Deciphering the Palaeocene–Eocene thermal maximum by Granger causality test

doi:10.21203/rs.3.rs-789514/v1

The Palaeocene–Eocene thermal maximum is a global warming period (~ 56 Ma), which is marked by a sharp negative carbon isotope excursion (CIE) that caused by the injection of massive isotopically-light carbon into the ocean-atmosphere. It is often considered that the carbon injection caused global warming. However, several studies have suggested that warming and environmental perturbations precede the onset of the CIE. Here we present Granger test to investigate the detailed mechanisms of this event. We show a shift from climate-warming driving carbon-emission scenario to a scheme in which carbon-injection causing global-warming during the CIE. The initial carbon emission might be from methane hydrates dissociation and/or permafrost thawing, possibly linked with astronomical paced warming. This change of causal direction may result from the warming feedback of the emitted carbon and additional carbon from other sources, such as volcanism, bolide impact, oxidation of marine organic matter, and wildfires burning peatlands.

Climate Analysis and Modeling

Paleoecology

climate warming

carbon emission

gas hydrate

oxygen isotope

The Paleocene–Eocene thermal maximum (PETM, ~ 56 Ma) is a period of rapid and prolonged global warming¹. Paleothermometer proxies (e.g. δ¹⁸O (oxygen isotope) and TEX₈₆ (‘tetraether index’ of tetraether lipids consisting of 86 carbon atoms)) analyses suggest that global temperature rise approximately 5–8°C during this interval^2,3. Associated with the climate warming is a dramatic negative carbon isotopic excursion (CIE) of 3–5‰⁴, which has been interpreted to be caused by the injection of massive ¹³C-depleted carbon into the ocean and atmosphere⁵. It is generally considered that the massive carbon injection into the ocean-atmosphere system caused global warming and environmental perturbations^6,7. However, several studies have found that global warming and environment change precedes the carbon isotope excursion, and proposed that the initial warming may have triggered the release of the isotopically-light carbon sources^8 − 14. Thus, despite strong correlation exists between the carbon cycle perturbation and the global warming and environment change, the exact driving mechanism between these factors still remains unclear.

In this study, we use the Granger causality test to further investigate the mechanisms between carbon release (inferred from δ¹³C data) and global warming (reconstructed from δ¹⁸O data). The Granger causality test is first introduced in econometrics by Nobel Prize winner Clive W. J. Granger¹⁵. It is used to examine the causality relationship between variables of time series. In brief, if variable Y can be explained by lagged variable X in the statistic model, it is then considered that X granger-cause Y. This method has been used to investigate the causality between greenhouse gas concentrations and global temperature, and has yielded different conclusions^16-20. Furthermore, in addition to data from 1850 to present day, his method has been applied to climatological series from the more recent past (e.g. time series data recovered from ice cores, covering ~ 800 kyr)^21-25. In this study, we explore the potential application of this method to deep-time climatological data recovered from core sediments and discuss its limitations.

Geochemical data generated of samples collected from the lower part of the drill core to the upper part would form a time series dataset. In this study, previously published data from the Millville core (ODP 174AX) are analysed, which is drilled in the expanded New Jersey shelf in the North Atlantic Ocean. Coupled δ¹³C and δ¹⁸O data are available across the Paleocene–Eocene interval of the drill core at 2 mm gap (Fig. 1)²⁶. Based on sedimentation rates estimated from the nearby area, the time gap is about 20–25 years¹². However, carbon cycle-climate modelling has estimated the sampling resolution of ~ 40 years¹⁴. The exact duration between two adjacent data points is hard to be precisely quantified. However, this would not affect the test result, as the sequence of the data is not changed. Oxygen isotope (δ¹⁸O) varies as a result of temperature fluctuations and thus paleoclimate can be reconstructed by analysing δ¹⁸O of the sediments²⁷. Carbon isotope record is used to reflect the addition of δ¹³C-depleted carbon into the ocean and atmosphere, although they do not follow a linear relationship²⁸. The data are divided into four intervals, with the first interval (Q1) covers the data before the onset of the CIE, the second and third intervals (Q2 and Q3) cover the onset of the CIE²⁶ and the fourth interval (Q4) covers the data after the CIE. The boundary between Q2 and Q3 is drawn based on the carbon isotope profile, where a pulse of large negative CIE occurred within the onset of the PETM CIE (Fig. 1).

