Time-scale and state dependence of the carbon-cycle feedback to climate

Abstract

Climate and atmospheric CO₂ concentration are intimately coupled in the Earth system: CO₂ influences climate through the greenhouse effect, but climate also affects CO₂ through its impact on the amount of carbon stored on land and in the ocean. The change in atmospheric CO₂ as a response to a change in temperature ($\varDelta CO_{2}/\varDelta T$) is a useful measure to quantify the feedback between the carbon cycle and climate. Using an ensemble of experiments with an Earth system model of intermediate complexity we show a pronounced time-scale dependence of $\varDelta CO_{2}/\varDelta T$. A maximum is found on centennial scales with $\varDelta CO_{2}/\varDelta T$ values for the model ensemble in the range 5–12 ppm °C⁻¹, while lower values are found on shorter and longer time scales. These results are consistent with estimates derived from past observations. Up to centennial scales, the land carbon response to climate dominates the CO₂ signal in the atmosphere, while on longer time scales the ocean becomes important and eventually dominates on multi-millennial scales. In addition to the time-scale dependence, modeled $\varDelta CO_{2}/\varDelta T$ show a distinct dependence on the initial state of the system. In particular, on centennial time-scales, high $\varDelta CO_{2}/\varDelta T$ values are correlated with high initial land carbon content. A similar relation holds also for the CMIP5 models, although for $\varDelta CO_{2}/\varDelta T$ computed from a very different experimental setup. The emergence of common patterns like this could prove to usefully constrain the climate–carbon cycle feedback.

Appendices

Appendix 1: Millennial $\eta$

Ice cores are the only available source of data to estimate $\eta$ at millennial time-scale. Local temperature can be estimated from ice cores using deuterium isotope measurements (e.g. Jouzel 2003). $\hbox {CO}_2$ can be measured directly from the air bubbles trapped in the ice. The main limitation of ice cores is the relatively low temporal resolution, particularly for $\hbox {CO}_2$ concentration data. For selected ice cores and time intervals in the past the data are resolved enough to allow an estimation of $\eta$ on millennial time-scales. This is the case for data from the EPICA Dome C (Monnin et al. 2001) ice core for the Holocene (1–10,000 years BP) with a resolution of the $\hbox {CO}_2$ and temperature records of around 100 and 10 years, respectively. Highly resolved data are available also from the Vostok (Pépin et al. 2001; Petit et al. 1999) ice core for the time interval between 138 and 124 ka (1,000 years ago), including the last interglacial period, the Eemian. During this period the resolution of $\hbox {CO}_2$ data is indicatively between 100 and 700 years, while it is around 50 years for temperature.

The local Antarctic temperature can be scaled to be representative of global mean temperature. Assuming that the temperature anomaly during the last glacial maximum (LGM) relative to preindustrial was in the range between $-3$ and $-7\,^{\circ }\hbox {C}$ as suggested by various modeling studies (Ganopolski et al. 1998; Masson-Delmotte et al. 2005; Schneider von Deimling et al. 2006), we normalize the ice core temperatures to match these range (i.e. the values $-3, -5$ and $-7\,^{\circ }\hbox {C}$) for the period 25–20 ka. We then filter the $\hbox {CO}_2$ and the normalized temperature time series in the selected time intervals with a band-pass filter centered at a period of around 1,000 years. Similarly to what is done for the model simulations, $\eta$ is computed from the regression between temperature and $\hbox {CO}_2$ after shifting the time series to maximize correlation. Results suggest $\eta$ values in the range 2.2–6.5 $\hbox {ppm}\,^{\circ }\hbox {C}^{-1}$.

Appendix 2: Seasonal $\eta$

Since on seasonal time-scales the $\hbox {CO}_2$ in the atmosphere cannot be considered to be well mixed and redistributed globally, on these time-scales the sensitivity of the atmospheric $\hbox {CO}_2$ to temperature depends on the geographical location considered. The latitudinal dependence is particularly strong, as the $\hbox {CO}_2$ variations are affected by the land area distribution. However, a global mean estimate can be obtained by considering measurements of $\hbox {CO}_2$ at stations at different locations.

The sensitivity at seasonal time-scale is computed considering the mean seasonal cycle of atmospheric $\hbox {CO}_2$ as recorded in 12 remote monitoring stations, covering the period 1982–2008 (Dalmonech and Zaehle 2013). It is assumed that most of the signal is due to the response of terrestrial ecosystems. Aggregated mean seasonal cycle of land temperature is computed considering the most contributing regions to the signal in the specific remote $\hbox {CO}_2$ station, according to the methodology reported in Dalmonech and Zaehle (2013). Stations where more than 20 % of the variability in the mean seasonal cycles is due to ocean have not been considered.

