1

Fig. 1. Location of the three districts used in the study: Nordre Land (A), Krødsherad (B), and Hole (C).

Table 1. Overview of the districts (A, B, and C) and their measured plots used in the study at two points in time (T1 and T2).
Training plot T1 Training plot T2 Validation plot T2
District Elev. Year n ps P Year n ps P n ps P
A 140–900 2003 193 250 0.73 2017 170 250 0.64 25 1000 0.28
B 130–660 2001 74 232.9 0.39 2016/17 75 232.9 0.35 43 3721 0.44
C 240–480 2005 78 250 1 2017 43 250 1 22 1000 1
Elev. = elevation above sea level (m); n = number of plots; ps = plot size (m2); P = proportion of spruce-dominated plots.
2

Fig. 2. Box plots showing the distribution of the field plot attributes per district (dominant heigh (Ho), volume (V), and stem number (N)) for the training plots measured at two points in time (T1 and T2) and the validation plots measured at T2. The mean value is indicated with a red dot.

Table 2. Summary of ALS instrument specifications and flight acquisition parameter settings for the different districts (A, B and C).
District year Instrument Mean flying altitude (m) Pulse repetition frequency (kHz) Scanning frequency (Hz) Mean point density (pts m–2)
First acquisition (T1)
A 2003 Optech ALTM 1233 800 33 40 1
B 2001 Optech ALTM 1210 650 10 30 1
C 2005 Optech ALTM 3100 2000 50 38 1
Second acquisition (T2)
A 2016 Riegl LMS Q-1560 2900 400 100 4
B 2016 Riegl LMS Q-1560 1300 534 115 12
C 2016 Riegl LMS Q-1560 1300 534 115 10
3

Fig. 3. Flowchart showing the main analysis of the methodology to calibrate forest attribute predictions from external models.

Table 3. Results of the two-sample Kolmogorov-Smirnov test between the training field plots measured at two points in time (T1 and T2) and the validation plots measured at T2 in the three districts (A, B and C).
Validation district A (T2) Validation district B (T2) Validation district C (T2)
District Statistic H V N H V N H V N
A (T1) D 0.39 0.28 0.22
p-value 0.002 0.04 0.22
A (T2) D 0.36 0.24 0.26 0.14 0.17 0.12 0.13 0.20 0.18
p-value 0.005 0.14 0.10 0.43 0.22 0.69 0.86 0.41 0.55
B (T1) D 0.19 0.21 0.21
p-value 0.25 0.14 0.20
B (T2) D 0.17 0.15 0.10
p-value 0.37 0.51 0.93
C (T1) D 0.22 0.28 0.19
p-value 0.38 0.14 0.52
C (T2) D 0.08 0.24 0.15
p-value 1 0.37 0.88
Table 4. Selected predictors and validation results for temporally and spatially externally models for Ho, V and N. RMSE% and relative mean difference of predictions (MD%) with corresponding 95% confidence intervals (CIRMSE, CIMD), and error model parameters (λ0, λ1, and σεm) were calculated after application of the models on validation datasets from districts A, B, and C.
Predictors* RMSE% CIRMSE MD% CIMD λ0 λ1 σεm
Temporal
A Ho H90, D0 8.3 5.8, 10.9 –2.0 –5.1, 1 7.0 0.7 1.5
V H70, D0 22.6 16.1, 29.1 9.1 –0.1, 17.4 90.8 0.8 62.0
N Hmax, D0, D9 25.8 19.0, 33.1 2.1 –8.4, 12.4 267.5 0.6 135.0
B Ho H90, D5 5.1 3.7,6.5 0.4 –1.2, 1.9 4.1 0.8 0.9
V H80, D0 15.6 9.8, 22.0 5.1 0.6, 9.6 49.7 0.9 37.0
N H80, D1 26.8 19.2, 34.8 –7.1 –13.9, –0.1 320.8 0.5 125.8
C Ho H90, D0, D7 4.5 3.3, 5.8 2.0 0.3, 3.8 2.3 0.9 0.8
V H40, D4 19.0 11.7, 26.9 5.9 –2.2, 14 52.5 0.9 44.4
N H90, D4 25.1 17.5, 34 –9.9 –18.1, –1.7 285.3 0.5 100.3
Spatial
B Ho H90 5.3 3.8, 6.7 1.5 –0.1, 3.1 5.2 0.8 0.7
V H90, D0, D8 21.2 14.1, 28.9 11.4 6.5, 16.6 1.7 1.1 46.6
N Hmax, H30, D0 26.0 17.4, 34.4 12.5 4.3, 20.1 266.8 0.8 158.8
C Ho H90 5.0 3.5, 6.6 –0.5 –2.3, 2.0 4.1 0.8 0.8
V H90, D0, D8 19.8 10.5, 29.1 4.7 –3.3, 12.4 48.9 0.9 46.0
N Hmax, H30, D0 26.3 18.5, 34.6 15.5 5.5, 25.4 291.7 0.8 145.9
* H30, H40, H70, H80 and H90 = 30, 40, 70, 80 and 90 percentiles of the laser canopy heights; Hmax = maximum laser canopy height; D0, D1, … D9 = canopy densities corresponding to the proportions of laser returns above each bin # 0, 1, … 9, respectively, to total number of returns (see text).
4

