1

1 2

Title: 3

Uncertainty in timber assortment estimates predicted from forest inventory data 4

Authors:

Markus Holopainen1, Mikko Vastaranta1, Jussi Rasinmäki1, Jouni Kalliovirta1, Antti

Mäkinen1, Reija Haapanen2, Timo Melkas3, Xiaowei Yu4 & Juha Hyyppä4

Addresses of affiliations:

1 University of Helsinki, Dept. of Forest Resource Management, Latokartanonkaari 7, 00014

Helsinki, Finland, markus.holopainen@helsinki.fi, mikko.vastaranta@helsinki.fi

2 Haapanen Forest Consulting, reija.haapanen@haapanenforestconsulting.fi 5

3 Metsäteho Ltd, timo.melkas@metsateho.fi 6

4 Finnish Geodetic Institute, yu.xiaowei@fgi.fi, juha.hyyppä@fgi.fi 7

Corresponding author:

Markus Holopainen, tel: +358 50 380 4984, e-mail: markus.holopainen@helsinki.fi

8

2

Abstract 1

2

Uncertainty factors related to inventory methodologies and forest-planning simulation computings in the 3

estimation of logging outturn assortment volumes and values were examined. The uncertainty factors 4

investigated were (i) forest inventory errors, (ii) errors in generated stem distribution, (iii) effect of generated 5

stem distribution errors on the simulation of thinnings and (iv) errors related to the prediction of stem form 6

and simulation of bucking. With respect to inventory errors, standwise field inventory (SWFI) was compared 7

with area-based airbone laser scanning and aerial photography (ALS) inventorying. Our research area, Evo, 8

is located in southern Finland. In all 31 logging sites (12 clear-cutting and 19 thinning sites) measured by 9

logging machines in winter 2008 were used as field reference data. The results showed that the generation of 10

stem distribution series using mean stock characteristics performed well when the series generated were 11

compared with the reference series measured by the logging machines. The generation of stem distribution 12

series using mean characteristics led to an RMSE of 1.3-2.7 m3/ha and a bias of -1.2-0.6 m3/ha in volume of 13

all assortments. Prediction of stem form and simulation of bucking led to a relative bias of -3.1- 36.5 % in 14

predicted saw timber volume. Errors related to pulpwood volumes were considerably larger. The most 15

prominent source of error in predicting assortment volumes was forest inventory errors, the bias and RMSE 16

of which varied between -9.3-13.8 m3/ha and 6.9-47.4 m3/ha, respectively, depending on the assortment and 17

inventory methodology. The effect of forest inventory errors on the value of logging outturn in clear-cuttings 18

was 29.1% (SWFI) and 25.8% (ALS). The respective RMSE values related to thinnings were 41.1% and 19

42%. 20

21

Keywords: low-pulse ALS, timber assortment estimates, stem distributions, stem form, planning 22

simulations, stand value 23

24

25

3

1. Introduction 1

2

Airborne laser scanning (ALS) is the most accurate remote-sensing technique for standwise forest inventory 3

providing accuracies ranging between 10% and 27% for the mean volume at stand or plot level (e.g. Næsset 4

1997, 2002, Holmgren 2003, Lim et al. 2003, Packalén and Maltamo 2006, Holopainen et al. 2008). For 5

comparison, the mean errors of traditional standwise field inventory (SWFI) used in operational forest 6

management planning vary for mean volume from 16% to 38% in Finland (Poso 1983, Haara and Korhonen 7

2004, Saari and Kangas 2005). Current ALS data acquisition costs are comparable to those of SWFI. The 8

two main approaches to deriving forest information from small-footprint ALS data have been those based on 9

laser canopy height distribution (area-based method, Næsset 1997, 2002) and individual tree detection 10

(Hyyppä and Inkinen 1999, Persson et al. 2002, Leckie et al. 2003, Popescu et al. 2003, Maltamo et al. 11

2004). 12

13

Most of the ALS research in forest inventory has focused on the estimation of mean characteristics, such as 14

plot or stand mean height or mean volume. However, from the standpoint of both forest value assessment 15

and operative timber harvesting, the prediction of species-specific assortment outturn volumes is by far the 16

most essential issue. For example, the economic value of a forest stand cannot be accurately determined on 17

the basis of total stem volume only. Instead, information on tree species and the stem distribution is required 18

to reliably determine the distribution of the total stem volume in various assortments. 19

20

Few results are available on the accuracy of ALS-based timber assortment estimation. One problem in 21

examination of timber assortment-level estimation accuracy is that it requires sufficiently accurate ground 22

reference data. In practice, the best method for acquiring such data is to use measuring data gathered by 23

logging machines. However, to utilize these kinds of data as reference data for an ALS inventory, a rather 24

complicated experimental arrangement is required to synchronize logging and imaging time schedules and 25

identify felled trees. 26

27

Peuhkurinen et al. (2007) studied preharvest measurements using high pulse (6.2 pulses / m2) ALS data of

two clearcutting stands in eastern Finland. Individual tree detection and area based ALS-estimation was

compared to SWFI and systematic plot sampling. Field reference data was collected using logging machine.

Results indicated that single tree detection produced the best results compared to other methods. The crucial

point of the method studied seemed to be the choice of diameter prediction model. Holopainen et al. (2009)

4

compared tree-level airborne laser-scanning (ALS) data accuracy with standwise estimation data accuracy as

input data for forest planning, using tree- and stand-level simulators. They concluded that tree-level ALS

data and tree-level simulator resulted in more accurate simulation results than standwise estimation with the

error levels assumed. To date, the superior costs of high-density ALS imaging have hindered development in

this aspect. Thus, for operational forest inventories low-pulse ALS data have been used. For example, several

forest organizations in Finland are currently replacing traditional SWFIs with area-level ALS inventories in

which low-density (less than two pulses per m2) ALS data are used as an auxilliary data source.

