LandscapeDNDC  1.36.0
TreeDyn - Tree dimensional Dynamics

Table of Contents

Mortality

Tree mortality rate (mort) is assumed to have a fixed component not related to stand density ( \( mort\_{natural}\)), e.g. caused by diseases, and a stand density related component ( \( mort\_{dens}\)). The latter only applies if trees are growing across a threshold of tree canopy coverage. Then, the number of trees is reduced to this threshold.

\[ mort = max(mort\_{dens}, mort\_{natural}) \]

\[ mort\_{natural} = \frac {MORTNORM}{365} \]

\[ if (relcover > 1) mort\_{dens} = 1.0 - (MORTCROWD \cdot \frac {cdr ^ {2}}{cdr\_{pot} ^ {2}}) \]

\[ relcover = \frac {(dbh \cdot cdr) ^ {2} \cdot PI \cdot 0.25 \cdot tree\_{number} }{10000 \cdot MORTCROWD} \]

with

  • dbh: diameter at breast height (1.3m) (m)
  • cdr: ratio between dbh and crown diameter
  • \( cdr\_{pot}\): ratio between dbh and potential crown diameter under unconstrained conditions
  • tree_number: number of trees per hectare
  • relcover: relation between actual tree cover and potential coverage with no constraints
  • PI: constant (3.146)
  • MORTNORM, MORTCROWD: parameters for annual intrinsic mortality rate and maximum tree coverage, respectively

Dimensional growth

All dimensional growth is calculated on the basis of the new wood volume which consists of sapwood and core(or heart)wood, reduced by fractions for underground wood parts (coarse roots) and branches.

\[ vol = \frac {(m\_{sap} + m\_{cor}) \cdot ( 1.0 - UGWDF) \cdot ( 1.0 - f\_{branch})}{DSAP } \]

with:

  • m_sap: living sapwood
  • m_cor: core (or heart)wood
  • f_branch: fraction of branch biomass of aboveground woody biomass
  • UGWDF: species-specific paramter describing the belowground fraction of total woody biomass
  • DSAP: species-specific wood density (kgDW dm-3)

The branch fraction is calculated based on a allometric relationship to stem diameter or based on crown volume (= option 'branchfraction, Model options). See Branch fraction. The new volume is then distributed into height- and diameter growth considering the a stand-density related optimum height:diameter ratio (Height-diameter ratio).

Sapwood:Foliage relation

Assuming a relation between sapwood area and foliage area (Sapwood to foliage area ration), which is calculated empirically in dependence on tree height, the sapwood biomass necessary to supply the maximum foliage in the crown can be determined assuming a cone shape decline within the canopy and throughout the rooting zone. This optimum sapwood biomass (mSap_opt) is then devided by current foliage (and bud) masses in order to gain a sapwood/foliage biomass ratio.

\[ qsm = \frac { mSap\_{opt} }{ mFol + mBud } \]

\[ mSap\_{opt} = 1000 \cdot DSAP \cdot mSap\_{demand} \cdot (height\_{base} + \frac { rooting\_{depth} } { 3.0 } + \frac { height - height\_{base} } { 3.0 } ) \]

\[ mSap\_{demand} = lai\_{max} \cdot qsfa \]

with

  • mFol, mBud: biomass of foliage and structural reserves (buds) (kg m-2)
  • height_base: crown base height (m)
  • rooting_depth: rooting depth (m)
  • lai_pot: potential leaf area calculated from foliage and bud mass weighted by specific leaf area, derived from canopy length and species-specific parameters (SLAMAX, SLAMIN)
  • qsfa: relation between sapwood area and foliage area using QSF_P1, and QSF_P2 (sap-fol-ratio)
  • DSAP: species-specific sapwood density (kg dm3)

The height at crown base is calculated EITHER from a parameterized relationship to tree height (= option 'height, described under 'PSIM') using the species-specific parameters HREF (tree height at which crown base height starts to increase) and CB (relation between crown base height and top height at a mature state) or based on crown diameter (crown-length) using the species specific parameters (CL_P1 and CL_P2).

Biomass and leaf area distribution

Foliage biomass throughout the foliated canopy and fine root biomass throughout the rooted soil are empirically distributed using the same function that depends on distribution length (either canopy depth or rooting depth) with different parameters [29], veglibs_biomass_distribution.

Leaf area throughout the foliated canopy follows foliage biomass distribution but is weighted by specific leaf area per canopy layer. The latter varies linearly between a predefined minimum (at the top of the canopy) and maximum value (SLAMIN, SLAMAX).

Forest disturbances

  • Defoliate
  • Regrowth
  • Throwing
  • Thinning
  • Harvest