Ecological Archives M071-008-A4

P. R. Moorcroft, G. C. Hurtt, and S. W. Pacala. 2001. A method for scaling vegetation dynamics: the ecosystem demography model (ED). Ecological Monographs 71:557-585.

Appendix D. Allocation and Allometry.

We combined the height-diameter allometry from O'Brien et al. (1999):

$$h=2.34D^{0.64}$$ (D.1)

where $D_{}$ is diameter (cm) and $h_{}$ is height (m), with allometric data from Saldarriaga et al. (1988)

$$\mbox{if } h<h_{max} B_l = 0.0419D^{1.56}{\rho({\bf x})}^{0.55}$$ (D.2)

$$B_s = 0.069 h^{0.572} D^{1.94}{\rho({\bf x})}^{0.931}$$

$$\mbox{if } h{\geq}h_{max} B_l = 0.0419D^{*1.56}{\rho({\bf x})}^{0.55}$$

$$B_s = 0.069h_{max}^{0.572} D^{1.94}{\rho({\bf x})}^{0.931}$$

where $\rho({\bf x})$ is the wood density of the plant functional type and $D_{}^*$ is the diameter from the O'Brien et al. (1999) allometry corresponding $h_{max}$:

$$D^* = 0.265 h_{max}({\bf x})^{1.56}.$$ (D.3)

The empirical allometric relationships defined above are used define the trajectory of active and structural tissue growth. The total amount of active tissue carbon $B_a^{opt}$ is given by the sum of its three components

$$B_a^{opt}=B_{sw}+B_l+B_r$$ (D.4)

-see Fig. A.2. $B_l$ is computed from the empirical relationships given in (D3) and $B_{sw}$ and $B_r$ are calculated in the following way. We assume that within each plant $B_r=B_l$ and a ``pipe'' model for amount of sapwood (specifies that a plant's sapwood cross-sectional area is proportional to its total leaf area (Shinozaki et al., 1964 a, b))

$$B_{sw} = 0.00128 l({\bf x}) B_l h.$$ (D.5)

Plants in positive carbon balance ( $\mbox{Prod}_{} > 0$) allocate new production to grow along the empirical allometric relationships given above. This requires that they allocate a fraction $q_a({\bf z},{\bf x})$ of new carbon for growth to $B_a$ and the remaining fraction $1-q_a({\bf z},{\bf x})$ to $B_s$, where

$$q_a({\bf z},{\bf x})=\frac{{\frac{dB_a^{opt}}{dB_s}}(B_s)}{{1+\frac{dB_a^{opt}}{dB_s}}(B_s)}.$$ (D.6)

and $\frac{dB_a^{opt}}{dB_s}$ is calculated using Eq.s (D1-D5).

In contrast, when in negative carbon balance, plants depart from this trajectory because their active compartment shrinks (due to tissue respiration and decay). Their inert structural compartment however, remains constant. If a plant with $B_a < B_a^{opt}$ subsequently comes back into positive carbon gain $\mbox{Prod}_{} > 0$, it then allocates all production to regrowing its active tissues until it recovers the $B_a^{opt}$ trajectory. Thus: $q_a({\bf z},{\bf x}) =1$ if $B_a < B_a^{opt}$.

Finally, if $q_l({\bf z}, {\bf x})$, $q_r({\bf z}, {\bf x})$, and $q_{sw}({\bf z}, {\bf x})$ are the fractions of $B_a$ in leaf, root, and sapwood, respectively, then:

$$q_l({\bf z},{\bf x}) = q_r({\bf z},{\bf x})= \frac{1}{2+ 0.00128 l({\bf x}) h}$$ (D.7)

$$q_{sw}({\bf z},{\bf x}) = 1-q_l({\bf z},{\bf x}) - q_r({\bf z},{\bf x}).$$

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