Technical Supplement 6B
Noisy Data and Data Analysis with Enriched Samples
Noisy Data. In enrichment experiments, the  data often seem noisy. While
normal duplicate samples in natural abundance studies agree by better than 1o/oo,
duplicate field samples in enrichment studies often disagree by >50o/oo when  values
are near 1000o/oo. The usual problem is that samples are not really homogeneous, poorly
pooled in the field, or poorly ground and prepared in the laboratory. The mass
spectrometer measurements can be still accurate to +1o/oo at high enrichments of
1000o/oo. If you want to work on improving the precision of your field replicates, first
test your mass spec lab by analyzing a crystallized compound that has been enriched with
heavy isotope. Are the replicates of this material +1 or +10o/oo? This level of precision is
the best you can hope for under ideal laboratory conditions. This also provides reference
for the possible precision you can achieve with your field samples, and can help guide
your efforts to better collect and prepare the field samples.
Data Analysis. There are four fine points that come up in data analysis when
working with enriched samples. Considering these points may help slightly improve the
accuracy in your final interpretations. These fine points are probably best handled in
computer spreadsheets.
1. The measurements underestimate actual enrichment. This is a little-known
problem, and you need to check with your isotope laboratory to see if it is actually a
problem in the way the data is calculated in that laboratory. The common problem is that
with artificially spiked samples, the heavy isotope signal spills over into parts of the
measurement array that are not normally included in the isotope counting. For example,
with nitrogen (N2) gas, most gas is 14N14N (mass 28), a small amount is 15N14N (mass 29)
and an extremely tiny amount is 15N15N (mass 30). The normal measurement considers
only masses 29 and 28, leaving mass 30 out of the picture. But when you add 15N to
tracer samples, it turns out you strengthen not only mass 29 but also mass 30, with
stronger additions leading to more and more of the heavy isotope appearing in mass 30.
Because this mass 30 isotope is not normally counted, many laboratories will
underestimate the true amount of heavy isotope in your enriched samples. So, the advice
here is to talk with the lab tech on this point. You can also refer to Technical Supplement
2A in the Chapter 2 folder on this CD for a more detailed exposition of these
measurement problems. There you will see that, for example, a sample measured at
1000o/oo in most laboratories underestimates the true value by about 4o/oo, i.e., the
actual number should be 1004o/oo, not 1000o/oo. These issues are also important for
N2O as well as N2 work when tracer-level 15N is added to systems (Bergsma et al. 2001).
2. Fractionation seems to change with enrichment, especially when isotope values
are expressed in  units. There are some odd features of fractionation in enrichment
experiments, as you will see if you work through problems 6 and 7 at the end of this
chapter. But overall, typical fractionation effects of 1-20o/oo are small enough to ignore
when enrichments are large, >1000o/oo. But on the other hand, why leave out
fractionation and increase your errors? Including fractionation in model evaluations of
the enrichment results is easily accommodated with I Chi practice.
3. Enrichment is expressed as E. In data analysis with enriched samples, one
usually expresses the isotope enrichment in a sample vs. a background control. A shorthand way to do this is to subtract out the isotope value of the control, but the better way
to make this correction is to use a more complex formula, expressing the enrichment
between two samples as the per mille enrichment value, E, where
E = [(1 – 2)/(2 + 1000)]*1000
(This equation is derived in the printed Appendix for the book, conversion 1). Example:
An isotope-enriched algal sample has a 15N value of 600o/oo and a control sample of
this same species has a value of 10o/oo. The value for E is 584.2o/oo, close to, but not
the same as the incorrect enrichment value of 590o/oo obtained by simple subtraction
(600-10 = 590o/oo).
4. Atom percent. For highly enriched C and N samples whose  values exceed
about 4,000 and 12,000o/oo, respectively, it is better to use an alternate and more exact
notation in mixing calculations, the atom percent notation that can be derived from the 
notation. Unfortunately, for highly enriched samples,  values become increasingly
unreliable in the simple mixing equations (Technical Supplement 2A in the Chapter 2
folder on this CD explains this in detail). So, it is better to switch to atom percent that is a
direct measure of “% isotope”, and use the atom percent values in the normal mixing
equations. Spreadsheets make it easy to convert  values to atom percent values, using
the following formula derived from the  equation (see printed Appendix for the book,
conversion 4):
atom percent of heavy isotope =  + 1000)/[( + 1000+ (1000/RSTANDARD)]
where  is the measured  value, and RSTANDARD is the known isotope ratio of the
standard.
Example: an aquatic insect from an isotope enrichment experiment has a 15N
value of 350o/oo, and two potential foods measure 80 and 700o/oo. What are the source
contributions for these two foods? Solution: convert the values to atom % values, using a
RSTANDARD value of 0.0036765 for 15N/14N in air N2, the standard for nitrogen work;
Table 2.1). Then substitute the atom percent values for  value into the two source
mixing equation discussed in Chapter 3:
f1 = fractional contribution of source 1 = (SAMPLE - SOURCE2)/(SOURCE1- SOURCE2)
 values for source 1, source 2 and the sample are 80, 700, and 350o/oo respectively, and
the corresponding atom % or “%15N” values are 0.39549%, 0.62112% and 0.49388%.
The solution is f1 = (0.49388 - 0.62112)/(0.39549 - 0.62112) = 0.5639, the fraction
contributed by the 80o/oo source 1, and the fraction contributed by the 700o/oo source 2
is 1- f1, or 0.4361.
We can compare this f1 = 0.5639 answer to that obtained with the original 
values, f1 = (350-700)/(80-700) = 0.5645, finding an almost identical result. So, in this
case, using the  values in the mixing equation is acceptable. However, in experiments
with much higher isotope enrichments, differences between the two methods start to
exceed 0.01 in the final fractional result (e.g., for the case when 15N-enriched values are
80, 11500 and 4946o/oo for source 1, source 2 and the sample, respectively, then f1 =
0.5639 when calculated with atom %, but f1 = 0.5739 when calculated with  values; the
difference in these f1 values equals 0.01). The results based on atom % are always the
correct results, and especially as 15N values become larger than 11,500o/oo, calculations
should be based on atom %. (Note: for carbon isotopes, the enrichment at which
differences in f start to exceed 0.01 is lower, about 3,900o/oo instead of 11,500o/oo. This
lower 3,900o/oo value for 13C enrichment is due to a difference in the isotope value of the
C vs. N standard used in the atom % calculations. See Table 2.1 for isotope values of
these standards).
Problems 9 and 10 in the Chpater 6 folder on this CD consider further when to use
atom % rather than  values for expressing isotope values in tracer addition experiments.
Further Reading
Bergsma, T.T., N.E. Ostrom, M. Emmons and G. P. Robertson. 2001. Measuring
simultaneous fluxes from soil of N2O and N2 in the field using the 15N-gas
“nonequilibrium” technique. Environmental Science and Technology 35:4307-4312.