Technical Supplement 6A
How much isotope should I add?
“How much isotope should I add?” is the most common question of the isotope
addition experiment. This essay answers this question, giving a guide to calculations
involved in setting up field experiments. The calculations focus center on a realistic
example, isotope additions to enclosures in lakes.
“How much isotope should I add?” The answer is this: figure out how much
heavy isotope is present or supplied naturally, and then, if costs allow, add 1-4 times that
amount. For many 15N addition experiments (which are the main focus of this section),
the isotope supply is the important point of attack. This is because natural background
concentrations are very low, and labeling the supply will slowly lead to a steady state and
constant label in the system. After turning over and replacing the natural isotope
distribution in your system, you can achieve constant values that reflect the added label.
These constant, steady state values will make all your final mixing model calculations
much simpler and believable, avoiding mixing muddles. But to attain these constant
isotope values, you will need to start thinking about longer-term experiments which are
harder to maintain. You realize this is getting harder, but then again, that is why you are
reading this, to be prepared. Good!
Now let’s turn to the calculations. Adding one, two, three, and four times the
existing amount of 15N in the nutrient supply to your system will give isotope values of
(approximately) 1000, 2000, 3000, and 4000o/oo, respectively. These are signals so large
that even if you miscalculate (or nature does something you don’t expect, which is fairly
routine), you will still have large signals to work with. Said another way: if you add too
little, you will put in a lot of work, and have nothing at the end. So, think big! But we
don’t want to add so much that we would fertilize the system. In the end, we realize we
have to make actual calculations to reach the right conclusions. An experienced friend
stops by and counsels us that although there are many steps to these calculations, they are
all simple algebra.
With these preamble thoughts behind us, we start thinking about an example, a
favorite lake experiment we are interested in. We are thinking about an addition of 15Nlabeled ammonium to an enclosure in a lake. The enclosure is a large cylinder about 15m
long (deep), 3m wide, and anchored at depth so that there is a natural sediment bottom
under this big tube. Lake biologists use such enclosures or limnocorrals for experimental
work – the whole lake is often too big for experiments, and offers no opportunity for
replicates, whereas the giant tubes are quite handy for experimental purposes. In our
example, it is still winter, and we are just in the planning stages, thinking of how to
manipulate the nitrogen cycle in these enclosures during next summer’s field season. We
are studying how newly synthesized nitrogen circulates compared to background or old
nitrogen, and want to label the new N to make sure we can follow the mixing dynamics.
Here we go with the calculations, which you will see are quite detailed. So you may want
to read the following quickly for an overview, then return to any parts you want to focus
on.
We decide we want to double the stock of heavy isotope being supplied naturally.
Let’s calculate how to do this. First, we find that the natural concentration of inorganic N
is about 1 millimole per cubic meter (m3) of lake water, and that most of this N is
ammonium N. We measure the volume of an enclosure and find that it is 100 m3, so that
we estimate there will be 100 millimoles of ammonium N in the enclosure when we set it
up. Next we find out that sediments release ammonium into the water column, with
projected rates of about 100 millimoles per day for sediment at the bottom of the
enclosure. We see that 100 millimoles of N released by sediments can replace the 100
miliimoles of N in the water column each day. So, ammonium N in the water column is
being consumed by phytoplankton but replaced at the same time by ammonium from
sediments - there is a balance going on here. Because of the low concentrations and likely
daily turnover of the ammonium pool, we will focus our labeling strategy on the
ammonium supply, with isotopes in plankton projected to change over a few days to
reflect the new 15N conditions.
Besides the natural N supply rate and the volume of the system, the final thing we
need to know for our calculations is the isotope value of the natural ammonium. We
don’t have a measurement of this value which can vary widely over the natural
abundance 15N range. But in terms of enrichment experiments with their very high
levels of 15N, the 15N content of natural materials and synthetic fertilizers are very similar
to that of atmospheric nitrogen gas. This gas has fractional 14N and 15N contents of
0.996337 and 0.003663, respectively (see Table 2.1 in Chapter 2). We adopt these values
as reasonable first-order estimates for the background natural ammonium.
