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Application of Future TerraSAR Data for Improvement of Forest ResourceAssessments

Stefan Leyk1, Michael Koehl2, Felicitas von Poncét3

1 Swiss Federal Institute WSL;CH-8903 Birmensdorf stefan.leyk@wsl.ch

2 Dresden University of Technology (TUD),Chair of Forest Biometrics and Computer Sciences,

Tharandt, Germany; koehl@frsws10.forst.tu-dresden.de

3.Infoterra GmbH, Development & consultancy,D-88 039 Friedrichshafen;

Felicitas.Poncet@astrium-space.com

Presented at ForestSAT SymposiumHeriot Watt University, Edinburgh,

August 5th-9th of August 2002

ABSTRACTIn the context of sustainable forest management new requirements related to thecontent, scale, timeliness and cost efficiency of information are being imposed ontimber suppliers and environmental conservationists. Traditionally, forest inventorieshave been based on cost-intensive and time consuming field inventories. Thus newrequirements and financial constraints in public and private sector have caused asignificant need for new cost-effective methods for data collection respectively thedevelopment of efficient inventory designs.

For extensive areas forest surveys cannot be realized as full tallies but have to utilizesampling approaches. The cost-efficiency of sampling surveys may be increased bythe integration of field assessments and wall-to-wall remote sensing imagery. In thiscontext, the integration of SAR (Synthetic Aperture Radar) as remote sensingcomponent into combined sampling methods is of great interest for forest inventoryand monitoring due to the sensitivity of radar to structural characteristics of forestsand its capability to cover large areas at low cost with high temporal resolution.

The current study presents an approach for an efficient integration of X-band dual-pol and L-band polarimetric SAR in preparation for the future TerraSAR system asa remote sensing component under boreal conditions. Two different samplingapproaches were examined in test areas located in the boreal forest of EasternFinland: (1) stratified sampling and (2) sampling with regression estimators. Twoalternative stratification rules were tested: stratification with and without terrestrial a-priori information. Simple and multiple linear regression estimators were applied.Using a terrestrial survey with systematically distributed samples provided a detailedreference data source for studying the relation of the backscatter signal as auxiliaryvariable and the terrestrial information as variable of interest. Segmentation wasperformed to estimate radar cross section as a basis to apply regression orstratification. This results either in a segment-wise estimate of the variable of interestor broad strata.

As a central problem of the integration of remote sensing data and field assessmentsappeared the so called Small Area Problem (SAP); as terrestrial sample plots coverthe segment area only partly, they do not reflect the entire variation of forest patches,resulting in differences between the information obtained on terrestrial sample plotsand segments as application objects in relation to size, position and sensitivity of thebackscatter means to bias caused by radar specific image features.

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As a consequence of the SAP the variance of the estimates of the stratified samplecould be reduced only to a certain level. A higher efficiency of this method could beshown by using a simulative reduced terrestrial sample. By using the Neyman-allocation instead of the proportional allocation (Cochran 1972) the reduction of therequired sample size for a given accuracy could be realized. The two alternativeallocation rules did not result in large differences since the accurateness ofstratification could not be studied due to the SAP.

A modification of the terrestrial sample plot design was suggested in order to enlargetheir size and thus improve their applicability on the segment level.

For the sampling with regression estimators design a sub-set of sample plots wasselected. Strong correlations could be found and enabled to develop an efficientcombined sampling approach. This was emphasized by the fact that even theestimators obtained for reduced sample sizes showed relations as strong as for thecomplete sample. The most sensitive bands were the L-HH and L-HV. Thefeasibility of the method depends on the mean timber volume and on the saturationpoint of the signal. At least in the areas studied, regression sampling proved to be anappropriate method to increase the efficiency of forest resource assessments. Sincethe calculation of regression estimators is a complex statistical problem due to theunderlying assumptions and constraints a specific test design was developed to verifytheir applicability to the segment level.

