Height increment model

The analysis of height increment models was needed to answer the hypothesis that a “Re- parameterised model based on Lithuanian data fits better under Lithuanian conditions regarding height increment ”. The results confirmed the hypothesis. Although, the study did not conduct any direct statistical check of the original SCHRÖDER (2004) height increment

(SCHRÖDER4OR_i

h5) models, the results of indirect tests did support the hypothesis.

Data from the National Forest Inventories of Lithuania and Saxony showed that mean stand height over age increases faster in Lithuania compared with Saxony (Figure 4-42). A similar result was produced by analyses of yield tables for Lithuania and Saxony. They indicate that mean stand height at Y1-40age increases faster in Lithuania than in Saxony, but in Mat101-

140_{age increases faster in Saxony (Figure 4-21). Important distinctions were also found by}

comparing stand top height (H100) and mean stand height (Hq) relations described by data that

CHAPTER 5: DISCUSSION

144 4-43). The trend line between H100 and Hq in the Lithuanian PEPs was steeper. These results

show different height growth conditions for pine trees in Lithuania and Saxony. The

SCHRÖDER4RePih5 model confirms that the model is suitable for local conditions in Lithuania,

for example densities of trees influence stand level variables. But, since tree densities in Lithuania and Saxony differ significantly, this is the weak point of the presented findings. Analysis of the SCHRÖDER4ReP_i

h5 model. The need to use data from the PEPs to model the data

that defined stand top height at the base age (100 years), as it was absent in Lithuanian yield tables, was both the most important and weakest aspect of the re-parameterisation procedure. The distance between Hq and H100 reduces with increases in both site fertility and mean stand

age. This correlation meant that simple linear regression models were inappropriate but that a logarithmic linear H100 model was suitable. The high level of the performance of the model

was due to its capabilities in statistical analysis, which were characterised by very high coefficients of determination and fulfilled regression assumptions and made the model suitable for estimating H100 values for Lithuanian yield tables.

As a result an important stand level value enriched the data of the Lithuanian yield tables, however, this particular H100 model cannot be treated at the same level as other models used

in the yield tables. This will only be achieved by improving the model, perhaps by using the National Forest Inventory data.

The SCHRÖDER4ReP_i

h5 model shares the same level of precision as developed H100 model

(Equation 4-3) with additional possible modelling errors. As a last step, the formula for the SCHRÖDER4OR_i

h5 model is presented in Equation 3-44. In the

context of pine trees in Saxony, the coefficient a0 is equal to 0 and coefficient a1 is equal to 1.

Thus, relative tree height increment is simply equal to the relative potential of the stand top height increment. However, in the SCHRÖDER4ReP_i

h5 model, the third step (Equation 3-44) is

added, enabling tree heights for pines in a stand to increase with the same relative potential.

This model, SCHRÖDER4ReP_i

h5, needs to be further developed and validated under various

growth conditions. One of the most important fields for further research is the development of the H100 model using Lithuania’s National Forest Inventory data, which is the most

appropriate and representative of the country’s data. This direction of research would also increase the plausibility of the SCHRÖDER4ReP_i

CHAPTER 5: DISCUSSION

145 5.4.5 Validation of re-parameterised basal area and height increment models

Data used for analysis. To validate re-parameterised basal area (SCHRÖDER7ReP_i

ba5) and height

increment (SCHRÖDER4ReP_i

h5) models, two validation plots, VP5 and VP7 were used. Although

these two VPs, provide good representation of the growth conditions of pines in Lithuania, the validation procedure hardly could be called reliable since only two VPs were used. This is the main weakness of this study.

Basal area increment models. The main results of the SCHRÖDER7ReP_i

ba5 model’s validation

were the remarkable negative bias when growth of trees was modelled from 34 to 59 years (VP5) and the degree of precision when growth of trees was simulated from 60 to 89 years (VP7). These results suggest the model’s capabilities to predict diameter growth, are to underestimate for trees at 34-59 years age and to be very precise for trees at 60-89 years age. The remarkable negative bias in plot VP5 could appear due to a couple of reasons. First, there might have been measurement failures in the field and second, the model tends to underestimate young trees.

There is a 12 year gap between the last two inventories (1996 and 2008) in VP5. During this time, trees’ identification numbers were lost and grid positions disappeared. According to Appendix 2, the site index HAB remained fairly static, at around 25m in the inventories of

1983 and 1996, yet at the last inventory in 2008 had increased to 28.4m. Similarly, between the 1996 inventory and the 2008 inventory, the site index DAB displayed a substantial increase

increased from 29.6 to 30.8cm. These increases in height and diameter could be either due to extremely intensive self-thinning (480 trees died between the inventories of 1996-2008), or due to measurement errors.

According to the yield tables (KULIEŠIS 1993), at a stocking level equal to 1 and HAB=24m,

Dq at 60 years should be 20.5cm. The predicted Dq value was 19.5 centimetres (Table 4-31),

which is too small, despite both a slightly higher HAB=25m (see Appendix 2) and a higher

stocking level of 1.13-1.2 (see Table 4-28).

Height increment models. The main results for the SCHRÖDER4ReP_i

h5 model were that

predictions for tree heights when growth of trees was modelled from 34 to 59 years (VP5) were underestimated and overestimated when growth of trees was simulated from 60 to 89 years (VP7). Despite the degree of bias for the two sites being circa 4% - positive (VP7) and negative (VP5) see Table 4-30.

A more important issue of concern is the model’s systematic tendency to underestimate the heights of smaller trees and to overestimate the heights of larger trees (Figure 4-58 and Figure

CHAPTER 5: DISCUSSION

146 4-60). The biggest values for relative height increment apply to the tallest trees that grow under very low competition. In the context of competing, the tallest trees in a stand normally endure less competition than ‘suppressed’ trees, the annual increments for which are considerably smaller. However, in the height growth model, which estimates relative tree height increment (SCHRÖDER4ReP_i

hrel), the relative potential for stand top height increment is

the same for all trees (Equation 4-5), which is the most likely reason for the non- homogeneous distribution of prediction residuals.

Stand level variables. The precision of predicted standing volumes is the most important information at stand level for practical forestry. The model’s inherent flaws in underestimating and overestimating tree diameters led to a reduction of the standing volume by 23% on VP5 and an increase by 2.2% on VP7 (see Table 4-31).

In conclusion, this validation procedure while showing the future objects of research and possible outcomes for re-parameterised models is unreliable for drawing any serious conclusions. Far more reliable results would be obtained if the validation procedure of the models was conducted using NFI data collected since 1998 (at the time of going to print the NFI archives hold 16 years of data).

In document Single Tree Level Simulator for Lituanian Pine Forests (Page 161-164)