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Rinnakkaistallenteet Luonnontieteiden ja metsätieteiden tiedekunta
2021
Economic losses in carbon forestry due to errors in inventory data
Ruotsalainen, Roope
Canadian Science Publishing
Tieteelliset aikakauslehtiartikkelit
© 2021 The Authors All rights reserved
http://dx.doi.org/10.1139/cjfr-2020-0251
https://erepo.uef.fi/handle/123456789/24812
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Title:
1
Economic losses in carbon forestry due to errors in inventory data 2
3
Authors:
4
Roope Ruotsalainen1*, Timo Pukkala1, Annika Kangas2, Mari Myllymäki3, Petteri Packalen1 5
*Corresponding author 6
E-mail addresses: roope.ruotsalainen@uef.fi, timo.pukkala@uef.fi, annika.kangas@luke.fi, 7
mari.myllymaki@luke.fi, petteri.packalen@uef.fi 8
9
Affiliation:
10
1) University of Eastern Finland, School of Forest Sciences, Yliopistokatu 7 (P.O. Box 111), FI-80101 11
Joensuu, Finland 12
2) Natural Resources Institute Finland (Luke), Bioeconomy and Environment, Yliopistokatu 6, FI- 13
80100 Joensuu, Finland 14
3) Natural Resources Institute Finland (Luke), Bioeconomy and Environment, Latokartanonkaari 9, FI- 15
00790 Helsinki, Finland 16
Abstract 17
Forestry can help to mitigate climate change by storing carbon in trees, forest soils and wood 18
products. Forest owners can be subsidized if forestry removes carbon from the atmosphere and 19
taxed if forestry produces emissions. Errors in forest inventory data can lead to losses in net present 20
value (NPV) if management prescriptions are selected based on erroneous data but not on correct 21
data. This study assesses the effect of inventory errors on economic losses in forest management 22
when the objective is to maximize the total NPV of timber production and carbon payments. Errors 23
similar as in airborne laser scanning based forest inventory were simulated in stand attributes with a 24
vine copula approach and nearest neighbor method. Carbon payments were based on the total 25
carbon balance of forestry (incl. trees, soil and wood-based products) and calculations were carried 26
out for 30 years using carbon prices of € 0, 50, 75, 100, 125 and 150 t-1. The results revealed that 27
increasing the carbon price and decreasing the level of errors led to decreased losses in NPV. The 28
inclusion of carbon payments for the maximization of the NPV decreased the effect of errors on the 29
losses, which suggests that the value of collecting more accurate forest inventory data may decrease 30
when the carbon price increases.
31 32
Keywords: Carbon credit, Carbon sequestration, Net present value, Random error, Value of 33
information 34
1. Introduction 35
Decisions are commonly made under uncertainty but the decision-maker can reduce the uncertainty 36
by collecting more relevant and accurate information. Value of information (VOI) in decision making 37
can be defined as the difference between the expected value of the decision with and without 38
additional information (Lawrence 1999; Birchler and Bütler 2007; Kangas 2010). If the expected 39
value of the decision increases, the additional information is valuable.
40 41
In forest management planning, VOI is often defined based on the net present value (NPV) (Kangas 42
2010; Kangas et al. 2014). Losses in NPV are called inoptimality losses. They may occur when forest 43
planning and management prescriptions are based on erroneous forest information. The VOI 44
originates from the reduction of inoptimality losses when more accurate forest inventory data 45
become available. Inoptimality losses have been commonly used in cost-plus-loss (CPL) analyses 46
where the inventory method that minimizes the sum of inventory costs and inoptimality losses is 47
considered as the best alternative (Burkhart et al. 1978; Hamilton 1978). CPL analyses have been 48
used, for example, to evaluate the effect of sampling error and interest rate (Borders et al. 2008), 49
alternative data sources (Eid et al. 2004; Duvemo et al. 2007), or to define the optimal interval and 50
accuracy of the inventory (Mäkinen et al. 2012).
51 52
Earlier studies on the inoptimality losses due to errors in forest inventory data used either observed 53
errors in a certain inventory method (e.g. Eid et al. 2004; Bergseng et al. 2015; Kangas et al. 2018), or 54
simulated errors (e.g. Eid 2000; Islam et al. 2009; Mäkinen et al. 2010; Islam et al. 2010). The use of 55
observed errors can be problematic since, typically, only one error (i.e. one prediction) per stand and 56
inventory method is available. Simulation of the errors associated with the observed stand attributes 57
is a more general approach since different combinations and levels of errors can be simulated. This 58
allows a more comprehensive analysis of the effect of errors on the expected losses (Kangas 2010).
59
Errors can be simulated without considering the dependencies between them, or they can be 60
simulated using a dependency structure that is similar to the observed error structure of a particular 61
inventory method or inventory case. For example, Eid (2000) simulated non-correlated random 62
errors to stand attributes and analyzed the effect of error levels on the extent of the losses. Mäkinen 63
et al. (2010) and Islam et al. (2010) considered the error structure of the data (i.e. error distributions 64
and dependencies between the errors) by simulating errors that were similar to the errors in forest 65
inventory based on airborne laser scanning (ALS) data.
