<content> Data2 </content>

09ba4279-0bde-4476-aec1-0caceb179010 174 Reg Curry 4 5 false false false 0 0 decimal

&[DATE] &[TIME] - &[FILENAME]

CO₂ FORCING SATURATION STUDY

Data2 185019684760028354588001851198778540301849220018522075950903065093600185321723698031228347001854255038560316987880018552602598603138780700185627824563032471299001857281181060323226730018582855484003260377600185930257216033412465001860332298460311314640018613491901803116545300186235599110030964431001863379534880308665370018644095254003028223000186543485133030062833001866449067000305719400018674808139003051036400186849449354030331600001869524731070310961900018705361233003371271700187156977664034242982001872630961500368346730018736704672003650682400187462866220038066693001875681048000394347370018766905825003973975300187770403283038854932001878709649540398656610018797597943704029951000188085805570042383706001881887965000426504630018829378882604494524000188399751456044764186001884100942980046416814001885101714450046483886001886103261360045779550001887108372750047751710001888120080170047672200001889120151630048792105001890130659120052569240001891136891570055295530001892137980890054816390001893136251510056512087001894141153290057156977001895149523890058047263001896154466090057892860001897161749270060218500001898170596100060628966001899186313540063107460001900196149070064675880001901202396390065567263001902207480030067020200001903226204620068589830001904228750920069665843001905243706200072638044001906254448600073817900001907290032460076488590001908278568680076245207001909290116740078473564001910304332600077902120001911309009820079168594001912324647700079326780001913351653300080310845001914318978640077861920001915314027670077114194001916339197300079146310001917354813850080935137001918349968640080481760001919303383940075151030001920353783700081413600001921310618420079451377001922325446270080570327001923369069770085984340001924370277700086240790001925374063360086590770001926367740750086077130001927401294720089788030001928399631180089363000001929428821150091823170001930395809600089783520001931353932030087241650001932319259160084260014001933336268340086600490001934365618710089939660001935383574250090969080001936420793060095085030001937449671530098650070001938422961920096477040001939447013500098272970001940488466400010343007000194149990927001073739400019424982524000107517670001943507527300010796097000194451624863001086088600019454289312500998161100019464608547000102560990001947516520550010801528000194854478850001099817600019495204035000106802320001950593024360012137298000195163814287001294123400019526467460600129455410001953665088500013239966000195467895290001376999000019557443896000145671240001956792601300015145513000195781856450001550921100019588417187300156085020001959885469000016598380000196093870110001609302000019619415042000162355690001962974728700016077983000196310266772000164280550001964108244650001668329300019651131060000016935702000196611862647000170854770001967122373690001763822400019681290528400018237686000196913761785000195977580001970148991240002059322800019711550385500020621949000197216224597000216151570001973170850940002232917600019741701107200022149474000197517052752000221120860001976179891120002307328800019771849863600024012407000197819069290000244823470001979196090200002429577200019801948852400024456057000198119022903000238528430001982188710970002341479600019831899191000023776866000198419647801000252868810001985203119020002560286500019862061496300026142145000198721250075000265898780001988220851300002725611500019892238663700027339980000199022728989000277055900001991231861020002815608800019922252817200027786177000199322755787000277296480001994229929470002888232300019952353208300028964485000199624258169000302707100001997244019060003180847100019982430377800030448243000199924853730000308566430002000255105540003080777300020012570629300030471537000200226276870000314049860002003276694900003374517000020042863250600034036494000200529614395000345053760002006306283970003596054000020073153464500036129227000200832074200000369545100002009315419220003681590000020103335590300038843814000201134504540000397828060002012350000200004065191500020133530165500040417810000201435450094000408462870002015354049000004093648500020163541665800039822910000201735989897000402209180002018367304250004057514400020193710427500040891020000202035126526000385655200002021369917340004054451400020223729383400040834870000202337791570000414164800001743 mat :

Data2 1850196847600283545880018511987785403018492200185220759509030650936001853217236980312283470018542550385603169878800185526025986031387807001856278245630324712990073 mat

Date Data2 1 col :

N Data2 rows : 174

Emission Data2 2 col 109 -^* :

Date max 2023

DATA Date Emission augment :

t.0 Date min : 1850

n.1 165 :

t.1 Date n.1 el : 2014

FIT TO EMISSION DATA

<content> FIT EMISSION DATA </content>

SMATH FIT USING al_nelqsolve

X DATA 1 N range 1 el :

