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[null,"choosen global path:",null,{"$f":"'global path'!C2","v":3},null,"macro is to be used EPM?",null,{"$f":"EPM!AM101","v":6.4355366612206089E-2}]
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[null,{"$f":"RF!A2","v":"RF"},"Regensburg Model resp. Regensburg Formula"]
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[null,{"$f":"EPM!B3","v":"EPM"},{"$f":"EPM!B2","v":"Cap Model"}]
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[null,"emissions key 2019",{"$f":"C8/$F$8","v":0.5032626143677319},{"$f":"D8/$F$8","v":0.46731528477003675},{"$f":"E8/$F$8","v":2.9422100862231352E-2},{"$f":"F8/$F$8","v":1}]
[null,"population key",{"$f":"C6/$F$6","v":0.17391304347826086},{"$f":"D6/$F$6","v":0.57971014492753625},{"$f":"E6/$F$6","v":0.24637681159420294},{"$f":"F6/$F$6","v":1}]
[null,"population growth",{"$f":"C7/C6-1","v":8.3333333333333481E-2},{"$f":"D7/D6-1","v":7.4999999999999956E-2},{"$f":"E7/E6-1","v":1.3529411764705879},{"$f":"F7/F6-1","v":0.39130434782608692}]
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[null,"Which population size is to be used for the convergence year 2050?",null,null,null,null,"frozen"]
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[null,null,"Country"]
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[null,"population 2050 bn",{"$f":"IF($G$14=\"forecast\",C7,C6)","v":1.2},{"$f":"IF($G$14=\"forecast\",D7,D6)","v":4},{"$f":"IF($G$14=\"forecast\",E7,E6)","v":1.7000000000000004},{"$f":"IF($G$14=\"forecast\",F7,F6)","v":6.9}]
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[null,"input data models"]
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[null,{"$f":"CDC!A2","v":"CDC"},null,null,null,"Percentage threshold",null,"change rates BAU"]
[null,{"$f":"LEFT('SPF-eq'!A2,LEN('SPF-eq'!A2)-3)","v":"SPF"},"Reduction rate at the beginnging of 2020 for each country",null,null,null,null,"share population key (spk)"]
[null,"EPM","Input of the quantiles of the Lorenz curve possible."]
[null,{"$f":"GQWF!A2","v":"GQWF"},"C2020","weighting of per capita in 2020"]

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[null,"Which global path will you select?",3,null,"input fields"]
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[null,"Sum 2018 - 2100",{"$f":"SUM(C6:C88)","v":767.19392249194743},{"$f":"SUM(D6:D88)","v":767.26170169773968},null,{"$f":"SUM(F6:F88)","v":766.91194032249405},null,{"$f":"SUM(H6:H88)","v":767.19392249194743},null,{"$f":"SUM(J6:J88)","v":767.25185268824043},null,{"$f":"SUM(L6:L88)","v":766.7740498339831},null,{"$f":"SUM(N6:N88)","v":767.05195395951716}]

{"sheet":"RF","index":4,"n_rows":127,"n_cols":17,"rows_kept":127,"cut":false,"hidden":false,"merged":[[0,14,0,26],[4,10,4,13],[4,1,4,3],[4,4,4,6],[4,7,4,9],[0,8,0,13],[0,6,0,7],[2,7,2,8]]}
["Regensburg Formula",null,null,null,null,null,"source:",null,"www.save-the-climate.info",null,null,null,null,null,"Climate Policy, Volume 17, 2017 - Issue 5: The Regensburg Model: reference values for the (I)NDCs based on converging per capita emissions"]
["RF",null,null,null,null,null,"convergence period: 2020 - 2050"]
["Sargl/Wolfsteiner/Wittmann"]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global"]
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["∑",null,{"$f":"SUM(C46:C95)","v":4.730879831791162},null,null,{"$f":"SUM(F46:F95)","v":15.769599439303878},null,null,{"$f":"SUM(I46:I95)","v":6.7020797617041437},null,null,{"$f":"SUM(L46:L95)","v":27.202559032799176}]
[]
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{"sheet":"C&C-exp","index":5,"n_rows":118,"n_cols":29,"rows_kept":118,"cut":false,"hidden":false,"merged":[[6,1,6,3],[6,4,6,6],[6,7,6,9],[6,10,6,13],[0,7,0,10]]}
["C&C: exponential approach",null,null,null,null,null,"source:","www.gci.org.uk",null,null,null,"convergence period: 2020 - 2050"]
["C&C-exp"]
[]
[]
[null,"Parameter a:",null,null,{"$f":"'input data'!C21","v":4},null,"Input value sheet \"input data\":",null,null,null,null,"parameter a of the weighting formula Ct"]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global"]
[]
["Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPt","Et","Per capita","Ct"]
[null,"bn","Gt","t","bn","Gt","t","bn","Gt","t","bn","Gt","t"]
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[]
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{"sheet":"C&C-lin","index":6,"n_rows":115,"n_cols":15,"rows_kept":115,"cut":false,"hidden":false,"merged":[[3,1,3,3],[3,4,3,6],[3,7,3,9],[3,10,3,13],[0,6,0,9]]}
["C&C: linear aproach",null,null,null,null,"source:","www.gci.org.uk",null,null,null,"convergence period: 2020 - 2050"]
["C&C-lin"]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global"]
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[2030,1.2,{"$f":"((1-$N19)*(C18/$L18)+$N19*(B19/$K19))*'global path'!$C18","v":5.6068552339544651},4.672379361628721,4,{"$f":"((1-$N19)*(F18/$L18)+$N19*(E19/$K19))*'global path'!$C18","v":15.809204767965593},3.9523011919913982,1.7000000000000004,{"$f":"((1-$N19)*(I18/$L18)+$N19*(H19/$K19))*'global path'!$C18","v":6.3162509929018933},3.7154417605305246,6.9,27.732310994821951,4.0191755064959347,0.35483870967741937]
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["∑",null,{"$f":"SUM(C9:C39)","v":183.31381945566736},null,null,{"$f":"SUM(F9:F39)","v":357.15329628859035},null,null,{"$f":"SUM(I9:I39)","v":116.29653061358546},null,null,{"$f":"SUM(L9:L39)","v":656.76364635784307}]
[]
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["∑",null,{"$f":"SUM(C45:C94)","v":4.730879831791162},null,null,{"$f":"SUM(F45:F94)","v":15.769599439303878},null,null,{"$f":"SUM(I45:I94)","v":6.7020797617041437},null,null,{"$f":"SUM(L45:L94)","v":27.202559032799176}]
[]
["∑",null,{"$f":"C95+C40","v":188.04469928745851},null,null,{"$f":"F95+F40","v":372.92289572789423},null,null,{"$f":"I95+I40","v":122.9986103752896},null,null,{"$f":"L95+L40","v":683.96620539064224}]
[]
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[]
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[]
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{"sheet":"CDC","index":7,"n_rows":48,"n_cols":35,"rows_kept":48,"cut":false,"hidden":false,"merged":[[7,32,7,33],[7,28,7,31],[7,19,7,21],[7,22,7,24],[0,9,0,13],[6,1,6,12],[6,19,6,27],[7,1,7,4],[7,5,7,8],[7,9,7,12],[7,25,7,27],[7,13,7,16],[1,9,1,35],[3,10,3,12]]}
["Common but Differentiated Convergence"]
["CDC","Niklas Höhne, Michel den Elzen, Martin Weiss",null,null,null,null,null,null,null,"Climate Policy, Volume 6, 2006 - Issue 2: Common but differentiated convergence (CDC): a new conceptual approach to long-term climate policy"]
[]
["Percentage threshold (PT):",null,null,null,null,null,0.95,null,null,null,"input values"]
["Parameter a (Ct := C&C exp):",null,null,null,null,null,{"$f":"'C&C-exp'!E5","v":4}]
[]
[null,"business as usual",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"CDC"]
[null,"Country A",null,null,null,"Country B",null,null,null,"Country C",null,null,null,"Global",null,null,null,null,null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"over threshold",null,null,null,"Global"]
["change rate (CRi)",null,0,null,null,null,0.03,null,null,null,0.02]
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["G-C&C"]
[]
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["∑",null,{"$f":"SUM(C9:C39)","v":253.28991557053203},null,null,{"$f":"SUM(F9:F39)","v":333.27303582261447},null,null,{"$f":"SUM(I9:I39)","v":70.200694964696666},null,null,{"$f":"SUM(L9:L39)","v":656.76364635784307}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C90","v":656.76364635784296}]
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{"sheet":"GQWF","index":10,"n_rows":56,"n_cols":25,"rows_kept":56,"cut":false,"hidden":false,"merged":[[8,21,8,23],[2,6,2,7],[16,1,16,3],[16,4,16,6],[16,7,16,9],[16,10,16,13],[4,0,4,8]]}
["General Quadratic Weigthing Formula",null,null,null,null,null,null,"convergence period: 2020 - 2050"]
["GQWF",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Input value"]
["Sargl/Wolfsteiner/Wittmann",null,null,null,null,null,"input value",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C2020","weighting of per capita in 2020"]
[]
["Determination of Ct",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"convex quadratic",null,null,{"$f":"(1/(2050-2019))^2","v":1.0405827263267429E-3}]
[null,null,null,null,null,"a","b","c","Ct",null,null,null,null,null,null,null,null,null,null,null,null,"conkave quadratic",null,null,{"$f":"-(1/(2050-2019))^2+2/(2050-2019)","v":6.555671175858481E-2}]
["Constraint 1 in 2019:",null,null,"t=2019",null,0,0,1,0,null,null,null,null,null,null,null,null,null,null,null,null,"linear",null,null,{"$f":"1/(2050-2019)","v":3.2258064516129031E-2}]
["Constraint 2 in 2050:",null,null,"t=2050",null,{"$f":"31^2","v":961},31,1,1,null,null,null,null,null,null,null,null,null,null,null,null,"other value",null,null,0.04]
["Constraint 3 in 2020:",null,null,"t=2020",null,1,1,1,{"$f":"Y9","v":0.04},null,null,null,null,null,null,null,null,null,null,null,null,"other value",null,null,{"$f":"VLOOKUP(V9,V5:Y8,4,FALSE)","v":0.04}]
[]
["Remodeled constraint 1",null,null,null,null,{"$f":"MMULT(MINVERSE(F7:H9),F7:I9)","v":1},6.9388939039072284E-18,0,-2.58064516129032E-4]
["Remodeled constraint 2",null,null,null,null,-2.2204460492503131E-16,0.99999999999999989,0,4.0258064516129025E-2]
["Remodeled constraint 3",null,null,null,null,0,0,1,0]
[]
["parameter of the parabola:",null,null,null,null,{"$f":"I11","v":-2.58064516129032E-4},{"$f":"I12","v":4.0258064516129025E-2},{"$f":"I13","v":0}]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global"]
[]
["Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPt","Et","Per capita","Ct"]
[null,"bn","Gt","t","bn","Gt","t","bn","Gt","t","bn","Gt","t"]
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[2035,1.2,{"$f":"((1-$N37)*(C$21/$L$21)+$N37*(B37/$K37))*'global path'!C23","v":6.2781785619620569},5.231815468301714,4,{"$f":"((1-$N37)*(F$21/$L$21)+$N37*(E37/$K37))*'global path'!$C23","v":10.680836252224678},2.6702090630561695,1.7000000000000004,{"$f":"((1-$N37)*(I$21/$L$21)+$N37*(H37/$K37))*'global path'!$C23","v":3.1069288651804858},1.8276052148120501,6.9,20.065943679367219,2.9081077796184376,0.5780645161290322]
[2036,1.2,{"$f":"((1-$N38)*(C$21/$L$21)+$N38*(B38/$K38))*'global path'!C24","v":5.6284642898082735},4.6903869081735614,4,{"$f":"((1-$N38)*(F$21/$L$21)+$N38*(E38/$K38))*'global path'!$C24","v":9.9729059018209174},2.4932264754552294,1.7000000000000004,{"$f":"((1-$N38)*(I$21/$L$21)+$N38*(H38/$K38))*'global path'!$C24","v":3.0098532737318222},1.7705019257246009,6.9,18.611223465361014,2.6972787630957988,0.60980645161290314]
[2037,1.2,{"$f":"((1-$N39)*(C$21/$L$21)+$N39*(B39/$K39))*'global path'!C25","v":5.0250527078276459},4.1875439231897049,4,{"$f":"((1-$N39)*(F$21/$L$21)+$N39*(E39/$K39))*'global path'!$C25","v":9.2775473122381609},2.3193868280595402,1.7000000000000004,{"$f":"((1-$N39)*(I$21/$L$21)+$N39*(H39/$K39))*'global path'!$C25","v":2.8983014879170459},1.7048832281864972,6.9,17.200901507982852,2.4928842765192538,0.64103225806451603]
[2038,1.2,{"$f":"((1-$N40)*(C$21/$L$21)+$N40*(B40/$K40))*'global path'!C26","v":4.4675570961706956},3.722964246808913,4,{"$f":"((1-$N40)*(F$21/$L$21)+$N40*(E40/$K40))*'global path'!$C26","v":8.598749802165278},2.1496874505413195,1.7000000000000004,{"$f":"((1-$N40)*(I$21/$L$21)+$N40*(H40/$K40))*'global path'!$C26","v":2.7747068741417724},1.6321805142010422,6.9,15.841013772477746,2.2957990974605429,0.67174193548387084]
[2039,1.2,{"$f":"((1-$N41)*(C$21/$L$21)+$N41*(B41/$K41))*'global path'!C27","v":3.9551417962824833},3.2959514969020693,4,{"$f":"((1-$N41)*(F$21/$L$21)+$N41*(E41/$K41))*'global path'!$C27","v":7.9400589998675022},1.9850147499668755,1.7000000000000004,{"$f":"((1-$N41)*(I$21/$L$21)+$N41*(H41/$K41))*'global path'!$C27","v":2.6414614054558787},1.5538008267387518,6.9,14.536662201605864,2.1067626379138931,0.7019354838709676]
[2040,1.2,{"$f":"((1-$N42)*(C$21/$L$21)+$N42*(B42/$K42))*'global path'!C28","v":3.4865783160290413},2.9054819300242012,4,{"$f":"((1-$N42)*(F$21/$L$21)+$N42*(E42/$K42))*'global path'!$C28","v":7.3045581788522762},1.8261395447130691,1.7000000000000004,{"$f":"((1-$N42)*(I$21/$L$21)+$N42*(H42/$K42))*'global path'!$C28","v":2.5008789754256098},1.4711052796621231,6.9,13.292015470306927,1.9263790536676704,0.73161290322580641]
[2041,1.2,{"$f":"((1-$N43)*(C$21/$L$21)+$N43*(B43/$K43))*'global path'!C29","v":3.0603028649410562},2.5502523874508802,4,{"$f":"((1-$N43)*(F$21/$L$21)+$N43*(E43/$K43))*'global path'!$C29","v":6.6948588548847203},1.6737147137211801,1.7000000000000004,{"$f":"((1-$N43)*(I$21/$L$21)+$N43*(H43/$K43))*'global path'!$C29","v":2.3551632763708694},1.3853901625710994,6.9,12.110324996196645,1.7551195646661804,0.76077419354838705]
[2042,1.2,{"$f":"((1-$N44)*(C$21/$L$21)+$N44*(B44/$K44))*'global path'!C30","v":2.6744739690454509},2.2287283075378759,4,{"$f":"((1-$N44)*(F$21/$L$21)+$N44*(E44/$K44))*'global path'!$C30","v":6.1131001970123631},1.5282750492530908,1.7000000000000004,{"$f":"((1-$N44)*(I$21/$L$21)+$N44*(H44/$K44))*'global path'!$C30","v":2.2063806186471697},1.2978709521453937,6.9,10.993954784704984,1.5933267803920266,0.78941935483870962]
[2043,1.2,{"$f":"((1-$N45)*(C$21/$L$21)+$N45*(B45/$K45))*'global path'!C31","v":2.3270289424543549},1.9391907853786292,4,{"$f":"((1-$N45)*(F$21/$L$21)+$N45*(E45/$K45))*'global path'!$C31","v":5.5609566244647244},1.3902391561161811,1.7000000000000004,{"$f":"((1-$N45)*(I$21/$L$21)+$N45*(H45/$K45))*'global path'!$C31","v":2.0564379060329423},1.2096693564899659,6.9,9.9444234729520211,1.4412207931814522,0.81754838709677413]
[2044,1.2,{"$f":"((1-$N46)*(C$21/$L$21)+$N46*(B46/$K46))*'global path'!C32","v":2.0157381426153105},1.6797817855127588,4,{"$f":"((1-$N46)*(F$21/$L$21)+$N46*(E46/$K46))*'global path'!$C32","v":5.0396528103681497},1.2599132025920374,1.7000000000000004,{"$f":"((1-$N46)*(I$21/$L$21)+$N46*(H46/$K46))*'global path'!$C32","v":1.90706582726564},1.1218034278033173,6.9,8.9624567802491004,1.2989067797462464,0.84516129032258069]
[2045,1.2,{"$f":"((1-$N47)*(C$21/$L$21)+$N47*(B47/$K47))*'global path'!C33","v":1.7382561011131257},1.4485467509276049,4,{"$f":"((1-$N47)*(F$21/$L$21)+$N47*(E47/$K47))*'global path'!$C33","v":4.5499851947123195},1.1374962986780799,1.7000000000000004,{"$f":"((1-$N47)*(I$21/$L$21)+$N47*(H47/$K47))*'global path'!$C33","v":1.7598071799568977},1.0351806940922925,6.9,8.0480484757823429,1.1663838370699047,0.87225806451612908]
[2046,1.2,{"$f":"((1-$N48)*(C$21/$L$21)+$N48*(B48/$K48))*'global path'!C34","v":1.4921687954741665},1.2434739962284722,4,{"$f":"((1-$N48)*(F$21/$L$21)+$N48*(E48/$K48))*'global path'!$C34","v":4.0923490241867144},1.0230872560466786,1.7000000000000004,{"$f":"((1-$N48)*(I$21/$L$21)+$N48*(H48/$K48))*'global path'!$C34","v":1.6160101143340466},0.95059418490238012,6.9,7.2005279339949269,1.043554773042743,0.89883870967741941]
[2047,1.2,{"$f":"((1-$N49)*(C$21/$L$21)+$N49*(B49/$K49))*'global path'!C35","v":1.2750365032308943},1.0625304193590788,4,{"$f":"((1-$N49)*(F$21/$L$21)+$N49*(E49/$K49))*'global path'!$C35","v":3.666769885393192},0.91669247134829801,1.7000000000000004,{"$f":"((1-$N49)*(I$21/$L$21)+$N49*(H49/$K49))*'global path'!$C35","v":1.4768259734626226},0.86872116086036599,6.9,6.4186323620867087,0.93023657421546502,0.92490322580645168]
[2048,1.2,{"$f":"((1-$N50)*(C$21/$L$21)+$N50*(B50/$K50))*'global path'!C36","v":1.0844318517897302},0.90369320982477519,4,{"$f":"((1-$N50)*(F$21/$L$21)+$N50*(E50/$K50))*'global path'!$C36","v":3.272938679402607},0.81823466985065174,1.7000000000000004,{"$f":"((1-$N50)*(I$21/$L$21)+$N50*(H50/$K50))*'global path'!$C36","v":1.3432113158505252},0.79012430344148521,6.9,5.7005818470428622,0.82617128218012492,0.95045161290322588]
[2049,1.2,{"$f":"((1-$N51)*(C$21/$L$21)+$N51*(B51/$K51))*'global path'!C37","v":0.91797284136457302},0.76497736780381087,4,{"$f":"((1-$N51)*(F$21/$L$21)+$N51*(E51/$K51))*'global path'!$C37","v":2.9102489975054988},0.7275622493763747,1.7000000000000004,{"$f":"((1-$N51)*(I$21/$L$21)+$N51*(H51/$K51))*'global path'!$C37","v":1.2159336367535676},0.7152550804432749,6.9,5.04415547562364,0.73103702545270144,0.97548387096774203]
[2050,{"$f":"RF!B40","v":1.2},{"$f":"((1-$N52)*(C$21/$L$21)+$N52*(B52/$K52))*'global path'!C38","v":0.77335076918943702},0.64445897432453092,{"$f":"RF!E40","v":4},{"$f":"((1-$N52)*(F$21/$L$21)+$N52*(E52/$K52))*'global path'!$C38","v":2.5778358972981237},0.64445897432453092,{"$f":"K52-E52-B52","v":1.7000000000000004},{"$f":"((1-$N52)*(I$21/$L$21)+$N52*(H52/$K52))*'global path'!$C38","v":1.0955802563517028},0.64445897432453092,{"$f":"RF!K40","v":6.9},4.4467669228392639,0.64445897432453092,1]
["∑",null,{"$f":"SUM(C22:C52)","v":244.2460906220374},null,null,{"$f":"SUM(F22:F52)","v":336.35935968704138},null,null,{"$f":"SUM(I22:I52)","v":76.158196048764268},null,null,{"$f":"SUM(L22:L52)","v":656.76364635784296}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C90","v":656.76364635784296}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L53-L55","v":0}]

{"sheet":"SPF-eq","index":11,"n_rows":108,"n_cols":23,"rows_kept":108,"cut":false,"hidden":false,"merged":[[1,1,1,26],[10,13,10,16],[6,15,6,16],[4,18,6,30],[3,1,3,3],[3,4,3,6],[3,7,3,9],[3,10,3,13],[5,10,7,13]]}
["Smooth Pathways Formula - equity (spk = 100%)"]
["SPF-eq","Smooth Pathways Formula; based on: Raupach et al. (2014) / Sharing a quota on cumulative carbon emissions / nature climate change DOI: 10.1038/NCLIMATE2384"]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global",null,null,null,null,null,null,null,"Description"]
[null,"RBA:",{"$f":"W8*'global path'!C89/K11*B11+(1-W8)*'global path'!C89*C11/L11","v":118.95064441576383},"Gt","RBB:",{"$f":"W8*'global path'!C89/K11*E11+(1-W8)*'global path'!C89*F11/L11","v":396.50214805254615},"Gt","RBC:",{"$f":"W8*'global path'!C89/K11*H11+(1-W8)*'global path'!C89*I11/L11","v":168.51341292233215},"Gt","RB:",{"$f":"C5+F5+I5","v":683.96620539064213},"Gt",null,null,null,null,null,"Raupach et al. have developed a formula to convert a budget of a country or global into a smooth emission pathway."]
