<content> DATA </content>

09ba4279-0bde-4476-aec1-0caceb179010 187 Reg Curry 4 5 false false false 0 3 decimal

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

CO₂ FORCING SATURATION STUDY

Data2 WORLD EMISSION DATA VS DATE.xlsx Sheet 2 A2:C175 importData.XLSX :

Data2 1850 1.9685 1008 +^* 2.8355 1009 +^* 1851 1.9878 1008 +^* 3.0185 1009 +^* 1852 2.0760 1008 +^* 3.0651 1009 +^* 1853 2.1724 1008 +^* 3.1228 1009 +^* 1854 2.5504 1008 +^* 3.1699 1009 +^* 1855 2.6026 1008 +^* 3.1388 1009 +^* 1856 2.7825 1008 +^* 3.2471 1009 +^* 1857 2.8118 1008 +^* 3.2323 1009 +^* 1858 2.8555 1008 +^* 3.2604 1009 +^* 1859 3.0257 1008 +^* 3.3412 1009 +^* 1860 3.3230 1008 +^* 3.1131 1009 +^* 1861 3.4919 1008 +^* 3.1165 1009 +^* 1862 3.5599 1008 +^* 3.0964 1009 +^* 1863 3.7953 1008 +^* 3.0867 1009 +^* 1864 4.0953 1008 +^* 3.0282 1009 +^* 1865 4.3485 1008 +^* 3.0063 1009 +^* 1866 4.4907 1008 +^* 3.0572 1009 +^* 1867 4.8081 1008 +^* 3.0510 1009 +^* 1868 4.9449 1008 +^* 3.0332 1009 +^* 1869 5.2473 1008 +^* 3.1096 1009 +^* 1870 5.3612 1008 +^* 3.3713 1009 +^* 1871 5.6978 1008 +^* 3.4243 1009 +^* 1872 6.3096 1008 +^* 3.6835 1009 +^* 1873 6.7047 1008 +^* 3.6507 1009 +^* 1874 6.2866 1008 +^* 3.8067 1009 +^* 1875 6.8105 1008 +^* 3.9435 1009 +^* 1876 6.9058 1008 +^* 3.9740 1009 +^* 1877 7.0403 1008 +^* 3.8855 1009 +^* 1878 7.0965 1008 +^* 3.9866 1009 +^* 1879 7.5979 1008 +^* 4.0300 1009 +^* 1880 8.5806 1008 +^* 4.2384 1009 +^* 1881 8.8797 1008 +^* 4.2650 1009 +^* 1882 9.3789 1008 +^* 4.4945 1009 +^* 1883 9.9751 1008 +^* 4.4764 1009 +^* 1884 1.0094 1009 +^* 4.6417 1009 +^* 1885 1.0171 1009 +^* 4.6484 1009 +^* 1886 1.0326 1009 +^* 4.5780 1009 +^* 1887 1.0837 1009 +^* 4.7752 1009 +^* 1888 1.2008 1009 +^* 4.7672 1009 +^* 1889 1.2015 1009 +^* 4.8792 1009 +^* 1890 1.3066 1009 +^* 5.2569 1009 +^* 1891 1.3689 1009 +^* 5.5296 1009 +^* 1892 1.3798 1009 +^* 5.4816 1009 +^* 1893 1.3625 1009 +^* 5.6512 1009 +^* 1894 1.4115 1009 +^* 5.7157 1009 +^* 1895 1.4952 1009 +^* 5.8047 1009 +^* 1896 1.5447 1009 +^* 5.7893 1009 +^* 1897 1.6175 1009 +^* 6.0219 1009 +^* 1898 1.7060 1009 +^* 6.0629 1009 +^* 1899 1.8631 1009 +^* 6.3107 1009 +^* 1900 1.9615 1009 +^* 6.4676 1009 +^* 1901 2.0240 1009 +^* 6.5567 1009 +^* 1902 2.0748 1009 +^* 6.7020 1009 +^* 1903 