Silva Fennica

Table 1. Summary of the two modelling data sets. h_L = Lorey’s mean height, d_g = 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)
h_L (m)	6.8	22.5	12.9	6.0	21.3	13.7
d_g (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)
h_L (m)	8.1	23.1	15.9	7.8	22.2	16.4
d_g (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)
h_L (m)	10.0	26.5	18.6	11.4	34.5	19.9
d_g (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)
h_L (m)	8.6	24.4	16.3	10.0	22.9	16.9
d_g (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

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

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 d_0f and h_70f.

Fig. 3. Distribution of h_70f and d_0f at the intended sample plots and the plots actually measured in the field for the ALS-assisted data set.

Fig. 4. Distribution of h_70f and d_0f at the ALS-assisted and ordinary sample plots.

Table 2. Summary of the validation data set. h_L = Lorey’s mean height, d_g = mean diameter by basal area, G = basal area, V = volume.
	Min	Max	Mean
Young forest (forest stratum I)			(n = 19)
h_L (m)	10.1	19.3	13.2
d_g (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)
h_L (m)	12.0	24.8	17.9
d_g (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)
h_L (m)	16.4	29.2	20.7
d_g (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)
h_L (m)	13.8	21.6	17.0
d_g (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	d_6f	h_90l	d_1l			15.9	0.93	3	18.2	0.91
Ordinary plots	72	h_meanf	d_4f	d_1l	d_9l		16.0	0.92	3	15.9	0.93
Spruce forest at low fertility sites (forest stratum II)
ALS-assisted plots	59	h_40f	h_70f	d_4f	h_0l		13.9	0.89	3	14.7	0.88
Ordinary plots	59	h_cvf	h_30f	d_3f	d_9f	h_10l	14.4	0.90	3	16.0	0.87
Spruce forest at high fertility sites (forest stratum III)
ALS-assisted plots	58	h_meanf	d_0f				14.3	0.89	3	15.6	0.87
Ordinary plots	58	h_meanl	d_1l	d_5l			16.7	0.88	4	17.5	0.87
Pine forest (forest stratum IV)
ALS-assisted plots	59	d_9f	h_50l	d_2l	d_8l		14.1	0.92	4	13.9	0.92
Ordinary plots	75	h_meanf	d_0f	d_7l			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
Method	Stratum	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
Method	Stratum	n	Mean volume	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

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.

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
	n	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