[6] Annual eddy-covariance NEP measurements at 20 temperate and boreal forest sites (8 temperate forest sites and 12 boreal forest sites over the region between 43.2°S to 60.7°N) used in this study are the same as those used by *Magnani et al.* [2007] (hereinafter referred to as MA07). Confounding effects of forest age have been subtracted by MA07 from short-term eddy-covariance NEP records, through averaging NEP over the entire rotation period with an age-dependent effect on light use efficiency and allocation. Thus, this age-corrected mean NEP dataset allows us to explore the effects of historical temperature change on ecosystem C balance. Monthly temperature reconstructions, with a spatial resolution of 0.5 degree, are from the Climatic Research Unit (CRU) dataset, School of Environmental Sciences, University of East Anglia, U.K. [*Mitchell and Jones*, 2005]. As we do not focus on interannual variability, the change in temperature (*δ*T) is expressed here by multiplying the linear trend of temperature (T) by the length of the period considered to impact NEP.

[7] Gradients of productivity and respiration in response to environmental change and disturbance will jointly lead to a net absorption or release of carbon, which appears to be the main determinant of the spatial patterns of NEP [*Luyssaert et al.*, 2007]. Without considering the effects of disturbance, NEP can be modeled by the difference between net primary productivity (NPP, gC m^{−2} yr^{−1}) input and heterotrophic respiration output described by soil organic C pool (C_{S}, gC m^{−2}) divided by its Mean Residence Time (t_{e}, yr) (equation 1).

where C is the total C storage in the terrestrial ecosystems. The efficiency of plants to transform incoming sunlight into NPP (light use efficiency) is generally reduced when plants are exposed to temperature differing from the optimum temperature [*Field et al.*, 1995]. Here, we use the formulation of the CASA model [*Field et al.*, 1995] to describe the temperature dependence of NPP by a function S_{T} which peaks around an optimal growth temperature T_{opt} (equation 2); for temperate and boreal forest, T_{opt} = 20°C). The optimal value of NPP in absence of temperature limitation, NPP_{opt} (1018 gC m^{−2} yr^{−1} at 20°C) is defined from the *Luyssaert et al.* [2007] ecological database.

where *MAT*(*t*) is the mean annual temperature for a given year *t*. The mean residence time of soil organic carbon in temperate and boreal forests, generally takes values between 20–60 years [*Bird et al.*, 1996]. Here, we will assume t_{e} = 40 years when MAT = 0°C and a decomposition rate (1/t_{e}) that exponentially increases with rising MAT (Q_{10} formulation with Q_{10} = 2), as given by equation (3) below.

Accordingly, equation (1) can be further expressed as a function of MAT (equation (4)).

The conceptual model defined by equation (4) does not account for different sensitivities of NEP to seasonal temperature changes [*Randerson et al.*, 1999; *Piao et al.*, 2008], and makes the simplification that forest carbon balance is only driven by a single climate variable, here temperature. One must keep in mind that other factors such as precipitation, N-deposition or rising atmospheric CO_{2} as well as changes in forest management and natural disturbance rates and intensity also likely play a role in controlling NEP [*Magnani et al.*, 2007].