The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!' but 'That's funny...' --Isaac Asimov
That’s Funny… random header image

How well can we predict the future of sea ice? And what do we do when the ice is gone?

November 11th, 2009 by eric
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Sea Ice Report — Summary of 2009 Pan-Arctic Sea Ice Outlook

The amount of sea ice in the Arctic grows and shrinks every year as the seasons change. The largest extent is in late winter, after which it melts throughout the summer. The minimum annual sea ice extent generally occurs in mid-September. This year (2009) it occurred around September 16. As of today (November 11) the sea ice has been growing more slowly than usual and is now at a record minimum for this time of year.

The smallest Arctic sea ice extent ever observed was in 2007 but in the past two years it has rebounded. However, there is a long-term decline in September sea ice extent going back at least 30 years, so although this year’s September ice minimum is near that predicted by the 30-year declining trend, it falls well short of the actual September ice minimum in 1979.

Early in this year’s melt season (May) a number of sea ice scientists made predictions about the year’s September minimum. They used a variety of methods, ranging from simple extrapolation of the 10-year decline trend to complicated computer models involving existing sea ice and weather conditions, but all of them predicted smaller minimums than were actually observed. The report shows that we still have a lot to learn about predicting inter-annual variations in complex natural phenomena like weather conditions and sea ice extent. Some factors affecting our ability to make predictions include large inter-annual variability in the historical record, limitations in our ability to interpret satellite data from sea ice covered areas (see this report by Barber et al.), and the long-term decline in ice thickness (and thus ice volume) as thick multi-year ice melts and is replaced by thinner, younger ice.

Nevertheless, it is clear that summer sea ice is an endangered environment in the Arctic. I think we should use this information to re-assess our priorities for research in the polar regions, but it is not clear which direction we should take. Should we focus on learning about the biology and ecosystem functions present today in multi-year ice and summer sea ice, as a method of archiving the environment in the literature so that it will continue to live on even after it is gone? Or should we look to the Antarctic as a model for what to expect in the future of the Arctic, focusing our resources on predicting the responses of ecosystems and food webs to the ongoing transition from large summer sea ice extents to small? I’m not yet sure, but we will have to move fast to make these kinds of decisions because nature is not going to wait for us–by the time my generation retires there may not be any summer ice left to study in the Arctic.

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Automated bacteria or virus counts in ImageJ

September 28th, 2009 by eric
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THIS IS EXPERIMENTAL, UNPUBLISHED SOFTWARE. USE AT YOUR OWN RISK.

I’ve written a free, open source script for ImageJ (free, open source) to count viruses (or bacteria, but not both at the same time) automatically from JPEG image files. If you have TIFFs you can batch convert them to JPEG using ImageMagick (free, open source) with the following command:

mogrify -format jpg *.tif

You can download the script here as a text file (JVirusCount), or the full source is written below. Opened in ImageJ (after opening any image in the desired directory), it will iteratively adjust the noise threshold and use the “Find Maxima” command to count the number of dots in every image file in the desired directory.

20071213-4-5

viruses in Arctic seawater

The output of the script is a tab-delimited text file for each image summarizing the number of dots detected at each threshold, which can be input into a Matlab (not free, closed source) script (MVirusCount) using an external function, regress2lines (free, open source). I haven’t tried using it with Octave (free, open source) but if you get it to work let me know. What I’ve found is that there is a significant change in the slope of this curve during the transition from measuring ‘noise’ to ‘particles’, but that it depends on the quality, brightness, and contrast of the image; MVirusCount determines the intersection of those two lines and the abundance of dots at that point. A program finding the maximum of the first derivative of the curve would likely work just as well or better.

Example graph of output

Example graph of output

As seen below, the program has the lowest relative error at high concentrations of viruses, and should probably not be used at concentrations less than 100 viruses per field without further testing. I should also note that the samples shown above are field samples from an extreme environment, so usage in a laboratory setting may be more precise.

computer counting of viruses

JVirusCount

list = getFileList(File.directory);

for (i=0; i<list.length; i++) {
run("Clear Results");
run("Set Measurements...", "  decimal=9");

for (noise=1; noise<42; noise++) {
 run("Find Maxima...", "noise=" + noise + " output=Count");
 rows = nResults-1;
 setResult("Noise", rows, noise);
 counts = getResult("Count", rows);
 setResult("logcount", rows, log(counts));
}

title = getTitle();
saveAs("Measurements", File.directory + title +".csv");
run("Open Next");
}

MVirusCount

clear all;                                                  
d=dir('*jpg.csv');                                          

for k=1:length(d);

  fname=d(k).name;
counts = dlmread(fname,'\t',1,0);
counts(end,:)=[];                
counts(:,end)=[];                

