A rule based model is introduced which is intended to aggregate results of the model LIGNUM. The trees are grown under the light conditions in the understorey of a gap.
For that reason the light model extension LIGNUM-canopy is used. The creation of this model has been done in four steps: aggregation of the light model, aggregation of the growth of the juvenile tree, implementation of the aggregated version as an L-system and at last the comparison of the simulation with the original data.
9.5.1 Aggregation of LIGNUM-canopy
The main target of the aggregation was a new simplified model with special aspects of the LIGNUM growth behaviour. Aggregation always means the loss of information. In the scope of the model triangle of Kurth(1999), the lost of information means an adjustment.
Here the physiological information which is simulated by LIGNUM is abstracted in the aggregation process. Thus in the model triangle the new model moves to the left side upward. The newly created model contains almost only architectural information. The only functionality which is held is that the architectural structure depends on the radiation income depicted by a hemispherical covering ratio.
The assessment of these results has several aspects. The first regards the simulation results of LIGNUM-canopy. Some aspects have already been discussed in the section about the sensitivity tests of LIGNUM-canopy. The simulations for instance also result in an enormous number of segments (see figure 40 on page 93). The dimensions of the other parameters (H, D, CE and CB) compared to the real measured trees in chapter 7 turned out to be reasonable. Nevertheless, to validate the growing behaviour of the simulated Scots pines, more real data, especially in combination with light measurements, would be necessary. One observation is indeed that the simulated trees react in a manner proportional to the reduction of the radiation income. The ratio RAD varied from 0.55 in the centre of the gap to 0.42 at its edge which is a relative reduction of 23.7%. The height of the tree is reduced by 21.1%, whereas the diameter reacted very sensitive to the light conditions with a reduction of 43.6%.
The other assessment aspects regard the aggregation process. This process had two tasks: the aggregation of the light model of LIGNUM and the aggregation of the growth
of the LIGNUM tree. The light model is simplified by using covering ratios. The ratio expresses the ratio of incoming radiation to the total radiation emerging from the hemi-sphere. This ratio was calculated at a reference point whose distance to the centre of the gap could be varied. It could be shown that this ratio decreases in relation to the distance of the reference point to the centre of the gap. The ratio RAD which expresses the ratio of incoming light calculated by LIGNUM showed that using a radius of the gap of 21 meters results in a light reduction of 23.7%. The other more simple ratios reflected this reduction in a stronger way. The ratio CR which only counts the non shaded sectors has a similar range but persistently calculates a very low radiation income. The ratio WCR which weights the non shaded sectors by their inclination angle corrects the level of light income near the centre. The ratio has a greater range and results in a lower radiation at the edge of the gap than the ratio RAD. The reason for such a behaviour is the counting method used in the ratios CR and WCR. In the calculation of RAD the canopy does not reduce the light of a shaded sector to zero which happens with the counting method of the ratios CR and WCR.
To aggregate the growth behaviour of LIGNUM Scots pines the relation between the light conditions and the annual growth was investigated. It was very easy to constitute a linear regression with high coefficients of determination between both. For measuring the light income the ratio WCR is used. The sense of using this ratio instead of RAD is that the aggregation should reduce the information about the amount of light which emerges from a sector. RAD includes more of such information. Additionally, this ratio reduces the light income from lower inclination angles by weighting the sector with the inclination angle which seemed to be reasonable.
9.5.2 The implementation
The aggregation of LIGNUM-canopy resulted in a new model. This new model is imple-mented using an L-system. Several problems had to be solved for this implementation: the representation of the light model, the representation of the canopy and the representation of the individual juvenile tree.
The light conditions are calculated by the sensitive function 15. This function returns a ratio which is equivalent to the inverted version of WCR. The used model of the hemi-sphere is due to den Dulk (1989). Figure 46 on page 103 gives the results. This figure also shows the results of the sensitive function 8 which returns the inverted equivalent to CR. The comparison with the calculations ofLIGNUM-canopy showed strong differences:
The LIGNUM-canopy calculations were always higher. The reason for that behaviour may lie in the differences of the light models. Both LIGNUM and the approach of den
Dulk divided the hemisphere into sectors and tried to keep the area of all sectors more or less evenly sized (turtle approach). The main difference between both approaches is the number of sectors. GROGRA uses only 46 sectors. The firmament of LIGNUM is in principle variable but was parameterized with 120 sectors. This very discrete way of parameterizing the sky may cause differences in the calculation of the ratios.
The canopy is represented by a spiral of palisades. This representation was imple-mented only as an improvization because no geometrical body like a box was available in GROGRA which would represent the canopy more reasonably. The problem of this rep-resentation was that one could not guarantee that some light beams would not “cheat”
through the canopy. Such light beams might be the reason for the peculiar maximum of CR as well as WCR at a distance of seven meters from the centre of the gap of the GROGRA version (see figure 46 on page 103).
The representation of the individual juvenile tree was very similar to the trees of the reconstruction of the tree stand in Syke. The only difference is that the juvenile trees do not use distance sensitivity. In contra to the reconstruction, the shapes of the LIGNUM trees were imaged very well by the irregular pyramids. Here, no maximum height of the crown extension would bring any advantages in the representation.
9.5.3 Results
The aggregation of the LIGNUM-canopy Scots pines should show that it is possible to implement such a model as an L-system, which is discussed in the last chapter below.
Nevertheless, another target was to show that is is possible to simulate juvenile Scots pines by aggregating an existingFSTMinstead of creating a purely empirical model. The validation of such approaches is very important as for instance Sterba (1990), Pretzsch (2001), Nagel et al. (2000) and Pretzsch and ˘Dursk´y (2001) noticed. A final assessment of the question if the simulation of juvenile trees was successful is not possible because the data for a quantitative validation are missing. However, first the model results have to be compared. Figure 48 on page 105 illustrates the differences between the LIGNUM-canopy results and the resulting values of the aggregated version. In the whole view the aggregation was successful. The scatterplot shows indeed some parts where the aggrega-tion differs from the original model. Especially the diameters show different values if the incoming radiation is strongly reduced. The explanation for this lies in the step from the LIGNUM-canopy calculation of the ratio WCR to that of GROGRA. The shape of both curves is different even in the GROGRA version with a correction factor. The gradient of the GROGRA version of WCR is steeper. This results in smaller dimensions of all parameters in the aggregated version of LIGNUM-canopy. A solution would be the
inte-gration of the LIGNUM light model into the L-system specification of GROGRA. Such an approach would not significantly increase the demand on computer resources.
Within the simulation runs function 8 was used to clarify the difference between the use of CR and WCR in the aggregated version. The correction factor for CR adapted the curve almost completely to the WCR curve (see figure 46 on page 103). The simulation results by applying the sensitive function 8 were also very similar. The conclusion here is that the use of WCR does not enhance the light model calculation. The light model could be even more reduced to CR.