(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 922662, 18922]*) (*NotebookOutlinePosition[ 937331, 19459]*) (* CellTagsIndexPosition[ 937287, 19455]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ Some simple models for carbon in the atmosphere and how earth \ temperature might be affected\ \>", "Title"], Cell[TextData[{ "This notebook has been written in ", StyleBox["Mathematica ", FontSlant->"Italic"], "by \n\n", StyleBox["Mark J. McCready\nProfessor and Chair of Chemical and \ Biomolecular Engineering\nUniversity of Notre Dame\nNotre Dame IN 46556\nUSA", FontSize->14], "\n\n", ButtonBox["Mark.J.McCready.1@nd.edu", ButtonData:>{ URL[ "mailto:mccready.1@nd.edu"], None}, ButtonStyle->"Hyperlink"], "\n", ButtonBox["http://www.nd.edu/~mjm/", ButtonData:>{ URL[ "http://www.nd.edu/~mjm/"], None}, ButtonStyle->"Hyperlink"], "\n\n\nIt is copyrighted to the extent allowed by whatever laws pertain to \ the World Wide Web and the Internet.\n\nI would hope that as a professional \ courtesy that this notice remain visible to other users. \nThere is no charge \ for copying and dissemination \n\nVersion: 01/29/04\nMore recent versions \ of this notebook should be available at the web site:\n", ButtonBox["http://www.nd.edu/~mjm/carbon-energy-model.nb", ButtonData:>{ URL[ "http://www.nd.edu/~mjm/carbon-energy-model.nb"], None}, ButtonStyle->"Hyperlink"], "\n\nIn this notebook, the \"textbook\" is Houghton et al. ", StyleBox["Climate Change 2001, The Scientific Basis, ", FontSlant->"Italic"], " Cambridge Press 2001\n " }], "Text"], Cell[CellGroupData[{ Cell["Goals of this Lecture", "Subtitle"], Cell[TextData[{ "This material is intended to give you a first level idea of how various \ processes interact to determine the concentration of carbon dioxide in the \ atmosphere and through changes in CO2, the temperature of the earth. Also, \ that are intended to show what different terms in the mathematical model mean \ physically. These models are very much more simple that those used for \ scientific work! Also, the output \"numbers\" are only relative. So please \ use these only for their educational value. \n\nHaving given the \ disclaimer...\n\nYou should see that the ", StyleBox["Simplest Model", FontSlant->"Italic"], " contains terms for the most important processes that goven the CO2. A \ source term represents fossil fuel emissions and deforestation, one sink term \ represents the absorption in the ocean. The other sink term represents the \ regrowth of forests and woody plants. \n\nThe next simplest model allows a \ linear increase in the CO emissions, which is close to one of the standard \ scenarios. The values of CO predicted are thus closer to the standard \ models." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Background and motivation", "Subtitle"], Cell[TextData[{ "As we have seen, measurements of atmospheric CO2 have increased \ substantially in the past 150 years. See ", ButtonBox["http://cdiac.esd.ornl.gov/trends/trends.htm", ButtonData:>{ URL[ "http://cdiac.esd.ornl.gov/trends/trends.htm"], None}, ButtonStyle->"Hyperlink"], " for all of our favorite measurements. Temperature change data could be \ considered to be less definitive, however, the best available modelling \ efforts point to increased CO2 concentration as a cause of some of the \ apparent warming in the 20th century. 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[2002] PNAS, 99, p1389 and Myneni et al. \ [2001] PNAS 98, p14784.