Papers on CO2-temperature correlation

This is a list of papers on the correlation between carbon dioxide concentration and temperature. This subject was suggested by Brad Carpenter in the paperlist suggestion thread. The list is not complete, and will most likely be updated in the future in order to make it more thorough and more representative.

UPDATE (February 25, 2016): Stips et al. (2016) added. Thanks to Keith Pickering for pointing it out.
UPDATE (January 9, 2014): Kang & Larsson (2013) and Attanasio et al. (2013) added.
UPDATE (March 29, 2012): Attanasio (2012) and Attanasio et al. (2012)added.
UPDATE (October 31, 2010): Sun & Wong (1996), Stern & Kaufmann (1999), Verdes (2005), Smirnov & Mokhov (2009) and Kodra et al. (2010) added.

Modern climate

On the causal structure between CO2 and global temperature – Stips et al. (2016)
Abstract: We use a newly developed technique that is based on the information flow concept to investigate the causal structure between the global radiative forcing and the annual global mean surface temperature anomalies (GMTA) since 1850. Our study unambiguously shows one-way causality between the total Greenhouse Gases and GMTA. Specifically, it is confirmed that the former, especially CO2, are the main causal drivers of the recent warming. A significant but smaller information flow comes from aerosol direct and indirect forcing, and on short time periods, volcanic forcings. In contrast the causality contribution from natural forcings (solar irradiance and volcanic forcing) to the long term trend is not significant. The spatial explicit analysis reveals that the anthropogenic forcing fingerprint is significantly regionally varying in both hemispheres. On paleoclimate time scales, however, the cause-effect direction is reversed: temperature changes cause subsequent CO2/CH4 changes.
Citation: Adolf Stips, Diego Macias, Clare Coughlan, Elisa Garcia-Gorriz & X. San Liang (2016), Scientific Reports 6, Article number: 21691, doi:10.1038/srep21691.

Granger Causality Analyses for Climatic Attribution – Attanasio et al. (2013) “This review paper focuses on the application of the Granger causality technique to the study of the causes of recent global warming (a case of climatic attribution). A concise but comprehensive review is performed and particular attention is paid to the direct role of anthropogenic and natural forcings, and to the influence of patterns of natural variability. By analyzing both in-sample and out-of-sample results, clear evidences are obtained (e.g., the major role of greenhousegases radiative forcing in driving temperature, a recent causal decoupling between solar irradiance and temperature itself) together with interesting prospects of further research.” Alessandro Attanasio, Antonello Pasini, Umberto Triacca, Atmospheric and Climate Sciences, Vol. 3 No. 4, 2013, pp. 515-522. doi: 10.4236/acs.2013.34054. [Full text]

Testing for linear Granger causality from natural/anthropogenic forcings to global temperature anomalies – Attanasio (2012) “In this paper, we analyze the Granger causality from natural or anthropogenic forcings to global temperature anomalies. The lag-augmented Wald test is performed, and its robustness is also evaluated considering bootstrap method. The results show there is no-evidence of Granger causality from natural forcings to global temperature. On the contrary, a detectable Granger causality is found from anthropogenic forcings to global temperature confirming that greenhouse gases have an important role on recent global warming.” Alessandro Attanasio, Theoretical and Applied Climatology, DOI: 10.1007/s00704-012-0634-x.

A contribution to attribution of recent global warming by out-of-sample Granger causality analysis – Attanasio et al. (2012) “The topic of attribution of recent global warming is usually faced by studies performed through global climate models (GCMs). Even simpler econometric models have been applied to this problem, but they led to contrasting results. In this article, we show that a genuine predictive approach of Granger analysis leads to overcome problems shown by these models and to obtain a clear signal of linear Granger causality from greenhouse gases (GHGs) to the global temperature of the second half of the 20th century. In contrast, Granger causality is not evident using time series of natural forcing.” Alessandro Attanasio, Antonello Pasini, Umberto Triacca, Atmospheric Science Letters, Volume 13, Issue 1, pages 67–72, January/March 2012, DOI: 10.1002/asl.365. [Full text]

