DSpace https://erepo.uef.fi
Rinnakkaistallenteet Luonnontieteiden ja metsätieteiden tiedekunta
2019
Nearest neighbor imputation of
logwood volumes using bi-temporal
ALS, multispectral ALS and aerial images
Räty, Janne
Informa UK Limited
Tieteelliset aikakauslehtiartikkelit
© Informa UK Limited All rights reserved
http://dx.doi.org/10.1080/02827581.2019.1589567
https://erepo.uef.fi/handle/123456789/7865
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Title page 1
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Title: Nearest Neighbor Imputation of Logwood Volumes using Bi-temporal ALS, Multi- 3
spectral ALS and Aerial Images 4
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Author list: Janne RÄTY*a, Petteri PACKALENb, Matti MALTAMOc 6
* corresponding author 7
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Author affiliations: a,b,c Faculty of Science and Forestry, School of Forest Sciences, University 9
of Eastern Finland, Yliopistokatu 7, P.O. Box 111, FIN-80101 Joensuu, Finland.
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ORCID of the corresponding author: 0000-0002-6578-8965 12
The corresponding author on Twitter: @JJRaty 13
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Email addresses: ajanne.raty@uef.fi, bpetteri.packalen@uef.fi, cmatti.maltamo@uef.fi 15
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Title: Nearest Neighbor Imputation of Logwood Volumes using Bi-temporal ALS, Multi- 22
spectral ALS and Aerial Images 23
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Abstract 25
We examine the nearest neighbor (NN) imputation of species-specific logwood volumes using 26
airborne laser scanning (ALS) data and aerial images. We compare different remote sensing 27
(RS) data combinations as predictor variables in an area-based prediction of logwood volumes 28
using separate training and validation data. We include multispectral leaf-on ALS data, bi-tem- 29
poral leaf-off ALS data and aerial images in the analyses. Two response configurations were 30
used in the NN imputations: (1) simultaneous imputation in which species-specific logwood 31
volumes are response variables, and (2) separate imputation by tree species in which the attrib- 32
utes of one tree species at a time are response variables. Although an unrealistic alternative in 33
practical implementation, the combination of leaf-on and leaf-off ALS metrics as predictors 34
proved to be the most successful RS data combination, according to the RMSE values associ- 35
ated with the predicted species-specific and dominant logwood volumes. The results show that 36
older leaf-off ALS data performed well in combination with leaf-on ALS data. In general, pre- 37
dictive performance was better with simultaneous imputation than with separate imputation by 38
tree species. Our finding promotes an awareness of how best to utilize various RS data in future 39
forest inventories.
40 41 42 43 44
Keywords: area-based approach, bi-temporal ALS, diameter distribution, logwood volume, 45
multispectral ALS, nearest neighbor imputation 46
47 48 49 50 51 52
1 Introduction 53
Forest inventories based on airborne laser scanning (ALS) have been successfully implemented 54
in boreal forests (e.g., Maltamo and Packalen 2014; Næsset 2014), temperate forests (e.g., Latifi 55
et al. 2010; Shang et al. 2017), and tropical plantations (e.g., Maltamo et al. 2017). Several 56
countries have adapted ALS-based forest inventories by applying an area-based approach 57
(ABA) as an operational standard (e.g., White et al. 2013; Maltamo and Packalen 2014; Næsset 58
2014). In ABA inventories, the statistical metrics are derived from a 3D point cloud for pre- 59
cisely located field measured plots (training data), and the metrics are used as predictor varia- 60
bles in models fitted with the training data. The resulting models are used to predict the forest 61
attributes of interest in a wall-to-wall manner for the entire inventory area.
62 63
In Finland, the required outcome of forest inventories is to be able to predict forest attributes 64
by tree species (Packalén and Maltamo 2007). Typically, the key species-specific forest attrib- 65
utes are volume, basal area, stem number, mean height and mean diameter, which are tradition- 66
ally used as inputs for forest simulations (Hynynen et al. 2002). Timber assortment volume is 67
usually the main attribute used to evaluate the economic value of a forest, and, usually, is ob- 68
tained by applying estimated forest attributes, theoretical diameter distribution models and taper 69
curves. It is also possible to predict timber assortment volume separately using ALS data 70
(Korhonen et al. 2008).
71 72
The species-specific prediction of forest attributes by ALS remote sensing is possible in boreal 73
forests due to the low number of tree species. Species-specific predictions have been operation- 74
ally implemented in Norway (Næsset 2014) and in Finland (Maltamo and Packalen 2014). In 75
Norway, the approach differs from the Finnish approach and includes visual interpretation 76
based on pre-classification of the main tree species from aerial images (Næsset 2014). The 77
development of prediction methods for species-specific attributes using ABA has been the fo- 78
cus of several studies, located mainly in Norway or Finland (e.g., Packalén and Maltamo 2007;
79
Breidenbach et al. 2010; Maltamo et al. 2015). According to the previous studies, the spectral 80
values of aerial images are the main data source used to acquire tree species information (e.g., 81
Packalén and Maltamo 2007; Maltamo and Packalen 2014).
82 83
Data sources other than aerial images have also been shown to decrease the error rates associ- 84
ated with species-specific forest attribute predictions. The applicability of leaf-off data in the 85
modeling of total forest attributes, compared to leaf-on ALS data, has been investigated in pre- 86
vious studies. For example, Bouvier et al. (2015) predicted stem volume in a deciduous tree 87
dominated area in France and reported that models based on leaf-off ALS may have a slightly 88
better predictive performance than leaf-on models. However, Anderson and Bolstad (2013) 89
found that leaf-off and leaf-on ALS data were comparable for the prediction of biomass in 90
mixed forests located in the United States. Although leaf-off ALS data have not been reported 91
to be superior to leaf-on ALS data for the prediction of forest attributes, ALS data acquired 92
under leaf-off conditions have been found to discriminate between coniferous and deciduous 93
tree species (Villikka et al. 2012; White et al. 2015). The intensity metrics derived from ALS 94
data have also been found to separate dominant tree species (e.g., Vauhkonen et al. 2014; Räty 95
et al. 2016).
