The Great Stasis

The poster on RealClimate who signs himself Victor (possibly Victor Grauer of my home town of Pittsburgh) is that rarity, a liberal AGW denier. Victor insists there's no correlation between carbon dioxide and mean global annual surface temperature. Of course there is--see, for example, here. Victor doesn't know his statistics. But let's look at a possible explanation for his mistake.

He insists, for example, that while CO₂ rose from 1940 to 1978, temperature fell. That's not quite true--while the slope of temperature versus year for that period is negative at -0.00236 K per year, the t-statistic on the slope is insignificant: t = -1.27, for p < 0.212. So the error bars are wider than the slope, and for all we know, given the noisiness of the data, it could have actually been rising. But give him his point for the moment. Does it prove what he thinks it does?

No. CO₂ is not the only thing that affects temperature. Other factors known to have effects on Earth's temperature are sunlight, volcanic aerosols, aerosols from pollution, heat cycles between the atmosphere and the ocean (such as El Niño), variations in cloudiness, other greenhouse gases, etc., etc., etc. So some other factor might have suppressed temperature during those years. By 1978 (actually, according to statistician Grant Foster, 1975) CO₂ had come to dominate everything else and global warming really took off.

Let's examine a bunch of data for the period. Here is data on temperature and several other factors for the years 1850-2019. Not all are complete, unfortunately, but we've got complete coverage from 1866 onward and 2018 backward.

dT is Hadley Centre CRUTEM4 temperature anomalies, baseline 1961-1990.
CO₂ is carbon dioxide level in parts per million by volume. Law Dome Ice Cores 1850-1958, Mauna Loa 1959-2019.
SN is sunspot number. Sunspot Index and Long-Term data Observations (SILSO).
TSI is Total Solar Irradiance (the solar constant), from Greg Kopp's web page.
SOI is the Southern Oscillation Index, a measure of the ENSO cycle, from assorted sources.
Aerosols is the NASA GISS forcings index for aerosols (Miller et al. 2021).