Exploring Granger causality between global average observed time series of carbon dioxide and temperature – Kodra et al. (2010) “Detection and attribution methodologies have been developed over the years to delineate anthropogenic from natural drivers of climate change and impacts. A majority of prior attribution studies, which have used climate model simulations and observations or reanalysis datasets, have found evidence for human-induced climate change. This papers tests the hypothesis that Granger causality can be extracted from the bivariate series of globally averaged land surface temperature (GT) observations and observed CO₂ in the atmosphere using a reverse cumulative Granger causality test. This proposed extension of the classic Granger causality test is better suited to handle the multisource nature of the data and provides further statistical rigor. The results from this modified test show evidence for Granger causality from a proxy of total radiative forcing (RC), which in this case is a transformation of atmospheric CO₂, to GT. Prior literature failed to extract these results via the standard Granger causality test. A forecasting test shows that a holdout set of GT can be better predicted with the addition of lagged RC as a predictor, lending further credibility to the Granger test results. However, since second-order-differenced RC is neither normally distributed nor variance stationary, caution should be exercised in the interpretation of our results.” [Full text]

From Granger causality to long-term causality: Application to climatic data – Smirnov & Mokhov (2009) “Quantitative characterization of interaction between processes from time series is often required in different fields of natural science including geophysics and biophysics. Typically, one estimates “short-term” influences, e.g., the widely used Granger causality is defined via one-step-ahead predictions. Such an approach does not reveal how strongly the “long-term” behavior of one process under study is affected by the others. To overcome this problem, we introduce the concept of long-term causality, which extends the concept of Granger causality. The long-term causality is estimated from data via empirical modeling and analysis of model dynamics under different conditions. Apart from mathematical examples, we apply both approaches to find out how strongly the global surface temperature (GST) is affected by variations in carbon dioxide atmospheric content, solar activity, and volcanic activity during the last 150 years. Influences of all the three factors on GST are detected with the Granger causality. However, the long-term causality shows that the rise in GST during the last decades can be explained only if the anthropogenic factor (CO₂) is taken into account in a model.” [Full text]

Correlation Analysis between Global Temperature Anomaly and two main factors (CO₂ and aa index) – Moon (2008) “We have made the correlation analysis between gloabl temperature anomaly and two main factos: geomagnetic activity (aa index) and CO₂ content. … These results imply that the CO₂ effect become very important since at least 1990.”

Is Granger causality analysis appropriate to investigate the relationship between atmospheric concentration of carbon dioxide and global surface air temperature? – Triacca (2005) “Many time series based studies use Granger causality analysis in order to investigate the connection between atmospheric carbon-dioxide concentrations and global mean temperature. This note re-examines the causal relationship between these variables and shows the inappropriateness of the Granger test to the problem under investigation.”

Assessing causality from multivariate time series – Verdes (2005) “In this work we propose a general nonparametric test of causality for weakly dependent time series. More precisely, we study the problem of attribution, i.e., the proper comparison of the relative influence that two or more external dynamics trigger on a given system of interest. We illustrate the possible applications of the proposed methodology in very different fields like physiology and climate science.”

Econometric analysis of global climate change – Stern & Kaufmann (1999) “This paper reports on research that applies econometric time series methods to the analysis of global climate change. The aim of this research was to test hypotheses concerning the causes of the historically observed rise in global temperatures. Longer term applications include quantification of the contribution of different forcing variables to historic warming and use of the model as a module in integrated assessment. Research to date has comprised three stages. In the first stage we used the concept of Granger causality and differences between the temperature record in the northern and southern hemispheres to investigate the causes of temperature increase. In the second stage we tested various global change time series for the presence of stochastic trends. We found that most series contain a stochastic trend with the greenhouse gas series containing I(2) stochastic trends. In the third stage we developed a structural time series to investigate some of the hypotheses suggested by the earlier stages and further tested for the presence of an I(2) trend in hemispheric temperature series. We found that the two temperature series share a common I(2) stochastic trend that may have its source in radiative forcing due to greenhouse gases. There is a second non-stationary component that appears only in the northern hemisphere and appears to be related to radiative forcing due to anthropogenic sulphur emissions.”

