I'm so stoked the Oceanography Department at UH Manoa just produced a promo describing just what goes on in the School of Ocean and Earth Science and Technology. A number of my friends and professors are in it. If anyone ever asks what I do again, rather than stumble through an unwieldy description, I'll simply point them here!
Showing posts with label Science. Show all posts
Showing posts with label Science. Show all posts
Friday, November 15, 2013
Thursday, September 20, 2012
Estimating Tsunami Travel Times
Want to know how long you have until a tsunami generated in Chile reaches your doorstep? To figure it out you need two things: the speed of the wave generated and the great circle distance between you and the location of tsunami origin.
Wave speed (c) is related to the depth (H) of the water body the wave is moving through:
c =
√(gH)
where g is acceleration due to gravity = 9.8 m/s2 and H is in meters. The average wave speed in open ocean is approximately 200 m/s. This is fine to use in back of the envelope calculations such as this.
To find the great circle distance between two points you need the radius of the earth (approximately 6370 km) and the spherical angle (ψ) between the points, given by:
ψ = arcos [ sin(φ1)sin(φ2) + cos(φ1)cos(φ2)cos(θ2
– θ1) ]
where φ1 and φ2 are the latitudes of the starting and ending points respectively. θ1 and θ2 are the longitudes of the starting and ending points respectively.
From there, use the spherical angle and radius to find arc length (s): s=rψ. Once you have that, you can find the travel time of the tsunami: t = s/c. Keep in mind that this is very general and rough!
I've generated a Matlab script calculating the travel time for a tsunami generated in Santiago, Chile to reach Honolulu, Hawaii (~11.5 hrs according to my script). If you want to pick different starting or ending points, just mess with the latitudes and longitudes.
Interested in tsunamis? Check out these sites:
Violent Hawaii: Deadly Tsunamis
NOAA Tsunami Website
%Long Gravity Wavesclose allInterested in tsunamis? Check out these sites:
Violent Hawaii: Deadly Tsunamis
NOAA Tsunami Website
clear all
c = 200; % speed of propagation (m/s)
r = 6370; % radius of Earth (km)
r2 = r*1000; % radius of Earth (m)
r = 6370; % radius of Earth (km)
r2 = r*1000; % radius of Earth (m)
lat1 = -35.846; % Latitude of santiago, Chile -33
lat2 = 21.467; % Latitude of Honolulu, Hawaii 22
lon1 = -72.719; % Longitude of Santiago, Chile -71
lon2 = -157.983; %Longitude of Honolulu, Hawaii -158
lat2 = 21.467; % Latitude of Honolulu, Hawaii 22
lon1 = -72.719; % Longitude of Santiago, Chile -71
lon2 = -157.983; %Longitude of Honolulu, Hawaii -158
cosangle = sin(lat1)*sin(lat2) + cos(lat1)*cos(lat2)*cos(lon2 - lon1);
angle = (acos(cosangle))*(180/pi); % angle in degrees
arclength = 2*pi*r2*(angle/360) % arclength between locations (m)time = (arclength/c)*(1/60)*(1/60) % travel time (hr)
Wednesday, September 12, 2012
Mars is cool, stop whining about money and religion
I just watched this clip on NASA's Mars Exploration Rover Mission (MER) and my mind was sufficiently blown. How cool are we, how ingenious, that we can design a series of small robots to not only travel a distance of 55 million kilometers (that's seven long months of loneliness) but to also successfully hit an inconceivably small target and survive?
I guess I must be alone in that though. You know, the doe-eyed wonder at our ability to create? Yea apparently I'm the only one who's not jaded because just about every comment under this clip was either about the 'ridiculous' cost or how this video somehow affronts their religious views (you gotta love people like that, or where would The Daily Show be?).
I don't care how much it costs, this stuff is cool. For all those complaining about how our government is wasting money on something completely useless, stop for two seconds and think about all the useless stuff you bought in the past week. Stuffing your face with Doritos isn't solving world hunger and all that music you purchased on iTunes isn't curbing anthropogenic climate change. Until you start spending money more judiciously I suggest you sit down. So go right ahead, cast the first stone.