66 67
The above-mentioned studies defined the VOI based on the NPV of timber production. They 68
considered the effects of errors on the optimality of management prescriptions and the losses were 69
calculated as a decrease in NPV when sub-optimal management prescriptions were implemented 70
instead of the optimal prescriptions. Indeed, VOI has been conventionally defined in this way 71
because economic profitability has been considered as a reasonable objective by the majority of 72
decision-makers. If the decision maker’s utility depends on variables that do not have a market 73
value, or if a part of the objectives is dealt with by constraining the planning problem, the calculation 74
of VOI becomes more complicated (e.g. Kangas et al. 2010; Kangas et al. 2014). However, if an 75
objective variable other than timber has a market value, the simplest method would be to add this 76
value to the net income from timber production. This would allow one to calculate the inoptimality 77
losses based on the total NPV of timber production and non-timber benefits.
78 79
Forest management can play an important role in climate change mitigation (e.g. Karjalainen 1996;
80
Liski et al. 2001; Matala et al. 2009; Pukkala 2014). Living trees sequester CO2 in photosynthesis and 81
store the carbon compounds in biomass. A part of the biomass carbon is transferred to the soil 82
carbon pool (also called dead organic matter, or DOM) in the form of dead trees, litter and harvest 83
residues. When forests are harvested, a part of biomass carbon is moved to the carbon pool of 84
wood-based products. The climate effect of wood-based products depends on the durability of the 85
products, their substitution effects and cascade use (recycling), and the carbon emissions of timber 86
harvesting and transport and product manufacturing (e.g. Pukkala 2011). In this study, the total 87
carbon balance of forestry was defined to be equal to the changes in the three carbon pools 88
(biomass, DOM and products) minus the carbon releases of harvesting, transport and manufacturing 89
plus the substitution effects of wood products (avoided fossil emissions due to the use of wood).
90 91
Carbon tax-subsidy schemes can be used as policy instruments to increase carbon sequestration in 92
forestry (e.g. Van Kooten et al. 1995; Pohjola and Valsta 2007; Pukkala 2011, 2020; Juutinen et al.
93
2018). Carbon tax-subsidy schemes are based on carbon credits, which define a market value of a 94
one ton of CO2 (equivalent to 1/3.67=0.272 tons of carbon) traded in carbon markets. Carbon credits 95
provide an economic incentive for activities that decrease the amount of CO2 in the atmosphere. The 96
simplest basis for carbon crediting would be the carbon balance of living biomass because it is easy 97
to estimate and monitor. However, since a part of biomass carbon is transferred to DOM and wood- 98
based products, a more justified basis for carbon crediting would be the total carbon balance of 99
forestry, which includes the carbon balances of tree biomass, DOM and wood-based products.
100
Consequently, the carbon balances of both forests (biomass and DOM) and wood-based products 101
are taxed or subsidized (Pukkala 2020). This carbon crediting scheme would entitle the forest owners 102
to obtain additional income when forestry as a whole decreases the amount of CO2 in the 103
atmosphere. On the other hand, if forestry acts as a carbon source, forest owners would be taxed.
104 105
The carbon forestry described above poses an interesting question: how do errors in inventory data 106
affect the inoptimality losses in the joint production of timber and carbon benefits, and how do the 107
losses compare to a baseline case where only timber production is maximized? This question is 108
gradually becoming more topical since, in the near future, carbon sequestration by forestry may 109
generate additional income to forest owners. Therefore, the optimality of management actions 110
depends on its effects on both timber production and carbon sequestration.
111 112
This study aimed to analyze how different levels of random errors in inventory data affect the 113
inoptimality losses in forest management. Losses in the total NPV of timber production and carbon 114
payments were assessed. Analyzes were carried out for 30 years and at different levels of carbon 115
pricing. Several realizations and levels of random errors were simulated for the species-specific 116
stand attributes using a canonical vine copula model and a nearest neighbor method, aiming to 117
provide similar joint distribution of errors as observed in the ALS-based forest inventory.
118 119
2. Materials and Methods 120
2.1. Sample plot data 121
We use sample plots measured in central Finland (approximately 62o 27’ N, 24o 13’ E) in 2013. The 122
circular sample plots with a fixed radius of 9 m were located in clusters 4.3 km apart. In total, 1956 123
sample plots were located on forestry land. Diameter at breast height (DBH: diameter at 1.3 m 124
height) was measured and tree species was determined for all trees. The species-specific mixed- 125
effects models of Eerikäinen (2009) were used to generalize the sample tree heights for each sample 126
plot, and the models of Laasasenaho (1982) were used to predict tree volumes. Stand attributes, 127
namely basal area, basal area-weighted mean diameter and basal area-weighted mean height were 128
calculated by tree-species (Scots pine, Norway spruce and all deciduous species) from trees with 129
DBH ≥ 5 cm. The most common deciduous trees in Finland are birches (silver birch: Betula pendula 130
and downy birch: Betula pubescens), aspen (Populus tremula), alder (mainly Alnus incana), willows 131
(Salix sp.), rowan (Sorbus aucuparia) and some other species accounting for a small fraction of the 132
volume of deciduous trees. Because silver birch is the most common deciduous tree species in 133
mineral soil sites, all deciduous trees were assumed to be silver birches.