Y DATA 1 N range 2 el :

nselect 1 N 3 range :

t y vline t 0 t y 22 mat :

t u F.exp a b c 13 mat u 1 el u 2 el u 3 el 13 mat : c a e b t t.0 - t.0 / *^* + vectorize 21 line :

u.exp 101010 - 31 mat u φ X u F.exp Y - : al_nleqsolve : 1.4923 36.1473 2.1976 - 31 mat

TRYING TO CREATE A LINEAR FIT WHERE THE DATA LEVELS OFF BETWEEN 2014 AND 2023

XX DATA n.1 DATA rows range 1 el :

YY DATA n.1 DATA rows range 2 el :

t u F.lin a b 12 mat u 1 el u 2 el 12 mat : a b t t.1 - t.1 / * + vectorize 21 line :

u.lin 101021 mat u φ XX u F.lin YY - : al_nleqsolve : 35.2403 487.6924 21 mat

XYPlot'XAxis'Min 1850 setprop 1

XYPlot'XAxis'Tick 50 setprop 1

Plot X nselect el Y nselect el augment t u.exp F.exp t u.lin F.lin t t.1 > cases XX YY augment t.1 t.1 u.lin F.lin vline 51 sys :

XYPlot'XAxis'Max 2050 setprop 1

XYPlot'YAxis'Min 10 - setprop 1

XYPlot'YAxis'Tick 10 setprop 1

XYPlot'YAxis'Max 100 setprop 1 ≡

Plot

TO GET CUMULATIVE EMISSIONS WE MUST SOLVE THE FOLLOWING ODE

t Q t u.exp F.exp t t.1 ≤ t u.lin F.lin cases :

t y t diff t Q λ t y * - ≡

Where Q(t) is the driving function = yearly emissions and λ = decay of CO₂ in the atmosphere.

SOLUTION TO THE ODE TO GET CUMULATIVE EMISSIONS

<content> ODE TO GET TOTAL CONCENTRATION </content>

τ 300 :

λ 1 τ / :

t.end 2200 :

ppm 1 7.8 / :

τ t.0 t.end range :

τ rows 351

t CO.2 ppm e λ t * -^s Q e λ s *^* s t.0 t int * * :

CO.2 t y t.end τ rows 1 + Rkadapt :

Plot CO.2 t.1 t.1 CO.2 vline 21 sys :

t y' ppm t Q * λ t y * - ≡

t.0 y ppm t.0 Q * ≡

Plot t CO.2 t.1 t.1 CO.2 vline 21 sys :

using time as number of steps in rkadapt:

CO2'XAxis'Min 1850 setprop 1

CO2'XAxis'Tick 50 setprop 1

CO2'XAxis'Max 2250 setprop 1

CO2'YAxis'Min 50 - setprop 1

CO2'YAxis'Tick 200 setprop 1

CO2'YAxis'Max 1400 setprop 1

Plot <content> Why??? </content>

There is a discrepancy between your method and mine, and I have not an idea why:

k 1 τ length range k n.1 ≤ Y k el ppm e λ τ k el * -^s u.exp F.exp e λ s *^* s t.0 τ k el int * * : Y k el ppm e λ τ k el * -^s u.lin F.lin e λ s *^* s t.1 τ k el int * * Y n.1 el + : if for

Your max:

Y max 1233.2524

Y n.1 el 165.679

Plot CO.2 τ Y augment t.1 t.1 CO.2 vline 31 sys :

My max:

By integration:

t.end CO.2 1156.6978

By ODE solver:

CO.2 2 col max 1156.6686

t.end y 1156.6686

t.1 CO.2 165.679

t.1 y 165.6248

(y function is generated by Rkadapt function)

Plot <content> ODE TO GET TOTAL CONCENTRATION </content>

NORMALIZE ODE SOLUTION TO ACTUAL PPM DATA

PPMDATA WORLD CO2 ppm UPDATE.xlsx co2-long-term-concentration B2:C131 importData.XLSX :