96 97
A multispectral Optech Titan ALS system with the ability to operate at three wavelengths has 98
been employed in many studies, especially for species classification purposes at the tree level 99
(e.g., Budei et al. 2017; Yu et al. 2017; Axelsson 2018). Kukkonen et al. (2019) predicted tree 100
species composition at the plot level in Finland and proposed that multispectral ALS data col- 101
lected by the Optech Titan system could predict tree species composition better than unispectral 102
ALS data. Dalponte et al. (2018) also implemented predictions at the plot level using the Optech 103
Titan system. They predicted forest attributes without considering tree species at the plot level 104
and reported that the results were better with multispectral than unispectral ALS data. The find- 105
ings of the aforementioned studies indicate that multispectral ALS and leaf-off ALS may offer 106
valuable information for the species-specific logwood predictions that are of interest in this 107
study.
108 109
National ALS data (comprising full coverage of a country) have been collected in many coun- 110
tries (e.g., in Finland by the National Land Survey of Finland; in Spain by the Instituto Ge- 111
ográfico Nacional; in Denmark by Kortforsyningen). National ALS data are often collected for 112
terrain modeling purposes (i.e. under leaf-off conditions), although the suitability for forest in- 113
ventories has also been proven (e.g., Villikka et al. 2012; Räty et al. 2018). National ALS data 114
acquisitions are also repeated over time, for example in Finland using a time interval that is still 115
under decision. In addition to national ALS data acquisitions, forest companies in many coun- 116
tries collect ALS data for their own forest inventories. To sum up, it is evident that multi-tem- 117
poral or bi-temporal ALS data will be available for many areas in the future due to repeated 118
ALS data acquisitions. The use of bi-temporal ALS data has been suggested as suitable for the 119
predictions of forest attributes. For example, Yu et al. (2004) was one of the first studies to use 120
bi-temporal ALS data to determine forest growth at the tree level. Since then, bi-temporal or 121
multi-temporal ALS or image-based point clouds have been used frequently, for example, in 122
the modeling of biomass or volume change (Bollandsås et al. 2018; Poudel et al. 2018), the 123
modeling of growth (Næsset and Gobakken 2005; Tompalski et al. 2018), and the quantification 124
of forest changes caused by forest fires (Bohlin et al. 2017; McCarley et al. 2017), climatic 125
changes (Nyström et al. 2013), snow damage (Vastaranta et al. 2011) or insect attacks (Solberg 126
et al. 2006). In Sweden, a data assimilation technique has also been proposed for the prediction 127
of forest attributes by means of an ALS data time series (Nyström et al. 2015). However, to the 128
best of our knowledge, bi-temporal ALS acquisitions have not been investigated in the context 129
of the ABA inventories applied in Finland.
130 131
Timber assortment volume is often computed in ABA forest inventories from a diameter distri- 132
bution that describes the size distribution of trees in an area-of-interest. Therefore, the success- 133
ful prediction of species-specific diameter distributions is a prerequisite for timber assortment 134
predictions. Species-specific diameter distributions are most commonly predicted in ALS- 135
based forest inventories by using the following practices: (1) prediction of diameter distribu- 136
tions by means of a nearest neighbor imputation (hereafter NN imputation) (Packalén and 137
Maltamo 2008; Peuhkurinen et al. 2008; Räty et al. 2018), (2) prediction or recovery of the 138
parameters of the diameter distributions that have been fixed to follow, for example, a Weibull 139
probability distribution (Gobakken and Næsset 2004; Thomas et al. 2008), or (3) fusion of the 140
aforementioned approaches with tree-level inventories (Hou et al. 2016).
141 142
The advantage of NN imputation in diameter distribution modeling is that the field-measured 143
trees of the inventory plots can be used directly to compile diameter distributions for areas-of- 144
interest. Moreover, the predicted diameter distribution is always compatible with the predicted 145
sum and mean attributes of the target of the prediction (cf. Packalén and Maltamo 2008; Pack- 146
alén and Maltamo 2007). Naturally, this requires that the forest attributes of interest are re- 147
trieved from the same nearest neighbors that are used in the construction of the diameter distri- 148
bution. In fact, the prediction of species-specific diameter distributions (starting points for fre- 149
quency diameter distributions) for logwood-sized trees actually refers to the prediction of spe- 150
cies-specific logwood volumes.
151 152
Räty et al. (2018) predicted species-specific diameter distributions by means of NN imputation.
153
They proposed different response variable configurations for NN imputation when the metrics 154
derived from ALS data and aerial images were used as predictor variables; separate NN impu- 155
tation by tree species performed better than simultaneous NN imputation. However, separate 156
validation data were not used, and the analyses were only implemented with leaf-off ALS data.
157
Therefore, studies that consider ALS data, for example, are needed to evaluate the potential of 158
separate NN imputation by tree species.
159 160
The time series of ALS data and, especially, repeated field measurements in an ALS inventory 161
context are still rare in Finland. Thus, we were motivated to determine whether the incorpora- 162
tion of metrics derived from older ALS data, as such, could decrease the errors in the traditional 163
ABA-based prediction of forest attributes. In addition to bi-temporal ALS data, we use both 164
leaf-off and leaf-on ALS data. Although the use of leaf-off and leaf-on data has been examined 165
in previous studies, none have concentrated on the prediction of species-specific logwood vol- 166
umes, which is usually an important attribute in describing the economic value of a forest. Here, 167
we apply NN imputation and 11 different RS data combinations to predict logwood volumes 168
by tree species. Our study objectives for the study are as follows:
169
• to examine the potential of bi-temporal ALS data (leaf-on and leaf-off) for species- 170
specific logwood volume predictions 171
• to assess the power of multispectral ALS for the prediction of species-specific logwood 172
volumes compared to a combination of ALS and aerial images 173
• to compare simultaneous NN imputation and separate NN imputation by tree species 174
for the prediction of logwood volumes.
