Table 1. The LIGNUM parameters used in this study. Parameters fixed during simulations are reported; the varied (-) and not used (NA) parameters are omitted. Other parameters are from Perttunen et al. (1998) for the synthetic simulation (Section 3.1) and Sievänen et al. (2008) for the real case study (Section 3.2). | |||

Parameter | Description | Synthetic | Real |

R | full exposure radiation for a tree segment, relative | 30.0 | 60.0 |

S_{max } | maximum shadow induced by a tree segment, relative | 10.0 | - |

S_{L} | shadow propagation distance, [m] | 0.55 | - |

V_{S} | linear voxel size, [m] | 0.02 | 0.02 |

R_{env} | radius of the circular boundary around the tree stem that the branches are not allowed to cross, [m] | 1.33 | - |

L_{R} | ratio between the radius and length of a tree segment, dimensionless | - | - |

Q | apical dominance parameter, varied between 0 (no dominance) and 1 (maximum dominance), dimensionless | - | - |

β, β_{init} _{max} | initial and maximal inclination angles, respectively: angles between the first branch segment and the segment it emanates from, [degree] | - , 95 | - |

∆β | inclination angle increment, [degree] | - | - |

∆ζ, ∆γ | intensity of the white noise added to the vertical (∆ζ) and horizontal (∆γ) orientations of the segments, [degree] | - , 5 | - |

T | number of iterations/years of simulation | - | - |

T_{sh} | when shedding a branch, the lower age limit for the branch segments | NA | - |

μ_{sh} | parameter to the Poisson variable determining number of the tip segments to shed | NA | - |

Table 2. Parameter estimation in the emulated “data” case. The tree shapes and fitted structural data sets are shown in Fig. 3. Parameters L and _{R}Q follow the normal distribution having two parameters: mean and standard deviation (std). Other LIGNUM parameters are from Perttunen et al. (1998) and R = 30.0, S = 10.0, _{max}S = 0.55 m, _{L}V= 0.02 m, _{S}R = 1.33 m, β_{env}_{max} = 95 degree, ∆γ = 5 degree, and original shedding options (Sievänen et al. 2008). See Table 1 for the parameter definitions. The genetic algorithm has stopped after 22 full iterations/generations, each generation consisted of 40 parameter sets. | |||

Parameter name | Data value | Model value (estimated) | Relative error, % |

L mean _{R}, | 0.009 | 0.0094 | 4.65 |

L, std _{R} | 0.001 | 0.0009 | 6.95 |

Q, mean | 0.2 | 0.2058 | 2.88 |

Q, std | 0.03 | 0.0213 | 28.88 |

T | 15 | 16 | 6.67 |

∆β | 10.0 | 9.7665 | 2.33 |

∆ζ | 5.0 | 4.3708 | 12.58 |

β_{init } | 35.0 | 40.4649 | 15.61 |