134 135
The sample plots located in the seedling stands were excluded from the sample plot data used in the 136
analyses. Also, some other plots of the original dataset of 1956 plots were rejected because of 137
missing information about site fertility, drainage status, or some other variable that was required in 138
calculations. As a result, 1501 sample plots were used for the analyses. Pine, spruce and deciduous 139
trees comprised 61.9 %, 23.4 %, and 14.7 % of the total volume, respectively. Summary statistics of 140
the sample plot data are presented in Table 1.
141 142
[Table 1]
143 144
In the majority of the sample plots (n = 1155), only the observed values of stand attributes were 145
available. A smaller proportion of the plots (n = 346) had both observed and predicted values of 146
stand attributes. The stand attributes were predicted using the k Nearest Neighbor (k-NN) 147
imputation method described in Packalén and Maltamo (2007). The predictions were based on 500 148
training sample plots. Metrics calculated from ALS and aerial image data were used in the prediction 149
of stand attributes for the 346 plots (for details, see Ruotsalainen et al. 2019). The observed and 150
predicted stand attributes of the 346 sample plots were used as the starting point for error 151
simulation.
152 153 154
2.3. Simulation of errors 155
Random errors, with similar distribution as the joint distribution of errors in the ALS inventory, were 156
simulated for tree species-specific values of basal area, basal area-weighted mean diameter, and 157
basal area-weighted mean height using a canonical vine copula model and a nearest neighbor 158
method. A detailed description of the methods used in the simulation, and a comparison of the 159
simulated errors with observed errors, can be found in the Appendix. The simulation process is 160
briefly described below.
161 162
Simulation of errors contained several steps. First, we used the sample plot data that included both 163
the observed and predicted values of stand attributes. Density functions were fitted to the observed 164
and predicted values of stand attributes using the logspline package (Kooperberg 2019) in R, v. 3.6.1 165
(R Core Team 2019). Cumulative probabilities of the fitted distributions were utilized to transform 166
the original values of stand attributes into new, uniformly distributed variables. Then, the 167
dependency structure of the multivariate distribution of stand attributes was modeled. A canonical 168
vine (C-vine) copula model was fitted to the transformed uniformly distributed values of the 169
observed and predicted stand attributes with the VineCopula package (Nagler et al. 2019) available 170
in R. The copula model was fitted with a method that jointly seeks an appropriate canonical vine tree 171
structure and pair-copula families with optimal parameter values (Dißmann et al. 2013).
172 173
The fitted copula model was used to simulate ten realizations of errors for the entire sample plot 174
data (n = 1501). This was carried out by simulating ten different copula populations that were ten 175
times larger than the total number of sample plots. The uniformly distributed values of each copula 176
population were transformed back into the original scale by calculating the quantiles of the fitted 177
density distributions at the simulated values. Consequently, the simulated populations contained 178
species-specific values of observed and predicted stand attributes. Then, for each sample plot, the 179
nearest neighbor was determined from the copula population by calculating Euclidean distances 180
between the standardized observed stand attributes and the simulated observed stand attributes in 181
the copula population.
182 183
The predicted stand attributes of the nearest neighbor were used to calculate the errors for the 184
observed stand attributes in the sample plot data. As we wanted to assess the effect of the 185
magnitude of random errors on inoptimality losses, systematic errors were removed by multiplying 186
the predicted stand attributes with factors that were calculated by dividing the mean of the 187
observed stand attribute by the mean of the corresponding predicted stand attribute. To form 188
datasets that describe different levels of random errors, the error vectors were multiplied by 189
different factors (1.0, 0.9, 0.8, …, 0.1) to reduce the level of random errors. For example, factor 0.5 190
implies that random errors were halved compared to error level 1.0 (as a result, the root mean 191
square errors (RMSE) of the stand attributes were also halved). Finally, stand attributes with 192
different levels of random errors were obtained when the errors were added to the observed values 193
of stand attributes.
194 195 196
2.4. Forest planning computations 197
Planning computations were carried out with the Monsu software (Pukkala 2004). The computations 198
consisted of the simulation of stand development under alternative treatment schedules, and the 199
selection of the optimal treatment schedule for each plot. Sample plots were treated as stands in 200
the computations. Stand development was simulated using individual-tree models that predict 201
diameter growth, survival, and ingrowth (Pukkala et al. 2013). Height growth was predicted with the 202
models described in Pukkala et al. (2009). Trees were partitioned into different timber assortments 203
using taper curve functions described in Laasasenaho (1982). Quality deductions to sawlog volumes 204
were made using the models developed in Mehtätalo (2002) and the correction factors reported by 205
Malinen (2007).
