Table 1. Summary of the two modelling data sets. hL = Lorey’s mean height, dg = mean diameter by basal area, G = basal area, V = volume.
  Ordinary sample plots ALS-assisted plots
Min. Max. Mean Min. Max. Mean
Young forest
(forest stratum I)
(n = 72)     (n = 59)
hL (m) 6.8 22.5 12.9 6.0 21.3 13.7
dg (cm) 6.9 24.4 12.8 5.1 26.2 14.2
G (m2 ha–1) 3.5 44.3 20.5 1.4 42.8 21.4
V (m3 ha–1) 18.4 440.8 140.2 4.4 374.8 155.0
Spruce (%) 0 100 61 0 100 57
Pine (%) 0 100 28 0 100 29
Deciduous (%) 0 69 11 0 70 13
Mature spruce forest, poor site quality
(forest stratum II)
(n = 59)     (n = 59)
hL (m) 8.1 23.1 15.9 7.8 22.2 16.4
dg (cm) 9.8 36.5 16.9 10.0 30.3 16.9
G (m2 ha–1) 8.4 48.4 27.1 2.9 49.5 28.1
V (m3 ha–1) 40.4 460.5 211.2 13.4 420.2 230.3
Spruce (%) 0 100 64 0 98 21
Pine (%) 0 100 26 0 51 10
Deciduous (%) 0 64 11 5 13 9
Mature spruce forest, good site quality
(forest stratum III)
(n = 58)     (n = 58)
hL (m) 10.0 26.5 18.6 11.4 34.5 19.9
dg (cm) 10.0 31.5 18.9 9.5 27.6 18.5
G (m2 ha–1) 6.0 47.9 28.1 9.9 66.7 33.8
V (m3 ha–1) 32.1 579.2 262.5 77.4 692.4 332.8
Spruce (%) 1 100 78 9 100 77
Pine (%) 0 87 13 0 90 12
Deciduous (%) 0 99 9 0 54 12
Mature pine forest
(forest stratum IV)
(n = 75)     (n = 59)
hL (m) 8.6 24.4 16.3 10.0 22.9 16.9
dg (cm) 9.9 30.6 18.0 10.3 30.6 19.1
G (m2 ha–1) 7.3 54.6 24.0 3.4 46.9 22.3
V (m3 ha–1) 39.1 584.1 196.3 21.4 426.9 186.0
Spruce (%) 0 100 26 0 99 28
Pine (%) 0 100 68 0 100 65
Deciduous (%) 0 40 6 0 56 7
1

Fig. 1. Visualization of the stratification of candidate plots based on the two ALS variables.

2

Fig. 2. Example of the use of two laser variables for plot selection in the municipality of Konsvinger in forest stratum IV. The plot shows the five pre-selected candidate plots in each ALS stratum defined by d0f and h70f.

3

Fig. 3. Distribution of h70f and d0f at the intended sample plots and the plots actually measured in the field for the ALS-assisted data set.

4

Fig. 4. Distribution of h70f and d0f at the ALS-assisted and ordinary sample plots.

