evaluating the robustness of plot databases in species-specific light

Evaluating the Robustness of Plot Databases in Species-Specific LightDetection and Ranging-Based Forest Inventory

Virpi Junttila and Tuomo Kauranne

Abstract: In recent years, airborne laser scanning (also known as light detection and ranging [LiDAR]), incombination with digital aerial photography has been used to estimate plot-level forest characteristics of newsites. Forest characteristics are defined both as parameters derived without regard to species, total standparameters, and species-specific stand parameters. The use of LiDAR has produced promising results, but itscosts have been high, because the numbers of sample plots needed for model development and calibration arerelatively high. Recently, the use of databases of sample plots from other formerly measured sites in theestimation of new site total stand parameters has been tested. Only a small number of sample plots were neededfor acceptable results. In this study, the use of databases is extended to species-specific forest stand parameterestimation with LiDAR histograms and digital aerial photography. The data processing includes LiDARhistogram calibration and statistically tuned plot selection from the databases. The samples of the calibration setand databases are weighted to avoid bias in the estimates. Data from seven different sites are used forcross-validation of the given method. The estimates of species-specific parameters are quite accurate, althoughtheir accuracies fall short of those attained for total forest parameters. The use of plot databases reduces thevariance in estimation error. FOR. SCI. 58(4):311–325.

Keywords: LiDAR-based forest inventory, sample plot database, species-specific estimates

I N COMPARTMENT-BASED FOREST INVENTORY, the forestcharacteristics of given areas are extracted from thefield measurements and given, e.g., as species-specific

stem diameter distributions. The forest stand parametersthat are used for management purposes include height oftrees, number of stems, basal area at breast height of tree,and volume of stems. The forest stand parameters based onstatistical values can be divided into total forest stand pa-rameters, which describe the forest characteristics withoutregard to tree species (e.g., total volume of stems located ina plot), and species-specific forest stand parameters, whichdefine the species-specific value of the parameter (e.g.,volume of spruce stems located in the plot).

Light detection and ranging (LiDAR)-based forest standparameter estimation at the compartment level has beenshown to produce good results, especially in the case of totalforest stand parameters. These estimates have been derivedusing different mathematical approaches, such as ordinaryleast-squares regression with step-wise variable selection(see Næsset 1997, 2002, Means et al. 2000, Næsset et al.2004, Holmgren 2004, and Rooker Jensen et al. 2006), kneighbor methods (k-nearest neighbors or k-most similarneighbors) with step-wise variable selection (Maltamo et al.2006), and Bayesian regression with automatic variableselection (Junttila et al. 2008). The methods use sample plotLiDAR data and field measurement-based forest standparameters as the training set of the model. The forest stand

parameters of target plots are then estimated using themodel thus obtained, with target plot LiDAR data as theinput.

In recent analyses, species-specific forest stand parame-ters have also been estimated in test sites (Packalen andMaltamo 2006, 2007). To obtain accurate estimates, a largenumber of sample plots is needed. Because LiDAR data donot correlate strongly with species-specific forest stand pa-rameters, features derived from digital aerial photographsare also added to the model.

The accuracy of species-specific estimates varies greatly,depending on the quality of the site, the set of LiDARvariables, and the features derived from digital aerial pho-tographs. In general, species-specific estimates are muchless accurate than total estimates that are aggregate esti-mates of all species. The fundamental reason for this is thatLiDAR measures first and foremost the height of trees.Because dominant trees in a homogeneous boreal forestoften have a relatively similar height/diameter ratio acrossdifferent tree species, this signal is represented in LiDARhistograms very prominently. Species-specific differencesonly show up in less statistically significant features of theLiDAR histogram and in the color information of aerialimages.

Since 2008, operational forest inventory in Finland hasadopted a LiDAR-based approach. Several commercial

Manuscript received April 1, 2010; accepted April 22, 2011; published online February 2, 2012; http://dx.doi.org/10.5849/forsci.10-034.

Virpi Junttila, Lappeenranta University of Technology, Department of Mathematics and Physics, P.O. Box 20, Lappeenranta, 53851, Finland—Phone:358503316465; Fax: 358-5-621-2898; [email protected]. Tuomo Kauranne, Lappeenranta University of Technology, Department of Mathematics andPhysics—tuomo. [email protected].

Acknowledgments: We thank Matti Maltamo and Petteri Packalen from the University of East Finland and Vesa Leppanen, Hanna Parviainen, JussiPeuhkurinen, and Martin Gunia from Arbonaut, Ltd., for providing data and features used in this study. We also thank our three anonymous reviewers formany constructive suggestions that have considerably improved the presentation.

Copyright © 2012 by the Society of American Foresters.

Forest Science 58(4) 2012 311

companies and research institutes have provided these ser-vices to the state-funded regional forest centers that arecharged with forest inventory on private forestlands. Dif-ferent providers use different estimation methods, such ask-nearest neighbors, k-most similar neighbors, and thesparse Bayesian regression used in the current article. Insome tests, regional forest centers have had several vendorsconduct inventories in the same area. In one such test, threevendors calculated both total and species-specific estimatesin the same area in Central Finland. As an example of thequality of the estimation results produced by the differentmethods in use, the relative root mean square error (RMSE)per sample plot in the total timber volume varied between21.6 and 24.4% among the three vendors, whereas theRMSE in the volume of the dominant tree species variedbetween 41.9 and 49.1% and was generally twice as high forthe minority species (Heikkila 2010). Therefore, the inferiorquality of species-specific estimates appears to be a genericphenomenon associated with LiDAR and not related to aparticular estimation method.

A significant amount of sample plots is needed as train-ing data for the models and especially for estimates ofspecies-specific forest stand parameters. However, in oper-ational use, the number of field measurements should be assmall as possible to keep the cost of LiDAR-based forestinventory attractive. In Junttila et al. (2008), the accuracy ofthe estimates of a set of total forest stand parameters wasverified by varying the number of field sample plots. Witha representative set of sample plots from the site, the esti-mates were found to remain good even with models definedwith only 50–70 sample plots. Maltamo et al. (2009) con-tinued the work by validating different sampling strategiesfor field sample plot selection. They showed that LiDARhistogram-based sample plot selection generally providesthe most accurate results, especially for plot-level totalvolume estimates and that a plot sample size of approxi-mately 50 is enough to produce reasonably accurate results.

