Ecological Archives M071-008-A8

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 H. Organic matter decomposition and nitrogen cycling.

Our below-ground biogeochemical sub-model consists of five pools: a fast carbon pool $C_1$ (containing dead and decaying leaves, fine roots, and sapwood), a slow carbon pool $C_2$ (containing decomposing structural material), associated nitrogen pools $N_1$ and $N_2$, and a pool of mineralized plant available nitrogen $N_{}$. The inputs to these pools consists of both litter from living plants and biomass from dead plants. The decomposition of organic matter in $C_1$ and $C_2$ mineralizes associated nitrogen in $N_1$ and $N_2$. Plants take up nitrogen from the pool of plant available nitrogen $N_{}$. In the current implementation, the nitrogen budget of every gap is closed, and each gap is initialized with $N_1=1.0$, $N_2=0$, and $N_{}=1.0$ kgN m$^{-2}$.

For each gap $y_{}$, our below-ground sub-model is:

$\displaystyle \frac{dC_1(y,t)}{dt}$ $\textstyle =$ $\displaystyle \sum_{i=1}^{R_y}{C_{litter}^{(i)}} + \sum_{i=1}^{R_y}{C_{a,dead}^{(i)}} - C_{1,decomp}(y,t)$ (H.1)
$\displaystyle \frac{dC_2(y,t)}{dt}$ $\textstyle =$ $\displaystyle \sum_{i=1}^{R_y}{C_{s,dead}^{(i)}} - C_{2,decomp}(y,t)$ (H.2)
$\displaystyle \frac{dN_1(y,t)}{dt}$ $\textstyle =$ $\displaystyle \sum_{i=1}^{R_y}{N_{litter}^{(i)}} + \sum_{i=1}^{R_y}{N_{a,dead}^{(i)}} - N_{1,min.}(y,t)$ (H.3)
$\displaystyle \frac{dN_2(y,t)}{dt}$ $\textstyle =$ $\displaystyle \sum_{i=1}^{R_y}{N_{s,dead}^{(i)}} - N_{2,min.}(y,t)$ (H.4)
$\displaystyle \frac{dN(y,t)}{dt}$ $\textstyle =$ $\displaystyle N_{1,min.}(y,t) +N_{2,min.}(y,t) - \sum_{i=1}^{R_y}{N_{up}^{(i)}}$ (H.5)

The variables $C_{litter}^{(i)}$, $N_{litter}^{(i)}$ are the carbon and nitrogen lost by the $ith_{}$ individual in the gap due to tissue decay, and $N_{up}^{(i)}$ is its rate of nitrogen uptake, obtained from the growth sub-model (Equation E7, E11 or E15, depending on current state of the plant) converted into per unit area rates (kg m$^{-2}$ yr$^{-1}$) by dividing by the size of the gap 225m$^{2}$. $C_{a,dead}^{(i)}$ and $C_{s,dead}^{(i)}$, are fluxes of carbon into the fast and structural carbon pools caused by the probabilistic death of an individual $i$ and $N_{a,dead}^{(i)}$ and $N_{s,dead}^{(i)}$ are the corresponding nitrogen inputs to the fast and structural nitrogen pools. $C_{a,dead}$, $C_{s,dead}^{(i)}$, $N_{a,dead}^{(i)}$, $N_{s,dead}^{(i)}$ are given by

$\displaystyle C_{a,dead}^{(i)}$ $\textstyle = \mu({\bf z},{\bf x},\bar{{\bf r}},t) B_a,$    
$\displaystyle C_{s,dead}^{(i)}$ $\textstyle = \mu({\bf z},{\bf x},\bar{{\bf r}},t) B_s,$    
$\displaystyle N_{a,dead}^{(i)}$ $\textstyle = \mu({\bf z},{\bf x},\bar{{\bf r}},t) B_a/(C:N)_a,$    
$\displaystyle N_{s,dead}^{(i)}$ $\textstyle = \mu({\bf z},{\bf x},\bar{{\bf r}},t) B_s/(C:N)_s,$   (H.6)

where $\mu({\bf z},{\bf x},\bar{{\bf r}},t)$ is the mortality rate of the individual (Equation F1) and the fluxes are converted to per unit area rates (kg m$^{-2}$ yr$^{-1}$) by dividing by the gap area 225m$^{2}$. Finally, if $W(y,t) = W_{crit}$, then the material lost through leaf drop (see Appendix E) enters the below-ground carbon pools. An amount $B_aq_l({\bf z},{\bf x})/2$ is added to $C_{1}(y)$ and an amount $B_a q_l({\bf z},{\bf x})/(2(C:N)_a)$ is added to $N_{1}(y)$.