[null,"TA",{"$f":"C5/C11","v":5.6643164007506588},null,"TB",{"$f":"F5/F11","v":20.33344348987416},null,"TC",{"$f":"I5/I11","v":137.25752678949854},null,"Global path ist different to the path in sheet \"global path\"."]
[null,"rA",0,null,"rB",0.03,null,"rC",0.02,null,null,null,null,null,null,"input values"]
[null,"mA",{"$f":"(1+SQRT(1+C7*C6))/C6","v":0.35308762055293236},null,"mB",{"$f":"(1+SQRT(1+F7*F6))/F6","v":0.11158262777315084},null,"mC",{"$f":"(1+SQRT(1+I7*I6))/I6","v":2.1384904787472729E-2},null,null,null,null,null,null,null,null,null,"share population key:",null,null,null,1]
["Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPt","Et","Per capita",null,null,null,null,null,"Limitations"]
[null,"bn","Gt","t","bn","Gt","t","bn","Gt","t","bn","Gt","t",null,"A","B","C",null,"-","The resulting global pathway ist different to the pathway in sheet \"global path\". So this model is comparable with the other models to a limited extent only."]
[2019,{"$f":"RF!B9","v":1.2},{"$f":"RF!C9","v":21},{"$f":"C11/B11","v":17.5},{"$f":"RF!E9","v":4},{"$f":"RF!F9","v":19.5},{"$f":"F11/E11","v":4.875},{"$f":"K11-E11-B11","v":1.7000000000000004},{"$f":"'global path'!$C$7-C11-F11","v":1.2277171013052595},{"$f":"I11/H11","v":0.72218653017956425},{"$f":"RF!K9","v":6.9},{"$f":"I11+F11+C11","v":41.727717101305259},{"$f":"L11/K11","v":6.047495232073226},"annual change rates",null,null,null,null,"-","The per capita emissions converge far into the future; as you can see on the remaining budgets as of 2051. So this model is comparable with the other models to a limited extent only."]
[{"$f":"A11+1","v":2020},{"$f":"B$11*(B$42/B$11)^(($A12-2019)/31)","v":1.2},{"$f":"-C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A11-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A11-$A$11)+2*C$8+C$7)","v":20.633128463331417},{"$f":"C12/B12","v":17.194273719442847},{"$f":"E$11*(E$42/E$11)^(($A12-2019)/31)","v":4},{"$f":"-F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A11-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A11-$A$11)+2*F$8+F$7)","v":19.733344496566019},{"$f":"F12/E12","v":4.9333361241415048},{"$f":"H$11*(H$42/H$11)^(($A12-2019)/31)","v":1.7000000000000004},{"$f":"-I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A11-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A11-$A$11)+2*I$8+I$7)","v":1.2397280559859212},{"$f":"I12/H12","v":0.72925179763877701},{"$f":"B12+E12+H12","v":6.9},{"$f":"I12+F12+C12","v":41.606201015883357},{"$f":"L12/K12","v":6.029884205200486},{"$f":"L12/L11-1","v":-2.9121191827218285E-3},{"$f":"C12/C11-1","v":-1.74700731746944E-2},{"$f":"F12/F11-1","v":1.1966384439282995E-2},{"$f":"I12/I11-1","v":9.7831615018575402E-3}]
[{"$f":"A12+1","v":2021},1.2,{"$f":"-C$11*EXP(-C$8*($A13-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A13-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)","v":18.883831124220123},15.736525936850104,4,{"$f":"-F$11*EXP(-F$8*($A13-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A13-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)","v":19.98642632965749},4.9966065824143726,1.7000000000000004,{"$f":"-I$11*EXP(-I$8*($A13-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A13-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)","v":1.26270399098388},0.74276705351992922,{"$f":"B13+E13+H13","v":6.9},{"$f":"I13+F13+C13","v":40.132961444861493},5.8163712238929701,{"$f":"L13/L12-1","v":-3.5409134577306101E-2},{"$f":"C13/C12-1","v":-8.4781003628223051E-2},{"$f":"F13/F12-1","v":1.2825085637941935E-2},{"$f":"I13/I12-1","v":1.8533044313243874E-2},null,"Simplification"]
[2022,1.2,16.349342124287709,13.624451770239759,4,19.966085365526965,4.9915213413817412,1.7000000000000004,1.2841527113546647,0.75538394785568497,6.9,37.599580201169339,5.4492145219085995,-6.312470230169176E-2,-0.13421476729272985,-1.0177389291622374E-3,1.698634083992423E-2,null,null,"We assumed that the emission power at the end of the base year are the emissions in the base year divided by one year."]
[2023,1.2,13.65163342114294,11.376361184285784,4,19.727237665418045,4.9318094163545112,1.7000000000000004,{"$f":"-I$11*EXP(-I$8*($A15-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A15-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A14-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A14-$A$11)+2*I$8+I$7)","v":1.3041285570104719},0.76713444530027741,6.9,34.682999643571456,5.0265216874741236,-7.7569497903787199E-2,-0.16500411347666388,-1.1962670485287541E-2,1.5555662094685285E-2]
[2024,1.2,11.112110172479731,9.2600918103997767,4,19.316250965259087,4.8290627413147718,1.7000000000000004,1.3226842520956836,0.77804956005628434,6.9,31.751045389834502,4.6016007811354349,-8.4535774986821188E-2,-0.18602339883593177,-2.083346422491883E-2,1.4228424786393745E-2,null,"Input values"]
[2025,1.2,8.8753959634722399,7.3961633028935339,4,18.77213759704523,4.6930343992613075,1.7000000000000004,1.3398709490343492,0.78815938178491107,6.9,28.987404509551819,4.2010731173263505,-8.7040941372201197E-2,-0.2012861800584862,-2.8168683933153638E-2,1.2993801741749467E-2,null,"-","reduction rate at the beginnging of 2020 for each country"]
[2026,1.2,6.9860689389819903,5.8217241158183253,4,18.127590800832422,4.5318977002081056,1.7000000000000004,1.3557382714355981,0.79749310084446934,6.9,26.469398011250011,3.8361446393115957,-8.686553835725741E-2,-0.21287242082111069,-3.4335290420748898E-2,1.1842425878913598E-2,null,"-","Share that is distributed over the population key"]
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[2028,1.2,4.189066502771448,3.49088875230954,4,16.641651778874007,4.1604129447185016,1.7000000000000004,1.3837058926726229,0.81394464274860157,6.9,22.214424174318076,3.2194817643939238,-8.2640153081059542E-2,-0.22929746698572329,-4.4126222311178687E-2,9.757864368254765E-3]
[2029,1.2,3.2032525887308232,2.6693771572756861,4,15.841563579804244,3.9603908949510611,1.7000000000000004,1.3958981654093634,0.82111656788786058,6.9,20.440714333944431,2.962422367238323,-7.9844961384334057E-2,-0.23533021339919513,-4.8077451066813381E-2,8.8113180707722893E-3]
[2030,1.2,2.4332475295649916,2.027706274637493,4,15.024910428331424,3.756227607082856,1.7000000000000004,1.4069550896863063,0.82762064099194466,6.9,18.865113047582721,2.7340743547221331,-7.7081517828622159E-2,-0.24038224830434596,-5.155129715313822E-2,7.9210106803888625E-3]
[2031,1.2,1.8378933269474773,1.5315777724562312,4,14.204109380395209,3.5510273450988024,1.7000000000000004,1.4169192506745389,0.83348191216149325,6.9,17.458921958017225,2.5302785446401774,-7.4539234724897541E-2,-0.24467473834195153,-5.4629347166588627E-2,7.0820746598629913E-3]
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[2035,1.2,0.57284981893722375,0.47737484911435313,4,11.050001307689627,2.7625003269224067,1.7000000000000004,1.4466554257915618,0.85097377987738909,6.9,13.069506552418412,1.8941313844084655,-6.7673855099665059E-2,-0.25688308392019876,-6.4085380887206722E-2,4.1603196704016465E-3]
[2036,1.2,0.42442363213675027,0.3536863601139586,4,10.321526597741197,2.5803816494352994,1.7000000000000004,1.4517504952135027,0.8539708795373544,6.9,12.197700725091451,1.7677827137813695,-6.6705336106636759E-2,-0.25910139428138479,-6.5925305315709615E-2,3.5219647547743982E-3]
[2037,1.2,0.31361092492831188,0.26134243744025992,4,9.6236985312820309,2.4059246328205077,1.7000000000000004,1.4559823598716832,0.85646021168922526,6.9,11.393291816082026,1.6512017124756559,-6.5947585298162248E-2,-0.26108986120908151,-6.7608997550021477E-2,2.9150082415216882E-3]
[2038,1.2,0.23116811756569766,0.19264009797141474,4,8.9581664027847978,2.2395416006961995,1.7000000000000004,1.4593852660772484,0.85846192122191056,6.9,10.648719786427744,1.5432927226706874,-6.5351791358779443E-2,-0.26288244703675345,-6.9155546210628582E-2,2.3371891716221782E-3]
[2039,1.2,0.17002259308263074,0.14168549423552562,4,8.3258895948105618,2.0814723987026404,1.7000000000000004,1.461992397401616,0.85999552788330336,6.9,9.9579045852948092,1.4431745775789577,-6.4873075354411003E-2,-0.26450673703171657,-7.058105191902686E-2,1.7864585760656304E-3]
[2040,1.2,0.12479907091446757,0.10399922576205631,4,7.7272648774927006,1.9318162193731752,1.7000000000000004,1.4638359043167384,0.86107994371572827,6.9,9.3158998527239074,1.3501304134382475,-6.4471870268668074E-2,-0.26598536905142134,-7.1899189930524354E-2,1.2609551994926527E-3]
[2041,1.2,9.1435649826009935E-2,7.6196374855008284E-2,4,7.1622345177297433,1.7905586294324358,1.7000000000000004,1.4649469330565807,0.86173349003328259,6.9,8.7186171006123345,1.2635676957409179,-6.4114338019309103E-2,-0.26733709509202697,-7.3121650250236425E-2,7.5898448491806825E-4]
[2042,1.2,6.6878084200854365E-2,5.5731736834045309E-2,4,6.6303778313131971,1.6575944578282993,1.7000000000000004,1.4653556537197403,0.86197391395278822,6.9,8.1626115692337926,1.1829871839469264,-6.3772215818434286E-2,-0.2685775807563614,-7.4258485267406749E-2,2.7900032003658204E-4]
[2043,1.2,4.8839726317282672E-2,4.0699771931068898E-2,4,6.1309884690987104,1.5327471172746776,1.7000000000000004,1.4650912876327595,0.86181840448985836,6.9,7.6449194830487528,1.1079593453693843,-6.3422359595831423E-2,-0.26972001514572774,-7.5318386812894267E-2,-1.8041086906761539E-4]
[2044,1.2,3.5615121017186641E-2,2.9679267514322202E-2,4,5.6631394290987558,1.4157848572746889,1.7000000000000004,1.4641821339920682,0.86128360823062811,6.9,7.1629366841080104,1.0381067658127552,-6.3046157648808943E-2,-0.27077558162762072,-7.6308908809402998E-2,-6.2054402231848105E-4]
[2045,1.2,2.5936575647633783E-2,2.1613813039694819E-2,4,5.2257375247924571,1.3064343811981143,1.7000000000000004,1.4626555958038239,0.86038564459048439,6.9,6.7143296962439152,0.9730912603252051,-6.2628919903674918E-2,-0.27175382514865865,-7.7236647584343121E-2,-1.0425876349701158E-3]
[2046,1.2,1.8864632634453919E-2,1.5720527195378267E-2,4,4.8175688113977202,1.20439220284943,1.7000000000000004,1.4605382051382776,0.8591401206695749,6.9,6.2969716491704517,0.9126045868362973,-6.2159301963819136E-2,-0.27266294167962157,-7.8107388949074208E-2,-1.4476344750061765E-3]
[2047,1.2,1.3704966804251456E-2,1.1420805670209547E-2,4,4.4373362722729368,1.1093340680682342,1.7000000000000004,1.4578556477170537,0.85756214571591372,6.9,5.908896886794242,0.85636186765133937,-6.1628793013119854E-2,-0.27351000839417206,-7.8926228977820534E-2,-1.8366910305984696E-3]
[2048,1.2,9.945678398719137E-3,8.2880653322659481E-3,4,4.0836908934418972,1.0209227233604743,1.7000000000000004,1.4546327868498992,0.85566634520582285,6.9,5.5482693586905159,0.80409700850587185,-6.1031277920873928E-2,-0.27430116827179318,-7.9697673814090209E-2,-2.2106858605660529E-3]
[2049,1.2,7.2102013154229372E-3,6.008501096185781E-3,4,3.7552571023224388,0.9388142755806097,1.7000000000000004,1.450893686737345,0.85346687455137915,6.9,5.2133609903752065,0.75555956382249367,-6.0362672873970458E-2,-0.27504177931678253,-8.0425722634124619E-2,-2.570476993476456E-3]
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["∑",null,{"$f":"SUM(C12:C42)","v":118.93706757499594},null,null,{"$f":"SUM(F12:F42)","v":359.89841936167005},null,null,{"$f":"SUM(I12:I42)","v":43.715461898851572},null,null,{"$f":"SUM(L12:L42)","v":522.5509488355176}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A42-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A42-$A$11)+2*C$8+C$7)","v":1.3576840767910424E-2},null,null,{"$f":"F$11*EXP(-F$8*($A42-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A42-$A$11)+2*F$8+F$7)","v":36.603728690876181},null,null,{"$f":"I$11*EXP(-I$8*($A42-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A42-$A$11)+2*I$8+I$7)","v":124.79795102348058},null,null,161.41525655512467]
["∑",null,{"$f":"SUM(C43:C44)","v":118.95064441576385},null,null,{"$f":"SUM(F43:F44)","v":396.5021480525462},null,null,{"$f":"SUM(I43:I44)","v":168.51341292233215},null,null,{"$f":"SUM(L43:L44)","v":683.96620539064224}]
[]
[null,null,null,null,null,"global path 2020 - 2100 sheet \"global path\":",null,null,null,null,null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L45-L47","v":0}]
[]
[]
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[2055,1.2,1.0277174337927275E-3,8.5643119482727297E-4,4,2.238140341276349,0.55953508531908724,1.7000000000000004,1.4188705612587569,0.83462974191691564,6.9,3.6580386199688988,0.53015052463317369,-5.4821231542151683E-2,-0.27865157606747559,-8.4058147554957774E-2,-4.4716238791190355E-3]
[2056,1.2,7.4083704113577582E-4,6.1736420094647985E-4,4,2.0488743221313932,0.5122185805328483,1.7000000000000004,1.4121290740631167,0.83066416121359787,6.9,3.4617442332356458,0.50170206278777474,-5.3661102882211154E-2,-0.2791432578877614,-8.4563963954567112E-2,-4.7513052844365689E-3]
[2057,1.2,5.3369165569229775E-4,4.4474304641024814E-4,4,1.8746246232777821,0.46865615581944553,1.7000000000000004,1.4050376927768724,0.82649276045698361,6.9,3.2801960077103467,0.4753907257551227,-5.2444147601167113E-2,-0.27960991951199399,-8.5046553110365242E-2,-5.0217656561948321E-3]