Year dT CO₂ SN TSI SOI Aerosols

1850 -0.239 284.7 126.3 1361.7005 -0.077

1851 -0.004 284.9 122 1361.5037 -0.027

1852 -0.137 285.0 102.7 1361.4177 0.004

1853 -0.326 285.1 74.1 1361.2921 0.110

1854 -0.125 285.3 39 1361.0975 0.237

1855 -0.522 285.4 12.7 1360.9770 -0.210

1856 -0.587 285.6   8.2 1360.8772 0.036

1857 -0.580 285.7 43.4 1360.9499 -0.335

1858 -0.555 285.9 104.4 1361.1913 -0.090

1859 -0.193 286.1 178.3 1361.4779 -0.051

1860 -0.649 286.2 182.2 1361.6335 -0.217

1861 -0.516 286.4 146.6 1361.6242 -0.022

1862 -0.756 286.5 112.1 1361.4956 -0.230

1863 -0.275 286.6 83.5 1361.3489 0.302

1864 -0.825 286.8 89.2 1361.2972 -0.092

1865 -0.453 286.9 57.8 1361.2800 -0.083

1866 -0.440 287.0 30.7 1361.1589 -0.16 0.039

1867 -0.603 287.1 13.9 1361.0301 -0.03 -0.471

1868 -0.424 287.2 62.8 1361.1520 -0.88 -0.317

1869 -0.393 287.4 123.6 1361.4661 0.55 0.057

1870 -0.549 287.5 232 1361.6794 -0.15 -0.236

1871 -0.659 287.7 185.3 1361.9733 -0.15 -0.087

1872 -0.355 287.9 169.2 1361.7310 1.91 -0.056

1873 -0.384 288.1 110.1 1361.6337 0.08 -0.259

1874 -0.483 288.4 74.5 1361.3396 0.59 -0.342

1875 -0.832 288.7 28.3 1361.0057 0.27 -0.019

1876 -0.497 289.0 18.9 1360.7805 0.44 -0.024

1877 -0.252 289.4 20.7 1360.7192 -1.80 -0.080

1878 -0.023 289.8   5.7 1360.6067 0.17 -0.127

1879 -0.553 290.2 10 1360.5930 1.27 -0.334

1880 -0.363 290.7 53.7 1360.7627 0.79 0.003

1881 -0.440 291.2 90.5 1361.0932 -0.59 -0.152

1882 -0.336 291.7 99 1361.1539 -0.60 0.065

1883 -0.617 292.1 106.1 1361.1109 -0.25 -0.364

1884 -0.724 292.6 105.8 1361.3241 -0.38 -0.262

1885 -0.693 293.0 86.3 1361.2171 -0.68 -0.138

1886 -0.532 293.3 42.4 1361.0569 0.70 -0.119

1887 -0.578 293.6 21.8 1360.8577 0.47 -0.058

1888 -0.594 293.8 11.2 1360.8100 -1.27 -0.101

1889 -0.276 294 10.4 1360.7764 0.16 -0.046

1890 -0.446 294.2 11.8 1360.7650 0.56 -0.191

1891 -0.536 294.3 59.5 1360.8840 -0.28 -0.218

1892 -0.633 294.5 121.7 1361.1688 0.52 -0.154

1893 -0.708 294.6 142 1361.3458 0.99 -0.104

1894 -0.484 294.7 130 1361.4701 0.21 -0.199

1895 -0.574 294.8 106.6 1361.3363 -0.25 -0.143

1896 -0.395 294.9 69.4 1361.2281 -1.55 -0.217

1897 -0.310 295.0 43.8 1360.9385 -0.68 0.060

1898 -0.396 295.2 44.4 1360.8914 0.57 -0.062

1899 -0.329 295.5 20.2 1360.8152 0.16 -0.352

1900 -0.194 295.8 15.7 1360.7290 -0.65 -0.337

1901 -0.157 296.1   4.6 1360.6394 0.07 -0.147

1902 -0.398 296.5   8.5 1360.6319 0.10 -0.067

1903 -0.432 296.8 40.8 1360.7228 0.47 0.204

1904 -0.533 297.2 70.1 1361.0143 0.39 -0.353

1905 -0.405 297.6 105.5 1361.0005 -1.79 0.039

1906 -0.184 298.1 90.1 1361.2441 0.21 -0.600