1

First studies to obtain tree species-specific estimates by means of low-pulse ALS data were undertaken by 2

Packalén and Maltamo (2006, 2007), Holopainen et al. (2008), Peuhkurinen et al. (2008) and 3

Packalén (2009). All of these studies showed that treespecies-specific volume estimates can be obtained 4

with lower accuracy than total volume estimates. Determination of stratum-level characteristics is, however, 5

essential for predicting assortment-level characteristics. 6

7

Peuhkurinen et al. (2008) performed one of the first studies to estimate timber assortment-level 8

characteristics, using low-pulse (0.7 m2/ha) ALS data. They developed the nearest neighbour search method 9

for feature selection of low-pulse ALS data and aerial photographs. In addition, they developed tree species-10

specific diameter distribution estimation methods and estimated the saw log timber volume, using the 11

estimated height distributions, and the stem data bank, using 14 clear-cut stands that were measured as 12

reference by a logging machine. Peuhkurinen et al. (2008) showed that the feature selection method proposed 13

was suitable for estimating tree species-specific volumes at the stand level. However, species-specific 14

accuracies as well as saw log estimation accuracy were much lower than those for total volume. 15

16

The economical value of the stand or estate can be estimated, using forest management planning simulations. 17

Forest planning is based on stand-level or tree-level models and simulators. When tree-level forest-planning 18

simulators are used, stem distributions can be formed, based on mean stock characteristics, by determining 19

and measuring the inventory unit (e.g. compartment) median trees and utilizing theoretical stem distributions 20

such as the Weibull distribution in the modelling and derivation phases, or it can be derived by enumerating 21

all trees present in the inventory unit, resulting in the true stem distribution series. Maltamo et al. (2006) 22

showed that size distributions of trees can be estimated, using locally modelled distribution functions in 23

which ALS-based canopy height metrics are used as predictors. 24

25

5

In forest inventories based on stand mean characteristics, e.g. SWFI or area-level low-pulse ALS inventory, 1

the stands’ stem distribution series are predicted, based on stand basal area, mean diameter and mean age. 2

Therefore, computing systems based on tree-level models are subject to input data, including inventory 3

errors as well as errors in the stem distribution series generated when stand-level data are transformed into 4

tree-level data required by the computing system. Thus, in the simulations the accuracy of predicted logging 5

outturn assortment volumes are influenced, apart from inventory errors, by errors related to the generation of 6

stem distributions and the prediction of stem form and simulation of bucking. However, to our knowledge 7

there are no studies available that simultaneously incorporate the effects of these errors on the prediction of 8

logging assortment outturns by forest-planning simulation computations, using operative inventory methods. 9

10

The objective here was to analyse the effects of various uncertainty factors on the prediction of assortment 11

outturn volumes and economic values carried out in current inventory methods and forest-planning 12

simulation computings. The analyses of the various uncertainty factors were partioned into three parts. The 13

first part dealt with the errors related to the prediction of diameter class bucking results. The second part 14

dealt with the effect of inventory method on the prediction of clear-cutting outturn volumes. This was 15

examined from three points of view: 1) errors in the generation of stem distribution series, 2) inventory 16

errors (SWFI vs. area-level low-pulse ALS and aerial photography inventory (ALS inventory)) and 3) the 17

combined effects of stem distribution generation and inventory errors. The third part dealt with the analysis 18

of inventory and stem distribution generation errors on the simulation of thinnings. 19

20

21

2. Study material 22

23

2.1 Study area and logging compartments 24

25

The forest compartments utilized in the study (Figure 1) were either thinned or clear-cut in winter 2008. 26

27 Figure 1. 28

29

The site quality of the study compartments varied from grovelike heaths (OMT) to barren heaths (CT). Basic 30

information regarding the study compartments is presented in Tables 1 and 2. The dominant species in the 31

compartments was either pine (Pinus L.) or spruce (Picea A. Dietr.). The clear-cutting compartments were 32

spruce-dominant (83%), whereas the thinning compartments were pine-dominant (79%). The delineation of 33

all study compartments was checked using global positioning system (GPS) measurements. 34

6

1

Table 1. Stock characteristics of the clear-cutting compartments (n = 12) according to the SWFI data. 2 3

Age BA N Dg Hg AreaMean 88 18.5 1228 30.5 19.1 1.1Min 51 12.3 211 22.8 14.4 0.2Max 123 24.0 9556 37.3 23.6 1.9Stdev 22 3.1 2771 3.9 3.1 0.6 4

5 6

Table 2. Stock characteristics of the thinning compartments (n = 19) according to the SWFI data. 7 8

Age BA N Dg Hg AreaMean 51 21.1 904 22.2 16.6 1.8Min 28 16.5 363 13.5 11.0 0.2Max 85 26.7 4410 27.3 20.8 7.6Stdev 13 2.9 875 3.1 2.2 1.7 9

10

The total study material consisted of three separate entities: 1) compartment and plot assortment outturn data 11

obtained by the logging machine, 2) SWFI data, 3) Results of the ALS inventory and field plot data used as 12

training data for the ALS inventory. 13

14

2.2 Assortment outturn data obtained by logging machine mensuration 15

16

Data obtained by the logging machines were utilized in the study as reference data. Of the compartments 17

studied, 12 were subjected to clear-cutting and 19 to thinning. The logging machines gathered STM data 18

according to the Standard for Forest Data and communication (StanForD 2006). An STM file includes data 19

for each felled tree regarding the logging machine’s position at the time of felling, stem diameters at 10-cm 20

intervals from the felling height to the final bucking height, tree species, bucking parameters and bucked 21

assortment volumes. 22

23

The compartments were logged using either Ponsse (Ponsse oyj, Vieremä, Finland) or John Deere (Deere 24

and Company, Moline, IL, USA) logging machines. The logging machine information obtained covered 25

5300 and 650 felled trees in the clear-cutting and thinning compartments, respectively. An STM file was 26

saved for each felled tree producing commercial timber. STM data were obtained for all trees felled in clear -27

cutting compartments. Stem distribution series, assortment outturn volumes and mean stock charateristics 28

7

(basal area, diameter, height and volume) for each clear-cutting compartment were derived, using stem 1

diameter and length information present in the STM files. 2

3

The diameter at breast-height (dbh) was derived as each stem’s 12th measured diameter (10-cm stump + 120 4

cm = 130 cm). Total tree height was estimated, based on the commercial timber height present in the STM 5

file. In the thinning compartments, analyses were restricted to 56 randomly situated plots. Each plot was 6

thinned in such a manner that the STM file included information on the plot in which the tree was felled, thus 7

making it possible to accurately determine thinning outturn for each thinning plot. Thinning compartment 8

outturn was derived based on the thinning plots located in the compartment. Each thinning compartment 9

included 1-6 circular thinning plots having a radius of 10 m. 10

11

2.2 Standwise field inventory 12

13

Each study compartment had data obtained in SWFI carried out during the years 2005-2007. SWFI stock 14

data include tree species stratum data, e.g. for basal area, stem count, mean diameter and mean height 15