The combination of both methods could be realised by stratified sampling withregression estimators and results in a cost-efficient design which is flexible for awide range of stand conditions such as tree species composition or timber volume.

Keywords and phrases: combined sampling methods, SAR, stratification, regression estimators, SAP

1.0 INTRODUCTIONThe fight against advancing deforestation, efforts to reduce the greenhouse gases in the atmosphere anddiscussions about climate and water protection are the driving forces for the development of a sustainablemanagement of natural resources and for the increasing need for adapted monitoring activities.In this context, high demands for forest resource assessments have been expressed with special emphasis tothematic content, scale, timeliness and cost efficiency for providing required information. Thus, conventionalcost-intensive and time-consuming field surveys have to be replaced. To conform to new requirements andfinancial constraints in public and private sector at the same time, new methods for more efficient inventorydesigns were investigated.These demands can be met by integration of remote sensing products as a data source into combined samplingmethods. During the last few years, the technology of geo-information and digital image analysis as well as thepotential to automate analysis processes developed rapidly; numerous optical as well as radar sensors providedata on an operational basis. The application of sensors in the range of microwaves renders the acquisition ofdata independently on clouds, the time of the day and the weather conditions possible. These are significantadvantages compared to optical sensors.The combination of terrestrial surveys and remote sensing products is widely accepted to be an appropriatemethod to increase the efficiency of a forest inventory. For the application of microwaves a great potential couldbe identified (Fransson 1999, FAO 1993, EUFORA 1996).

In this study different combined sampling methods based on airborne E-SAR (Experimental Synthetic ApertureRadar) data were tested under boreal conditions. The objective of the study presented was to show their potentialto increase the efficiency in the context of operational forest resource assessments, where growing stock wasselected as a key attribute to demonstrate the operational application of the methods developed.Alternative sampling methods, such as stratified sampling and sampling with regression estimators were appliedto demonstrate the gain in efficiency compared to survey approaches that are limited to field assessments only.The relations between Radar and terrestrial information were studied in a test area for which radar imagery andfield assessments were available for the same point in time.The work took place within the framework of the ProSmartII project, spearheaded by InfoTerra GmbH and co-funded by DLR (Deutsches Zentrum für Luft- und Raumfahrt e.V.). The aim of ProSmart is to develop productconcepts and methods on the basis of simulated SAR data in preparation for the future TerraSAR X-band dual-pol and L-band polarimetric SAR system. Thus, the existing possibilities can be demonstrated to potential users

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of these products. By directly involving these potential users, the products can be adapted to tendencies on themarket and demands of clients.

The presented study was done on behalf of the Infoterra GmbH (Friedrichshafen/ Germany) as a part of theProSmart II forestry project “INVENT” (Development and validation of a concept for the operational use ofradar derived information for commercially oriented boreal forest inventories). Stora Enso Forest ConsultingLtd and Jaakko Pöyry Soil and Water (Finland) represented the potential users of Terra-SAR derived geo-information products and formulated the demands for a product that enables the user to realize a woodprocurement inventory in the boreal region. Detailed user requirements are listed and described in Kretschmar etal. (2000).

2.0 STUDY AREA AND DATA

2.1 Study AreaThe study area of the project “INVENT” is located in south-eastern Finland near the Finish-Russian border. StoraEnso Ltd. is the owner of the 5 000 ha boreal forest area, within which an area of 712.5 ha in size was selected asstudy area. The following descriptions concern this part.Due to the extensive management during recent years, short-term impacts in larger extents can be excluded.Some parts of the study area are hilly with rocky portions. About 5 percent of the area is covered by water. Themost frequent stand site is the Myrtillus-Type (finish nomenclature); mire sites can be observed especially closedto small lakes.Approximately 90 percent of the forests are dominated by pine. Smaller proportions consist of spruce, birch andlarch. The variation inside the stands has shown to be higher than expected caused by mixtures of tree speciesand the existence of several stand layers. The mean growing stock was estimated to be between 120-150 m3/ha.

