Remote Sensing of Environment 155 (2014) 248–256

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Remote Sensing of Environment

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Applying airborne γ-ray and DEM-derived attributes to the localimprovement of the existing individual-tree growth model fordiameter increment

Cheikh Mohamedou a,⁎, Timo Tokola a, Kalle Eerikäinen b

a School of Forest Sciences, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finlandb Finnish Forest Research Institute, Joensuu Unit, P.O. Box 68, FI-80101 Joensuu, Finland

⁎ Corresponding author.

http://dx.doi.org/10.1016/j.rse.2014.08.0330034-4257/© 2014 Elsevier Inc. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 3 June 2014Received in revised form 20 August 2014Accepted 23 August 2014Available online 20 September 2014

Keywords:Forest characteristicsγ-RaySite effectsTopographic wetness indexTree attributesTree growth

Airborne gamma-ray data (γ-ray), measuring gamma radiation naturally emitted from the earth's crust hasproved useful for predicting the character and distribution of soil properties in forested landscapes. In addition,digital elevation models (DEMs) provide a reliable source of information regarding the hydrological propertiesof soils. The growth potential of a forest stand is an important parameter in forest management and planning, sothat accurate prediction of growth is needed. The present study looked into applying γ-ray data in combinationwith DEM-derived attributes for improving the existing individual-tree growth model. To adapt the nationalmodel to local conditions, the data of 1118 sample trees and 9987 tally located within 197 sample plots in South-eastern Finland were used. Trees were distributed subjectively to reflect the stands' composition and structure.Themain aimwas to test the suitability of airborne γ-ray in combinationwith DEM-derived attributes for localizinga general parametric prediction model for the trees' growth (diameter at breast height increment for the period offive years). Linear mixed effect procedures were used to fit models derived from the γ-ray and DEM. Of the variousmodels constructed for comparison purposes, the best result was obtainedwith broadleaved trees, followed by Scotpine (Pinus sylvestris L.) while Norway spruce (Picea abies L.) revealed little improvement. The improvement wasfound to bemore accurate in less fertile site types (Vaccinum type (VT) and Calluna type (CT)) as well as onmineralsoils. The result was found to be effective in reducing the root mean square error (RMSE) and the bias.

© 2014 Elsevier Inc. All rights reserved.

1. Introduction

Tree and stand growth are significant parameters in forest manage-ment and planning (e.g., Ledermann & Sterba, 2006; Sironen, 2009;Soares et al., 1995). Volume of growing stock is the most importantparameter in forest inventories (Räty & Kangas, 2007), whereas growthinformation is very important for decision-making for a sound forestmanagement (Sironen et al., 2008). Modeling has traditionally beenused to assess forest growth; in forest inventory, modeling is a way toovercome the difficulties associated with direct measurement of treeparameters (slow, costly, or unmeasurable) (Burkhart & Tomé, 2012).Themodel was fitted for estimation in a large area termed the “nationalmodel.” The latter model tends to be biased regionally while on thenational level, it is unbiased (Räty & Kangas, 2007; Sironen, 2009;Sterba et al., 2002). There is a need for localization to adapt the modelto local conditions. Localization is the process by which the local biasis removed (Räty & Kangas, 2010; Sterba et al., 2002).

There are several methods to achieve localization; the global modelcan be adjusted locally by detecting trends in residuals and correctingaccordingly by adding a coefficient or an equation. Another alternative

could be refitting the global model to each region at a time and removethenon-significant variables, or create a newmodel for different regionsindependently (Räty & Kangas, 2007, 2010). Another alternative is toapply the spatial indices to find homogenous areas where the valuesare clustered. If the national model has homogenous residual trends,the process of localization might not be worthwhile. However, if thenational model has non-homogenous residuals then the localizationprocess might be worthwhile (Räty & Kangas, 2008). Since it is difficultto explain the whole range of natural variations using a sample-basednational model, even for a given species, there is a vital need for ameans of localization to improve the overall estimate (Burkhart &Tomé, 2012; Sterba et al., 2002).

A possible way to improve growth estimation in the boreal forest isto use soil hydrological properties by introducing remote sensing datasuch as airborne gamma-rays (γ-ray). These remote sensing-deriveddata represent the gamma-ray naturally emitted from the earth'scrust, and measure the abundance of potassium (γK), thorium (γTh)and uranium (γU). Potassium can be measured directly, while Th andU are expressed through indicators (Bierwirth & Brodie, 2005; Grasty,1997; Hyvönen et al., 2005; Zhang et al., 1998; Wilford, 2002). Theflux of γ-ray radiation declines with increasing soil moisture (Grasty,1997; Minty, 1997), a fact that can be directly attributed to tree growth,

249C. Mohamedou et al. / Remote Sensing of Environment 155 (2014) 248–256

in which soil moisture plays a major role, and as radiation is affected bysoil water content, a relation can then be established between the γ-rayand the moisture content.