We do these things because that's what makes us human. We do it because we can. And you know what, we'll probably come up with a way to turn a profit on space exploration (or exploitation) sometime anyway. Baby steps guys.
And to all those who felt their religious views were somehow threatened by this video, how indescribably sensitive can you be? And how does that thought process work?
space exploration = science = thinking differently = blasphemy ???
We went to Mars. We didn't blow a hole through heaven, I promise. This huge fear of scientific thinking in religious communities is just silly. The two are not mutually exclusive. Just calm down and give everyone a hug or something.
I guess I must be alone in that though. You know, the doe-eyed wonder at our ability to create? Yea apparently I'm the only one who's not jaded because just about every comment under this clip was either about the 'ridiculous' cost or how this video somehow affronts their religious views (you gotta love people like that, or where would The Daily Show be?).
I don't care how much it costs, this stuff is cool. For all those complaining about how our government is wasting money on something completely useless, stop for two seconds and think about all the useless stuff you bought in the past week. Stuffing your face with Doritos isn't solving world hunger and all that music you purchased on iTunes isn't curbing anthropogenic climate change. Until you start spending money more judiciously I suggest you sit down. So go right ahead, cast the first stone.
We do these things because that's what makes us human. We do it because we can. And you know what, we'll probably come up with a way to turn a profit on space exploration (or exploitation) sometime anyway. Baby steps guys.
And to all those who felt their religious views were somehow threatened by this video, how indescribably sensitive can you be? And how does that thought process work?
space exploration = science = thinking differently = blasphemy ???
We went to Mars. We didn't blow a hole through heaven, I promise. This huge fear of scientific thinking in religious communities is just silly. The two are not mutually exclusive. Just calm down and give everyone a hug or something.
Monday, May 7, 2012
Ocean acidification and deep sea communities: can past events provide clues to future responses?
Ocean acidification (OA) is one of the largest issues resulting from anthropogenic pumping of CO₂into the atmosphere. CO₂in the atmosphere dissolves into oceans, leading to a decrease in pH (called the bicarbonate buffer system):
CO₂+H₂O ↔ H₂CO₃ ↔ HCO₃¯+H⁺ ↔ CO₃¯+H⁺
Atmospheric CO₂doubling will likely lower pH of the entire ocean > 0.1 unit.
The normal variation of pH in open seawater (7.6.2),
so .1 units is very significant.
Effects on marine organisms include physiological responses (regulating acid-base imbalance) as well a dissolution of calcium carbonate support structures like shells, tests, or exoskeletons as saturation horizons rise. It is possible deep sea organisms may be particularly vulnerable. For example, the internal control of pH is critical for proper physiological functioning, so many organisms have evolved elaborate methods to regulate internal pH. However, the pH in most of the deep sea is stable over thousands of years, so deep sea organisms have not needed methods to rapidly adapt to or regulate changes in pH. Ocean acidification may be too fast for these deep sea organisms to adapt to (Seibel and Walsh, 2002).
Changes in carbonate saturation horizons are one of the biggest worries when people talk about effects of OA on organisms. The solubility of calcium carbonate (CaCO₃) increases with decreasing temperature and increasing pressure. In the north Pacific, the rate of rise for aragonite saturation horizon is around 1 m y¯¹. At atmospheric CO₂ = 780 ppm (near the end of this century), the subarctic North Pacific and Southern Ocean will be undersaturated with respect to aragonite (Fabry et al., 2008; Feely et al., 2006; Orr et al., 2005.) Major planktonic calcium carbonate producers like coccolithophores, foraminifera, and euthecosomatous pteropods (organisms responsible for nearly all the export flux of calcium carbonate to the deep sea) may be at risk as well. In lab studies, foraminifera and pteropods for example showed possible reduced calcification with decreasing pH (Feely et al., 2004; Orr et al., 2005).
Effects on marine organisms include physiological responses (regulating acid-base imbalance) as well a dissolution of calcium carbonate support structures like shells, tests, or exoskeletons as saturation horizons rise. It is possible deep sea organisms may be particularly vulnerable. For example, the internal control of pH is critical for proper physiological functioning, so many organisms have evolved elaborate methods to regulate internal pH. However, the pH in most of the deep sea is stable over thousands of years, so deep sea organisms have not needed methods to rapidly adapt to or regulate changes in pH. Ocean acidification may be too fast for these deep sea organisms to adapt to (Seibel and Walsh, 2002).