175
2 Methods 176
2.1 Study area 177
The study area (Figure 1) is located in Eastern Finland near the municipality of Liperi (62°31´
178
N 29°23´ E). The study area is approximately 43,000 hectares and extends over the regions of 179
North Karelia and Southern Savonia. The forest in the study area represents a typical managed 180
Finnish boreal forest where coniferous tree species are the dominant vegetation. The main tree 181
species that occur in the area are Scots pine (Pinus sylvestris [L.]), Norway spruce (Picea abies 182
[L.] Karst.), silver birch (Betula pendula) and downy birch (Betula pubescens). In many forest 183
stands, several deciduous tree species, e.g. aspen (Populus tremula) and grey alder (Alnus 184
incana), occur occasionally in the lower canopy layers. The age distribution of the measured 185
training plots show that the majority of stands are middle-aged forests (52 %). The proportion 186
of stand development classes of young and mature forests is 27 % and 21 %, respectively.
187 188
2.2 Field data 189
The sample plots used as training data in this study consisted of 424 circular plots with a fixed 190
radius (see Figure 1). The fixed radius was either 9 m (71 % of plots) or 12.62 m (29 % of 191
plots). The 12.62 m radius was selected if the stem number inside a plot was less than 20. Field 192
measurements for the training data were carried out between June and September 2016. For the 193
majority of the sample plots, a systematic cluster sampling design was applied over the inven- 194
tory area. Four sample plots were established in the corners of a square-shaped cluster (300 x 195
300 m), and the distance between adjacent clusters was fixed at 1200 m. However, 27 % of the 196
sample plots were located in the inventory area by the Finnish Forest Centre, who applied their 197
own sampling design (Suomen metsäkeskus 2016). Although the sampling design of the Finn- 198
ish Forest Center differs from systematic cluster sampling, the principle of tree measurements 199
was broadly similar for all 424 sample plots. Seedling or sapling plots and dead trees (2 % of 200
the trees in training data) were excluded from the training data. The dead trees were usually 201
broken by wind or snow and, therefore, did not significantly affect the dominant canopy of the 202
sample plots. We did not use sample plots that were located at the edges of the stand. The 203
centers of the sample plots were accurately located by means of the global navigation satellite 204
system (GNSS). The coordinates of the plot centers were corrected afterwards using reference 205
stations (post-correction). For every plot, diameter at breast height (DBH), height, and species 206
of trees with DBH ≥ 5 cm were measured. The main sample plot attributes for the training data 207
are presented in Table 1.
208 209
[Fig 1 near]
210 211 212
Field measurements for the validation data were carried out between June and October 2017.
213
Selection of the validation plots was based on a dense systematic network with no overlap with 214
the training plots. The validation plots (105 squared plots) were sampled from the systematic 215
network using a priori information of development classes and dominant tree species. The de- 216
velopment classes were determined by means of ALS data collected in summer 2016. The dom- 217
inant tree species in the plots were fetched from the open-access dataset of the National Forest 218
Inventory (Natural Resources Institute Finland 2013). The proportions of development classes 219
and dominant tree species for the sampling were computed from the training data. Our objective 220
was to ensure that the proportions of forest development classes and dominant tree species in 221
the validation data were in accordance with the training data. Seedling or sapling stands, and 222
dead trees were excluded from the measurements. Only validation plots located entirely within 223
the forest stand were measured. In the field, individual plots were located by means of a tree 224
map visualized through a canopy height model (resolution 0.5 m). The original 900 m2 (30 x 225
30 m) plots were divided into four 225 m2 (15 x 15 m) subplots using the XY coordinates of 226
the trees. The XY coordinates of trees were determined in the field using a canopy height model 227
and the triangulation approach proposed by Korpela et al. (2017). The area of each subplot is 228
similar to the plot size in the training data, and the area of each subplot is almost similar to the 229
area of grid size used in operational wall-to-wall forest inventories in Finland (Maltamo and 230
Packalen 2014). Thus, the validation data consisted of 420 validation subplots. As with the 231
training plots; DBH, height, and species of trees with DBH ≥ 5 cm were measured. The main 232
plot attributes for the validation data are presented in Table 1.
233 234
[Table 1 near here]
235 236
We assigned deciduous species to a single group, as deciduous species other than birches play 237
only a minor role in Finnish forestry. In addition, it is virtually impossible to detect minor de- 238
ciduous species by means of remote sensing. Therefore, three tree species groups were estab- 239
lished: pine, spruce, and deciduous. We used DBH and height measurements to calculate the 240
basal area and volume of every tree. Stem volumes were computed with models described in 241
Laasasenaho (1982) using DBH and height as predictor variables, whereas logwood volumes 242
were calculated with taper curves presented by Laasasenaho (1982). Volume models or taper 243
curves fitted for birch were used for all deciduous species. The bucking parameters related to 244
the logwood calculations are presented in Table 2. Finally, the following attributes were com- 245
puted to the plot level: volume (V), logwood volume (Vlog), basal area (G), stem number (N), 246
diameter and height of basal area median tree (DGM and HGM). The attributes were calculated 247
for tree species groups, dominant species, minor species, and total growing stock.
248 249
[Table 2 near here]
250
2.3 Remote sensing data 251
Leaf-on multispectral ALS data (hereafter M-ALS) were acquired in June 2016 at an altitude 252
of 850 m above ground level using a fixed-wing airplane equipped with a Teledyne Optech 253
Titan laser scanner system. The Teledyne Optech Titan device is capable of measuring up to 254
four range and intensity measurements from each pulse using three individual active channels.
255
Each channel has a fixed wavelength that enables multispectral mapping of targets. The wave- 256
lengths of the channels are 1550 nm (first channel), 1064 nm (second channel), and 532 nm 257
(third channel). The data from the second channel were also used individually in the modeling 258
and are equivalent to the unispectral leaf-on ALS data (hereafter M-CH2-ALS). An illustration 259
of M-ALS on coniferous dominated and deciduous dominated forests is presented in Figure 2.