In Finland, the applications of the γ-ray method include mineralexplorations, soil moisture and texture mappings, and calculations ofwater equivalent values for snow and peat research, for instance(Hyvönen et al., 2005). Forestry applications comprise, inter alia, suit-ability assessments of sites for Scots pines (Hyvönen et al., 2003) andsite index estimations (Wang et al., 2007). The γ-ray backscatteringhas been found to be a very useful tool for predicting the soil charactersand distributions, especially for forested landscapes (Bierwirth et al.,1996, 1998), but the relation between γ-ray and tree growth in forestareas has so far not been established. Yet, the hypothesis in the currentstudy has been advanced that γ-rays are able to explain local bias innational growth models.

Wetness indices derived from a digital elevation model (DEM) arethe most widely used attributes for describing the effect of topographyon the soil moisture distribution (Gessler et al., 2000; Kokkila 2002).Wetness indices provide a valuable source of information regardingsoil properties for use in resource management (Frazier et al., 2005);two of the best known are the Steady Wetness Index (Beven & Kirkby,1979; Moore et al., 1993; Sørensen & Seibert, 2007) and the QuasiDynamic Wetness index (Barling et al., 1994). The DEM topographicattributes can be divided into two main groups: primary attributes,including slope, hillshade, aspect, solar radiation, profile, flow direction,upslope catchment area, and compound attributes that can be derivedfrom these, such as wetness indices (Boukheir et al., 2009; Mooreet al., 1993; Mummery et al., 1999). Moore et al. (1993) found a signif-icant correlation between soil attributes (pH, organic matter, A-horizonthickness, phosphorus content) and quantified terrain attributes. Theeffect of topography on tree growth is well established, even if treegrowth is also controlled by many other factors (Oberhuber & Kofler,2000). Furthermore, forest cover can be substantially explained bywet-ness capabilities of soils (Bader & Ruijten, 2008). For instance, the Topo-graphic Wetness Index (TWI) was applied in many studies as atopographic factor influencing the radial growth of trees (Byun et al.,2010, 2013; Seo & Park, 2010).

Fig. 1. Stud

Assuming that site quality is linked to growth, γ-ray backscatteringhas a role in the prediction of soil properties and thus site quality. Theconcept can be extended further; the main aim of the study was totest the suitability of airborne γ-ray variables in combination withDEM-derived variables for localizing a general parametric predictionmodel for the trees' growth (diameter at breast height increment forthe period of five years). The second aim was to select the best possiblecombination of information for improving periodic growth predictions.

2. Data and methods

2.1. Data

The study area is located in southeastern Finland (south borealforest zone, see Fig. 1). Field data collected from the two studysites, i.e. Kiihtelysvaara and Matalansalo, consisted of 1118 sampletrees and 9987 tally trees located within 197 plots. The plots weredistributed subjectively to reflect stand composition and structure.The plots varied in shapes and sizes; three rectangular plot types(20 m × 20 m, 25 m × 25 m and 30 m × 30 m) were used, whereas afixed radius of 9 mwas applied for circular plots. The plots representedthe four main forest site types identified using Cajander's (1926) forestsite type system: Myrtillus type (MT, 38%), Oxalis-Myrtillus type (OMT,19%), Vaccinum type (VT, 41%) and Calluna type (CT, 2%).

The proportions by different tree species in the study area were 67%,13% and 19% for Scot pine (Pinus sylvestris L.), Norway spruce (Piceaabies L.), and broadleaved trees (Silver birch (Betula pendula Roth),downy birch (Betula pubescens Ehrh.) and aspen (Populus tremula L.)),respectively. The majority of the sample tree observations came fromthe Kiihtelysvaara location (80%). The increment of diameter at breastheight over the bark (dbh) for a five year period (id5) was recorded byincrement borer (measurement of annual rings was done in the labora-tory). The growth recording was available only for the sample trees.

Remote sensing data consisted of DEM (resolution 25m×25m) andγ-ray. The DEMwas obtained from the National Land Survey of Finland,mainly based on photogrammetry, aerial photographs, and manualediting as well as field verification. Basically, two groups of variables

y area.

Table 1Estimates for the parameters of generalization model, where σu

2s, σu

2p and σe

2 are for var-iances estimated for random stand-effects, random plot-effects and random errors of themodel, respectively.

Matalansalo location,n = 223. Dependent = id5

Kiihtelysvaara location,n = 895. Dependent = id5

Parameters Estimate Std.Error Estimate Std.Error

β1 −1.7867 0.3884 −2.6874 0.1991β2 0.8222 0.1560 0.9708 0.0776β2 −0.0005 0.0002 −0.0004 0.0001β4 0.2567 0.0375 0.2299 0.0649β5 – – 0.3105 0.0527σu

2s 0.1284 – – –

σu2p 0.0231 – 0.1338 –

σe2 0.1935 – 0.1450 –

AIC 413.1303 – 1018.911

250 C. Mohamedou et al. / Remote Sensing of Environment 155 (2014) 248–256

were extracted: theDEM-derived variables from theDEM-derived attri-butes (e.g., TWI, Solar, and Hillshade) and the γ-ray windows.