[2058,1.2,3.8422948049880289E-4,3.2019123374900241E-4,4,1.7143301976399528,0.42858254940998819,1.7000000000000004,1.3976142412898724,0.82212602428816006,6.9,3.1123286684103242,0.45106212585656869,-5.1176008660896444E-2,-0.28005342335662808,-8.5507479016014631E-2,-5.2834536220366379E-3]
[2059,1.2,2.7646254348744103E-4,2.3038545290620088E-4,4,1.5669866572341924,0.3917466643085481,1.7000000000000004,1.3898759458930101,0.81757408581941748,6.9,2.95713906567069,0.42857087908270869,-4.9862858095543028E-2,-0.28047545147098008,-8.5948168333382924E-2,-5.5367891713242745E-3]
[2060,1.2,1.9881042800440959E-4,1.6567535667034132E-4,4,1.4316461369497837,0.35791153423744593,1.7000000000000004,1.3818394525869451,0.81284673681584985,6.9,2.8136843999647332,0.40778034782097583,-4.8511301809007312E-2,-0.2808775268558541,-8.6369925142369297E-2,-5.7821659046710661E-3]
[2061,1.2,1.4289280188568187E-4,1.190773349047349E-4,4,1.3074165554782784,0.3268541388695696,1.7000000000000004,1.3735208439261442,0.80795343760361404,6.9,2.6810802922063082,0.38856236118932003,-4.7128280542084622E-2,-0.28126103182820705,-8.6773943829572708E-2,-6.0199530743080265E-3]
[2062,1.2,1.0265029877550702E-4,8.5541915646255852E-5,4,1.1934604022101283,0.29836510055253207,1.7000000000000004,1.3649356554097949,0.80290332671164388,6.9,2.5584987079186985,0.37079691419111571,-4.5720967269777368E-2,-0.2816272238987233,-8.7161320384583019E-2,-6.2504974382543432E-3]
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["∑",null,{"$f":"SUM(C51:C100)","v":1.3576840077360335E-2},null,null,{"$f":"SUM(F51:F100)","v":36.318564962148869},null,null,{"$f":"SUM(I51:I100)","v":60.943941575908291},null,null,{"$f":"SUM(L51:L100)","v":97.276083378134544}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A100-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A100-$A$11)+2*C$8+C$7)","v":6.9055009037044834E-10},null,null,{"$f":"F$11*EXP(-F$8*($A100-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A100-$A$11)+2*F$8+F$7)","v":0.28516372872732182},null,null,{"$f":"I$11*EXP(-I$8*($A100-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A100-$A$11)+2*I$8+I$7)","v":63.854009447572288},null,null,{"$f":"I102+F102+C102","v":64.139173176990155}]
["∑",null,{"$f":"SUM(C101:C102)","v":1.3576840767910426E-2},null,null,{"$f":"SUM(F101:F102)","v":36.603728690876189},null,null,{"$f":"SUM(I101:I102)","v":124.79795102348058},null,null,{"$f":"SUM(L101:L102)","v":161.4152565551247}]
[]
["∑",null,{"$f":"C103+C43","v":118.95064441576385},null,null,{"$f":"F103+F43","v":396.50214805254626},null,null,{"$f":"I103+I43","v":168.51341292233215},null,null,{"$f":"SUM(C105:I105)","v":683.96620539064224}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L105-L107","v":0}]

{"sheet":"SPF-in","index":12,"n_rows":108,"n_cols":23,"rows_kept":108,"cut":false,"hidden":false,"merged":[[4,18,6,30],[5,10,7,13],[10,13,10,16],[3,1,3,3],[3,4,3,6],[3,7,3,9],[3,10,3,13]]}
["Smooth Pathways Formula - inertia (spk = 0%)"]
["SPF-in",{"$f":"'SPF-eq'!B2","v":"Smooth Pathways Formula; based on: Raupach et al. (2014) / Sharing a quota on cumulative carbon emissions / nature climate change DOI: 10.1038/NCLIMATE2384"}]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global",null,null,null,null,null,null,null,"Description"]
[null,"RBA:",{"$f":"W8*'global path'!C89/K11*B11+(1-W8)*'global path'!C89*C11/L11","v":344.21462066407162},"Gt","RBB:",{"$f":"W8*'global path'!C89/K11*E11+(1-W8)*'global path'!C89*F11/L11","v":319.62786204520938},"Gt","RBC:",{"$f":"W8*'global path'!C89/K11*H11+(1-W8)*'global path'!C89*I11/L11","v":20.123722681361119},"Gt","RB:",{"$f":"C5+F5+I5","v":683.96620539064213},"Gt",null,null,null,null,null,"Raupach et al. have developed a formula to convert a budget of a country or global into a smooth emission pathway."]
[null,"TA",{"$f":"C5/C11","v":16.391172412574839},null,"TB",{"$f":"F5/F11","v":16.391172412574839},null,"TC",{"$f":"I5/I11","v":16.391172412574839},null,"Global path ist different to the path in sheet \"global path\"."]
[null,"rA",{"$f":"'SPF-eq'!C7","v":0},null,"rB",{"$f":"'SPF-eq'!F7","v":0.03},null,"rC",{"$f":"'SPF-eq'!I7","v":0.02}]
[null,"mA",{"$f":"(1+SQRT(1+C7*C6))/C6","v":0.12201689724559649},null,"mB",{"$f":"(1+SQRT(1+F7*F6))/F6","v":0.13552210013743388},null,"mC",{"$f":"(1+SQRT(1+I7*I6))/I6","v":0.1313092293852946},null,null,null,null,null,null,null,null,null,"share population key:",null,null,null,0]
["Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPt","Et","Per capita",null,null,null,null,null,"Limitations"]
[null,"bn","Gt","t","bn","Gt","t","bn","Gt","t","bn","Gt","t",null,"A","B","C",null,"-","The resulting global pathway ist different to the pathway in sheet \"global path\". So this model is comparable with the other models to a limited extent only."]
[2019,{"$f":"RF!B9","v":1.2},{"$f":"RF!C9","v":21},{"$f":"C11/B11","v":17.5},{"$f":"RF!E9","v":4},{"$f":"RF!F9","v":19.5},{"$f":"F11/E11","v":4.875},{"$f":"K11-E11-B11","v":1.7000000000000004},{"$f":"'global path'!$C$7-C11-F11","v":1.2277171013052595},{"$f":"I11/H11","v":0.72218653017956425},{"$f":"RF!K9","v":6.9},{"$f":"I11+F11+C11","v":41.727717101305259},{"$f":"L11/K11","v":6.047495232073226},"annual change rates",null,null,null,null,"-","The per capita emissions converge far into the future; as you can see on the remaining budgets as of 2051. So this model is comparable with the other models to a limited extent only."]
[{"$f":"A11+1","v":2020},{"$f":"B$11*(B$42/B$11)^(($A12-2019)/31)","v":1.2},{"$f":"-C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A11-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A11-$A$11)+2*C$8+C$7)","v":20.950957341623223},{"$f":"C12/B12","v":17.459131118019354},{"$f":"E$11*(E$42/E$11)^(($A12-2019)/31)","v":4},{"$f":"-F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A11-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A11-$A$11)+2*F$8+F$7)","v":19.711563813975829},{"$f":"F12/E12","v":4.9278909534939572},{"$f":"H$11*(H$42/H$11)^(($A12-2019)/31)","v":1.7000000000000004},{"$f":"-I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A11-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A11-$A$11)+2*I$8+I$7)","v":1.2356653493811827},{"$f":"I12/H12","v":0.72686197022422494},{"$f":"B12+E12+H12","v":6.9},{"$f":"I12+F12+C12","v":41.898186504980231},{"$f":"L12/K12","v":6.0722009427507579},{"$f":"L12/L11-1","v":4.0852798934845058E-3},{"$f":"C12/C11-1","v":-2.3353646846084875E-3},{"$f":"F12/F11-1","v":1.0849426357734782E-2},{"$f":"I12/I11-1","v":6.4740061594588116E-3}]
[{"$f":"A12+1","v":2021},1.2,{"$f":"-C$11*EXP(-C$8*($A13-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A13-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)","v":20.67950971092813},17.232924759106776,4,{"$f":"-F$11*EXP(-F$8*($A13-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A13-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)","v":19.849273463877751},4.9623183659694377,1.7000000000000004,{"$f":"-I$11*EXP(-I$8*($A13-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A13-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)","v":1.2362760275915718},0.72722119270092445,{"$f":"B13+E13+H13","v":6.9},{"$f":"I13+F13+C13","v":41.765059202397453},6.0529071307822395,{"$f":"L13/L12-1","v":-3.1774001141303687E-3},{"$f":"C13/C12-1","v":-1.2956335420329812E-2},{"$f":"F13/F12-1","v":6.9862366680559784E-3},{"$f":"I13/I12-1","v":4.9421003081051573E-4},null,"Simplification"]
[2022,1.2,20.193988698158591,16.82832391513216,4,19.635448358799124,4.908862089699781,1.7000000000000004,1.2180257831567864,0.7164857547981095,6.9,41.047462840114505,5.9489076579876095,-1.7181739377056915E-2,-2.3478361893317201E-2,-1.077243988137655E-2,-1.4762273171582296E-2,null,null,"We assumed that the emission power at the end of the base year are the emissions in the base year divided by one year."]
[2023,1.2,19.547155631688383,16.28929635974032,4,19.156983585694576,4.789245896423644,1.7000000000000004,{"$f":"-I$11*EXP(-I$8*($A15-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A15-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A14-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A14-$A$11)+2*I$8+I$7)","v":1.1855471721172659},0.6973806894807445,6.9,39.889686389500227,5.781113969492786,-2.8205798129934956E-2,-3.2030971005207576E-2,-2.4367397390757106E-2,-2.6664961849448665E-2]
[2024,1.2,18.782475367855142,15.652062806545953,4,18.484394765794463,4.6210986914486156,1.7000000000000004,1.1426182414787203,0.67212837734042352,6.9,38.409488375128326,5.5665925181345397,-3.7107286327563549E-2,-3.9119771604703368E-2,-3.5109327984305772E-2,-3.6210225664727425E-2,null,"Input values"]
[2025,1.2,17.935555848468368,14.946296540390307,4,17.674574124860555,4.4186435312151389,1.7000000000000004,1.0923026829132656,0.64253098994897961,6.9,36.702432656242188,5.319193138585824,-4.4443594307065126E-2,-4.5090942636678011E-2,-4.3811044461812054E-2,-4.4035318830844772E-2,null,"-","reduction rate at the beginnging of 2020 for each country"]
[2026,1.2,17.035379604947138,14.196149670789282,4,16.773111058378674,4.1932777645946686,1.7000000000000004,1.0370684327733741,0.61004025457257283,6.9,34.845559096099187,5.0500810284201716,-5.0592656283430126E-2,-5.0189481225255794E-2,-5.1003382605632863E-2,-5.0566798932121015E-2,null,"-","Share that is distributed over the population key"]
[2027,1.2,16.105356011848102,13.421130009873419,4,15.816243312701005,3.9540608281752512,1.7000000000000004,0.97888790070096121,0.57581641217703583,6.9,32.900487225250068,4.7681865543840676,-5.5819792286439851E-2,-5.4593652426092931E-2,-5.7047720148474479E-2,-5.6100957500773596E-2]
[2028,1.2,15.164219220719673,12.636849350599729,4,14.832495138325783,3.7081237845814456,1.7000000000000004,0.91932255230190663,0.54077797194229793,6.9,30.916036911347362,4.4805850596155592,-6.0316745472988154E-2,-5.8436261231112785E-2,-6.219859892931956E-2,-6.085002006501572E-2]
[2029,1.2,14.226793342847856,11.85566111903988,4,13.844050419758247,3.4610126049395618,1.7000000000000004,0.85959417878144961,0.5056436345773232,6.9,28.930437941387552,4.1928170929547175,-6.4225533681874336E-2,-6.1818275258838429E-2,-6.6640488289356425E-2,-6.4969986182653927E-2]
[2030,1.2,13.30464353058909,11.087202942157575,4,12.867901646403027,3.2169754116007567,1.7000000000000004,0.80064484920769274,0.47096755835746623,6.9,26.973190026199809,3.9091579748115666,-6.7653587517516489E-2,-6.481782577676598E-2,-7.0510345148848907E-2,-6.8578093045398192E-2]
[2031,1.2,12.406629074093985,10.338857561744987,4,11.916809487694749,2.9792023719236873,1.7000000000000004,0.74318725151077913,0.43716897147692879,6.9,25.066625813299513,3.6328443207680454,-7.0683675570015869E-2,-6.7496318441787162E-2,-7.3911985407048686E-2,-7.1764150801410742E-2]
[2032,1.2,11.539372433154071,9.6161436942950598,4,11.000102524564781,2.7500256311411952,1.7000000000000004,0.68774687980996152,0.40455698812350666,6.9,23.227221837528813,3.3662640344244656,-7.3380597351669685E-2,-6.9902681522962085E-2,-7.6925536493350544E-2,-7.4598119906007954E-2]
[2033,1.2,10.707656218918785,8.9230468490989878,4,10.124342240745236,2.5310855601863089,1.7000000000000004,0.63469731247250039,0.3733513602779413,6.9,21.466695772136521,3.1111153292951479,-7.5795808801712328E-2,-7.2076381887602459E-2,-7.9613829222395793E-2,-7.713530790880474E-2]
[2034,1.2,9.9147584892280918,8.262298741023411,4,9.2938745817460102,2.3234686454365026,1.7000000000000004,0.58428964251602977,0.34369978971531157,6.9,19.792922713490132,2.8685395236942219,-7.7970688941282007E-2,-7.4049606513306387E-2,-8.2026825965742511E-2,-7.9420014810059003E-2]
[2035,1.2,9.1627352910575013,7.6356127425479183,4,8.5112861525673509,2.1278215381418377,1.7000000000000004,0.53667696531722164,0.31569233253954204,6.9,18.210698408942072,2.6392316534698654,-7.993889166604351E-2,-7.5848867018558974E-2,-8.4204754679574889E-2,-8.1488141726732577E-2]
[2036,1.2,8.4526581451687264,7.0438817876406059,4,7.7777803666188277,1.9444450916547069,1.7000000000000004,0.49193469441826299,0.2893733496578017,6.9,16.722373206205816,2.4235323487254803,-8.17280682659286E-2,-7.7496197732764838E-2,-8.618036954700059E-2,-8.3369091260535377E-2]
[2037,1.2,7.7848130962745472,6.4873442468954563,4,7.0934865087046859,1.7733716271761715,1.7000000000000004,0.45007736136835153,0.26475138904020673,6.9,15.328376966347584,2.2215039081663162,-8.3361148723849143E-2,-7.9010062565454398E-2,-8.7980609590242231E-2,-8.5087174222200024E-2]
[2038,1.2,7.1588670249446977,5.9657225207872484,4,6.4577126749310949,1.6144281687327737,1.7000000000000004,0.41107245727848829,0.24180732781087541,6.9,14.02765215715428,2.0329930662542433,-8.4857308249200569E-2,-8.040605003470136E-2,-8.9627834351049929E-2,-8.6662666105396302E-2]
[2039,1.2,6.5740061159814189,5.4783384299845164,4,5.8691518511317184,1.4672879627829296,1.7000000000000004,0.37485178975851996,0.22050105279912935,6.9,12.818009756871657,1.8576825734596603,-8.6232705710890478E-2,-8.1697412024187899E-2,-9.114075732792748E-2,-8.8112610997506002E-2]
[2040,1.2,6.0290506854735355,5.0242089045612799,4,5.3260489452827429,1.3315122363206857,1.7000000000000004,0.34132075712714816,0.20077691595714592,6.9,11.696420387883427,1.6951333895483225,-8.7501054396292188E-2,-8.2895485780443035E-2,-9.2535160040926878E-2,-8.9451440669317761E-2]
