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1. The October 14 2019 issue of the Oxford “Global Climate Change Collection” provides natural and anthropogenic forcings for global warming and tests them against the HadCRU temperature reconstructions from 1850 to 2017. In the presentation, regression analysis is used to show evidence of a close agreement between forcings and observed temperature. This result is shown below in Figure 1, Figure 2, and Figure 3. Regression analysis shows good agreement between forcings and temperature in support of the AGW hypothesis that anthropogenic forcing contributes significantly to the observed warming. A bibliography of selected works in the study of the contribution of anthropogenic forcing in the warming “since pre-industrial times” is included below .
2. In this work, the correlation  presented with regression analysis in the Oxford document is tested with detrended correlation analysis and the split half test for reliability of the observed correlations with temperature of the anthropogenic forcings and total forcings (anthropogenic plus natural forcings) included in the Oxford document. Source data correlation derives from responsiveness at an annual time scale (the object variable in the causation test) as well as a contribution derived from shared trends. Detrended correlation removes the contribution from shared trends so that only the responsiveness of temperature to forcings at an annual time scale is considered. The split half test for reliability provides information on whether observed full span correlations indicate a uniform relationship across the full span of the data. The results are summarized in Figure 4, Figure 5, Figure 6, and Figure 7.
3. The table in Figure 4 is a summary of the results of correlation analysis. Correlation and detrended correlation between HadCRUT4 mean global surface temperature reconstructions 1850-2017 with two combinations of the three forcings provided by the Oxford Climate Change Collection. These correlations are computed between temperature and anthropogenic forcings and also between temperature and “total forcings” computed as the sum of anthropogenic and natural forcings provided in the Oxford document. Three different time spans are studied as full span, first half, and second half. The data in the table of Figure 4 are displayed graphically in the three charts that follow for easy visualization. It is noted that the source data correlations as well as detrended correlations of temperature with anthropogenic forcings are very strong and much higher than those between temperature and total forcings, (anthropogenic + natural forcings).
4. Figure 5 shows the correlations and detrended correlations in the full span of the data 1850-2017 between temperature and anthropogenic forcings (ANTHRO) and between temperature and total forcings computed as the sum of anthropogenic and natural forcings (TOTAL). Here we see the anomalous result that both correlation and detrended correlation are much stronger for ANTHRO than for TOTAL with the odd interpretation that inclusion of known natural forcings weakens the causal relationship between forcings and temperature.
5. However, this relationship is exactly in reverse in the first half of the time span 1850-1933 shown in Figure 6 where we find that total forcings (anthropogenic + natural) show higher correlations than anthropogenic forcings alone. Yet these results too are odd in the sense that the expected results show much lower correlations than the anomalous results in Figure 5.
6. Results for the second half of the time span (1934-2017) appear in Figure 7. They show the same odd pattern seen for the full span in Figure 5 but with higher correlation values indicating that the full span results are likely influenced mostly by the second half that contain high anthropogenic forcing values than natural forcing values. This pattern is the likely source of the popular claim by climate scientists that empirical evidence for AGW warming that in theory must be evaluated “since pre-industrial times” should instead be evaluated in some later period when the correlations are stronger. This issue is discussed in three related posts where it is shown that the empirical evidence thus presented contains the circular reasoning fallacy [LINK]  [LINK] [LINK] .
7. Conclusion: Correlation analysis shows that anthropogenic forcing alone explains warming since 1850 better than total forcing computed as the sum of anthropogenic forcing and natural forcing. This anomalous pattern in the correlation analysis of forcings against temperature may indicate that the the observed warming since 1850 is not well understood and that the anthropogenic forcings published in the Oxford document may have been “tuned” to the HadCRUT4 temperatures in the sense that the temperature data may have played a role in their estimation; with the very same temperature data then used to test the validity of the forcings thus derived.  If that is the case the the regression analysis presented for the test of forcings that supports the validity of AGW as having a significant anthropogenic component is an exercise in circular reasoning.