Another approach to reduce the required number of sam-ple plots is to attach data from different, previously mea-sured sites to the data from a new site to improve estimationaccuracy. The effect of using two different sets of sampleplots obtained from different forests has been studied byNæsset et al. (2005) and Suvanto and Maltamo (2010). Inthe analysis of Næsset et al. (2005), the direct mixing ofsample plots from the two sites had a mostly negligibleeffect on the quality of estimates for all three differentestimation methods that were tested. In their study, onlytotal forest parameters were estimated. A relatively largenumber of training set plots were native plots, i.e., plotslocated on the target site whose forest stand parameterswere predicted, because there were only two sites. Whenmany plot databases are used together, it is likely that themajority of plots will be alien, i.e., not from the target site.This may introduce bias into the estimates.

Suvanto and Maltamo (2010) predicted six new targetarea forest stand parameters by using one database. Theyused LiDAR height histograms and a different number ofrandomly chosen target area (new site) sample plots(10–212 plots) combined with 472 database plots. No cal-ibration of LiDAR histograms and no plot selection based

on new site forest stand parameter distribution were used.They verified the results using cases in which only the newsite sample plots were used in the training set of the model.When the plot number was at least 50–120, the best resultswere obtained by using the mixed model with only ran-domly selected new site training set plots. This result con-firms the results produced earlier (Junttila et al. 2008; Mal-tamo et al. 2009). For smaller sample plot set sizes, the useof a database improved the RMSE%. However, Bias% wasa problem with every database-based model, varying alongwith the weight the database was given in the model. Thisproblem probably came from the differences in the foreststand parameter distributions in the two separate areas. Inaddition, the difference in the LiDAR scanning equipmentmay have had some influence on the results.

In our previous article (Junttila et al. 2010), we used anovel correction technique to infer relationships betweenLiDAR and forest stand parameters. This technique usedthe sample plots from the new site to recalibrate previ-ously calibrated databases over different spatial areas.Our methodology reduced the number of sample plotsneeded from the new site substantially. We evaluated thequality of these estimates using only a small number ofcalibration plots measured in the new site (between 20and 70), which were complemented by the full set ofmeasured plots from the three other databases that wereavailable. LiDAR scanning and measured total foreststand parameters were used. We computed estimates bycombining suitable plots from plot databases with cali-bration plots at the new site. These were compared withestimates that used only calibration plots. When all thedatabases were used together, it was shown that the combinedestimates were consistently better, or at least as good, asthose produced with just the calibration plots.

However, several technical issues were left unresolved.The most important of these was the accuracy of species-specific estimation. In this article, the use of databases isassessed for species-specific forest stand parameter estima-tion. Another important issue we discuss is the effect thatdatabases of different sizes have on estimates. If the numberof plots used from the database is larger than the number ofplots used from the target site, i.e., calibration plots, then thedatabase plots dominate in the model. This can be thoughtof as sampling in clusters, in which each cluster may pos-sess a different number of samples, an issue that needs to beproperly accounted for in the estimation method. In addi-tion, the possible bias due to differences in forest standparameter distributions of sites of different qualities needsto be addressed in more detail.

With a few additions, the general methodology we use inthis article is similar to the one we used in our previousarticle. The question of bias and the proper weighting ofdata originating from different types of sites are discussedand implemented in some detail. Resulting estimates weretested using cross-validation of multiple test sites. Thisvalidation is performed together with the validation of spe-cies-specific forest stand parameter estimates derived usingdatabases.

312 Forest Science 58(4) 2012

Study Sites and Biometric Data

In this article, seven separate test sites, s, in differentparts of Finland were used either as a new site to beestimated or as databases. The sites sj, j � 1, …, 7 in orderare located at Matalansalo (Heinavesi), Juuka, Loppi-Janakkala, Pello, Lieksa, Kuhmo, and Karttula (Figure 1).

The sample plots on the study sites were measured witha number of different sampling strategies. Some sites wereequipped with a regular sample plot grid, some others wereequipped with regularly sampled plot clusters, and stillothers were equipped with randomly selected plots. Thesedifferences were ignored in the estimation process, becausethey are likely to vary in operational use as well.

Sample plots were always circular plots with a 9-mradius. They were positioned at first with a handheld globalpositioning systems (GPS), and the exact position of the plotcenter was later calculated during measurement and differ-entially corrected offline. This method generally ensured aposition error of less than 1 m, which has been deemedadequate to align LiDAR data and field plots so that theirareas overlap to a degree exceeding 90%. LiDAR data wereclipped to plot extent before LiDAR parameters wereextracted.

In this article, there were 20 forest stand parameters,based on field measurements. They were derived in a sim-ilar manner at each site, using models of Veltheim (1987).The forest stand parameters consist of the total parametersmedian tree diameter (Dgm), median tree height (Hgm),stem number (N), basal area (G), and volume (V), supple-

mented with corresponding species-specific parametersDgm1, Dgm2, Dgm3, Hgm1, Hgm2, Hgm3, N1, N2, N3,G1, G2, G3, V1, V2, and V3. Here the indices 1–3 refer tothese species: 1 for Scots pine (Pinus sylvestris), 2 forNorway spruce (Picea abies), and 3 for hardwoods treatedas a group, but mostly comprising birch (Betula verrucosa).The forest stand parameters of the measured Nsj

plots ofeach site sj were stored in an Nsj

� 20 matrixYsj

�(ysj1, ysj2

, …, ysj20) in the same order. The parameterscan also be divided into four subsets: total forest standparameters of site sj were stored in Ytot, sj

�(ysj1

, ysj2, …, ysj5

), species 1 specific parameters in Ysp1,sj�

(ysj6, ysj9

, …, ysj18), species 2 specific parameters inYsp2, sj

�(ysj7, ysj10, …, ysj19), and species 3 specific param-

eters in Ysp3, sj� (ysj9

,y sj11, …, ysj20).The pairwise correlation scatterograms of the total forest

stand parameters of plots of these test sites are shown inFigure 2. The characteristics of the sites are also shown inTable 1. At least 400 plots have been measured in the fieldon each site. It can be seen from these measurements thatthe test sites are not similar. The shapes of forest standparameter distributions vary and the mean values of param-eters differ between the sites. For instance, total forest standparameter distributions for Matalansalo, Juuka, Loppi-Janakkala, Lieksa, and Karttula are quite similar. In addi-tion, the distributions of Pello and Kuhmo resemble eachother. However, when taking the species-specific parame-ters into consideration, there are differences: see, e.g., Fig-ure 3 for the scatterplot of spruce parameters.

The seven areas were chosen from a wide geographicalrange of forest types to test the robustness of the plotdatabase approach. There are some areas that have similarforest characteristics, which can therefore be expected tosupport one another. One area, Pello, is of a type that istotally different from the other six areas. It was included toverify that inappropriate plots would not harm the accuracy ofthe estimates and that the estimation process would automati-cally discount the potential harmful impact of such plots.

