Appendix C
Supplementary figures
First returns Pearson
Last returns Pearson
Combined Pearson
First returns MSE
Last returns MSE
Combined MSE
non-sp. CI (CI-1)
Correlation and MSE
0.0 0.4 0.8
H90
Correlation and MSE
0.0 0.4 0.8
H95
2
4
6
8
10
Search radius (m)
12
2
12
Correlation and MSE
0.0 0.4 0.8
H60
Correlation and MSE
0.0 0.4 0.8
H70
4
6
8
10
Search radius (m)
2
4
6
8
10
Search radius (m)
12
2
12
Correlation and MSE
0.0 0.4 0.8
STD
Correlation and MSE
0.0 0.4 0.8
Mean percentile
4
6
8
10
Search radius (m)
2
4
6
8
10
Search radius (m)
12
2
4
6
8
10
Search radius (m)
12
Figure C. 1.The observed Pearson correlation and unit scale standardized MSE of a regression through the origin
between the best ALS-metric variables of Error! Reference source not found. (header of subplots) and CI-1, the nonspatially explicit CI (CI-1) (Error! Reference source not found.). Calculations were done for the first, last and combined ALSreturns, for search radii of 1 to 12 m around the subject tree.
Lorimer´s CI
First returns Pearson
Last returns Pearson
Combined Pearson
First returns MSE
Last returns MSE
Combined MSE
Correlation and MSE
0.0 0.4 0.8
H90
Correlation and MSE
0.0 0.4 0.8
H95
2
4
6
8
10
Search radius (m)
12
2
12
Correlation and MSE
0.0 0.4 0.8
H60
Correlation and MSE
0.0 0.4 0.8
H70
4
6
8
10
Search radius (m)
2
4
6
8
10
Search radius (m)
12
2
12
Correlation and MSE
0.0 0.4 0.8
STD
Correlation and MSE
0.0 0.4 0.8
Mean percentile
4
6
8
10
Search radius (m)
2
4
6
8
10
Search radius (m)
12
2
4
6
8
10
Search radius (m)
12
Figure C. 2. The observed Pearson correlation and unit scale standardized MSE of a regression through the origin
between the best ALS-metric variables of Error! Reference source not found. (header of subplots) and Lorimer´s CI (CI-2)
(Error! Reference source not found.). Calculations were done for the first, last and combined ALS-returns, for search radii
of 1 to 12 m around the subject tree.
First returns Pearson
Last returns Pearson
Combined Pearson
First returns MSE
Last returns MSE
Combined MSE
Martin and Ek CI
Correlation and MSE
0.0 0.4 0.8
H90
Correlation and MSE
0.0 0.4 0.8
H95
2
4
6
8
10
Search radius (m)
12
2
12
Correlation and MSE
0.0 0.4 0.8
H60
Correlation and MSE
0.0 0.4 0.8
H70
4
6
8
10
Search radius (m)
2
4
6
8
10
Search radius (m)
12
2
12
Correlation and MSE
0.0 0.4 0.8
STD
Correlation and MSE
0.0 0.4 0.8
Mean percentile
4
6
8
10
Search radius (m)
2
4
6
8
10
Search radius (m)
12
2
4
6
8
10
Search radius (m)
12
Figure C. 3.The observed Pearson correlation and unit scale standardized MSE of a regression through the origin
between the best ALS-metric variables of Error! Reference source not found. (header of subplots) and Martin and Ek CI
(CI-4) (Error! Reference source not found.). Calculations were done for the first, last and combined ALS-returns, for
search radii of 1 to 12 m around the subject tree.
First returns Pearson
Last returns Pearson
Combined Pearson
First returns MSE
Last returns MSE
Combined MSE
Daniels CI
Correlation and MSE
0.0 0.4 0.8
H90
Correlation and MSE
0.0 0.4 0.8
H95
2
4
6
8
10
Search radius (m)
12
2
12
Correlation and MSE
0.0 0.4 0.8
H60
Correlation and MSE
0.0 0.4 0.8
H70
4
6
8
10
Search radius (m)
2
4
6
8
10
Search radius (m)
12
2
12
Correlation and MSE
0.0 0.4 0.8
STD
Correlation and MSE
0.0 0.4 0.8
Mean percentile
4
6
8
10
Search radius (m)
2
4
6
8
10
Search radius (m)
12
2
4
6
8
10
Search radius (m)
12
Figure C. 4. The observed Pearson correlation and unit scale standardized MSE of a regression through the origin
between the best ALS-metric variables of Error! Reference source not found. (header of subplots) and Daniels CI (CI-5)
(Error! Reference source not found.). Calculations were done for the first, last and combined ALS-returns, for search radii
of 1 to 12 m around the subject tree.