The decomposition rates $C_{1,decomp}(y,t)$ and $C_{2,decomp}(y,t)$ have intrinsically different decay times, which are modified by a common (0-1) function $A(y,t)$ of soil temperature, soil moisture, and potential evapotranspiration taken directly from the Century model (Parton et al. 1987) . The decomposition rates are:

$\displaystyle C_{1,decomp}(y,t) = 11.0A(y,t)C_1(y,t),$     (H.7)


$\displaystyle C_{2,decomp}(y,t) = 0.22A(y,t)C_2(y,t)c_{im}^*.$     (H.8)

Since nitrogen is mineralized during the decomposition of organic matter, the nitrogen mineralization rates $N_{1,min.}(y,t)$ and $N_{2,min.}(y,t)$ are directly proportional to the decomposition rates and are:

$\displaystyle N_{1,min.}(y,t) = 11.0A(y,t)N_1(y,t),$     (H.9)


$\displaystyle N_{2,min.}(y,t) = 0.22A(y,t)N_2(y,t)c_{im}^*.$     (H.10)

As equations (H8) and (H10) imply, the decomposition of high $\mbox{C:N}_{}$ structural material, and the associated nitrogen mineralization are halted if $N$ becomes rare, analogous to the shutdown of plant photosynthesis by water and nitrogen limitation. Given available soil nitrogen, the value $c_{im}^*$ is: $c_{im}^* = {1\over(1+(D:S)_{im})}$ where $(D:S)_{im}$ is the immobilization demand for nitrogen relative to the supply of $N_{}$. The demand for nitrogen in this process $D=0.22A(y,t)C_2*0.65$ is calculated as the nitrogen necessary for a reduction in the $\mbox{C:N}_{}$ ratio of the decaying structural material from $150_{}$ to $10_{}$, and assuming a respiration of 30% (Parton et al. 1987). The supply of nitrogen is assumed to be proportional to available $N_{}$ in the soil ( $S_{}= \nu N_{}$), with $\nu_{}=40$ set to a high value (relative to that of plants) under the assumption that microbes have greater access to available nitrogen than plants.

In the PDEs the terms in the below-ground sub-model equations (H1)-(H5) become integrals:

$\displaystyle d C_1(a,t) \over d t$ $\textstyle =$ $\displaystyle \int_{-\infty}^{\infty}\int_{{\bf z}_0}^{\infty}n({\bf z}, {\bf x},a,t)C_{litter}({\bf z},{\bf x},\bar{{\bf r}},t)d{\bf z}d{\bf x}$  
  $\textstyle +$ $\displaystyle \int_{-\infty}^{\infty}\int_{{\bf z}_0}^{\infty}n({\bf z}, {\bf x... ..._{a,dead}({\bf z}, {\bf x},\bar{{\bf r}},t)d{\bf z}d{\bf x} - C_{1,decomp}(a,t)$ (H.11)
$\displaystyle d C_2(a,t) \over d t$ $\textstyle =$ $\displaystyle \int_{-\infty}^{\infty}\int_{{\bf z}_0}^{\infty}n({\bf z}, {\bf x... ...C_{s,dead}({\bf z},{\bf x},\bar{{\bf r}},t)d{\bf z}d{\bf x} - C_{2,decomp}(a,t)$ (H.12)
$\displaystyle d N_1(a,t) \over d t$ $\textstyle =$ $\displaystyle \int_{-\infty}^{\infty}\int_{{\bf z}_0}^{\infty}n({\bf z}, {\bf x},a,t)N_{litter}({\bf z},{\bf x},\bar{{\bf r}},t)d{\bf z}d{\bf x}$  
  $\textstyle +$ $\displaystyle \int_{-\infty}^{\infty}\int_{{\bf z}_0}^{\infty}n({\bf z}, {\bf x... ...)N_{a,dead}({\bf z}, {\bf x},\bar{{\bf r}},t)d{\bf z}d{\bf x} - N_{1,min.}(a,t)$ (H.13)
$\displaystyle d N_2(a,t) \over d t$ $\textstyle =$ $\displaystyle \int_{-\infty}^{\infty}\int_{{\bf z}_0}^{\infty}n({\bf z}, {\bf x... ...N_{s,dead}({\bf z}, {\bf x},\bar{{\bf r}},t)d{\bf z}d{\bf x} - N_{2,,min.}(a,t)$ (H.14)
$\displaystyle d N(a,t) \over d t$ $\textstyle =$ $\displaystyle N_{1,min.}(a,t) + N_{2,min.}(a,t) - \int_{-\infty}^{\infty}\int_{... ...({\bf z}, {\bf x},a,t)N_{up}({\bf z}, {\bf x},\bar{{\bf r}},t)d{\bf z}d{\bf x}.$  
      (H.15)

The reader may note that the $C_2:N_2$ ratio is constant since all inputs to the structural decay pool have the same $\mbox{C:N}_{}$ (all structural material in the model has a $\mbox{C:N}_{}$ of $150_{}$), and since the mineralization of nitrogen in $N_2$ is linked to the decomposition of $C_2$. In contrast, the $C_1:N_1$ ratio floats because different functional types in the model have different $\mbox{(C:N)}_a$ (see Appendix C).


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