The γ-ray data was provided by the Geological Survey of Finland(GTK) along North–south and East–west flight lines at 200 m intervalsand altitudes at the approximate range from 30 to 40m. The data repre-sents the major γ-emitting elements detectable by an aircraft-mountedγ-spectrometer and comprised the windows for γK, γTh and γU. Potas-sium is detected directly and uranium and thorium indirectly via theirproduct-decay series (Grasty, 1997; Hyvönen et al., 2005; Wilford,2002; Zhang et al., 1998). The interpolated γ-ray windows were pre-sented in a raster format and interpolated onto a 50 m × 50 m grid.The ratio between the three windows was calculated as it was less af-fected by possible attenuation within the data. The units of measure-ment of a radiometric survey were counts per second (cps). Thecorrected airborne γ-ray was converted to equivalent concentrationon the ground (e.g.,γTh and γU in ppmwhile γK indicated percentage).

The Topographic wetness index (TWI) (Beven & Kirkby, 1979;Sørensen & Seibert, 2007) was calculated from the DEM, whereas FlowAccumulation was obtained according to Jenson and Domingue (1988).TWI calculation was conducted as follows:

TWI ¼ lnflowaccumulation � 25ð Þ þ 1

tan slopedeg þ 0:0001� �

� 3:1415 � 180−1Þ

8<:

9=;; ð1Þ

where Slopedeg is the maximum rate of elevation changes between sub-ject cells and its neighbors, in degrees; and Flow Accumulation is thenumber of neighbor cells that flow into the downslope cell. Other vari-ables extracted from DEM were: Hillshade obtained as the shaded illu-mination of each cell in regard to the light source angle (sun), theazimuth angle (315° (NW)with the default altitude of 45°; representedas a raster), and Solar (Wh−1 m−2) calculated according to Fu and Rich(2002) as the amount of solar radiation within the growing season. AllDEM-derived attribute values were created using ArcGIS (ESRI, 2011).

The different datasets (field data,γ-ray andDEM-derived attributes)were projected into Finland's uniform coordinate system. To increasethe reliability of current analysis, all raster datasets were resampled(nearest neighborhood) to match the smallest plot size within thefield data (the grid cell size was set to 18 m). Nevertheless, severalother pixel sizes were examined simultaneously. The Zonal Statistics(plot defined as a zone) was applied to extract the averages of pixelvalues of different rasters from each plot at a time. Only the plots thatcontain the sample trees were selected for the analysis and extractionof remote sensing variables. On completion of zonal extraction, eachplot had its unique value extracted from each raster.

Soil types in the study areaweremainlymineral soil (85%)while thepeat soils were also quite common (14%). The descriptive statistics re-vealed that the γ-ray had greater variability within peat land comparedto mineral soils. The standard deviation (SD) was 0.33, 1.08, 0.48 (min-eral) and 0.44, 1.57, 0.57 (peat) for γK, γTh, γU, respectively. Further-more, the DEM-derived variables showed less variability within themineral soil. The SD was 1.91, 4.27, and 51.08 for TWI, Hillshade andSolar on mineral soils, respectively, and 1.38, 3.53, 32.72 for the samevariables on peat land, respectively. The id5 was larger in mineral(mean = 1.19 cm) than in peat land (mean = 0.71 cm). The meandbh was correspondingly smaller in peat soil.

2.2. Generalization of sample trees information

The increment of dbh for five years (id5) was available only for sam-ple trees. To obtain the information for the tally trees, there was a needto generalize the growth information. The generalization, in otherwords, is the process of getting the info for tally trees from the sampletrees themselves. Therefore, we applied the extracted parametersfrom sample trees to construct separate models for Kiihtelysvaara andMatalansalo locations. The Nonlinear Mixed effects procedure (NLME)

was used for the analysis (see Pinheiro & Bates, 2002). The nonlinearmixed-effects model with parameters for random stand (Matalansaloonly) and plot (Matalansalo and Kiihtelysvaara) effects was fitted byrestricted maximum likelihood (REML). The non-linear model was ob-tained with the following form:

id5ijk ¼ exp�

β1þ usi þ upij

� �þ β2 � ln dbh0ijk

� �þ β3 � dbh0ijk

2

þβ4 � Znsij þ β5 � Zbij þ eijk

�;

ð2Þ

where id5ijk is the future diameter increment of five years of tree k atstand location i within plot j (cm); β1, β2,…, βn are parameters forfixed effects; dbh0ijk is dbh at breast height at the beginning of the grow-ing period (cm); Znsij is a dummy variable indicating the existence ofspruce; Zbij is a dummy variable indicating the existence of broadleavedtree; usi is a parameter for random stand-effects; upij is a parameter forrandom plot-effects; and eijk is a parameter for random errors of themodel.

