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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.