2.2620 1009 +^* 6.8590 1009 +^* 1904 2.2875 1009 +^* 6.9666 1009 +^* 1905 2.4371 1009 +^* 7.2638 1009 +^* 1906 2.5445 1009 +^* 7.3818 1009 +^* 1907 2.9003 1009 +^* 7.6489 1009 +^* 1908 2.7857 1009 +^* 7.6245 1009 +^* 1909 2.9012 1009 +^* 7.8474 1009 +^* 1910 3.0433 1009 +^* 7.7902 1009 +^* 1911 3.0901 1009 +^* 7.9169 1009 +^* 1912 3.2465 1009 +^* 7.9327 1009 +^* 1913 3.5165 1009 +^* 8.0311 1009 +^* 1914 3.1898 1009 +^* 7.7862 1009 +^* 1915 3.1403 1009 +^* 7.7114 1009 +^* 1916 3.3920 1009 +^* 7.9146 1009 +^* 1917 3.5481 1009 +^* 8.0935 1009 +^* 1918 3.4997 1009 +^* 8.0482 1009 +^* 1919 3.0338 1009 +^* 7.5151 1009 +^* 1920 3.5378 1009 +^* 8.1414 1009 +^* 1921 3.1062 1009 +^* 7.9451 1009 +^* 1922 3.2545 1009 +^* 8.0570 1009 +^* 1923 3.6907 1009 +^* 8.5984 1009 +^* 1924 3.7028 1009 +^* 8.6241 1009 +^* 1925 3.7406 1009 +^* 8.6591 1009 +^* 1926 3.6774 1009 +^* 8.6077 1009 +^* 1927 4.0129 1009 +^* 8.9788 1009 +^* 1928 3.9963 1009 +^* 8.9363 1009 +^* 1929 4.2882 1009 +^* 9.1823 1009 +^* 1930 3.9581 1009 +^* 8.9784 1009 +^* 1931 3.5393 1009 +^* 8.7242 1009 +^* 1932 3.1926 1009 +^* 8.4260 1009 +^* 1933 3.3627 1009 +^* 8.6600 1009 +^* 1934 3.6562 1009 +^* 8.9940 1009 +^* 1935 3.8357 1009 +^* 9.0969 1009 +^* 1936 4.2079 1009 +^* 9.5085 1009 +^* 1937 4.4967 1009 +^* 9.8650 1009 +^* 1938 4.2296 1009 +^* 9.6477 1009 +^* 1939 4.4701 1009 +^* 9.8273 1009 +^* 1940 4.8847 1009 +^* 1.0343 1010 +^* 1941 4.9991 1009 +^* 1.0737 1010 +^* 1942 4.9825 1009 +^* 1.0752 1010 +^* 1943 5.0753 1009 +^* 1.0796 1010 +^* 1944 5.1625 1009 +^* 1.0861 1010 +^* 1945 4.2893 1009 +^* 9.9816 1009 +^* 1946 4.6085 1009 +^* 1.0256 1010 +^* 1947 5.1652 1009 +^* 1.0802 1010 +^* 1948 5.4479 1009 +^* 1.0998 1010 +^* 1949 5.2040 1009 +^* 1.0680 1010 +^* 1950 5.9302 1009 +^* 1.2137 1010 +^* 1951 6.3814 1009 +^* 1.2941 1010 +^* 1952 6.4675 1009 +^* 1.2946 1010 +^* 1953 6.6509 1009 +^* 1.3240 1010 +^* 1954 6.7895 1009 +^* 1.3770 1010 +^* 1955 7.4439 1009 +^* 1.4567 1010 +^* 1956 7.9260 1009 +^* 1.5146 1010 +^* 1957 8.1856 1009 +^* 1.5509 1010 +^* 1958 8.4172 1009 +^* 1.5609 1010 +^* 1959 8.8547 1009 +^* 1.6598 1010 +^* 1960 9.3870 1009 +^* 1.6093 1010 +^* 1961 9.4150 1009 +^* 1.6236 1010 +^* 1962 9.7473 1009 +^* 1.6078 1010 +^* 1963 1.0267 1010 +^* 1.6428 