Guide to I Chi Spreadsheets
This folder contains electronic models for examples presented in this book. The
models are constructed in Excel workbooks with spreadsheet calculations. To orient
yourself to what is supposed to happen in these workbooks, you may want to find the
corresponding section in the book, then read the text about that example before actually
opening a workbook.
When you open the workbook, you will find spreadsheets that generally have
master variables in the upper left sections. These master variables are highlighted in bold
and are there for you to manipulate. Type in a value and watch what happens in the
isotope graphs. Change those master values to get a feeling for linkages between mixing
and fractionation, the big themes of the book. One of the simplest and most informative
things to do in each spreadsheet is to set fractionations equal to zero, so that only mixing
controls dynamics. Change the gain terms, then the loss terms and observe the effects on
mixing. After understanding these mixing effects, then turn on fractionation again by
typing in a non-zero  fractionation value, and watch what happens. Try it! With gains
and losses involved in mixing fixed at constant values, you can evaluate fractionation.
And don’t forget to try various combinations of the individual mixing and fractionation
values you have been using – the combined effects are most complex, and most
interesting. In sum, try manipulating the master variables in the spreadsheets of this
Appendix – you may be surprised how much isotopes change, depending on how you set
up mixing and fractionation in these examples.
In some examples, you may find that changing master variables leads to odd and
nonsense results. Two particular problems deserve mention. First, when loss terms are
too great, pools or reservoirs start to have negative values and many odd features result in
the I Chi graphs. If this is happening, make the loss terms smaller, so that amounts in
pools always stay positive. Second, changing master variables can give data off the
charts, beyond the normal scales. To reset the scale of an x-axis or y-axis in a graph, use
your cursor to click on the axis. A box labeled “format axis” should appear. Click again
on the tab labeled “scale”, and reset the “maximum” value to a higher number, then click
on the “ok” button. The scale will reset, and now your data should appear on the chart.
Back-up versions of the workbooks are provided, so that if you change variables
and overwrite the original material, you have a spare copy to use for reference. Generally,
if you want to save your work, you can make your own copy of the workbook and save
your work therein.
Beyond simply typing in different values and saving your new scenarios, also you
can access the mathematics in these worksheets. You can look more closely at the math
underlying the spreadsheets by clicking on individual cells, examining the formulas used
at each location. Those formulas appear in the toolbar line just above the worksheet, and
if you use your cursor to click on the formula there, color highlighting appears so that
you can see spreadsheet values used in the equation.
The examples have similar math, the “I Chi” equations introduced in section 4.3.
Calculations are done sequentially in horizontal rows in the spreadsheet, with the results
in the final columns copied into the first columns of the next row. Each row represents
one time step with typically several processes happening across the columns in that time
step/row. This is the step-by-step philosophy of I Chi. There are detailed examples in
Section 4.4 about how this math is set up and actualized in the spreadsheets – consult that
section 4.4 to get a feel for how the calculations are set up in a sequential manner in rows
and columns.
Finally, you can write your own examples, and introduce your own I Chi
equations, amending the workbook models. The equations are actually simple algebra,
summarized in Section 4.3. Writing your own I Chi is not nearly as hard as it may look at
first glance, but then again, thinking with math is its own challenge.
For those who are interested, there are several more I Chi examples in this folder
(Answers to Problems, I Chi Spreadsheets), where the workbooks give answers to
problems posed in Chapters 4 and 7.
Special notes on individual workbooks:
Workbooks 4.6a and 4.6b, Exact vs. I Chi Simple and Exact vs. Ratio. These workbooks
compare different ways of calculating the same I Chi problem, and are included for
readers interested in errors. Section 4.6 gives a detailed guide to these workbooks,
reproduced below.
Workbook 4.6a:
The worksheet “short form simple” shows the calculations for exact budgeting of
heavy and light isotopes in columns A-U, then columns AA-AK show the normal I Chi
calculations based on . Differences between the two methods in calculated  values are
given in column AM. Graphs show the  values vs. time and the differences between the
two methods vs. time. The exact budgeting is based on fractional abundances, or “F”
values, and the title “F-based” calculations refers to the exact budgeting approach.
In the remaining worksheets, the equations are extended from 10 time steps to
about 2000 time steps in a “long form” comparison. Different scenarios are compared
where gain>>>loss, gain = loss, and gain <<< loss. You can change master variables
highlighted in bold (see cells K2, K3 and P2 and P3) to explore similarities and
dissimilarities between the two methods of calculating  values in these dynamic gainloss models.
Workbook 4.6b:
Workbook 4.6b is parallel to workbook 4.6a, but gives comparisons between the I
Chi model with exact equations for both fractionation and mixing vs. a model with the
exact fractionation equations but the simpler I Chi mixing equations of section 4.2.
Inspection of the various scenarios presented in workbook 4.6b shows very little
difference at all in any scenario. This simple substitution for fractionation is therefore
recommended to readers interested in gaining exactness generally, those interested in
hydrogen isotopes that have large fractionations, and those working with highly enriched
samples.
Workbooks 5.7 and 5.8, A Muddy Case and the Qualquan Chronicles. The increment
across the rows is a unit of space rather than time, and values do not wrap around from
one row to the next. The ends of sections 5.8 and 5.9 give explanations of these special I
Chi examples, and those explanations are reproduced below:
Workbook 5.7. This workbook implements a spatial I Chi approach for the mud core, and
the spatial approach used here (and in the next section) is a little different than the timebased I Chi models used otherwise in this book. The difference is that in these spatial
models, there is no time-based wrap-around from one section of the core to the next. (The
time-based wrap-around step is described in section 4.4, step 6). Instead, there is a
different initial condition for each section of the core. In this case, the different initial
condition in each row is a different amount of human nitrogen that can be determined by
the reader. The subsequent equations of the row use this initial condition for that row to
calculate the total amount and isotope value of the nitrogen, but these results do not wrap
around and influence the calculations of the next row. Thus, the model simulates N
deposited sequentially, without disturbance from processes such as bioturbation or
diagenesis that would operate across core sections.
Workbook 5.8 in Appendix 1. This workbook implements a spatial I Chi approach for the
qualquan landscape, and the spatial approach used here (and in the previous section) is a
little different than the time-based I Chi models used otherwise in this book. The
difference is that in these spatial I Chi models, there is no time-based wrap-around from
one row of the model to the next. (The time-based wrap-around step is described in
section 4.4, step 6). Instead, there is a different initial condition for each row, i.e., a
different value for the open water:marsh ratio. The subsequent equations of the row use
this initial condition to calculate qualquan results, but these results do not wrap around
and influence the calculations of the next row. The consequence is that Figures 5.31 and
5.32 compile qualquan results into smooth trends using many individual landscapes that
differ in their open water:marsh ratios. These figures do not portray results for a single
landscape with linked production and consumption processes.
Workbook 7.2, Isotopium. The fractionation factors of this workbook 7.2 follow a
slightly different usage than in the rest of this book. Fractionations are given in terms of
heavy/light isotopes instead of light/heavy isotopes for the closed system reactions of this
workbook. Thus, the workbook uses - instead of  and H/L instead of L/H. These
differences are explained in Box 2.1 in Chapter 2. The reason for this switch is to follow
closely the derivations for closed system equations given in Section 7.3. In most cases,
you can substitute – simply for  values where the fractionation is 100o/oo or less
because - and  will have the approximately the same value (see Box 2.1). For larger
fractionations, however, there is a difference, especially that - values cannot exceed
1000o/oo, while  values can.