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Fig. 1. Locations of Pinus sylvestris forest experimental sites used in this study. Sites from western Norway were excluded from the analysis due to the distinctly different climate of that region.

Table 1. Summary statistics of stand-level metrics for thinned and unthinned plots of the model development dataset used in this study. Metrics were derived from even-aged Pinus sylvestris forests in Norway and comprise number of growth intervals (N), total stand age (AGE), site index for Scots pine at base age 40 (SI40), dominant height (HTDOM), number of trees per hectare (TPH), basal area (BA), total stem volume (VOL), age at thinning intervention (AGETHIN), and basal area removed at thinning (BAREM). Values refer to measurements at the beginning of a growth interval and SI40 was derived using the dominant height model developed in this study.
Treatment N AGE SI40 HTDOM TPH BA VOL AGETHIN BAREM
(year) (m) (m) (# ha–1) (m2 ha–1) (m3 ha–1) (year) (m2 ha–1)
Unthinned 250 Mean 51 11.2 13.9 2280 28 187
SD 15 2.5 3.6 1147 11.7 115
Min 22 5.1 6.8 900 8.7 40
Max 109 17.4 28.2 6080 56.5 620
Thinned 781 Mean 55 11.6 15.3 1380 24.8 184 44 4.7
SD 15 2.4 4.2 633 8 96 11 3.3
Min 16 6.1 6.1 280 5.5 20 16 0.1
Max 109 18.2 28.7 4730 53.1 667 77 24.4
Table 2. Abbreviations and definitions of the stand-level variables used in this work. Subscripts of 1 or 2 denote values at the beginning and the end of a measurement period, respectively.
Abbreviation Definition
AGE1,2 Total stand age (years)
AGETHIN Total stand age at the time of thinning (years)
BA1,2 Total stand basal area (m2 ha–1)
BAAFTER Total stand basal area after thinning (m2 ha–1)
BABEFORE Total stand basal area before thinning (m2 ha–1)
BAREM Total stand basal area removed in a thinning (m2 ha–1)
HTDOM Dominant height (m)
HTTHIN Dominant height at the time of thinning (m)
QMD1,2 Quadratic mean diameter (cm)
SI40 Site index (HTDOM at base stand age of 40 years, m)
TPH1,2 Stem density (number of trees ha–1)
TPHAFTER Stem density after thinning (number of trees ha–1)
TPHBEFORE Stem density before thinning (number of trees ha–1)
VOL1,2 Total stem volume over bark (m3 ha–1)
Table 3. Parameter estimates (standard errors) and model fit statistics including mean error (ME), mean absolute error (MAE), and relative MAE (MAE%) for the individual components (Eqs. 5–9) of the stand-level growth and yield model for thinned and unthinned, even-aged Pinus sylvestris forests in Norway. Seemingly unrelated regression was used to derive parameter estimates.
HTDOM2 TPH2 BA2 VOL2 TPHAFTER/TPHBEFORE
βi1 68.41819 –1.56856 1.46553 0.65394 –1.91239
(1.84110) (0.12049) (0.01025) (0.01095) (0.03209)
βi2 –24.04110 0.00284 0.52449 0.96928 1.94414
(1.82025) (0.00489) (0.01996) (0.00330) (0.03759)
βi3 1.46991 4.14779 0.17701 0.91504
(0.01026) (0.25666) (0.00978) (0.00406)
βi4 4.87715 16.53755 –2.05278
(0.23971) (1.07667) (0.24101)
βi5 –386.71670 –0.06848
(97.76230) (0.00646)
ME 0.01458 –0.11108 0.02192 0.13014 –0.00041
MAE 0.34876 46.25402 0.74455 3.92983 0.03386
MAE% 2.18346 2.74474 2.71853 1.97324 5.17959
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Fig. 2. Residual plots for Eqs. 5–8 representing HTDOM2, TPH2, BA2, and VOL2 of observations from thinned and unthinned plots. Eqs. 5–8 belong to the presented growth and yield model for single-species stands of Pinus sylvestris growing in Norway. View larger in new window/tab.

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Fig. 3. Dominant height (HTDOM), trees per hectare (TPH), basal area (BA), and total stem volume (VOL) residuals (Eqs. 5–8) plotted over plot latitude for thinned and unthinned plots. Eqs. 5–8 belong to the presented growth and yield model for even-aged stands of Pinus sylvestris growing in Norway. View larger in new window/tab.

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Fig. 4. Predictions in stem density, basal area, and total stem volume for three even-aged Pinus sylvestris stands in Norway representing different site indices (SI40 5, 11, and 17 representing dominant stand heights of 5, 11, and 17 m at age 40 years, respectively). Predictions were derived using 5 year prediction intervals and comprise different management scenarios including an unthinned treatment and a single thinning removing 25% of the basal area at 8, 10, or 12 m dominant stand height for SI40 5, 11, and 17, respectively. View larger in new window/tab.

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Fig. 5. Comparison of site-index (base age 40 years) curves for even-aged stands of Pinus sylvestris in Norway derived from Tveite (1976) and Sharma et al. (2011) and Eq. 5 of this study. View larger in new window/tab.

Table 4. Prediction accuracy metrics including mean error (ME), mean absolute error (MAE), and relative MAE (MAE%) for predicted number of stems per hectare (TPH), basal area (BA), quadratic mean diameter (QMD), and total stem volume (VOL) as derived from this study’s component models as well as existing, previously published models for even-aged Pinus sylvestris stands in Norway. Fit statistics are presented for observations from thinned and unthinned permanent sample plots of this study’s model development dataset and an independent dataset from the Norwegian National Forest Inventory (NFI).
Component Model Unthinned Thinned
ME MAE MAE% ME MAE MAE%
Model development dataset
TPH This study 5.6835 87.2168 3.9172 –1.8884 33.6900 2.3851
Eid & Øyen (2003) –106.9901 135.1629 6.2082 –26.4859 37.7290 2.6150
BA This study –0.0949 1.0599 3.5686 0.0639 0.8764 3.3289
Brantseg (1969) –1.4966 1.8999 5.7684 –0.5530 1.1390 4.1720
QMD This study (BA & TPH) 0.0108 0.2529 1.8431 0.1238 0.3215 2.0004
Blingsmo (1984) 0.2010 0.3145 2.1849 0.2684 0.3709 2.3439
VOL This study –1.4335 9.6842 4.9385 1.2319 9.8617 4.8670
Gizachew & Brunner (2011) –28.0282 28.3641 12.1442 –28.8161 29.0331 13.2350
Independent NFI dataset
TPH This study –14.7621 29.8658 3.1212 –3.8224 14.5595 2.1439
Eid & Øyen (2003) –27.3764 27.8525 2.9961 –9.6650 10.1904 1.5891
BA This study –0.3519 0.8225 4.6591 0.5458 0.8415 4.1951
Brantseg (1969) –0.4961 0.9223 5.0509 0.3200 0.7340 3.9558
QMD This study (BA & TPH) –0.0582 0.4344 2.5864 0.3087 0.5349 2.5887
Blingsmo (1984) –0.0688 0.3225 1.9894 0.3396 0.5242 2.5556
VOL This study –11.3532 12.7894 10.4393 –3.5742 9.2175 5.6481
Gizachew & Brunner (2011) –16.3738 16.8886 13.5945 –8.2044 11.6250 8.4833