Table 2. Summary of the validation data set. hL = Lorey’s mean height, dg = mean diameter by basal area, G = basal area, V = volume.
  Min Max Mean
Young forest
(forest stratum I)
(n = 19)
hL (m) 10.1 19.3 13.2
dg (cm) 7.5 22.0 12.7
G (m2 ha–1) 6.6 35.5 20.5
V (m3 ha–1) 36.1 328.1 144.6
Spruce (%) 0 99 69
Pine (%) 0 100 26
Deciduous (%) 0 19 5
Mature spruce forest, poor site quality
(forest stratum II)
(n = 20)
hL (m) 12.0 24.8 17.9
dg (cm) 10.2 27.1 17.5
G (m2 ha–1) 12.5 36.3 26.7
V (m3 ha–1) 82.2 389.5 236.4
Spruce (%) 22 100 76
Pine (%) 0 64 15
Deciduous (%) 0 38 9
Mature spruce forest, good site quality
(forest stratum III)
(n = 20)
hL (m) 16.4 29.2 20.7
dg (cm) 14.0 27.9 18.6
G (m2 ha–1) 18.9 49.6 34.3
V (m3 ha–1) 156.2 565.0 347.1
Spruce (%) 15 100 81
Pine (%) 0 82 14
Deciduous (%) 0 20 6
Mature pine forest
(forest stratum IV)
(n = 19)
hL (m) 13.8 21.6 17.0
dg (cm) 11.6 24.3 17.4
G (m2 ha–1) 11.6 33.9 22.6
V (m3 ha–1) 80.6 323.3 188.2
Spruce (%) 0 84 25
Pine (%) 15 100 74
Deciduous (%) 0 8 2
Table 3. Predictors selected to each model and their RMSE and R2 in the model data.
  n OLS predictors OLS RMSE
(%)
OLS R2 PLS latent
components
PLS RMSE
(%)
PLS R2
Young forest
(forest stratum I)
ALS-assisted plots 59 d6f h90l d1l     15.9 0.93 3 18.2 0.91
Ordinary plots 72 hmeanf d4f d1l d9l   16.0 0.92 3 15.9 0.93
Spruce forest at low fertility sites
(forest stratum II)
ALS-assisted plots 59 h40f h70f d4f h0l   13.9 0.89 3 14.7 0.88
Ordinary plots 59 hcvf h30f d3f d9f h10l 14.4 0.90 3 16.0 0.87
Spruce forest at high fertility sites
(forest stratum III)
ALS-assisted plots 58 hmeanf d0f     14.3 0.89 3 15.6 0.87
Ordinary plots 58 hmeanl d1l d5l     16.7 0.88 4 17.5 0.87
Pine forest
(forest stratum IV)
ALS-assisted plots 59 d9f h50l d2l d8l 14.1 0.92 4 13.9 0.92
Ordinary plots 75 hmeanf d0f d7l     21.4 0.84 4 19.9 0.86
Table 4. Relative RMSE and D between the reference and predicted volume in a cross-comparison test.
Method Stratum Laser-assisted model, ordinary plots Ordinary model, laser-assisted plots
n Mean volume RMSE% D% n Mean volume RMSE% D%
OLS I 72 140.2 17.9 3.5 59 155.0 16.7 2.5
II 59 211.2 21.5 3.1 59 230.3 22.5 1.7
III 58 262.5 18.5 0.6 58 332.8 17.1 2.9
IV 75 196.3 27.3 2.0 59 186.0 20.9 5.8*
PLS I 72 140.2 18.8 –4.4* 59 155.0 18.7 4.9*
II 59 211.2 20.6 1.2 59 230.3 18.9 –2.0
III 58 262.5 18.4 –0.1 58 332.8 16.7 3.5
IV 75 196.3 25.0 3.7 59 186.0 23.7 –4.0
*Mean difference statistically significant at p = 0.05
Table 5. Relative RMSE and D between the reference and predicted volume in the validation plots.
Method Stratum n Mean volume Laser-assisted model Ordinary model
RMSE% D% RMSE% D%
OLS I 19 144.6 15.3 2.7 15.1 4.9
II 20 236.4 14.0 1.6 15.6 4.3
III 20 347.1 15.7 8.4* 16.9 10.4*
IV 19 188.2 17.3 1.7 17.0 2.9
PLS I 19 144.6 15.3 1.7 16.3 5.6
II 20 236.4 14.3 2.6 13.8 0.4
III 20 347.1 15.8 6.8 17.2 9.9*
IV 19 188.2 18.2 3.1 16.8 2.1
*Mean difference statistically significant at p = 0.05
5

Fig. 5. Cross-comparison of the OLS models. Black = predictions for ordinary plots using the ALS-assisted model, white = prediction for ALS-assisted plots using ordinary model.

6

Fig. 6. OLS model predictions for the validation plots.

Table 6. Results of reducing the number of plots by sub-sampling. The RMSE and D are PLS averages after 300 iterations.
  n Forest stratum I Forest stratum II Forest stratum III Forest stratum IV
RMSE (%) D (%) RMSE (%) D (%) RMSE (%) D (%) RMSE (%) D (%)
ALS-assisted All 15.3 1.7 14.3 2.6 15.8 6.8 18.2 3.1
50 15.3 1.6 14.9 2.3 16.0 6.4 18.1 2.6
40 16.0 2.2 15.0 1.7 16.7 5.8 18.1 2.0
30 15.9 2.1 16.2 1.3 17.0 6.2 18.7 2.4
20 16.6 3.4 17.2 1.3 18.6 5.8 19.7 1.5
15 17.1 2.9 17.5 1.2 19.2 6.0 20.0 1.6
Ordinary All 16.3 5.6 13.8 0.4 17.2 9.9 16.8 2.1
50 16.6 5.0 14.0 0.1 17.0 9.3 17.7 2.0
40 17.2 5.4 14.8 –0.5 17.1 8.9 18.4 1.4
30 17.5 5.1 15.5 –0.2 18.4 9.3 19.1 0.8
20 18.3 6.0 16.6 0.3 19.5 9.0 21.0 –0.4
15 20.7 5.9 18.4 0.3 21.1 9.1 22.6 –0.4