Remote Sensing Data

The test data for the test sites consist also of LiDARmeasurements from the area. To achieve better species-spe-cific estimates, features derived from digital aerial photo-graphs were also used where possible. In one site, Mata-lansalo, digital aerial photographs were not available.

LiDAR Data

LiDAR scanning of the different areas was conductedfrom 2004 until 2008. Three different types of scannerswere used, namely the Optech ALTM 3600, the LeicaALS50, and the Leica ALS60. Flying height varied between700 and 2,000 m, and scanner pulse frequency varied be-tween 58,900 and 125,100 Hz.

The set of candidate variables derived from LiDARmeasurements for each sample plot used in estimation ofeach forest stand variable is similar to the set that we usedin our previous article (Junttila et al. 2010). It consists ofpercentile points and cumulative percentile parts of the firstFigure 1. Location of the test sites.


and last pulse heights of nonground hits (height �2 m),percentile intensities of first and last pulse intensities ofnonground hits, mean of first pulse heights �5 m, SD offirst pulse height, and the number of measurements �2 m offirst and last pulse heights divided by the total number of thesame measurements of each plot. These 38 candidate vari-ables for each plot of site sj were stored in the Nsj

� 38matrix Xsj, LiDAR.

Digital Imagery

To improve the accuracy of estimates of species-specificforest stand parameters, digital aerial photography was alsoused in this study. The digital aerial photographs that weretaken have pixel sizes of 0.5 m and three or four channels.Digital ortho-rectified aerial images were used with 0.5-mspatial resolution. The channels used for visually assessing

Figure 2. Pairwise correlation plots between some stand parameters for different test sites. The scale ineach figure in a column is equal.

Table 1. Mean characteristics of the test sites.

Matalansalo Juuka Loppi Pello Lieksa Kuhmo Karttula

Annual heat sum (degree days) 1150 1000 1250 850 1050 900 1100Mean volume (m3/ha) 203.4 145.5 203.2 102.8 194.8 195.3 205.9Mean timber height (m) 17.0 14.7 17.4 11.7 15.9 15.7 17.7Mean basal area 24.7 20.3 22.9 17.8 23.1 25.1 24.0Mean no. of stems 1,506.9 1,284.6 1,109.0 1,325.2 1,185.3 1,003.8 1,150.7Maximum timber height (m) 30.6 25.2 33.7 20.9 30.6 23.7 35.5Scots pine (vol %) 53.2 67.2 45.3 38.6 61.1 64.8 29.1Norway spruce (vol %) 34.5 21.7 41.5 34.1 24.1 24.0 45.0Hardwoods (vol %) 12.3 11.0 13.2 27.3 14.8 11.2 25.9No. of measured plots 472 511 441 553 483 470 538


tree species were in most cases blue, green, red, and near-infrared. No direct feature extraction was performed onthem, but they were visually interpreted instead. Dependingon the site, the number of pixels per tree crown variedgreatly, but there were typically 1,000 pixels per sampleplot and some 50–100 per dominant tree crown.

Two features drawn from the aerial photographs wereavailable in all test sites except one, Matalansalo. Suchdatabases with incompatible information content are verylikely to occur in real-life forest inventory.

Features derived from digital aerial photographs wereadded to the candidate variables of the estimation models.These features are the percentage of all pixels of the aerialpicture of a plot that are classified as hardwood (Hwd) andthe percentage of pixels that are classified as conifer trees(Cnf). The classification was performed subjectively by ahuman interpreter. The feature values are between 0 and100% and they follow the rule Hwd � Cnf � hits toground � 100%; that is, all the pixels of the aerial pictureof the plot were classified to one of the three classes. For

each site sj, these two features were stored in an Nsj� 2

matrix Xsj, aerial.The histograms of the distributions of Hwd and Cnf in

sites Juuka, Loppi-Janakkala, Pello, Lieksa, Kuhmo, andKarttula are shown in Figure 4. The subjective classificationof pixel shares introduces a subjective element to themethod. Different sites have been classified by differentindividuals, and by incorporating such classifications, wealso analyze the impact of such subjective estimates in thecontext of using plot databases for species-specific esti-mates, as they add another layer of nonhomogeneity be-tween sample plots and potentially become a source of bias.Because no additional information about the quality ofsubjective classification was available, the features of dig-ital aerial photographs were nevertheless assumed to beclassified in a uniform manner for each site. Thus, nocalibration was applied to the database aerial photographfeatures, when they were used to estimate new sitecharacteristics.

Both the LiDAR variables and the aerial photo-derived

Figure 3. Pairwise correlation plots of species 2 (spruce) forest stand parameter values for different sites.The scale in each figure in a column is equal.


features were used as candidate variables in total and spe-cies-specific forest stand parameter estimation. Thus, thecandidate variables matrix of site sj is an Nsj

�40 matrixXsj

� (Xsj, LiDAR, Xsj, aerial).

Species-Specific Regression Estimates

In this article, the emphasis is on the verification of theprecision of the species-specific forest stand parameter es-timates. The total and species-specific forest stand param-eters were estimated with the sparse linear Bayesian regres-sion (Tipping 2001), which automatically selects thevariables used for estimation from the set of candidatevariables. Possible negative estimate values that occur, es-pecially in the case of species-specific forest stand param-eters, were set to 0.

The estimates of total forest stand parameters, stem num-ber, basal area, and volume were used to calibrate thecorresponding species-specific stand parameter estimates,because the total values are sums of corresponding species-specific values. For instance, the total volume estimate y5

and the sum of species-specific volume estimates y5, s � y18

� y19 � y20 must be equal. To maintain this equality, thespecies-specific volume estimates (which are generally es-timated with less precision than the total estimates) weremultiplied with y5/y5, s. In cases in which all the estimates ofspecies-specific parameters of a plot were zero, the totalestimate was also set to zero. In the case of zero total valueestimates combined with nonzero species-specific esti-mates, the total value estimate was set to the sum of spe-cies-specific estimates.

For estimation of responses from variable-response datacontaining many zeros and clear clusters (zero and nonzerovalues), better results could be obtained by also using clas-sification and clustering, as well as using different formu-lations of the variables. In this study, the available data didnot contain information that could be used to classify zeroand nonzero values of different species-specific responses.Thus, only the regression approach was used to estimate theforest stand parameter values. In addition, because the em-

phasis of this article is not on finding the best possiblemethod for species-specific estimates, but on verifying theeffects of the use of databases, the straightforward sparseBayesian method was deemed adequate.

