Growing Stock Estimation for Small-Areas
from Large-Area Forest Inventory data and Satellite Data in Korea
Jong Su Yim1, Sung Ho Kim2, Jin Hyun Jeong2 and Man Yong Shin1
1
Department of Forest Resources, College of Forest Sciences, Kookmin University, Seoul 136702, Korea; 82-2-910-4815; jsyim@kookmin.ac.kr; yong@kookmin.ac.kr
2
Division of Forest Resource Information, Korea Forest Research Institute, Seoul 130-712,
Korea; 82-2-961-2842; shkimfri@forest.go.kr; jinhyun@forest.go.kr
Introduction
The Korean National Forest Inventory (NFI) has been implemented to provide forest information
at the national as well as the local levels. The NFI should address (i) estimates of the total
growing stock for the entire country, (ii) different forest strata (e.g., forest cover types, dominant
tree species, age classes, etc.) and (iii) different ownerships and administrative units (KFRI,
2008). Until the 4th NFI system in Korea, which was carried out by a rotation system by
administrative unit (province) over a 10-years period, forest statistics for small-area units were
derived from a calibration method using administrative units due to a small sample size (KFS,
2004). In this case, the forest statistics may not represent a real forest because this method did not
incorporate spatial heterogeneity of forests across an administrative unit. The Korean NFI system
has changed to a systematic sampling, in which field plots are systematically distributed and have
been collected about 20% of a total samples per year (KFRI, 2008). Therefore, suitable estimators
for small-areas are needed to predict reliable forest statistics.
Small-area estimation is a statistical method that allows to estimate various information at a
subpopulation or domain which do not consider in sampling design process (Rao 2003). The
objective of this study is to determine a suitable method for estimating forest growing stock at a
small-area unit in Korea. To achieve this goal, two calibration methods were applied; (i)
administrative and (ii) space-based geographic neighboring units. In addition, the k-nearest
neighbor (k-NN) technique by combining forest inventory data and satellite data was also used
(Tomppo et al. 2008).
Materials and Methods
A. Source data
Field data from the 5th Korean NFI were collected in 2006~2008 years. In this study, three small
areas; Muju (Jeon-Buk province), Youngdong (Chung-Buk province) and Kimcheon (Kyung-Buk
province) were selected. These counties belong to different administrative units, but they are
geographically contiguous with each other (Figure 1).
The field plots were post-stratified three forest cover types (coniferous, deciduous, and mixed
forests) based on basal areas by tree species per field plot. Post-stratified field plots were used to
estimate stratum weights and means for each stratum (Table 1).
Figure 1. Location of the three counties in this study.
Table 1. Number of field plots for forest strata and two different calibration methods.
Calibration
NFI*-field data
County
Administrative unit
Geographical unit
C
D
M
C
D
M
C
D
M
Muju
21
30
28
181
223
162
152
213
156
Youngdong
8
50
23
126
298
218
108
209
144
Kimcheon
33
37
22
697
737
599
189
234
204
NFI* = National Forest Inventory; C = Coniferous cover type; D = Deciduous, M = Mixed
B. Calibration method
The calibration using administrative units (ADU) ignores the spatial heterogeneity that may cause
high estimation errors. While the calibration method using geographic neighboring units (GEO)
considers spatial characteristics of forests (Rao 2003). For the GEO, there are several neighboring
counties for each county which are border on the three counties, respectively; Youngdong (6
counties), Muju (5 counties), and Kimcheon (7 counties) (Figure 2). The numbers of available
samples per stratum for the two calibration methods are shown in Table 1.
Youngdong county
Muju county
Kimcheon city
Figure 2. The diagram showing neighboring counties of each study county that represented by
blue color.
Table 2. Estimators of stratum mean and weight for the two calibration methods
Administrative unit
Geographical unit
Stratum weight ( wh , p )
Stratum weight ( wh , g )
Stratum mean ( y h , p )
Stratum mean ( y h , g )
wh , p 
nh , p
y h, p 
np
v
i I h , p
wh, g 
i,h
nh , p
nh, g
y h, g 
ng
v
i I h , g
i,h
nh , g
wh , p : stratum weight for each stratum h within an administrative unit p, vi , h : growing stock at plot i in stratum h
nh , p : number of samples in stratum h within an administrative unit p,
n p : total samples within an administrative unit p, I h , p : samples in stratum h within an administrative unit p, ,
wh , g : stratum weight per stratum h within a geographical unit g,
nh , g : number of samples in stratum h within a geographical unit g,
n g : total samples within a geographical unit g, I h , g : samples in stratum h within a geographical unit g.
In order to estimate stratum weight and stratum mean for the two calibration methods, the
estimators for simple random sampling with post-stratification were applied (Table 2).
C. k-Nearest Neighbor
Using the k-NN technique, various thematic maps of forest attributes can be generated by
combining forest inventory data and satellite data (Tomppo et al. 2008). In this study, thematic
maps of growing stock and forest cover type derived from the k-NN technique by combining a
Landsat TM-5 (acquired on April 28. 2005) and the NFI-field data within the imagery (n=2733)
were produced. In the k-NN process, general options were applied as shown in Table 3. In order
to produce a forest cover map, the post-stratified NFI-field plots within the imagery were used as
training data. The number of available plots of non-forest was very small compared to those of
other forests(Table 4).