1907 -0.606 298.5 102.8 1361.1264 -0.20 -0.295

1908 -0.457 298.9 80.9 1361.1528 0.28 -0.178

1909 -0.423 299.3 73.2 1361.0208 0.29 -0.398

1910 -0.333 299.7 30.9 1360.9185 1.26 -0.545

1911 -0.415 300.1   9.5 1360.7133 -0.64 -0.294

1912 -0.434 300.4   6 1360.6625 -0.98 -0.454

1913 -0.306 300.8   2.4 1360.7110 -0.68 -0.330

1914 -0.063 301.1 16.1 1360.7851 -0.93 -0.144

1915 -0.06 301.4 79 1361.0964 0.16 -0.046

1916 -0.346 301.7 95 1361.4054 0.64 -0.105

1917 -0.652 302.1 173.6 1361.5701 2.14 -0.391

1918 -0.417 302.4 134.6 1361.7757 0.05 -0.323

1919 -0.275 302.7 105.7 1361.4560 -1.09 -0.411

1920 -0.262 303.0 62.7 1361.1199 0.09 -0.363

1921 -0.099 303.4 43.5 1360.8915 0.66 -0.360

1922 -0.248 303.8 23.7 1360.7013 0.33 -0.309

1923 -0.263 304.1   9.7 1360.5976 -0.36 -0.427

1924 -0.314 304.5 27.9 1360.6045 0.34 -0.441

1925 -0.212 305.0 74 1360.7004 -0.24 -0.383

1926 -0.064 305.4 106.5 1361.0393 -0.49 -0.498

1927 -0.223 305.8 114.7 1361.3065 0.27 -0.630

1928 -0.146 306.3 129.7 1361.2413 0.42 -0.231

1929 -0.469 306.8 108.2 1361.1000 0.46 -0.373

1930 -0.108 307.2 59.4 1361.1858 0.03 -0.335

1931 -0.072 307.7 35.1 1360.9547 0.39 -0.378

1932 -0.076 308.2 18.6 1360.8472 -0.68 -0.265

1933 -0.317 308.6   9.2 1360.8356 0.09 -0.112

1934 -0.025 309.0 14.6 1360.8648 -0.01 -0.088

1935 -0.163 309.4 60.2 1360.9766 0.14 -0.286

1936 -0.117 309.8 132.8 1361.4379 0.03 -0.615

1937 -0.032 310.0 190.6 1361.7170 0.08 -0.251

1938 0.152 310.2 182.6 1361.6735 0.87 -0.356

1939 -0.002 310.3 148 1361.6299 0.02 -0.606

1940 -0.041 310.4 113 1361.3999 -1.52 -0.446

1941 -0.029 310.4 79.2 1361.2455 -1.45 -0.584

1942 -0.046 310.3 50.8 1361.0801 0.02 -0.801

1943 0.010 310.2 27.1 1360.9052 0.36 -0.635

1944 0.107 310.1 16.1 1360.9080 -0.28 -0.801

1945 -0.119 310.1 55.3 1361.1456 0.42 -0.493

1946 -0.078 310.1 154.3 1361.2842 -0.79 -0.453

1947 -0.005 310.2 214.7 1361.7197 0.16 -0.410

1948 0.000 310.3 193 1361.9235 -0.23 -0.652

1949 -0.108 310.5 190.7 1361.7306 -0.21 -0.422

1950 -0.301 310.7 118.9 1361.6156 1.51 -0.475

1951 -0.107 311.1 98.3 1361.1933 -0.69 -0.708

1952 -0.063 311.5 45 1361.1126 -0.22 -0.811

1953 0.129 311.9 20.1 1361.0253 -0.77 -0.710

1954 -0.145 312.4   6.6 1360.9819 0.23 -0.541

1955 -0.192 313.0 54.2 1361.1123 0.90 -0.286

1956 -0.426 313.6 200.7 1361.4949 1.02 -0.826

1957 -0.078 314.2 269.3 1362.0982 -0.45 -0.881

1958 0.041 314.9 261.7 1362.3628 -0.50 -0.743

1959 0.019 315.97 225.1 1362.0576 -0.10 -0.589

1960 -0.068 316.91 159 1361.9256 0.29 -0.656

1961 0.039 317.64 76.4 1361.5795 -0.01 -0.826

1962 0.027 318.45 53.4 1361.1854 0.39 -0.909