(Oksanen-Peltola et al. 1997). If a logging compartment’s boundary deviated markedly from the respective 16

inventory compartment’s boundary, new inventory data for the logging compartment were calculated as 17

weighted means of the inventory compartments intersecting the logging compartment. Inventory 18

compartment data were updated to the time of logging with the SIMO system (Rasinmäki et al. 2009). 19

20

2.3. ALS inventory 21

22

The ALS data were acquired in midsummer 2006. The flying altitude was 1900 m. The density of the pulses 23

returned within the field plots was 1.8/m2 (only, first, intermediate or last; 1.3/m2 if only or first pulses were 24

considered). A digital elevation model (DEM) and consequently heights above ground level were computed 25

by the data provider. Same-date aerial photographs were obtained with a Vexcel Ultracam digital camera, as 26

well. The photographs were orthorectified, resampled to a pixel size of 0.5 m and mosaiced to a single image 27

covering the entire area. The near-infrared (NIR), red (R) and green (G) bands were available. 28

29

8

A modelling field reference data for ALS-inventory were gathered from the study area in midsummer 2007. 1

Treewise field measurements from 264 fixed-radius (10 m) plots were collected and plot level characteristics 2

calculated. There was a 1-year gap between the acquisition of ALS data and field measurements and logging 3

machine measurements; the latest growth in height was subtracted. 4

5

Several statistical and textural features were extracted from the ALS data and aerial photographs. The 6

extraction window was 16 x 16 m, which has been used in operative ALS inventories in Finland. The 7

features included means and standard deviations of spectral values of aerial photographs and ALS height and 8

intensity, Haralick textural features (Haralick et al. 1973; Haralick 1979) derived from spectral values, ALS 9

height and intensity, and standard texture referring to a set of averages and standard deviations of spectral 10

values, ALS height and intensity. The height statistics for the first and last pulses were calculated as in 11

Suvanto et al. (2005): mean and maximum height, standard deviation and coefficient of variation of height, 12

heights at which certain relative amounts of laser points had accumulated as well as percentages of laser 13

points accumulated at various relative heights. Only pulses exceeding a 2-m height limit were included to 14

remove hits to ground vegetation and bushes. Finally, percentages of points under 2-m in height were added. 15

The total number of features in final dataset was 172. All features were standardized to a mean of 0 and std 16

of 1. ALS-feature selection was based on the genetic algorithm method presented by Holopainen et al. 17

(2008). A reduced set of features (11 features, see Holopainen et al., 2008) was used in the estimation of 18

stand characteristics. 19

20

The estimation method was k-NN, which has long been used in Finnish remote sensing -aided forest 21

inventory applications (e.g. Kilkki and Päivinen 1987; Tokola 1990, Muinonen and Tokola 1990; Tomppo 22

1991). The nearest neighbours were determined by calculating the Euclidean distances between the 23

observations in the n-dimensional feature space. The number of nearest neighbours was set at 5. 24

25

3. Methodologies 26

27

3.1 Determination of the stem distribution series 28

29

9

Based on mean characteristics obtained by the SWFI and ALS inventory, stem distribution series were 1

generated for each study compartment. Reference stem distribution series were derived for each 2

compartment, using logging machine STM data. These series are based on the felled trees and do not include 3

generation errors. STM data measured in clear-cutting compartments enable accurate determination and 4

mensuration of mean stock characteristics. 5

6

In addition, stem distribution series for clear-cutting compartments were predicted, based on mean stand 7

characteristics derived from the reference stem distribution series. Generation of stem distribution series was 8

carried out with the SIMO system incorporating the Weibull distribution for 1-cm diameter classes. Separate 9

distribution models were applied for pine (Mykkänen 1986), spruce (Kilkki et al. 1989) and birch (Betula L.) 10

(Siipilehto 1999). 11

12

3.2 Determination of assortment volumes and prices 13

14

The stem form of each diameter class in the generated stem distribution series was predicted, using 15

Laasasenaho's (1982) stem curves. The predicted stem form was then used to determine assortment volumes 16

for each diameter class. Bucking was performed, using Näsberg's (1985) dynamic algorithm. Saw timber 17

reductions were not applied. 18

19

With respect to thinnings, analyses were performed to determine how close the SWFI and ALS inventory-20

based simulated thinning outturns were to the true outturns. The simulated thinning outturn basal areas were 21

set equal to the respective true values. The thinning procedure was kept constant in all cases, because the 22

objective was not to investigate the functionality of the thinning model or the effects of inventory data 23

accuracy on the timing of loggings but to clarify whether the accuracy of the inventory data was sufficient to 24

reliably simulate thinnings. In addition to inventory data accuracy, other influencing factors included the 25

accuracy of the stem distribution series generated and the similarity of the simulated thinning to the actual 26

thinning. The basal area and assortment volumes of the actual thinning were derived from the STM files. The 27

thinnings were simulated as underthinnings and the bucking value matrices used in the simulations were 28

identical to those used in the actual thinnings. 29

10

1

The assortment volumes for each felled tree saved in the STM files were used as reference volumes. These 2

logging machine data were first classified into 1-cm diameter classes. The mean assortment volumes for each 3

diameter class were then calculated. This procedure enables direct comparison between predicted and 4

reference assortment volumes. The logging outturns were valuated, using mean assortment prices in southern 5