3.1 Granger causality test

Granger causality was first introduced in econometrics to test potential causality relationships between variables of time series data¹⁵. It is based on incremental forecasting power. Here we consider two nested models, the unrestricted regression model

$${\text{Y}}{\text{t}}={{\mu }}{1}+ \sum {\text{i}=1}^{\text{k}}{\text{a}}{\text{j}}{\text{Y}}{\text{t}-\text{i}}+ \sum {\text{i}=1}^{\text{k}}{\text{b}}{\text{i}}{\text{X}}{\text{t}-\text{i}}+ {{\epsilon }}_{\text{t}}$$

and the restricted model

$${\text{Y}}{\text{t}}={{\mu }}{2}+ \sum {\text{i}=1}^{\text{k}}{\text{c}}{\text{i}}{\text{Y}}{\text{t}-\text{i}}+ {\text{v}}{\text{t}}$$

where µ₁ and µ₂ are constants; a, b, and c are the coefficients of the models; ε_t and v_t are univariate white noise; i is the lag of the models and k is the highest lag. For example, Y_t is the current sample, and Y_t-1 is the sample before Y_t. Y_t-1 is one sampling gap stratigraphically lower than sample Y_t. The Granger causality relationship between variable Y and variable X is determined by comparing the estimation accuracies for this climatic factor by the unrestricted and the restricted models. The null hypothesis of noncausality corresponds to:

$${\text{H}}{0}:{\text{B}}{1}= {\text{B}}{2}=\dots = {\text{B}}{\text{k}}=0$$

A significant statistics (P-value < 0.05) implies that the null hypothesis is rejected. The increase in the explanatory power of the unrestricted model (including variable X) compared to the restricted model (not including variable X) suggests causality from X to Y. Before we perform a Granger causality test, it is necessary to determine if the time series is stationary, as nonstationary of time series may cause spurious causality results²⁹. This can usually be done with the unit root test process³⁰. If the series has a unit root, then the time series is not stationary. Nonstationary time series data can achieve stationary by taking the first difference. For nonstationary time series data, the Toda-Yamamoto method can be applied³¹. This procedure would require the maximum order of integration (d) of the investigated series. The optimal lag number is selected by using Akaike information criteria (AIC)³².

3.2 Unit root test

In this study, the augmented Dicky–Fuller (ADF) test method is used for unit root test³⁰. The null hypothesis is that the series has a unit root and contains a stochastic trend. The model of the augmented Dickey–Fuller (ADF) test is specified as follow:

$${\varDelta \text{y}}{\text{t}}={\alpha } + {\beta }\text{t} + {\gamma }{\text{y}}{\text{t}-1}+ \sum {\text{i} = 1}^{\text{p}}{{\delta }}{\text{i}}{\varDelta \text{y}}{\text{t}-1}+ {\text{w}}{\text{t}}$$

where y is the investigated variable and w_t is a random error term. The lagged first differences of the dependent variables provide correction for possible serial correlation. The optimum number of lags (p), in this paper, was selected based on log likelihood³³, Hannan-Quinn criterion³⁴, and Akaike information Criterion³². The null hypothesis is given by γ = 0. The alternative hypothesis is that the series is stationary. Unit root tests are also performed for cases 1) without trend with constant and 2) without trend or constant and the decision is made based on three-step ADF test³⁵. Unit root test was performed on the data for the whole period and the four quarters individually with results listed in Table 1.

Table 1. 3-step ADF test results for d¹³C and d¹⁸O data.