1963 0.024 318.99 39.9 1361.0138 -0.32 -0.903

1964 -0.283 319.62 15 1360.8779 0.54 -1.001

1965 -0.233 320.04 22 1360.8301 -0.95 -0.762

1966 -0.132 321.38 66.8 1360.9332 -0.54 -0.785

1967 -0.090 322.16 132.9 1361.1374 0.25 -0.970

1968 -0.207 323.04 150 1361.4356 0.20 -1.037

1969 -0.114 324.62 149.4 1361.5281 -0.66 -0.776

1970 -0.054 325.68 148 1361.4117 0.29 -1.105

1971 -0.202 326.32 94.4 1361.2392 1.07 -0.974

1972 -0.225 327.45 97.6 1361.1948 -0.83 -1.136

1973 0.138 329.68 54.1 1361.0660 0.64 -1.150

1974 -0.278 330.18 49.2 1360.9792 0.96 -1.000

1975 -0.065 331.11 22.5 1360.9566 1.33 -1.077

1976 -0.354 332.04 18.4 1360.9440 0.06 -1.322

1977 0.082 333.83 39.3 1361.0500 -1.14 -1.507

1978 -0.047 335.40 131 1361.2295 -0.29 -1.550

1979 0.039 336.84 220.1 1361.7566 -0.26 -1.137

1980 0.125 338.75 218.9 1361.6909 -0.43 -1.064

1981 0.300 340.11 198.9 1361.7126 0.07 -1.239

1982 -0.020 341.45 162.4 1361.4217 -1.45 -1.024

1983 0.317 343.05 91 1361.3923 -0.95 -1.047

1984 -0.047 344.65 60.5 1360.9775 -0.14 -1.261

1985 -0.042 346.12 20.6 1360.8359 -0.02 -1.151

1986 0.106 347.42 14.8 1360.8877 -0.32 -1.387

1987 0.264 349.19 33.9 1360.9677 -1.48 -1.111

1988 0.361 351.57 123 1361.2840 0.74 -1.254

1989 0.234 353.12 211.1 1361.7357 0.62 -1.258

1990 0.490 354.39 191.8 1361.6844 -0.33 -1.366

1991 0.380 355.61 203.3 1361.5875 -1.01 -1.349

1992 0.094 356.45 133 1361.5255 -1.23 -1.066

1993 0.177 357.10 76.1 1361.3081 -1.11 -1.236

1994 0.331 358.83 44.9 1361.1154 -1.35 -1.351

1995 0.570 360.82 25.1 1361.0200 -0.33 -1.357

1996 0.228 362.61 11.6 1360.9005 0.56 -1.510

1997 0.490 363.73 28.9 1361.0787 -1.29 -1.057

1998 0.841 366.70 88.3 1361.4702 -0.23 -1.525

1999 0.556 368.38 136.3 1361.7339 0.79 -1.159

2000 0.474 369.55 173.9 1361.9522 0.72 -1.078

2001 0.668 371.14 170.4 1361.9009 -0.08 -1.161

2002 0.762 373.28 163.6 1361.9725 -0.72 -1.190

2003 0.758 375.80 99.3 1361.4971 -0.43 -1.646

2004 0.660 377.52 65.3 1361.2960 -0.63 -1.260

2005 0.863 379.80 45.8 1361.1431 -0.46 -1.261

2006 0.805 381.90 24.7 1361.1004 -0.28 -1.264

2007 0.895 383.79 12.6 1361.0004 0.03 -1.308

2008 0.682 385.60   4.2 1360.9794 1.00 -1.163

2009 0.731 387.43   4.8 1360.9856 -0.13 -1.020

2010 0.914 389.90 24.9 1361.2296 0.95 -1.308

2011 0.707 391.65 80.8 1361.4640 1.40 -1.408

2012 0.761 393.85 84.5 1361.5920 -0.18 -1.411

2013 0.826 396.52 94 1361.6117 0.35 -1.265

2014 0.866 398.65 113.3 1361.5882 -0.38 -0.989

2015 1.151 400.83 69.8 1361.7017 -1.17 -1.084

2016 1.292 404.24 39.8 1361.3384 -0.46 -0.840

2017 1.120 406.55 21.7 1361.2147 0.11 -1.115