A Bayesian Statistical Analysis of the Enhanced Greenhouse Effect – Tol & De Vos (1998) “This paper demonstrates that there is a robust statistical relationship between the records of the global mean surface air temperature and the atmospheric concentration of carbon dioxide over the period 1870–1991. As such, the enhanced greenhouse effect is a plausible explanation for the observed global warming. Long term natural variability is another prime candidate for explaining the temperature rise of the last century. Analysis of natural variability from paleo-reconstructions, however, shows that human activity is so much more likely an explanation that the earlier conclusion is not refuted.” [Full text]

Global-scale temperature patterns and climate forcing over the past six centuries – Mann et al. (1998) “Time-dependent correlations of the reconstructions with time-series records representing changes in greenhouse-gas concentrations, solar irradiance, and volcanic aerosols suggest that each of these factors has contributed to the climate variability of the past 400 years, with greenhouse gases emerging as the dominant forcing during the twentieth century.” [Full text]

Dependence of global temperatures on atmospheric CO₂ and solar irradiance – Thomson (1997) “Changes in global average temperatures and of the seasonal cycle are strongly coupled to the concentration of atmospheric CO₂. I estimate transfer functions from changes in atmospheric CO₂ and from changes in solar irradiance to hemispheric temperatures that have been corrected for the effects of precession. They show that changes from CO₂ over the last century are about three times larger than those from changes in solar irradiance.” [Full text]

Global Warming and Global Dioxide Emission: An Empirical Study – Sun & Wong (1996) “In this paper, the dynamic relationship between global surface temperature (global warming) and global carbon dioxide emission (CO₂) is modelled and analyzed by causality and spectral analysis in the time domain and frequency domain, respectively. Historical data of global CO₂ emission and global surface temperature anomalies over 129 years from 1860–1988 are used in this study. The causal relationship between the two phenomena is first examined using the Sim and Granger causality test in the time domain after the data series are filtered by ARIMA models. The Granger causal relationship is further scrutinized and confirmed by cross-spectral and multichannel spectral analysis in the frequency domain. The evidence found from both analyses proves that there is a positive causal relationship between the two variables. The time domain analysis suggests that Granger causality exists between global surface temperature and global CO₂ emission. Further, CO₂ emission causes the change in temperature. The conclusions are further confirmed by the frequency domain analysis, which indicates that the increase in CO₂ emission causes climate warming because a high coherence exists between the two variables. Furthermore, it is proved that climate changes happen after an increase in CO₂ emission, which confirms that the increase in CO₂ emission does cause global warming.”

Interannual extremes in the rate of rise of atmospheric carbon dioxide since 1980 – Keeling et al. (1995) Abstract doesn’t say it, but they make an interesting comparison with carbon dioxide record and temperature record. “The marked discrepancy between the predicted and observed anomalies on the decadal timescale after 1980, and differences throughout the record on shorter timescales, may be related to climate forcing involving air temperature, because anomalous variations in CO₂ and in temperature have tended to occur coherently, as suggested by comparing Fig. 2a with Fig. 2b. Many of these coherent anomalies are associated with El Niño events (arrows in Fig. 2a), but they also occur on the decadal timescale (solid curves) as previously noted by Keeling et al. (see p. 211 of ref. 1), and confirmed by rigorous analysis of coherence.” [Full text]

Coherence established between atmospheric carbon dioxide and global temperature – Kuo et al. (1990) “The hypothesis that the increase in atmospheric carbon dioxide is related to observable changes in the climate is tested using modern methods of time-series analysis. The results confirm that average global temperature is increasing, and that temperature and atmospheric carbon dioxide are significantly correlated over the past thirty years. Changes in carbon dioxide content lag those in temperature by five months.”

Past climate

What is the link between temperature and carbon dioxide levels? A Granger causality analysis based on ice core data – Kang & Larsson (2013) “We use statistical methods to analyze whether there exists long-term causality between temperature and carbon dioxide concentration. The analysis is based on a the Vostok Ice Core data from 400,000 to 6,000 years ago, extended by the EPICA Dome C data which go back to 800,000 years ago. At first, to make the data equidistant, we reconstruct it by linear interpolation. Then, using an approximation of a piecewise exponential function, we adjust for a deterministic trend. Finally, we employ the Granger causality test. We are able to strongly reject the null hypothesis that carbon dioxide concentration does not Granger cause temperature as well as the reverse hypothesis that temperature does not Granger cause carbon dioxide concentration.” Jian Kang, Rolf Larsson, Theoretical and Applied Climatology, July 2013, DOI: 10.1007/s00704-013-0960-7.