260 261
[Fig 2 near here]
262 263
We used two unispectral leaf-off ALS datasets in this study. The most recent unispectral leaf- 264
off ALS data (hereafter S16-ALS) was acquired between April 30 2016 and May 3 2016 at an 265
altitude of 2400 m above ground level with a Leica ALS60 laser scanner. The Leica ALS60 is 266
capable of capturing up to four echoes, including range and intensity measurements, from an 267
emitted pulse. The older unispectral leaf-off ALS data (hereafter S11-ALS) was acquired be- 268
tween April 25 2011 and April 26 2011 at an altitude of 2200 m above ground level. Since S11- 269
ALS data were gathered about five years before the field measurements, possible forest treat- 270
ments were also taken into account. We accounted for thinned plots in the training and valida- 271
tion data by comparing the S16-ALS and S11-ALS fveg metrics. The fveg describes the canopy 272
density, and it is computed from the proportion of first-of-many and only echoes above 2 m to 273
all echoes. The plot was treated as a thinned plot if the percentage decrease in fveg metrics was 274
> 35 %. The validity of the exclusion threshold was checked with the aid of photographs taken 275
during the field measurements. In total, 31 training plots and 28 validation plots (15 x 15 m;
276
corresponding to seven 30 x 30 m plots) were excluded from the analysis when S11-ALS was 277
employed. Detailed specifications of all ALS acquisitions are presented in Table 3. The S11- 278
ALS and S16-ALS datasets for coniferous and deciduous dominated forests are shown in Figure 279
3.
280 281
[Figure 3 near here]
282 283
[Table 3 near here]
284 285
The ALS echoes were assigned to four classes according to the return order: first of many, last 286
of many, only, and intermediate. Subsequently, the only echoes were added to both first of many 287
and last of many echo categories. Thus, three echo categories were formed for the computing 288
of metrics: first, last, and intermediate. Firstly, the ALS echoes were classified into vegetation 289
and ground hits following the method proposed by Axelsson (2000). The echoes classified as 290
ground hits were used to interpolate the digital terrain model (DTM) by means of a Delaunay 291
triangulation. The above-ground heights of ALS echoes were calculated by subtracting DTM 292
from the initial ellipsoidal heights of echoes. The intensity values of the M-ALS and S16-ALS 293
data were calibrated for the range following the method of Korpela et al. (2010). The intensity 294
values of the S11-ALS echoes were not calibrated due to the absence of trajectory information.
295 296
Aerial images (AI) were captured with a DMC Z/I Intergraph (01-0128) digital aerial camera 297
on 23 and 24 May 2016 by the National Land Survey of Finland. The camera had a focal length 298
of 30 mm and records four spectral bands that include red, green, blue, and near-infrared. The 299
flight altitude of the image acquisition was 4100 m above ground level. The camera model has 300
3456 x 1920 pixels in multispectral bands, which resulted in a ground sampling distance (GSD) 301
of about 160 cm. External orientations were determined by a bundle block adjustment using 302
ground and tie points. The aerial images were not ortorectified or pansharpened.
303 304
2.4 Metrics computed from remotely sensed data 305
The metrics computed from the M-ALS, S16-ALS, S11-ALS data, and the spectral values of 306
aerial images were used as predictor variable candidates in the modeling phase (see Table 4).
307
The ALS echo categories first, last, and intermediate were used in the calculation of metrics.
308
The 5, 10, …, 95 % height percentiles were computed and density metrics were computed using 309
fixed height values for 0.5, 2, 5, 10, 15, and 20 m. Furthermore, the proportions of the echo 310
categories were also computed. For the intensity values of the ALS echoes, the statistical met- 311
rics of mean, standard deviation, maximum, minimum, kurtosis, skewness, and percentiles (5, 312
10, …, 95 %) were computed. The height cutoff was set at 1.3 m to avoid the effect of ground 313
hits in the computation of the metrics. The height cutoff was not used in the computation of 314
density metrics. The ratio metrics between the channels of the M-ALS data were computed, as 315
Yu et al. (2017) found ratio metrics to be useful in tree species discrimination. We computed 316
the ratio metrics for 60, 65, …, 95 % height percentiles, and for 55, 60, …, 95 % intensity 317
percentiles.
318 319
The spectral values of the aerial images were fetched for ALS echoes following the method 320
proposed by Packalén et al. (2009). The aerial image metrics were computed using the ALS 321
echoes assigned to the first echo category. The ALS echoes were projected to unrectified aerial 322
images using external and internal orientation. Since the aerial images overlap, the ALS echoes 323
have multiple spectral values. To deal with this, the average pixel value by bands was retrieved 324
for every ALS echo. Finally, the statistical plot-level metrics (mean, standard deviation, mini- 325
mum, and maximum) were computed from the average pixel values.
326 327
[Table 4 near here]
328 329
2.5 Prediction of logwood volumes 330
We predicted logwood volumes by applying the NN imputation that uses the most similar 331
neighbor distance metric (MSN; see Moeur and Stage 1995). The MSN has been frequently 332
used in other studies (e.g., Packalén and Maltamo 2008; Maltamo et al. 2009; Räty et al. 2018) 333
for the prediction of species-specific forest attributes and diameter distributions. The MSN 334
method applies canonical correlation analysis to solve the distance metrics. The distance metric 335
determines the nearest neighbors most similar to the target of the prediction, according to the 336
predictor variables. In this study, we fitted the NN models to the training data, and the models 337
were used to predict the validation data.
338 339
The squared distance for neighbors was calculated as follows:
340
𝑑𝑖𝑗2 = (𝒙𝑖− 𝒙𝑗)𝚪𝚲2𝚪𝑇(𝒙𝑖− 𝒙𝑗)𝑇 (1) 341
where 𝑑𝑖𝑗2 is the squared distance between target i and neighbor j, xi is a vector of predictor 342
variables from the target plot, xj is a vector of predictor variables from the reference plot, Γ is 343
the matrix of canonical coefficients of the predictors and Λ2 is the diagonal matrix of squared 344
canonical correlations.
345 346
The weightings of the nearest neighbors were determined by taking an inverse of the squared 347
distance:
348
𝑊𝑖𝑗 =
1 𝑑𝑖𝑗2
∑ 1 𝑑𝑖𝑗2 𝑘1
(2)
349
where 𝑊𝑖𝑗 is the weight value between the target plot i and reference plot j, k is the number of 350
nearest neighbors and 𝑑𝑖𝑗2 is as presented in Equation 1.