2018 0.941 408.52   7 1361.2560 0.09 -1.015

2019 1.158 411.44   3.6 -0.79 -0.851

Year	dT	CO₂	SN	TSI	SOI	Aerosols
1850	-0.239	284.7	126.3	1361.7005		-0.077
1851	-0.004	284.9	122	1361.5037		-0.027
1852	-0.137	285.0	102.7	1361.4177		0.004
1853	-0.326	285.1	74.1	1361.2921		0.110
1854	-0.125	285.3	39	1361.0975		0.237
1855	-0.522	285.4	12.7	1360.9770		-0.210
1856	-0.587	285.6	8.2	1360.8772		0.036
1857	-0.580	285.7	43.4	1360.9499		-0.335
1858	-0.555	285.9	104.4	1361.1913		-0.090
1859	-0.193	286.1	178.3	1361.4779		-0.051
1860	-0.649	286.2	182.2	1361.6335		-0.217
1861	-0.516	286.4	146.6	1361.6242		-0.022
1862	-0.756	286.5	112.1	1361.4956		-0.230
1863	-0.275	286.6	83.5	1361.3489		0.302
1864	-0.825	286.8	89.2	1361.2972		-0.092
1865	-0.453	286.9	57.8	1361.2800		-0.083
1866	-0.440	287.0	30.7	1361.1589	-0.16	0.039
1867	-0.603	287.1	13.9	1361.0301	-0.03	-0.471
1868	-0.424	287.2	62.8	1361.1520	-0.88	-0.317
1869	-0.393	287.4	123.6	1361.4661	0.55	0.057
1870	-0.549	287.5	232	1361.6794	-0.15	-0.236
1871	-0.659	287.7	185.3	1361.9733	-0.15	-0.087
1872	-0.355	287.9	169.2	1361.7310	1.91	-0.056
1873	-0.384	288.1	110.1	1361.6337	0.08	-0.259
1874	-0.483	288.4	74.5	1361.3396	0.59	-0.342
1875	-0.832	288.7	28.3	1361.0057	0.27	-0.019
1876	-0.497	289.0	18.9	1360.7805	0.44	-0.024
1877	-0.252	289.4	20.7	1360.7192	-1.80	-0.080
1878	-0.023	289.8	5.7	1360.6067	0.17	-0.127
1879	-0.553	290.2	10	1360.5930	1.27	-0.334
1880	-0.363	290.7	53.7	1360.7627	0.79	0.003
1881	-0.440	291.2	90.5	1361.0932	-0.59	-0.152
1882	-0.336	291.7	99	1361.1539	-0.60	0.065
1883	-0.617	292.1	106.1	1361.1109	-0.25	-0.364
1884	-0.724	292.6	105.8	1361.3241	-0.38	-0.262
1885	-0.693	293.0	86.3	1361.2171	-0.68	-0.138
1886	-0.532	293.3	42.4	1361.0569	0.70	-0.119
1887	-0.578	293.6	21.8	1360.8577	0.47	-0.058
1888	-0.594	293.8	11.2	1360.8100	-1.27	-0.101
1889	-0.276	294	10.4	1360.7764	0.16	-0.046
1890	-0.446	294.2	11.8	1360.7650	0.56	-0.191
1891	-0.536	294.3	59.5	1360.8840	-0.28	-0.218
1892	-0.633	294.5	121.7	1361.1688	0.52	-0.154
1893	-0.708	294.6	142	1361.3458	0.99	-0.104
1894	-0.484	294.7	130	1361.4701	0.21	-0.199
1895	-0.574	294.8	106.6	1361.3363	-0.25	-0.143
1896	-0.395	294.9	69.4	1361.2281	-1.55	-0.217
1897	-0.310	295.0	43.8	1360.9385	-0.68	0.060
1898	-0.396	295.2	44.4	1360.8914	0.57	-0.062
1899	-0.329	295.5	20.2	1360.8152	0.16	-0.352
1900	-0.194	295.8	15.7	1360.7290	-0.65	-0.337
1901	-0.157	296.1	4.6	1360.6394	0.07	-0.147
1902	-0.398	296.5	8.5	1360.6319	0.10	-0.067
1903	-0.432	296.8	40.8	1360.7228	0.47	0.204
1904	-0.533	297.2	70.1	1361.0143	0.39	-0.353
1905	-0.405	297.6	105.5	1361.0005	-1.79	0.039