Statistical Theory and Methodology

In our previous work, three databases were used toestimate the new site total forest stand parameters (seeJunttila et al. 2010). In the procedure we introduced, only asmall set of sample plots (between three and nine stands,including approximately 20–70 plots, total), called the cal-ibration set, was measured in the new site to gain informa-tion about the LiDAR measurement properties and the for-est stand parameter distributions of the new site. Theestimation of forest stand parameters was performed usingthe calibration set and the three databases that wereavailable.

The databases were processed to fit the new site calibra-tion data in two ways. First, the LiDAR histograms of eachdatabase were calibrated to avoid differences due to poten-tially different measurement equipment and flight altitudesusing Ncal calibration plots and their most similar pairs fromeach database. The calibration was performed with separatelinear calibration coefficients for each measured feature inthe LiDAR histograms: first pulse height, last pulse height,first pulse intensity, and last pulse intensity. Automatic gaincontrol in some scanners makes intensity difficult to cali-brate reliably. This should be taken into account in variableselection. The sparse Bayesian method used in the currentarticle performs variable selection automatically. The dif-ference in percentile values of aboveground (height �2 m)hits of these features between the calibration set and eachdatabase was minimized using the calibration coefficient.

In a second stage, a set of Ndjdatabase plots from each

database dj were selected. The goal of this step was toimprove the accuracy of model calibration by increasing thesize of the teaching set. To avoid bias due to different foreststand parameter distributions in the new site and in the

Figure 4. Histograms of distribution of plot-wise Hwd and Cnf of each site.


databases, only plots that fit the calibration set total foreststand parameter distribution were selected.

In this article, we widen these steps to include estimationof species-specific forest stand parameters. In addition tobeing used for the estimation of new site parameters, thecharacteristics of species-specific forest stand parameterswere used in database processing within two steps of theprocedure: in the most similar pair selection and in plotselection.

There were also more databases available in this article.In total, there were seven measured sites, six of which alsocontained information from digital aerial photographs ofeach plot. With an increasing number of database plotsavailable, more attention needs to be paid to the weight ofdatabases in the estimation of forest stand parameters. Da-tabase data may be biased compared with data from the newsite, and it should not be trusted more than the calibrationset, which represents a sample of the true data.

Overview of the Processing Technique

The estimation procedure was performed similarly to theone introduced in Junttila et al. (2010), with some modifi-cations discussed here. The procedure is shown as a step-by-step overview in Figure 5. Steps that are modified in thisarticle are shown with an asterisk.

Calibration Set Selection

As in our former study, the calibration set for the cross-validation procedure was chosen randomly from the newsite. The LiDAR histograms were used as the selectioncriteria, thus providing the only information about the newsite at this first stage of the procedure. The range of the

forest stand variable distribution needs to cover the new sitecharacteristics as well as possible. In this study, 85% per-centile points of first pulse height and intensity were used asthe criteria for accepting the calibration set. The SD of thesevariables among the selected calibration set plots was re-quired to be at least 90% of their deviation in the full set ofthe new site LiDAR histogram. The intensity of LiDARmeasurements was used in this study as a calibration setselection criterion, because it is known to correlate withspecies-specific forest stand parameters and thus improvecoverage of those species-specific parameters in the newsite calibration set (Korpela et al. 2010).

Pair Selection and LiDAR HistogramCalibration

In the calibration step, the most similar neighbor of eachof the calibration plots was selected from each database.The neighbors were selected according to the weighted sumof distances between the calibration set plot and databaseplots in terms of both total and species-specific forest standparameters. As in the procedure with total parameters only,the weight of a forest stand parameter in the summationdepends on the expected precision of the LiDAR estimatesof each parameter—the more precise the LiDAR estimate,the more weight it gets in the pair selection. For instance,Hgm, which is estimated very precisely with LiDAR, isweighted more than stem number, a value for which theestimates are less precise. Species-specific forest stand param-eters are weighted less, because they generally correlate onlyslightly with LiDAR measurements. If there is no significantcorrelation, their weight in pair selection will be negligible.

After the acceptable pairs are selected, the calibration

Figure 5. Step-by-step overview of the algorithm.


itself was performed in a manner similar to that of thecalibration of total forest stand parameters. The differencesin percentile points of ordered cumulative sums of eachtype of histogram measurement between the pairs wereminimized using a linear coefficient for the databasemeasurements.

Only the LiDAR measurements with height �2 m wereused to define the percentile points, as they are assumed todescribe the trees of the plot. Because all the plots used inthis study were from mature forests, there were enough firstpulse measurements to fulfill this condition. However, thevariables drawn from the last pulse LiDAR measurementshave to be used with special caution. For some plots, theremay be only a few, if any, measurements with last pulseheights �2 m. In such cases, there was not enough non-ground data for height and intensity variables. These plotscould not be used for LiDAR calibration, because therewere no pairs for the last pulse height and intensity calibra-tion procedures.

In the estimation of forest stand parameters, the missingvariables of last pulse data, i.e., plots that contain zero oronly a few LiDAR last pulse measurements with height �2m, are a problem. In this study, the database plots containingzero last pulse nonground measurements were left out fromthe training set. If the new site itself contained plots withmissing last pulse data �2 m, the variables containing lastpulse data were also left out. In such cases, there were only27 candidate variables.

Plot Selection

The species-specific forest stand parameter measure-ments were used in the modified plot selection step of theprocedure. Heuristic selection in accordance with the multi-normal distribution was used, as in the plot selection stepwith total forest stand parameters. The distribution of non-zero values of all the forest stand parameters was trans-formed so that it is as close to a multinormal distribution aspossible. In this study, the transformed matrix Yt of foreststand parameters consisted of

ykt � yk, for k � 2, 9, 10, 11 (1)

ykt � �yk, for k � 1, 3, . . . , 8, 12, . . . , 20. (2)

That is, the species-specific value of the parameter wastransformed with the same transformation as the total valueof the same forest stand parameter, with all other parametersexcept Hgm being transformed by taking the square root oftheir value. The transformed distributions are not exactlymultinormal, and different sites may have different shapesof distribution. This means that the shape of the scattero-gram between many pairs of forest stand parameters variesconsiderably from site to site. Thus, it is still an openquestion whether there exists a better approach for plotselection. However, the results achieved with this approachare acceptable (the chosen plots are within the range of thecalibration set distribution) and robust against changes indistributions, as is seen below in our experimental results.