Fig. 4. MD% and RMSE% distributions from 1000 iterations in simulations of different calibration approaches (as boxplots) using external prediction models of dominant height in district B. The MD% (upper panel) and RMSE% (lower panel) of uncalibrated external predictions are displayed with dashed lines (blue = spatial, red = temporal) with corresponding confidence intervals displayed as colored areas around the respective lines.

5

Fig. 5. MD% (upper) and RMSE% (lower) distributions from 1000 iterations in simulations of different calibration approaches (as boxplots) using external prediction models of volume in district C. The uncalibrated external predictions are displayed with dashed lines (blue = spatial, red = temporal) with the corresponding confidence intervals as colored areas around the respective lines.

6

Fig. 6. MD% and RMSE% distributions from 1000 iterations in simulations of different calibration approaches (as boxplots) using external prediction models of stem number in district C. The MD% (upper panel) and RMSE% (lower panel) of uncalibrated external predictions are displayed with dashed lines (blue = spatial, red = temporal) with corresponding confidence intervals displayed as colored areas around the respective lines.

Table 5. Median values of RMSE%, MD%, λ0, λ1, and σεm after 1000 iterations of applying the different calibration approaches (C1, C2, and C3) using 20 calibration plots, and the new inventory where the prediction models were created with 60 plots (NI60) for each district (A, B, and C).
Ho V N
A NI60 8.4 –1.5 8.2 0.6 1.5 22.8 4.1 75.0 0.8 67.7 27.2 11.8 235.9 0.8 148.9
Temporal C1 8.5 –1.5 8.0 0.7 1.5 22.5 3.7 88.0 0.8 63.0 29.4 6.2 319.6 0.6 150.4
Temporal C2 9.3 –1.8 8.3 0.6 1.7 25.3 6.3 64.9 0.9 76.6 30.4 5.5 301.55 0.6 163.3
Temporal C3 9.0 –1.6 8.1 0.6 1.6 23.9 4.6 56.3 0.89 73.4 31.9 11.2 227.9 0.8 185.8
B NI60 5.1 –1.1 2.9 0.9 0.9 19.4 7.6 33.6 1.0 45.7 26.0 7.2 210.8 0.8 177.3
Temporal C1 5.6 –1.1 4.0 0.8 0.9 17.2 6.6 48.6 0.9 38.8 24.9 5.2 293.7 0.7 149.5
Temporal C2 5.1 –0.9 2.8 0.9 0.9 17.2 6.7 31.4 1.0 40.7 26.7 5.3 302.6 0.7 163.0
Temporal C3 5.3 –0.9 2.5 0.9 0.9 18.8 6.8 31.3 1.0 44.1 26.4 5.4 262.0 0.7 168.5
Spatial C1 6.2 –1.0 4.5 0.8 1.0 19.5 6.7 13.0 1.0 47.2 22.9 4.9 209.2 0.8 153.4
Spatial C2 5.9 –0.7 3.0 0.9 1.0 18.6 6.2 29.9 1.0 43.8 24.0 4.0 189.6 0.8 162.7
Spatial C3 5.8 –0.8 3.3 0.8 1.0 22.0 7.5 21.1 1.0 52.1 25.7 4.9 184.2 0.8 175.6
C NI60 4.3 0.3 1.9 0.9 0.9 18.5 1.8 29.0 0.9 46.9 26.5 –3.1 284.6 0.6 154.8
Temporal C1 4.2 –0.2 2.2 0.9 0.8 19.2 1.8 51.4 0.8 45.8 24.6 –4.1 313.8 0.5 119.7
Temporal C2 4.2 –0.2 1.4 0.9 0.9 20.3 1.8 38.2 0.9 50.4 26.1 –4.8 304.9 0.5 135.7
Temporal C3 4.4 –0.0 1.3 0.9 0.9 21.8 1.5 32.5 0.9 54.8 26.1 –5.1 273.0 0.6 145.2
Spatial C1 5.2 0.1 4.2 0.8 0.8 19.6 0.3 48.0 0.8 47.2 23.9 –5.9 246.2 0.6 131.0
Spatial C2 4.7 0.2 2.0 0.9 0.9 20.8 0.4 35.6 0.9 51.9 25.8 –6.6 256.7 0.6 141.8
Spatial C3 4.9 0.2 2.1 0.9 1.0 21.5 –0.4 29.3 0.9 54.0 33.6 2.7 276.5 0.7 223.5