heard it on hydrophones 1, 2, and 3?  Easy - there's a simple equation for that!

The sound speed in water is 1500 m/s (which is why I put the hydrophones 15 m apart - to make the math easier).

We've replaced some of the words with numbers, something I HATED in high school.  Oh wait, I still hate it, so I'll just explain what the equations mean: The time difference between hydrophone 1 and 2 (t21) is equal to the difference between the distance between the whale and hydrophone 1 and the distance between the whale and hydrophone 2 (d2-d1) divided by the speed of sound.  Holy mother of god, this is just geometry!  I could have been doing this when I was 15! Some of you over-achiever types probably took geometry in 8th grade, so you could have done this when you were 14. Not me!

With a little algebraic rearrangement (which I am not going to bore you with, since you can look it up here), we get:

**

Sx and Sy are the x and y locations of the whale. C the speed of sound in salt water, 1500 m/s.  dh is the distance between the hydrophones, which in this case is 15 m, and all the ts refer to the time difference between the hydrophones (the small numbers tell you which two hydrophones: t21 is the difference between the arrival at hydrophone 2 and 1, etc).  All you have to do now is plug in the numbers. Edited 5/12/2012: To make it even easier, I've provided a spreadsheet here.

**

Then you can graph the location of the whale (-16.7, ±241.7), along with the locations of your hydrophones at (0, 0), (0, 15), and (0, 30).  I've just made designated hydrophone 1 at (0, 0) to make things easy, but in real life you'd have a GPS on the boat and you'd have to add the length of the hydrophone cable to the location of the boat's gps.

You might notice something funny about this equation - it actually gives two solutions - one on either side of the line of hydrophones.  That's a big problem with using three (or four, five, etc.) hydrophones in a row - you're not really sure what side of you the whale's on.  The reason for this is that there are two possible solutions for Sy. However, you can figure out which side the whale is on by turning the boat.  The location that stays in relatively the same place regardless of where the hydrophones are is the correct one.  Other ways to fix the left-right ambiguity? Make your hydrophones into a 2D shape (hard to do when dragging them behind a boat because 2d shapes are not very streamlined)*** or use DIFAR.

I wish I had done this kind of math in high school - it is totally within the realm of a high school student!  I think I might have paid better attention to something cool like finding whales.  On the other hand, maybe not.  That boy across the room WAS pretty dreamy.  Not all kids will be interested enough in whales and dolphins to get interested in math and physics, but the cool thing about math and physics is that, regardless of what you're into, I bet it applies.  From video games to raising miniature ponies, there's math in there somewhere.  Sometimes it just takes the right spark to get people interested.

P.S. If I made any mistakes above, please call me out.  Like I said, I didn't do so well in math class.  Also, if you're interested in a copy of the xcel spreadsheet with the equations already in it, shoot me a message and I'll send you a copy.

* This isn't always the case - sometimes the sound bounces off the bottom or the surface to get to the hydrophone, but I'm ignoring those cases here for simplicity.

** Edit: May 9, 2012. I made a HUGE mistake the first time I posted this and completely ignored the equation for t1 (I thought t1 was a typo for t12).  This is now fixed.

*** Edit: May 8, 2012.  Changed "3D" to "2D" because of a comment from Sam Denes. I had thought a straight line was already 2D, but apparently a straight line is 1D and adding another point off the line makes something 2D.

Note: I got to talk to a bunch of high school math teachers about this math.  Recap here.

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Honolulu to Kauai in One Minute

Twice a month, I sail on a shipping tug from Honolulu to either Kauai or the Big Island. On the way, I collect acoustic and GPS data on whales and dolphins. For those of you who haven't spent the night on a tug boat crossing the Kaʻieʻie Waho channel, here's a taste of what it's like (if it was sped up a LOT and you skipped the night-time part AND had really nice weather).

iTimelapse is really fun. :)


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