206 207
Treatment alternatives were simulated for a 30-year period, which included three 10-year sub- 208
periods. For each stand, several treatment schedules were simulated, and possible treatments were 209
timed to take place in the middle of each sub-period. Treatment alternatives included different 210
thinning approaches (thinning from below and thinning from above), seed tree felling, clear-felling, 211
and removal of upper canopy if the stand had two separate canopy layers. The development of each 212
stand was also simulated without any cuttings.
213 214
The revenues from cuttings were calculated by subtracting the harvesting costs from the roadside 215
values of the harvested trees. For Scots pine and Norway spruce, roadside prices of € 57, 35, and 30 216
m-3 were used for sawlog, small log and pulpwood, respectively. Roadside prices of € 45 and 30 m-3 217
were used for birch sawlog and pulpwood, respectively. The harvesting costs were calculated with 218
the time consumption models described in Rummukainen et al. (1995) using an hourly cost of € 65 h- 219
1 for the forwarder and € 90 h-1 for the harvester. The NPV of timber production was calculated for 220
each management schedule by discounting all revenues and costs incurred during the 30-year 221
planning period to the present, with an interest rate of 3 %. The NPV of the growing stock at the end 222
of the planning period was predicted with updated models of Pukkala (2005), and the discounted 223
value of the ending growing stock was added to the NPV of the treatment schedule.
224 225
The total carbon balance of forestry was calculated for all simulated treatment alternatives. The 226
carbon balance comprises changes in three carbon pools: 1) living biomass, 2) DOM (soil), and 3) 227
wood-based products. The carbon pool of living biomass was initialized for each stand using the 228
biomass models described by Repola et al. (2007), and then multiplying the estimated dry biomass 229
with species-specific carbon fractions (carbon content around 50 % of the dry biomass). Growth and 230
ingrowth increased the amount of carbon stored in the living biomass, whereas mortality and the 231
harvest of trees decreased the amount of carbon stored in this pool. The carbon pools of dead 232
organic matter and wood-based products were initialized with the models described in Pukkala 233
(2014).
234 235
The soil carbon pool is positively affected by the harvest residuals, dead trees, and litter production, 236
whereas decomposition of dead organic matter decreases the pool. Litter production in the stand 237
was calculated using the species-specific turnover rates reported in Pukkala (2014). The effect of 238
decomposition on the soil carbon pool was estimated using the Yasso07 model (Liski et al. 2009).
239 240
The carbon pool of wood-based products included the carbon of the products made of harvested 241
wood. The carbon pool decreased when products were discarded and the discarded products 242
decomposed or were used as biofuel. The carbon balance of products also included their 243
substitution effects (reduced carbon emissions from fossil-fuel-based materials due to the use of 244
wood). Those discarded products that were used as bioenergy had the same substitution effect as 245
other types of bioenergy. Carbon emissions from harvesting, transport and product manufacturing 246
were also included in the carbon balance of wood products.
247 248
Harvested trees were first divided into sawlog and pulpwood. Then, they were divided into the 249
following end-product categories: 1) sawn wood, veneer and plywood, 2) mechanical mass, 3) 250
chemical mass, 4) bioenergy, and 5) “new product types” (mainly dissolving pulp used for textiles).
251
Each end-product category had a specific production release rate, annual disposal rate, substitution 252
rate, and cascade use rate (recycling rate). It was assumed that the only type of recycling was to use 253
discarded products as energy. The proportions of end-product categories and their parameters were 254
obtained from Hurmekoski et al. (2020) and Pukkala (2020). A detailed description of the carbon 255
balance calculations can be found in earlier studies (e.g. Pukkala 2014; Pukkala 2017).
256 257
Revenues and costs related to the total carbon balance of forestry were calculated for each 258
treatment schedule by multiplying the estimated carbon balance of each 10-year sub-period with a 259
given carbon price. If the carbon balance was positive, forest owners received subsidies (revenues) 260
for the sequestered carbon, while a negative carbon balance led to taxes (costs). Carbon subsidies 261
and taxes related to the carbon balance were discounted from the middle of each sub-period to the 262
present, with a 3 % interest rate.
263 264
The optimal management prescription of each stand was selected from the simulated treatment 265
alternatives. As there were no constraints and the stands were assumed to be independent 266
calculation units, the management prescription that led to the greatest total NPV (i.e. NPV of timber 267
production + NPV of carbon payments) was selected for each stand. The selection of the optimal 268
management prescriptions was repeated at carbon pricing levels of € 0, 50, 75, 100, 125 and 150 t-1 269
(equivalent to € 0, 13.63, 20.45, 27.27, 34.09 and 40.91 t-1 CO2). A carbon price of € 0 t-1 means that 270
the forest owner was not subsidized or taxed based on the total carbon balance of forestry, and 271
consequently, only the NPV of timber production was maximized.
272 273 274
2.5. Calculation of inoptimality losses 275
Inoptimality losses were determined as a decrease in the NPV due to errors in the stand attributes.
