1

Fig. 1. The location of field sample plot clusters.

Table 1. The main attributes of the 265 studied field plots. Min = minimum, Max = maximum, Sd = Standard deviation.
Attribute Population Mean Min1 Max Sd
Volume (m3 ha–1) Total 124.2 1.42 403.3 78.3
Scots pine 88.8 0.45 294.2 61.7
Norway spruce 39.2 0.19 400.6 55.8
Deciduous trees 17.6 0.25 167.5 23.8
Basal area (m2 ha–1) Total 16.8 0.43 44.6 7.9
Scots pine 11.5 0.14 33.1 6.6
Norway spruce 5.6 0.08 39.2 6.7
Deciduous trees 2.8 0.08 18.7 3.2
Mean diameter (cm) Total 14.3 6.6 33.6 4.4
Scots pine 17.6 6.1 41.6 6.9
Norway spruce 12.1 5.0 27.9 4.8
Deciduous trees 10.8 5.1 44.6 5.4
Mean height (cm) Total 12.0 2.7 23.9 3.4
Scots pine 13.9 5.0 28.3 4.8
Norway spruce 9.6 3.5 21.9 3.7
Deciduous trees 10.6 2.7 23.6 4.0
Number of stems (ha–1) Total 1014 196 2790 507
Scots pine 538 39 1965 362
Norway spruce 365 39 2476 401
Deciduous trees 307 39 2397 308
Mean crown base height (dm) Total 48.9 8.7 129.6 21.0
Scots pine 67.3 8.8 189.3 34.1
Norway spruce 20.1 3.0 62.6 13.5
Deciduous trees 42.5 7.0 137.0 23.7
Basal-area-weighted mean crown base height (dm) Total 58.9 8.8 155.5 25.9
Scots pine 70.9 8.9 188.5 34.4
Norway spruce 22.9 3.0 64.2 15.6
Deciduous trees 46.4 7.0 142.4 26.9
1 The Min-values present the smallest observations > 0, because all factually observed species-specific min-values would have been zeroes due to the absence of species in many plots (Scots pine was met on 246 plots, Norway spruce on 185 plots and deciduous trees on 218 plots).
Table 2. The distribution of plots according to categorical stand characteristics. DBH is the arithmetic mean of the DBH at the plot-level. The dominant species was determined as the species with the largest proportion from the sum of tree stem volumes in a plot.
Characteristic Sub class N %
Soil type   Mineral soil 201 75.8
Peat soil 64 24.2
Site type   Fertile / Oxalis-Myrtillus type (OMT) 2 0.8
Moderate / Vaccinium Myrtillus type (MT) 181 68.3
Poor / Vaccinium vitis-idaea type (VT) 82 30.9
Development class   T2 (DBH < 8 cm) 8 3.0
02 (8 cm ≤ DBH < 16 cm) 184 69.4
03 (16 cm ≤ DBH < 24 cm) 65 24.5
04 (DBH ≥ 24 cm) 8 3.0
Dominant species   Scots pine 208 78.5
Norway spruce 42 15.8
Deciduous trees 15 5.7
Table 3. The ALS metrics used in this study. Suffices single and first refer to using only single or first-of-many echoes, respectively; otherwise, the metrics were computed using pooled single and first-of-many echoes.
ALS metric Definition
CBHas CBH prediction based on alpha shapes (see Section 2.3.3)
Hmax Maximum height
Hmean Mean height
Hstd Standard deviation of height
Vegeratio Ratio of the number of echoes above 2 m to the total number of echoes
H05…H95 ith percentile of height
D05…D95 Relative density at height i
Imean Mean intensity
Imeansingle Mean intensity (single echoes)
Imeanfirst Mean intensity (first-of-many echoes)
Istd Standard deviation of intensity
Istdsingle Standard deviation of intensity (single echoes)
Istdfirst Standard deviation of intensity (first-of-many echoes)