351 352
Since the distance metrics were calculated by means of the coefficients and correlations re- 353
trieved from the canonical correlation analysis, the effect of the response variables was also 354
taken into account (see Maltamo et al. 2009; Räty et al. 2018). Here, we predict logwood vol- 355
umes by applying the following response configurations in the NN imputation: (1) species- 356
specific logwood volumes with simultaneous NN imputation (hereafter SimLog) and (2) spe- 357
cies-specific sum and mean attributes (V, G, N, DGM and HGM) with separate NN imputation 358
by tree species (hereafter SepSM). The selection of SimLog response configuration is justified 359
by the NN approach that directly predicts multiple response variables. The simultaneous pre- 360
diction of multiple responses has been previously utilized, especially for species-specific forest 361
attributes. The SepSM response configuration was selected as it was successfully used for di- 362
ameter distribution predictions in Räty et al. (2018).
363 364
In practice, tree list (i.e. diameter distribution) is predicted as a byproduct in NN imputation.
365
The tree list can be compiled into a frequency diameter distribution using weightings (Equation 366
2) to determine the tree-wise frequencies of a target plot. Since the imputed tree list is a source 367
for the predicted forest attributes, logwood volume (m3/ha) can be retrieved from the deter- 368
mined neighborhood (k = 5) for a target plot i as presented in Equations 3 and 4.
369
𝑆𝑖 = {𝑆𝑖1, 𝑆𝑖2, 𝑆𝑖3, 𝑆𝑖4, 𝑆𝑖5} (3) 370
371
where Si is a tree list for a target plot, and Si1 comprises the trees from the first nearest neighbor, 372
and Si2, Si3, Si4, and Si5 comprises the trees from the second, third, fourth, and fifth nearest 373
neighbor, respectively.
374 375
Every tree in Si has a logwood volume and a weighting value Wn that is in correspondence with 376
the weighting Wij (Eq. 2) of the neighbor plot from which the tree has been retrieved. The trees 377
also have factor Fn that is used to scale the logwood volumes to the hectare level. Thus, logwood 378
volume at the hectare level for a target plot t can be calculated from the tree list St, consisting 379
of n trees as follows:
380
𝐿𝑜𝑔𝑤𝑜𝑜𝑑 𝑣𝑜𝑙𝑢𝑚𝑒𝑡 = ∑𝑛𝑖=1𝑉𝑙𝑜𝑔𝑛 × 𝑊𝑛 × 𝐹𝑛 (4) 381
382
Where Vlogn is logwood volume for tree n, Wn is a weighting value retrieved from NN imputa- 383
tion for tree n, and Fn is a factor applied to scale the logwood volume of tree n to the hectare 384
level.
385
2.6 Selection of predictor variables for nearest neighbor imputation 386
The selection of predictor variables for NN imputation was implemented by following the al- 387
gorithm (VSSA) presented by Packalén et al. (2012). The selection procedure is based on a 388
heuristic optimization algorithm known as Simulated Annealing (Kirkpatrick et al. 1983). The 389
aim of the VSSA algorithm is to minimize the cost function by solving the NN model repeatedly 390
over a fixed number of times. The cost function was formulated using either the weighted or 391
the ordinary arithmetic mean of the relative root mean squared error (RMSE) values associated 392
with the response variables. Here, we used the weighted mean of the RMSE values only if the 393
species-specific logwood volumes were simultaneously used as response variables (SimLog).
394
Otherwise, the mean RMSE value was computed using the ordinary arithmetic mean. The 395
weighting scheme was created according to the observed species-specific logwood proportions.
396
The weightings were set to 0.43, 0.52 and 0.05 for pine, spruce and deciduous logwood vol- 397
umes, respectively. In VSSA, the optimization process is controlled by the number of iterations 398
and the temperature parameter value. We used 2500 iterations in VSSA for each selection of 399
predictor variables. The initial temperature value was fixed at one. The temperature value was 400
linearly decreased until 80 % of the iterations were done and was then set to zero.
401 402
2.7 Performance assessments 403
We computed the error rates for logwood volume predictions using RMSE. Moreover, the mean 404
difference (BIAS) was computed to determine possible systematic errors in the predictions. We 405
present RMSE and BIAS values in a relative manner, which means that the absolute value was 406
divided by the observed mean value of the corresponding attribute. In several cases, we refer to 407
|BIAS| that implies the non-negative absolute value of BIAS. The RMSE and BIAS values were 408
calculated as follows:
409 410
𝑅𝑀𝑆𝐸 = 100 ×√
∑𝑛 (𝑦̂𝑖−𝑦𝑖)2 𝑖=1
𝑛
𝑦̅ (5)
411
𝐵𝐼𝐴𝑆 = 100 ×
∑𝑛 (𝑦̂𝑖−𝑦𝑖) 𝑖=1
𝑛
𝑦̅ (6)
412 413
We computed the error rates for the prediction of dominant, minor, species-specific and total 414
logwood volumes. The dominant tree species for a sample plot was determined with respect to 415
volume. The minor species group included species groups that had the second and third highest 416
growing stock in a plot.
417 418
Error rates fluctuate among multiple NN imputations due to the heuristic selection of predictor 419
variables. For these reasons, the entire prediction process was repeated 50 times and the RMSE 420
and BIAS values were computed as means of all repetitions.
421 422
3 Results 423
3.1 Effect of response configurations 424
The error rates associated with total logwood predictions were almost always higher when 425
SepSM was used as a response set compared to SimLog (cf. Table 5 and Table 6). In general, 426
SepSM produced lower error rates and lower BIAS values for the prediction of dominant log- 427
wood volumes when ALS metrics were used with aerial image metrics. The lowest error rates 428
for dominant, minor, and total logwood predictions were achieved using the response configu- 429
ration of SimLog.
430 431
The error rates and BIAS values for logwood volume predictions by tree species using various 432
RS data combinations with SimLog and SepSM are presented in Figure 4. SepSM was found 433
to perform better in the prediction of deciduous logwood volumes. With a few exceptions, the 434
error rates and BIAS values computed with the different RS data combinations were similar in 435
SimLog and SepLog. An examination of BIAS values between the response configurations 436
provided little information. Principally, the absolute bias (|BIAS|) values for coniferous log- 437
wood volume predictions were moderate. However, higher |BIAS| values were observed with 438
RS data combinations where aerial images were not included, or where there was a combination 439
of leaf-on and leaf-off ALS data.