Time series	t + c ADF P-value	P-value of t	c ADF P-value	1 difference data t + c ADF P-value	Conclusion
Alld¹³C	0.0847 (3)	0.002		0.0000 (7)	I(1)
Alld¹⁸O	0.0000 (1)				I(0)
Q1d¹³C	0.0000 (0)				I(0)
Q1d¹⁸O	0.2707 (1)	0.8799	0.0095 (0)		I(0)
Q2d¹³C	0.0214 (2)				I(0)
Q2d¹⁸O	0.0003 (0)				I(0)
Q3d¹³C	0.0025 (0)				I(0)
Q3d¹⁸O	0.0016 (0)				I(0)
Q4d¹³C	0.0000 (0)				I(0)
Q4d¹⁸O	0.0003 (0)				I(0)

Notes: The numbers in the parentheses indicate the optimal lag length suggested by the Akaike Information Criterion (AIC). t + c means the estimation with trend and constant. c means estimation with constants only.

In order to provide some robustness in deciding the stationarity of the series, additional tests like Phillips–Perron (PP), Kwiatkowski–Phillips–Schmidt–Shin (KPSS) and Dickey–Fuller Generalized Least Squares (DF–GLS) are conducted^36-39. The PP and DF–GLS unit root tests have a null hypothesis of a unit root process, while the KPSS test have a null hypothesis of a stationary series. These results are listed in Table 2.

Table 2. Additional unit root test results.

Time series		PP	DF-GLS	KPSS
All d¹³C	c	-1.19	1.26	1.89
	c+t	-6.31	-1.34	0.23
	none	-0.87
All d¹⁸O	c	-2.84*	-0.10	1.80***
	c+t	-8.94***	-4.43***	0.11
	none	0.73
Q1 d¹³C	c	-5.53***	-3.63***	0.69**
	c+t	-6.28***	-6.38***	0.07
	none	-0.12	-	-
Q1 d¹⁸O	c	-3.31**	-2.44**	0.18
	c+t	-3.31*	-3.56**	0.16
	none	-0.40	-	-
Q2 d¹³C	c	-4.35***	-0.85	0.95***
	c+t	-5.52***	-2.62	0.13
	none	-4.12***	-	-
Q2 d¹⁸O	c	-4.51***	-2.13**	0.77***
	c+t	-5.20***	-4.94***	0.08
	none	0.21	-	-
Q3 d¹³C	c	-3.17**	-2.33**	0.74***
	c+t	-4.72***	-4.62***	0.05
	none	-0.03	-	-
Q3 d¹⁸O	c	-4.61***	-2.25**	0.42
	c+t	-5.03***	-4.86***	0.08
	none	-0.05	-	-
Q4 d¹³C	c	-6.15***	-1.50	0.74***
	c+t	-7.12***	-7.05***	0.07
	none	0.72	-	-
Q4 d¹⁸O	c	-4.89***	-0.23	0.29
	c+t	-5.10***	-1.52	0.07
	none	0.80	-	-

***Significant at 1%.**Significant at 5%. *Significant at 10% level. The lower of the P-value, the higher the significant level. Notes: The lag lengths were determined by the Akaike Information Criteria (AIC) for the DF-GLS test, while the bandwidths in the Phillips–Perron (PP) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) tests were determined by the method of Newey–West. Critical values for the DF-GLS and PP tests are based upon MacKinnon (1996)³⁸. Critical values for the KPSS test are from Kwiatkowski et al. (1992)³⁷.

Granger causality test was performed on the d¹³C and d¹⁸O data of the whole sampled period and each individual interval. Both directions of the causality relationship (i.e. from d¹³C to d¹⁸O and vice versa) were examined and the results are listed in Table 3.

Table 3. Results of Granger causality test.

periods	optimum lag	P-value	maximum order of integration (d)
from d¹³C to d¹⁸O:
all	3	0.2738	1
Q4	1	0.9186	0
Q3	1	0.0763*	0
Q2	1	0.0808*	0
Q1	1	0.0120**	0
from d¹⁸O to d¹³C:
all	3	0.3444	1
Q4	1	0.3170	0
Q3	1	0.7131	0
Q2	1	0.0455**	0
Q1	1	0.8618	0

^**Significant at 5%. ^*Significant at 10% level. The lower of the P-value, the higher the significant level.