1906	-0.184	298.1	90.1	1361.2441	0.21	-0.600
1907	-0.606	298.5	102.8	1361.1264	-0.20	-0.295
1908	-0.457	298.9	80.9	1361.1528	0.28	-0.178
1909	-0.423	299.3	73.2	1361.0208	0.29	-0.398
1910	-0.333	299.7	30.9	1360.9185	1.26	-0.545
1911	-0.415	300.1	9.5	1360.7133	-0.64	-0.294
1912	-0.434	300.4	6	1360.6625	-0.98	-0.454
1913	-0.306	300.8	2.4	1360.7110	-0.68	-0.330
1914	-0.063	301.1	16.1	1360.7851	-0.93	-0.144
1915	-0.06	301.4	79	1361.0964	0.16	-0.046
1916	-0.346	301.7	95	1361.4054	0.64	-0.105
1917	-0.652	302.1	173.6	1361.5701	2.14	-0.391
1918	-0.417	302.4	134.6	1361.7757	0.05	-0.323
1919	-0.275	302.7	105.7	1361.4560	-1.09	-0.411
1920	-0.262	303.0	62.7	1361.1199	0.09	-0.363
1921	-0.099	303.4	43.5	1360.8915	0.66	-0.360
1922	-0.248	303.8	23.7	1360.7013	0.33	-0.309
1923	-0.263	304.1	9.7	1360.5976	-0.36	-0.427
1924	-0.314	304.5	27.9	1360.6045	0.34	-0.441
1925	-0.212	305.0	74	1360.7004	-0.24	-0.383
1926	-0.064	305.4	106.5	1361.0393	-0.49	-0.498
1927	-0.223	305.8	114.7	1361.3065	0.27	-0.630
1928	-0.146	306.3	129.7	1361.2413	0.42	-0.231
1929	-0.469	306.8	108.2	1361.1000	0.46	-0.373
1930	-0.108	307.2	59.4	1361.1858	0.03	-0.335
1931	-0.072	307.7	35.1	1360.9547	0.39	-0.378
1932	-0.076	308.2	18.6	1360.8472	-0.68	-0.265
1933	-0.317	308.6	9.2	1360.8356	0.09	-0.112
1934	-0.025	309.0	14.6	1360.8648	-0.01	-0.088
1935	-0.163	309.4	60.2	1360.9766	0.14	-0.286
1936	-0.117	309.8	132.8	1361.4379	0.03	-0.615
1937	-0.032	310.0	190.6	1361.7170	0.08	-0.251
1938	0.152	310.2	182.6	1361.6735	0.87	-0.356
1939	-0.002	310.3	148	1361.6299	0.02	-0.606
1940	-0.041	310.4	113	1361.3999	-1.52	-0.446
1941	-0.029	310.4	79.2	1361.2455	-1.45	-0.584
1942	-0.046	310.3	50.8	1361.0801	0.02	-0.801
1943	0.010	310.2	27.1	1360.9052	0.36	-0.635
1944	0.107	310.1	16.1	1360.9080	-0.28	-0.801
1945	-0.119	310.1	55.3	1361.1456	0.42	-0.493
1946	-0.078	310.1	154.3	1361.2842	-0.79	-0.453
1947	-0.005	310.2	214.7	1361.7197	0.16	-0.410
1948	0.000	310.3	193	1361.9235	-0.23	-0.652
1949	-0.108	310.5	190.7	1361.7306	-0.21	-0.422
1950	-0.301	310.7	118.9	1361.6156	1.51	-0.475
1951	-0.107	311.1	98.3	1361.1933	-0.69	-0.708
1952	-0.063	311.5	45	1361.1126	-0.22	-0.811
1953	0.129	311.9	20.1	1361.0253	-0.77	-0.710
1954	-0.145	312.4	6.6	1360.9819	0.23	-0.541
1955	-0.192	313.0	54.2	1361.1123	0.90	-0.286
1956	-0.426	313.6	200.7	1361.4949	1.02	-0.826
1957	-0.078	314.2	269.3	1362.0982	-0.45	-0.881
1958	0.041	314.9	261.7	1362.3628	-0.50	-0.743
1959	0.019	315.97	225.1	1362.0576	-0.10	-0.589
1960	-0.068	316.91	159	1361.9256	0.29	-0.656
1961	0.039	317.64	76.4	1361.5795	-0.01	-0.826
1962	0.027	318.45	53.4	1361.1854	0.39	-0.909
