**CONTROL ID:** 1787970

**TITLE:** Theoretical Analysis of the Global Land Carbon Cycle: What Determines the Trajectory of Future Carbon Uptake?

**AUTHORS (FIRST NAME, LAST NAME):** Yingping Wang^{1}, Matthew J. Smith^{2}, Yiqi Luo^{3}, Maria Leite^{4}, Folashade Agusto^{5}, Benito Chen^{6}, Forrest M. Hoffman^{7}, Belinda Elizabeth Medlyn^{8}, Martin Rasmussen^{9}

**INSTITUTIONS (ALL):** 1. Marine and Atmospheric Research, CSIRO, Aspendale, VIC, Australia.

2. Microsoft Research, Cambridge, United Kingdom.

3. Dept. of Microbiology and plant biology, University of Oklahoma, Norman, OK, United States.

4. Dept of Mathematics and Statistics, The University of Toledo, Toledo, OH, United States.

5. Dept of Mathematics and statistics, Austin Peay State University, Knoxville, TN, United States.

6. Dept. of Mathematics, University of Texas, Arlington, TX, United States.

7. oak Ridge National Lab, Oak Ridge, TN, United States.

8. Dept. of Biological Sciences, Macquarie University, North Ryde, NSW, Australia.

9. Dept of Mathematics, Imperial College of London, London, United Kingdom.

**ABSTRACT BODY:** The global land surface has taken up about 29%
of anthropogenic CO_{2} 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, *F*_{max},
the number of years it takes to reach *F*_{max},
*t*_{max}, 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
[CO_{2}], β, the temperature sensitivity of soil carbon
decomposition, *Q*_{10}, and the sensitivity of global mean
land surface to atmospheric [CO_{2}], φ.

Our theoretical analyses reveal that a theoretical maximal
amount carbon accumulated by land biosphere can be estimated from
*F*_{max} 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 5^{th} assessment report of the
IPCC. The maximal amount of carbon accumulated, *t*_{max}
and t1 increases with β and decreases with *Q*_{10}
and φ. The sensitivities of all three model predictions to β
and *Q*_{10} increase with φ.

**INDEX TERMS:** 0428 BIOGEOSCIENCES Carbon cycling, 0466 BIOGEOSCIENCES Modeling, 0315 ATMOSPHERIC COMPOSITION AND STRUCTURE Biosphere/atmosphere interactions.

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**Additional Details**

**Previously Presented Material:** 0%

**Contact Details**

**CONTACT (NAME ONLY):** Yingping Wang

**CONTACT (E-MAIL ONLY):** yingping.wang@csiro.au

**TITLE OF TEAM:** non-autonomonous working group