4.1 Stationarity of the series data

It is known from other physical variables and more-detailed studies of the Earth system that climate variability itself is a function of the climate, and that the massive PETM transition, therefore, tend to be expected to involve a non-stationary transition. It has been proposed that the Millville data series are not stationary¹⁴. Based on Fig. 1, it is intuitive to conclude that both the δ¹³C and δ¹⁸O data in Q1 and Q4 are stationary, while Q2 and Q3 (i.e. the PETM transition) are not stationary. However, the ADF unit root test results (Table 1) and the majority of other tests suggest that δ¹³C and δ¹⁸O data of the Q2 and Q3 quarters are stationary, despite the whole period δ¹³C data are not stationary (Table 2). Likewise, stationarity has also been suggested for recent glaciation and interglaciation transitions that are tend to be assumed nonstationary^22,40. The difference between stationary and nonstationary conclusions drawn by different authors has been attributed to the differing time-spans of data analysed²².

4.2 Causality test results

The first quarter (Q1) covers the majority of the data before the CIE (Fig. 1). In theory, the δ¹³C and δ¹⁸O should behave independently in steady-state. However, a causality relationship is detected from δ¹³C to δ¹⁸O (Fig. 1, Table 3). Generally, the δ¹³C driving δ¹⁸O perturbations can be explained by carbon injection causing climate warming. Nonetheless, the δ¹⁸O data display a trend of cooling instead of warming. A pre-PETM cooling event has also been reported in the Eastern North Sea Basin⁴¹. This cooling has been linked with large scale volcanic eruption associated with the North Atlantic Igneous Province (NAIP). Large amounts of sulphuric aerosol acid together with a small amount of isotopically-light carbon into the atmosphere may ultimately exert as climate cooling effect because sulphur can increase planetary albedo⁴¹.

The second quarter (Q2) covers the initial excursions for both the δ¹³C and δ¹⁸O data (Fig. 1). Previously, the theory that global warming driving the carbon release mainly comes from observed geological records that the proxies for environmental perturbations start to shift before the CIE^9-13. It usually needs expanded sections with high sedimentary rate to clearly discern the sequence of different datasets. For example, at the Wilson Lake section (New Jersey shelf), climate warming precedes the onset of the CIE as inferred from the TEX₈₆ thermometer record¹². This is also supported by the biotic change that the onset of the Apectodinium (a subtropical genus) acme is detected ~ 40 cm below the CIE¹². The nearby Bass River section also shows a similar pattern, with half of the total warming occurred below the CIE¹². The Millville site is close to the Wilson Lake and Bass River sections, however, δ¹³C and δ¹⁸O data from this section start to shift simultaneously (Fig. 1). It is not feasible to spot their sequence and causality relationship based on the isotope stratigraphy profile alone. Even so, our Granger causality test result is able to show a significant (at 5%) Granger causality from the δ¹⁸O to δ¹³C in this period (Fig. 1; Table 3), indicating the mechanism that climate warming driving the carbon release. Scenarios that environmental change may cause the onset of the CIE have also been reported for other sections in southwest Pacific Ocean^9,12, North Sea^11,12, high Arctic¹⁰, Southern Ocean¹³ and North America⁴².

Climate warming causing the carbon injection that responsible for the CIE is consistent with the hypothesis of methane release from gas hydrate system^43,44. Gas hydrates are crystalline compounds that formed under high-pressure how temperature conditions, mainly containing water and CH₄, with δ¹³C typically < − 60‰⁴⁵. Large volumes of gas hydrates are stored in continental slope and its size is sensitive to seafloor temperature change. In the event of global warming, enormous gas hydrates were converted to free methane gas. The massive amount of free ¹³C-depleted methane would be able to drive the observed CIE. Permafrost thawing is another alternative/additional source of carbon⁴⁶. A substantial amount of soil organic carbon was stored in the Antarctica and Circum-Arctic, and this terrestrial carbon is readily discharged when the temperature reached a certain threshold. The initial climate change might be caused by Earth’s astronomical configurations that favourable inducing warming, which is the original proposed mechanism of the methane hydrate dissociation hypothesis^44,47,48. A weak causality from δ¹³C to δ¹⁸O (at 10%) has also been found in this interval. This can be interpreted by the positive feedback from the carbon release. Once a significant amount of methane was released, the increased concentration of CH₄ and CO₂ (by oxidization of CH₄) in the atmosphere would be able to further warm the ocean.