276
The management prescriptions that led to the greatest NPV were selected for each stand based on 277
‘error-free’ and erroneous data. The management prescriptions selected for the erroneous data 278
were simulated with the ‘error-free’ data to determine the expected losses resulting from the use of 279
erroneous data in decision-making. The inoptimality losses were defined as the difference in NPV 280
between the optimal and sub-optimal management prescriptions. Inoptimality losses were 281
calculated separately for different error realizations (1–10), error levels (1.0, 0.9, 0.8, …, 0.1) and for 282
different levels of carbon pricing (€ 0, 50, 75, 100, 125 and 150 t-1) as follows:
283 284
(1) 285
286
where NPVopt i is the NPV (€ ha-1) of stand i in the management schedule selected based on ‘error- 287
free’ data, NPVerr i is the NPV (€ ha-1) of the same stand in the management schedule, selected based 288
on erroneous data but simulated with the ‘error-free’ data, n is the number of stands (n = 1501).
289 290 291
(
opt i err i)
loss
opt i 1
1
100
n
i
n i
NPV NPV NPV
NPV
=
=
-
= å ´
å
3. Results 292
The inoptimality losses are presented as a function of the error rate in Figure 1. Increasing the price 293
of carbon and decreasing the level of errors decreased inoptimality losses. When NPV was 294
maximized at a carbon price of € 0 t-1, inoptimality losses varied between 0.24 % and 4.43 %, 295
depending on the level of error. When the carbon price was € 50, 75, 100, 125, or 150 t-1, 296
inoptimality losses varied between 0.1–3.92 %, 0.08–3.36 %, 0.06–2.39 %, 0.04–1.67 %, and 0.03–
297
1.14 %, respectively.
298 299
[Figure 1]
300 301
The standard deviations associated with the inoptimality losses at each error level show that the 302
variation in losses decreased as the magnitude of errors decreased and the price of carbon increased 303
(Fig. 2). For example, when NPV was maximized at a carbon price of € 50 t-1 and error levels were 1.0 304
and 0.5, the standard deviations associated with the inoptimality losses were 0.17 % and 0.11 %, 305
respectively. When the price of carbon was increased to € 100 t-1, the standard deviations of 306
inoptimality losses were 0.08 % and 0.04 % with error levels 1.0 and 0.5, respectively.
307 308
[Figure 2]
309 310
Increasing the price of carbon increased the number of stands in which the optimal management 311
prescription was “no cutting” in both the ‘error-free’ and erroneous data. When the carbon price 312
was set at € 0 t-1 and the error level was 1.0, the “no cutting” management alternative was selected, 313
on average, only for 3.9 % of the stands in the ‘error-free’ and erroneous data. Correspondingly, 17.4 314
%, 38 %, and 59.1 % of the stands were given a “no cutting” prescription during the 30-year period 315
when NPV was maximized at carbon prices of € 50, 100, and 150 t-1, respectively.
316 317
The effect of under- and overestimation on inoptimality losses was assessed by dividing the data into 318
under- and overestimates based on the sums of species-specific basal areas. Inoptimality losses due 319
to underestimation decreased as the price of carbon increased (Fig. 3). A trend of decreasing losses 320
was also evident when the stand basal area was overestimated, but the effect of carbon price was 321
not as strong as in the case of underestimation. The difference in inoptimality losses due to under- 322
and overestimation decreased as the error rate of species-specific volumes decreased.
323 324
[Figure 3]
325 326
The mean inoptimality losses (€ ha-1) were calculated by dividing the sum of the losses in the ten 327
error realizations by the total number of plots (15010) in the realizations. When the carbon price 328
was lower than € 100 t-1 and the error level was 0.5–1.0, the mean inoptimality losses were greater 329
than in the case where carbon price was € 0 t-1 (Fig. 4). When the level of random errors was less 330
than or equal to 0.4, carbon prices greater than or equal to € 50 t-1 led to smaller mean losses than in 331
the case where the carbon price was € 0 t-1. Figure 4 also illustrates the difference in considering the 332
inoptimality losses in relative (%) and absolute (€ ha-1) terms. Increasing the carbon price increased 333
the total NPV (NPV of timber production + NPV of carbon payments), which means that inoptimality 334
losses (%) can be lower than in the case where the carbon price is € 0 t-1 (Fig. 1).
335 336
[Figure 4]
337 338
4. Discussion 339
The results showed that paying for carbon sequestration decreases the relative losses in NPV that 340
result from errors in forest inventory data. Paying forest owners at least € 100 t-1 for carbon 341
sequestration also results in lower inoptimality losses in absolute terms than maximizing NPV 342
without carbon payments. Carbon payments compensate for the losses in timber revenues. The 343
management prescription that led to the greatest total NPV was selected for each stand. Constraints 344
were not introduced, since it would have complicated the calculation of the value of information 345
(e.g. Eyvindson and Kangas 2014). Therefore, the results of this study reflect the expected 346
inoptimality losses in a situation where erroneous forest inventory data are used to maximize the 347
overall economic benefit from timber production and carbon sequestration.
