ForGEM - principle equations

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FORGEM


Principal equations in ForGEM

An overview is presented of the principal state and empirical equations used in ForGEM. See (Kramer, 2001, Kramer et al., 2008) for details and references.


number of trees


with:

N: number (# trees plot-1)

x: seeds, seedlings, trees

New: new individual seed, seedling or tree in the population

Mrt: mortality of individual tree, or tree-cohort in case of seeds and seedlings

weight


with:

W: weight (kg tree-1)

y: foliage, branches, heartwood, sapwood, coarse roots, fine roots, reserves

f: fraction

NPP: net primary production (kg tree-1 d-1)

T: turnover (d-1)


allocation

Empirical equations are used for both allocation Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("<p>Error fetching URL: Could not resolve host: mathoid.testme.wmflabs.org </p>") from server "http://mathoid.testme.wmflabs.org":): {f_{y}

and the rate of change of structural features. Empirical coefficients of these equations are indicated as , with  a numeric identifier. See  allocation parameters for the values of  for different tree species.




with:

fl: foliage; br: branches; st: stem (= heartwood + sapwood); sh: shoot (foliage+branches+stem)


The fraction of NPP allocated to the plant components Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("<p>Error fetching URL: Could not resolve host: mathoid.testme.wmflabs.org </p>") from server "http://mathoid.testme.wmflabs.org":): {f_{y}

are derived such that the tree strives for partitioning ratios between plant organs, . A fixed fraction of NPP is allocated to the roots.

structural features

Structural features simulated by the ForGEM model are stem volume, tree height and stem diameter


stem volume


With:


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allocation of NPP to stem

: wood density


height


with:

H: tree height (m) t: tree age (yr)

See height parameters for the values of for different tree species.

stem diameter


with:

V: volume (dm^3 stem^-1)

D: stem diameter at breast height (cm)

e: exponent of the natural logarithm.