[2041,1.2,5.5225499707265513,4.6021249756054594,4,4.8263353610501909,1.2065838402625477,1.7000000000000004,0.31036588049987124,0.1825681649999242,6.9,10.659251212276613,1.5448190162719728,-8.8674067895271547E-2,-8.4010027642884677E-2,-9.3824444605441704E-2,-9.0691456587111863E-2]
[2042,1.2,5.0528599711951543,4.2107166426626286,4,4.3677366571005152,1.0919341642751288,1.7000000000000004,0.28186088207164151,0.16580051886567143,6.9,9.7024575103673101,1.4061532623720738,-8.9761811862294039E-2,-8.5049479320438715E-2,-9.502006587662537E-2,-9.184320899681353E-2]
[2043,1.2,4.6182069834742236,3.8485058195618533,4,3.9478579527386515,0.98696448818466287,1.7000000000000004,0.25567155333374103,0.15039503137278881,6.9,8.8217364895466162,1.2785125347169009,-9.0772984048590022E-2,-8.6021182102563154E-2,-9.6131872712444277E-2,-9.2915797841162773E-2]
[2044,1.2,4.2167390898395212,3.5139492415329343,4,3.5642509914028722,0.89106274785071804,1.7000000000000004,0.23165961899211229,0.13627036411300719,6.9,8.0126497002345047,1.161253579744131,-9.1715139107912069E-2,-8.6931550506790578E-2,-9.7168379898184831E-2,-9.3917113689549692E-2]
[2045,1.2,3.8465675295050161,3.2054729412541803,4,3.2144661395116323,0.80361653487790807,1.7000000000000004,0.20968577003666677,0.12334457060980396,6.9,7.2707194390533152,1.0537274549352631,-9.2594870478298286E-2,-8.7786214050201705E-2,-9.8136986630553258E-2,-9.4854032183285697E-2]
[2046,1.2,3.5057995975157326,2.9214996645964439,4,2.8960920620082469,0.72402301550206172,1.7000000000000004,0.18961201193122723,0.11153647760660423,6.9,6.5915036714552064,0.95529038716742121,-9.3417958606658358E-2,-8.8590133768725043E-2,-9.9044153425661974E-2,-9.5732572133670923E-2]
[2047,1.2,3.1925644717929806,2.6604703931608173,4,2.6067853630569466,0.65169634076423666,1.7000000000000004,0.17130345055040808,0.10076673561788708,6.9,5.9706532854003349,0.86531207034787461,-9.4189492565025956E-2,-8.9347698580579338E-2,-9.9895546397335666E-2,-9.6558024960252564E-2]
[2048,1.2,2.9050331588911824,2.4208609657426523,4,2.344292098215579,0.58607302455389476,1.7000000000000004,0.15462961868118752,9.0958599224227929E-2,6.9,5.4039548757879494,0.78318186605622453,-9.4913970469211129E-2,-9.0062805447533312E-2,-0.10069615571783974,-9.7335061352509578E-2]
[2049,1.2,2.6414335688226416,2.2011946406855349,4,2.1064627423850268,0.52661568559625671,1.7000000000000004,0.13946542911638971,8.2038487715523342E-2,6.9,4.8873617403240583,0.70831329569913881,-9.5595382888641667E-2,-9.0738926425595001E-2,-0.10145039349472806,-9.8067819698004044E-2]
[{"$f":"A41+1","v":2050},{"$f":"RF!B40","v":1.2},2.4000615747941296,2.0000513123284414,{"$f":"RF!E40","v":4},1.891261926815309,0.47281548170382726,{"$f":"K42-E42-B42","v":1.7000000000000004},0.12569182615234231,7.3936368324907228E-2,{"$f":"RF!K40","v":6.9},4.4170153277617814,0.64014714895098279,-9.6237282516168032E-2,-9.1379165040329946E-2,-0.10216217511925152,-9.8759979812292786E-2]
["∑",null,{"$f":"SUM(C12:C42)","v":321.55839680052622},null,null,{"$f":"SUM(F12:F42)","v":303.78217631684129},null,null,{"$f":"SUM(I12:I42)","v":19.031754323347027},null,null,{"$f":"SUM(L12:L42)","v":644.37232744071457}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A42-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A42-$A$11)+2*C$8+C$7)","v":22.656223863545428},null,null,{"$f":"F$11*EXP(-F$8*($A42-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A42-$A$11)+2*F$8+F$7)","v":15.845685728368183},null,null,{"$f":"I$11*EXP(-I$8*($A42-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A42-$A$11)+2*I$8+I$7)","v":1.0919683580140913},null,null,39.593877949927702]
["∑",null,{"$f":"SUM(C43:C44)","v":344.21462066407167},null,null,{"$f":"SUM(F43:F44)","v":319.6278620452095},null,null,{"$f":"SUM(I43:I44)","v":20.123722681361119},null,null,{"$f":"SUM(L43:L44)","v":683.96620539064224}]
[]
[null,null,null,null,null,"global path 2020 - 2100 sheet \"global path\":",null,null,null,null,null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L45-L47","v":0}]
[]
[]
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[2093,1.2,2.6680576400212652E-2,2.2233813666843877E-2,4,1.212836330511019E-2,3.0320908262775476E-3,1.7000000000000004,9.5812543810427832E-4,5.6360319888486949E-4,6.9,3.9767065143427122E-2,5.7633427744097276E-3,-0.10769935338101833,-0.10389641012028195,-0.11562008490435605,-0.11196661518492157]
[2094,1.2,2.3904977147769541E-2,1.992081428980795E-2,4,1.0724385101055167E-2,2.6810962752637918E-3,1.7000000000000004,8.5071475623418012E-4,5.0042044484363524E-4,6.9,3.548007700505889E-2,5.142040145660708E-3,-0.1078024773240478,-0.10403070798803993,-0.11575990665314817,-0.11210503092644963]
[2095,1.2,2.1414992716236814E-2,1.7845827263530678E-2,4,9.4814690213091551E-3,2.3703672553272888E-3,1.7000000000000004,7.5523050381273021E-4,4.4425323753690001E-4,6.9,3.1651692241358699E-2,4.5872017741099558E-3,-0.10790238034585786,-0.10416175745079326,-0.11589625587239705,-0.11224003312711495]
[2096,1.2,1.9181630086610224E-2,1.5984691738841855E-2,4,8.3813411838502411E-3,2.0953352959625603E-3,1.7000000000000004,6.7036393307152824E-4,3.9433172533619301E-4,6.9,2.8233335203531995E-2,4.0917877106568107E-3,-0.10799918727125746,-0.10428967495904207,-0.11602926033786842,-0.11237174652342408]
[2097,1.2,1.7178788401153222E-2,1.4315657000961018E-2,4,7.4077726243387543E-3,1.8519431560846886E-3,1.7000000000000004,5.9494779629762698E-4,3.4996929193978051E-4,6.9,2.5181508821789603E-2,3.6494940321434204E-3,-0.10809301698655172,-0.1044145714630943,-0.11615904163255253,-0.11250028984756599]
[2098,1.2,1.5382977081556781E-2,1.2819147567963984E-2,4,6.5463544843298097E-3,1.6365886210824524E-3,1.7000000000000004,5.2794133895039692E-4,3.1055372879435107E-4,6.9,2.2457272904836987E-2,3.2546772325850702E-3,-0.10818398278801034,-0.10453655273359597,-0.11628571551706313,-0.11262577618441938]
[2099,1.2,1.3773060544561455E-2,1.1477550453801213E-2,4,5.7842973371969725E-3,1.4460743342992431E-3,1.7000000000000004,4.6841684346063221E-4,2.7553931968272478E-4,6.9,2.0025774725219062E-2,2.9022861920607332E-3,-0.10827219270663158,-0.10465571966076148,-0.11640939227427949,-0.11274831330334101]
[2100,1.2,1.2330027123982401E-2,1.0275022603318668E-2,4,5.1102521445029123E-3,1.2775630361257281E-3,1.7000000000000004,4.1554756931475728E-4,2.4443974665573951E-4,6.9,1.7855826837800071E-2,2.5878009909855175E-3,-0.10835774980961466,-0.10477216853220483,-0.11653017702936719,-0.11286800396689467]
["∑",null,{"$f":"SUM(C51:C100)","v":22.551884926092182},null,null,{"$f":"SUM(F51:F100)","v":15.807264645149509},null,null,{"$f":"SUM(I51:I100)","v":1.0887306265605419},null,null,{"$f":"SUM(L51:L100)","v":39.447880197802228}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A100-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A100-$A$11)+2*C$8+C$7)","v":0.10433893745325071},null,null,{"$f":"F$11*EXP(-F$8*($A100-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A100-$A$11)+2*F$8+F$7)","v":3.8421083218675517E-2},null,null,{"$f":"I$11*EXP(-I$8*($A100-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A100-$A$11)+2*I$8+I$7)","v":3.2377314535498615E-3},null,null,{"$f":"I102+F102+C102","v":0.14599775212547608}]
["∑",null,{"$f":"SUM(C101:C102)","v":22.656223863545431},null,null,{"$f":"SUM(F101:F102)","v":15.845685728368185},null,null,{"$f":"SUM(I101:I102)","v":1.0919683580140918},null,null,{"$f":"SUM(L101:L102)","v":39.593877949927702}]
[]
["∑",null,{"$f":"C103+C43","v":344.21462066407167},null,null,{"$f":"F103+F43","v":319.6278620452095},null,null,{"$f":"I103+I43","v":20.123722681361119},null,null,{"$f":"SUM(C105:I105)","v":683.96620539064224}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L105-L107","v":0}]

{"sheet":"SPF-spk","index":13,"n_rows":108,"n_cols":26,"rows_kept":108,"cut":false,"hidden":false,"merged":[[10,13,10,16],[3,22,3,23],[3,1,3,3],[3,4,3,6],[3,7,3,9],[3,10,3,13],[4,18,6,30],[5,10,7,13]]}
["Smooth Pathways Formula - equity (spk variabel); free input weighting population"]
[{"$f":"CONCATENATE(\"SPF-\",ROUND(W8*100,0))","v":"SPF-50"},{"$f":"'SPF-eq'!B2","v":"Smooth Pathways Formula; based on: Raupach et al. (2014) / Sharing a quota on cumulative carbon emissions / nature climate change DOI: 10.1038/NCLIMATE2384"}]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global",null,null,null,null,null,null,null,"Description",null,null,null,"input value"]
[null,"RBA:",{"$f":"W8*'global path'!C89/K11*B11+(1-W8)*'global path'!C89*C11/L11","v":231.58263253991771},"Gt","RBB:",{"$f":"W8*'global path'!C89/K11*E11+(1-W8)*'global path'!C89*F11/L11","v":358.06500504887777},"Gt","RBC:",{"$f":"W8*'global path'!C89/K11*H11+(1-W8)*'global path'!C89*I11/L11","v":94.31856780184664},"Gt","RB:",{"$f":"C5+F5+I5","v":683.96620539064213},"Gt",null,null,null,null,null,"Raupach et al. have developed a formula to convert a budget of a country or global into a smooth emission pathway."]
[null,"TA",{"$f":"C5/C11","v":11.027744406662748},null,"TB",{"$f":"F5/F11","v":18.362307951224501},null,"TC",{"$f":"I5/I11","v":76.824349601036701},null,"Global path ist different to the path in sheet \"global path\"."]
[null,"rA",{"$f":"'SPF-eq'!C7","v":0},null,"rB",{"$f":"'SPF-eq'!F7","v":0.03},null,"rC",{"$f":"'SPF-eq'!I7","v":0.02}]
[null,"mA",{"$f":"(1+SQRT(1+C7*C6))/C6","v":0.1813607503263894},null,"mB",{"$f":"(1+SQRT(1+F7*F6))/F6","v":0.12227978157380519},null,"mC",{"$f":"(1+SQRT(1+I7*I6))/I6","v":3.374757155179052E-2},null,null,null,null,null,null,null,null,null,"share population key:",null,null,null,0.5,null,{"$f":"B11/K11","v":0.17391304347826086},{"$f":"C11/L11","v":0.5032626143677319}]
["Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPt","Et","Per capita",null,null,null,null,null,"Limitations"]
[null,"bn","Gt","t","bn","Gt","t","bn","Gt","t","bn","Gt","t",null,"A","B","C",null,"-","The resulting global pathway ist different to the pathway in sheet \"global path\". So this model is comparable with the other models to a limited extent only."]
[2019,{"$f":"RF!B9","v":1.2},{"$f":"RF!C9","v":21},{"$f":"C11/B11","v":17.5},{"$f":"RF!E9","v":4},{"$f":"RF!F9","v":19.5},{"$f":"F11/E11","v":4.875},{"$f":"K11-E11-B11","v":1.7000000000000004},{"$f":"'global path'!$C$7-C11-F11","v":1.2277171013052595},{"$f":"I11/H11","v":0.72218653017956425},{"$f":"RF!K9","v":6.9},{"$f":"I11+F11+C11","v":41.727717101305259},{"$f":"L11/K11","v":6.047495232073226},"annual change rates",null,null,null,null,"-","The per capita emissions converge far into the future; as you can see on the remaining budgets as of 2051. So this model is comparable with the other models to a limited extent only."]
[{"$f":"A11+1","v":2020},{"$f":"B$11*(B$42/B$11)^(($A12-2019)/31)","v":1.2},{"$f":"-C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A11-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A11-$A$11)+2*C$8+C$7)","v":20.894772381654917},{"$f":"C12/B12","v":17.412310318045765},{"$f":"E$11*(E$42/E$11)^(($A12-2019)/31)","v":4},{"$f":"-F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A11-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A11-$A$11)+2*F$8+F$7)","v":19.723983954892105},{"$f":"F12/E12","v":4.9309959887230264},{"$f":"H$11*(H$42/H$11)^(($A12-2019)/31)","v":1.7000000000000004},{"$f":"-I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A11-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A11-$A$11)+2*I$8+I$7)","v":1.2394923721104334},{"$f":"I12/H12","v":0.72911316006496063},{"$f":"B12+E12+H12","v":6.9},{"$f":"I12+F12+C12","v":41.858248708657456},{"$f":"L12/K12","v":6.0664128563271671},{"$f":"L12/L11-1","v":3.1281751416041281E-3},{"$f":"C12/C11-1","v":-5.0108389688134913E-3},{"$f":"F12/F11-1","v":1.1486356661133623E-2},{"$f":"I12/I11-1","v":9.5911922971951835E-3}]
[{"$f":"A12+1","v":2021},1.2,{"$f":"-C$11*EXP(-C$8*($A13-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A13-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)","v":20.334486613652501},16.945405511377086,4,{"$f":"-F$11*EXP(-F$8*($A13-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A13-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)","v":19.927139169977409},4.9817847924943521,1.7000000000000004,{"$f":"-I$11*EXP(-I$8*($A13-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A13-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)","v":1.2610930543153955},0.74181944371493835,{"$f":"B13+E13+H13","v":6.9},{"$f":"I13+F13+C13","v":41.522718837945305},6.0177853388326525,{"$f":"L13/L12-1","v":-8.0158602202282658E-3},{"$f":"C13/C12-1","v":-2.6814638502323795E-2},{"$f":"F13/F12-1","v":1.0299907744292902E-2},{"$f":"I13/I12-1","v":1.742703923880029E-2},null,"Simplification"]
[2022,1.2,19.385220674904559,16.154350562420468,4,19.822228252377556,4.955557063094389,1.7000000000000004,1.2798951813680191,0.7528795184517757,6.9,40.487344108650134,5.8677310302391499,-2.4935138118869937E-2,-4.6682562327912791E-2,-5.2647254934573562E-3,1.4909389111519955E-2,null,null,"We assumed that the emission power at the end of the base year are the emissions in the base year divided by one year."]