The range of the acceptable plots was defined by the

characteristics of the calibration set plots in terms of meanMahalanobis distance. The mean Mahalanobis distance,

Mah(x, xm,C, p) � trace �(x � xm)C�1(x � xm)T�/p, (3)

is used to define the distance of the (1 � p) vector x fromthe center of distribution xm with (p � p) covariance C. Inthis case, p � 5, because the five different parameters usedin the plot selection were as follows: Dgm, Hgm, N, G, andV.

The heuristic selection rule in the case of total foreststand parameters was (Junttila et al. 2010)

exp(�mt,i) � exp(�Mah(Ytot, djit , y� tot, c

t , Ctot, ct ,5)/2) � ri (4)

where Ytot, djit is the vector of transformed total forest stand

parameters of plot i of database j, y� tot, ct and Ctot, c

t are themean and covariance of the transformed calibration set totalforest stand parameters, and ri is a random number, ri �[0, 1]. The plots containing total forest stand parametercharacteristics close to the calibration set distribution centerare more likely to be selected than those that are far from it.

In the case of species-specific estimation, for each spe-cies spr, r � 1, 2, 3, the nonzero values (i.e., plots contain-ing trees of the species spr) of the transformed calibrationset parameters were used to define the mean and covarianceof the distribution: y�spr, c

t and Cspr, ct . The mean Mahalanobis

distances of plot i for the three different sets spr of species-specific parameters r � 1, 2, 3 were set to

mspr,i � Mah�Yspr,djit , y�spr,c

t , Cspr,ct , 5�/2, if Yspr,dji

t � 0, (5)

and otherwise to zero. In this case, the heuristic selection ofplot i was based on the maximum mean Mahalanobis distanceof all of the four different types of forest stand parameters:

exp��max�mt,i, msp1,i, msp2,i, msp3,i�� ri . (6)

Thus, for each species, only the plots that fit within themultinormal space of the nonzero values of the calibrationset parameters of the species were included in the model.

However, the amount of zero and nonzero values of eachspecies also defines site quality. Because the regression-based estimation approach of forest stand parameters doesnot classify the zero and nonzero values (e.g., whether anindividual plot contains spruce or not), the ratio of zeroversus nonzero values in the training set affects the model.If there are too many zero values compared with nonzerovalues, it is likely that the estimates will be biased towardtoo small trees. Thus, it is important that the quality of theselected database distribution is also handled in terms ofspecies ratios.

In this study, there were seven classes of plots. Theclasses consist of all the possible combinations of the threespecies (where at least one species is always present in theplot):

species � {(1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 0),

(1, 0, 1), (0, 1, 1), (1, 1, 1)}, (7)

where 1 refers to a species present on the plot and 0 refersto a species not present. For example, plots containing pine


and hardwood, but no spruce, belong to the class 5, species(5) � (1, 0, 1). Each plot belongs to just one of theseclasses.

For the new database dj consisting of Ndjselected plots,

the number of plots belonging to each class cl � 1, …, 7 isNdj, cl. The ratio of plots belonging to class cl from the plotsof the new database is �dj, cl � Ndj, cl/Ndj

. It is also knownthat in the Nc calibration plots, there were Nc, cl plots be-longing to class cl, producing the ratio �c, cl � Nc,cl/Ndj

.Reselection among the selected plots was performed

according to the species class ratios. If the ratio of thecalibration set c for a certain class is smaller than that for thenew database dj, then the number of database plots contain-ing that class must be decreased and vice versa. Thus, foreach plot i in the database dj, the ratio of the class ratios isdefined by

ci ��c,cli

�dj,cli(8)

where cli is the class to which plot i belongs. If class cli isoverrepresented in the new database, ci � 1; if it is under-represented, ci � 1. Defining the selection probability pi �[0, 1], the heuristic selection is performed by the rule

pi �ci

max �c�� ri, (9)

where ri is a random number ri � [0, 1]. The plots withclasses that have the largest ratio between the class ratio inthe calibration set and the class ratio in the new databasehave a selection probability of 1. This means that theseclasses are strongly represented in the calibration set butweakly represented in the new database. Plots with a classthat is not represented in the calibration set but that is wellrepresented in the new database have a selection probabilityclose to 0. They will thus probably be discarded. Thereselected plots of the database j are labeled with dj.

Estimation Calculation Using MultipleDatabases

If the forest stand parameter distributions on the new sitediffer from the selected database distributions, a bias mayoccur when using databases. This may be expected to hap-pen whenever an alien site, i.e., a database, is used in theestimation of another site.

The database forest stand parameter distribution maycontain plots that are out of the range of the new sitedistribution or the mean and covariance of the databasestand parameters may be different from those of the newsite. These conditions resemble the case in which plotsampling on the new site does not include the collection ofa representative set of all relevant forest types, but in whichsome types of the forest are over- or underrepresented infield measurements. The selected plots of the databaseswere considered to be samples from the new site.

The only true data are the calibration data from the newsite itself, data that are expected to contain an unbiaseddistribution of the forest stand parameters that represent thefull range of forest types on the site. To achieve such

calibration data, special attention needs to be paid to theselection procedure of the calibration plots. The databasesare to be noninformative extensions to the calibration set,reinforcing the information in the calibration set, but notgiving new information about the new site itself. Thus, if thecalibration set range does not cover the range of new siteforest stand parameters, then neither will the databases.

The calibration set size, Nc, may be small compared withthe size of the selected plots of each database dj, Ndj

, andwhen all the J new databases available are used, its relativesize becomes even smaller. However, because the data-base(s) contain only alien plots, one should never rely moreon them than on the calibration set.

Bias

The aim in the use of databases is to achieve a smallerRMSE in the new site verification set than when only thecalibration set is used, while the bias is kept close to zero forthe forest stand parameters.

For the estimates, the most reliable data of the responsevariables, i.e., forest stand parameters, are provided by thecalibration set, which is assumed to be unbiased and “true.”The mean of the calibration set response may be assumed tobe the mean of the estimated responses of the new site,which is derived either by using only the calibration set, orby using both the calibration set and the databases.

To achieve estimates with a response mean equal to thecalibration set mean, the input in the sparse Bayesian re-gression was normalized with the following calibration setcharacteristics:

yk3yk � y� kc

�kc, �k, (10)

where yk is the vector of forest stand parameter k, y�kc is thecalibration set mean, and �kc is the calibration set SD offorest stand parameter k. In addition, candidate variableswere normalized with respect to their calibration set char-acteristics. The regression itself was then performed withouta constant term, i.e., the regression line goes through thecalibration set mean with a slope defined by the calibrationset combined with the databases.

For clarity, the index k is left out from the rest of theequations in this article. Each of the regression modelsdiscussed here is assumed to be a model of an individualforest stand parameter, independent of the other forest standparameters.