Changes in carbonate saturation horizons are one of the biggest worries when people talk about effects of OA on organisms. The solubility of calcium carbonate (CaCO₃) increases with decreasing temperature and increasing pressure. In the north Pacific, the rate of rise for aragonite saturation horizon is around 1 m y¯¹. At atmospheric CO₂ = 780 ppm (near the end of this century), the subarctic North Pacific and Southern Ocean will be undersaturated with respect to aragonite (Fabry et al., 2008; Feely et al., 2006; Orr et al., 2005.) Major planktonic calcium carbonate producers like coccolithophores, foraminifera, and euthecosomatous pteropods (organisms responsible for nearly all the export flux of calcium carbonate to the deep sea) may be at risk as well. In lab studies, foraminifera and pteropods for example showed possible reduced calcification with decreasing pH (Feely et al., 2004; Orr et al., 2005).
So
to be blunt, this is bad.
But what is going to happen? Is there another way, besides controlled laboratory experiments, to gauge where the ocean is headed? Other than just sitting and waiting around to see what happens, I mean.
We could look to the past.
The Paleocene-Eocene Thermal Maximum
About 55 million years ago, sea surface temperatures rose rapidly, about 5-10°C in only a thousand years. This rapid warming was likely due to increases in greenhouse forcing, just like today. Rather than anthropogenic however, this rapid influx of carbon to the atmosphere may have come from methane hydrates at the bottom of the ocean. For those of you who are isotopically inclined, δ¹³C records from deep sea sediment cores show a rapid initial decrease (around 20,000 years) followed by a gradual recovery (~130,000 years) back to similar δ¹³C values found before the excursion. The magnitude of the drop in δ¹³C values (-3‰) suggest the carbon source was very depleted in 13C, pointing to methane hydrates as the likely source. This carbon isotope excursion was the signature of the Paleocene-Eocene Thermal Maximum (PETM) (Zachos et al., 2005).
Part of influx of CO2 to the atmosphere dissolved into the oceans, lowering pH. This resulted in a rise in the lysocline and calcite compensation depth (CCD) which promoted the dissolution of seafloor carbonate. The CCD shoaled over 2 km within just a few thousand years, but recovery was gradual, around 60,000 years. Ultimately this CO2 would be sequestered through chemical weathering of silicate rocks (Zachos et al., 2005).
All marine communities experienced major changes, including migrations to higher latitudes, evolutionary radiations, and extinctions. There were also distinct responses between planktonic and benthic organisms. Planktonic organisms weren't particularly affected, but did experience radiation and diversification. However for benthic organisms, the PETM marked the largest extinction event in the last 90 million years. 30 to 50% of benthic species became extinct. It's important to keep in mind that gauging PETM effects on marine ecosystems relies entirely on microfossils, as no macroinvertibrate fossils have been described (Rodriguez-Tovar et al., 2011; McInerney and Wing, 2011).
Surprisingly, the driving force affecting these organisms may have been temperature rather than ocean acidification. Temperature affects bottom water oxygenation and increases metabolic rates, meaning organisms need more food to maintain base metabolism (McInerney and Wing, 2011).
Applicability?
Can we expect to see similar responses from marine organisms today? How similar was the PETM to today's global warming/ ocean acidification problem? It turns out we are likely in for much worse. for one, the rate of carbon input was much different. In the PETM, carbon was input to the atmosphere over an 8,000 year period. Contrast that with our pumping CO2 into the atmosphere over a mere 300 years. That's less than the mixing time of the ocean. The longer CO2 input rate during the PETM meant less severe acidification and carbonate dissolution in the surface ocean.
Something else to consider: there was no ice during the PETM. No glaciers, snow. Nothing. No ice means no ice/albedo feedback (warming leads to melting of ice, revealing darker surfaces which absorb more heat, leading to more warming) which means an absence of greater warming at polar latitudes. In contrast, the most drastic warming today is at the poles (McInerney and Wing, 2011; Ridgwell and Schmidt, 2010).