[2023,1.2,18.191425678058579,15.15952139838215,4,19.477476193679365,4.8693690484198413,1.7000000000000004,{"$f":"-I$11*EXP(-I$8*($A15-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A15-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A14-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A14-$A$11)+2*I$8+I$7)","v":1.2960607035590357},0.76238864915237381,6.9,38.96496257529698,5.647096025405359,-3.7601417600219844E-2,-6.1582739596636404E-2,-1.7392194979736431E-2,1.263034850536604E-2]
[2024,1.2,16.860335181254214,14.050279317711846,4,18.949483905085344,4.7373709762713361,1.7000000000000004,1.3097439045035912,0.77043759088446528,6.9,37.11956299084315,5.3796468102671229,-4.7360486511124678E-2,-7.3171312703096514E-2,-2.7107838990215738E-2,1.055753091423961E-2,null,"Input values"]
[2025,1.2,15.470337360456455,12.891947800380379,4,18.285000229655111,4.5712500574137778,1.7000000000000004,1.3210917316294797,0.7771127833114585,6.9,35.076429321741045,5.0835404814117453,-5.5041964518981912E-2,-8.2441885398767067E-2,-3.506605661444484E-2,8.66415723476055E-3,null,"-","reduction rate at the beginnging of 2020 for each country"]
[2026,1.2,14.077593777898727,11.73132814824894,4,17.522440033914222,4.3806100084785555,1.7000000000000004,1.3302441131734497,0.78249653716085255,6.9,32.930277924986399,4.7725040470994777,-6.1185001958692031E-2,-9.0026710478706362E-2,-4.1704139248745942E-2,6.9278925337614705E-3,null,"-","Share that is distributed over the population key"]
[2027,1.2,12.721256075259902,10.601046729383253,4,16.693183355652934,4.1732958389132335,1.7000000000000004,1.3373342622177375,0.78666721306925724,6.9,30.751773693130573,4.4567787961058798,-6.6155051494504624E-2,-9.6347268150912435E-2,-4.7325411110340942E-2,5.32996085009807E-3]
[2028,1.2,11.42756361212345,9.5229696767695415,4,15.822685897020165,3.9556714742550412,1.7000000000000004,1.3424889682776069,0.78969939310447446,6.9,28.592738477421221,4.1438751416552488,-7.0208477639507438E-2,-0.1016953401050078,-5.2146881759253305E-2,3.8544634692310176E-3]
[2029,1.2,10.213049756570783,8.5108747971423195,4,14.931427080041232,3.7328567700103079,1.7000000000000004,1.3458288769310798,0.79166404525357614,6.9,26.490305713543094,3.8391747410932018,-7.3530304400131197E-2,-0.10627933449122917,-5.6327909356197248E-2,2.4878481182291079E-3]
[2030,1.2,9.0870397840488408,7.5725331533740343,4,14.035718345816491,3.5089295864541228,1.7000000000000004,1.3474687579638669,0.79262868115521568,6.9,24.470226887829199,3.5464096938882896,-7.6257286252500167E-2,-0.11025207938475967,-5.9988153136549816E-2,1.2184914894428633E-3]
[2031,1.2,8.0535871706202116,6.7113226421835099,4,13.148391309408424,3.2870978273521061,1.7000000000000004,1.347517762483605,0.79265750734329687,6.9,22.549496242512241,3.2680429336974259,-7.8492555631851313E-2,-0.11372819289761726,-6.3219210769682066E-2,3.6367833724071374E-5]
[2032,1.2,7.1129658620150451,5.9274715516792043,4,12.279382719240829,3.0698456798102072,1.7000000000000004,1.3460796694398169,0.79181157025871562,6.9,20.738428250695691,3.0055693116950275,-8.0315230652566405E-2,-0.11679532221822697,-6.6092388773504984E-2,-1.0672163913724164E-3]
[2033,1.2,6.2628125450342225,5.2190104541951854,4,11.436230859894025,2.8590577149735061,1.7000000000000004,1.3432531219704344,0.79014889527672594,6.9,19.042296526898681,2.7597531198403886,-8.1786898375006301E-2,-0.11952163604788923,-6.8664026411168977E-2,-2.0998366839303229E-3]
[2034,1.2,5.498993972040374,4.5824949767003123,4,10.624496034444221,2.6561240086110551,1.7000000000000004,1.3391318539776762,0.78772461998686816,6.9,17.462621860462271,2.5308147623858361,-8.2956100605039995E-2,-0.12196095085098457,-7.0979226931881523E-2,-3.0681246336600188E-3]
[2035,1.2,4.8162591215233483,4.0135492679361242,4,9.8481160268600263,2.4620290067150066,1.7000000000000004,1.3338049073222038,0.7845911219542373,6.9,15.998180055705578,2.318576819667475,-8.3861508109065008E-2,-0.1241563191355346,-7.3074525612057184E-2,-3.9779104945114607E-3]
[2036,1.2,4.2087237100219923,3.5072697583516605,4,9.1097059414665438,2.2774264853666359,1.7000000000000004,1.327356840008278,0.78079814118133983,6.9,14.645786491496814,2.1225777523908427,-8.4534213235489153E-2,-0.12614259245029924,-7.497983201858327E-2,-4.8343406734581151E-3]
[2037,1.2,3.6702247278392086,3.058520606532674,4,8.4108105146853518,2.1027026286713379,1.7000000000000004,1.3198679257189951,0.77639289748176166,6.9,13.400903168243556,1.9421598794555877,-8.4999417680711398E-2,-0.12794828534372238,-7.6719866840035289E-2,-5.6419751370220261E-3]
[2038,1.2,3.1945747861154103,2.6621456550961753,4,7.7521158676361352,1.9380289669090338,1.7000000000000004,1.311414345045975,0.77142020296822045,6.9,12.258104998797521,1.7765369563474667,-8.5277697711759526E-2,-0.12959695304647745,-7.8315240356340188E-2,-6.4048686298783242E-3]
[2039,1.2,2.7757397571860487,2.3131164643217073,4,7.1336266936670256,1.7834066734167564,1.7000000000000004,1.3020683687454806,0.76592256985028251,6.9,11.211434819598555,1.624845626028776,-8.5385969470945233E-2,-0.13110822471577299,-7.9783272661236193E-2,-7.1266387589856706E-3]
[2040,1.2,2.4079581567915724,2.0066317973263104,4,6.554814032379312,1.638703508094828,1.7000000000000004,1.2918985333391788,0.75994031372892856,6.9,10.254670722510063,1.4861841626826178,-8.533823836856147E-2,-0.13249858868877562,-8.1138625014056664E-2,-7.8105233568497301E-3]
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["∑",null,{"$f":"SUM(C12:C42)","v":228.39056397717752},null,null,{"$f":"SUM(F12:F42)","v":332.98106674128212},null,null,{"$f":"SUM(I12:I42)","v":39.893856784500301},null,null,{"$f":"SUM(L12:L42)","v":601.26548750296001}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A42-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A42-$A$11)+2*C$8+C$7)","v":3.1920685627401761},null,null,{"$f":"F$11*EXP(-F$8*($A42-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A42-$A$11)+2*F$8+F$7)","v":25.083938307595592},null,null,{"$f":"I$11*EXP(-I$8*($A42-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A42-$A$11)+2*I$8+I$7)","v":54.424711017346368},null,null,82.700717887682131]
["∑",null,{"$f":"SUM(C43:C44)","v":231.58263253991771},null,null,{"$f":"SUM(F43:F44)","v":358.06500504887771},null,null,{"$f":"SUM(I43:I44)","v":94.318567801846669},null,null,{"$f":"SUM(L43:L44)","v":683.96620539064213}]
[]
[null,null,null,null,null,"global path 2020 - 2100 sheet \"global path\":",null,null,null,null,null,{"$f":"'global path'!C89","v":683.96620539064213}]
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[]
[]
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[2080,1.2,4.3218837509866673E-3,3.6015697924888894E-3,4,0.12204236451009098,3.0510591127522746E-2,1.7000000000000004,0.67757553635441781,0.39857384491436332,6.9,0.80393978461549542,0.11651301226311528,-3.4810910351775082E-2,-0.15303252965337555,-0.10170316073993413,-2.0805699050215676E-2]
[2081,1.2,3.6596545822987388E-3,3.0497121519156159E-3,4,0.10960588957749162,2.7401472394372905E-2,1.7000000000000004,0.66337206989081565,0.39021886464165617,6.9,0.77663761405060605,0.11255617594936319,-3.3960467049092946E-2,-0.15322697389459961,-0.10190293331764366,-2.0962189012935006E-2]
[2082,1.2,3.0982064285400499E-3,2.5818386904500417E-3,4,9.8415475140666175E-2,2.4603868785166544E-2,1.7000000000000004,0.64936512005538916,0.38197948238552293,6.9,0.75087880162459542,0.10882301472820223,-3.3167093583922336E-2,-0.15341561372331114,-0.10209683512411805,-2.1114771741493232E-2]
[2083,1.2,2.6223259326083811E-3,2.1852716105069843E-3,4,8.8349036337870168E-2,2.2087259084467542E-2,1.7000000000000004,0.63555728523604316,0.37385722660943704,6.9,0.72652864750652169,0.10529400688500314,-3.2428874094447613E-2,-0.1535987052211738,-0.10228512120078626,-2.1263591765089296E-2]
[2084,1.2,2.2190738560411895E-3,1.849228213367658E-3,4,7.9296084452835647E-2,1.9824021113208912E-2,1.7000000000000004,0.62195077496250306,0.36585339703676645,6.9,0.70346593327137985,0.10195158453208403,-3.1743709369608575E-2,-0.15377648962426416,-0.10246803202712507,-2.1408786571436633E-2]
[2085,1.2,1.8774492236261296E-3,1.5645410196884414E-3,4,7.1156674859849112E-2,1.7789168714962278E-2,1.7000000000000004,0.60854743285300472,0.35796907814882623,6.9,0.68158155693647993,9.8779935787895637E-2,-3.1109361946113578E-2,-0.1539491943835144,-0.10264579454522449,-2.15504870305957E-2]
[2086,1.2,1.5881023175408956E-3,1.3234185979507465E-3,4,6.3840443526442692E-2,1.5960110881610673E-2,1.7000000000000004,0.59534875846624402,0.35020515203896702,6.9,0.66077730431022763,9.5764826711627185E-2,-3.0523497026183732E-2,-0.15411703413548816,-0.10281862309918977,-2.1688817788421799E-2]
[2087,1.2,1.3430895559604717E-3,1.1192412966337265E-3,4,5.7265725625321617E-2,1.4316431406330404E-2,1.7000000000000004,0.58235592810621029,0.34256231065071185,6.9,0.64096474328749242,9.2893441056158321E-2,-2.9983719013196408E-2,-0.15428021159229532,-0.10298672029742129,-2.1823897631879308E-2]
[2088,1.2,1.1356642576795676E-3,9.463868813996397E-4,4,5.135875011837493E-2,1.2839687529593732E-2,1.7000000000000004,0.569569814624721,0.3350410674263064,6.9,0.62206422900077551,9.0154236087068906E-2,-2.9487603623526315E-2,-0.15443891835832935,-0.10315027780482289,-2.195583982989413E-2]
[2089,1.2,9.6009813187134495E-4,8.0008177655945412E-4,4,4.6052904500577529E-2,1.1513226125144382E-2,1.7000000000000004,0.55699100626605969,0.32764176839179976,6.9,0.60400400889850858,8.7536812883841825E-2,-2.9032725658051706E-2,-0.1545933356808693,-0.10330947707193316,-2.2084752449441636E-2]
[2090,1.2,8.1152905685404758E-4,6.7627421404503965E-4,4,4.1288064223113707E-2,1.0322016055778427E-2,1.7000000000000004,0.54461982459470804,0.32036460270276934,6.9,0.58671941787467574,8.5031799691981991E-2,-2.8616682619961198E-2,-0.15474363514041911,-0.10346449000635927,-2.221073865139267E-2]
[2091,1.2,6.8583133804721958E-4,5.7152611503934973E-4,4,3.700998164721131E-2,9.2524954118028274E-3,1.7000000000000004,0.53245634154702159,0.31320961267471853,6.9,0.57015215453228019,8.2630747033663784E-2,-2.8237114432667965E-2,-0.15488997928688408,-0.10361547959198003,-2.2333896965168631E-2]
[2092,1.2,5.7950517588825157E-4,4.8292097990687631E-4,4,3.3169729708494022E-2,8.2924324271235056E-3,1.7000000000000004,0.52050039564444717,0.30617670332026298,6.9,0.55424963052882947,8.0326033409975281E-2,-2.7891719564747119E-2,-0.15503252222581787,-0.10376260046069619,-2.2454321546508615E-2]
[2093,1.2,4.8958254055075446E-4,4.0798545045896205E-4,4,2.9723195792626833E-2,7.4307989481567083E-3,1.7000000000000004,0.5087516074060261,0.29926565141530942,6.9,0.53896438573920369,7.8110780541913574E-2,-2.7578267891746888E-2,-0.1551714101598245,-0.10390599942044776,-2.2572102416703377E-2]
[2094,1.2,4.1354705170890647E-4,3.4462254309075541E-4,4,2.6630621633919077E-2,6.6576554084797693E-3,1.7000000000000004,0.49720939399465536,0.29247611411450308,6.9,0.52425356268028334,7.5978777200041064E-2,-2.7294610642489947E-2,-0.15530678188873337,-0.10404581594402118,-2.2687325687718363E-2]
[2095,1.2,3.4926580695510329E-4,2.9105483912925275E-4,4,2.385618534753059E-2,5.9640463368826474E-3,1.7000000000000004,0.48587298313158556,0.28580763713622676,6.9,0.51007843428607125,7.3924410766097279E-2,-2.7038687771124947E-2,-0.15543876927225775,-0.10418218262147982,-2.2800073771718887E-2]
[2096,1.2,2.9493139934944285E-4,2.4577616612453574E-4,4,2.1367621991535607E-2,5.3419054978839017E-3,1.7000000000000004,0.47474142631124749,0.27925966253602785,6.9,0.49640397970213257,7.1942605753932257E-2,-2.6808533089774822E-2,-0.15556749765843791,-0.10431522557954054,-2.291042557787859E-2]
[2097,1.2,2.4901261954365407E-4,2.0751051628637839E-4,4,1.9135879326498711E-2,4.7839698316246779E-3,1.7000000000000004,0.46381361134773513,0.27283153608690297,6.9,0.4831985032937775,7.002876859330108E-2,-2.6602277476258429E-2,-0.15569308628066059,-0.10444506487062344,-2.301845669635727E-2]
[2098,1.2,2.1021255671337482E-4,1.7517713059447902E-4,4,1.7134805696876032E-2,4.283701424219008E-3,1.7000000000000004,0.45308827428251419,0.26652251428383184,6.9,0.47043329253610361,6.8178738048710663E-2,-2.6418150450918998E-2,-0.15581564862610209,-0.10457181483432854,-2.3124239571269967E-2]
[2099,1.2,1.7743300013674799E-4,1.4786083344729001E-4,4,1.5340867200294594E-2,3.8352168000736486E-3,1.7000000000000004,0.44256401068226836,0.26033177098956956,6.9,0.45808231088269968,6.6388740707637631E-2,-2.6254480389387047E-2,-0.15593529277759466,-0.10469558443306437,-2.3227843662278591E-2]
[2100,1.2,1.4974420400017585E-4,1.2478683666681322E-4,4,1.3732891537573899E-2,3.4332228843934748E-3,1.7000000000000004,0.43223928635384468,0.25425840373755565,6.9,0.44612192209541873,6.4655351028321553E-2,-2.6109693614306817E-2,-0.15605212173176541,-0.10481647756456802,-2.3329335597141787E-2]
["∑",null,{"$f":"SUM(C51:C100)","v":3.191262708953071},null,null,{"$f":"SUM(F51:F100)","v":24.967820899041229},null,null,{"$f":"SUM(I51:I100)","v":38.002363700654968},null,null,{"$f":"SUM(L51:L100)","v":66.161447308649272}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A100-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A100-$A$11)+2*C$8+C$7)","v":8.058537871051027E-4},null,null,{"$f":"F$11*EXP(-F$8*($A100-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A100-$A$11)+2*F$8+F$7)","v":0.11611740855436117},null,null,{"$f":"I$11*EXP(-I$8*($A100-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A100-$A$11)+2*I$8+I$7)","v":16.4223473166914},null,null,{"$f":"I102+F102+C102","v":16.53927057903287}]
["∑",null,{"$f":"SUM(C101:C102)","v":3.1920685627401761},null,null,{"$f":"SUM(F101:F102)","v":25.083938307595592},null,null,{"$f":"SUM(I101:I102)","v":54.424711017346368},null,null,{"$f":"SUM(L101:L102)","v":82.700717887682146}]
[]
["∑",null,{"$f":"C103+C43","v":231.58263253991771},null,null,{"$f":"F103+F43","v":358.06500504887771},null,null,{"$f":"I103+I43","v":94.318567801846669},null,null,{"$f":"SUM(C105:I105)","v":683.96620539064213}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L105-L107","v":0}]

{"sheet":"ESPM","index":14,"n_rows":33,"n_cols":12,"rows_kept":33,"cut":false,"hidden":false,"merged":[[9,5,9,7],[2,2,2,9],[30,1,30,7],[32,1,33,8]]}
[]
[null,"Extended Smooth Pathway Model"]
[null,"ESPM","Wirtschaftsdienst 2021/2: Calculation of Paris-Compatible Emission Paths with the ESPM Using the Example of the EU",null,null,null,null,null,null,null,"Zenodo","Wirtschafsdienst"]
[null,null,"inspired by:",{"$f":"'SPF-eq'!B2","v":"Smooth Pathways Formula; based on: Raupach et al. (2014) / Sharing a quota on cumulative carbon emissions / nature climate change DOI: 10.1038/NCLIMATE2384"}]
[]
[]
[]
[]
[]
[null,"For a comprehensive mathematical description, we refer to:",null,null,null,"https://doi.org/10.5281/zenodo.4540475"]
[]
[null,null,"complete ESPM","web app\nEU","use of\nRM Scenario Types\nwith a known budget","calculation of global paths"]
[null,"published Tools:","here","here","here","here"]
[]
[null,"The following figures show the relationship between SPFR and ESPM with the same framework data:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"The course of the reduction rates for SPFR corresponds to scenario type RM-5-rad."]
[]
[null,"An iterative solution method, which is not integrated here, must be used to calculate the paths. For this we refer to the tools above."]

{"sheet":"EPM","index":15,"n_rows":119,"n_cols":42,"rows_kept":119,"cut":false,"hidden":false,"merged":[[1,3,1,4],[14,37,14,38],[14,24,14,26],[3,23,5,31],[14,28,14,30],[14,31,14,33],[14,34,14,36],[2,2,2,18]]}
[]
[null,"Cap Model",null,"input values",null,null,"solver",null,null,"original scenario global path:",null,null,3,null,"choosen scenario global path:",null,null,{"$f":"'global path'!C2","v":3}]
[null,"EPM","cap model; based on: Chakravartya et al. / Sharing global CO2 emission reductions among\none billion high emitters / 11884–11888   PNAS   July 21, 2009   vol. 106   no. 29 / doi 10.1073 pnas.0905232106",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Description"]
[null,"source data:","http://data.worldbank.org/indicator/SI.DST.04TH.20/countries?display=default",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Chakravarty et al. insinuate that the income and emissions distribution correlated. Each person is attributed his emissions or a cap, whatever is the least. The cap is calculated for each year such that the emissions of the global pathway are met."]
[]
[null,"Country A",null,null,null,null,null,null,"Country B",null,null,null,null,null,null,"Country C"]
[null,"Data of the probability density functions",null,null,null,null,null,null,"Data of the probability density functions",null,null,null,null,null,null,"Data of the probability density functions"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"If you change the quantile values of countries, you have to do the following optimization with the help of the Excel solver:"]
[null,null,"G income","G emissions",null,null,null,null,null,"G income","G emissions",null,null,null,null,null,"G income","G emissions",null,null,null,null,null,"- For each country: minimize the target value by adjusting the parameter a (variable)"]
[null,"a",1.5667140078250585,{"$f":"C10","v":1.5667140078250585},null,null,null,null,"a",0.78102068816147474,{"$f":"J10","v":0.78102068816147474},null,null,null,null,"a",2.7860406584318342,{"$f":"Q10","v":2.7860406584318342},null,null,null,null,null,"- Redefine caps for each year. Target = 0 by adjusting the caps of the individual years (variables)."]