The parameter estimates obtained for the non-linear mixed-effectsgeneralization model for id5 are shown (Table 1) for Matalansalo andKiihtelysvaara. The transformations of dbh at the beginning of the grow-ing period were highly significant. The existence of spruce had an influ-ence in Matalansalo, while in Kiihtelysvaara the existence of both birchand spruce was highly significant. The random coefficients representedmore than 60% of the variance in the total datasets. It can be concludedthat both locations had good data fits (see Fig. 2). The construction oftwo models locally was beneficial in the current study case.

Generalization process was needed to obtain the variables necessary(e.g., dbh0) for calculating the inputs of the National Model (NModel)for diameter increment by Pukkala et al. (2013).

2.3. Estimating Local Bias (LBias)

The National Model used to predict id5 (id5[NModel]), hereafter re-ferred to as (Pukkala et al., 2013), was set as the basis to be improved.The National Model for the trees' growth (diameter at breast heightincrement for the period of five years) is a species-specific nonlinearprediction model. It is a natural exponential function, the interceptterm of which was specified for “site effects” since it was assumedthat the available site variables (forest site type, temperature sum) didnot fully explain all local site-effects. However, data used by Pukkalaet al. (2013) comprised several plots measured in the same geographi-cal location that were aggregated, i.e. clustered, in same site whendetermining the random hierarchical structure of the data for the esti-mation. Therefore, the site-effects estimated for the National Model byPukkala et al. (2013) also comprises data-specific cluster-effects. Inthe fixed part of the National Model, which was finally utilized as thegeneral predictor of “id5”, the forest site was described using a

Fig. 2. Goodness-of-fit plots obtained for id5 of sample trees (y-axis = true id5 (cm), x-axis = predicted id5 (cm)).

Table 2The descriptive statistics of the modeled data.

Sample trees, n = 1118 Pine, n = 759

Mean Min Max SD Mean Min Max SD

dbh0jk, cm 16.00 1.44 45.20 6.99 17.21 4.34 38.58 6.28dbh5jk, cm 17.14 1.90 47.35 7.15 18.30 4.55 39.00 6.43id5jk, cm 1.13 0.07 4.37 0.69 1.09 0.07 4.33 0.61LBias 0.01 −1.50 3.15 0.60 −0.16 −1.50 2.39 0.50γk 1.19 0.00 2.56 0.40 1.19 0.00 2.56 0.37γth 4.43 0.82 8.32 1.33 4.39 0.82 8.32 1.25γu 1.14 0.00 2.49 0.51 1.04 0.00 2.49 0.47TWI 8.53 5.21 15.46 1.87 8.57 5.21 15.46 1.84Hillshade 179.43 154.00 192.00 4.17 179.50 154.00 192.00 3.87Solar(×1000)

520.84 472.66 661.42 49.96 513.89 486.09 661.42 43.10

Spruce, n = 145 Broadleaved, n = 214

Mean Min Max SD Mean Min Max SD

dbh0 15.13 3.45 42.15 6.79 12.33 1.44 45.20 8.11dbh5 16.62 3.95 43.50 6.87 13.36 1.90 47.35 8.36id5 1.49 0.09 4.37 0.88 1.03 0.08 4.06 0.72LBias 0.16 −0.92 2.09 0.60 0.50 −0.56 3.15 0.65γk 1.36 0.31 2.56 0.42 1.09 0.00 2.09 0.43γth 4.92 0.82 8.32 1.41 4.25 0.82 8.32 1.49γu 1.45 0.33 2.49 0.49 1.25 0.00 2.39 0.54TWI 9.06 5.21 15.46 1.98 8.03 5.83 12.82 1.77Hillshade 178.61 154.00 192.00 5.73 179.74 163.00 192.00 3.89Solar(×1000)

555.31 486.13 652.86 62.86 522.11 472.66 652.86 53.14

251C. Mohamedou et al. / Remote Sensing of Environment 155 (2014) 248–256

temperature sum (sum of daily temperatures minus 5° of those days onwhich the daily temperature is at least 5°) and Cajander's (1926) forestsite types, competition by stand basal area at the start of the growthperiod and by the basal areas in larger trees obtained by species(e.g., Vanclay, 1994), tree size by diameter at breast height, and standstructure by standard deviation and skewness of the diameter distribu-tion and by using species-specific values of the basal areas in larger trees(see Pukkala et al., 2013).

The dependent variable in the subsequent analysis was set to theLocal Bias (LBias):

LBiasjk ¼ yjk −yjk ð3Þ

where yjk is measured id5jk (cm) and ŷjk is predicted id5jk (cm) obtainedusing NModel by Pukkala et al. (2013).

Thus, an improved predictor for id5 is id5jk[NModel] + LBiasjk..The analysis for estimating LBias took place exclusively inside the

sample trees for which the actual measurement of growth was record-ed. Principal Component analysis used in dimension reduction resultedin six components, totaling about 87% of the variation. A linear mixed-effects model was applied to the estimation of LBias:

LBiasjk ¼ β1 x1jk þ ⋯þ βnxnjk þ upj þ ejk; ð4Þ

where: x1jk,…, xnjk are independent variables of thefixedmodel part;β1,β2,...., βn are parameters for fixed effects; upj is a parameter for randomplot-effect; and ejk is a parameter for random errors of the model.

