The global land surface has taken up about 29{\%} of anthropogenic CO2 emissions since preindustrial times. Yet it remains uncertain whether this significant buffer to the effects of anthropogenic climate change will continue in future. Some models predict that the global land biosphere will remain a carbon sink by the end of this century, but others predict it to become a major source. It is therefore important to understand what causes this divergence in predictions. In this presentation, we combined numerical and mathematical analysis to reveal general behaviour of global land models. Our analysis is based on the recognition that the terrestrial carbon cycle generally can be mathematically expressed by a system of first-order linear ordinary differential equations subject to an initial condition as follows: dC/dt = x(t)AC BU(t) with C(t=0)=C0 where C(t) is the C pool size, A is the C transfer matrix, U is the photosynthetic input, B is a vector of partitioning coefficients, C0 is the initial value of the C pool, and x is an environmental scalar. In this equation, the linear carbon transfer among pools within one ecosystem is represented by matrix A and vector B, and the nonlinearity of environmental influences is represented by environmental scalar x(t) on carbon transfer and U(t) for carbon influx. We investigate how important variation in parameters controlling terrestrial carbon cycling are for three key predictions of the dynamics of future land carbon: the maximum carbon uptake, Fmax, the number of years it takes to reach Fmax, tmax, and the year in which the land biosphere changes from a carbon sink to a source, t1 (if it happens). The parameters included the sensitivity of net primary production to atmospheric [CO2], {\beta}, the temperature sensitivity of soil carbon decomposition, Q10, and the sensitivity of global mean land surface to atmospheric [CO2],{\phi}. Our theoretical analyses reveal that a theoretical maximal amount carbon accumulated by land biosphere can be estimated from Fmax and the residence times of the different carbon pools, and that an estimate on the time it takes for the system to approach its new equilibrium can be obtained from the residence time of the slowest pool. Our numerical analyses reveal that a 3-D parameter space can bound the range of land carbon uptake trajectories from 1850 to 2100 predicted by all Earth System Models for the 5th assessment report of the IPCC. The maximal amount of carbon accumulated, tmax and t1 increases with {\beta} and decreases with Q10 and {\phi}. The sensitivities of all three model predictions to {\beta} and Q10 increase with {\phi}

}, author = {Wang, Y. and Smith, M.J. and Luo, Y. and Leite, M. and Augusto, F. and Chen, B. and Hoffman, F.M. and Medlyn, B.E. and Rasmiussen, M.}, booktitle = {Talk at 2013 Fall Meeting, AGU, San Francisco, Calif., 9-13 Dec.}, month = {December}, note = {Talk: Abstract B51L-02 presented at 2013 Fall Meeting, AGU, San Francisco, Calif., 9-13 Dec.}, publisher = {American Geophysical Union}, title = {Theoretical analysis of the global land carbon cycle: what determines the trajectory of future carbon uptake?}, url = {http://research.microsoft.com/apps/pubs/default.aspx?id=217347}, year = {2013}, }