348 349
A comparison of different carbon pricing levels also showed that increasing the price of carbon 350
decreased the effect of errors, which indicates that increasing the carbon price decreases the value 351
of collecting more accurate forest inventory data. Finnish Forest Centre, the organization 352
responsible for the stand level forest management inventories of private forests in Finland, can 353
utilize this information when planning new inventories in cases where both timber and carbon 354
credits are sold. From the perspective of forest owners, errors in inventory data seem to become 355
less problematic as the carbon price increases, implying that less accurate inventory data may be 356
adequate. However, from a governmental or societal point of view, it can be argued that carbon 357
subsidies and taxes should be based on the most accurate inventory data to ensure correct carbon 358
payments. The use of less accurate inventory data may result in reduced cost efficiency of the 359
carbon payments.
360 361
In this study, the carbon credits were based on the total carbon balance of forestry (incl. trees, DOM 362
and products). If the credits had been based on the within-forest carbon balance (trees and DOM), 363
the effect of the carbon price on the results would have been greater (Pukkala 2020) because 364
product carbon decreases the effect of cuttings on the total carbon balance of forestry. On the other 365
hand, the calculation of the total carbon balance of forestry includes more uncertainties than 366
calculating only the within-forest carbon balance since several assumptions related to the 367
manufacturing process, substitution effects and life cycles of the products have to be made 368
(Hurmekoski et al. 2020).
369
370
In our study, carbon prices greater than or equal to € 50 t-1 led to lower relative inoptimality losses 371
compared to the case where NPV was maximized with a carbon price of € 0 t-1. This was mainly 372
because carbon credits often made it favorable to refrain from cuttings. A closer examination of the 373
management prescriptions showed that increasing the carbon price meant that most of the selected 374
cuttings were thinnings from above. This is because thinning from above results in a better carbon 375
balance than thinning from below (Díaz-Yáñez et al. 2020). In addition, thinning from above also 376
leads to a higher proportion of sawlogs, and consequently, greater timber revenues.
377 378
Our results indicate that underestimation of the basal area results in greater losses than 379
overestimation (Fig. 3). Underestimation can lead to postponed treatments and, consequently, 380
revenues from cuttings are realized later. Previous studies that investigated the effect of errors on 381
inoptimality losses have also noted that underestimation of stand attributes can lead to greater 382
losses compared to overestimation (e.g. Mäkinen et al. 2010; Kangas et al. 2018). Moreover, our 383
results indicate that the inclusion of carbon credits in the maximization of NPV decreases the losses 384
due to underestimation, and makes underestimates less problematic than in timber-oriented 385
management. This is mainly due to the positive effect of carbon credits on NPV, which compensate 386
for the losses in the NPV of timber production.
387 388
The value of information depends on the usage of forest inventory data. In the current study, forest 389
inventory data were used to maximize the total NPV of timber production and carbon payments.
390
However, this type of analysis could be extended also to other sources of income from forests. For 391
example, forest owners can protect a part of their forests and receive compensations for refraining 392
from all cuttings and other silvicultural operations (METSO forest biodiversity program 2020).
393
Furthermore, non-wood forest products, like berries and mushrooms, can provide additional income 394
to forest owners (e.g. Miina et al. 2016; Tahvanainen et al. 2018).
395
396
Errors similar to the ALS inventory were simulated for the species-specific stand attributes. For the 397
sake of simplicity, we removed systematic errors from the simulated predictions. The errors at level 398
1.0 were similar to those obtained in the ALS-based inventory, except for the basal area of 399
deciduous trees for which the RMSE value differed notably from the corresponding error rate in the 400
ALS-based predictions (Appendix). In addition, the modeled and observed correlation structures of 401
errors were similar, although the correlations were generally lower within the errors associated with 402
the simulated predictions than with the ALS-based predictions (Appendix). The correlations between 403
the errors were assumed to remain the same when the level of errors was decreased gradually, even 404
though the correlations of errors may change when the ALS-based predictions are aggregated to the 405
stand level. However, we believe that the above-mentioned inaccuracies and limitations do not 406
change the conclusions on the effects of random errors and carbon prices on inoptimality losses.
407 408 409
5. Conclusions 410
The study shows that if other economic objectives, in addition to NPV of timber production, are 411
included in the analysis of the value of information, the importance of errors in forest inventory data 412
can change. Inoptimality losses decreased when the price of carbon was increased and the level of 413
errors decreased. When the total NPV was maximized using a carbon price of € 100 t-1 and an 414
interest rate of 3 %, the losses were always lower than in the case where NPV of timber production 415
was maximized. Therefore, the joint production of timber and carbon benefits is reasonable.
416 417 418
Acknowledgements 419
RR was financially supported by the Doctoral Programme in Forests and Bioresources at the 420
University of Eastern Finland. MM was financially supported by the Academy of Finland (Project 421
numbers 295100 and 306875). PP and TP were supported by the Strategic Research Council of the 422
Academy of Finland for the FORBIO project (Decision Number 314224).