Finland at the time of logging (Table 3). 6

7 Table 3. Mean assortment prices at the time of logging in southern Finland (MetInfo, April 2008). 8 9

Saw wood, €/m3 Pulp wood, €/m3

Pine 58.66 16.51Spruce 57.96 23.96Birch 51.56 15.02 10

11

12

3.3 Calculation of the effects of various sources of error 13

14

3.3.1 Effect of stem form prediction and simulated bucking on assortment outturns 15

16

The effects of stem form prediction on assortment outturns was caused by deviations in the true and 17

predicted stem form. The logging machine STM data included diameter measurements for the commercial 18

part of the stem at intervals of 10 cm. 19

20

Based on these data and the logging machine operator's professional skill (the operator takes into account 21

defects etc.) the stem is bucked into assortments. When bucking is simulated, stem form is predicted by tree 22

species, dbh and total stem length. The stem is then bucked into assortments, based on the predicted stem 23

form. An average saw timber reduction (pulpwood transition) caused by defects was not used in the 24

simulations. 25

26

The combined error in stem form prediction and simulated bucking on the prediction of single-tree 27

assortment volumes was analysed, by first determining the true mean assortment outturns for each diameter 28

class, based on the logging machine STM data. The respective outturns were then predicted for each 29

diameter class, using common stem form functions having only tree species, dbh and stem length as 30

independent variables (Table 4, Alternative 1). 31

32

11

1

3.3.2 Effects of inventory method on predicted clear-cutting outturns 2

3

The effects of the inventory method on the predicted clear-cutting outturns were clarified via errors arising in 4

the generation of the stem distribution series, inventory errors and the combined effects of the afore-5

mentioned errors. These analyses were restricted to clear-cutting compartments only, since the true stem 6

distribution, the generated stem distribution using true mean stock characteristics and the true assortment 7

volumes were available for clear-cutting compartments only. The effects of the inventory method used were 8

derived as follows (Table 4, Alternatives 2-4): 9

10

2) The effects of stem distribution generation were derived by comparing the true stem distribution series 11

with those series predicted, using mean stock characteristics. The differences in volume were distinguished 12

by comparing the true diameter class mean volumes with the respective predicted volumes, the only source 13

of error hence being the generation procedure of the stem distribution. Comparisons were carried out, using 14

logging machine STM data only. 15

16

3) The effects of inventory errors present in the compartment and ALS inventories were derived by 17

comparing stem distributions that were predicted using the true mean stock characteristics with those 18

predicted using the mean stock characteristics derived in the respective inventory. 19

20

4) The combined effects of errors rising in the generation of stem distributions and inventory errors were 21

derived by comparing the stem distribution series derived from the inventory data with those derived from 22

the logging machine data. 23

24

3.3.3 Effect of inventory method on predicted thinning outturns 25

26

The effects of the inventory method on the predicted thinning outturns were clarified by investigating the 27

combined effects of errors arising in the generation of the stem distribution series and inventory errors (Table 28

4, Alternative 5). True assortment outturns for the thinning compartments were derived from the logging 29

machine STM data. The thinnings were simulated in the stem distribution series that were generated, using 30

the mean stock characteristics derived by the inventory in a manner in which the basal area of the simulated 31

outturn equalled that of the actual thinning. The effects of the inventory method were then determined by 32

12

comparing the actual and predicted thinning outturns. In the SIMO system, the thinning simulations can be 1

controlled by a comprehensive set of parameters, the functionality of which was tested. 2

3

Table 4. Principles used in the error analyses. 4 5

Alternative Source of error Input data Reference data

1 Stem form prediction and simulated bucking 

Stem form of a given diameter class predicted by tree species, dbh and total

height

Stem profiles present in the logging machine's STM data

2 Generation of the stem distributions

Mean characteristics derived from the STM data

Logging machine's STM data

3 Inventory error Mean characteristics derived in the inventory

Mean characteristics derived from the logging

machine's STM data

4 Combined errors Mean characteristics derived in the inventory

Logging machine's STM data

5 Combined errors in prediction of thinnings

Simulated thinning of the stem distribution series

predicted by mean characteristics derived in the

inventory

Thinned stems present in the logging archives STM

data 6

7

4. Results 8

9

4.1 Error in simulated bucking 10

11

Analyses were restricted to diameter classes ranging from 20 cm to 40 cm (Figures 2 and 3, Table 5), since 12

most of the STM stems fell into these classes. On the other hand, the bucking process is economically 13

important only when applied to larger size stems consisting of several individual logs. 14

-100

-50

0

50

100

150

200

250

10 15 20 25 30 35 40

Erro

r, dm

3

DBH class

Pine

Spruce

Birch

15

13

Figure 2. 1

-350

-300

-250

-200

-150

-100

-50

0

50

10 15 20 25 30 35 40

Erro

r, dm

3

DBH class

Pine

Spruce

Birch

2 Figure 3. 3 4 Table 5. Saw timber and pulpwood volume prediction errors by diameter class. 5 6 Saw wood Pine Spruce BirchDiameter class dm3 % dm3 % dm3 %

10-14 -2 -100.0 0 * 0 *15-19 15 18.0 5 10.8 0 *20-24 -3 -1.0 28 12.5 19 36.525-29 4 0.7 -15 -3.1 -2 -0.630-34 -15 -1.9 10 1.3 61 11.135-39 37 3.3 -5 -0.5 102 12.2

Pulp wood Pine Spruce BirchDiameter class dm3 % dm3 % dm3 %

10-14 -8 -9.7 -3 -4.9 -4 -6.915-19 -34 -27.4 -7 -6.2 -18 -10.020-24 -37 -32.8 -42 -37.7 -67 -22.225-29 -60 -48.8 -21 -23.5 -87 -34.130-34 -81 -61.3 -34 -39.8 -153 -55.135-39 -126 -74.3 -19 -25.9 -180 -64.3 7

8

By inspecting Table 5 and Figures 2 and 3, one can note that with respect to pine and birch, bucking errors 9

increase with increasing stem size. However, with spruce they apparently decrease. The relative bias varied 10

in the range -1.9-3.3%, -3.1-12.5% and -0.6-36.5.% for pine, spruce and birch, respectively. The pulpwood 11

relative biases were considerably larger than the respective saw timber statistics: namely -74.3 to -32.8%, -12

39.8 to -23.5% and -64.3 to -22.2% for pine, spruce and birch, respectively. This is a consequence of the fact 13

that in reality some saw timber-dimensioned wood is always bucked as pulpwood due to quality defects. 14

15

4.2 Determined stem distributions 16

14

1

True stem distribution series were determined by a logging machine (STM). In addition to the true stem 2

distribution series, three other series were formed for each clear-cutting compartment investigated in the 3

study: i) predicted series generated on the basis of mean stock characteristics derived from the true stem 4

distribution series (PRED), ii) predicted series generated on the basis of mean stock characteristic output by 5

the compartment inventory (SWFI) and iii) predicted series generated on the basis of mean stock 6

characteristic output by the ALS inventory (ALS). The essential results concerning stem distribution series 7

generation are presented in Figure 4. The results are analysed further in the following chapters. 8