[null,"b",{"$f":"C12/C10","v":34866.142836442385},{"$f":"D12/D10","v":11.169875237340747},null,null,null,null,"b",{"$f":"J12/J10","v":15014.718634345252},{"$f":"K12/K10","v":6.2418320972723089},null,null,null,null,"b",{"$f":"Q12/Q10","v":153.42798802110258},{"$f":"R12/R10","v":0.25921607712145089}]
[null,"E",{"$f":"17420000/318.9","v":54625.274380683601},{"$f":"AC19","v":17.5},null,null,null,null,"E",{"$f":"2416635506076/206077898","v":11726.805880347247},{"$f":"AF19","v":4.875},null,null,null,null,"E",{"$f":"8168695870/19110000","v":427.45661276818419},{"$f":"AI19","v":0.72218653017956425},null,null,null,null,null,"Limitations"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"- The per capita emissions converge far into the future. So is it comparable with the models with converging per capita emissions upto 2050 to a limited extent only."]
[null,"Data of the Lorenz curve",null,null,null,null,null,null,"Data of the Lorenz curve",null,null,null,null,null,null,"Data of the Lorenz curve",null,null,null,null,null,null,null,"- Actual correlation between emission and income distribution?"]
[null,null,null,"≈ USA",null,null,null,null,null,null,"≈ Brazil",null,null,null,null,null,null,"≈ Niger",null,null,null,null,null,null,"Global",null,null,null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global"]
[null,"population\nshare","income\nshare","quantiles","squares","population\nshare","emission\nshare",null,"population\nshare","income\nshare","quantiles","squares","population\nshare","emission\nshare",null,"population\nshare","income\nshare","quantiles","squares","population\nshare","emission\nshare"]
[null,0,0,null,null,{"$f":"B17","v":0},0,null,0,0,null,null,{"$f":"I17","v":0},0,null,0,0,null,null,{"$f":"P17","v":0},0,null,null,"Year\nt","Popu-lation\nPt","Et","Per capita","Cap","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Et","square"]
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["∑",null,{"$f":"SUM(C9:C39)","v":114.2197645839727},null,null,{"$f":"SUM(F9:F39)","v":380.73254861324233},null,null,{"$f":"SUM(I9:I39)","v":161.81133316062795},null,null,{"$f":"SUM(L9:L39)","v":656.76364635784307}]
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{"sheet":"G-C&C = RF","index":17,"n_rows":52,"n_cols":25,"rows_kept":52,"cut":false,"hidden":false,"merged":[[2,18,2,20],[0,7,0,11],[3,13,3,16],[3,1,3,4],[3,5,3,8],[3,9,3,12]]}
["Comparision of G-C&C and RF",null,null,null,null,null,null,null,null,null,null,null,null,"convergence period: 2020 - 2050"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Comparison to RM"]
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[]
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["∑",null,{"$f":"SUM(C9:C39)","v":305.50878147574412},null,null,null,{"$f":"SUM(G9:G39)","v":315.45266303406379},null,null,null,{"$f":"SUM(K9:K39)","v":35.802201848035125},null,null,null,{"$f":"SUM(O9:O39)","v":656.76364635784296}]
[]
[null,null,null,null,null,null,null,null,null,null,null,"global path:",null,null,{"$f":"'global path'!C90","v":656.76364635784296}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"O40-O42","v":0}]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"G-C&C ≙ RM"]

{"sheet":"G-LIMITS = RF","index":18,"n_rows":43,"n_cols":18,"rows_kept":43,"cut":false,"hidden":false,"merged":[[3,1,3,3],[3,4,3,6],[3,7,3,9],[3,10,3,13]]}
["Comparison of RF and G-LIMITS"]
[]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global"]
[]
["Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPt","Et","Per capita","Ct",null,"RM - \nG-LIMITS\nA","RM -\nG-LIMITS\nB","RM - \nG-LIMITS\nC"]
[null,"bn","Gt","t","bn","Gt","t","bn","Gt","t","bn","Gt","t"]
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["∑",null,{"$f":"SUM(C9:C39)","v":305.50878147574412},null,null,{"$f":"SUM(F9:F39)","v":315.45266303406379},null,null,{"$f":"SUM(I9:I39)","v":35.802201848035104},null,null,{"$f":"SUM(L9:L39)","v":656.76364635784296}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C90","v":656.76364635784296}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L40-L42","v":0}]

{"sheet":"SPF = RF","index":19,"n_rows":108,"n_cols":26,"rows_kept":108,"cut":false,"hidden":false,"merged":[[101,15,101,17],[8,15,8,17],[3,19,3,20],[3,1,3,3],[3,4,3,6],[3,7,3,9],[3,10,3,13],[5,10,7,13]]}
["Comparision SPF and RF"]
[{"$f":"CONCATENATE(\"SPF-\",ROUND(T8*100,0))","v":"SPF-16"}]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global",null,null,null,null,null,null,null,null,"input value"]
[null,"RBA:",{"$f":"T8*'global path'!C89/K11*B11+(1-T8)*'global path'!C89*C11/L11","v":308.98458991296116},"Gt","RBB:",{"$f":"T8*'global path'!C89/K11*E11+(1-T8)*'global path'!C89*F11/L11","v":331.65057204577687},"Gt","RBC:",{"$f":"T8*'global path'!C89/K11*H11+(1-T8)*'global path'!C89*I11/L11","v":43.331043431904078},"Gt","RB:",{"$f":"C5+F5+I5","v":683.96620539064213},"Gt"]
[null,"TA",{"$f":"C5/C11","v":14.713551900617198},null,"TB",{"$f":"F5/F11","v":17.007721643373173},null,"TC",{"$f":"I5/I11","v":35.293996789517927},null,"Global path ist different to the path in sheet \"global path\"."]
[null,"rA",{"$f":"'SPF-eq'!C7","v":0},null,"rB",{"$f":"'SPF-eq'!F7","v":0.03},null,"rC",{"$f":"'SPF-eq'!I7","v":0.02}]
[null,"mA",{"$f":"(1+SQRT(1+C7*C6))/C6","v":0.13592910899482435},null,"mB",{"$f":"(1+SQRT(1+F7*F6))/F6","v":0.13105311061826475},null,"mC",{"$f":"(1+SQRT(1+I7*I6))/I6","v":6.5339536376087484E-2},null,null,null,null,null,null,"share population key:",null,null,null,0.1563944281631455,"solver: variable",null,null,"global path:",null,{"$f":"'global path'!C2","v":3}]
["Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPt","Et","Per capita",null,null,"RM - \nSPM"]
[null,"bn","Gt","t","bn","Gt","t","bn","Gt","t","bn","Gt","t",null,null,"A","B","C"]
[2019,{"$f":"RF!B9","v":1.2},{"$f":"RF!C9","v":21},{"$f":"C11/B11","v":17.5},{"$f":"RF!E9","v":4},{"$f":"RF!F9","v":19.5},{"$f":"F11/E11","v":4.875},{"$f":"K11-E11-B11","v":1.7000000000000004},{"$f":"'global path'!$C$7-C11-F11","v":1.2277171013052595},{"$f":"I11/H11","v":0.72218653017956425},{"$f":"RF!K9","v":6.9},{"$f":"I11+F11+C11","v":41.727717101305259},{"$f":"L11/K11","v":6.047495232073226},null,null,{"$f":"RF!C9-'SPF = RF'!C11","v":0},{"$f":"RF!F9-'SPF = RF'!F11","v":0},{"$f":"RF!I9-'SPF = RF'!I11","v":0}]
[{"$f":"A11+1","v":2020},{"$f":"B$11*(B$42/B$11)^(($A12-2019)/31)","v":1.2},{"$f":"-C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A11-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A11-$A$11)+2*C$8+C$7)","v":20.939552694170402},{"$f":"C12/B12","v":17.449627245142004},{"$f":"E$11*(E$42/E$11)^(($A12-2019)/31)","v":4},{"$f":"-F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A11-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A11-$A$11)+2*F$8+F$7)","v":19.715857240288244},{"$f":"F12/E12","v":4.928964310072061},{"$f":"H$11*(H$42/H$11)^(($A12-2019)/31)","v":1.7000000000000004},{"$f":"-I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A11-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A11-$A$11)+2*I$8+I$7)","v":1.2386267760239917},{"$f":"I12/H12","v":0.72860398589646558},{"$f":"B12+E12+H12","v":6.9},{"$f":"I12+F12+C12","v":41.894036710482638},{"$f":"L12/K12","v":6.0715995232583531},null,null,{"$f":"RF!C10-'SPF = RF'!C12","v":-0.39233723585738645},{"$f":"RF!F10-'SPF = RF'!F12","v":-0.59466908550096775},{"$f":"RF!I10-'SPF = RF'!I12","v":-1.3867629845136564E-2}]
[{"$f":"A12+1","v":2021},1.2,{"$f":"-C$11*EXP(-C$8*($A13-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A13-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)","v":20.608016746228088},17.173347288523409,4,{"$f":"-F$11*EXP(-F$8*($A13-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A13-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)","v":19.87609134997183},4.9690228374929575,1.7000000000000004,{"$f":"-I$11*EXP(-I$8*($A13-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A13-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)","v":1.2552909923131281},0.73840646606654581,{"$f":"B13+E13+H13","v":6.9},{"$f":"I13+F13+C13","v":41.739399088513046},6.0491882736975429,null,null,{"$f":"RF!C11-'SPF = RF'!C13","v":-0.57732520851127589},{"$f":"RF!F11-'SPF = RF'!F13","v":-1.1870411359555568},{"$f":"RF!I11-'SPF = RF'!I13","v":-3.390619847666021E-2}]
[2022,1.2,20.02251213831741,16.685426781931177,4,19.699511216018323,4.9248778040045806,1.7000000000000004,1.2648918576900527,0.74405403393532499,6.9,40.986915212025785,5.9401326394240268,null,null,{"$f":"RF!C12-'SPF = RF'!C14","v":-0.56741961962005405},{"$f":"RF!F12-'SPF = RF'!F14","v":-1.492022774594826},{"$f":"RF!I12-'SPF = RF'!I14","v":-4.7267342556383207E-2}]
[2023,1.2,19.252950799744269,16.04412566645356,4,19.266440387763254,4.8166100969408134,1.7000000000000004,{"$f":"-I$11*EXP(-I$8*($A15-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A15-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A14-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A14-$A$11)+2*I$8+I$7)","v":1.2682562276318308},0.74603307507754735,6.9,39.787647415139354,5.7663257123390368,null,null,{"$f":"RF!C13-'SPF = RF'!C15","v":-0.42737991662172092},{"$f":"RF!F13-'SPF = RF'!F15","v":-1.5856268444821069},{"$f":"RF!I13-'SPF = RF'!I15","v":-5.4744257379205852E-2}]
[2024,1.2,18.35557610079934,15.296313417332783,4,18.642551810666816,4.6606379526667041,1.7000000000000004,1.2661346172794126,0.74478506898788954,6.9,38.264262528745569,5.545545294021097,null,null,{"$f":"RF!C14-'SPF = RF'!C16","v":-0.20788617301251477},{"$f":"RF!F14-'SPF = RF'!F16","v":-1.5288718858801111},{"$f":"RF!I14-'SPF = RF'!I16","v":-5.7051114128285008E-2}]
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[2026,1.2,16.347712703188222,13.623093919323519,4,17.025717958490702,4.2564294896226755,1.7000000000000004,1.248091411985655,0.73417141881509096,6.9,34.621522073664579,5.0176118947339967,null,null,{"$f":"RF!C16-'SPF = RF'!C18","v":0.32294568452052985},{"$f":"RF!F16-'SPF = RF'!F18","v":-1.1477627363400753},{"$f":"RF!I16-'SPF = RF'!I18","v":-4.8657074416808221E-2}]
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[2043,1.2,3.6122312332895206,3.0101926944079338,4,4.2906906131702769,1.0726726532925692,1.7000000000000004,0.79464292715240603,0.46743701597200343,6.9,8.6975647736122035,1.260516633856841,null,null,{"$f":"RF!C33-'SPF = RF'!C35","v":0.14385388409335675},{"$f":"RF!F33-'SPF = RF'!F35","v":0.78258185095222732},{"$f":"RF!I33-'SPF = RF'!I35","v":0.32042296429423467}]
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[2046,1.2,2.6362399510477807,2.1968666258731506,4,3.1884085970244591,0.79710214925611478,1.7000000000000004,0.70884431166402173,0.41696724215530678,6.9,6.5334928597362616,0.9468830231501828,null,null,{"$f":"RF!C36-'SPF = RF'!C38","v":-0.36884576902975486},{"$f":"RF!F36-'SPF = RF'!F38","v":0.63938459769563449},{"$f":"RF!I36-'SPF = RF'!I38","v":0.39649624559279051}]
[2047,1.2,2.3691767350651034,1.9743139458875862,4,2.8823132675496588,0.72057831688741469,1.7000000000000004,0.68138622866096021,0.40081542862409414,6.9,5.9328762312757224,0.85983713496749592,null,null,{"$f":"RF!C37-'SPF = RF'!C39","v":-0.52599726303712968},{"$f":"RF!F37-'SPF = RF'!F39","v":0.59057037911257915},{"$f":"RF!I37-'SPF = RF'!I39","v":0.42118301473554198}]
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[{"$f":"A41+1","v":2050},{"$f":"RF!B40","v":1.2},1.7114541447994505,1.4262117873328755,{"$f":"RF!E40","v":4},2.1185186790482398,0.52962966976205994,{"$f":"K42-E42-B42","v":1.7000000000000004},0.60294837639172805,0.35467551552454585,{"$f":"RF!K40","v":6.9},4.4329212002394183,0.6424523478607852,null,null,{"$f":"RF!C40-'SPF = RF'!C42","v":-0.93810337561001356},{"$f":"RF!F40-'SPF = RF'!F42","v":0.45931721824988347},{"$f":"RF!I40-'SPF = RF'!I42","v":0.49263187995997448}]
["∑",null,{"$f":"SUM(C12:C42)","v":294.78639477853488},null,null,{"$f":"SUM(F12:F42)","v":313.16497631578534},null,null,{"$f":"SUM(I12:I42)","v":31.056795946125455},null,null,{"$f":"SUM(L12:L42)","v":639.00816704044564}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A42-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A42-$A$11)+2*C$8+C$7)","v":14.198195134426141},null,null,{"$f":"F$11*EXP(-F$8*($A42-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A42-$A$11)+2*F$8+F$7)","v":18.485595729991662},null,null,{"$f":"I$11*EXP(-I$8*($A42-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A42-$A$11)+2*I$8+I$7)","v":12.274247485778625},null,null,44.958038350196432]
["∑",null,{"$f":"SUM(C43:C44)","v":308.98458991296104},null,null,{"$f":"SUM(F43:F44)","v":331.65057204577698},null,null,{"$f":"SUM(I43:I44)","v":43.331043431904078},null,null,{"$f":"SUM(L43:L44)","v":683.96620539064202}]
[]
[null,null,null,null,null,"global path 2020 - 2100 sheet \"global path\":",null,null,null,null,null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L45-L47","v":0}]
[]
[]
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[{"$f":"A52+1","v":2053},{"$f":"B52","v":1.2},1.2285575111833804,1.0237979259861505,{"$f":"E52","v":4},1.5467189591225772,0.38667973978064429,{"$f":"H52","v":1.7000000000000004},0.53084509583893968,0.31226182108172917,6.9,3.3061215661448973,0.47914805306447783,null,null,{"$f":"RF!C48-'SPF = RF'!C53","v":-0.71046945142298812},{"$f":"RF!F48-'SPF = RF'!F53","v":0.18024124007873055},{"$f":"RF!I48-'SPF = RF'!I53","v":0.2031129888216161}]
[2054,1.2,1.0986687869737199,0.91555732247809996,4,1.3909135846260856,0.3477283961565214,1.7000000000000004,0.50826728963372325,0.29898075860807244,6.9,2.9978496612335288,0.43447096539616359,null,null,{"$f":"RF!C49-'SPF = RF'!C54","v":-0.64873835706142746},{"$f":"RF!F49-'SPF = RF'!F54","v":0.10885451508155608},{"$f":"RF!I49-'SPF = RF'!I54","v":0.12913415274202455}]
[2055,1.2,0.98195139163468514,0.81829282636223766,4,1.2500477674542729,0.31251194186356823,1.7000000000000004,0.48642188260763852,0.28613051918096377,6.9,2.7184210416965966,0.39397406401399948,null,null,{"$f":"RF!C50-'SPF = RF'!C55","v":-0.59268829069655404},{"$f":"RF!F50-'SPF = RF'!F55","v":4.7495902339497631E-2},{"$f":"RF!I50-'SPF = RF'!I55","v":6.5034177054714037E-2}]