2.2 Data2.2.1 Remote Sensing Data and Terrestrial Reference Data

For this study a multi-frequent and multi-polarimetric E-SAR-system for high-resolution data of five bands(XHH, XVV, LHH, LHV and LVV) from the year 2001 were available. The quality was partially not satisfyingbecause of signal disturbances in the X-band data.

For geo-referencing and evaluation digital true-colour aerial photographs of the Stora-Enso-Mosaic could beused. Due to some geographical inaccuracies they were used for visual comparison only.

During a field campaign in August 2001 a systematic sample of 114 circular field plots with 8.5m in diameterwas assessed in the study area. Several attributes were measured for individual trees, such as stem number (N),diameter at breast height (DBH) or total height.

In addition digital standregister data (GIS) from theStora Enso Ltd. was availableas a second source ofterrestrial information.

Illustration 1: Subsetof the study area;right: SAR data withgeo-referencedlocations of fieldplots; left: result ofthe segmentation

2.2.2 Pre Analysis

SegmentationBasically, the aim of segmentation is the reduction of the variance of backscatter values by subdividing the totalarea into smaller patches, which are as homogeneous as possible and thus result in the reduction of Speckle.Segmentation was performed with the software eCognition, which requires the definition of different parameters

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like scale, shape and colour. The resulting segment means and other derived features could be used for signatureanalysis.

Signature analysisTo investigate the relation between the radar backscatter and terrestrial information a first signature analysis wasperformed in two steps: Firstly, the relation between the segment backscatter means and the GIS information wasstudied. Secondly, the terrestrial information from field plot and the extracted backscatter means from therespective sample plot areas were used to facilitate a more detailed approach of investigation. Thus, two differentlevels of spatial resolution were analysed.

The segment means were related to GIS information and did not show significant trends for separation of classesor correlation. The reason can be found in the different spatial resolution of information units. While the segmentmeans still show a high variance inside one GIS stand polygon the GIS information naturally gives one value forthis area. The high variance of the segment means indicates heterogeneity inside the stand. The existing trendssolely could give advices for further analysis.

In the second part of the signature analysis, more detailed information on small spatial units, i.e. the sample plots,was available and allowed for study of the relation between the backscatter means of the field plots and theterrestrial information: The separation of tree species could not be verified. For growing stock a weak correlationwas found and showed a significant separability of three growing stock classes. An even more promising trendcould be found after the introduction of an index value that was derived as a function including stem number (N)and DBH (index value=√N ·DBH). Using the index value as terrestrial information a higher correlation ofgrowing stock volume and backscatter means could be found and enabled to separate ordinal classes for laterclassification processes.These findings still did not satisfy the demands for a practical application of combined sampling methods due tothe so-called Small Area Problem. Since this problem is of central importance for the methodology of this studyit will be explained in the next section.

3.0 METHODS

3.1 Methodological approachBoth methods, stratified sampling and sampling with regression estimators, should be applied for a forestinventory with focus to the growing stock and the gain in efficiency compared to 1-phase sampling (fieldassessments only) should be determined.The principal approach is presented in illustration 1. Basically, the relations between the radar signal and theterrestrially assessed growing stock had to be examined and implemented in the classification processes and theregression analyses. The means of both, the radar backscatter and the terrestrial values, were taken from insidethe sample plots for analysis. The relations found were applied for entire segments in the sampling procedure(application), which allowed covering the entire study area.

The equations applied were takenfrom the relevant literature forsampling methods (see Köhl 1994,Bainbridge 1992, Borders/Shivers1996, Cochran 1972, Bortz 1999,Sachs 1997) and are summarized byLeyk, 2002. A selection will bepresented in this paper.

Illustration 2: Overviewmethodological approach

3.1.1 The Small Area Problem (SAP), Selection, valid Range

As a central problem of the integration of SAR data and field assessments the so-called Small Area Problemappeared. The SAP results from differences between sampling units as analysis objects and segments asapplication objects. These differences appeared in relation to size, position and sensitivity of means to bias

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where extreme backscatter values occurred. Classification results and regression models were based on theanalysis on the level of sample plots using the terrestrial variables of interest and the backscatter as auxiliaryvariable. To apply these models to the level of segments both data categories and their comparability to eachother had to be examined in more detail.