The analyses examined several options, and then selected the bestpossibility to improve id5 estimation, and the following four optionswere tested and evaluated:

- Trees located onMineral and Peat soils (with only Peat as explanato-ry variable, its interaction with species, excluding γ-ray or DEM-derived variables);

- Trees located on Mineral and Peat soils (γ-ray or DEM-derivedvariables, excluding peat as explanatory variable);

- Trees located on mineral soil datasets; and- Trees located on Mineral and Peat soils (γ-ray or DEM-derivedvariables and peat as explanatory variables).

The evaluation criteria were performed by the root mean squareerror (RMSE), BIAS, RMSE%, BIAS% and Akaike information criterion(AIC). Significance was set at p-level = 0.005. All statistical analysiswas performed in R (R Core Team, 2012) and IBM SPSS statistics 19(Norusis, 2012). The descriptive statistics of modeled data representedin Table 2. In this study, the RMSEs and biases were determined asfollows:

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXnl¼1

yl− ylð Þ2n

vuut ð5Þ

BIAS ¼Xn yl− ylð Þ ð6Þ

l¼1

n

where yl is the observed value, yl is the predicted value of the given char-acteristic, and n is the number of observations. The relative, i.e., percent,RMSEs (RMSE%) and biases (BIAS%) were calculated by dividing theabsolute RMSEs and biases by the means of the respective values fromthe observations yð Þ and multiplying the resulting quotients by 100.

3. Results

3.1. Improvement of id5 estimates

3.1.1. Trees on mineral and peat soils with only peat soil effects andexcluding γ-ray or DEM-derived variables

The estimation of LBias did not produce good results with which toproceed. The overall results of the improvedmodel were biased. The in-tercept was highly insignificant. However, the separate species-specificresults differed; the improvedmodel did result in lowering the BIAS andRMSE. Yet the only clear improvement was noticed in broadleavedtrees. In the case of broadleaved, the RMSE was going from 0.8195 cm

Table 3Estimates for the parameters of model for LBias.σu

2pand σe

2 are for variances estimated forrandom plot-effects and random errors of the model, respectively.

On mineral soil only, n = 949 On mineral & peat soils, n = 1118

Parameter Estimate Std. Error Parameter Estimate Std. Error

Intercept −15.08 4.44 Intercept −12.65 4.33ln(Solar) 1.14 0.34 ln(Solar) 0.95 0.33Zns ∗ γTh −0.09 0.03 Zns ∗ γTh −0.12 0.03Zns ∗ γU 0.52 0.12 Zns ∗ γU 0.44 0.12Zb −1.25 0.57 Zns ∗ TWI 0.03 0.02Zb ∗ γK −0.50 0.17 Zb −1.32 0.51Zb ∗ U 0.34 0.12 Zb ∗ γK −0.47 0.15Zb ∗ TWI 0.06 0.03 Zb ∗ γU 0.30 0.10Zb ∗ Solar 0.00 0.00 Zb ∗ TWI 0.07 0.02σu

2p 0.1325 0.0235 Zb ∗ Solar 0.00 0.00

σe2 0.1874 0.0100 Zb ∗ Zpeat −0.40 0.12

AIC 1366.833 – Zpeat −0.28 0.12σu

2p 0.1751 0.0082

σe2 0.1463 0.0240

AIC 1538.93 –

252 C. Mohamedou et al. / Remote Sensing of Environment 155 (2014) 248–256

to 0.6329 cm. The RMSE was reduced; (0.5251 to 0.4895 cm) and(0.6162 to 0.5933 cm) of pine and spruce, respectively. The AIC was at1552.81.

3.1.2. Trees on mineral and peat soils with γ-ray or DEM-derived variablesand excluding peat soil effects

The overall results of sample trees expressed elimination of bias inthe study area as whole and in locations separately (Kiihtelysvaaraand Matalansalo). All model parameters were significant at p-level0.005. In terms of species, the pine was moderately changed while thespruce changed little. Their RMSE values were lowered in both cases;values were (0.5251 to 0.4941 cm) and (0.6162 to 0.6018 cm) of pineand spruce respectively, broadleaved revealed noticeable changes inRMSE (0.8195 to 0.6389 cm) or almost 14% changes. On the otherhand, the AIC criteria were as at 1554.11.

3.1.3. Trees on mineral soilsThe results and the summary statistics of the two locations together of

the study area are illustrated in Table 3. The variables in the models wereall significant at the p-level of 0.05. The result, as shown in Table 3, indi-cated that solar energy had a positive effect on the LBias estimation andtherefore on the growth improvement when the solar radiation washigh. Consequently, we expect a positive effect on diameter growth out-comes. However, the existence of hardwood did have a negative effecton the estimation of growth. The interaction between species and γ-rayvariables (γth and γk) had a negative effect on growth estimation.