But what is going to happen? Is there another way, besides controlled laboratory experiments, to gauge where the ocean is headed? Other than just sitting and waiting around to see what happens, I mean.
We could look to the past.
The Paleocene-Eocene Thermal Maximum
About 55 million years ago, sea surface temperatures rose rapidly, about 5-10°C in only a thousand years. This rapid warming was likely due to increases in greenhouse forcing, just like today. Rather than anthropogenic however, this rapid influx of carbon to the atmosphere may have come from methane hydrates at the bottom of the ocean. For those of you who are isotopically inclined, δ¹³C records from deep sea sediment cores show a rapid initial decrease (around 20,000 years) followed by a gradual recovery (~130,000 years) back to similar δ¹³C values found before the excursion. The magnitude of the drop in δ¹³C values (-3‰) suggest the carbon source was very depleted in 13C, pointing to methane hydrates as the likely source. This carbon isotope excursion was the signature of the Paleocene-Eocene Thermal Maximum (PETM) (Zachos et al., 2005).
Part of influx of CO2 to the atmosphere dissolved into the oceans, lowering pH. This resulted in a rise in the lysocline and calcite compensation depth (CCD) which promoted the dissolution of seafloor carbonate. The CCD shoaled over 2 km within just a few thousand years, but recovery was gradual, around 60,000 years. Ultimately this CO2 would be sequestered through chemical weathering of silicate rocks (Zachos et al., 2005).
All marine communities experienced major changes, including migrations to higher latitudes, evolutionary radiations, and extinctions. There were also distinct responses between planktonic and benthic organisms. Planktonic organisms weren't particularly affected, but did experience radiation and diversification. However for benthic organisms, the PETM marked the largest extinction event in the last 90 million years. 30 to 50% of benthic species became extinct. It's important to keep in mind that gauging PETM effects on marine ecosystems relies entirely on microfossils, as no macroinvertibrate fossils have been described (Rodriguez-Tovar et al., 2011; McInerney and Wing, 2011).
Surprisingly, the driving force affecting these organisms may have been temperature rather than ocean acidification. Temperature affects bottom water oxygenation and increases metabolic rates, meaning organisms need more food to maintain base metabolism (McInerney and Wing, 2011).
Applicability?
Can we expect to see similar responses from marine organisms today? How similar was the PETM to today's global warming/ ocean acidification problem? It turns out we are likely in for much worse. for one, the rate of carbon input was much different. In the PETM, carbon was input to the atmosphere over an 8,000 year period. Contrast that with our pumping CO2 into the atmosphere over a mere 300 years. That's less than the mixing time of the ocean. The longer CO2 input rate during the PETM meant less severe acidification and carbonate dissolution in the surface ocean.
Something else to consider: there was no ice during the PETM. No glaciers, snow. Nothing. No ice means no ice/albedo feedback (warming leads to melting of ice, revealing darker surfaces which absorb more heat, leading to more warming) which means an absence of greater warming at polar latitudes. In contrast, the most drastic warming today is at the poles (McInerney and Wing, 2011; Ridgwell and Schmidt, 2010).
Check out this video:
We are heading for something unprecedented. The PETM at best
provides a framework for the mimimum damage today's anthropogenically induced
problems will cause deep sea marine life.
Helpful link:
Tuesday, April 17, 2012
It's official!
Now it feels real. Finally! I have a Bachelor's degree. And with only a few months to spare before I start my Masters work at UH Manoa. This absolutely made my day.
Friday, March 30, 2012
The Adventures of Flat Stanley
My niece Kawena sent over Flat Stanley in February. Clad in an Aloha shirt and carrying a suitcase, I took him all around the island of Oahu. One of the first places we went was the west side, to a beach called Makaha. It's one of my favorite places to surf, and this day was really fun! The waves were about head high and it was pretty packed since just about everyone goes to Makaha when there is a west swell. Of course Stanley couldn't surf with me, but he had some fun on the sand.
On another day, I took Stanley into the lab with me. I work in a marine biology lab. One part of my work is to catch fish in the wild and look in their stomachs to see what they've been eating.