423
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Tables 424
425
Table 1. Main characteristics of the sample plot data. BA = basal area, D = basal area-weighted mean 426
diameter, H = basal area-weighted mean height, and SD = standard deviation.
427
Minimum Maximum Mean SD
Pine
BA (m2 ha-1) 0 36.2 11.5 7.6
D (cm) 5.8 44.7 19.8 5.8
H (m) 6.0 31.3 15.6 4.1
Spruce
BA (m2 ha-1) 0 40.1 4.2 7.1
D (cm) 5.0 51.4 14.6 7.2
H (m) 3.9 27.6 12.2 5.1
Deciduous
BA (m2 ha-1) 0 35.6 3.0 4.4
D (cm) 5.0 38.5 12.6 5.6
H (m) 4.6 27.9 13.1 4.2
428
Figure captions 429
430
Fig. 1 Inoptimality losses when net present value (NPV) was maximized at different carbon pricing 431
levels. Lines were fitted to the obtained inoptimality losses at the different error realizations and 432
levels using polynomial models without an intercept. The x-axis corresponds to the mean of relative 433
root mean square errors (RMSE) calculated from species-specific volumes. The vertical line denotes 434
the assumed stand-level error, i.e. errors are halved compared to errors at level 1.0.
435 436
Fig. 2 Standard deviations associated with inoptimality losses at different error levels at different 437
carbon pricing levels.
438 439
Fig. 3 The effect of under- (left figure) and overestimation (right figure) on inoptimality losses at 440
different carbon pricing levels. Data were divided into under- and overestimates based on the sum 441
of species-specific values of basal area. The lines were fitted to the inoptimality losses using 442
polynomial models without an intercept. The x-axis is the mean of the relative root mean square 443
errors (RMSE) calculated from species-specific volumes.
444 445
Fig. 4 Difference between mean inoptimality losses when net present value (NPV) was maximized at 446
carbon prices between € 50 and 150 t-1,and when NPV was maximized at a carbon price of € 0 t-1 447
(i.e. NPV of timber production was maximized). Mean inoptimality losses were calculated as the 448
average of losses (€ ha-1) obtained at each error level.
449
450
Fig. 1 451
452
Fig. 2 453
454
Fig. 3 455
456
Fig. 4 457
Appendix 458
459
1. Simulation of erroneous stand attributes 460
The erroneous stand attributes were simulated in steps 1–5 described below. Computations were 461
conducted in R, v. 3.6.1 (R Core Team 2019) using functions of the logspline, v. 2.1.14 (Kooperberg 462
2019) and VineCopula, v. 2.2.0 (Nagler et al. 2019) packages.
463 464
1. Fitting logspline density functions to the observed and predicted values of stand attributes and 465
transforming the values to the range [0, 1].
466
a. The simulation of erroneous stand attributes was based on the observed and predicted 467
values of stand attributes in the 346 sample plots. The stand attributes included basal 468
area, basal area-weighted mean diameter and basal area-weighted mean height by tree 469
species (pine, spruce and all deciduous trees).
470
b. Logspline density functions were fitted to the observed and predicted values of stand 471
attributes using the logspline function. For basal areas, basal area-weighted mean 472
diameters and basal area-weighted heights, density functions were bound to the ranges 473
of 0–40, 5–45, and 3–30, respectively. The ranges were selected based on the values of 474
stand attributes in the sample plot data.
475
c. The original values of stand attributes were transformed to the range [0, 1] using the 476
plogspline function. The function gives the cumulative probabilities of the fitted 477
distributions of the stand attribute values. A small amount of uniformly distributed 478
random noise was added to the zero values of the basal areas before fitting the logspline 479
density functions to ensure that the transformed values of the basal areas 480
approximately followed the uniform distribution.
481 482
2. Fitting a vine copula model.
483
a. A canonical vine (C-vine) copula model was fitted to the 18-dimensional (i.e. 9 observed 484
and 9 predicted stand attributes) uniformly distributed dataset using the 485
RVineStructureSelect function of the VineCopula package. The function implements a 486
method that jointly seeks an appropriate vine tree structure and pair-copula families 487
with optimal parameter(s) (Dißmann et al. 2013). The method constructs a nested set of 488
trees sequentially. The root node of each tree is the node that maximizes the sum of 489
absolute empirical Kendall’s taus compared to all other nodes. Appropriate pair-copula 490
families were selected according to the Akaike Information Criterion (AIC). For further 491
detail on vine copulas, see e.g. Aas et al. (2009), Joe (2014), and Czado (2019).
492 493
The following steps were repeated 10 times with different random seeds to create several 494
realizations of erroneous stand attributes:
495
3. Simulating a copula population.
496
a. The copula model was used to simulate an 18-dimensional copula population of size 497
n=15010, i.e. ten times the total number of sample plots.
498
b. The uniformly distributed values of stand attributes (the copula population) were 499
transformed back to the original scale by calculating the quantiles of the fitted empirical 500
marginal distributions at the simulated values. This was carried out with the qlogspline 501
function.