% from 10:end because it has sigmoidal shape screwing things up
[m, R, idiv, G] = regress2lines(counts(10:end,3),counts(10:end,4));

xy = [1, m(5); (m(1)*1+m(2)), (m(1)*m(5)+m(2)); m(5), 40; (m(3)*m(5)+m(4)), (m(3)*40+m(4));];

store_fname{k,1} = fname;
store_intercept(k,1) = m(5);
store_count(k,1) = exp((m(1)*m(5)+m(2)));

%  subplot(1,length(d),k)
hold off
plot(counts(:,3),counts(:,4),'bs')
hold on
plot(xy(1,:),xy(2,:),'b-')
plot(xy(3,:),xy(4,:),'r-')
title({fname});

drawnow
pause

end

fid = fopen('output.csv','a');
for k=1:length(store_fname);
fprintf(fid,'%s\t%0.5g\t%0.5g\n', store_fname{k}, store_intercept(k), store_count(k));
%  sprintf('%s\t%0.5g', store_fname{k}, store_intercept(k))
end

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Almost technically a doctor

September 18th, 2009 by eric
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I successfully defended my doctoral dissertation on September 9, 2009, and am now wrapping up some edits before I submit the final thesis! I broadcast the talk live on ustream — I even had a question from the virtual audience! (thanks John). A PDF copy of my talk is available here. The most recent draft of the thesis is available here.

Next stop: Hamilton, ON. See you there.

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How many bacteria are in the ocean? And how far is it between bacteria in the ocean?

August 25th, 2009 by eric
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There are about 1,000,000 bacteria per milliliter (1/5 of a teaspoon) of water in the coastal ocean. A lot of these bacteria degrade dead plant and algae material and turn them into useful nutrients which can allow further growth of plants and algae and animals. Without bacteria in the oceans to regenerate these nutrients, life there would be impossible!

Bacteria are small. Very small. The length of a bacterium is about 1/1,000,000 of a meter (one meter is 3.3 feet). One milliliter of water has the same volume as one cubic centimeter (cc) of water, which, being a cube, has three characteristic dimensions, or sides: length, width, and height. The length of each of those sides is 1 centimeter (cm, 1/100 of a meter, or about 3/8 of an inch). If the 1,000,000 bacteria in that one cubic centimeter of ocean water were spread out evenly, they would also make a cube. Each side of the cube would have 100 bacteria because 100 x 100 x 100 = 1,000,000. The distance between each bacterium on that side would then be 1 cm/100 bacterium = 0.01 cm between each bacterium.

Now let’s scale up the whole thing so that we can actually see it. Let’s make a bacterium the same length as an M&M (about 1 cm), which is an increase by a factor of 10,000. In that case the distance between each bacterium (M&M) would be 0.01 cm * 10,000 = 100 cm = 1 meter. So each bacterium would be about one meter from any other bacterium in any direction.

There are also a lot of viruses in ocean water that can infect the bacteria — about 10x more than there are bacteria, and each virus is about 1/100 as long as a bacterium. So scaled up, a virus would be about 1 cm/100 = 0.01 cm, which is a bit smaller than the length of a grain of table salt. Divided into all three directions, there would be about $\sqrt[3]{10}$ ~ 2.2 viruses (salt grains) on the line between each bacterium.

Remember that these bacteria and viruses are not there to hurt you! They act like nature’s recycling bin, taking in waste products and returning useful nutrients to the environment.

distance-between-bacteria

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Enrichment of microorganisms into sea ice brine

July 20th, 2009 by eric
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As seawater freezes into sea ice, all of the dissolved constituents of the water become concentrated within the solid ice matrix that forms. Because it is more dense than seawater due to the high salt content, a lot of this ‘brine’ will drain from the ice by gravity. However, some brine remains in the ice down to −55°C, the eutectic point of seawater, at which point the ice transitions to a complete solid with no liquid fraction. Between the freezing point of seawater (about −2°C) and the eutectic, there will be brine with a salinity dependent on the temperature of the ice, up to about 8 times that salinity of seawater. But it’s not just salts that are concentrated, but also nutrients, particles, and microorganisms living within the seawater, including viruses and bacteria. A former student in the lab, Dr. Llyd Wells, discussed the consequences of this concentration effect in detail in a 2006 paper in Environmental Microbiology: “Modelled and measured dynamics of viruses in Arctic winter sea-ice brines“. In this paper he used a mathematical model to predict contact rates between bacteria and viruses as a function of temperature in sea ice brine, showing that “virus-bacteria contact rates in underlying −1°C seawater were … up to 600 times lower than those in ice brines at or below −24°C.” Two contrasting factors affected the relative contact rates. First, the brine concentrating effect described above, which increases contact rates by increasing the concentrations of viruses and bacteria in the ice. Second, the diffusivity decreases as a factor of increasing viscosity at lower temperatures, which decreases the contact rates. In the figure shown below, Llyd shows that the result of these contrasting effects is overall a positive one, with very high potential contact rates occurring in the upper, colder sea ice.