The fish in the picture below is an opah, a moonfish. It lives in really deep water out in the open ocean and is a really popular fish to eat here in Hawaii. My friend had been looking at their stomachs and saw only... mushy stuff. Now that might not seem weird until you look at their mouths. They have essentially no teeth! Their mouths are like vacuums, just sucking up their prey (usually fish). So you would expect their stomachs to house whole fish! But nope, just mushy stuff. We started wondering if they were actually eating jellyfish.
We decided to look a little deeper. We could feel this rough patch of something deep in the throat of this fish. When we looked, we found rows and rows of small sharp teeth, pointed inward towards the stomach. Imagine having teeth in the bottom of your throat! We are guessing these opah suction fish into their stomachs and these sharp teeth prevent the fish from swimming back out. Anyway, Stanley was there watching this whole discovery.
On another day, I took Stanley into the lab with me. I work in a marine biology lab. One part of my work is to catch fish in the wild and look in their stomachs to see what they've been eating.
The fish in the picture below is an opah, a moonfish. It lives in really deep water out in the open ocean and is a really popular fish to eat here in Hawaii. My friend had been looking at their stomachs and saw only... mushy stuff. Now that might not seem weird until you look at their mouths. They have essentially no teeth! Their mouths are like vacuums, just sucking up their prey (usually fish). So you would expect their stomachs to house whole fish! But nope, just mushy stuff. We started wondering if they were actually eating jellyfish.
We decided to look a little deeper. We could feel this rough patch of something deep in the throat of this fish. When we looked, we found rows and rows of small sharp teeth, pointed inward towards the stomach. Imagine having teeth in the bottom of your throat! We are guessing these opah suction fish into their stomachs and these sharp teeth prevent the fish from swimming back out. Anyway, Stanley was there watching this whole discovery.
More Stanley adventures to come!
Sunday, February 26, 2012
The Oceans Sciences Conference 2012, Salt Lake City, Utah
My first conference! Oh, and I gave a talk! Maybe you missed that. I got the incredible opportunity to present my research at a major international conference. Needless to say I was excited... but mostly terribly nervous.
I submitted my abstract in October, with the full anticipation that I'd be assigned a poster. It's not very common for an undergrad to get a talk, so I wasn't expecting much. Honestly I just hoped my abstract would be accepted. In November I got the email that I was given a speaker slot, and I was instantaneously on cloud-9. But as November melted into December and December into January, the nerves started to take hold. I was going to be surrounded by these pillars of science, the experts that I cite endlessly in any paper or presentation. I needed to prepare.
 |
| Flying in to Salt Lake City |
I got into Salt Lake City last Saturday, not nearly as prepared as I wanted to be. On the plane over, I suddenly got this crazed new idea for the direction I wanted to go in, and began completely reorganizing my talk. This was probably not a good idea. So night one consisted of me endlessly tweaking my talk.
On Sunday, with fresh powder on the ground, my advisor, another researcher, and I decided to go skiing. Avoid the stress of my talk for a couple hours (maybe it was just procrastination). My advisor and his colleague were originally from the mainland and had been skiing since forever. In contrast, this would be the third time I had ever seen snow. I had been snowboarding once before so I stuck with that. The geography was incredible on the way up to Brighton.
 |
| Heading up to Brighton |
Snowboarding was incredibly fun but also pretty painful. I managed to not fall getting off the lifts, but that's just about the only place I didn't fall. Trying to keep up with two experienced skiers is not the safest thing to do when you're on a snowboard for the second time in your entire life. I would get into the flow of it, get some good speed, then promptly catch an edge and fall. I fell pretty hard a couple of times, but I just kept wanting to go fast. By the third run, my advisor and his friend had ditched me and I was on my own, so I plugged in my iPod and just listened to music for the rest of the day as I explored the runs. Music and snowboarding is so much better than just snowboarding. It was more fun and I felt like I fell less for some reason. I'd just tune out and then suddenly I'd be at the bottom of the hill, lining up for the lift again.
 |
| Starting out... |
 |
| Something a little steeper. |
 |
| Heading back to the city |
That night a number of my labmates flew in so the house quickly became filled. And by filled I mean overbooked. Some of us had to sleep two to a bed (luckily they were queen sized beds!). Everyone was some combination of excited, nervous, and jet-lagged. For dinner we grilled up some sort of pork, some flounder, asparagus, and potatoes. Being the 'rabbit' that I am, I stuck with the veggies.