Stable Carbon Cycle–Climate Relationship During the Late Pleistocene – Siegenthaler et al. (2005) “A record of atmospheric carbon dioxide (CO₂) concentrations measured on the EPICA (European Project for Ice Coring in Antarctica) Dome Concordia ice core extends the Vostok CO₂ record back to 650,000 years before the present (yr B.P.). Before 430,000 yr B.P., partial pressure of atmospheric CO₂ lies within the range of 260 and 180 parts per million by volume. This range is almost 30% smaller than that of the last four glacial cycles; however, the apparent sensitivity between deuterium and CO₂ remains stable throughout the six glacial cycles, suggesting that the relationship between CO₂ and Antarctic climate remained rather constant over this interval.” [Full text]

Timing of Atmospheric CO₂ and Antarctic Temperature Changes Across Termination III – Caillon et al. (2003) “We have measured the isotopic composition of argon in air bubbles in the Vostok core during Termination III (~240,000 years before the present). This record most likely reflects the temperature and accumulation change, although the mechanism remains unclear. The sequence of events during Termination III suggests that the CO₂ increase lagged Antarctic deglacial warming by 800 ± 200 years and preceded the Northern Hemisphere deglaciation.”

Carbon dioxide and climate over the past 300Myr – Retallack (2002) “Large and growing databases on these proxy indicators support the idea that atmospheric CO₂ and temperature are coupled. In contrast, CO₂–temperature uncoupling has been proposed from geological time-series of carbon isotopic composition of palaeosols and of marine phytoplankton compared with foraminifera, which fail to indicate high CO₂ at known times of high palaeotemperature. Failure of carbon isotopic palaeobarometers may be due to episodic release of CH₄, which has an unusually light isotopic value (down to −110[promille], and typically −60[promille]δ13C) and which oxidizes rapidly (within 7–24 yr) to isotopically light CO₂.” [Full text]

The phase relations among atmospheric CO₂ content, temperature and global ice volume over the past 420 ka – Mudelsee (2001) “Over the full 420 ka of the Vostok record, CO2 variations lag behind atmospheric temperature changes in the Southern Hemisphere by 1.3±1.0 ka, and lead over global ice-volume variations by 2.7±1.3 ka. However, significant short-term changes in the lag of CO₂ relative to temperature, subsequent to Terminations II and III, are also detected.” [Full text]

Covariation of carbon dioxide and temperature from the Vostok ice core after deuterium-excess correction – Cuffey & Vimeux (2001) “Here we incorporate measurements of deuterium excess from Vostok in the temperature reconstruction and show that much of the mismatch is an artefact caused by variations of climate in the water vapour source regions. Using a model that corrects for this effect, we derive a new estimate for the covariation of CO₂ and temperature, of r² = 0.89 for the past 150 kyr and r² = 0.84 for the period 350–150 kyr ago. Given the complexity of the biogeochemical systems involved, this close relationship strongly supports the importance of carbon dioxide as a forcing factor of climate. Our results also suggest that the mechanisms responsible for the drawdown of CO₂ may be more responsive to temperature than previously thought.”

Atmospheric CO₂ Concentrations over the Last Glacial Termination – Monnin et al. (2001) “A record of atmospheric carbon dioxide (CO₂) concentration during the transition from the Last Glacial Maximum to the Holocene, obtained from the Dome Concordia, Antarctica, ice core, reveals that an increase of 76 parts per million by volume occurred over a period of 6000 years in four clearly distinguishable intervals. The close correlation between CO₂ concentration and Antarctic temperature indicates that the Southern Ocean played an important role in causing the CO₂ increase. However, the similarity of changes in CO₂ concentration and variations of atmospheric methane concentration suggests that processes in the tropics and in the Northern Hemisphere, where the main sources for methane are located, also had substantial effects on atmospheric CO₂ concentrations.”

Atmospheric CO₂ concentration and millennial-scale climate change during the last glacial period – Stauffer et al. (1998) “To compare the rapid climate changes recorded in the Greenland ice with the global trends in atmospheric CO₂ concentrations as recorded in the Antarctic ice, an accurate common timescale is needed. Here we provide such a timescale for the last glacial period using the records of global atmospheric methane concentrations from both Greenland and Antarctic ice. We find that the atmospheric concentration of CO₂ generally varied little with Dansgaard–Oeschger events (<10 parts per million by volume, p.p.m.v.) but varied significantly with Heinrich iceberg-discharge events (20 p.p.m.v.), especially those starting with a long-lasting Dansgaard–Oeschger event.” [Full text]

Closely related

Papers on GHG role in historical climate changes is very closely related list of papers, some papers exist in both lists.