440 441
The lowest error rates for logwood volume predictions of pine (53.5 %) and spruce (43.8 %) 442
were achieved with SimLog. Overall, the results showed that SimLog performed better in per- 443
formance assessments of the predictions (Table 5, Table 6, and Figure 4). Hence, we will here- 444
after only focus on SimLog.
445 446
3.2 Effect of bi-temporal ALS metrics 447
The results showed that the combination of M-CH2-ALS + S16-ALS provided the lowest error 448
rates for the prediction of dominant, minor, and total logwood volumes (Table 5). Compared to 449
the RS data combination with the aerial image metrics, the replacement of the aerial image 450
metrics of M-CH2-ALS + AI by leaf-off-metrics (S16-ALS) in SimLog led to an improvement 451
in error rates by 10.3 %, 39.0 % and 15.7 % for the dominant, minor and total logwood volumes, 452
respectively. The best predictive performance in the validation data can be seen in Figure 5 453
where the median iteration with respect to RMSE of the dominant logwood is presented. The 454
M-CH2-ALS + S16-ALS combination predicted dominant logwood volumes broadly similar 455
to the M-CH2-ALS + AI combination (Figure 5). In contrast, the superiority of M-CH2-ALS + 456
S16-ALS was evident in the prediction of minor logwood volumes for deciduous dominated 457
plots. In general, the dominant and total logwood predictions based on the leaf-off ALS data 458
were more biased compared to the predictor sets that used metrics from leaf-on ALS (e.g., S16- 459
ALS + AI versus M-CH2-ALS + AI; see Table 5 or Table 6). The |BIAS| values for dominant 460
and minor logwood volumes were high in all cases.
461 462
The error rates associated with species-specific logwood predictions followed the same trend 463
as the error rates for dominant and minor logwood volumes (Figure 4). The species-specific 464
error rates associated with logwood predictions confirmed the advantage of using leaf-off met- 465
rics for species-specific volume predictions. When SimLog was applied, the replacement of 466
aerial image metrics with leaf-off metrics had a decreasing effect on the prediction error of all 467
tree species (see Figure 4). For SimLog, the lowest species-specific error rates were always 468
achieved with a RS data combination that included leaf-off ALS metrics.
469 470
The NN imputations where the leaf-off and leaf-on ALS metrics were used as predictor varia- 471
bles predicted the logwood volume of minor species better than cases where leaf-on ALS and 472
aerial image metrics were used as predictors (cf. M-CH2-ALS + S16-ALS and M-CH2-ALS + 473
AI in Table 5, Table 6, and in Figure 5 and Figure 4). The combination of the older leaf-off 474
ALS data and the more recent leaf-on ALS data was effective in the prediction of logwood 475
volumes (Tables 5 and 6, Figure 6). However, slight degradations were observed in the error 476
rates for dominant, total, spruce and deciduous logwood predictions (Table 5 and Figure 4).
477 478
3.3 Effect of multispectral metrics 479
In general, the inclusion of multispectral metrics (M-ALS) slightly improved the predictions of 480
logwood volumes compared to those predicted with unispectral leaf-on ALS data (Table 5, 481
Table 6 and Figure 4). The benefit of multispectral ALS metrics compared to unispectral leaf- 482
on ALS metrics can be seen in the error rates associated with the predicted pine and deciduous 483
logwood volumes (Figure 4). In general, the error rates associated with the prediction of spe- 484
cies-specific logwood volumes were higher when the multispectral metrics were used instead 485
of the metrics derived simultaneously from the aerial images and unispectral ALS data.
486 487
[Table 5 near here]
488 489
[Table 6 near here]
490 491
492 493
[Fig 4 near here]
494 495
[Fig 5 near here]
496 497 498
[Fig 6 near here]
499 500 501 502 503 504 505
4 Discussion 506
507
4.1 Remote sensing data combinations 508
The main results of our study indicate that ALS data acquired in leaf-off conditions offer valu- 509
able information for species-specific logwood predictions, especially for minor species. The 510
results showed that the inclusion of leaf-off metrics in addition to leaf-on ALS metrics produced 511
surprisingly good predictions compared to the combination of leaf-on ALS and aerial image 512
metrics. We found that when selecting the predictors from the metrics derived from S16-ALS 513
or S11-ALS datasets, height and density metrics were more frequently selected than the inten- 514
sity metrics. Therefore, it is evident that the separation of tree species for species-specific pre- 515
dictions comes from the height distribution of ALS echoes. Under leaf-off conditions, ALS 516
pulses better penetrate deciduous dominated canopies compared to ALS pulses emitted under 517
leaf-on conditions and, therefore, the higher proportion of echoes includes returns from the 518
ground or lower vegetation (Hill and Broughton 2009). Due to these reasons, the inclusion of 519
the metrics derived from leaf-off data mainly affects the predictions associated with deciduous 520
forests. Surprisingly, our findings show better predictive performance even for coniferous spe- 521
cies when the aerial image metrics were replaced by the leaf-off metrics (see Figure 4 and Table 522
5). The finding indicates that the height distribution of ALS echoes between pine and spruce 523
dominated forests are not similar and is in general agreement with Villikka et al. (2012), who 524
reported that leaf-off ALS data provide lower error rates to leaf-on data when coniferous and 525
deciduous volumes are predicted with ABA. However, they only provided predictions for de- 526
ciduous and coniferous species, and, therefore, the predictive power of leaf-off data between 527
coniferous species cannot be compared. Both Villikka et al. (2012) and White et al. (2015) 528
reported that the replacement of leaf-on data by leaf-off data when a model is fitted with leaf- 529
on data causes a serious bias in predictions. Our results generally show that the inclusion of 530
leaf-off ALS data as predictor variables might increase |BIAS| values for the prediction of total 531
logwood volumes (Tables 5 and 6). Nevertheless, large changes in |BIAS| values were not ob- 532
served here for the prediction of dominant, minor, or species-specific logwood volumes.