The inclusion of γ-ray windows per se was not statistically signifi-cant. The γ-ray window values and DEM-derived variables (i.e., Solarand TWI) were correlated. As a result, the interaction between specieseffect and γ-ray tended to perform better in LBias estimation, and like-wise, DEM-related variables.

Table 4Trees' RMSE and BIAS on mineral soil.

Sample trees RMSE and BIAS

Study area Kiihtelysvaara Matalan

id5jk [NModel]RMSE 0.5975 0.5291 0.8185RMSE% 50.08% 50.19% 47.48%Bias 0.0583 −0.0145 0.3361Bias% 4.94% −1.38% 19.50%

id5jk [improved]RMSE 0.5330 0.4954 0.6573RMSE% 44.67% 46.99% 38.13%Bias −0.0066 −0.0113 0.0110Bias% −0.56% −1.07% 0.64%

The fixed part of the linearmixedmodel was used for the estimationimprovement of id5. The results as illustrated in Tables 4 represent theRMSE and BIAS changes. Apparently, the study area had lower RMSEand BIAS, while regarding the locations, the RMSE and BIAS tendedto be high (Matalansalo). In both locations, the RMSE and BIASwere lowered in the resulting improved model, particularly in theMatalansalo location.

Taken together, these results suggest that applying the improve-ment only on mineral soil would be advantageous. It produced by farthe best results in terms of lowering RMSE and bias by locations andby species-specific.

The species-specific (Table 4) were different from the reaction of allthe trees. The improvement in RMSE went from a moderate change ofpine to high change of broadleaved. Interestingly, there were no differ-ences in the case of spruce between the improved national model'sRMSE and national model's RMSE. The clearest evidence of improve-ment was clear in the case of broadleaved trees.

3.1.4. Trees on mineral and peat soils with γ-ray or DEM-derived variablesand peat soil effects

It was apparent that the improvement in id5 was much more obvi-ous in broadleaved trees followed by pine trees. Despite the relativelylower observation in spruce, the predicted and true values were nearlyfollowing the same trend. The bias was largely eliminated from thenational model particularly in Kiihtelysvaara.

The coefficients were fairly following a trend similar to that of treesin mineral soil (Table 3); however, the magnitude of γK interaction,broadleaved effect, and solar was increased. The results (Table 5) wereadopted to demonstrate further details. Figs. 3, 4, and 5 represent vari-ous aspects of results obtained with the model (Table 5).

The bias in id5 predictions obtained for pine and broadleaved treeswas eliminated to a certain extent (Table 5). Yet again, spruce showedno noticeable changes in both RMSE and BIAS, and no improvementwas achieved in either of the datasets.

Based on the options evaluated above, it was found that the fourthanalysis option (trees in mineral and peat soils with γ-ray or DEM-derived variables and peat soil effects) was the best option to improvethe estimation of dbh increment. As comparable to the same samplesize (n = 1118), the peat effect was necessary to include along withother explanatory variables. AIC criteria backed these results; 1554.81without the peat effect and 1538.93 with the peat effect and other ex-planatory variable.

From Fig. 3, it can be seen that in general, the γ-ray (here referred toas γth) showed noticeably better results in the case of pine andbroadleaved. In locations where γth concentration was high, the im-provement was negligible (pine). The low γth areas resulted in betterimprovement of a national model for pine and broadleaved. However,for spruce, the residual was not affected by γth concentration. Still,γth tend to be better in spruce where γth has a relatively lowconcentration.

Species-specific RMSE and BIAS

salo Pine Spruce Broadleaved

0.4923 0.6174 0.897242.74% 42.36% 78.57%−0.1030 0.1713 0.5936−8.95% 11.75% 51.99%

0.4748 0.6075 0.666141.23% 41.68% 58.33%0.0127 −0.1046 −0.00291.10% −7.18% −0.25%

Table 5Sample trees' RMSE and BIAS (mineral & peat soils).

Sample trees RMSE and BIAS Species-specific RMSE and BIAS

Study area Kiihtelysvaara Matalansalo Pine Spruce Broadleaved

id5jk[NModel]RMSE 0.6042 0.5408 0.8101 0.5251 0.6162 0.8195RMSE% 53.30% 54.58% 47.48% 48.04% 41.31% 79.29%Bias 0.0060 −0.0611 0.2754 −0.1628 0.1555 0.5035Bias% 0.53% −6.17% 16.14% −14.89% 10.43% 48.71%

id5jk[improved]RMSE 0.5305 0.4940 0.6567 0.4781 0.6075 0.6399RMSE% 46.80% 49.86% 38.49% 43.73% 40.72% 61.91%Bias −0.0029 −0.0054 0.0073 0.0022 −0.1301 0.0653Bias% −0.25% −0.54% 0.43% 0.20% −8.72% 6.32%

253C. Mohamedou et al. / Remote Sensing of Environment 155 (2014) 248–256

The Topographic Wetness Index (TWI) behaved well in all moistureclasses (Fig. 4); the current resultswere expected, asmoisture is directlylinked to tree growth. Pine and broadleaved showed clear evidence ofgrowth reading improvement at all ranges of wetness classes. TWI inthe case of spruce seems to bemore influential in reducing the residualsin the high moisture area only (TWI N 11).