Day 1 of the conference was exciting! The Salt Palace Convention Center is huge and I spent most of the morning wandering around various ballrooms. Thousands of people were in attendance, filling in and out of ballrooms as they attempted to see every talk of interest. This was impossible to me as so many cool talks were going on at the same time. I sat in on a session entitled "137: Biodiversity, Biogeochemistry and Ecology: Establishing Linkages Between Molecular Diversity and Ecosystem Functioning" and another called: "004: The Southern Ocean and Its Role in the Climate System."
 |
| Sitting in one of the talks... |
 |
| Massive poster sessions! |
Days 2 and 3 were a blur. Endlessly sitting in talks, then frantically speeding to the next one in the ballroom across the entire building. Day 3, Wednesday, was filled with plenary talks an there was a really interesting one about shark conservation and the impacts of the shark fin soup industry.
Day 4. Before I knew it, Thursday was here. The day of my talk. There was an entire session devoted to the type of work I'd be presenting: compound specific isotope analysis of amino acids (AA-CSIA): 123: Compound-specific amino acid analysis: a rapidly evolving tool for ecology, paleoceanography and biogeochemical cycle research. The line up of speakers was amazing. Marylin Fogel, the opening speaker, basically pioneered this entire method over 20 years ago. Other big names included Matt McCarthy, Yoshito Chikaraishi, and my advisor Brian Popp. Put simply, this room was filled with anyone who understood the AA-CSIA method. And here I was, fresh out of my undergraduate life, with a B.S. in Global Environmental Science. The talks started at 8:00 am and I didn't talk until 10:45, so I had plenty of time to work up my nerves. I had to keep telling myself to think of Max (a dog) who lives a stress free life.
On top of the sheer stress that comes from having to give a presentation to an audience of experts, I had two additional reasons to worry:
1) Both of my prospective advisors for grad school were in attendance, so this almost felt like a job interview.
2) My talk was essentially going against everything that the guy presenting before me was supporting. And the guy before me was Yoshito Chikaraishi, one of the biggest names in this type of science.
But you know what, I did it! I could feel my voice shaking a bit, but it wasn't bad. I knew my stuff and I could feel the repetition taking over as I settled into it. And I did alright! I didn't really get any difficult questions after, so I felt pretty good. After I sat back down, all the adrenaline left and I suddenly felt exhausted yet elated. It was over!
The poster session started at 4 pm every day and there was free beer for the first hour. I hadn't really taken advantage of this until now. I had to celebrate!
 |
| Title slide of my talk |
Here are some pics of the city:
 |
| Mormon temple |
 |
| The capitol building |
 |
| Inside the capitol building |
 |
| Beautiful ceiling, Capitol building |
 |
| View from the top! Salt Lake City |
 |
| See you at the next conference! |
P.S. Here's a link to my abstract!
Hoen, D. K.; Popp, B. N.; Drazen, J. C.; Hussey, N. E.; Kim, S. L.; Wallsgrove, N. J.; Humphreys, R. L.; COMPOUND SPECIFIC ISOTOPE ANALYSIS IN FOOD WEB STUDIES: THE NEED FOR ACCURATE ESTIMATES OF TROPHIC ENRICHMENT FACTORS
Hoen, D. K.; Popp, B. N.; Drazen, J. C.; Hussey, N. E.; Kim, S. L.; Wallsgrove, N. J.; Humphreys, R. L.; COMPOUND SPECIFIC ISOTOPE ANALYSIS IN FOOD WEB STUDIES: THE NEED FOR ACCURATE ESTIMATES OF TROPHIC ENRICHMENT FACTORS
Saturday, October 1, 2011
Calculating Pi: Monte Carlo Integration
Thank you physicists, Matlab, and (pseudo)random number generators. Welcome to Monte Carlo integration. A couple of days ago, my boyfriend was telling me how he has surpassed me in his Matlab skills. Dorky, I know. Not one to be bettered, I set out to prove him wrong. He had an assignment to approximate the value of pi using Monte Carlo integration in C. I'd do it in Matlab.