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[2094,1.2,9.3515283734813826E-3,7.792940311234486E-3,4,1.4586900153949589E-2,3.6467250384873973E-3,1.7000000000000004,6.9476692381473359E-2,4.0868642577337258E-2,6.9,9.3415120908904331E-2,1.3538423320131061E-2,null,null,{"$f":"RF!C89-'SPF = RF'!C94","v":-9.3515283734813826E-3},{"$f":"RF!F89-'SPF = RF'!F94","v":-1.4586900153949589E-2},{"$f":"RF!I89-'SPF = RF'!I94","v":-6.9476692381473359E-2}]
[2095,1.2,8.2627279567221643E-3,6.8856066306018041E-3,4,1.2953764787736924E-2,3.238441196934231E-3,1.7000000000000004,6.5837151746648059E-2,3.8727736321557675E-2,6.9,8.7053644491107141E-2,1.2616470216102484E-2,null,null,{"$f":"RF!C90-'SPF = RF'!C95","v":-8.2627279567221643E-3},{"$f":"RF!F90-'SPF = RF'!F95","v":-1.2953764787736924E-2},{"$f":"RF!I90-'SPF = RF'!I95","v":-6.5837151746648059E-2}]
[2096,1.2,7.2996330825201919E-3,6.0830275687668266E-3,4,1.1501750221893814E-2,2.8754375554734535E-3,1.7000000000000004,6.2380066168949311E-2,3.6694156569970174E-2,6.9,8.118144947336331E-2,1.1765427459907725E-2,null,null,{"$f":"RF!C91-'SPF = RF'!C96","v":-7.2996330825201919E-3},{"$f":"RF!F91-'SPF = RF'!F96","v":-1.1501750221893814E-2},{"$f":"RF!I91-'SPF = RF'!I96","v":-6.2380066168949311E-2}]
[2097,1.2,6.447878215902654E-3,5.3732318465855456E-3,4,1.0211001728834032E-2,2.552750432208508E-3,1.7000000000000004,5.9096915355605795E-2,3.476289138565046E-2,6.9,7.5755795300342488E-2,1.0979100768165577E-2,null,null,{"$f":"RF!C92-'SPF = RF'!C97","v":-6.447878215902654E-3},{"$f":"RF!F92-'SPF = RF'!F97","v":-1.0211001728834032E-2},{"$f":"RF!I92-'SPF = RF'!I97","v":-5.9096915355605795E-2}]
[2098,1.2,5.6947188565521986E-3,4.7455990471268325E-3,4,9.0638094916729584E-3,2.2659523729182396E-3,1.7000000000000004,5.5979526904093024E-2,3.2929133472995892E-2,6.9,7.0738055252318188E-2,1.025189206555336E-2,null,null,{"$f":"RF!C93-'SPF = RF'!C98","v":-5.6947188565521986E-3},{"$f":"RF!F93-'SPF = RF'!F98","v":-9.0638094916729584E-3},{"$f":"RF!I93-'SPF = RF'!I98","v":-5.5979526904093024E-2}]
[2099,1.2,5.0288515366908593E-3,4.1907096139090494E-3,4,8.0443812371916584E-3,2.0110953092979146E-3,1.7000000000000004,5.302006638022505E-2,3.1188274341308844E-2,6.9,6.6093299154107568E-2,9.5787390078416763E-3,null,null,{"$f":"RF!C94-'SPF = RF'!C99","v":-5.0288515366908593E-3},{"$f":"RF!F94-'SPF = RF'!F99","v":-8.0443812371916584E-3},{"$f":"RF!I94-'SPF = RF'!I99","v":-5.302006638022505E-2}]
[2100,1.2,4.4402533888797044E-3,3.7002111573997539E-3,4,7.1386383631542941E-3,1.7846595907885735E-3,1.7000000000000004,5.0211027259600138E-2,2.9535898388000074E-2,6.9,6.1789919011634137E-2,8.9550607263237866E-3,null,null,{"$f":"RF!C95-'SPF = RF'!C100","v":-4.4402533888797044E-3},{"$f":"RF!F95-'SPF = RF'!F100","v":-7.1386383631542941E-3},{"$f":"RF!I95-'SPF = RF'!I100","v":-5.0211027259600138E-2}]
["∑",null,{"$f":"SUM(C51:C100)","v":14.164967570017836},null,null,{"$f":"SUM(F51:F100)","v":18.429828488477757},null,null,{"$f":"SUM(I51:I100)","v":11.403118582197846},null,null,{"$f":"SUM(L51:L100)","v":43.997914640693438},null,null,null,{"$f":"SUM(P12:P100)","v":1.2882989589824019},{"$f":"SUM(Q12:Q100)","v":-0.37254233089525118},{"$f":"SUM(R12:R100)","v":4.4367081415956355E-2},{"$f":"SUM(P101:R101)","v":0.9601237095031071}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A100-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A100-$A$11)+2*C$8+C$7)","v":3.3227564408307424E-2},null,null,{"$f":"F$11*EXP(-F$8*($A100-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A100-$A$11)+2*F$8+F$7)","v":5.5767241513908002E-2},null,null,{"$f":"I$11*EXP(-I$8*($A100-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A100-$A$11)+2*I$8+I$7)","v":0.87112890358077422},null,null,{"$f":"I102+F102+C102","v":0.96012370950298964},null,null,null,{"$f":"P101^2/RF!C98^2+Q101^2/RF!F98^2+R101^2/RF!I98^2","v":1.9598662549407273E-5},null,null,null,"square deviation","solver: target value min"]
["∑",null,{"$f":"SUM(C101:C102)","v":14.198195134426143},null,null,{"$f":"SUM(F101:F102)","v":18.485595729991665},null,null,{"$f":"SUM(I101:I102)","v":12.27424748577862},null,null,{"$f":"SUM(L101:L102)","v":44.958038350196425},null,null,null,{"$f":"P101/RF!C98","v":4.1525927199402559E-3},{"$f":"Q101/RF!F98","v":-1.1247502752783894E-3},{"$f":"R101/RF!I98","v":1.0438261684627618E-3},null,"deviation from RM budget"]
[]
[null,null,{"$f":"C103+C43","v":308.98458991296104},null,null,{"$f":"F103+F43","v":331.65057204577698},null,null,{"$f":"I103+I43","v":43.331043431904078},null,null,{"$f":"SUM(C105:I105)","v":683.96620539064213}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L105-L107","v":0}]

{"sheet":"SPF = C&C_exp","index":20,"n_rows":108,"n_cols":26,"rows_kept":108,"cut":false,"hidden":false,"merged":[[8,15,8,17],[101,15,101,17],[3,19,3,20],[3,1,3,3],[3,4,3,6],[3,7,3,9],[3,10,3,13],[5,10,7,13]]}
["Comparision SPF and C&C exp"]
[{"$f":"CONCATENATE(\"SPF-\",ROUND(T8*100,0))","v":"SPF-50"}]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global",null,null,null,null,null,null,null,null,"input value"]
[null,"RBA:",{"$f":"T8*'global path'!C89/K11*B11+(1-T8)*'global path'!C89*C11/L11","v":230.81303194650883},"Gt","RBB:",{"$f":"T8*'global path'!C89/K11*E11+(1-T8)*'global path'!C89*F11/L11","v":358.32764134392352},"Gt","RBC:",{"$f":"T8*'global path'!C89/K11*H11+(1-T8)*'global path'!C89*I11/L11","v":94.825532100209799},"Gt","RB:",{"$f":"C5+F5+I5","v":683.96620539064213},"Gt"]
[null,"TA",{"$f":"C5/C11","v":10.991096759357564},null,"TB",{"$f":"F5/F11","v":18.375776479175563},null,"TC",{"$f":"I5/I11","v":77.237282106272772},null,"Global path ist different to the path in sheet \"global path\"."]
[null,"rA",{"$f":"'SPF-eq'!C7","v":0},null,"rB",{"$f":"'SPF-eq'!F7","v":0.03},null,"rC",{"$f":"'SPF-eq'!I7","v":0.02}]
[null,"mA",{"$f":"(1+SQRT(1+C7*C6))/C6","v":0.18196546202700351},null,"mB",{"$f":"(1+SQRT(1+F7*F6))/F6","v":0.12219898433646989},null,"mC",{"$f":"(1+SQRT(1+I7*I6))/I6","v":3.3600688940035067E-2},null,null,null,null,null,null,"share population key:",null,null,null,0.50341643882091736,"solver: variable",null,null,"global path:",null,{"$f":"'global path'!C2","v":3}]
["Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPt","Et","Per capita",null,null,"RM - \nSPM"]
[null,"bn","Gt","t","bn","Gt","t","bn","Gt","t","bn","Gt","t",null,null,"A","B","C",null,{"$f":"COUNT($T$8)","v":1}]
[2019,{"$f":"RF!B9","v":1.2},{"$f":"RF!C9","v":21},{"$f":"C11/B11","v":17.5},{"$f":"RF!E9","v":4},{"$f":"RF!F9","v":19.5},{"$f":"F11/E11","v":4.875},{"$f":"K11-E11-B11","v":1.7000000000000004},{"$f":"'global path'!$C$7-C11-F11","v":1.2277171013052595},{"$f":"I11/H11","v":0.72218653017956425},{"$f":"RF!K9","v":6.9},{"$f":"I11+F11+C11","v":41.727717101305259},{"$f":"L11/K11","v":6.047495232073226},null,null,{"$f":"'C&C-exp'!C11-'SPF = C&C_exp'!C11","v":0},{"$f":"'C&C-exp'!F11-'SPF = C&C_exp'!F11","v":0},{"$f":"'C&C-exp'!I11-'SPF = C&C_exp'!I11","v":0},null,{"$f":"{32767;32767;0.000001;0.01;FALSE;FALSE;TRUE;1;1;1;0.0001;TRUE}","v":32767}]
[{"$f":"A11+1","v":2020},{"$f":"B$11*(B$42/B$11)^(($A12-2019)/31)","v":1.2},{"$f":"-C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A11-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A11-$A$11)+2*C$8+C$7)","v":20.894100932579619},{"$f":"C12/B12","v":17.411750777149685},{"$f":"E$11*(E$42/E$11)^(($A12-2019)/31)","v":4},{"$f":"-F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A11-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A11-$A$11)+2*F$8+F$7)","v":19.724056924744673},{"$f":"F12/E12","v":4.9310142311861682},{"$f":"H$11*(H$42/H$11)^(($A12-2019)/31)","v":1.7000000000000004},{"$f":"-I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A11-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A11-$A$11)+2*I$8+I$7)","v":1.2394955180713652},{"$f":"I12/H12","v":0.72911501063021467},{"$f":"B12+E12+H12","v":6.9},{"$f":"I12+F12+C12","v":41.857653375395657},{"$f":"L12/K12","v":6.0663265761442977},null,null,{"$f":"'C&C-exp'!C12-'SPF = C&C_exp'!C12","v":-0.59475275912184955},{"$f":"'C&C-exp'!F12-'SPF = C&C_exp'!F12","v":-0.51828080846807012},{"$f":"'C&C-exp'!I12-'SPF = C&C_exp'!I12","v":0.1485429514734109},null,{"$f":"{0;0;1;100;0;FALSE;TRUE;0.075;0;0;FALSE;30}","v":0}]
[{"$f":"A12+1","v":2021},1.2,{"$f":"-C$11*EXP(-C$8*($A13-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A13-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)","v":20.330461752619243},16.942051460516037,4,{"$f":"-F$11*EXP(-F$8*($A13-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A13-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)","v":19.927599275176931},4.9818998187942327,1.7000000000000004,{"$f":"-I$11*EXP(-I$8*($A13-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A13-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)","v":1.2611144499479678},0.74183202938115733,{"$f":"B13+E13+H13","v":6.9},{"$f":"I13+F13+C13","v":41.519175477744142},6.017271808368716,null,null,{"$f":"'C&C-exp'!C13-'SPF = C&C_exp'!C13","v":-0.80907645482108848},{"$f":"'C&C-exp'!F13-'SPF = C&C_exp'!F13","v":-1.0647416277445387},{"$f":"'C&C-exp'!I13-'SPF = C&C_exp'!I13","v":0.29576915039103779}]
[2022,1.2,19.376041304156388,16.146701086796991,4,19.823339058122656,4.955834764530664,1.7000000000000004,1.2799514106251308,0.75291259448537096,6.9,40.479331772904175,5.8665698221600246,null,null,{"$f":"'C&C-exp'!C14-'SPF = C&C_exp'!C14","v":-0.70336927941463401},{"$f":"'C&C-exp'!F14-'SPF = C&C_exp'!F14","v":-1.3488393624716153},{"$f":"'C&C-exp'!I14-'SPF = C&C_exp'!I14","v":0.45308234423659366}]
[2023,1.2,18.17646897457314,15.14705747881095,4,19.479394797244595,4.8698486993111487,1.7000000000000004,{"$f":"-I$11*EXP(-I$8*($A15-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A15-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A14-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A14-$A$11)+2*I$8+I$7)","v":1.2961666427890037},0.76245096634647258,6.9,38.952030414606739,5.6452217992183673,null,null,{"$f":"'C&C-exp'!C15-'SPF = C&C_exp'!C15","v":-0.41566667044704886},{"$f":"'C&C-exp'!F15-'SPF = C&C_exp'!F15","v":-1.4352150130019012},{"$f":"'C&C-exp'!I15-'SPF = C&C_exp'!I15","v":0.618747665498526}]
[2024,1.2,16.839733875850186,14.03311156320849,4,18.952286629278149,4.7380716573195372,1.7000000000000004,1.3099128368689748,0.77053696286410256,6.9,37.101933341997309,5.3770917886952621,null,null,{"$f":"'C&C-exp'!C16-'SPF = C&C_exp'!C16","v":-4.5367251761405214E-2},{"$f":"'C&C-exp'!F16-'SPF = C&C_exp'!F16","v":-1.3767673796177675},{"$f":"'C&C-exp'!I16-'SPF = C&C_exp'!I16","v":0.7906546451065255}]
[2025,1.2,15.44467839381889,12.870565328182408,4,18.288703274400319,4.5721758186000798,1.7000000000000004,1.3213354551742924,0.7772561501025248,6.9,35.054717123393502,5.0803937859990578,null,null,{"$f":"'C&C-exp'!C17-'SPF = C&C_exp'!C17","v":0.33821922771344148},{"$f":"'C&C-exp'!F17-'SPF = C&C_exp'!F17","v":-1.2164987398995919},{"$f":"'C&C-exp'!I17-'SPF = C&C_exp'!I17","v":0.96629777986721166}]
[2026,1.2,14.047707438736722,11.706422865613936,4,17.527015968053973,4.3817539920134934,1.7000000000000004,1.330573042855832,0.78269002520931275,6.9,32.905296449646528,4.7688835434270329,null,null,{"$f":"'C&C-exp'!C18-'SPF = C&C_exp'!C18","v":0.68908679777896253},{"$f":"'C&C-exp'!F18-'SPF = C&C_exp'!F18","v":-0.98910424360721549},{"$f":"'C&C-exp'!I18-'SPF = C&C_exp'!I18","v":1.1427689436099517}]
[2027,1.2,12.688072011876486,10.573393343230405,4,16.698574187674637,4.1746435469186594,1.7000000000000004,1.337757526209387,0.78691619188787454,6.9,30.72440372576051,4.4528121341681892,null,null,{"$f":"'C&C-exp'!C19-'SPF = C&C_exp'!C19","v":0.97914764986608205},{"$f":"'C&C-exp'!F19-'SPF = C&C_exp'!F19","v":-0.72233614783445432},{"$f":"'C&C-exp'!I19-'SPF = C&C_exp'!I19","v":1.3167659502320839}]
[2028,1.2,11.392015764945256,9.4933464707877135,4,15.828813342189534,3.9572033355473835,1.7000000000000004,1.3430144988181212,0.7900085287165417,6.9,28.563843605952911,4.1396874791236105,null,null,{"$f":"'C&C-exp'!C20-'SPF = C&C_exp'!C20","v":1.1939517510039828},{"$f":"'C&C-exp'!F20-'SPF = C&C_exp'!F20","v":-0.43816907197220267},{"$f":"'C&C-exp'!I20-'SPF = C&C_exp'!I20","v":1.4846221168827496}]
[2029,1.2,10.176016636314174,8.4800138635951452,4,14.938200539028372,3.7345501347570931,1.7000000000000004,1.3464634960118076,0.79203735059518077,6.9,26.460680671354353,3.8348812567180222,null,null,{"$f":"'C&C-exp'!C21-'SPF = C&C_exp'!C21","v":1.329273503534953},{"$f":"'C&C-exp'!F21-'SPF = C&C_exp'!F21","v":-0.15378827567674591},{"$f":"'C&C-exp'!I21-'SPF = C&C_exp'!I21","v":1.6423619921760442}]
[2030,1.2,9.04930989562056,7.5410915796838003,4,14.043041023543111,3.5107602558857778,1.7000000000000004,1.3482182581020794,0.79306956358945824,6.9,24.440569177265751,3.5421114749660507,null,null,{"$f":"'C&C-exp'!C22-'SPF = C&C_exp'!C22","v":1.3883730492090844},{"$f":"'C&C-exp'!F22-'SPF = C&C_exp'!F22","v":0.11758043659419926},{"$f":"'C&C-exp'!I22-'SPF = C&C_exp'!I22","v":1.7857883317529115}]
[2031,1.2,8.0158419757005888,6.6798683130838246,4,13.156164830106889,3.2890412075267221,1.7000000000000004,1.3483869828368142,0.79316881343341994,6.9,22.520393788644292,3.2638251867600423,null,null,{"$f":"'C&C-exp'!C23-'SPF = C&C_exp'!C23","v":1.379777713512599},{"$f":"'C&C-exp'!F23-'SPF = C&C_exp'!F23","v":0.36598315760472211},{"$f":"'C&C-exp'!I23-'SPF = C&C_exp'!I23","v":1.9106046928404803}]
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[2037,1.2,3.6408206433629253,3.0340172028024379,4,8.4194577868025959,2.104864446700649,1.7000000000000004,1.3215122237374004,0.77736013161023532,6.9,13.381790653902922,1.939389949841003,null,null,{"$f":"'C&C-exp'!C29-'SPF = C&C_exp'!C29","v":0.64551008109813779},{"$f":"'C&C-exp'!F29-'SPF = C&C_exp'!F29","v":1.1101880898621825},{"$f":"'C&C-exp'!I29-'SPF = C&C_exp'!I29","v":2.0634126831196111}]