Prop_first Proportion of first-of-many echoes
Table 4. Features selected for the tree list imputations. The RMSEs refers to those of basal-area weighted plot-level mean CBHs and the Impr. columns give the improvement in RMSE (%) compared to the previous step.
Step X-feature(s) Y-feature(s) RMSE RMSE
k = 1 Impr. k = 5 Impr.
1   All Heightmin 3.11 - 2.77 -
All Heightmin + Height70 1.59 49.04 1.42 48.58
All Heightmin + Height70 + Diameter80 1.54 2.59 1.36 4.24
2   Hmean Heightmin + Height70 + Diameter80 1.47 4.95 1.34 1.49
Hmean + D90 Heightmin + Height70 + Diameter80 1.30 11.19 1.23 7.97
Hmean + D90 + H10 Heightmin + Height70 + Diameter80 1.30 0.57 1.23 0.38
Table 5. The RMSEs and biases obtained with different methods when predicting the plot-level arithmetic mean crown base height (CBHARI) or basal-area-weighted mean crown base height (CBHBAW) for the whole study data.
CBHARI PMk-NN LME-model α-shape LR-model
RMSE (dm) 12.65 15.61 16.42 11.29
%-RMSE 25.89 31.95 33.59 23.10
BIAS (dm) –0.64 –8.43 –9.67 –0.01
%-BIAS –1.30 –17.25 –19.79 –0.02
CBHBAW
RMSE (dm) 14.47 17.42 15.16 12.29
%-RMSE 24.59 29.60 25.76 20.89
BIAS (dm) 1.05 –8.91 0.31 0.02
%-BIAS 1.78 –15.13 0.53 0.03
Table 6. The RMSEs and biases obtained with different methods when predicting the plot-level arithmetic mean CBH for the plots dominated by different species or mixed plots.
Scots pine (n = 201) PMk-NN LME-model α-shape LR-model
RMSE (dm) 12.71 14.00 15.55 11.14
%-RMSE 24.68 27.19 30.21 21.63
BIAS (dm) 1.10 –6.25 –8.50 0.79
%-BIAS 2.14 –12.14 –16.52 1.53
Norway spruce (n = 38)
RMSE (dm) 9.32 17.48 14.11 7.97
%-RMSE 20.86 39.12 31.57 17.83
BIAS (dm) –2.71 –13.93 –9.66 0.19
%-BIAS –6.07 –31.17 –21.62 0.42
Deciduous species (n = 15)
RMSE (dm) 18.93 27.63 29.21 16.88
%-RMSE 55.66 81.24 85.90 49.64
BIAS (dm) –13.68 –20.46 –22.46 –8.34
%-BIAS –40.23 –60.15 –66.03 –24.55
Mixed (n = 11)
RMSE (dm) 10.88 13.98 14.81 7.60
%-RMSE 30.50 39.19 41.51 21.29
BIAS (dm) –7.41 –12.76 –13.58 –3.67
%-BIAS –20.78 –35.75 –38.08 –10.30
Table 7. The RMSEs and biases obtained with different methods when predicting the plot-level basal-area-weighted mean CBH for the plots dominated by different species or mixed plots .
Scots pine (n = 201) PMk-NN LME-model α-shape LR-model
RMSE (dm) 13.88 12.81 14.72 11.54
%-RMSE 22.31 20.58 23.66 18.54
BIAS (dm) 4.34 –4.58 2.24 2.20
%-BIAS 6.97 –7.36 3.60 3.53
Norway spruce (n = 38)
RMSE (dm) 14.04 26.33 13.38 11.63
%-RMSE 26.04 48.84 24.82 21.57
BIAS (dm) –6.80 –22.86 –0.45 –5.94
%-BIAS –12.61 –42.39 –0.83 –11.02
Deciduous species (n = 15)
RMSE (dm) 21.28 33.07 24.12 21.04
%-RMSE 55.80 86.74 63.26 55.19
BIAS (dm) –14.95 –24.82 –18.34 –9.66
%-BIAS –39.20 –65.11 –48.12 –25.33
Mixed (n = 11)
RMSE (dm) 14.99 20.67 12.73 11.72
%-RMSE 35.27 48.67 29.98 27.59
BIAS (dm) –10.15 –18.07 –6.79 –5.95
%-BIAS –23.89 –42.54 –15.98 –14.02
2

Fig. 2. Residuals of the different methods in the prediction of arithmetic mean CBH.

3

Fig. 3. Residuals of the different methods in the prediction of basal-area-weighted mean CBH.