Now that we have all the numbers, let’s start the calculations about how much N
we need to spike the N supply. Of the daily 100 millimole N supply, the quantity of 15N is
100*.003663 = 0.3663 millimoles, and the quantity of 14N is 100*.996337 = 99.6337
millimoles. Converting these molar quantities to grams, we find further that 99.6337*
14mg/millimole of 14N = 1395mg of 14N, and 0.3663 millimoles of 15N * 15mg/millimole
of 15N = 5.5mg 15N. So, to double the amount of 15N, we need to add an additional 5.5mg
of 15N, and this will occur against a much larger background of 1395mg of 14N.
To really see the result of our efforts, we need to use the  formula to check our
target of 11mg total 15N that is composed of 5.5mg of natural 15N an equal 5.5mg amount
of 15N spike. Substituting these values in the  equation where we remember that R =
15 14
N/ N, we find that
 = ((RENRICHED/RNATURAL)-1)*1000 = ((11/1395)/(5.5/1395))-1)*1000 = 1000o/oo
It checks out, and we did get what we wanted, 1000o/oo when we doubled the existing
heavy isotope amounts.
But how much will this 5.5mg of 15N cost? To calculate this, we check the
internet and find a price for 15N-labeled ammonium chloride, 15NH4Cl. We find a listing
at Sigma Chemicals where 10% 15N-labeled ammonium chloride costs $147 for 25 grams
of compound. Then we have to calculate how much 15N is actually in this 25 g. The
formula weight (mass) of this compound is 53.49, and of this, a fraction 14/53.49 =
0.2617 is nitrogen. But for the spiked compound that is 10%15N and 90%14N, the masses
of N and the compound become 14.1 and 53.59, respectively, so that the fraction of N in
the spiked compound is slightly higher, 0.2631. Using this 0.2631 value, we calculate that
the total amount of nitrogen in the spiked compound is 25g * 26.3% = 6.58g ammonium
nitrogen. With 10% of this total as 15N, we calculate 0.658g (658mg) total 15N per 25g of
compound. To get our 5.5mg of 15N we want for each bag, we will need a small fraction
(fraction = 5.5/658 = 0.00836) of the material in a bottle, or 208.75mg weighed from the
25g bottle (208.75 = .00836*25). We discover with delight that this is very affordable at a
final cost of $147*.00836 = $1.23 for each daily dose of 15N label.
And now one of those math moments occurs, a detail that will need some algebra.
Here it is: when we add the 5.5mg of 15N, we realize we are also adding 9x that amount
as 14N, because the compound is 10% 15N, and 90% 14N. So we will be adding 9x5.5mg =
49.5mg of 14N along with the 5.5mg of 15N, and the total isotope in the daily 100
millimole supply after addition will be 1395 + 49.5 = 1444.5 mg 14N and 5.5 + 5.5 mg =
11 mg 15N. Using the trusty  definition, we have
 = [(11/1444.5)/(5.5/1395)-1]*1000 = 931.5o/oo
This makes sense – we don’t get to the target 1000o/oo because we are diluting the 15N
with 14N by using the 10% labeled compound. We realize we can work this out with
algebra to get to 1000o/oo, focusing in on the thought that we want the “ratios” or
“(RENRICHED/RNATURAL)” part of the  definition to equal 2, so that when we subtract one
and multiply by 1000, we will have 1000o/oo. The algebra for this is 2 =
[(5.5+x)/(1395+9x)]/(5.5/1395), and x = 5.92mg instead of 5.5mg. (Note: you can avoid
this algebra by buying 99% 15N labeled compounds, instead of the 10% labeled
compounds, but the 99% labeled material is more expensive per unit of 15N). So, we stick
with our 10% labeled material, and calculate the cost for a daily dose: we are using
5.92mg of 15N out of the 658mg of 15N in the bottle (224.92mg of compound out of the
total of 25g), which is 0.9% or $1.32 per daily dose, just 9 cents more per day.