1963	0.024	318.99	39.9	1361.0138	-0.32	-0.903
1964	-0.283	319.62	15	1360.8779	0.54	-1.001
1965	-0.233	320.04	22	1360.8301	-0.95	-0.762
1966	-0.132	321.38	66.8	1360.9332	-0.54	-0.785
1967	-0.090	322.16	132.9	1361.1374	0.25	-0.970
1968	-0.207	323.04	150	1361.4356	0.20	-1.037
1969	-0.114	324.62	149.4	1361.5281	-0.66	-0.776
1970	-0.054	325.68	148	1361.4117	0.29	-1.105
1971	-0.202	326.32	94.4	1361.2392	1.07	-0.974
1972	-0.225	327.45	97.6	1361.1948	-0.83	-1.136
1973	0.138	329.68	54.1	1361.0660	0.64	-1.150
1974	-0.278	330.18	49.2	1360.9792	0.96	-1.000
1975	-0.065	331.11	22.5	1360.9566	1.33	-1.077
1976	-0.354	332.04	18.4	1360.9440	0.06	-1.322
1977	0.082	333.83	39.3	1361.0500	-1.14	-1.507
1978	-0.047	335.40	131	1361.2295	-0.29	-1.550
1979	0.039	336.84	220.1	1361.7566	-0.26	-1.137
1980	0.125	338.75	218.9	1361.6909	-0.43	-1.064
1981	0.300	340.11	198.9	1361.7126	0.07	-1.239
1982	-0.020	341.45	162.4	1361.4217	-1.45	-1.024
1983	0.317	343.05	91	1361.3923	-0.95	-1.047
1984	-0.047	344.65	60.5	1360.9775	-0.14	-1.261
1985	-0.042	346.12	20.6	1360.8359	-0.02	-1.151
1986	0.106	347.42	14.8	1360.8877	-0.32	-1.387
1987	0.264	349.19	33.9	1360.9677	-1.48	-1.111
1988	0.361	351.57	123	1361.2840	0.74	-1.254
1989	0.234	353.12	211.1	1361.7357	0.62	-1.258
1990	0.490	354.39	191.8	1361.6844	-0.33	-1.366
1991	0.380	355.61	203.3	1361.5875	-1.01	-1.349
1992	0.094	356.45	133	1361.5255	-1.23	-1.066
1993	0.177	357.10	76.1	1361.3081	-1.11	-1.236
1994	0.331	358.83	44.9	1361.1154	-1.35	-1.351
1995	0.570	360.82	25.1	1361.0200	-0.33	-1.357
1996	0.228	362.61	11.6	1360.9005	0.56	-1.510
1997	0.490	363.73	28.9	1361.0787	-1.29	-1.057
1998	0.841	366.70	88.3	1361.4702	-0.23	-1.525
1999	0.556	368.38	136.3	1361.7339	0.79	-1.159
2000	0.474	369.55	173.9	1361.9522	0.72	-1.078
2001	0.668	371.14	170.4	1361.9009	-0.08	-1.161
2002	0.762	373.28	163.6	1361.9725	-0.72	-1.190
2003	0.758	375.80	99.3	1361.4971	-0.43	-1.646
2004	0.660	377.52	65.3	1361.2960	-0.63	-1.260
2005	0.863	379.80	45.8	1361.1431	-0.46	-1.261
2006	0.805	381.90	24.7	1361.1004	-0.28	-1.264
2007	0.895	383.79	12.6	1361.0004	0.03	-1.308
2008	0.682	385.60	4.2	1360.9794	1.00	-1.163
2009	0.731	387.43	4.8	1360.9856	-0.13	-1.020
2010	0.914	389.90	24.9	1361.2296	0.95	-1.308
2011	0.707	391.65	80.8	1361.4640	1.40	-1.408
2012	0.761	393.85	84.5	1361.5920	-0.18	-1.411
2013	0.826	396.52	94	1361.6117	0.35	-1.265
2014	0.866	398.65	113.3	1361.5882	-0.38	-0.989
2015	1.151	400.83	69.8	1361.7017	-1.17	-1.084
2016	1.292	404.24	39.8	1361.3384	-0.46	-0.840
2017	1.120	406.55	21.7	1361.2147	0.11	-1.115
2018	0.941	408.52	7	1361.2560	0.09	-1.015
2019	1.158	411.44	3.6		-0.79	-0.851