9 Figure 4. 10 11

4.3 Effects of inventory method on predicted clear-cutting outturns 12

13

4.3.1 Error in the generation of stem distributions by mean stock characteristics 14

15

Logging machine STM data were used solely in the analysis of stem distribution generation errors. The true 16

stem distributions were derived directly from the STM data obtained from the clear-cutting compartments. 17

The STM data contained information on each felled stem, including commercial wood. The same STM data 18

were used to calculate the true mean stock characteristics for each compartment, based on which stem 19

distributions were finally predicted (PRED). Comparisons of these two stem distributions revealed errors due 20

to the stem distribution generation process. 21

22

Figure 4 shows that at clear-cutting sites the number of small trees was underestimated in the predicted stem 23

distribution. On the other hand, prediction of the numbers of the more valuable saw timber stems succeeds 24

better which is important with respect to the determination of compartment stock value. The effect of stem 25

distribution generation on compartment assortment volumes is presented in Table 6 and the effect on 26

compartment assortment values in Table 7. 27

28 Table 6. Effect of stem distribution generation on predicted compartment assortment volumes, m3/ha. 29 30

Saw wood Pulp woodPine Spruce Birch Pine Spruce Birch

BIAS -0.8 0.0 -0.7 -0.6 -1.2 0.6BIAS% -2.6 0.0 -8.5 -8.5 -5.3 5.6RMSE 2.6 2.7 1.3 1.5 2.2 1.6

RMSE% 9.0 2.6 16.5 20.1 9.4 13.6 31 32 33 Table 7. Effect of stem distribution generation on predicted compartment assortment outturn values, €/ha. 34

15

1 BIAS BIAS% RMSE RMSE%-107.1 -1.2 229.1 2.6 2

3

When the absolute (m3/ha) results are analysed (Table 6), one notes that stem distribution generation resulted 4

in almost unbiased estimates with respect to all assortments examined. The greatest bias was found in spruce 5

pulpwood (-1.2 m3/ha). The relative biases ranged from -8.5% to 5.6%. The absolute root-mean-squared-6

error (RMSE) values varied from 1.3 m3/ha to 2.7 m3/ha and the relative RMSE values from 2.6% to 20.1%. 7

The relative bias and RMSE values are, however, not totally realistic with respect to all assortments, due to 8

the minor actual logging outturns. When the effects of stem distribution generation on the economic value of 9

compartment assortments are analysed (Table 7), one notes the minor magnitude of the relative bias and 10

RMSE values. 11

12

4.3.2 Effect of inventory error 13

14

The mean stock characteristics produced by the SWFI and the ALS inventory were used to derive stem 15

distributions for each clear-cutting compartment. The stem distributions derived were compared with the 16

stem distributions formed on the basis of the true mean stock characteristics (derived from the logging 17

machine data, PRED). These comparisons revealed the effect of inventory error on compartment stem 18

distributions (Figure 4), assortment outturns (Table 8) and assortment values (Table 9). 19

20

Spruce was by far the most common (87%) tree species in the clear-cutting compartments. The results 21

concerning spruce, especially those concerning relative accuracy, can therefore be considered as the most 22

reliable. The great magnitude of the pine- and birch-related relative errors are a consequence of the 23

relatively minor respective logging outturns. A more realistic view of the effect of inventory error on pine 24

and birch assortment volumes can therefore be acquired by examining the absolute accuracy statistics. 25

26 Table 8. Effect of inventory error on predicted assortment amounts, m3/ha. 27 28

16

Saw wood Pulp woodPine Spruce Birch Pine Spruce Birch

ALS BIAS 6.5 13.8 -3.8 4.5 4.6 12.4ALS BIAS% 63.0 12.3 -50.4 149.8 19.6 103.5ALS RMSE 18.8 47.4 8.2 8.3 10.2 16.2ALS RMSE% 182.8 42.3 107.9 278.1 43.1 135.3

SWFI BIAS 3.0 -9.3 6.4 5.0 -4.6 3.2SWFI BIAS% 28.7 -8.3 83.9 167.0 -19.4 26.7SWFI RMSE 21.8 29.7 17.1 18.3 6.9 14.8SWFI RMSE% 211.2 26.5 224.2 613.8 28.9 123.5 1

2 3 Table 9. Effect of inventory error on predicted compartment stock value, €/ha. 4

BIAS BIAS% RMSE RMSE%ALS 1354.4 15.3 2280.6 25.8SWFI -12.7 -0.1 2573.3 29.1 5

6

Table 8 shows that the ALS inventory-related bias ranged from -3.8 m3/ha to 13.8 m3/ha and RMSE from 8.2 7

m3/ha to 47.4 m3/ha. The respective compartment inventory statistics ranged from -9.3 m3/ha to 6.4 m3/ha 8

and from 6.9 m3/ha to 29.7 m3/ha. 9

10

When only the most valuable part of the stems, i.e. saw timber, was analysed one notes that the most 11

accurate estimates for both the SWFI and ALS inventories were found in spruce saw timber. The ALS 12

inventory bias and RMSE of spruce saw timber were 13.8 m3/ha (12.3%) and 47.4 m3/ha (42.3%). The 13

respective SWFI statistics were -9.3 m3/ha (-8.3%) and 29.7 m3/ha (26.5%). The absolute spruce pulpwood 14

bias and RMSE were even considerably less than the respective spruce saw timber statistics. The relative 15

statistics are, however, of similar magnitude. 16

17

The effect of inventory error on predicted compartment stock value is presented in Table 9. The ALS 18

inventory overestimated the clear-cutting compartment value by 15.3%, while the SWFI was almost 19

unbiased. The respective relative RMSE statistics were 25.8% and 29.1% for the ALS inventory and SWFI, 20

respectively. In other words, the ALS inventory resulted in slightly more accurate estimates, however results 21

were biased. 22

23

4.3.3 Combined errors 24

25

17

The combined effects of all error sources examined, i.e. errors related to inventory, generation of stem 1

distributions, stem form prediction and simulated bucking are presented in Table 10 and the effects of 2

combined errors on stand value in Table 11. 3

4 Table 10. Combined errors. 5

Saw wood Pulp woodPine Spruce Birch Pine Spruce Birch

ALS BIAS 8.9 20.5 -1.8 0.2 -5.1 14.6ALS BIAS% 100.8 19.4 -22.2 5.3 -21.1 123.9ALS RMSE 19.9 46.2 9.2 6.0 11.5 19.1ALS RMSE% 225.0 43.7 116.5 142.5 47.1 161.8