But I had to figure out what Monte Carlo integration was first.
Enter Wikipedia. I don't care what professors say about it, Wikipedia is a magical place filled with more knowledge than could ever be stuffed into my head. I'm not going to start citing the website in anything important, but I will give it my thanks. So here it is: Monte Carlo integration offers an approximate evaluation of definite integrals using random numbers.
So what did I have to do exactly? My bf gave me a hint: use a circle and a square. After some more prodding he added, "put the circle in the square." Alright. Thanks a lot.
So I drew up a circle with radius = 1, inside a square with sides = 2 (Figure 1).
We know that the area of the square is L2= 22 = 4.
We know the area of the circle is
A = πr2. To find π, we need to know the area of the circle. Unfortunately, that's impossible to know without π.
But there is another way to find pi. I first set the center of the circle as (0,0) in a coordinate plane. I then could generate sets of random numbers between -1 and 1 and use these as x and y coordinates. Using Pythagorean's Theorem I can find the distance of these points from the center (the origin):
c = √(a2 + b2).
The script was pretty easy to write (find it at the bottom of this page). The hardest part for me was actually plotting the figure. Obviously, the more iterations (# of points) you do, the more accurate your result will be (Table 1). It also vastly increases the computing time. Past 1,000,000 iterations, my Matlab program got pissed and said it didn't have enough memory.
But I had to figure out what Monte Carlo integration was first.
Enter Wikipedia. I don't care what professors say about it, Wikipedia is a magical place filled with more knowledge than could ever be stuffed into my head. I'm not going to start citing the website in anything important, but I will give it my thanks. So here it is: Monte Carlo integration offers an approximate evaluation of definite integrals using random numbers.
So what did I have to do exactly? My bf gave me a hint: use a circle and a square. After some more prodding he added, "put the circle in the square." Alright. Thanks a lot.
So I drew up a circle with radius = 1, inside a square with sides = 2 (Figure 1).
 |
| Figure 1: Circle with radius = 1 within a square with sides = 2. |
We know the area of the circle is
A = πr2. To find π, we need to know the area of the circle. Unfortunately, that's impossible to know without π.
But there is another way to find pi. I first set the center of the circle as (0,0) in a coordinate plane. I then could generate sets of random numbers between -1 and 1 and use these as x and y coordinates. Using Pythagorean's Theorem I can find the distance of these points from the center (the origin):
c = √(a2 + b2).
If a point's distance from the origin is < 1, then it falls within the circle. The ratio of points within the circle to the total number of points (points within the square) is proportionate to the ratio of the area of the circle to the area of the square:
# points in circle = πr2 where r=1
# points total 4
So:
π = 4(# points in circle)
# points total
With that in mind, my Matlab adventure began. The script was pretty easy to write (find it at the bottom of this page). The hardest part for me was actually plotting the figure. Obviously, the more iterations (# of points) you do, the more accurate your result will be (Table 1). It also vastly increases the computing time. Past 1,000,000 iterations, my Matlab program got pissed and said it didn't have enough memory.
# of Iterations
|
Approximate value of Pi
|
10
|
2.4
|
100
|
3.24
|
1000
|
3.092
|
10000
|
3.1104
|
100000
|
3.13168
|
1000000
|
3.143080
|
Here's my Matlab script for 1000 iterations:
% Calculating pi using Monte Carlo integration
close all
clear all
n = 2*(rand(2,1000))- 1; % generates random numbers between -1 and 1
t=sum(n.*n,1)<1;
pts = 0; % starting value for total points
circ = 0; % starting value for points within circle
for R = 1:1000;
d = sqrt((n(1,R))^2 + (n(2,R))^2);
pts = pts + 1;
if d <= 1;
circ = circ + 1;
end
end
format long
Pi = (4*circ)/pts
plot(n(1,~t),n(2,~t),'b.','MarkerSize',15)
hold on
plot(n(1,t),n(2,t),'r.','MarkerSize',15)
theta = linspace(0,2*pi,100);
x = cos(theta);
y = sin(theta);
plot(x,y,'k');
axis ('equal');
axis([-1 1 -1 1]);
title('100 Iterations');
Monday, September 26, 2011
Trawling the deep: aliens in our bathtub
I recently went on a research cruise in the Pacific ocean, trawling, deploying CTDs, and (scientific) fishing. Here are just a few of the organisms we pulled up from our own salty bathtub.