Frequency
0.15 0.30
Observed dbh on plot
0.00
a)
50
90
130
170
210
250
290
330
Observed dbh (mm)
370
410
450
490
Frequency
0.15 0.30
Predicted dbh outside plot edge
0.00
b)
50
90
130
170
210
250
290
330
Predicted dbh (mm)
370
410
450
490
Relative frequence
0.0 0.2 0.4 0.6
Relative frequence of species-totals in or outside the plot
Predicted species in buffer
Observed species on plot
conifer
others
Tree species class
c)
pine
Figure C. 5. Performance of models predicting buffer tree attributes. The Figure shows a histogram for aggregated
data of the observed dbh for all trees inside the plot i.e. for the original data (subplot a) and the predicted dbh values
according to the glm-model (subplot b). In subplot c the observed frequencies of the tree species classes “Conifer”,
“Pine”, and “Others” relative to the total is calculated and compared between original data (grey bars), and the
predictions made by the multicategorical logit glm-model (white bars).
Hegyi´s CI
a)
Ori = No correction
LE = Linear expansion
RW = Restricted weighting
SE = Sim. annealing
CP = Cross product
OR = Olkin ratio
S
400
NS
121.65 120.67 121.7
NS
S
122.9
122.95 121.82
NS
AIC
300
200
Daniels CI
S
400
122
NS
S
OR
CP
SE
RW
LE
Ori
100
Martin and Ek CI
S
NS
S
400
121.71 122.07 123.77 123.73 122.16
NS
S
S
NS
122.06 121.39 122.08 123.42 123.3 122.2
S
400
NS
S
OR
CP
SE
Ori
SE
RW
LE
Lorimer´s CI
RW
100
OR
100
CP
200
Ori
200
LE
AIC
300
AIC
300
Non-spatially expl. CI
S
NS
400
122.29 121.77 122.32 123.75 123.56 122.4
122.38
S
S
NS
122.48
124.4
123.37
122.5
OR
CP
SE
RW
OR
CP
SE
100
RW
100
LE
200
Ori
200
Ori
AIC
300
AIC
300
NS
Figure C. 6.The Akaike´s information criterion (AIC) (Akaike 1974) is on the y-axis, calculated for each of the groups
on the x-axis. The tickmark “Ori” means no plot edge bias correction. The tickmark “LE” means linear expansion plot
edge bias correction according to Martin et al. (1977). RW means regression according to Equation (3) using restrictions
on parameters. SE is the simulated annealing method of Pommerening (2013). CP is the cross product method using
Equation (3). OR is Olkin ratio estimator according to Equation (2). The numbers above the boxes are the means of the
AIC in each class. The letters above the numbers are the result of a paired t-test, testing H0: Mean is different from the
original class “Ori”. “S” means that the paired t-test is significant on the 5% level, “NS” means non-significant. The
horizontal line in the boxplot is the median. Upper and lower quartiles of the distribution are the boxlimits. Whiskers
indicate upper (95th) and lower (5th) percentiles. Non-overlapping notches indicate that medians are significantly
different on the 5% level according to a median based test (Verzani 2005).
Hegyi´s CI
a)
0.5
-0.04
Tjøstheim´s A
Ori = No correction
LE = Linear expansion
RW = Restricted weighting
SE = Sim. annealing
CP = Cross product
OR = Olkin ratio
NS
NS
S
NS
NS
-0.03
-0.03
-0.01
-0.02
-0.03
0
Daniels CI
0.5
NS
NS
NS
NS
NS
-0.01
-0.01
-0.02
-0.03
-0.01
0.5
-0.04
0
OR
CP
NS
NS
S
NS
NS
-0.03
-0.03
-0.02
-0.04
-0.03
0
Lorimer´s CI
0.5
OR
CP
SE
RW
Non-spatially expl. CI
NS
NS
NS
NS
NS
-0.04
-0.03
-0.02
-0.03
-0.03
0.5
0
Tjøstheim´s A
-0.03
LE
Ori
OR
CP
SE
RW
LE
-0.5
Ori
-0.5
0
NS
NS
NS
0
0.01
-0.01
0
OR
CP
SE
RW
OR
CP
SE
RW
LE
-0.5
Ori
-0.5
NS
0
Ori
Tjøstheim´s A
SE
Martin and Ek CI
Tjøstheim´s A
Tjøstheim´s A
-0.02
RW
LE
Ori
-0.5
Figure C. 7. The spatial rank correlation Tjøstheim´s A is on the y-axis, calculated for each of the groups on the xaxis. The tickmark “Ori” means no plot edge bias correction. The tickmark “LE” means linear expansion plot edge bias
correction according to Martin et al. (1977). RW means regression according to Equation (3) using restrictions on
parameters. SE is the simulated annealing method of Pommerening (2013). CP is the cross product method using
Equation (3). OR is Olkin ratio estimator according to Equation (2). The numbers above the boxes are the means of
Tjøstheim´s A in each class. The letters above the numbers are the result of a paired t-test, testing H0: Mean is different
from the original class “Ori”. “S” means that the paired t-test is significant on the 5% level, “NS” means non-significant.