1010 +^* 1964 1.0824 1010 +^* 1.6683 1010 +^* 1965 1.1311 1010 +^* 1.6936 1010 +^* 1966 1.1863 1010 +^* 1.7085 1010 +^* 1967 1.2237 1010 +^* 1.7638 1010 +^* 1968 1.2905 1010 +^* 1.8238 1010 +^* 1969 1.3762 1010 +^* 1.9598 1010 +^* 1970 1.4899 1010 +^* 2.0593 1010 +^* 1971 1.5504 1010 +^* 2.0622 1010 +^* 1972 1.6225 1010 +^* 2.1615 1010 +^* 1973 1.7085 1010 +^* 2.2329 1010 +^* 1974 1.7011 1010 +^* 2.2149 1010 +^* 1975 1.7053 1010 +^* 2.2112 1010 +^* 1976 1.7989 1010 +^* 2.3073 1010 +^* 1977 1.8499 1010 +^* 2.4012 1010 +^* 1978 1.9069 1010 +^* 2.4482 1010 +^* 1979 1.9609 1010 +^* 2.4296 1010 +^* 1980 1.9489 1010 +^* 2.4456 1010 +^* 1981 1.9023 1010 +^* 2.3853 1010 +^* 1982 1.8871 1010 +^* 2.3415 1010 +^* 1983 1.8992 1010 +^* 2.3777 1010 +^* 1984 1.9648 1010 +^* 2.5287 1010 +^* 1985 2.0312 1010 +^* 2.5603 1010 +^* 1986 2.0615 1010 +^* 2.6142 1010 +^* 1987 2.1250 1010 +^* 2.6590 1010 +^* 1988 2.2085 1010 +^* 2.7256 1010 +^* 1989 2.2387 1010 +^* 2.7340 1010 +^* 1990 2.2729 1010 +^* 2.7706 1010 +^* 1991 2.3186 1010 +^* 2.8156 1010 +^* 1992 2.2528 1010 +^* 2.7786 1010 +^* 1993 2.2756 1010 +^* 2.7730 1010 +^* 1994 2.2993 1010 +^* 2.8882 1010 +^* 1995 2.3532 1010 +^* 2.8964 1010 +^* 1996 2.4258 1010 +^* 3.0271 1010 +^* 1997 2.4402 1010 +^* 3.1808 1010 +^* 1998 2.4304 1010 +^* 3.0448 1010 +^* 1999 2.4854 1010 +^* 3.0857 1010 +^* 2000 2.5511 1010 +^* 3.0808 1010 +^* 2001 2.5706 1010 +^* 3.0472 1010 +^* 2002 2.6277 1010 +^* 3.1405 1010 +^* 2003 2.7669 1010 +^* 3.3745 1010 +^* 2004 2.8633 1010 +^* 3.4036 1010 +^* 2005 2.9614 1010 +^* 3.4505 1010 +^* 2006 3.0628 1010 +^* 3.5961 1010 +^* 2007 3.1535 1010 +^* 3.6129 1010 +^* 2008 3.2074 1010 +^* 3.6955 1010 +^* 2009 3.1542 1010 +^* 3.6816 1010 +^* 2010 3.3356 1010 +^* 3.8844 1010 +^* 2011 3.4505 1010 +^* 3.9783 1010 +^* 2012 3.5000 1010 +^* 4.0652 1010 +^* 2013 3.5302 1010 +^* 4.0418 1010 +^* 2014 3.5450 1010 +^* 4.0846 1010 +^* 2015 3.5405 1010 +^* 4.0936 1010 +^* 2016 3.5417 1010 +^* 3.9823 1010 +^* 2017 3.5990 1010 +^* 4.0221 1010 +^* 2018 3.6730 1010 +^* 4.0575 1010 +^* 2019 3.7104 1010 +^* 4.0891 1010 +^* 2020 3.5127 1010 +^* 3.8566 1010 +^* 2021 3.6992 1010 +^* 4.0545 1010 +^* 2022 3.7294 1010 +^* 4.0835 1010 +^* 2023 3.7792 1010 +^* 4.1416 1010 +^* 1743 mat :

