T model – a simple carbon allocation model for tree growth Two case studies for both high and low [CO2] by Li Guangqi (Macquarie University)

Tree ring width is one of the most important materials for past climate reconstruction. However, “divergence” problem (correlation strength between temperature and ring width breaks where temperature was conferred as the limiting factors in high elevation and high latitude regions and ring width data are previously applied for temperatures) challenges the classical dendrochronology principle of the single-limiting factor and uniformitarian, which means the same strength of the most limited factor had the same strength in the past. Physiology research has shown that tree growth is jointly controlled by multiple factors, e.g., photosynthesis active radiation (PAR), temperature, soil moisture (represented by actual to equilibrium evapotranspiration α), air moisture (vapour pressure deficit, VPD), and CO2. Therefore, we build a forward process-based modelling method to simulate realistic ring width and to illustrate the climate control on tree growth. We combined a simple generic light-use-efficiency GPP model (P model, Wang et al., 2014) with a species-specific carbon allocation tree growth model (T mode, Li et al., 2014). The P model provides values for gross primary production (GPP) per unit of absorbed photosynthetically active radiation (PAR). Absorbed PAR is estimated from the current leaf area. GPP is allocated to foliage, transport tissue, and fine- root production and respiration in such a way as to satisfy well-understood dimensional and functional relationships. Our approach thereby integrates two modelling approaches separately developed in the global carbon-cycle and forest- science literature.

Li Fig 1

Figure1 Ageing effect simulated by T model

Figure 2 Climate control analysis for both the observation and simulation (example from Callitris in Great West Woodland (west Australia))

Figure 2 Climate control analysis for both the observation and simulation (example from Callitris in Great West Woodland (west Australia))

T model can represent both the ontogenetic (ageing effect, figure 1) and the effects of multiple environmental variations (climate control, figure2) and trends (simulation VS observation, figure 3). Both the observation and simulation shows the same positive response to PAR and soil moisture (α), and negative to VPD, which is the opposite of moisture availability in the atmosphere. This climate control pattern has been found consistent for at least three sites, e.g. Pinus in Changbai Mountain (northeast China), Callitris in Great West Woodland (west Australia), and Juniperus in Hamilton (west USA).

Li Fig 3

Figure 3 Simulation VS observation (example from Juniperus in Hamilton, west USA)

However, missing [CO2] signal was found in the observation for Callitris in GWW. After the time-dependent tuning for all of the parameter, we found only the ratio of fine root mass to foliage area (ζ) is the only one changed during the past century (Figure 4). There is a ~14% increase of root allocation as the fast increase of [CO2] since 1950. This missing [CO2] signal has been found in the past 150 year research for the tropical forests (van der Sleen et al., 2015), where increasing water use efficiency has been found along with the increase of [CO2], but no increase for the radial growth. The [CO2] signal is also missed in the tree ring research (Kienast and Luxmoore, 1988; Gedalof and Berg, 2010).

Li Fig 4

Figure 4 Time-dependent tuning with real [CO2] (example from Callitris in Great West Woodland (west Australia))

In the cold and low [CO2] glacial period, Juniperus needs to reduces ~25% of root carbon allocation (Figure 5) to get the observed ring width from the fossil data, which is quite similar to today’s growth rate. Besides the changing carbon allocation strategy, the glacial climate change also benefit tree growth by reducing photorespiration (decreasing temperature), wetter moisture for both air (increasing relative humidity and decreasing temperature) and soil (increasing precipitation).

Figure 5 Potential strategies for glacial Juniperus to keep the same stem growth in low [CO2] conditions.

Figure 5 Carbon allocation strategy for glacial Junperus grew at the similar rate as today

Figure 5 Carbon allocation strategy for glacial Junperus grew at the similar rate as today


Wang, H., Prentice, I. C., and Davis, T. W.: Biophsyical constraints on gross primary production by the terrestrial biosphere, Biogeosciences, 11, 5987–6001, doi:10.5194/bg-11-5987-2014, 2014.

Li, G., Harrison, S. P., Prentice, I. C., and Falster, D.: Simulation of tree-ring widths with a model for primary production, carbon allocation, and growth, Biogeosciences, 11, 6711– 6724, doi:10.5194/bg-11-6711-2014, 2014.

van der Sleen, P., Groenendijk, P., Vlam, M., Anten, N. P., Boom, A., Bongers, F., Pons, T. L., Terburg, G., and Zuidema, P. A.: No growth stimulation of tropical trees by 150 years of CO2 fertilization but water-use efficiency increased, Nat. Geosci., 8, 24–28, 2015.

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