Table 3. Applied characteristics in the k-nearest neighbor method
Growing stock map
(continuous)
Operational options
Forest cover type map
Satellite source
Landsat TM-5 (path 115, row 35)
Distance metric
Euclidean distance metric
Distance-weighting for neighbors
Value of k
Inversely proportional to the distance
5
1
Table 4. Distribution of field plots for each stratum for mapping forest cover type
Stratum
Number of points
Coniferous (C)
Forest
Deciduous (D)
Mixed (M)*
929
949
855
Mixed forest*: 24-74 % of the sum of basal areas by deciduous tree species
Non-forest
Total
220
2953
D. Test Statistics
In order to compare the estimated stratum mean and weight for different methods, two teststatistics; T-test and Chi-square test were conducted, respectively (Table 5).
Table 5. Test-statistics used in this study.
T- test
t* 
Chi-square test
D
SE D
 
2
(observed  exp ected ) 2
exp ected
where D is the mean difference between stratum means of a pairs of two methods, SE D is the
standard error of D , the expected classes are the areas per each stratum from digital forest maps,
while the observed classes are derived from the three methods.
Results and Discussion
The stratum weights and stratum means of growing stock for different methods were shown in
Table 6. Overall, the variation in the estimated stratum mean and weight using the k-NN method
was small while it was relatively large using the NFI-field data(Table 6).
Table 6. Stratum weights and means derived from different methods.
County
Muju
Youngdong
Kimcheon
Forest
strata
C
D
M
C
D
M
C
D
M
NFI-field data
Mean
(m3/ha)
198.7
98.5
131.8
142.2
101.0
107.6
159.0
108.6
133.6
weight
0.27
0.38
0.35
0.10
0.62
0.28
0.36
0.40
0.24
Calibration
Administrative unit
Geographical unit
Mean
Mean
weight
weight
(m3/ha)
(m3/ha)
172.6
0.33
162.5
0.29
99.6
0.39
105.6
0.41
122.4
0.28
125.8
0.30
151.4
0.20
150.5
0.23
102.1
0.46
106.4
0.45
122.3
0.34
114.7
0.31
133.8
0.34
146.2
0.30
112.8
0.36
106.8
0.37
125.4
0.29
117.7
0.33
Table 7. The result of the T-test for pairs of different methods.
SE D
n
Classification*
D
A
B
C
D
E
F
*
9
9
9
9
9
9
-4.30
-5.06
-4.15
-0.15
-0.91
0.75
4.75
4.90
8.41
5.77
4.94
2.56
t- value
-0.90
-1.03
-0.49
-0.03
-0.18
0.29
k-NN map
Mean
(m3/ha)
143.7
126.3
135.1
129.1
115.5
121.6
132.2
115.8
124.6
weight
0.29
0.44
0.26
0.31
0.38
0.30
0.32
0.38
0.30
Prob.< t
0.3933
0.3344
0.6369
0.9777
0.8581
0.7786
A :Calibration (ADU) - Field data,
B:Calibration (GEO) - field data,
C:k-NN map - field data
D:Calibration (ADU) - k-NN map, E:Calibration (GEO) - k-NN map, F:Calibration (ADU) - Calibration (GEO)
When paired of the estimated stratum mean from NFI-field data with those for the other methods
(Classification A, B, and C), the mean difference was relatively high (-5.06 to -4.15m3/ha) (Table
7). In contrast, the other pairs (Classification D, E, and F) were lower than 1m3/ha. However, the
estimated stratum means of growing stock by the different methods didn’t show statistically
significant (Table 7).
Table 8 shows the result of the Chi-square test for digital forest maps derived from aerial photo
interpretation with different methods. It shows that the stratum weights for the calibration with
geographical unit and the k-NN were close to the true strata. However, the difference between
NFI-field data and digital forest maps was the highest that means that the stratum weights from
field data only within a county could not provide reliable stratum weights.
Table 8. Chi-square result for the different methods with digital forest maps.
Calibration
County
NFI
Administrative unit Geographical unit
Muju
Youngdong
Kimcheon
677.5
30780.6
23227.7
517.3
8253.3
14521.2
32.6
6580.6
14139.6
k-NN map
344.6
2322.9
16016.0
Conclusion
This study shows a calibration method based on space-based geographical units is suitable to
provide more reliable forest information in the context of small-areas than one with
administrative units. The k-NN map also provides similar results to the calibration method based
on geographical units.
The 5th NFI has been implemented over a 5-year period that means the NFI system collects about
20% of the total samples over the entire country per year. When the total samples are collected, it
is possible to provide more reliable and accurate forest information at a local level.
Acknowledgement
This work was carried out with the support of ‘Forest Science & Technology Projects (Project No.
S120707L1101104) provided by Korea Forest Service.
Literature Cited
Korea Forest Research Institute (KFRI). 2008. The field manual for the 5th National Forest
Inventory.
Korea Forest Service (KFS). 2004. The reorganization of National Forest Inventory System by a
change of demands of society and international process for forest resource III. 284p. (in Korean)
Rao, J.N. 2003. Small area estimation. John Wiley & Sons, Inc.
Tomppo, E., Olsson, H. Stahl, G., Nilsson, M., Hngner, O. and Katila, M. 2008. Combining
national forest inventory field plots and remote sensing data for forest database. Remote Sensing
of Environment 112:1982-1999.