Probability Sampling

The basic idea of probability sampling is introduced inthe book Model Assisted Survey Sampling (Sarndal et al.1992). The selection of the plots used in the regression ofnew site forest parameter estimates can be thought of assurvey sampling from a frame population UF consisting ofthe population of all the J databases D � D1 � D2 � … �DJ and the population of the new site Sn, UF � D � Sn.

The target population U is part of the frame population,U � UF, and it contains the part of the frame population thatfits the new site population statistics. The aim of this study


was to estimate the forest stand parameters Yv on the plotsv, v � U, belonging to the verification set v of the targetpopulation, from which only the candidate variables, Xv, areobserved. The measured samples from the new site, thecalibration plots c, c � Sn, are assumed to contain the fulldataset of independent variables and responses, (Xc, Yc),from the new site. The samples from the databases, d � D,contain the dataset (Xd, Yd).

The sample selection of the target population was per-formed using the information from the calibration plots: theplot selection of each database was performed heuristicallyusing the forest stand parameter distributions of the calibra-tion plots as measurement statistics. These selected plotsd, d � D together with the calibration set form the samples � d � c of the target population, s � U.

The databases often contain plots from forest types thatare not present in the new site. Such plots can contaminatestatistical models with inappropriate sample information.This problem is termed over-coverage. To avoid over-cov-erage in the model calibration step, plots that do not fit tothe plot distribution of the new site are simply left out fromthe training set.

Another and more serious problem is under-coverage.There may be plot types in the new site that are not includedin the frame of databases and in the calibration set becausethere is only a limited number of databases available, andthese contain only certain types of forests. Under-coveragemay lead to errors in the estimates, because the observationsof those forest types are missing or are represented only inthe calibration set samples. The problem of under-coverageis likely to diminish as the number of available databasesincreases and the database coverage of different forest typesis improved.

The errors in observations due to different sources ofdata, i.e., the differences due to LiDAR measurement equip-ment and flying altitudes during measurement, were as-sumed to be negligible after the LiDAR measurement cal-ibration process in this study. The measurement andprocessing errors were also assumed to be negligible.

The use of the selected databases can be thought of ascluster sampling from the target population, with each da-tabase and the one calibration set being an individual clus-ter. The size of each cluster may be different, and the totalsize of the J � 1 clusters in the target is N � Nc � Nd1

�… � dj

� Nc � Nd. These clusters were then used in theregression to maintain the estimates of the verification sam-ples in the target population.

There is some ambiguity in the interpretation betweenweighted regression and inclusion probability, whensampling is combined with model-based estimation (seePfeffermann 1993). For the current study, we have con-sistently used the term inclusion probability, because thetests carried out here also involve sampling the calibra-tion set from a more comprehensive frame population,and such terminology allows for a unified presentation ofthe sampling process. In operational application, the roleof the calibration set is to define a prior distribution thatis used as a weight in sampling plots from the databases.In this case, all calibration plots are assigned an inclusionprobability of one, and the relation between the calibration

set and the databases resembles weighted regression, withweighted inverse inclusion probability as the regressionweight.

The elements i, i � 1, …, N of the target population mayeach have a different probability �i of inclusion in thesample. In this study, the calibration set samples are drawnfrom the total target population of size N, and thus theprobability that the sample i from the calibration set c isselected is �i � �c � Nc/N, i � c. The probability that thesample i from the database d is selected is �i � �d �Nd/N, i � d. Thus, the inclusion probability is smaller forthe cluster with a sample size that is smaller than that for theother clusters, and the samples of the cluster are underrep-resented in the population. This approach is suitable when-ever the number of calibration plots is small compared withthe total number of plots selected.

Hansen and Hurwitz (1943) and Horvitz and Thompson(1952) have applied the principle of � expansion to anestimate of the total population. In the estimation of vari-ables of the total population, the ith element in the popula-tion, when present in the sample, will represent �i

�1 pop-ulation elements. For regression, � expansion is included inthe matrix multiplication.

In ordinary regression, the estimates for each forest standparameter at hand are based on the linear equation

y � Xw � �, (11)

where y is the target vector, i.e., the forest stand parameter,X is the matrix containing candidate variables used in theestimation, w is the linear regression weight vector, which isassumed to be sparse, and � is the error vector with zeromean and variation �2. The ordinary regression estimate forthe weight is w � (XTX)�1XTy.

In the Bayesian formulation of regression, the likelihoodof the data plot i is normally distributed as

p�yi�w,�2� � N�yi�Xiw, �2�

� �2��1/ 2exp��1

2�2 �yi � Xiw�2� (12)

and the total likelihood of the sample s consisting of the Nc

samples from the calibration set c together with the collec-tion of the Nd samples d from the available databases is

p�ys�w, �2, �� i�s

N�yi�Xiw, �2� � N�ys�Xsw,�2IN�. (13)

Using likelihoods in this form, samples of the calibrationset have proportion Nc/N of the cumulative effect in themodel training. If Nd is large compared with Nc, databasesdominate the model training procedure. Any differences inthe forest stand parameter distribution density or the shapeof databases compared with the new site may lead to biasedestimates.

If the � estimator is included, in the spirit of Sarndalet al. (1992, Chapter 5.10), the variance of the estimateerror of the sample i is now �2�i. Thus, the variance hasspatial variation, and �2IN is replaced with �2�s, where�s is an N � N diagonal matrix with diagonal elements�i corresponding to i � s. The ordinary regression


estimate for the weight of the variance would be, as inSarndal et al.,

w � �XsTs

�1Xs��1�Xs

Ts�1ys�. (14)

In Bayesian formulation, the total likelihood of the � esti-mated training set plots is

N(ysXsw,�2�s). (15)

In other words, the error variance is allowed to be larger forthe samples that are measured from the clusters with largesample size. For clusters with low inclusion probability,only small residuals are allowed. With this approach, thetotal representativeness of both the calibration set and thedatabase is equal in the estimation procedure.

This new variance matrix can easily be included in thesparse Bayesian regression procedure. In practice, themeasurements (Xs, Ys) in the likelihood are replaced withestimators, (Xs, Ys) � �s

�1/2(Xs, Ys), in the sparse Bayes-ian regression method. In this method, because of the priordistribution of the weights, the number of selected variablesdepends on the size of the data compared with the precisionof the estimate, not on the scale of the data. Thus, theweighting in this form affects only the mutual weighting ofthe different sources of data, as in ordinary weighted re-gression. More details of the sparse Bayesian regressionmethod are found in Tipping (2001) and details of itsapplication to forest stand parameter estimation are found inJunttila et al. (2008).