533 534
The advantage of utilizing older ALS data in forest inventories has received little attention in 535
the literature. Typically, multi-temporal or bi-temporal ALS data have been examined to assess 536
changes in forested areas (e.g., Næsset and Gobakken 2005; Bohlin et al. 2017). The results of 537
this study suggest that bi-temporal ALS data, consisting of leaf-on and leaf-off ALS data, can 538
be used in species-specific ABA inventories as a replacement for aerial image metrics (Figure 539
5). Our findings indicate that a 5-year time interval between leaf-on and leaf-off ALS data is 540
not a serious issue in order to benefit from leaf-off ALS data in the prediction of species-specific 541
logwood volumes. Instead, silvicultural activity causes problems in the prediction process since 542
the silvicultural operations that take place between two ALS acquisitions can distort the predic- 543
tion. We detected thinnings by comparing canopy cover metrics (fveg) derived from bi-temporal 544
ALS data and using a fixed change threshold (percentage decrease in fveg metrics > 35 %). It 545
is evident that more investigations are needed how to detect thinnings when using multi-tem- 546
poral ALS data.
547 548
The inclusion of spectral metrics of aerial images or leaf-off ALS metrics lowered the error 549
rates more than the inclusion of multispectral ALS metrics. Previous studies have applied mul- 550
tispectral ALS data to determine tree species at the tree-level (e.g., Budei et al. 2017; Axelsson 551
et al. 2018) and at the area-level (Kukkonen et al. 2019). These studies have reported improve- 552
ments when multispectral features are included in the models. Our findings indicate that the 553
benefits of using the first and third channels of the Optech Titan instrument (1550nm and 554
532nm) rather than the second channel only (1064nm) are minor in regard to logwood volume 555
predictions, and the extent of the benefit depends on the tree species under consideration. There- 556
fore, tree species composition over the inventory area has an effect on the benefits achieved 557
from multispectral ALS metrics. For example, the replacement of unispectral ALS with multi- 558
spectral ALS may improve species-specific error rates more in deciduous dominated inventory 559
area than coniferous dominated inventory area. However, our findings clearly show that the 560
combination of AI and ALS metrics or the combination of leaf-off and leaf-on ALS metrics is 561
preferable to multispectral ALS data when the prediction of species-specific logwood volumes 562
is deemed to be of interest.
563 564
4.2 Response configurations in the nearest neighbor imputations 565
Räty et al. (2018) investigated the response configurations of NN imputation. According to their 566
results, separate imputation by tree species (equivalent to SepSM) resulted in the lowest error 567
rates for spruce and deciduous logwood volumes when the metrics from leaf-off ALS data and 568
aerial images were used as predictor variables. The error rates of species-specific and dominant 569
logwood volumes presented here are in agreement with the results of Räty et al. (2018). For 570
example, in the present study, RMSE values of 64.2 %, 53.4 %, and 128.1 % for pine, spruce, 571
and deciduous trees, respectively were achieved using leaf-off ALS and aerial image metrics 572
with SepSM. Corresponding values for SimLog were 62.0 %, 54.5 %, and 141.2 % for pine, 573
spruce, and deciduous trees, respectively.
574 575
Räty et al. (2018) evaluated the goodness of the response configurations according to the spe- 576
cies-specific logwood volume, pulpwood volume and total volume attributes. The usage of nu- 577
merous evaluation attributes means that any response configuration used for diameter distribu- 578
tion predictions should also describe all the evaluation attributes. The selection of evaluation 579
attributes is especially problematic when diameter distributions are predicted, since diameter 580
distribution is an entity that should describe the whole size distribution of trees in a forest. In 581
the literature, several different forest attributes are used to assess the goodness of diameter dis- 582
tributions (e.g. timber assortment volumes, error indices of frequency distribution etc.). We 583
separately predicted logwood-sized trees of diameter distribution to avoid the aforementioned 584
challenges. With SimLog, it was logical to select the species-specific logwood volumes as eval- 585
uation attributes for the goodness of diameter distribution, since those attributes were also re- 586
sponse variables in the NN imputation. The results showed that timber assortments could be 587
treated as individual entities in the NN imputation of diameter distribution. Typically, NN im- 588
putations are used to predict whole diameter distribution at a time (mean and sum attributes are 589
responses), and, therefore, timber assortment volumes (pulpwood and logwood) can be pre- 590
dicted simultaneously. However, predicting diameter distribution according to timber assort- 591
ments ensures that the configurations of NN imputation can be better adjusted for every impu- 592
tation. For example, we adjusted the weighting schemes (with SimLog) in the predictor selec- 593
tion process to take into account the tree species proportions in the inventory area.
594
595
4.3 Performance assessments of logwood predictions 596
Previous studies that consider species-specific predictions of timber assortment have not in- 597
cluded performance analysis at the dominant or minor tree species level, although tree species 598
level has been used (Packalén and Maltamo 2008; Peuhkurinen et al. 2008; Räty et al. 2018).
599
Peuhkurinen et al. (2008) employed a database of individual stems for logwood volume predic- 600
tion, estimated height-diameter distributions, and a specific distance metric in NN imputation.
601
As such, any comparison with our results must be carried out with caution. The error rates 602
associated with the logwood volume predictions presented in this study are higher than those 603
reported by Packalén and Maltamo (2008), and may be due to the study design and tree species 604
proportions in the training data. In our study, we used separate validation data, while Packalén 605
and Maltamo (2008) used the modeling data as validation data with a leave-one-out cross vali- 606
dation, whereby the nearest neighbors from the same stand as the target plot were excluded.
607
Moreover, the number of subunits for aggregation has an averaging (i.e. improving) effect on 608
stand level error rates. In our study, we always used four subunits, while Packalén and Maltamo 609
(2008) used an average of seven subunits per stand.
610 611
The BIAS values associated with the dominant and minor logwood volumes were very high 612
(Table 5 and 6). This may be due to the higher logwood volume stock for every species in the 613
validation data compared to the training data (Table 1). The underestimation of dominant log- 614
wood volumes (Tables 5 and 6) can be seen in the upper left scatter plot of Figure 5, where the 615
plots that were most challenging to predict were those with a dominance of deciduous species.