Data2 rows 174.00

Data2 1850.00 1.97 108^* 2.84 109^* 1851.00 1.99 108^* 3.02 109^* 1852.00 2.08 108^* 3.07 109^* 1853.00 2.17 108^* 3.12 109^* 1854.00 2.55 108^* 3.17 109^* 1855.00 2.60 108^* 3.14 109^* 63 mat

Date Data2 1 col :

Emission Data2 2 col 109^/ :

DATA Date Emission augment :

x Date :

FIT TO EMISSION DATA

<content> FIT EMISSION DATA </content>

SMATH FIT USING al_nelqsolve

Date 165 el 2014

X Date :

Y Emission :

X max 2023

to X min eval : 1850

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 to - to / *^* + vectorize 21 line :

u.exp 101010 - 31 mat u φ X u F.exp Y - : al_nleqsolve : 1.4923 36.1474 2.1976 - 31 mat

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

DEFINE SUBSET OF DATA TO FT

t.o 2014 :

j 1100 range :

tt j el t.o j + :

tt max 2114.00

DATA2014 DATA 165 DATA rows 12 submatrix :

XX DATA2014 1 col :

YY DATA2014 2 col :

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

u.lin 101021 mat u φ XX u F.lin YY - : al_nleqsolve : 35.2403 487.7664 21 mat

2014 u.lin F.lin 35.2403

YY 1 el 35.45

FIT2 j el u.lin 1 el u.lin 2 el tt j el t.o - t.o / * + :

FIT2 max 59.459

FIT2 min 35.4824

SELECT EVERY nth CASE POINT TO PLOT

nselect 1 Data2 rows 3 range :

Xnew X nselect el :

Ynew Y nselect el :

Ynew Xnew Ynew augment :

FIT2 tt FIT2 augment :

t ulin FIT FIT2 :

EMISSION'XAxis'Min 1850 setprop 1

EMISSION'XAxis'Tick 50 setprop 1

EMISSION'XAxis'Max 2050 setprop 1

EMISSION'YAxis'Min 10 - setprop 1

EMISSION'YAxis'Tick 10 setprop 1

EMISSION'YAxis'Max 100 setprop 1 ≡

Plot Ynew t u.exp F.exp t u.lin FIT XX YY augment 41 sys :

Plot

TO GET CUMULATIVE EMISSIONS WE MUST SOLVE THE FOLLOWING ODE

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 / :

enddate 2200 :

z 1850 enddate range :

u.lin 35.2403 487.7664 21 mat

a b c 31 mat u.exp 1 el u.exp 2 el u.exp 3 el 31 mat :

z Q1 c a e b z to - to / *^* + :

a2 b2 21 mat u.lin 1 el u.lin 2 el 21 mat :

z Q2 a2 b2 z t.o - t.o / * + (:

CO.2 z 1850 enddate range z 2014 ≤ Y z el e λ z * -^s Q1 e λ s *^* s 1850 z int * eval : Y z el e λ z * -^s Q2 e λ s *^* s 2014 z int * Y 2014 el + eval : if for Y 21 line eval :

CO.2 CO.2 1850 CO.2 rows 11 submatrix :

CO.2 rows 351

Date 1850 enddate range :

Date min 1850

Date max 2200

Date rows 351

CO.2 Date CO.2 7.8 / augment :

CONCENTRATION'XAxis'Min 1850 setprop 1

CONCENTRATION'XAxis'Tick 50 setprop 1

CONCENTRATION'XAxis'Max 2250 setprop 1

CO.2 2 col max 1233.3186

CONCENTRATION'YAxis'Min 50 - setprop 1

CONCENTRATION'YAxis'Tick 100 setprop 1

CONCENTRATION'YAxis'Max 1000 setprop 1

CO.2

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 rows 130

PPMDATA 1302 el 419.315

CO.2 1741 el 2023

NORM PPMDATA 1302 el CO.2 1742 el - :

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

PPMDATA 1301 el 2023

CO.2 1742 el 206.9822

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

CO.2 PPMDATA CO.2NORM 3 1 sys <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>

enddate 2200

z1 1850 enddate range :

z1 rows 351

T.o 14.0 °C * :

δt 1 yr * :

CO.2NORM 12 el 212.3328

T.o 287.15 K *

CO.2INITIAL CO.2NORM 12 el :

k 1 z1 rows range :

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

T 1 el T.o :

k 1 z1 rows range T k 1 + el 1 C.e / 1 α - (S * 4 / ΔFCO2 k el + ε σ * T k el 4^* (- (* δt * T k el + eval : for

T rows 352

Date rows 351

T 287.15 K * 287.094 K * 287.0654 K * 287.0508 K * 287.0433 K * 51 mat

Temission T T.o - :

Temission 0 0.056 K * - 0.0846 K * - 0.0992 K * - 0.1067 K * - 0.1107 K * - 61 mat

Temission Temission 2 T rows 11 submatrix :

Temission Date Temission augment :

Temission 1850 0.056 K * - 1851 0.0846 K * - 1852 0.0992 K * - 1853 0.1067 K * - 1854 0.1107 K * - 1855 0.1128 K * - 1856 0.1141 K * - 72 mat

TEMP'XAxis'Min 1850 setprop 1

CO2'XAxis'Tick 100 setprop 0

TEMP'XAxis'Max 2250 setprop 1

TEMP'YAxis'Min .5 - setprop 1

CO2'YAxis'Tick 0.1 setprop 0

TEMP'YAxis'Max 2 setprop 1

Temission 1 1 sys

END OF WORKSHEET