Process of Validation

In this study, data from seven different sites were avail-able. The modified procedure that uses database informa-tion in the estimation of forest parameters in a new site wastested using cross-validation. One site at a time was used asthe new site, and the others were used as databases. In thecase of Matalansalo as the new site, only the LiDAR vari-ables were used; otherwise, both LiDAR variables andfeatures of digital aerial photographs were used as thecandidate variables for the weighted sparse Bayesian model.

For each site, a repetition procedure was performed with50 calibration plots that were randomly selected from thenew site using given selection criteria. In former studiesconcerning total forest stand parameters (Junttila et al. 2008,2010, Maltamo et al. 2009, Suvanto and Maltamo 2010),this amount of sample plots selected with sufficient criteriafrom the site has been shown to be enough to producetolerable estimates. However, the stability of the estimatesdeteriorated significantly when only 50 sample plots wereused, and thus the reliability of the results was not goodenough for operational use. In this study, this amount isassumed to be large enough to get reasonable results, butstill small enough to show the performance of the givenmethod.

In our previous article, the Matalansalo calibration setwas gathered in stand-level field measurements, with thestands assumed to be homogeneous and consisting of asmall number of plots. However, for the species-specificparameter estimates, better coverage of the forest types ofthe area was needed, and thus Matalansalo was also handled

at the plot level; that is, the calibration set was gatheredusing individual plots of heterogeneous forest types as dis-cussed in this article.

Estimates for each forest stand parameter were derivedwith measurements of the calibration set from the new siteonly, and the calibration set was complemented by thedatabases. The optimal estimates for each verification setwere the estimates derived using the leave-one-plot-outprocedure in the full set of plots of the new site, and theseestimates were used as the benchmark against which the useof databases was tested. The error of each forest standparameter estimate was verified using the rest of the mea-sured plots from the new site as verification plots. Thisprocedure was repeated 50 times for each site to verify therobustness of the use of databases.

Results

The results of the precision of total and species-specificforest stand parameter estimates for the new site Mata-lansalo are shown in Table 2, for the new site Lieksa inTable 3 and Figure 6, for Pello in Table 4, and for Loppi-Janakkala in Table 5. In the tables, the medians of RMSE%of the repetitions, together with their maximum values, areshown for estimates derived with the calibration set only,with the calibration set together with selected plots from allthe databases, and with the full, dense set of measured plotsin the new site, i.e., the optimal results.

For each site in the cross-validation procedure, the trendin results is similar. The RMSE% of each of the 50 repeti-tions varies considerably using only the 50 plots of thecalibration set. The quality of forest stand parameter esti-mates depends on the quality of the calibration set, meaninghow well it represents the characteristics of the new site.The range of calibration set results is thus large, eventhough the median of RMSE% is tolerable. However, when

Table 2. Median and maximum of RMSE% estimation re-sults in Matalansalo in 50 repeated calibration plot selectionsusing databases.

Median RMSE% (maximum)

c c � all databases Optimal

Dgm 17.1 (25.2) 15.0 (16.8) 13.9 (14.2)Hgm 10.5 (14.2) 9.5 (10.5) 8.8 (9.1)N 33.0 (46.8) 29.4 (34.0) 27.9 (28.5)G 19.7 (27.4) 17.8 (19.8) 16.3 (16.7)V 24.6 (35.6) 21.6 (24.2) 20.5 (20.9)Dgm1 75.0 (99.2) 67.0 (73.8) 62.8 (65.6)Dgm2 40.6 (60.5) 39.0 (50.1) 34.4 (35.4)Dgm3 80.0 (101.5) 76.5 (86.0) 72.2 (74.6)Hgm1 66.7 (91.1) 59.1 (65.8) 55.7 (58.2)Hgm2 38.7 (48.9) 36.9 (44.8) 33.8 (34.9)Hgm3 67.6 (91.1) 63.8 (68.0) 60.8 (62.6)N1 73.5 (91.8) 68.3 (75.8) 64.0 (65.9)N2 67.6 (92.2) 64.0 (71.0) 58.2 (60.2)N3 110.8 (145.3) 105.2 (118.8) 92.8 (97.3)G1 55.7 (68.6) 50.8 (58.0) 47.0 (48.5)G2 69.4 (83.3) 64.8 (70.6) 57.8 (59.8)G3 131.5 (181.0) 120.1 (133.1) 111.9 (116.7)V1 63.9 (76.7) 59.2 (67.8) 53.5 (55.6)V2 80.0 (108.0) 75.0 (86.9) 67.3 (70.2)V3 153.9 (238.9) 141.8 (162.6) 134.1 (140.4)


the plots selected from the five databases are included, theresults generally become more stable. The medians of theRMSE% for forest stand parameters are smaller or remainthe same in 97% of the tested forest stand parameters (20parameters in seven test sites), which are closer to those ofthe optimal RMSE%. The maxima of RMSE% of the 50repetitions are significantly smaller for the estimates de-rived with databases. The optimal RMSE% derived with theleave-one-plot-out procedure using the dense set of plots onthe new site remains best in each case. For all the sites in thecross-validation, average Bias% of the 50 repetitions re-mained close to zero, depending on the calibration set bias.

Given the absence of digital aerial photographs of thearea, the estimates in Matalansalo were derived using onlythe LiDAR histograms. The results for the total forest standparameters were similar to those in our former article (Table2). Thus, the modification of the procedure did not harm theestimation accuracy. Even though six databases (Juuka,Loppi-Janakkala, Pello, Lieksa, Kuhmo, and Karttula) wereused, the bias remained insignificant. For all the forest standparameters, the RMSE% results became consistently betterwhen all the databases were used, in addition to the cali-bration set information.

In the case of Lieksa as the new site, other sites exceptingMatalansalo were used as databases (Juuka, Loppi-Janakkala, Pello, Kuhmo, and Karttula), which allowed theuse of digital aerial photographs as candidate variables inthe sparse Bayesian regression, in addition to LiDAR his-tograms. The precision of the estimates was consistentlybetter when all databases, in addition to the calibration setinformation, were used (Table 3). The median, and espe-cially the maximum, of the RMSE% results for each foreststand parameter were many percentage points smaller.Thus, the reliability of the estimates improves when data-bases are used. An example of the RMSE% distribution ofthe 50 repetitions in Lieksa is shown in Figure 6. Bias wasalso avoided by using the weighted regression approach,discussed earlier, and the Bias% stayed close to zero.