The diameter classes (Fig. 5) have a larger effect when the trees aresmall in the case of spruce and pine while for broadleaved there is noreal influence, little effect when the trees were very small (dbh lessthan 5 cm) and a steady influence (dbh over 5 cm). The nationalmodel tended to overestimate the small trees.

3.2. Effect of site types

Further analysis showed different behaviors of the improved andNModel when comparing the results based on site types. The

Fig. 3. Residuals (Y-axis), γTh classes (ppm) (X-a

improvement was less obvious when obtained for the fertile sites(OMT + MT site types) with RMSE reduced from 0.6545 (NModel) cmto 0.5874 (ImprovedModel) cm (nearly 5% as change). On the otherhand, in the case of trees representing less fertile site types (VT + CT),the RMSE decreased from 0.5307 cm to 0.4446 cm (more than 9%change). However, the bias was reduced from 0.1675 to 0.0482 andfrom −0.2063 to −0.0699 when calculated for OMT + MT & VT + CT,respectively.

4. Discussion

In the present study, a special caution was exercised in the general-ization process. Measuring growth directly is more appropriate andgives accurate outcomes in modeling (Mehtätalo, 2004a). Large-scaleforest inventories are, however, usually characterized by low numberof sample trees measured (Eerikäinen, 2009). Since it was a crucial

xis). Data is shown from the model (Table 5).

Fig. 4. Residuals (y-axis), TWI classes (X-axis). Data is shown from the model (Table 5).

254 C. Mohamedou et al. / Remote Sensing of Environment 155 (2014) 248–256

and determined factor in the accuracy of subsequent results, the gener-alization process was sufficiently precise to conduct the study (Fig. 2).There might, however, be a slight possible source of error from thegrowths predicted for tally tree, which were used only to derive thecompetition indices and other inputs, necessary for the calculation ofnational model output. Hence, the current study and its fitted modelswere based on appropriate modeling data.

One of the issues that emerged was related to the relatively largenumber of explanatory variables. However, all variables (Table 5)were statistically significant. The dimension reductions of the PCAmethod did not improve the overall accuracy of the model (confirmedby RMSE and AIC criteria) (Table 5). The cause for this was not clear,but it was likely that many of the components extracted did not exem-plify the whole variation within the datasets.

It was noticeable that the improvement of Id5 produced betterresults in the case of mineral soil only. One suggestion could be tohave separate models for mineral and peat as in other national models(Hynynen, 2002). On the other hand, this option was not the best inthe present study; the lack of an adequate number of observations(i.e., trees on peat soil) within the dataset posed a limitation. Moreover,the national model, which was improved in the present study (Pukkalaet al., 2013) was applied to both mineral and peat soils.

Considering the less fertile site types (VT+ CT), the γ-ray and DEM-derived tended to performbetter in growth improvement as anticipatedin comparison with the more fertile site types (OMT + MT). However,the current study suggested that the model could be applied to bothclassification groups (fertile and less-fertile site types). The better appli-cability of the improved model in VT + CT site types agrees with thetheory that γ-ray and DEM-derived attributes explain the moisturecapabilities of the soil. The capability of γ-ray and DEM-derived wasmasked in the case of the fertile soil while in less fertile soil it was

able to explain some variation in the growth. Bierwirth et al. (1996),for instance, have implied that for γ-ray data to be constructive for thedeterminations of soil classification, the terrain should be geomor-phologically or geologically homogenous.

The overall results reported rather good predictions obtained withthe improved national model (Figs. 3, 4 and 5). The γ-ray and DEM-derived variables were efficient in reducing the BIAS and improvedthe overall accuracy confirmed by the decreased RMSE. Regardingspruce, however, the present study was unable to detect any trend inthe regional residual that could be improved, and only a very slight im-provement was achieved for spruce trees. There were various potentialexplanations for the spruce case starting from the comparatively lownumber of observations (n = 145). The variation within explanatoryvariableswas also obviously different in comparisonwith the other spe-cies (e.g., pine and broadleaved). As discussed above, it was found thatthe improved models tended to be better in less fertile site types. Infact, the spruce trees were mostly located (94%) in the more fertilesite types (OMT + MT). Species' response to soil moisture differs(Lagergren & Lindroth, 2002); shade-tolerant species (such as spruce)may survive and regenerate in the undergrowth for long periods(Mehtätalo, 2004b), and the nature of growth of understory sprucesas slow-growing trees might play a part here. In addition, sprucemight not be affected by topographic changes of wetness, though,pine as a light-demanding species can respond in growth immediatelyupon a change in its local environment (Miina, 1994). It is also notewor-thy that the national model dataset was also fitted with spruce as theprimary species.