In the third quarter (Q3), only the causality relationship from δ¹³C to δ¹⁸O is significant (at 10%, Table 3). This indicates that the carbon emission from submarine gas hydrates and permafrost may have reached its maximum. The geological process has shifted from a warming-driven carbon releasing dominated scenario to the scheme that carbon release is driving the global warming and environmental changes. This shift of driving mechanism might be caused by the positive feedback of the released carbon from gas hydrates destabilization and/or permafrost thawing, together with additional carbon injection from sources such as volcanic outgassing and thermogenic volatile and methane during the emplacement of the NAIP^49,50, wildfires burning peatlands⁵¹ and oxidation of organic matter in shallow continental seaways⁵².

When coming into the fourth quarter (Q4), there is no causal relationship between the δ¹³C and δ¹⁸O data, despite that this interval is still at the ‘body’ of the CIE (Fig. 1, Table 3). It is possible that each profile of δ¹³C and δ¹⁸O is progressing independently within their own cycle, or only minor causality exists that is not detected by this method. Over the whole investigated period, no causality exists for the δ¹³C and δ¹⁸O data (Fig. 1). This might result from the fact that there are multiple directions of causality within the whole period. We have noted several large gaps in the data due to the CaCO₃ dissolution⁵³. However, the effect of the missing data is hard to evaluate.

The above discussion is based on assumption of stationary Q2 and Q3 interval series data. We acknowledge that some unit root test results do not suggest stationarity of the series, although the majority of unit root tests yielded stationarity (Tables 1 and 2). In the case of nonstationarity, these data would achieve stationary by taking the first difference – I(1). The Toda–Yamashita method was then applied to investigate the causality for data in Q2 and Q3. Results suggest that the significant causality previously found on the level data no longer exist (Table 3). Nonetheless, a relatively small P-value is found from δ¹⁸O to δ¹³C for Q2 (0.1305) and from δ¹³C to δ¹⁸O for Q3 (0.1176) that have the same direction as previous Granger test results for the level data (Table 2, 3). In addition, from Table 2’s results, we found supporting evidence that δ¹⁸O and δ¹³C are stationary time series by using different unit-root testing methods (PP, DF-GLS and KPSS).

4.3 Limitations

4.3.1 Quarters’ boundaries and data size

Granger causality result suggests that the whole time series data of δ¹³C and δ¹⁸O show no significant causal relations, and that significant causality only emerges when pieces of the data are separated from each other into "quarters" (Fig. 1). The choice of these quarters is clearly influenced by the authors' interpretation. We chose the quarters based on the behaviour of the carbon and oxygen isotope trends, i.e. before and after the PETM excursions (Q1 and Q4; Fig. 1). The PETM excursion is further divided into two parts (Q2 and Q3) by another obviously dramatic carbon isotope shift. However, even with the reference to the same criteria, location of the boundaries would be different by each observer and thus the result of the test would inevitably be affected.

In addition to the uncertainty regarding the quarters’ boundaries, division of the dataset would also reduce the data size. We acknowledge that the data size is not large (281 for each series), compared with other subjects where this method is applied, like economic studies (e.g., research about the stock market). The fact that significance was only found in separated quarters rather than the whole series further indicates the notion of "P-hacking", i.e., if enough datasets are tested, a low P-value is inevitably found⁵⁴. However, as previously stated, we divide the dataset based on background geological information about the PETM²⁶ and observable jumps in the scatter plot (Fig. 1), rather than purposely reporting significant P-values.

Inferred causalities are based on local δ¹³C and δ¹⁸O profiles from Millville. Although these profiles are largely controlled by global carbon cycle and climate change, we need to note that other sections may not have a similar profile. Thus additional studies on data from multiple sections would further validate the application of this method and the interpretation of the results. However, Millville is the only section that currently has cm-resolution bulk isotope records. Nonetheless, the changes in δ¹³C and δ¹⁸O records are consistant with most other perlagic sequences and foraminifer isotope data from neaby PETM Sect. ^14,55-57.

