GEOSTATISTICAL TECHNIQUE FOR GROWING STOCK ESTIMATES ON SMALL FOREST STANDS USING INVENTORY, ENVIROMENTAL AND LANDSAT 8 DATA

Regular forest inventory on state owned forest delivers plenty of data and information enabling detailed insight in forest structure and quantities. Current methodology for forest assessment on private properties considers time-consuming, low-intensive terrestrial measurement and observation on scattered small forest stands distributed on hilly and plane position around complex of state owned forests. Here are evaluated two modeling techniques: ordinary least square (OLS) regression and geographically weighted regression (GWR) estimating growing stock quantities of point sample inside the smallest state owned forest stands (area less then 10 ha). Used material contained forest attributes local estimates from regular inventory distributed in unique management class: beech and fir mixed forest on deep silicate soil, environmental and transformed spectral Landsat 8 data. Obtained results pointed out statistical significance of normalized standardized spectral radiance of NIR and SWIR Landsat bands in regression models. The GWR estimates achieve up to almost 30% higher variability explanation then OLS models. Also, GWR showed wider range then OLS estimates with smaller prediction errors. Evaluation on sample stand level resulted in reliable estimates of particular species or groups and total mean growing stock for all small stands. Further research about potential of GWR and other geo-statistical techniques for forest attribute estimates on more intensive point sample inside small spatial unit and/or whole spatial unit is recommended.


INTRODUCTION -Uvod
Recent studies about forest characteristics on large area integrate all available information compiled with multivariate analysis and geographic information system tools.
Lately forest terrain observations and measurements, environmental and remote sensing data are used as for land use classification so for prediction of forest end environmental management related variables (BARHOSA ET  Periodical intensive forest inventory on state owned management unit level deliver plenty of data and information for statistical characterization of forest resources. Knowing that spatial variation of forest characteristics over space could be modeled it is interesting to examine if regression based estimation of the most important forest attributes on small stands outside of forest complex are efficient enough to use such approach for private forest characterization.
Usually private forest properties are distributed on hilly sides around state forests and/or randomly scattered around with small area. Current forest resource characterization on private properties is based on limited measurement and ocular classification and estimation mainly without possibility to determine statistical estimation error. So compilation of terrestrial, environmental and spectral data could be examined in order to estimates forest characteristics on scattered small areas. Such possibility opens alternative solution for current time-consuming and manly nonreliable forest production estimates as the most important management information of private forest.
In this paper are developed and compared OLS and GWR regression models for the growing stock using forest inventory sample divided on the sub sample covering stands with more than 10 ha size and the sub sample with smaller stands (less then 10 ha) compiled with environmental and Landsat 8 spectral data. Estimates are developed using the first sub sample and evaluated on known ground data on the second sub sample.

MATERIAL AND METHODS OF RESEARCH -Materijal i metode istraživanja
Study area includes part of the state owned forest stands in Management unit Oskova. Study area, also as a part of the Forest Management area "Sprečko" is located in the north east part of Bosnia situated between Longitudes 18° 29 -18° 37' and Latitudes 44° 23 -44° 17' (Figure 1). The terrestrial measurement for the research was conducted in the summer 2012 and was part of regular forest inventory. Terrestrial sample in this study consists of 3034 sample plots distributed on square grid of 200 meter distance covering unique management class (code 1203). Each sample plot was consisted of system of concentric circles with one centre and different range radius. Forests species, diameter at the breast height and height are recorded as geo-position of circle centre and local estimates of forest attributes (growing stock total, per groups and the main species) are produced following standard inventory procedure. According to management classes classification chosen management class is named as beech and fir mixed forest on deep silicate soils.
Ground sample is divided in two sub samples: the first one consisting sample points in stands with more then 10 ha size (n=2993) and the second sub sample with smaller stands (less then 10 ha) (n=41). Information about forest stands with area less then 10 ha are given in table 2. As additional information here are used environmental data obtained using digital elevation model: slope, aspect, hill shade and altitude. Hill shade is calculated using information about elevation and azimuth of Landsat 8 satellite image complied in this study. A Landsat 8 imagery (Path 188/Row 29) covered the study area and was acquired on 21 July 2015. The pre-processing of the image included merging bands in one image, assigning projection that fits Bosnia (E=3908), changing image resolution to 20 m and extraction the study area from satellite image. Then digital values transformation was completed calculation top of reflection values. Not all bands were included in the research. It was used reflectance of six spectral bands [Blue RT , Red RT , Green RT , Near infrared (NIR RT ) and two short wave infrared (SWIR1 RT and SWIR2 RT bands). The pre-processing is performed using QGIS Open Source.
In this study two statistical approaches were used: parametrical ordinary leastsquares regression (OLS) and geo-statistical technique: geographically weighted regression (GWR). For OLS regression is used Statgraphics Plus 5.0 and GWR regression analysis is applied using Windows Application for Geographically Weighted Regression Modeling GWR4 (NAKAYA 2014).
The OLS regression is the most commonly statistical technique used for estimating forest attributes, where the depended variable is estimated by producing unbiased minimum sum of squared residuals depending of the predictors (MONTGOMERY ET AL., 2001). The equation used to perform OLS is given below:  are the regression residuals. Regression models, based on correlation anaylsis, are determined using stepwise regression and normalised standardized predictors. The same statisticaly significant predictors are used in GWR models. Geographically weighted regression considers geographically varying parameters. Conventional (Gaussian) GWR model is described by the equation: To fit a Gaussian GWR model it is necessary to specify several inputs behind dependent variable and predictors: (1) location variables as (x, y) coordinates, (2) character of independent variable (local, global) and (3) the kernel function for geographical weighting to estimate local coefficients, its bandwidth size, and model selection criteria that are necessary for finding the best bandwidth and for comparing it with other modeling results using the same data. Here are used terrain geo-location of sample plots (x, y), local character independent variables, fixed Gaussian distance, golden section search for optimal bandwidth size and AICc criterion. Detailed method and procedure description are given in NAKAYA (2014) and CHARLTON ET AL. (2006).
For OLS and GWR models determinations and correlation coefficients are obtained and compared. Growing stock estimates on known sample-based geolocation in small forest stand (less then 10 ha) are determined as prediction on nonsampled points. Samples based on OLS and GWR estimates are then compared with terrestrial determined samples using t-test for each small stand.
Also, growing stock distribution for broadleaves and conifers are compared in order to analyze differences in ranges of OLS and GWR estimates.