Now we think about summertime logistics. We are assuming that the sediment at
the bottom of the bag supplies 100 millimoles of unlabeled N each day during a typical
experiment that lasts 10 days. So, the additions will cost a total of 10 days x $1.32/day =
$13.20 per enclosure, supplementing the natural supply of N with a tiny and cheap
amount of added 15N. This sounds easy, and it is.
Next, the low cost of the single enclosure experiment leads us to think about more
replicate enclosures, and we decide we would like to run the experiments in triplicate.
This will mean 3 times as much label, but still an affordable cost of $39.60. With this
rather small cost in mind, we realize that we can easily add much more label, and decide
to increase additions to 4x background instead of 1x background, targeting 4000o/oo
instead of 1000o/oo, just in case there are leaks in our bags, the ammonium
concentrations are higher than we expected, etc. – any of a number of reasons that nature
might dilute our label and ruin our summer plans. For a 4000o/oo label, we work out the
math as above, considering now that in the “ratios” part of the  definition, we want a
value of 5 = [(5.5+x)/(1395+9x)]/(5.5/1395), so that x = 26.745mg 15N for one daily
addition to a single enclosure. Multiplying by 30 (for 3 enclosures of 10 days each), we
find we need 802mg of 15N, somewhat more than the 658mg that is in whole bottle we
can order for $147. So, no problem, we will get two bottles – a little extra anyway in case
there are any spills or other unforeseen catastrophes. We call up and tell the story to the
nice salesperson, that we want two bottles and not just one bottle - “better safe than
sorry”, the salesperson is quick to agree, happy to help a customer spend more money.
Later we remember one of our early concerns – we don’t want to add too much
ammonium because that might fertilize the system. We want to do a true tracer addition
experiment, one that is subtle where only the isotope color is changed, not the amounts.
We read about tracer experiments and find that if total N concentrations change <5%,
scientists generally consider this a low-level tracer addition. Our daily additions with the
10% labeled ammonium will add 26.745mg of 15N to each enclosure, but also 9x that
amount of 14N = 240.705mg, for a total of 267.45mg N to the natural daily sediment
supply of 1400mg total N. This is a 19% increase over the natural rate, a little above the
5% limit for true tracer experiments. At this point, we act as purists, and drop back to a
1000o/oo target label because that will cut the total N addition from 267.45mg to 59.2mg.
Using 59.2 mg results in a 4.2% increase in total N vs. background, well within the 5%
limit for true tracer experiments. So, first 1000o/oo, then 4000o/oo, and now back to
1000o/oo - up and down we go with our enrichments, changing our minds to get the best
scientific balance.
But for now, we are happy to have finished the calculations for the three
enclosures that will have label additions this first summer. We move on to plans for
control enclosures. We plan three parallel enclosures that have no ammonium additions,
and three other enclosures with additions of normal ammonium chloride that lacks added
15
N label and is quite cheap (<$1). As you sit there at the end of the winter’s day, you
think that setting up and tending 9 enclosures sounds about right for the coming
summer’s field work.
But you also wonder if you have thought of everything, and so contact an expert
who routinely does this type of experiment. Fortunately, the expert finds few mistakes in
your work, and indeed the expert points out only two flaws which you can fix. First, he
tells you that additions should be made frequently at 0.1-0.5x turnover rates of the target
pool that is ammonium in this case. Frequent additions are needed so that the target pool
will keep a fairly constant isotope value. Thinking about this, you realize that because
ammonium is turning over about once per day in your mesocosms, 15N additions made
once a day would result in very high 15N values just after the addition, but low values 24
hours later just before the next addition. In other words, ammonium isotope values would
oscillate strongly between additions. Although these oscillations might dampen out over
time as the sediment source of unlabeled N becomes slowly labeled, you resolve to make
the additions every 6 hours instead of every 24 hours. The more frequent additions could
mean some sleep-deprived nights, but then again, it is only for 10 days, and friends will
help sometimes. Also, you start to make some long-term plans to buy peristaltic pumps so
that you can add the labeled ammonium continuously, which is very frequently indeed.