616
The saturation of deciduous dominated plots as a cluster in the upper left scatter plot of Figure 617
5 suggests that there is a shortage of deciduous dominated neighbors in the training data. The 618
BIAS values were clearly higher for deciduous logwood predictions compared to coniferous 619
logwood predictions (Figure 4), which indicates that the training data were not sufficiently 620
comprehensive to predict deciduous logwood volumes. In examining the BIAS values, it should 621
be noted that the average logwood volumes were relatively low in the study area (see Table 1).
622
Since low averages increase the relative |BIAS| values, the values cannot be readily compared, 623
for example, to the corresponding values computed for the species-specific volumes in previous 624
studies.
625 626
4.4 Practical applicability of the findings 627
In Finland, the possibility of utilizing two or more ALS datasets from a large-scale inventory 628
area is unlikely, although the potential could be realized in the future. The first complete ALS 629
data coverage of Finland will be completed by 2020. In addition, several forest operators have 630
acquired their own ALS datasets. Therefore, operational applications of the fusion of leaf-off 631
and leaf-on ALS data are possible. At the very least, the finding in this study that metrics de- 632
rived from leaf-off ALS data could substitute for aerial image metrics could be applied in cases 633
where the acquisition of aerial images has failed, for example, due to unexpected weather con- 634
ditions. The determination of a satisfactory time interval between bi-temporal ALS data acqui- 635
sitions for forest inventories requires further study. The acquisition of both leaf-off and leaf-on 636
ALS data for an inventory area over a short time interval is not reasonable from an economical 637
viewpoint. Therefore, single sensor solutions, such as multispectral ALS, may be more attrac- 638
tive for future species-specific forest inventories. Unfortunately, the results of this study did not 639
indicate that multispectral ALS data could offer a single sensor solution for species-specific 640
ALS-based forest inventories. In general, the findings of this study reveal new possibilities to 641
combine multiple RS data sources and encourage repeat national ALS data acquisitions in for- 642
ested countries.
643 644
5 Conclusions 645
The results indicate that the combination of leaf-on and leaf-off ALS metrics provide lower 646
error rates than the traditional combination of ALS and aerial image metrics for the prediction 647
of species-specific logwood volumes. Our findings also show that recent leaf-off ALS data can 648
be replaced by older leaf-off ALS data without a significant deterioration in logwood prediction 649
error rates. We also explored metrics derived from multispectral ALS data. The results indicate 650
that the multispectral metrics lead to a slight improvement in the error rates associated with 651
logwood volume predictions. Overall, the outcome of this study encourages a deeper investiga- 652
tion of the possibilities of combining different multi-temporal ALS datasets in area-based forest 653
inventories. In the future, multi-temporal ALS datasets will be increasingly available from in- 654
ventory areas. As such, methods and applications that incorporate all available ALS data from 655
an inventory site are welcome.
656 657
Funding details 658
This study is a contribution to the project Comparative test to predict species-specific diameter 659
distributions in forest information systems financed by the Finnish Forest Centre. This study 660
was also supported by the project Sustainable, climate-neutral, and resource-efficient forest- 661
based bioeconomy (FORBIO, decision number 314224), funded by the Strategic Research 662
Council at the Academy of Finland. The Finnish Society of Forest Sciences supported this work 663
with a scholarship granted to the corresponding author.
664 665 666
Disclosure statement 667
No potential conflict of interest was reported by the authors.
668 669
670
Availability of data and material 671
The raw leaf-off ALS datasets supporting the conclusions of this article are available in the 672
repository of National Land Survey Finland, https://tiedostopalvelu.maanmittauslai- 673
tos.fi/tp/kartta. The multispectral ALS data, and the field data will not be shared due to the 674
ownership of the data.
675 676
Data deposition 677
No data deposition.
678
Acknowledgements 679
We acknowledge the support provided by the Strategic Research Council of the Academy of 680
Finland for the FORBIO project (decision number 314224), led by Prof. Heli Peltola at the 681
School of Forest Sciences, UEF. We would like to express our gratitude to Prof. Heli Peltola 682
and Prof. Jyrki Kangas for the acquisition of the financial support for the fieldwork needed to 683
conduct this study. We also would like to thank the Finnish Society of Forest Science for the 684
scholarship awarded to the corresponding author.
685 686
Captions for figures 687
Figure 1. Location of the study area and sample plots in Finland.
688
689 690
Figure 2. This figure demonstrates the multispectral ALS data (M-ALS). The leftmost figure 691
describes the data around a validation plot in a coniferous dominated forest, and the rightmost 692
in a deciduous dominated forest. In the color ramp, black describes the lowest heights and yel- 693
low describes the highest heights.
694
695 696
Figure 3. This figure demonstrates leaf-off ALS datasets used in this study (the uppermost 697
figures: S16-ALS; the bottom figures: S11-ALS). The leftmost figures describe the data around 698
a validation plot in a coniferous dominated forest, and the rightmost in a deciduous dominated 699
forest. In the color ramp, black describes the lowest heights, and yellow describes the highest 700
heights.
701
702 703
Figure 4. Species-specific root mean squared error (RMSE; %) and mean difference (BIAS;
704
%) error values for logwood volume predictions in terms of remote sensing data and response 705
configurations. For the abbreviations of remote sensing data combinations, please refer to sec- 706
tion 2.3.
707
708
709 710
Figure 5. Predicted vs. observed dominant and minor tree species logwood volumes presented 711
in 30 x 30 m validation data. Remote sensing data combinations of M-CH2-ALS + S16-ALS 712
(leftmost) and M-CH2-ALS + AI (rightmost) were used. The SimLog response configuration 713
was employed in all combinations. The median iteration (25th of 50) with respect to the root 714
mean squared error (RMSE) value associated with the dominant logwood volume is presented.
715
For the abbreviations of remote sensing data, please refer to section 2.3.
716 717
718
Figure 6. Predicted vs. observed dominant and minor tree species logwood volumes presented 719
with 30 x 30 validation data. Remote sensing data combination of M-CH2-ALS + S11-ALS 720
was used. The SimLog response configuration was employed in all combinations. The median 721
iteration (25th of 50) with respect to the root mean squared error (RMSE) value associated with 722
dominant logwood volume is presented. For the abbreviations of remote sensing data, please 723
refer to section 2.3.
724 725
726
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