SWFI BIAS 4.7 -3.8 7.8 0.9 -11.9 1.8SWFI BIAS% 52.7 -3.6 98.9 20.3 -49.0 15.4SWFI RMSE 20.7 34.3 20.3 11.7 13.3 12.9SWFI RMSE% 234.6 32.5 256.4 278.9 54.7 109.4 6

7

Table 10 shows that ALS inventory-related bias ranged from -5.1 m3/ha to 20.5 m3/ha and RMSE from 6.0 8

m3/ha to 46.2 m3/ha. The respective SWFI statistics ranged from -11.9 m3/ha to 7.8 m3/ha and from 11.7 9

m3/ha to 34.3 m3/ha. 10

11

Table 11. Effect of combined errors on stand value (€/m3). 12 BIAS BIAS% RMSE RMSE%

ALS 1718.9 20.2 2329.0 27.4SWFI 210.9 2.5 2890.1 33.4 13

14

The effect of combined errors on predicted compartment stock value shows that the ALS inventory 15

overestimated the clear-cutting compartment value by 20.2%, while the SWFI overestimated the respective 16

characteristic by 2.5%. The RMSE% values were 27.4% and 33.4% for ALS- and compartment inventory, 17

i.e. combined errors resulted in the same level of uncertainty as inventory errors alone (see Tables 8 and 10). 18

19

4.4 Effect of inventory method on predicted thinning outturns 20

21

The effect of thinning simulation was determined by comparing the stem distribution series generated on the 22

basis of the ALS inventory and SWFI data with the respective true STM series (Figure 5), compartment 23

assortment outturns (Table 12) and logging outturn values (Table 13). 24

25 Figure 5. Realized and simulated logging outturns by diameter class. 26 27 28

18

Table 12. Accuracy of thinning assortment outturn simulated on the basis of ALS inventory and SWFI data. 1 2

Saw wood Pulp woodPine Spruce Birch Pine Spruce Birch

ALS BIAS -5.8 2.2 0.0 -13.9 0.0 5.1ALS BIAS% -38.3 238.7 * -61.6 1.2 91.6ALS RMSE 10.6 3.3 0.1 18.9 7.0 11.7ALS RMSE% 69.6 369.5 * 84.0 231.9 210.2

SWFI BIAS -1.7 1.9 1.2 -6.3 0.3 -1.3SWFI BIAS% -11.2 215.9 * -28.0 11.2 -22.5SWFI RMSE 11.5 3.7 3.8 10.6 1.8 6.0SWFI RMSE% 75.6 408.1 * 47.2 59.7 106.7 3

*no assortment in the reference 4 5 Table 13. Accuracy of thinning assortment value (€/ha) simulated on the basis of ALS inventory and SWFI 6 data. 7 8

BIAS BIAS% RMSE RMSE%ALS -364.8 -24.8 617.2 42.0SWFI -39.3 -2.7 603.8 41.1 9

10

Similar to that of the clear-cutting compartments, the ALS inventory overestimated the number of small-11

diameter stems. This is probably a result of underestimation of the mean diameter, which affects the stem 12

distribution composition. 13

14

Since the thinning outturns are relatively small, the analyses are best restricted to absolute statistics only. 15

With respect to saw timber volume, the bias and RMSE values ranged according to the ALS inventory from -16

5.8 m3/ha to 2.2 m3/ha and from 3.3 m3/ha to 10.6 m3/ha. The respective SWFI statistics varied from -1.7 17

m3/ha to 1.9 m3/ha and from 3.7 m3/ha to 11.5 m3/ha. In thinnings, species specific assortmentwise results are 18

not reliable, because assortment outturns are small (only few m3/ha), that led to notably more imprecise 19

relative estimates than in clear cuttings (see Tables 10 and 12). Results of pine assortments are most reliable, 20

since 79% of the thinning compartments were pine-dominant. 21

22

5. Discussion 23

24

In the present study we investigated the effects of ALS inventory and SWFI errors, and errors in the 25

generation of stem distributions, stem form prediction and bucking simulation on the prediction of logging 26

assortment outturns by forest-planning simulation computations. Analyses were performed for clear-cuttings 27

and thinnings separately. In the clear-cuttings, field reference data consisted of a total of 5300 stems felled in 28

12 logging compartments. In the thinnings, the field reference data were obtained from 56 circular plots (r = 29

19

10 m) placed randomly in 19 logging compartments. The dataset contained data for a total of 650 felled 1

stems. 2

3

The error sources analysed here can be grouped into pure inventory errors and simulation errors, depending 4

on the inventory method, when stem distributions are formed and single-tree stem forms are predicted. The 5

clear-cutting field data could be used to analyse all sources of error studied, since the data measured by the 6

logging machine provided the true stem distribution and the true stem form for all felled trees. 7

8

As expected, the most significant source of error in the prediction of clear-cutting assortment outturns was 9

the inventory error. Errors related to stem form prediction and simulated bucking as well as generation of 10

stem distributions cause also uncertainty. However, the effects of combined errors are similar to those of 11

inventory errors alone (see Tables 8 and 10), probably due to different error sources that can reverse each 12

other. The effects of ALS inventory error as well as ALS-combined errors on stand value were biased. 13