The second flaw that the expert notes is that you limited yourself to a 1000o/oo
spike signal by working with a 10% labeled compound. If you used a somewhat more
expensive but readily available 99% 15N labeled ammonium chloride instead of the 10%
labeled compound, you could easily have additions to  values of 4000o/oo and higher.
This makes sense because with a more concentrated 99% compound replacing your 10%
spiked compound, you should get a much stronger 15N tracer signal. You calculate that
adding 99% pure 15N, you could enrich the ammonium pool to 12,600o/oo while still
satisfying the philosophical tracer requirement that the total ammonium concentrations
should increase less than 5% above background levels. You find this calculation
convincing, and decide that the next time you have to buy 15N, you will think hard about
buying compounds with 99% 15N.
Later that spring, it occurs to you that you could also add a 13C label to the
inorganic carbon pools in your enclosures. Phytoplankton uptake of this 13C label would
provide a second label besides 15N for tracing the fate of new plankton production, and
would also let you see when and where carbon and nitrogen cycle together, and when
they diverge. You go through similar calculations to those outlined above for 15N, but
there is a difference. In the carbon cycle, phytoplankton use dissolved inorganic carbon
(DIC, present mostly as bicarbonate) for photosynthesis. But background standing stocks
of DIC are quite high, do not turn over rapidly, and phytoplankton rarely deplete these
DIC stocks. In this case, you don’t target the supply for label addition. Instead, you think
about a one-time label addition to existing stocks. But because the background DIC
stocks are high, an affordable label in terms of costs ($/experimental enclosure) only
brings the signal to about 100o/oo, in a range where you have to worry about
fractionations that can range from 10-30o/oo. (And in case you are wondering, yes,
fractionation is generally quite similar in spiked systems and unspiked systems. For
example, if a 20o/oo fractionation during photosynthesis lowers carbon isotopic
compositions from a -10o/oo DI13C value to a phytoplankton organic carbon value near 30o/oo in an unspiked enclosure or natural lake, then the same 20o/oo fractionation will
apply in a spiked system, with +100o/oo DIC yielding phytoplankton organic carbon with
values near 80o/oo. Problems 6 and 7 at the end of the chapter involve exact comparisons
of fractionation differences in spiked and natural systems).
With these thoughts in mind, you decide to do the 13C addition in just one
enclosure, just to see how it works, then perhaps do more 13C additions in following
years. You hasten to order the 13C-labeled bicarbonate.
With your plans complete, you begin to think about how much fun you will have
this first “Isotope Summer”, and alert your friends that this endeavor will likely lend
itself to summer reruns for the next few years. They look at you and see isotope
happiness beaming back at them, and so wish you much luck this coming summer.
And then the summer arrives. You spend almost the whole summer just setting up
the nine enclosure experiments, only to find that just when you think everything is
perfect, it turns out that your enclosures aren’t fastened well to the bottom and all blow
away in the wind and waves of a big storm. In the end, you only have results from two
days. Ouch! And later the next winter, when you receive the 15N results from just these
first two days, you discover that even before the storm, you had many leaks at the bottom
of your enclosures, where the cylinders were supposedly firmly fastened to the mud.
Storms, faulty fasteners and bad luck – just one of those things, you sigh over beer.
But you are at the start of your graduate career, and more summers are down the
road. And besides, you have true grit, you are plucky, and anyway it was lots of fun to
work at the lake during the summer. You take a deep breath, square your shoulders and
start another round of planning new experiments for “Isotope Summer 2 – the Rerun”.
This time, the enclosures won’t include mud, but will be just giant plastic tubes, crimped
and sealed together at the bottom like a giant condom - a new summer, a new
experimental design. Of course it will work.
Having made these bold revisions, you realize the new plans also change your 15N
addition strategy, because now the only supply of new N to the enclosures will be N that
you add – but that is easy. You just add 100 millimoles of unlabeled N each day, just
replacing the supply from the sediment. You can add unlabeled N along with your 15N
spike, and you can make up a stock solution that combines both kinds of N. This sounds
good, but then the dreaded question repeats itself: “to make the stock solution, how much
isotope should I add”?