4.3.2 Linearity and potential omitted variables

To apply the granger test, an underlying assumption is that the δ¹³C and δ¹⁸O data have a linear relationship over this interval, which is difficult to characterize in the geological record. It is known that δ¹³C and δ¹⁸O data vary together in geological records, showing the interactions of geological processes^27,58. δ¹³C and δ¹⁸O are proxies of the behaviour of certain elements of the climate system, and are probably not appropriately characterized as having a direct cause and effect relationship. If they are causally involved, there are certainly other variables that are omitted in the bivariate system, such as pCO₂⁵⁹. To put this in a simplified PETM scenario, the δ¹³C shift was driven by addition of isotopically-light carbon (¹³C depleted) into the ocean and atmosphere – a process would unavoidably increase the pCO₂ level and the temperature. The carbon emission could also be caused by temperature rise as discussed previously. The oxygen isotope fractionation of the seawater (and thus the carbonates) is linked with temperature, and paleotemperature can be reconstructed with oxygen isotope data using some sort of equations (e.g., T (°C) = 16.5–4.3(δ¹⁸O_CaCO3 - δ18O_w-AMW) + 0.14(δ¹⁸O_CaCO3 - δ¹⁸O_w-AMW)²)⁶⁰. There are methods that can be used to estimate ancient pCO₂ levels, however, that would generally require other geochemical proxies (e.g. boron isotopes), and may involve large error with the estimation. Assuming linear relationship is not contradicting the true general co-movements between δ¹³C and δ¹⁸O, after controlling for structure breaks of the data. However, we would like to emphasise that the real geological scenario would be much more complicated than that as explained above.

4.3.3 Age-model

Granger causality is typically applied to time series whose timing is well known. Unlike recent monitored climate series data, climate series data recovered from drill cores involve some sort of uncertainty regarding the timing. A constant sedimentation rate (thus a linear depth-time translation) is obviously difficult to meet across this interval. According to nearby area sedimentation rates, the time gap is calculated to be about 20–25 years¹². However, Zeebe et al., (2016)¹⁴ estimated a sampling resolution of ~ 40 years based on carbon cycle-climate modelling. Indeed, numerous studies have suggested highly variable sedimentation rates during the PETM as a response to hydrological perturbations⁶¹. However, our unequal spaced data is not affecting our causality's conclusion under linear's hypothesis, since our data has neither serious missing observations' problem nor high density of observations in the same period.

In summary, the Granger causality test suggests that the initial carbon release of the CIE might be caused by astronomical paced climate warming^8,46,47. This causality relationship was then reversed to carbon emission driving the climate warming in the later stage of the CIE, possibly due to extra carbon liberated from other sources including volcanic and thermogenic volatile and methane⁶², submarine gas hydrates dissociation^43,44, decomposition of permafrost⁴⁶, desiccation of a large epicontinental sea⁵² and wildfires burning peatlands⁵¹. This study demonstrates the potential application of Granger causality test in deep-time climate research to investigate the detailed mechanisms that drive climate change in Earth history. Limitations of applying Granger causality test include stationarity time-scale of the data series, which are difficult to characterize for geological data. Furthermore, unlike modern monitored data, geological data derived from geochemistry analyses of core samples are generally sparse.

Acknowledgments

Z.L. is grateful for the funding of GIG Head grant.

Data availability

All geochemical data used in this study are from already published data (Wright and Schaller, 2013) and properly cited.

Author contributions

Z.L., H.L and W.L designed the study. Z.L, Y.H. and X.J. performed the statistical analysis. All authors contributed to the interpretation of the data. Z.L. and W.L. wrote the paper with input from all authors.

Competing interests

The authors declare no competing interests.

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No competing interests reported.

Deciphering the Palaeocene–Eocene thermal maximum by Granger causality test

Status:

Version 1

Abstract

Figures

1 Introduction

2 Dataset

3 Methodology

3.1 Granger causality test

4 Results And Discussion

4.1 Stationarity of the series data

4.2 Causality test results

4.3 Limitations

4.3.1 Quarters’ boundaries and data size

4.3.2 Linearity and potential omitted variables

4.3.3 Age-model

5 Conclusions

Declarations

References

Additional Declarations

Status:

Version 1