sea ice diffusivity, wells and deming 2006

The equations used were as follows:

J  =  2\pi dD_vVB

where J = contact rate, “d is the spherical diameter of the average cell (cm), Dv the viral diffusivity (cm2 s-1), and V and B the [in situ] concentrations of viruses and bacteria respectively (ml-1 [brine or seawater]).”

D_v  =  \dfrac{kT}{3\pi \mu dv}

“where k is Boltzmann’s constant, T the temperature (Kelvin), \mu the viscosity (g cm-1 s-1), and dv the spherical diameter of the average virus (cm)”. Dv can be estimated with the following equation (determined empirically from Figure 1) where t is temperature (°C).

D_v = 40.5882 \times 10^{-9} \times 10^{0.0325t}

The authors provide the following values for constants:

\begin{tabular}{ccc} constant & value & units\\\hline k & 1.38 \times 10^{-16}& g cm^2 K^{-1} s^{-2}\\ d & 0.5 \times 10^{-4}& cm\\ dv & 60 \times 10^{-7} & cm\\ \end{tabular}

but they don’t provide for the calculation of \mu, the viscosity in the ice, referring to a 1975 paper by George Cox (which references a 1960 paper by Dale Kaufmann [which itself references a 1929 paper by Stakelbeck and Plank]).

The following multiple linear equation can be used to estimate the viscosity (in centipoise = 0.01 * g cm-1 s-1) as a function of temperature (T) and brine salinty (S) in the ice, but it is not very good:
\mu = -0.0835419T + 0.0066835S+1.7724989

[The raw data and R script to calculate the multiple linear regression are available here]

A better empirical equation was determined using ZunZun.com, an amazingly useful site for curve fitting. I used the Function Finder, which identified a Reciprocal Polynomial as the best available curve. The simplified equation for that curve is (mu in centipoise= 0.01 * g cm-1 s-1):
\mu = \dfrac{1}{0.62 + 0.020T + 0.00014T^2 -0.0012S -0.000030ST}

T-S-viscosity

Finally, to calculate the relative contact rates between seawater and sea ice, given concentrations of bacteria and viruses (per volume brine or seawater):
\dfrac{J_i}{J_w}  =  \dfrac{D_{vi}}{D_{vw}} \times \dfrac{B_i}{B_w} \times \dfrac{V_i}{V_w}

which can be generalized to:
\dfrac{J_i}{J_w}  =  \dfrac{D_{vi}}{D_{vw}} \times \dfrac{f_B}{V_{br}} \times \dfrac{f_V}{V_{br}}

where Vbr is the brine volume fraction (calculator available here), “the subscripts i and w indicate sea ice and water column respectively. The terms fB and fV represent the fraction of bacteria and viruses retained in the brine and serve as a correction to account for possible partitioning within the solid phase … as well as for two major mechanisms of loss: destruction due to impinging ice crystals or osmotic stress and release with rejected brine.

If passive entrainment into the ice (proportional to salts) is expected for both viruses and bacteria, then f_B = f_V = \dfrac{S_i}{S_w}, where S is the bulk salinity of the ice or water.

If active entrainment into the ice is expected (complete/active concentration of bacteria and viruses into ice), then f_B = f_V =  1

If the concentration of bacteria (or viruses) in the ice is 0 then fB = 0.

Another enrichment index has been used by others, including Riedel (2006), originally from Gradinger and Ikalvko (1998). Their index (Is) is 0 when the concentration in ice is 0 (Is = 0 when Ci = 0) and is 1 when the concentration in ice is proportional to the salt retained in the ice (Is = 0 when Ci/Cw =Si/Sw).

I_s = \dfrac{C_i}{C_w} \dfrac{S_w}{S_i}

A third index can be created such that at a value of 0 indicates passive enrichment and a value of 1 indicates complete/active enrichment. A value less than zero indicates loss or mortality in the ice (-1 indicates an in situ concentration of 0). Any value greater than 1 indicates production or growth within the ice.

E = \dfrac{\dfrac{C_i}{C_w}-\dfrac{S_i}{S_w}}{1-\dfrac{S_i}{S_w}}

temperature bulk salinity brine concentrating factor

temperature bulk salinity brine concentrating factor

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