The horizontal line in the boxplot is the median. Upper and lower quartiles of the distribution are the boxlimits.
Whiskers indicate upper (95th) and lower (5th) percentiles. Non-overlapping notches indicate that medians are
significantly different on the 5% level according to a median based test (Verzani 2005).
References
Akaike H. 1974. A new look at the statistical model identification. IEEE Trans Autom Control. 19:
716-723.
Braastad H. 1966. Volume tables for birch. Commun Nor For Res Inst. 21: 265-365. In Norwegian
with English summary.
Brantseg A. 1967. Volume functions and tables for Scots pine. South Norway. Commun Nor For Res
Inst. 22: 695-739. In Norwegian with English summary.
Ene L, Næsset E, Gobakken T. 2012. Single tree detection in heterogeneous boreal forests using
airborne laser scanning and area-based stem number estimates. Int J Remote Sens. 33: 5171-5193.
Fitje A, Vestjordet E. 1977. Stand height curves and new tariff tables for Norway spruce. Rep Nor
For Res Inst. 34: 23-68. In Norwegian with English summary.
Gobakken T, Næsset E. 2004. Estimation of diameter and basal area distributions in coniferous
forest by means of airborne laser scanner data. Scand J For Res. 19: 529-542.
Goldberger AS. 1968. The Interpretation and Estimation of Cobb-Douglas Functions. Econometrica.
36: 464-472.
Huang SM, Titus SJ, Wiens DP. 1992. Comparison of nonlinear height-diameter functions for major
Alberta tree species. Can J For Res. 22: 1297-1304.
Johannsen VK. 2002. Selection of diameter-height curves for even-aged oak stands in Denmark
(working paper no. 16). Hørsholm (Denmark): The Royal Veterinary and Agricultural University,
Danish Forest and Landscape Research Institute.
Martin GL, Ek AR, Monserud RA. 1977. Control of plot edge bias in forest stand growth simulation
models. Can J For Res. 7: 100-105.
Montgomery DC, Peck EA, Vining GG. 2006. Introduction to linear regression analysis. 4th ed.
Hoboken, New Jersey: Wiley.
Näslund M. 1936. Skogsförsöksanstalens gallringsförsök i tallskog [Experiments on thinning in pine
forest by the Swedish Institute of Experimental Forestry]. Rep Swed Inst Exp For. 29: 1-169 In
Swedish with German summary.
Pedersen RØ, Bollandsås OM, Gobakken T, Næsset E. 2012. Deriving individual tree competition
indices from airborne laser scanning. For Ecol Manage. 280: 150-165.
Pommerening A. 2013. CRANCOD - A Program for the Analysis and Reconstruction of Spatial Forest
Structure. [Internet]. Prof. Dr. Arne Pommerening, Bern University of Applied Sciences, School of
Agricultural, Forest and Food Sciences; [1.1.2013]. Available from:
http://www.crancod.org/wiki/index.php?title=Main_Page
Ratkowsky DA. 1990. Handbook of nonlinear regression models. New York: Marcel Dekker.
Seber GAF, Wild CJ. 2003. Nonlinear regression. Hoboken, New Jersey: Wiley.
Tveite B. 1977. Site-index curves for Norway spruce (Picea abies (L.) Karst.) Commun Nor For Res
Inst. 33: 1-84. In Norwegian with English summary.
Verzani J. 2005. Using R for introductory statistics. Boca Raton, Florida: Chapman & Hall/CRC.
Vestjordet E. 1967. Functions and tables for volume of standing trees. Norway spruce. Commun
Nor For Res Inst. 2: 543-574. In Norwegian with English summary.