However, this could have resulted from the small number of stands examined (n = 12). The most reliable 14

results for the accuracy of the two inventory methods were derived for spruce saw timber and pulpwood 15

assortments, because spruce was clearly the most common tree species in the clear-cutting compartments. In 16

addition, one must take into account the fact that since the study data covered clear-cutting compartments 17

only, the results cannot be generalized to consider all development classes. 18

19

Our results concerning the accuracy of low-pulse ALS inventory were slighly poorer than the plot-level ALS 20

results in a study by Peuhkurinen et al. (2008) obtained with a k-NN method using ALS features and aerial 21

photographs. Peuhkurinen et al. (2008) obtained relative RMSEs for spruce saw log volumes of 32.1% and 22

bias of -2.3%, respectively. This accuracy is somewhat comparable with our results of uncertainty effects 23

caused by ALS inventory in prediction of spruce saw log assortment. 24

25

One must also consider the estimation technique applied in the ALS inventory, i.e. the nonparametric k-26

nearest neighbour (k-NN) method. Regression, in which each variable is modelled separately, results in more 27

accurate variable-specific results than k-NN. However, k-NN have the property of predicting all required 28

variables simultaneously, preserving the concordance between variables. The k-NN method was chosen for 29

this study, since the objective was to examine the assortment-level estimation and prediction accuracy of 30

practical inventory and planning methodologies. 31

32

20

The study showed that the generation of stem distribution series on the basis of mean stock characteristics 1

functioned well when compared with the true series and assortment volumes derived by logging machine 2

measurements. Stem distribution generation by mean stock characteristics caused only minor RMSE values. 3

Errors stemming from stem form prediction and bucking simulation were considerably greater in magnitude 4

than those caused by stem distribution generation. The minor errors encountered in the prediction of saw 5

timber volumes were a positive finding with respect to assessment of economic stock value. Pine saw timber 6

volume was predicted more accurately than the respective spruce and birch characteristics. Stem form 7

prediction and bucking simulation led to the overestimation of saw timber and underestimation of pulpwood. 8

Bucking simulated on the basis of stem dbh is a prediction that cannot take into account the stem's true form 9

or defects and other quality factors. The actual bucking result is also influenced by the logging machine 10

operator’s ability to optimize saw timber output during the bucking process. With respect to saw-timber 11

sized stems, the observation of quality issues most affect the assortment outturns of large birch stems. 12

13

The effects of ALS inventory and SWFI errors have previously been examined (e.g. by Holopainen et al. 14

2009) with respect to the timing of loggings and the net present value of logging outturns. In these studies 15

the basic assumption was that erroneous inventory data result in inoptimal timing of loggings which leads to 16

losses in logging revenues. Here examination of thinnings was founded on different starting points. The 17

thinning outturn basal area was derived from the logging machine data by each logging compartment and 18

tree species. These characteristics were then used as starting points for predicted thinning outturns derived on 19

the basis of ALS inventory and SWFI data. Therefore, the differences found depict the ability of SWFI and 20

ALS inventory to form stem distribution series resembling the true series derived from the logging machine 21

data and the functionality of the simulation models for predicting thinning outturns. By forcing the predicted 22

thinning outturn basal area to be equal to the realized outturn basal area, it is possible to examine the errors 23

caused by the inventory method. 24

25

Analysis of thinnings showed that errors stemming from the inventory method cause considerable variation 26

in the generation of stem distributions, which in turn resulted in large errors in the predicted assortment 27

outturns. The absolute assortment outturn errors were similar in magnitude to those found in clear-cuttings, 28

but the relative errors were substantially greater, due to the smaller absolute outturns. 29

30

21

One additional error source is that the applied distribution models are based on data from NFI plots. In this 1

study they are applied by using STM data which is truncated and does not include small trees. Thus when 2

calculating mean characteristics from the STM data there is slight source of bias. 3

4

Aineisto on pieni, joten keskivirheisiin ja harhoihin on suhtauduttava varauksella 5

6

One of central objectives of the study was to clarify the range of variation in predicted assortment outturn 7

value. Based on the results, stem distribution generation or stem form prediction and bucking simulation did 8

not led to significant errors in compartment level assortment outturn values. Instead, the effect of inventory 9

error proved to be substantial. The ALS inventory resulted in slighly more accurate results in stand value 10

prediction than SWFI. However, ALS inventory resulted biased estimations, which reasons should be 11

investigated in further studies. 12

13

6. Conclusions 14

15

The results of our study clarify issues related to the uncertainty of assortment-level volume and value 16

prediction in forest-planning simulation computations based on inventory methods applied currently and in 17

the near future. The magnitude of uncertainty related to assortment-level logging outturns predicted in forest-18

planning simulations by the studied sources of uncertainty proved to be quite significant. The most 19

significant source of uncertainty proved to be the error related to the compartment inventory (SWFI) and the 20

ALS inventory, the resulting assortment-level errors of which were considerably greater than those found 21

for predicted mean volume in previous studies. Operative preharvest measurement would require more 22

accurate input data than current SWFI and ALS inventories. Our results showed that estimation accuracy of 23

assortment outturns with ALS inventory and SWFI were at the same level, i.e. methods should be developed 24

further. 25

26

27

Acknowledgments

This study was made possible by financial aid from the Finnish Academy project Improving Forest Supply 28

Chain by Means of Advanced Laser Measurements (L-Impact). 29

30

22

References 1

2

Brandtberg T, Warner T, Landenberger R and McGraw J (2003) Detection and analysis of individual leaf-off 3

tree crowns in small footprint, high sampling density lidar data from the eastern deciduous forest in 4

North America. Remote Sens. Environ, 85:290-303. 5

Haara A and Korhonen K (2004) Kuvioittaisen arvioinnin luotettavuus. Metsätieteen aikakauskirja 4:489-6

508. (in Finnish). 7

Holmgren J (2003) Estimation of forest variables using airborne laser scanning. PhD Thesis. Acta 8

Universitatis Agriculturae Sueciae, Silvestria 278, Swedish University of Agricultural Sciences, 9

Umeå, Sweden. 10

Holopainen M, Haapanen R, Tuominen S, Viitala, R (2008) Performance of airborne laser scanning- and 11

aerial photograph-based statistical and textural features in forest variable estimation. In Hill, R., 12

Rossette, J. and Suárez, J. 2008. Silvilaser 2008 proceedings:105-112. 13

Holopainen M, Mäkinen A, Rasinmäki J, Hyyppä J, Hyyppä H, Kaartinen H, Viitala R, Vastaranta M, Kangas 14

A (2009) Effect of tree level airborne laser scanning accuracy on the timing and expected value of 15

harvest decisions. European Journal of Forest Research, in press. 16

Hyyppä J, Inkinen M (1999) Detecting and estimating attributes for single trees using laser scanner. The 17