\ \>", "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Simplest Carbon Balance model", "Subtitle"], Cell[TextData[{ "For this section, I used some insight, but not the complete equations \ from:\n", ButtonBox["http://www.atmos.washington.edu/honors_220/model/model_\ instructions.html", ButtonData:>{ URL[ "http://www.atmos.washington.edu/honors_220/model/model_instructions.\ html"], None}, ButtonStyle->"Hyperlink"], ", by Professor David Battisti, university of Washington, Atmospheric \ Science Department, ", ButtonBox["david@atmos.washington.edu", ButtonData:>{ URL[ "mailto:david@atmos.washington.edu"], None}, ButtonStyle->"Hyperlink"], StyleBox["\n", FontFamily->"Comic Sans MS"], "and Professor Nathan Mantua, ", ButtonBox["mantua@atmos.washington.edu", ButtonData:>{ URL[ "mailto:mantua@atmos.washington.edu"], None}, ButtonStyle->"Hyperlink"], StyleBox["\n\n", FontFamily->"Comic Sans MS"], StyleBox["The Model:", FontFamily->"Comic Sans MS", FontSize->16], "\n\nIf we take the atmosphere as a \"control volume\" for our simplest \ mass balance, we can write:\n", StyleBox["\nrate of change of carbon in the atmosphere = rate of addition \ by fossil fuel use and forest burning -\n \ rate of absorption into the ocean-\n \ rate of net \ fixation by plan growth", FontSlant->"Italic"], "\n \n\ The source number matches the current value from the text: \"Climate Change \ 2001\" Chapter 3, p 208, and is held constant for this model.\n \nThe sink \ terms contain a driving force times a transfer coefficient, as discussed in \ class. The \"thermodynamic driving force\" is assumes proportional to the \ current concentration and a \"preindustrial\" value of CO2 concentration. A \ preindustrial value assumes that the \"trees/net tree growth\" are in \ equilibrium with this value from the last century. Likewise with the oceans. \ You can think about how valid either of these assumptions is.\n\nThe key \ feature of the \"simplest model\" is that the source term is constant!" }], "Text"], Cell[BoxData[{ \(\(F = \ 7.5;\) (*\(\(*\)\(\ \ \)\(fossil\)\(\ \)\(fuel\)\)\ + \ forest\ burning\ **) \), "\[IndentingNewLine]", \(\(\[CapitalGamma]\ = \ .014;\) (*\(*\)\(\ \ \)\(Ocean\)\(\ \)\(uptake\ \)\(\ \)\(coefficient\ --\)\(\ \)\(value\)\(\ \)\(obtained\)\(\ \)\(by\)\(\ \ \)\(fitting\)\ **) \), "\[IndentingNewLine]", \(\(\[Beta]\ = \ .018;\) (*\(*\)\(\ \ \)\(Land\)\(\ \)\(uptake\)\(\ \ \)\(coefficient\ --\)\(\ \)\(value\)\(\ \)\(obtained\)\(\ \)\(by\)\(\ \ \)\(fitting\)\ **) \), "\[IndentingNewLine]", \(\(Co\ = \ 280;\) (*\(\(*\)\(\ \ \)\(PreIndustrial\)\(\ \)\(CO2\)\(\ \)\(value\)\ \), \ PPM**) \), "\[IndentingNewLine]", \(\(Cpresent\ = \ 370;\)\ (*\(\(*\)\(\ \ \)\(Current\)\(\ \)\(CO2\)\(\ \)\(value\)\), \ \ PPM**) \), "\[IndentingNewLine]", \(\(tfinal = \ 100;\) (*\(*\)\(\ \ \)\(total\)\(\ 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This will allow us to \ more easily make the functional dependence of the source be something other \ than a linear increase.\ \>", "Text"], Cell[BoxData[ \(\(Clear[F, t];\)\)], "Input", CellLabel->"In[499]:="], Cell[BoxData[{ \(\(Fo = \ 7.5;\)\ (*\(\(*\)\(\ \ \)\(fossil\)\(\ \)\(fuel\)\)\ + \ forest\ burning\ **) \), "\[IndentingNewLine]", \(\(\[Psi] = \ .12;\)\ \ (*\(*\)\(\ \ \)\(Rate\)\(\ \)\(of\)\(\ \ \)\(fossil\)\(\ \)\(fuel\)\(\ \)\(increase\)\(\ \)\(in\)\(\ \)\(Pg/ year\)\ **) \), "\[IndentingNewLine]", \(\(\[CapitalGamma]\ = \ .014;\) (*\(*\)\(\ \ \)\(Ocean\)\(\ \)\(uptake\ \)\(\ \)\(coefficient\ --\)\(\ \)\(value\)\(\ \)\(obtained\)\(\ \)\(by\)\(\ \ \)\(fitting\)\ **) \), "\[IndentingNewLine]", \(\(\[Beta]\ = \ .018;\) (*\(*\)\(\ \ \)\(Land\)\(\ \)\(uptake\)\(\ \ \)\(coefficient\ --\)\(\ \)\(value\)\(\ \)\(obtained\)\(\ \)\(by\)\(\ \ \)\(fitting\)\ **) \), "\[IndentingNewLine]", \(\(Co\ = \ 280;\) (*\(\(*\)\(\ \ \)\(PreIndustrial\)\(\ \)\(CO2\)\(\ \)\(value\)\ \), \ PPM**) \), 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We use the 0-dimension balance from the \ Energy balance lecture,\n", Cell[BoxData[ ErrorBox[\(URL[\(\(http\)\(:\)\) // \(www . nd . edu/\(\(~\)\(mjm\)\)\)/ energy_balance _lect . nb]\)]]], " " }], "Text"], Cell[BoxData[ \(\(Clear[F, t];\)\)], "Input", CellLabel->"In[794]:="], Cell[BoxData[{ RowBox[{\(Fo = \ 6;\), " ", \( (*\(\(*\)\(\ \ \)\(fossil\)\(\ \)\(fuel\)\)\ + \ burning\ **) \)}], "\[IndentingNewLine]", RowBox[{\(\[Psi] = .12\ *0;\), " ", \( (*\(*\)\(\ \ \)\(Rate\)\(\ \)\(of\)\(\ \)\(fossil\)\(\ \ \)\(fuel\)\(\ \)\(increase\)\ **) \)}], "\[IndentingNewLine]", RowBox[{\(\[CapitalGamma]\ = \ .014;\), \( (*\(*\)\(\ \ \)\(Ocean\)\(\ \ \)\(uptake\)\ **) \)}], "\[IndentingNewLine]", RowBox[{\(\[Beta]\ = \ .018;\), \( (*\(*\)\(\ \ \)\(Land\)\(\ \ \)\(uptake\)\ **) \)}], "\[IndentingNewLine]", RowBox[{\(Co\ = \ 280;\), \( (*\(*\)\(\ \ \)\(PreIndustrial\)\(\ \)\(value\)\ **) \ \)}], "\[IndentingNewLine]", RowBox[{\(tfinal\ = \ 100;\), "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{\(S = 1370\ \ ;\), " ", RowBox[{"(*", RowBox[{"*", " ", "Solar", " ", "Constant", " ", RowBox[{"W", "/", FormBox[\(m\^2\), "TraditionalForm"]}]}], " ", "**)"}], " "}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Sigma]", "=", RowBox[{"5.670", FormBox[\(10\^\(-8\)\), "TraditionalForm"]}]}], ";"}], " ", RowBox[{"(*", RowBox[{"*", " ", "Boltzman", " ", "Constant", " ", RowBox[{"W", "/", FormBox[\(m\^2\), "TraditionalForm"]}], FormBox[\(K\^4\), "TraditionalForm"]}], " ", "**)"}]}], "\[IndentingNewLine]", RowBox[{\(\[Epsilon] = .99;\), " ", \( (*\(*\)\(\ \ \)\(Surface\)\(\ \)\(emmisivity\)\ \ \ \ **) \)}], \ "\[IndentingNewLine]", RowBox[{\(\[Alpha] = .3\ ;\), \( (*\(*\)\(\ \ \)\(Average\)\(\ \ \)\(Albedo\)\ **) \)}]}], "Input", CellLabel->"In[795]:="], Cell[BoxData[{ \(\(c[1] = 370;\) (*\(*\)\(\ \ \)\(Initial\)\(\ \)\(carbon\)\(\ \)\(dioxide\)\(\ \ \)\(value\)\ **) \), "\[IndentingNewLine]", \(\(F[1] = Fo;\) (*\(*\)\(\ \ \)\(fossil\)\(\ \)\(fuel\)\(\ \)\(initial\)\(\ \ \)\(value\)**) \), "\[IndentingNewLine]", \(\(dt = 1;\) (*\(*\)\(\ \ \)\(size\)\(\ \)\(of\)\(\ \)\(time\)\(\ \ \)\(step\)\(\ \)\(in\)\(\ \)\(years\)\ **) \), "\[IndentingNewLine]", \(\(index\ = \ tfinal;\) (*\(*\)\(\ \ \)\(total\)\(\ \)\(years\)\(\ \)\(for\)\(\ \ \)\(the\)\(\ \)\(run\)\ **) \), "\[IndentingNewLine]", \(\(t[1] = 0;\) (*\(*\)\(\ \ \)\(Initial\)\(\ \)\(time\)\ **) \), "\ \[IndentingNewLine]", \(\(tau[ 1]\ = \ .62;\) (*\(*\)\(\ \ \)\(Initial\)\(\ \)\(value\)\(\ \ \)\(of\)\(\ \)\(the\)\(\ \)\(IR\)\(\ \)\(transmittence\)\ **) \), "\ \[IndentingNewLine]", \(\(T[1]\ = \ 288. \ ;\) (*\(*\)\(\ \ \)\(Initial\)\(\ \)\(average\)\(\ \)\(earth\)\ \(\ \)\(temperature\)\ **) \), "\[IndentingNewLine]", \(\(\[Eta] = \ .00015;\) (*\(*\)\(\ \ \ \)\(Sensitivity\)\(\ \)\(of\)\(\ \ \)\(tau\)\(\ \)\(to\)\(\ \)\(increased\)\(\ \)\(water\)\(\ \)\(vapor\)\(\ \ \)\(in\)\(\ \)\(the\)\(\ \)\(atmosphere\ --\)\(\ \)\(a\)\(\ \)\(guess\)\ **) \ \), "\[IndentingNewLine]", \(\(\[Xi]\ = \ .00009;\) (*\(*\)\(\ \ \)\(Sensitivity\)\(\ \)\(of\)\(\ \ \)\(tau\)\(\ \)\(to\)\(\ \)\(increased\)\(\ \)\(CO2\)\(\ \)\(in\)\(\ \ \)\(the\)\(\ \)\(atmosphere\ --\)\(\ \)\(a\)\(\ \)\(guess\)\ **) \)}], "Input",\ CellLabel->"In[805]:="], Cell["\<\ Here is the start of the loop. 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