FIGURE 1: DISPLAY OF CORRELATION BETWEEN FORCING & TEMPERATURE 

FIGURE 2: REGRESSION RESULTS FOR ANTHROPOGENIC FORCING

FIGURE 3: REGRESSION RESULTS FOR NATURAL FORCING

FIGURE 4: DETRENDED CORRELATION ANALYSIS: SUMMARY OF RESULTS

FIGURE 5: RESULTS FOR THE FULL SPAN: 1850-2017

FIGURE 6: RESULTS FOR THE FIRST HALF OF THE SPAN: 1850-1933

FIGURE 7: RESULTS FOR THE 2ND HALF OF THE SPAN: 1934-2017

ANTHROPOGENIC FORCING BIBLIOGRAPHY

1. Wigley, T. M. L., R. L. Smith, and BDl Santer. “Anthropogenic influence on the autocorrelation structure of hemispheric mean temperatures. Science 282.5394 (1998): 1676-1679.  It is shown that lagged correlations for and cross-correlations between observed hemispheric-mean temperature data differ markedly from those for unforced (control-run) climate model simulations. The differences can be explained adequately by assuming that the observed data contain a significant externally forced component involving both natural (solar) and anthropogenic influences and that the global climate sensitivity is in the commonly accepted range. Solar forcing alone cannot reconcile the differences in autocorrelation structure between observations and model control-run data.
2. Folland, Chris K., et al. “Influences of anthropogenic and oceanic forcing on recent climate change.” Geophysical Research Letters 25.3 (1998): 353-356.  We report a new approach to climate change detection and attribution using an atmospheric general circulation model (AGCM), complementary to the traditional approach using coupled ocean‐atmosphere models (CGCM). Ensembles of simulations were run with an AGCM forced with the observed history of sea‐surface temperature (SST) and sea‐ice extent and repeated with a variety of forcing factors added incrementally. SST changes alone give a warming of only about 0.15°C in annual global land surface air temperature between 1950 and 1994. Addition of changing greenhouse gases, including off‐line calculations of tropospheric ozone, give a further warming of 0.15°C, still 0.2 °C less than observed. This deficit in warming derives from the Northern Hemisphere (NH) winter half‐year as the summer half‐year NH temperature is well‐simulated. In the lower stratosphere, little cooling is simulated using the observed changes of SST alone but increasing the concentration of greenhouse gases and decreasing the concentration of stratospheric ozone leads to a cooling close to that observed. Inclusion of changes to tropospheric ozone with other forcing factors, the first time this has been attempted, gives good simulations of tropospheric and stratospheric temperature changes; these are significantly more similar to observations than using SST variations alone. Despite the uncertainties, these simulations strongly indicate a discernible anthropogenic effect on the annual mean thermal structure of the atmosphere, the first time this has been shown in the presence of the observed variations of SST and sea‐ice extent.
3. Stott, Peter A., et al. “External control of 20th century temperature by natural and anthropogenic forcings.” science 290.5499 (2000): 2133-2137.  A comparison of observations with simulations of a coupled ocean-atmosphere general circulation model shows that both natural and anthropogenic factors have contributed significantly to 20th century temperature changes. The model successfully simulates global mean and large-scale land temperature variations, indicating that the climate response on these scales is strongly influenced by external factors. More than 80% of observed multidecadal-scale global mean temperature variations and more than 60% of 10- to 50-year land temperature variations are due to changes in external forcings. Anthropogenic global warming under a standard emissions scenario is predicted to continue at a rate similar to that observed in recent decades.
4. Zorita, E., et al. “Natural and anthropogenic modes of surface temperature variations in the last thousand years.” Geophysical Research Letters 32.8 (2005).  The spatial patterns of surface air‐temperature variations in the period 1000 to 2100, simulated with the ECHO‐G atmosphere‐ocean coupled model, are analyzed. The model was driven by solar, volcanic and greenhouse gas forcing. The leading mode of temperature variability in the pre-industrial period represents an almost global coherent variation of temperatures, with larger amplitudes over the continents and Northern Hemisphere. This mode also describes a large part of the spatial structure of the warming simulated in the 21st century. However, in the 21st century, regional departures from this spatial structure are also present and can be ascribed to atmospheric circulation responses to anthropogenic forcing in the last decades of the 21st century.