Well, for a 1000o/oo label, the amount you add is just the amount you have
already calculated, 224.9mg of the 10% labeled N compound + unspiked ammonium
chloride that has 1400mg of N. Remembering that the fraction of N in un-spiked
ammonium chloride is 0.2617 (= 14/53.49, the mass of N in the compound/total mass of
the compound), we divide 1400 by 0.2617, obtaining 5349.6mg for the amount of
unspiked compound. Summarizing, the totals are 224.92mg of the 10% labeled
compound and 5349.6mg of the unlabeled compound per enclosure per day. You divide
the daily additions by 4 to account for the additions you are planning to make every six
hours (because you still have not figured out how to organize peristaltic pumps for
continuous additions), obtaining 56.23mg labeled compound and 1337.4mg unlabeled
compound that you want to add every 6 hours to each enclosure. That is the answer.
In the end, you decide to make up your stock solution so that you can use 10mls
of stock solution each time you make an addition to an enclosure. A dose of 10 mls will
be easy to measure and work with, even in stormy conditions you now know sometimes
haunt your lake research site. You see that if you have 1200mls of your stock solution,
you will have enough to spike 3 enclosures 4 times a day for 10 days, using 10mls for
each spike addition. Good. Of course, when the time comes to actually do this, you make
a double batch of 2400mls for safety, in case you spill some. Let’s finish by calculating
how much ammonium chloride we will need for these 2400mls: yes, 240 doses times
10mls each will be 2400mls, and the amount of unlabeled ammonium chloride will be
240 x 1337.4mg = 321g and the amount of 10% labeled ammonium chloride will be 240
x 56.23mg = 13.5g. These are the answers you circle in red on your spreadsheet. You
remind yourself to recheck this all tomorrow one more time, to make sure all the
calculations are correct.
But, yawn…by now all these spiking calculations are starting to sound familiar.
You realize you are gaining experience here, and begin smiling that happy isotope smile
once again, looking out your winter window with anticipation, hoping the storms will
stay away from your enclosures next summer. And, they do – your persistent pays off,
and the experiment works well. So you begin thinking about “Isotope Summer III– the
Rerun Revisited”, but now you find yourself are itching to add tracer to streams that feed
the lake. New isotope horizons beckon constantly for those interested in the golden spike
award…
Problem 8 in the Chapter 6 folder on this CD asks you to calculate how much
isotope you should add for a stream ecosystem experiment.
Further Reading
Coleman, D.C., and B. Fry. 1991. Carbon Isotope Techniques. Academic Press, Inc.
Fry, B., C.H. Hopkinson Jr., A. Nolin, U.L. Zweifel, and B. Norrman. 1996. Long-term
decomposition of DOC from experimental diatom blooms. Limnology and
Oceanography 41:1344-1347.
Knowles, R. and T.H. Blackburn. 1993. Nitrogen Isotope Techniques. Academic Press,
Inc.
Norrman, B., U.L. Zweifel, C.S. Hopkinson Jr., and B. Fry. 1995. Production and
utilization of dissolved organic carbon during an experimental diatom bloom. Limnology
and Oceanography 40:898-907.
Ostrom, N.E., L.O. Hedin, J.C. von Fischer and G.P. Robertson. 2002. Nitrogen
transformations and NO3- removal at a soil-stream interface: a stable isotope approach.
Ecological Applications 12:1027-1043.
Schimel, D.S. 1993. Theory and Application of Tracers. Academic Press, Inc.
Tobias, C.R., M. Cieri, B.J. Peterson, L.A. Deegan, J. Vallino and J. Hughes. 2003.
Processing watershed-derived nitrogen in a well-flushed New England estuary.
Limnology and Oceanograpy 48:1766-1778.
Tobias, C.R., S.A. Macko, I.C. Anderson, E.A. Canuel and J.W. Harvey. 2001. Tracking
the fate of a high concentration groundwater nitrate plume through a fringing marsh: a
combined groundwater tracer and in situ isotope enrichment study. Limnology and
Oceanography 46:1977-1989.