Let's do some math. First, a regression of dT on CO₂ alone, using the R-based freeware statistics package Gretl:

Model 1: OLS, using observations 1867-2019 (T = 153)
Dependent variable: dT

             coefficient   std. error    t-ratio    p-value 
  ----------------------------------------------------------
  const      -4.17731      0.132377      -31.56    2.31e-068 ***
  CO2         0.0128167    0.000408405    31.38    4.77e-068 ***

Mean dependent var  -0.044229   S.D. dependent var   0.451814
Sum squared resid    4.124960   S.E. of regression   0.165280
R-squared            0.867060   Adjusted R-squared   0.866179
F(1, 151)            984.8466   P-value(F)           4.77e-68
Log-likelihood       59.32611   Akaike criterion    -114.6522
Schwarz criterion   -108.5913   Hannan-Quinn        -112.1902
rho                  0.360023   Durbin-Watson        1.277002

Here's what that looks like with the predicted values (blue) and the actual values (red) both graphed against time:

chart image

This may give us a clue to Victor's confusion. The CO₂-based regression curve is relatively smooth, while the actual dT values have all kinds of zigzags up and down. Maybe what Victor means by "correlation" is "conformity to the original shape." That's not what the term means in statistics, of course.

Let's see what happens when we try for the best fit using the table data:

Model 2: OLS, using observations 1867-2019 (T = 153)
Dependent variable: dT

               coefficient   std. error   t-ratio    p-value 
  -----------------------------------------------------------
  const        -3.07818      0.375077     -8.207    1.05e-013 ***
  CO2           0.00965124   0.00120088    8.037    2.77e-013 ***
  SOI          -0.0479114    0.0170797    -2.805    0.0057    ***
  SOI_1        -0.0465968    0.0169148    -2.755    0.0066    ***
  Aerosols_1    0.102327     0.0465809     2.197    0.0296    **
  dT_1          0.335131     0.0746078     4.492    1.42e-05  ***

Mean dependent var  -0.044229   S.D. dependent var   0.451814
Sum squared resid    3.146518   S.E. of regression   0.146304
R-squared            0.898593   Adjusted R-squared   0.895144
F(5, 147)            260.5209   P-value(F)           3.67e-71
Log-likelihood       80.03923   Akaike criterion    -148.0785
Schwarz criterion   -129.8958   Hannan-Quinn        -140.6924
rho                  0.018642   Durbin's h           0.598684

Not much difference in variance accounted for; we're now getting 90% instead of 87%. But this one looks different. With a number of factors brought into play, the graph looks like this:

chart image

This one is more zigzagged, and comes closer to the original shape. It's especially closer during the 1940-1978 period Victor was worried about. Our hypothesis about what might be causing the discrepancy is confirmed; the warming effect of CO₂ was temporarily overwhelmed by other factors.

Page created:	05/01/2022
Last modified:	05/01/2022
Author:	BPL