5. Pasini, Antonello, Massimo Lorè, and Fabrizio Ameli. “Neural network modelling for the analysis of forcings/temperatures relationships at different scales in the climate system.” Ecological Modelling 191.1 (2006): 58-67.  A fully non-linear analysis of forcing influences on temperatures is performed in the climate system by means of neural network modelling. Two case studies are investigated, in order to establish the main factors that drove the temperature behaviour at both global and regional scales in the last 140 years. In particular, our neural network model shows the ability to catch non-linear relationships among these variables and to reconstruct temperature records with a high degree of accuracy. In this framework, we clearly show the need of including anthropogenic inputs for explaining the temperature behaviour at global scale and recognise the role of El Niño southern oscillation for catching the inter-annual variability of temperature data. Furthermore, we analyse the relative influence of global forcing and a regional circulation pattern in determining the winter temperatures in Central England, showing that the North Atlantic oscillation represents the driven element in this case study. Our modelling activity and results can be very useful for simple assessments of relationships in the complex climate system and for identifying the fundamental elements leading to a successful downscaling of atmosphere–ocean general circulation models.
6. Meehl, Gerald A., Julie M. Arblaster, and Claudia Tebaldi. “Contributions of natural and anthropogenic forcing to changes in temperature extremes over the United States.” Geophysical Research Letters 34.19 (2007).  Observations averaged over the U.S. for the second half of the 20th century have shown a decrease of frost days, an increase in growing season length, an increase in the number of warm nights, and an increase in heat wave intensity. For the first three, a nine member multi‐model ensemble shows similar changes over the U.S. in 20th century experiments that combine anthropogenic and natural forcings, though the relative contributions of each are unclear. Here we show results from two global coupled climate models run with anthropogenic and natural forcings separately. Averaged over the continental U.S., they show that the observed changes in the four temperature extremes are accounted for with anthropogenic forcings, but not with natural forcings (even though there are some differences in the details of the forcings). This indicates that most of the changes in temperature extremes over the U.S. are likely due to human activity.
7. Zhou, Liming, et al. “Detection and attribution of anthropogenic forcing to diurnal temperature range changes from 1950 to 1999: comparing multi-model simulations with observations.” Climate Dynamics 35.7-8 (2010): 1289-1307.  Observations show that the surface diurnal temperature range (DTR) has decreased since 1950s over most global land areas due to a smaller warming in maximum temperatures (T _max) than in minimum temperatures (T _min). This paper analyzes the trends and variability in T _max, T _min, and DTR over land in observations and 48 simulations from 12 global coupled atmosphere-ocean general circulation models for the later half of the 20th century. It uses the modeled changes in surface downward solar and longwave radiation to interpret the modeled temperature changes. When anthropogenic and natural forcings are included, the models generally reproduce observed major features of the warming of T _max and T _min and the reduction of DTR. As expected the greenhouse gases enhanced surface downward longwave radiation (DLW) explains most of the warming of T _max and T _min while decreased surface downward shortwave radiation (DSW) due to increasing aerosols and water vapor contributes most to the decreases in DTR in the models. When only natural forcings are used, none of the observed trends are simulated. The simulated DTR decreases are much smaller than the observed (mainly due to the small simulated T _min trend) but still outside the range of natural internal variability estimated from the models. The much larger observed decrease in DTR suggests the possibility of additional regional effects of anthropogenic forcing that the models can not realistically simulate, likely connected to changes in cloud cover, precipitation, and soil moisture. The small magnitude of the simulated DTR trends may be attributed to the lack of an increasing trend in cloud cover and deficiencies in charactering aerosols and important surface and boundary-layer processes in the models.
8. Kaufmann, Robert K., et al. “Reconciling anthropogenic climate change with observed temperature 1998–2008.” Proceedings of the National Academy of Sciences 108.29 (2011): 11790-11793.  Given the widely noted increase in the warming effects of rising greenhouse gas concentrations, it has been unclear why global surface temperatures did not rise between 1998 and 2008. We find that this hiatus in warming coincides with a period of little increase in the sum of anthropogenic and natural forcings. Declining solar insolation as part of a normal eleven-year cycle, and a cyclical change from an El Nino to a La Nina dominate our measure of anthropogenic effects because rapid growth in short-lived sulfur emissions partially offsets rising greenhouse gas concentrations. As such, we find that recent global temperature records are consistent with the existing understanding of the relationship among global surface temperature, internal variability, and radiative forcing, which includes anthropogenic factors with well known warming and cooling effects.