Photogrammetric Journal of Finland 16:27-42. 18

Kilkki P, Päivinen R (1986) Weibull function in the estimation of the basal-area DBH-distribution. 19

Silva Fenn. 20:149–156. 20

Kilkki P, Päivinen R (1987). Reference sample plots to combine field measurements and satellite data in 21

forest inventory. Department of Forest Mensuration and Management, University of Helsinki. 22

Research notes, 19, 210-215. 23

Laasasenaho J (1982) Taper curve and volume functions for pine, spruce and birch. Communicationes. 24

Institute Forestalis Fenniae 108. 74 p. 25

Leckie D, Gougeon F, Hill D, Quinn R, Armstrong L and Shreenan R (2003) Combined high-density lidar 26

and multispectral imagery for individual tree crown analysis. Can. J. For. Res.29:633–649. 27

23

Lim K, Treitz P, Wulder M, St.Onge B, Flood M (2003) LIDAR remote sensing of forest structure. Progress 1

in Physical Geography 27:88-106. 2

Maltamo M, Eerikäinen K, Pitkänen J, Hyyppä J and Vehmas M (2004) Estimation of timber volume and 3

stem density based on scanning laser altimetry and expected tree size distribution functions. Remote 4

Sens. Environ. 90:319–330. 5

Maltamo M, Malinen J, Packalén P, Suvanto A, Kangas J (2006) Nonparametric estimation of stem volume 6

using airborne laser scanning, aerial photography, and stand-register data. Can J For Res 36:426-436. 7

MetInfo (2008) http://www.metla.fi/metinfo/ (April 2008). 8

Muinonen E, Tokola T (1990). An application of remote sensing for communal forest inventory. Proceedings 9

from SNS/IUFRO workshop: The usability of remote sensing for forest inventory and planning, 26-28 10

February 1990, Umeå, Sweden. Remote Sensing Laboratory, Swedish University of Agricultural 11

Sciences, Report 4, 35-42. 12

Mykkänen R (1986) Weibull-funktion käyttö puuston läpimittajakauman estimoinnissa. M. Sc. 13

thesis. University of Joensuu, Faculty of Forestry. 80 p. (In Finnish). 14

Næsset E (1997) Estimating timber volume of forest stands using airborne laser scanner data. Remote Sens. 15

Environ. 61:246-253. 16

Naesset E (2002) Predicting forest stand characteristics with airborne scanning laser using a practical two-17

stage procedure and field data. Remote Sens. Environ. 80:88-99. 18

Oksanen-Peltola L, Paananen R, Schneider H, Ärölä E (1997) Solmu, Metsäsuunnittelun maastotyöopas. 19

Metsätalouden kehittämiskeskus Tapio. 81 p (in Finnish). 20

Näsberg M (1985) Mathematical programming models for optimal log bucking. Linko¨ping studies 21

in science and technology. Dissertation No. 132, 200 pp. ISBN 91-7372- 932-9. 22

Packalén P (2009) Using airborne laser scanning data and digital aerial photographs to estimate growing 23

stock by tree species. Summary of doctoral thesis. University of Joensuu, Faculty of Forest Sciences. 24

Dissertationes Forestales 77. 41 p. 25

Packalén P, Maltamo M (2006) Predicting the plot volume by tree species using airborne laser scanning and 26

aerial photographs. Forest Science, 56, 611-622. 27

24

Packalén P, Maltamo M (2007) The k-MSN method in the prediction of species specific stand attributes 1

using airborne laser scanning and aerial photographs. Remote Sensing of Environment, 109, 328-341. 2

Persson Å, Holmgren J, Söderman U (2002) Detecting and measuring individual trees using an airborne 3

laser scanner. Photogrammetric Engineering and Remote Sensing 68:925-932. 4

Peuhkurinen J, Maltamo M, Malinen J, Pitkänen J, Packalén P (2007) Preharvest measurement of marked 5

stands using airborne laser scanning. Forest Science 53:653-661. 6

Peuhkurinen J, Maltamo M, Malinen, J (2008) Estimating species-specific diameter, distributions and saw 7

log recoveries of boreal forests from airborne laser scanning data and aerial photographs: a 8

distribution-based approach. Silva Fennica, 42:625-641. 9

Popescu S, Wynne R, Nelson R (2003) Measuring individual tree crown diameter with lidar and assessing 10

its influence on estimating forest volume and biomass. Canadian Journal of Forest Research 29:564–11

577. 12

Poso S (1983) Basic features of inventory by compartments. Silva Fennica 17: 313–349 (in Finnish). 13

Rasinmäki J, Kalliovirta J, Mäkinen A (2009) SIMO: an adaptable simulation framework for multiscale 14

forest resource data. Comput Electron Agric 66:76-84. 15

Saari A, Kangas A (2005) Kuvioittaisen arvioinnin harhan muodostuminen. Metsätieteen aikakauskirja 16

1/2005:5-18. 17

Siipilehto J (1999) Improving the accuracy of predicted basal-area diameter distribution in 18

advanced stands by determining stem number. Silva Fennica 34: 331– 349. 19

StanForD (2006) Skogsforsk: Standard for forest data and communications. Available online at 20

www.skogsforsk.se/. 21

Suvanto A, Maltamo M, Packalén P, Kangas, J (2005) Kuviokohtaisten puustotunnusten ennustaminen 22

laserkeilauksella. Metsätieteen aikakauskirja, 2005, 413-428. 23

Tokola T (1990) Satelliittikuvan ja VMI-koealatiedon käyttö metsätalousalueen puuston inventoinnissa. 24

Joensuun yliopisto, metsätieteellinen tiedekunta. Lisensiaattitutkimus. 53 s. 25

Tomppo E (1991) Satellite image-based national forest inventory of Finland. International Archives of 26

Photogrammetry and Remote Sensing, 28, 419-424. 27

28

25

1

2

26

Figure legends: 1

2

Figure 1. Location of the study area and logging compartments studied. 3

4

Figure 2. Saw timber volume prediction errors by diameter class. 5

6

Figure 3. Pulpwood volume prediction errors by diameter class. 7

8

Figure 4. Generated stem distributions by diameter class, based on true and inventory-based mean stock 9

characteristics. 10

11

Figure 5. Realized and simulated logging outturns by diameter class. 12

13

14