[2038,1.2,3.167171156379716,2.6393092969830967,4,7.7606679819577948,1.9401669954894487,1.7000000000000004,1.3131910630401507,0.77246533120008842,6.9,12.241030201377662,1.774062348025748,null,null,{"$f":"'C&C-exp'!C30-'SPF = C&C_exp'!C30","v":0.52677220571337324},{"$f":"'C&C-exp'!F30-'SPF = C&C_exp'!F30","v":1.1020876521347827},{"$f":"'C&C-exp'!I30-'SPF = C&C_exp'!I30","v":1.9711237132519286}]
[2039,1.2,2.7503496440287556,2.2919580366906298,4,7.1420353254806912,1.7855088313701728,1.7000000000000004,1.3039769733457405,0.76704527843867065,6.9,11.196361942855187,1.6226611511384328,null,null,{"$f":"'C&C-exp'!C31-'SPF = C&C_exp'!C31","v":0.43102211322131456},{"$f":"'C&C-exp'!F31-'SPF = C&C_exp'!F31","v":1.0620828474297213},{"$f":"'C&C-exp'!I31-'SPF = C&C_exp'!I31","v":1.8471952980996407}]
[2040,1.2,2.3845572934471768,1.9871310778726474,4,6.5630381445449615,1.6407595361362404,1.7000000000000004,1.2939380488631258,0.76114002874301501,6.9,10.241533486855264,1.48428021548627,null,null,{"$f":"'C&C-exp'!C32-'SPF = C&C_exp'!C32","v":0.36004873336247423},{"$f":"'C&C-exp'!F32-'SPF = C&C_exp'!F32","v":0.99472780823072426},{"$f":"'C&C-exp'!I32-'SPF = C&C_exp'!I32","v":1.6957054418584643}]
[2041,1.2,2.0643518495306186,1.7202932079421822,4,6.0227434454503879,1.505685861362597,1.7000000000000004,1.2831388587048309,0.75478756394401803,6.9,9.3702341536858373,1.3580049498095417,null,null,{"$f":"'C&C-exp'!C33-'SPF = C&C_exp'!C33","v":0.31275388598830967},{"$f":"'C&C-exp'!F33-'SPF = C&C_exp'!F33","v":0.90526538929926836},{"$f":"'C&C-exp'!I33-'SPF = C&C_exp'!I33","v":1.522071567223231}]
[2042,1.2,1.7846894789517567,1.4872412324597972,4,5.5199084426995242,1.379977110674881,1.7000000000000004,1.2716406054971969,0.74802388558658628,6.9,8.5762385271484778,1.2429331198765909,null,null,{"$f":"'C&C-exp'!C34-'SPF = C&C_exp'!C34","v":0.28566676571150795},{"$f":"'C&C-exp'!F34-'SPF = C&C_exp'!F34","v":0.79935485016028807},{"$f":"'C&C-exp'!I34-'SPF = C&C_exp'!I34","v":1.332694641684709}]
[2043,1.2,1.5409428352177912,1.2841190293481595,4,5.0530641730979156,1.2632660432744789,1.7000000000000004,1.259501277357316,0.74088310432783278,6.9,7.8535082856730227,1.1381896066192787,null,null,{"$f":"'C&C-exp'!C35-'SPF = C&C_exp'!C35","v":0.27371618990076985},{"$f":"'C&C-exp'!F35-'SPF = C&C_exp'!F35","v":0.68274540487860413},{"$f":"'C&C-exp'!I35-'SPF = C&C_exp'!I35","v":1.1344535924996255}]
[2044,1.2,1.3289020848758604,1.1074184040632171,4,4.620583972944118,1.1551459932360295,1.7000000000000004,1.2467757935026285,0.73339752558978133,6.9,7.1962618513226069,1.0429365001916822,null,null,{"$f":"'C&C-exp'!C36-'SPF = C&C_exp'!C36","v":0.27116550924787308},{"$f":"'C&C-exp'!F36-'SPF = C&C_exp'!F36","v":0.56092186320186421},{"$f":"'C&C-exp'!I36-'SPF = C&C_exp'!I36","v":0.9341075564767567}]
[2045,1.2,1.1447640643479735,0.95397005362331133,4,4.2207391943102763,1.0551847985775691,1.7000000000000004,1.2335161437468614,0.72559773161580066,6.9,6.5990194024051112,0.95637962353697259,null,null,{"$f":"'C&C-exp'!C37-'SPF = C&C_exp'!C37","v":0.27256211009166909},{"$f":"'C&C-exp'!F37-'SPF = C&C_exp'!F37","v":0.43876754655559225},{"$f":"'C&C-exp'!I37-'SPF = C&C_exp'!I37","v":0.73769941672997041}]
[2046,1.2,0.98511348840227164,0.82092790700189311,4,3.8517441900823641,0.96293604752059103,1.7000000000000004,1.2197715221288021,0.71751266007576575,6.9,6.0566292006134379,0.87777234791499092,null,null,{"$f":"'C&C-exp'!C38-'SPF = C&C_exp'!C38","v":0.27352449972985027},{"$f":"'C&C-exp'!F38-'SPF = C&C_exp'!F38","v":0.32030028463367799},{"$f":"'C&C-exp'!I38-'SPF = C&C_exp'!I38","v":0.55007394901796136}]
[2047,1.2,0.84689915512439651,0.70574929593699709,4,3.5117922993366477,0.87794807483416193,1.7000000000000004,1.2055884549077831,0.70916967935751929,6.9,5.5642799093688273,0.80641737816939518,null,null,{"$f":"'C&C-exp'!C39-'SPF = C&C_exp'!C39","v":0.271207967787362},{"$f":"'C&C-exp'!F39-'SPF = C&C_exp'!F39","v":0.20853179506291264},{"$f":"'C&C-exp'!I39-'SPF = C&C_exp'!I39","v":0.37461268986760721}]
[2048,1.2,0.72740733238170119,0.60617277698475103,4,3.1990843082613765,0.79977107706534412,1.7000000000000004,1.1910109231536623,0.70059466067862475,6.9,5.11750256379674,0.74166703823141156,null,null,{"$f":"'C&C-exp'!C40-'SPF = C&C_exp'!C40","v":0.26436651648478948},{"$f":"'C&C-exp'!F40-'SPF = C&C_exp'!F40","v":0.10547512975617268},{"$f":"'C&C-exp'!I40-'SPF = C&C_exp'!I40","v":0.21323763700516052}]
[2049,1.2,0.62423392223048602,0.52019493519207172,4,2.9118506415284493,0.72796266038211233,1.7000000000000004,1.1760804801477889,0.69181204714575795,6.9,4.7121650439067242,0.68292247013140928,null,null,{"$f":"'C&C-exp'!C41-'SPF = C&C_exp'!C41","v":0.25304995982190104},{"$f":"'C&C-exp'!F41-'SPF = C&C_exp'!F41","v":1.2283996937493047E-2},{"$f":"'C&C-exp'!I41-'SPF = C&C_exp'!I41","v":6.6656474957521139E-2}]
[{"$f":"A41+1","v":2050},{"$f":"RF!B40","v":1.2},0.53525654652760757,0.44604712210633968,{"$f":"RF!E40","v":4},2.6483683498831034,0.66209208747077586,{"$f":"K42-E42-B42","v":1.7000000000000004},1.1608363638045418,0.68284491988502438,{"$f":"RF!K40","v":6.9},4.3444612602152528,0.62963206669786265,null,null,{"$f":"'C&C-exp'!C42-'SPF = C&C_exp'!C42","v":0.23809422266182945},{"$f":"'C&C-exp'!F42-'SPF = C&C_exp'!F42","v":-7.0532452584979755E-2},{"$f":"'C&C-exp'!I42-'SPF = C&C_exp'!I42","v":-6.5256107452839052E-2}]
["∑",null,{"$f":"SUM(C12:C42)","v":227.6829764691891},null,null,{"$f":"SUM(F12:F42)","v":333.17263109686911},null,null,{"$f":"SUM(I12:I42)","v":39.938748471663679},null,null,{"$f":"SUM(L12:L42)","v":600.79435603772151}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A42-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A42-$A$11)+2*C$8+C$7)","v":3.1300554773197122},null,null,{"$f":"F$11*EXP(-F$8*($A42-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A42-$A$11)+2*F$8+F$7)","v":25.15501024705447},null,null,{"$f":"I$11*EXP(-I$8*($A42-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A42-$A$11)+2*I$8+I$7)","v":54.886783628546148},null,null,83.171849352920333]
["∑",null,{"$f":"SUM(C43:C44)","v":230.8130319465088},null,null,{"$f":"SUM(F43:F44)","v":358.32764134392357},null,null,{"$f":"SUM(I43:I44)","v":94.825532100209827},null,null,{"$f":"SUM(L43:L44)","v":683.96620539064179}]
[]
[null,null,null,null,null,"global path 2020 - 2100 sheet \"global path\":",null,null,null,null,null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L45-L47","v":0}]
[]
[]
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[{"$f":"A52+1","v":2053},{"$f":"B52","v":1.2},0.33594061293494559,0.27995051077912136,{"$f":"E52","v":4},1.9841419537263114,0.49603548843157785,{"$f":"H52","v":1.7000000000000004},1.1135818519734499,0.65504814821967627,6.9,3.4336644186347067,0.49763252443981254,null,null,{"$f":"'C&C-exp'!C50-'SPF = C&C_exp'!C53","v":0.1821474468254467},{"$f":"'C&C-exp'!F50-'SPF = C&C_exp'!F53","v":-0.25718175452500369},{"$f":"'C&C-exp'!I50-'SPF = C&C_exp'!I53","v":-0.37962376731289416}]
[2054,1.2,0.28723460416174618,0.2393621701347885,4,1.7997424152874082,0.44993560382185205,1.7000000000000004,1.0974327865746432,0.64554869798508407,6.9,3.1844098060237975,0.46150866753968078,null,null,{"$f":"'C&C-exp'!C51-'SPF = C&C_exp'!C54","v":0.16269582575054631},{"$f":"'C&C-exp'!F51-'SPF = C&C_exp'!F54","v":-0.2999743155797665},{"$f":"'C&C-exp'!I51-'SPF = C&C_exp'!I54","v":-0.46003134419889535}]
[2055,1.2,0.24543654217654898,0.20453045181379081,4,1.6315120626821145,0.40787801567052862,1.7000000000000004,1.0811351177507333,0.63596183397101946,6.9,2.9580837226093966,0.42870778588541975,null,null,{"$f":"'C&C-exp'!C52-'SPF = C&C_exp'!C55","v":0.14382655876158212},{"$f":"'C&C-exp'!F52-'SPF = C&C_exp'!F55","v":-0.3339683928883439},{"$f":"'C&C-exp'!I52-'SPF = C&C_exp'!I55","v":-0.52967905808838078}]
[2056,1.2,0.20959600894173191,0.17466334078477661,4,1.478170946692714,0.3695427366731785,1.7000000000000004,1.064716297558121,0.6263037044459534,6.9,2.7524832531925671,0.39891061640471986,null,null,{"$f":"'C&C-exp'!C53-'SPF = C&C_exp'!C56","v":0.12590277574395542},{"$f":"'C&C-exp'!F53-'SPF = C&C_exp'!F56","v":-0.35984166440708942},{"$f":"'C&C-exp'!I53-'SPF = C&C_exp'!I56","v":-0.58942635258673048}]
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[2094,1.2,3.9656044451237028E-4,3.3046703709364194E-4,4,2.6778322006109606E-2,6.6945805015274015E-3,1.7000000000000004,0.50158076061978818,0.29504750624693415,6.9,0.52875564307041023,7.6631252618900025E-2,null,null,{"$f":"'C&C-exp'!C91-'SPF = C&C_exp'!C94","v":-3.9656044451237028E-4},{"$f":"'C&C-exp'!F91-'SPF = C&C_exp'!F94","v":-2.6778322006109606E-2},{"$f":"'C&C-exp'!I91-'SPF = C&C_exp'!I94","v":-0.50158076061978818}]
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[2097,1.2,2.3835351348638965E-4,1.9862792790532473E-4,4,1.9246646973921061E-2,4.8116617434802653E-3,1.7000000000000004,0.46808959002246553,0.2753468176602738,6.9,0.48757459050987301,7.0662984131865655E-2,null,null,{"$f":"'C&C-exp'!C94-'SPF = C&C_exp'!C97","v":-2.3835351348638965E-4},{"$f":"'C&C-exp'!F94-'SPF = C&C_exp'!F97","v":-1.9246646973921061E-2},{"$f":"'C&C-exp'!I94-'SPF = C&C_exp'!I97","v":-0.46808959002246553}]
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[2099,1.2,1.6963349648064987E-4,1.4136124706720822E-4,4,1.5432146145268472E-2,3.8580365363171179E-3,1.7000000000000004,0.44677048256546215,0.26280616621497765,6.9,0.46237226220721123,6.7010472783653796E-2,null,null,{"$f":"'C&C-exp'!C96-'SPF = C&C_exp'!C99","v":-1.6963349648064987E-4},{"$f":"'C&C-exp'!F96-'SPF = C&C_exp'!F99","v":-1.5432146145268472E-2},{"$f":"'C&C-exp'!I96-'SPF = C&C_exp'!I99","v":-0.44677048256546215}]
[2100,1.2,1.4307564369152033E-4,1.1922970307626694E-4,4,1.3815712730967586E-2,3.4539281827418965E-3,1.7000000000000004,0.4364094326611756,0.25671143097716204,6.9,0.45036822103583474,6.5270756671860108E-2,null,null,{"$f":"'C&C-exp'!C97-'SPF = C&C_exp'!C100","v":-1.4307564369152033E-4},{"$f":"'C&C-exp'!F97-'SPF = C&C_exp'!F100","v":-1.3815712730967586E-2},{"$f":"'C&C-exp'!I97-'SPF = C&C_exp'!I100","v":-0.4364094326611756}]
["∑",null,{"$f":"SUM(C51:C100)","v":3.1292884500384615},null,null,{"$f":"SUM(F51:F100)","v":25.038104324534402},null,null,{"$f":"SUM(I51:I100)","v":38.21760065811219},null,null,{"$f":"SUM(L51:L100)","v":66.384993432685036},null,null,null,{"$f":"SUM(P12:P100)","v":16.323049929299398},{"$f":"SUM(Q12:Q100)","v":-5.4532871682706645},{"$f":"SUM(R12:R100)","v":5.9170931592066616},{"$f":"SUM(P101:R101)","v":16.786855920235396}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A100-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A100-$A$11)+2*C$8+C$7)","v":7.6702728125196105E-4},null,null,{"$f":"F$11*EXP(-F$8*($A100-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A100-$A$11)+2*F$8+F$7)","v":0.11690592252005776},null,null,{"$f":"I$11*EXP(-I$8*($A100-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A100-$A$11)+2*I$8+I$7)","v":16.669182970433962},null,null,{"$f":"I102+F102+C102","v":16.786855920235272},null,null,null,{"$f":"P101^2/'C&C-exp'!C100^2+Q101^2/'C&C-exp'!F100^2+R101^2/'C&C-exp'!I100^2","v":9.554808610865325E-3},null,null,null,"square deviation","solver: target value min"]
["∑",null,{"$f":"SUM(C101:C102)","v":3.1300554773197136},null,null,{"$f":"SUM(F101:F102)","v":25.155010247054459},null,null,{"$f":"SUM(I101:I102)","v":54.886783628546155},null,null,{"$f":"SUM(L101:L102)","v":83.171849352920304},null,null,null,{"$f":"P101/'C&C-exp'!C100","v":6.6049038516830513E-2},{"$f":"Q101/'C&C-exp'!F100","v":-1.5459027712314884E-2},{"$f":"R101/'C&C-exp'!I100","v":7.038005103761609E-2},null,"deviation from C&C exp budget"]
[]
[null,null,{"$f":"C103+C43","v":230.8130319465088},null,null,{"$f":"F103+F43","v":358.32764134392357},null,null,{"$f":"I103+I43","v":94.825532100209841},null,null,{"$f":"SUM(C105:I105)","v":683.96620539064224}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L105-L107","v":0}]

{"sheet":"glossary","index":21,"n_rows":21,"n_cols":3,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Country A","≈ developed countries"]
[null,"Country B","≈ emerging countries"]
[null,"Country C","≈ developing countries"]
[]
[]
[null,{"$f":"comparison!B43","v":"C&C-exp"},{"$f":"comparison!C43","v":"C&C: exponential approach"}]
[null,{"$f":"comparison!B44","v":"C&C-lin"},{"$f":"comparison!C44","v":"C&C: linear aproach"}]
[null,{"$f":"CDC!A2","v":"CDC"},{"$f":"CDC!A1","v":"Common but Differentiated Convergence"}]
[null,{"$f":"comparison!B50","v":"EPM"},{"$f":"comparison!C50","v":"Cap Model"}]
[null,"ESPM","Extended Smooth Pathway Model"]
[null,{"$f":"comparison!B42","v":"GQWF"},{"$f":"comparison!C42","v":"General Quadratic Weigthing Formula"}]
[null,{"$f":"comparison!B45","v":"LIMITS"},{"$f":"comparison!C45","v":"LIMITS"}]
[null,{"$f":"comparison!B46","v":"pc20"},{"$f":"comparison!C46","v":"Allocation per capita starting 2020"}]
[null,{"$f":"comparison!B41","v":"RF"},{"$f":"comparison!C41","v":"Regensburg Model resp. Regensburg Formula"}]
[null,{"$f":"comparison!B49","v":"SPF-50"},{"$f":"comparison!C49","v":"Smooth Pathways Formula (spk = 50%)"}]
[null,{"$f":"comparison!B47","v":"SPF-eq"},{"$f":"comparison!C47","v":"Smooth Pathways Formula - equity (spk = 100%)"}]
[null,{"$f":"comparison!B48","v":"SPF-in"},{"$f":"comparison!C48","v":"Smooth Pathways Formula - inertia (spk = 0%)"}]
[null,"spk","share population key; weighting population"]
[]
[null,"2020 - 2050","convergence periond per capita emissions: RF, GQWF, C&C, LIMITS, CDC"]

{"sheet":"imprint","index":22,"n_rows":14,"n_cols":3,"rows_kept":14,"cut":false,"hidden":false,"merged":[[13,2,13,3]]}
[]
[null,"Authors:"]
[]
[null,"Andreas Wolfsteiner, Master of Economics"]
[null,"Günter Wittmann, Master of Mathematics"]
[null,"save-the-climate@online.ms"]
[]
[null,"last update:","2021-03-14"]
[null,"Actual data used is from 2018."]
[]
[null,"You can download the most recent version of the tool here:"]
[null,"http://www.save-the-climate.info"]
[]
[null,"DOI","10.5281/zenodo.4540475"]

{"sheet":"intern","index":23,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":true,"merged":[]}