Saturday, September 10, 2011
Open ocean aquaculture: what's the problem?
"Look out Hawaii! Open ocean aquaculture (OOA) has many problems," warns Neil Frazer, professor of geophysics at UH Manoa. Focusing on the new OOA system off the Big Island, Frazer cites multiple shortcomings of the system in his November 2010 article to the Honolulu Star Advertiser. First, he argues OOA of carnivorous fish is "worse than over-fishing" because production of these fish requires massive amounts of food in the form of wild caught fish; fish that would otherwise be feeding people of Third World countries. Second, farmed fish have higher levels of pollutants than wild caught fish. Third, sewage from these caged fish negatively impacts the ocean environment. He further argues that OOA can act as an agent of disease for wild populations of fish. Wild fish would starve or get eaten when they fall ill. However there are no predation or starvation pressures on these caged fish, allowing them to spread disease over long periods of time.
One of his arguments stood in stark opposition to what we had heard in the aquaculture class I'm taking this semester: the sewage issue. In class we learned one of the pros of offshore, open-ocean cages was that you did not have to worry about waste products. The waste would be distributed by oceanic currents and diluted thanks to the massive expanse of the ocean itself. No worries, right? Frazer argues dilution is not the solution; it just becomes someone else’s problem. These differing opinions I believe are a result of each person’s different experiences with aquaculture. My professor is speaking from an aquaculturist’s point of view. Someone who has been in the business to do just that: business. After all, aquaculture is a business, not a science. Frazer’s viewpoint is that of an observer, a possible consumer (although not likely judging by the article). His interests lie with environmental well-being, not with making money. Both opinions are valid; they just come from differing points of view.
One of his arguments stood in stark opposition to what we had heard in the aquaculture class I'm taking this semester: the sewage issue. In class we learned one of the pros of offshore, open-ocean cages was that you did not have to worry about waste products. The waste would be distributed by oceanic currents and diluted thanks to the massive expanse of the ocean itself. No worries, right? Frazer argues dilution is not the solution; it just becomes someone else’s problem. These differing opinions I believe are a result of each person’s different experiences with aquaculture. My professor is speaking from an aquaculturist’s point of view. Someone who has been in the business to do just that: business. After all, aquaculture is a business, not a science. Frazer’s viewpoint is that of an observer, a possible consumer (although not likely judging by the article). His interests lie with environmental well-being, not with making money. Both opinions are valid; they just come from differing points of view.
In oligotrophic and relatively fast moving waters like Hawaii, I don’t think a few OOA operations would be a problem. The added nutrients from the waste may add to increase in primary productivity, but not much. And would increasing primary productivity a bit be such a bad thing? It may increase food availability for higher trophic position fishes, commercially important fishes. Could OOA increase wild stock biomass? Further, the cages themselves may attract fish, providing refuge in an otherwise featureless environment. This is an observed phenomenon; buoys miles from the islands have been found to attract fishes in larger concentrations than they’d be otherwise.
The promotion of disease in wild stocks is one of Frazer’s most troubling arguments. By protecting and feeding sick fish, OOA cages are a “reservoir of infection.” Diseases among caged fish could transfer to wild populations. Further, Frazer worries some caged fish escape the nets and interbreed with wild stocks, lowering the genetic robustness of the population. Is it possible that OOA is hurting populations of wild fish?
Frazer ends the article by talking about the advantages of Native Hawaiian fishponds and seems to suggest we should be using that aquaculture method rather than OOA. But could we support our demand for aquatic protein entirely from fishponds? What Frazer fails to mention is that the Native Hawaiian population was much smaller than Hawaii's population today, and even with that smaller population it is highly unlikely they were able to provide for themselves enough protein through fishponds.
I think we need to give OOA a chance. We are over-fishing our wild fish stocks and will soon need an alternative source of fish protein. Plus, OOA is far more sustainable and ecologically friendly than mass cattle, pig, and chicken production. Although we could all just become vegetarians and avoid this whole issue. Anyone?
Check out the article here.
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