<content> WORLD PPM DATA </content>

PPMDATA 1850 284.00165 1851 287.1281 1854 288.05444 1855 285.56558 1857 283.1621 1859 286.6331 1862 287.17456 1863 285.35333 1864 286.65414 1867 285.0523 1868 288.7642 1870 287.15613 1873 286.6551 1874 291.5582 1877 289.32812 1880 287.77072 1883 292.46393 1884 289.4945 1886 288.11575 1887 294.3418 1889 292.34238 1890 290.91754 1892 295.17194 1893 295.08795 1894 293.48767 1899 296.16443 1900 294.22073 1902 295.61063 1904 295.99136 1905 299.0236 1906 298.47754 1909 301.50415 1910 297.8691 1911 298.36343 1913 301.29773 1914 300.7001 1916 301.91516 1918 303.85223 1919 304.61322 1920 301.87585 1923 304.6901 1925 304.84253 1928 306.84332 1929 305.62305 1931 305.7409 1932 308.25555 1933 307.11163 1934 308.3531 1935 306.3198 1936 308.30164 1937 307.40768 1938 311.0677 1939 310.83423 1940 310.37598 1941 309.77048 1942 312.37192 1944 312.36163 1945 310.93842 1946 312.26343 1947 311.61462 1948 311.57095 1949 309.694 1950 312.83102 1952 312.18445 1954 312.73138 1955 314.71396 1956 315.34207 1957 315.34427 1958 315.3368 1959 314.15894 1960 313.09338 1961 318.20657 1962 317.75082 1963 318.3751 1964 319.12347 1965 319.544 1966 320.98157 1967 321.33356 1969 323.56235 1970 324.55707 1971 325.95483 1972 329.38318 1974 331.5498 1976 332.3657 1977 333.95795 1979 336.85333 1980 338.9125 1981 340.11084 1982 340.85583 1983 342.53 1984 344.07333 1985 345.5375 1986 346.96835 1987 348.68335 1988 351.15918 1989 352.7875 1990 354.0575 1991 355.39334 1992 356.09 1993 356.83414 1994 358.33167 1995 360.17166 1996 361.9325 1997 363.04666 1998 365.69583 1999 367.79416 2000 368.965 2001 370.56583 2002 372.58334 2003 375.14084 2004 376.95166 2005 378.98083 2006 381.14835 2007 382.9 2008 385.02084 2009 386.49667 2010 388.75415 2011 390.62 2012 392.64917 2013 395.39584 2014 397.34415 2015 399.64917 2016 403.06583 2017 405.21667 2018 407.61084 2019 410.07166 2020 412.44333 2021 414.70334 2022 417.07666 2023 419.31497 1302 mat :

PPMDATA 1302 el 419.315

CO.2 1741 el 2022.017

NORM PPMDATA 1302 el CO.2 1742 el - :

PPMDATA rows 130

Plot CO.2 PPMDATA CO.2NORM 31 sys :

PPMDATA 1301 el 2023

CO.2 1742 el 197.9841

CO.2NORM CO.2 2 col NORM + :

CO.2NORM CO.2 1 col CO.2NORM augment :

Plot <content> PHYSICAL CONSTANTS </content>

Stephen Boltzmann Constant per degree Kelvin: \[REGION[c6ca0ceb25294e95880f22eda0369aea]]\

σ 5.6704 108 -^* W m 2^K 4^* / * :

EARTH ALBEDO: \[REGION[667c3486fc0c4982bc1d03e82bf5a5bd]]\

α 0.32956 :

SOLAR CONSTANT: \[REGION[73fe225adb5243d794839c68c5c98bb9]]\

S 1370 W m 2^/ * :

Earth Emissivity, since earth is not a black body: \[REGION[794974438f25443b9d3058f78b4586d2]]\

ε 0.6062 :

SPECIFIC HEAT CAPACITY OF EARTH: \[REGION[114662057025470db2cf73f9dfafdd73]]\

C.e 2.08 108^* J m 2^K * / * :

<content> TDFC TEMPERATURE ANOMALY </content>

CO.2INITIAL CO.2NORM 12 el : 221.2404

k 1 τ rows range :

ΔFCO2 k el 5.35 CO.2NORM k 2 el CO.2INITIAL + CO.2INITIAL / ln * W m 2^/ * :

T.o 14.0 °C * : 287.15 K *

δt 1 yr * :

T 1 el T.o :

κ 2 τ rows (range T κ el 1 C.e / 1 α - (S * 4 / ΔFCO2 κ 1 - el + ε σ * T κ 1 - el 4^* (- (* δt * T κ 1 - el + eval : for

Temission τ T T.o - augment :

Plot Temission t.1 012 mat Temission t.1 1 findrows stack 21 sys :

TEMP'XAxis'Min 1850 setprop 1

CO2'XAxis'Tick 100 setprop 1

T T.o - Δ°C 0 0.056 - 0.0846 - 0.0992 - 41 mat

There is a "change" temp unit, Δ°C = Δ°K

TEMP'XAxis'Max 2250 setprop 1

TEMP'YAxis'Min .5 - setprop 1

CO2'YAxis'Tick 0.1 setprop 1

TEMP'YAxis'Max 2 setprop 1

Plot <content> END OF WORKSHEET </content>