The γK, γU and γTh variables contributed significantly to theimproved growth model in an interactive form. Uranium, being in gen-eral related to discharges of groundwater, can have completely differentresponses to similar types of soils (Bierwirth et al., 1996). Yet despite

Fig. 5. Residuals (y-axis), dbh classes (cm) (X-axis). Data is shown from the model (Table 5).

255C. Mohamedou et al. / Remote Sensing of Environment 155 (2014) 248–256

Uraniumwindow behavior, it was significant in improving growth esti-mation. The bestwindow for assessing the suitability of pine sites undernorthern boreal forest conditions isγK (Hyvönen et al., 2003). However,it was not abundant in the study area, and this could explain why thegrowth improvement was moderate in case of pine. Moreover, pinetrees situated along an almost equal site distribution between less fertile(VT + CT) and more fertile (OMT+MT) forest site types for which theproportions of observations accounted for 54% and 44%, respectively,and implied moderate growth improvement expectation. Thorium, onthe other hand, has been empirically shown to predict the clay contentof soils (Bierwirth et al., 1996). In the study area, γTh concentrationswere obviously high and γK concentrations relatively low, consistentwith the fact that low Potassium and high Thorium are inmost cases as-sociated with clay content and the presence of other resistant minerals(Wilford, 1992). Tree growth depends on the proportion of clay in thesoil, as it retains moisture and nutrients (Wilford, 1992). As a result, inmineral-only soils the γTh showed equal significance along with solarenergy. However, the AIC criterion was better in the case of the solar in-clusion in the improvedmodel, whichmay be due to partial collinearitybetween the explanatory variables. Nevertheless, the radiometric distri-bution patterns are always complexmixtures of effects and are not sim-ple to interpret, as they require more caution (Bierwirth et al., 1996).

As expected, the solar radiation (Table 3) behaved rather well in im-proving the growth estimation, since this radiation is one of the primarydriving factors affecting tree and timber growth (Bartelink, 1998; Donget al., 2012). Although the present results were applied to improve thepredictability of growth, the findings observed in this study mirrorthose of previous studies (Wang et al., 2007) that have examinedthe relation of γ-ray and DEM-derived on forest parameters, such assite index. The latter studies revealed that DEM-derived variables

performed slightly better than the γ-ray windows. The current workprovided insight about the possibilities of using DEM-derived or γ-rayto improve the overall growth estimation. Even so, the decision to seewhich group of explanatory variables (γ-ray or DEM-derived) wouldthe best to employ depends on many other factors that are beyondthe current work scope.

TWI index, was found to be significant in the present study in improv-ing the growth estimation, which corresponds to the earlier findings byOberhuber and Kofler (2000). Still, the limited terrain variation in thestudy area affected TWI in a certain way, particularly in moist locations(e.g., broadleaved). The Hillshade was neither influential nor significantin any model parameterizations tested. The reason for this was notclear. It might be due to the pronounced multicollinearity between thetwo groups of variables (γ-ray and DEM-derived variables) in additionto the low variation in topography in the region.

Other methods (e.g., Räty & Kangas, 2007; Sironen, 2009) of modellocalizations were considered too robust to be used in this analysis. Onthe other hand, the geographical extent of the present study data limit-ed the applicability of spatial indices in model localization.

Although the national model (Pukkala et al., 2013) predicted thebroadleaved more accurately than other models (Hynynen, 2002), thepresent study found it biased regionally in comparison with otherspecies (pine & spruce). This result may to some extent explain thesignificant change and improvement of RMSE between the nationalmodel and the improved model. However, this finding must beinterpreted with caution, because the datasets collected fromMatalansalo and Kiihtelysvaara differ in size. The stage of standdevelopment (i.e., young to mature) has a major effect on the growthpattern (Mehtätalo, 2004a) that may also explain differences betweenthe two study sites.

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5. Conclusions

The present results were significant in two major respects. First, theγ-ray along with DEM-derived variables could be used for improvingthe existing single-tree national growth model. Second, the combina-tion of both would always be an added advantage. The tree species' re-sponses were not the same: γ-ray and DEM-derived variables wereuseful in the case of broadleaved and contributed significantly to thereduction of RMSE and BIAS which improved the overall accuracy. Dif-ferent results were also obtained by different groups of forest sitetypes; the improvement was found to be more accurate in less fertilesite types. Further studies are recommended, for instance: i) to investi-gate species behaviors in a large geographical extent, ii) to analyze theissue of spatial indices in the model localization in the existence of γ-ray, and iii) to research the suitability of DEM-derived variables in com-parison to γ-ray.

Acknowledgment

This study was conducted in the University of Eastern Finland's(UEF) School of Forest Sciences and the Finnish Forest ResearchInstitute's Joensuu Unit. The researchwas funded by the Finnish Cultur-al Foundation (Grant-00130675, Central Fund).We are grateful to theseinstitutions for resources and funding.Wewould like to thankDr. SannaHärkönennen and Dr. Jari Vauhkonen for their help in data compilation.We are especially grateful to Yolande Mclean for language revision.

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