RESULTS -Rezultati istraživanja
In order to perform OLS and GWR regressions modelling, correlation between target variables (growing stock for the main species, groups: conifers and broadleaves and total) and spectral and environmental predictors are calculated ( The same predictors are used for GWR modeling and following models are determined: Geographically weighted regression considers local character of predictors with estimates of coefficient means in equations above. So, prediction values are connected with varying geo-position of circle centre in relation with predictors.
Following figures present observed versus predicted growing stock quantities of two regression types for broadleaves and conifers that are similar as the main species: beech and fir too. a.
b. Figure 1. Observed versus OLS and GWR predicted growing stock for broadleaves (a.) and conifers (b.) Slika 1. Observirane prema OLS i GWR procjenjenim vrijednostima drvne zalihe za lišćare (a.) i četinare (b.) Both regression methods show in average overestimated quantities less then ground observations and underestimate quantities above ground average. But it is visible that GWR slopes for both broadleaves and conifers are closer to ground observation then OLS slopes.
Determination and correlation of OLS and GWR models are given in table 6. The GWR models deliver higher determinations then OLS models. Determination improvement is achieved for all models and ranges from 18% to 30%. Finally, evaluation of OLS and GWR growing stock estimates using corresponding sample on stand level using t-test was performed for stands with less then 10 ha area (Table 7.   Obtained results related to significance of mean differences between ground and estimated sample values show non-significant differences for species or/and groups/total for both methods mainly. Then, we found that important information about possible estimates is related to sampling distribution of target variables. So here are graphically presented growing stock distributions for sample and predictions based on OLS and GWR models.  It is visible that GWR growing stock distributions have wider range and closer shape to ground distributions then OLS distributions for both groups (broadleaves, conifers). Significant correlations between spectral data and forest attributes are found and presented in this paper confirmed their role as in quoted researches where particular spectral bands or their transformations also become significant predictors. Also, GWR estimates deliver higher determinations up to 30% for all forest attributes then OLS estimates in all environmental conditions. Related to sample means differences the OLS estimates give better results than GWR for some small stands. ZHANG ET AL., (2008) found that OLS estimates are appropriate in homogenous forest stands without spatial autocorrelation (regularly distributed over space). Authors reported that GWR gave more accurate precision in case of clustered or randomly distributed trees over space. These points out the role of spatial patterns of plot (tree) locations. So detailed spatial pattern analysis should contribute to regression method selection too.

DISCUSSION
Analyzing whole ground sample and its estimates, the GWR preserves variability better what is influential for point based estimations (Figure 3.). Obtained results show potentials of OLS and GWR to integrate in small stand estimations to calculate not only forest attribute mean estimates then error assessment as on stand so for management class level.

CONCLUSIONS -Zaključci
Here are applied OLS and GWR regression estimates of forest attributes on geo-located points distributed on regular sampling scheme in order to connect with current standard inventory methodology.
The results of this study indicate that the geographically weighted regression method was more accurate in representing the variability of growing stock, providing up to 30% higher R 2 then ordinary least square regression. Then comparing observed and estimated values it is visible that, in average, GWR estimates are more close to observed then OLS estimates. Also, GWR growing stock estimates distributions cover larger range of values so it could be expected that this method preserve attributes variability more realistic on dispersed small forest stands with clustered or randomly distributed trees mainly situated on hilly position around state owned forests. In this case only transformed spectral Landsat 8 bands data were found as significant so further research could analyze other transformation as vegetation indexes, Tassel Cap and/or PCA components.
Obtained results indicate possibility to apply GWR on more intensive geolocated points sample inside small stand. Also, GWR has potential to determine estimates and statistics for whole spatial units what could be analyzed in further research as other geo-statistical techniques compiling inventory, environmental and spectral data (MENG 2014