Table 1. Site and initial stand characteristics of the 1711 selected National Forest Inventory permanent plots.
  Site index a)
(m) 		Stand age b)
(years) 		Diameter at
breast height b)
(cm) 		Mean height b)
(m) 		Basal area
(m2 ha–1) 		No. of stems
ha–1
Average 21.7 79 20.6 15.5 21.2 2526
Min 8.0 17 5.7 8.0 0.5 32
5%-percentile 13.0 25 10.6 8.5 8.1 318
95%-percentile 32.0 155 33.5 24.0 38.3 7669
Max 38.0 255 59.7 35.0 61.7 28482
Stdv 5.7 42 7.3 4.9 9.3 2841
a) Site index (H100) calculated based on site factors for Scots pine and Norway spruce, respectively (Hägglund and Lundmark 1977)
b) Basal area weighted mean (ƩX×d2 / Ʃd2)
Table 2. Initial site and stand characteristics of the 57 blocks from the thinning experiment used for evaluating long-term Heureka simulations.
  Latitude Site index a) Basal area
(m2 ha–1) 		No. of stems
ha–1 		Top height
(m) 		Stand age
(years)
Scots pine Average   21.3 24.1 2151 13.4 41.0
Min 56°23´N 14.8 14.6 1295 11.8 32.0
40 blocks Max 67°29´N 26.9 36.3 3585 15.4 58.0
Stdv   3.4 4.65 542 1.07 6.47
Norway spruce Average   29.6 32.8 3136 13.8 29.8
Min 56°06´N 22.0 23.7 1346 12.6 23.0
17 blocks Max 63°14´N 32.3 39.0 4931 16.2 37.0
Stdv   2.6 4.90 1009 1.01 3.86
a) Site index (H100) according to site factors (Hägglund and Lundmark 1977)
Table 3. Description of the thinning treatments used in the experiments that provided the data against which the Heureka simulations were evaluated.
Species Treatment Number
of plots 		No. of
thinnings 		First thinning
Thinning grade a)
(%) 		Thinning
quotient b) 		Basal area
after thinning
(m2 ha–1) 		No. of stems ha–1
after thinning
Scots pine A 40 3–4 25.5 0.73 17.9 1265
B 16 2–3 43.1 0.73 13.0 869
C 40 1 59.4 0.73 9.6 563
D 16 3–4 50.6 0.72 11.7 760
F 40 3–4 24.3 1.16 18.1 1743
I 40 0        
Norway spruce A 17 3–6 22.3 0.71 25.2 1992
B 15 2–3 40.3 0.72 19.7 1408
C 17 1 64.8 0.72 11.1 684
D 9 4–6 43.9 0.71 19.4 1405
F 10 3–5 20.8 1.18 25.8 2580
I 17 0        
a) Percentage of basal area removed
b) Ratio of the diameters of removed and retained trees
Table 4. Summary of the evaluated basal area growth models and the alternative implementations of growth models in the Heureka system.
Name Basal area growth model Level Remarks
Growth models
OLD_S Ekö (1985) Stand Temporary NFI plots 1973–1977
OLD_T Söderberg (1986) Tree Temporary NFI plots 1973–1977
NEW_S Elfving (2010a) Stand Permanent NFI plots est. 1983–1987
NEW_T Elfving (2010a) Tree Permanent NFI plots est. 1983–1987
Configurations of Heureka
HEU_OLD Söderberg (1986) Tree OLD_T in use
HEU_NEW Elfving (2010a) Combined tree-stand NEW_S+NEW_T in use
1

Fig. 1. The standard deviation of residuals by NEW_S for the NFI-data in absolute (res, triangle) and transformed (zres, circle) terms in different classes of estimated growth.

Table 5. Basal area growth (iG, m2 ha–1) over a five year period based on observations of permanent National Forest Inventory plots and estimates generated using various basal area growth models. Residuals were calculated in absolute and relative terms. Significant deviation from 0 for relative residuals was marked with (*) (p < 0.001).
Variable 5 years basal area
growth (m2 ha–1) 		Residuals a) (m2 ha–1) Relative residuals b)
  Mean Std.dev. Mean Std.dev. r2 Mean Std.dev. r2
Observed 2.24 1.53            
OLD_S 2.40 1.38 –0.15 0.84 0.70 –0.043* 0.23 0.72
NEW_S 2.32 1.27 –0.07 0.76 0.75 –0.030* 0.22 0.75
OLD_T 2.30 1.42 –0.06 0.87 0.67 –0.008 0.24 0.70
NEW_T 2.12 1.17 0.13 0.82 0.71 0.033* 0.23 0.73
a) res = iGobs – iGest
b) zres = ln(iGobs + 1) – ln(iGest + 1) + Szres2 / 2
2

Fig. 2. Average relative residuals for basal area growth by OLD_S (unfilled circle), NEW_S (filled circle), OLD_T (unfilled triangle) and NEW_T (filled triangle) for plots measured in different measurement years in the NFI-data.

3

Fig. 3. Difference between average observed and estimated basal area growth (iG, m2 ha–1) over a five year period for the output of the different growth models (OLD_S (unfilled), NEW_S (horizontally hatched), OLD_T (black), NEW_T (obliquely hatched)) relative to observed data from the National Forest Inventory. The residuals are presented for different levels of: (a) the site index (H100), (b) initial total stand age, (c) initial basal area of trees with DBH values above 99 mm, the proportion of the overall basal area that consists of (d) Scots pine, (e) Norway spruce and (f) broadleaved tree species.

4

Fig. 4. Relative residuals for the mean annual basal area growth (iG, m2 ha–1 year–1) under different treatments and simulation lengths when comparing the output of Heureka simulations to data from a thinning experiment. Residuals and loess lines for Heureka simulations using HEU_NEW (circle, solid line) and HEU_OLD (cross, dashed line) are shown. Separate calculations were performed for plots of Scots pine and Norway spruce under treatments including light thinning from below (A) and above (F), as well as non-thinned plots (I). For a description of the thinning treatments, see Table 3.

Table 6. The standard deviations of residuals by HEU_NEW and HEU_OLD (ln(obs)-ln(est)) for basal area and volume growth in the GG-trials over the whole observation period. The variation was split on within and between blocks by variance analyses. There were 40 pine blocks with 4–6 plots per block and 17 spruce blocks with 3–6 plots per block.
Species Function Basal area growth Volume growth
within between within between
Pine HEU_NEW 0.070 0.119 0.075 0.117
HEU_OLD 0.068 0.182 0.075 0.163
Spruce HEU_NEW 0.101 0.156 0.098 0.180
HEU_OLD 0.099 0.123 0.093 0.155