The mean seasonal cycle of $\hbox {CO}_2$ computed with this procedure always lags the seasonal cycle of land temperature. The lag as detected is mostly due to transport of carbon in the atmosphere. Time series are shifted in order to have the maximum (negative) correlation between $\hbox {CO}_2$ and T. The sensitivity is hence computed for each month and the statistics are computed on the monthly values for each of the 12 stations. Resulting values range from $-0.6$ for northern boreal stations to values close to 0 for extremely southern stations in the southern hemisphere. The mean over all stations is $-0.37 \,\hbox {ppm}\,^{\circ }\hbox {C}^{-1}$.

Appendix 3: Carbon-cycle feedback factor, $\lambda _{\beta \gamma }$

Following Gregory et al. (2009) the carbon-cycle feedback factor for non-$\hbox {CO}_2$ forcings, $\lambda _{\beta \gamma }$ can be defined as:

$$\begin{aligned} \lambda _{\beta \gamma }=-\frac{\gamma }{2.12+\beta }\phi =\eta \phi , \end{aligned}$$

(7.1)

where $\phi \,\left[\hbox {Wm}^{-2}\,\hbox {ppm}^{-1}\right]$ is the slope in the linear approximation of the radiative forcing of $\hbox {CO}_2$, valid for small departures of $\hbox {CO}_2$ from the reference state:

$$\begin{aligned}&F(\varDelta CO_2)=F_{2x}\frac{ln[(CO_2^{ref}+\varDelta CO_2)]}{ln 2}\approx \phi \varDelta CO_2\end{aligned}$$

(7.2)

$$\begin{aligned}&\phi =\frac{F_{2x}}{CO_2^{ref}\mathrm {ln}2}. \end{aligned}$$

(7.3)

$\phi$ depends on the reference state. F$_{2x}$ = 3.7 Wm$^{-2}$ is the radiative forcing for a doubling of $\hbox {CO}_2$. For $\hbox {CO}_2^{ref}$ = 280 ppm, $\phi$ = 0.019 Wm$^{-2}$ ppm$^{-1}$.

$\lambda _{\beta \gamma }$ as we define it, has the sign reversed compared to Gregory et al. (2009), with a positive $\lambda _{\beta \gamma }$ implying a positive feedback.

Appendix 4: Relation of $\eta$ to the carbon-cycle sensitivity parameters $\beta$ and $\gamma$

Simulations with Earth System Models (ESMs) allow to separate the effects of temperature (climate) and $\hbox {CO}_2$ changes on land and ocean carbon fluxes. In Friedlingstein et al. (2003) these two effects are represented by the carbon-concentration sensitivity $\beta$ and the carbon-climate sensitivity $\gamma$. Without external $\hbox {CO}_2$ emissions, $\eta$ can be expressed in terms of the changes in the land ($\varDelta C_L$) and ocean ($\varDelta C_O$) carbon pools as follows:

$$\begin{aligned} \frac{\varDelta CO_2}{\varDelta T}=\frac{-1/\mu (\varDelta C_L+\varDelta C_O)}{\varDelta T} \end{aligned}$$

(8.1)

$\mu \approx$ 2.12 GtC $\hbox {ppm}^{-1}$ is the conversion factor between $\hbox {CO}_2$ in ppm and carbon mass in Gt. Assuming that the carbon-cycle response to climate and $\hbox {CO}_2$ concentration combine linearly, the changes in land and ocean carbon pools can be expressed in terms of the climate–carbon ($\gamma _L,\gamma _O$) and concentration-carbon sensitivity parameters ($\beta _L,\beta _O$) as in Friedlingstein et al. (2003):

$$\begin{aligned} \varDelta C_L&=\beta _L \varDelta CO_2+\gamma _L \varDelta T\end{aligned}$$

(8.2)

$$\begin{aligned} \varDelta C_O&=\beta _O \varDelta CO_2+\gamma _O \varDelta T \end{aligned}$$

(8.3)

Which inserted into Eq. (8.1) gives, after rearranging:

$$\begin{aligned} \eta =\frac{\varDelta CO_2}{\varDelta T}=-\frac{\gamma _L+\gamma _O}{\mu +\beta _L+\beta _O}=-\frac{\gamma }{2.12+\beta } \end{aligned}$$

(8.4)

with $\gamma =\gamma _L+\gamma _O$ and $\beta =\beta _L+\beta _O$. This approximate formula allows to compute the carbon-cycle feedback to climate from idealized experiments, as those from the C4MIP and CMIP5 model intercomparison projects. However, it has to be stressed that linearity is assumed between the carbon–climate and the carbon-concentration feedback, a strong requirement which was shown to not always be met (Zickfeld et al. 2011). Due to the aforementioned complex interactions between temperature, $\hbox {CO}_2$ and carbon fluxes, it is difficult to isolate $\gamma$ and $\beta$ from observations. However, $\eta$ can be easily derived from observations and Eq. 8.4 can then be used to constrain the quantity $-\gamma /(\mu +\beta )$, as was done in Cox and Jones (2008).