502
c. Simulated values for the observed basal areas < 0.02 m2 ha-1, were set to 0. The 503
corresponding values of basal area-weighted mean diameter and basal area-weighted 504
mean height were considered missing and were set to -1.
505 506
4. Attaching simulated predicted stand attributes to the observed values (without random noise) in 507
the sample plot data (n=346) used for fitting the copula model and to new sample plot data (n = 508
1155) from the same inventory area.
509
a. First, observed stand attributes in the sample plot data (n = 1501) and simulated 510
observed values of stand attributes in the copula population were normalized so that 511
each variable had a mean of 0 and a standard deviation of 1.
512
b. The value of -100 was added to the normalized values of the species-specific basal area- 513
weighted mean diameter and basal area-weighted mean height if the original value was 514
-1, i.e. the value was missing. This was carried out to ensure that the nearest neighbour 515
searched from the copula population contained the same tree species as the sample plot 516
in question.
517
c. Euclidean distances between the normalized observed stand attributes in the sample 518
plot data and the normalized simulated observed stand attributes in the copula 519
population were calculated in a 9-dimensional space (basal area, basal area-weighted 520
mean diameter and basal area-weighted mean height for pine, spruce, and all deciduous 521
trees). An observation of the copula population, which had the shortest Euclidean 522
distance to the observed stand attributes of the sample plot in the field data, was 523
selected, and the corresponding simulated predicted stand attributes were assigned to 524
the sample plot. This procedure was followed to ensure consistency between the 525
selected simulated predicted stand attributes and the observed values of stand 526
attributes in the sample plot data.
527 528
5. Generating erroneous stand attributes at different random error levels.
529
a. Simulated predicted stand attributes were corrected so that they had equal means as 530
the observed stand attributes. This was carried out by multiplying the predicted values 531
of the stand attributes with the corresponding ratio of means (i.e. value of predicted 532
stand attribute was multiplied by a factor equal to the mean of the observed stand 533
attribute divided by the mean of the predicted stand attribute).
534
b. Errors in the stand attributes were calculated by extracting the observed stand 535
attributes from the corresponding predicted stand attributes. The differences between 536
observed and predicted stand attributes were multiplied by factors that ranged from 1.0 537
to 0.1 (1.0, 0.9, 0.8, …, 0.1). Finally, the random errors were added to the observed stand 538
attributes, which resulted in erroneous stand attributes.
539 540 541
2. Assessment of errors 542
Errors in the original ALS-based predictions and in the simulated predictions were evaluated by 543
comparing the correlation structure of errors, and by visually inspecting the error distributions. In 544
addition, the errors were measured using absolute and relative RMSE, which were calculated as 545
follows:
546 547
548
549
550
551
where yi is the correct value of stand attribute, ŷi is the erroneous value of stand attribute, n is the 552
number of observations, and ȳ is the mean of correct values. Absolute and relative RMSE values of 553
the stand attributes are presented in Table A1.
554 555
( )
RMSE =
2 1
n
ˆ
i i
i
y y n
=
å -
( )
Relative RMSE =
2 1
ˆ
100
n
i i
i
y y n y
=
-
´
å
Table A1. Root mean square errors (RMSE) associated with the airborne laser scanning (ALS) based 556
predictions and simulated predictions when the level of errors was similar to the sample plot-level 557
errors (i.e. error level is 1.0, RMSE values are calculated as the mean of ten realizations). BA = basal 558
area, D = basal area-weighted mean diameter, H = basal area-weighted mean height.
559
ALS-based predictions Simulated predictions
RMSE Rel. RMSE RMSE Rel. RMSE
Pine
BA (m2 ha-1) 5.8 49.9 5.2 45.4
D (cm) 4.5 22.7 4.6 23.3
H (m) 2.2 14.2 2.6 16.4
Spruce
BA (m2 ha-1) 5.3 127.8 5.8 136.6
D (cm) 6.1 43.0 6.6 44.8
H (m) 4.1 34.1 4.5 37.1
Deciduous
BA (m2 ha-1) 2.7 86.7 3.9 131.9
D (cm) 5.4 42.4 5.4 43.0
H (m) 3.8 28.9 4.0 30.5
560 561
The similarity of error dependency structures was assessed by calculating Pearson’s correlation 562
coefficients between the errors (Fig. A1). The density histograms of the error distributions in the 563
original ALS-based predictions and in the simulated predictions were compared (Fig. A2).
564
565
Fig. A1 Correlation matrices of observed (top) and simulated (bottom) errors. Correlation matrix of 566
simulated errors was calculated as the mean of ten error correlation matrices. Pearson’s correlation 567
coefficients were calculated from observations where all stand attributes were available, i.e.
568
observations that had missing values were discarded. For abbreviations, please refer to Table A1.
569
570
571
Fig. A2 Distributions of errors in the original data (bars coloured in grey) and in the simulated data 572
(bars coloured in red) when the level of errors was similar to the sample plot-level errors, i.e. error 573
level is 1.0. Simulated data were selected randomly from the ten error realizations. For 574
abbreviations, please see Table A1.
575
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