One would expect to have problems with estimates ofPello, because the characteristics of the forest in Pello arevery different from the characteristics in the other sites.However, the scatterplots of Figures 2 and 3 show that interms of total and species-specific forest stand parameterdistributions, Pello is predominantly a subset of the othersites. The largest values (e.g., stem number) were not cov-ered by the other sites, but because there is a linear estimatethat is unbiased in terms of stem number, those values werewell estimated using the calibration set as complemented by

Table 3. Median and maximum of RMSE% estimation re-sults in Lieksa in 50 repeated calibration plot selections usingdatabases.




Table 4. Median and maximum of RMSE% estimation re-sults in Pello.




Table 5. Median and maximum of RMSE% estimation re-sults in Loppi-Janakkala.





databases, even if they did not cover all the variation inPello (Table 4).

The only cases in which the median of RMSE% of thedatabase-assisted estimates is not consistently smaller arethose of Loppi-Janakkala G2 and V2 (Table 5) and JuukaN2 and G2. In Figure 3, it is shown that a part of thescatterplot of G2 and V2 of Loppi-Janakkala is not coveredby the G2-V2 scatterplots in the other sites. Thus, it isexpected that some types of Loppi-Janakkala species 2 typeplots are missing from the databases and that the database-assisted estimates are incorrect. This can be seen in Figure7, in which the under-coverage of the database plots usingone selection of calibration set plots is shown, and the effectof missing training set values on the estimates is illustrated.The large values of both G2 and V2 present in Loppi-Janakkala are poorly estimated. In addition, the under-cov-

erage of the calibration set in terms of G2-V2 distributioncauses under-coverage in the plots selected from the data-base. Such plots are not accepted into the training set,because the plot selection is performed with respect to thecalibration set distribution characteristics.

Discussion and Conclusions

In this article, the procedure for the use of databases inestimation of total forest stand parameters introduced earlierby the authors (Junttila et al. 2010) was extended to theestimation of species-specific forest stand parameters withmultiple databases. The modified procedure was shown toretain the accuracy of the total parameter estimates attainedwith the original procedure.

Estimation of species-specific forest stand parameters

Figure 6. Histograms of the RMSE% values of 50 repeated calibration plot selections in Lieksa, with arandomly selected calibration set of 50 plots for species-specific forest stand parameters of volume V1, V2,and V3. The histograms of the estimates with the calibration set only (top), of the estimates with thecalibration set complemented by all the selected database plots (middle), and of the optimal estimates(bottom) are shown. The scale of figures in each column is equal. The median of the results of each databaseis shown with a vertical bold dashed line, and the minimum and maximum of the range are shown with avertical dashed line.

Figure 7. Left: scatterogram of G2-V2 plot distribution in Loppi-Janakkala (●, new site plots; E,calibration plots; �, selected database plots). The true new site plot distribution is only partly covered bythe calibration set and database plots. Middle, G2 as a function of 50th percentile height of the first LiDARreturns (Hf50%) (●, new site plots; �, selected database plots). The plots of the new site, which representforest types that are not covered by the selected database plots, are marked with �. Right: true forest standparameters G2 and V2 plotted against the estimates derived using only the calibration set data (●) andusing calibration set data complemented by accepted database plots (�).


with database information showed promising results. Asmight be expected, the best results for the new site estimateswere derived by using several hundred measured plots fromthe new site and then using them again to predict the foreststand parameters for the rest of the new site. If there aredatabases that have characteristics similar to the ones of thenew site, it is possible to achieve estimates close to optimallevel by using only 50 plots from the new site itself. How-ever, LiDAR data and the two features derived from thedigital aerial photographs do not correlate well enough withthe species-specific forest stand parameters, and thus, thespecies-specific estimates are less accurate than the esti-mates of total forest stand parameters. In the future, datafrom other sources also need to be included in the model toimprove the overall accuracy of species-specific forest standparameter estimates.

According to the results presented, it seems that the useof plot databases can improve the accuracy of forest inven-tory results computed with a small number of sample plots.Furthermore, plot databases can be adopted in such a waythat the resulting improvement in the accuracy of theseestimates is robust against considerable variability in Li-DAR equipment and flight parameters, as well as in types offorest. Although the accuracy of such results mostly fallsshort of that obtained with an extensive field campaign, thesavings in cost from using plot databases are also consid-erable. Potential additional cost is mostly due to preprocess-ing of plot databases and involves method development andcomputation only.

The method adopted in the current study is but oneamong many possible alternatives, and we make no claimsthat it is the optimal one. Some evident improvement couldbe obtained by preprocessing digital aerial image featurestoo, but this would require an approach different from theone used on LiDAR features here.

The results obtained for the test site Loppi-Janakkalaindicate that little improvement in the accuracy of estimatescan be expected if the total variability of forest type in thetarget area is not represented in the databases. Whether thissituation can be addressed by changing the method anddistributions used in plot selection remains a topic of furtherwork.

The same observation is also true of the set of calibrationplots. The calibration plots must also faithfully represent theextremes of forest type that are present in the target area. Ifthe number of calibration plots is small, it seems advisablenot to cluster them, as this tends to decrease the variabilitypresent in the set of plots. This effect was displayed with theMatalansalo test site, where both clustered and nonclusteredcalibration plot selection methods were tried.

When looking at the cost-benefit analysis of plot data-bases, we can refer to the operational practice of inventoryby compartments. The accuracy of LiDAR-based estima-tion, with a plot-level error in total timber volume of slightlymore than 20% and a corresponding stand-level error ofsome 15% (Heikkila 2010), is clearly superior to the esti-mation accuracy of inventory by compartments (Haara andKorhonen 2004). In species-specific estimation, the accu-racy of both methods is quite similar.

The estimated cost of inventory by compartments in

Finland exceeds 10 €/ha. In a typical LiDAR inventoryproject, with 100,000 ha, the cost per ha of LiDAR andinventory calculations is less than 1 €. The cost of measur-ing 1,000 sample plots adds another 1 €/ha to the cost,thereby more than doubling it. If only 100 plots weremeasured and plot databases were used instead, the cost offield measurement would come down to 0.10 €/ha, and thetotal cost would be reduced by 40% or more. Because theaccuracy of the species-specific estimates seen in our ex-perimental results is still better than with compartment-based estimation, this is an attractive possibility.

An effort worth making is to keep refining the use of plotdatabases to the point at which their adoption could evenimprove on the accuracy of forest parameter estimation thatis obtainable with extensive field campaigns. This potentialrests with the extremely large variance in forest types thatlarge plot databases can represent. By a judicious matchbetween the type of target forest and the selection of plotsfrom databases, it should be possible to represent any forestto a very high degree of detail in its variability. However,much additional work seems necessary before this goal canbe achieved.

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