To determine the growth of a tree we use some simple principles that allow
us to conclude lengths of new tree segments, number of new buds, senescence
of sapwood and foliage, diameter growth of the tree etc.

2.1 Length of a New Tree Segment

The length of a tree segment is determined basically by branching and
the local light conditions in the tree crown. Branch order effect shortens
the length of a tree segment compared to the other tree segments in similar
light conditions but in more favourable (closer the main stem) position
in a tree. This mimics e.g., the effect of slowing down the fluid and nutrient
flow in the branches of the tree.

Relative shadiness shortens the tree segment according to its local light
climate. For example at the top of a Scots pine the light climate is ideal and
gradually get worse within the crown due to the self shading.

2.1 Length of a New Tree Segment | 2.2 New Buds | 2.3 Diameter Growth |
2.4 Sapwood Senescence | 2.4 Gradual Bending of Branches

2.2 New Buds

Number of new buds at the tip of the branches is simply determined with
the help of the foliage mass of the mother tree segment (i.e., the tree segment
behind the leading bud). The more foliage the mother tree segment has
the more vital is the branch and more buds can be produced. For example
a Scots pine has usually 4-6 new buds in the main stem and 2-4 in branches.

2.1 Length of a New Tree Segment | 2.2 New Buds | 2.3 Diameter Growth |
2.4 Sapwood Senescence | 2.4 Gradual Bending of Branches

2.3 Diameter Growth

The most important single hypothesis in determing the diameter growth is
that of sapwood equivalence. This means that the tree segment below a
junction (A0 in the figure) of several tree segments must produce equal
amount of sapwood than the tree segments just above (A1,A2 and A3 in the
figure) in terms of area . This is called the pipe model principle.

2.1 Length of a New Tree Segment | 2.2 New Buds | 2.3 Diameter Growth |
2.4 Sapwood Senescence | 2.4 Gradual Bending of Branches

2.4 Sapwood Senescence

Sapwood is a major "maintenance" cost for a tree. If the sapwood is
no longer needed for transportation of water and nutrients it can
be killed. The living sapwood turns to dead heartwood.

In the model we have basically two hypothesis to determine sapwood
senescence. For the first, according two the pipe model (in 2.3) we assume
that the effect of sapwood senescence is propagated downwords in a tree.
That is, the tree segment below in a junction must match the heartwood
area coming from above the junction. Secondly, the local senescence of
sapwood in a tree segment is controlled by the death of foliage. Sapwood
is needed to support foliage and when the foliage dies in a tree segment
the sapwood area proportional to the mass of death foliage can be killed.

2.1 Length of a New Tree Segment | 2.2 New Buds | 2.3 Diameter Growth |
2.4 Sapwood Senescence | 2.4 Gradual Bending of Branches

2.5 Gradual Bending of Branches

Finally, the architecture of a tree is affected by gradual bending of
branches. In LIGNUM we don't have a model (physiological or based on
strength calculations) for such phenomena, but a simple algorithm
can implement branch bending shown in figure. This is suitable for example
for young Scots pine trees.

2.1 Length of a New Tree Segment | 2.2 New Buds | 2.3 Diameter Growth |
2.4 Sapwood Senescence | 2.4 Gradual Bending of Branches