The small number of pixels per sample plot (56 pixels) led to a high sensitivity of their mean values to bias insituations where extreme backscatter values occurred. The occurrence of radar specific imaging characteristicssuch as radar shadows led to biased backscatter means of numerous sample plots (see illustration 3). In addition,inaccuracies of the sample plot positions in the field caused by GPS-deviations augmented these effects.Deviations between expected and observed backscatter values caused that the true relations between field dataand resulting backscatter were hidden. Transferring this situation inside any segment would lead to a muchsmaller impact to its mean due to the high number of pixels determining the mean backscatter of a segment. Thesize of segments is mainly influenced by the scale parameters used in the segmentation process and has beentuned to meet given stand borders. Thus, rather large patches were created compared to sample plots.

The true relation between field information and backscatter could only be investigated if biased means on thesample plot level could be identified and eliminated from the analysis. After truncating the available data set theprojection of the analysis results from the sample plot level to the segment level could be realised. Therefore, theproperties of the analysis object (field plot boundary) and the application object (segment boundary) werecompared and the general applicability of the sampling method could be tested.

Illustration 3: Two examples of the SmallArea Problem; above: Field plot crossingthe forest edge, the terrestrial growingstock has been measured inside the standbecause of the GPS-navigation error.Thus, the terrestrial information did notconform to the backscatter mean whichhas been a significantly smaller value thanwould have been expected in relation tomeasured growing stock.

Below: Typical case of a radar shadow.The measured backscatter mean has beenbiased extremely and did not conform tomeasured terrestrial growing stock.

For the regression analysis an improvement of the relationship between field data and backscatter could beexpected for unbiased sampling units. For the application of stratification, however, the truncation of data can beseen as a spatial filter and results in the elimination of variability making inference about the performance of theapproach more complicated.

3.2 Stratified SamplingTwo different approaches for stratification were applied in this study: Pre-stratification with a-priori-informationand pre-stratification without terrestrial a-priori-information. In order to examine the effects of stratification inmore detail a reduced sample size of field plots was simulated. The following equations were applied to estimatethe variance and standard error of means, )y(v St

and )y(s St, and totals, )Y(v and )Y(s :

��

�

L

h h

hhSt n

sw)y(v1

22)y(v)y(s StSt �

)y(vN)Y(v St2

� )Y(v)Y(s �

wh: weight of the strata hSty : estimated mean of the stratified sample

N: total number of elements of the sample 2hs : variance of the strata h

nh: number of elements of strata h

6

Stratified Sampling with a-priori-informationThis approach can be applied where information about the area is available before the terrestrial data is assessed.A-priori-information can be derived from remote sensing components or from previous assessments on smallrepresentative areas. Where the analysis on the level of sample plots was satisfying supervised classificationcould be done to derive thematic classes and thus define thematic strata on the level of segments (see illustration2).Due to the small number of sample units available for the study, terrestrial a-priori-information had to besimulated. Attributes such as growing stock or the introduced index value were used for different stratificationrules. An alternative approach was the integration of regression estimates after their conversion into ordinal data.In spite of the realized separation of those classes problems were to be expected caused by the SAP.

Stratified Sampling without terrestrial a-priori-informationAs a second scenario for stratified sampling, the lack of any terrestrial pre-information was assumed. In this casethe strata have to be derived from classes that are obtained from unsupervised classification processes. Usually,the resulting strata are non-thematic. In this study, single bands, combinations of bands and hierarchicalapproaches were applied to derive strata on the basis of pure backscatter mean values. A comparison of bothapproaches is of major interest for practical applications, as the derivation of terrestrial information is a timeconsuming process.

Simulation of a reduced sample sizeTo demonstrate the effect of stratification in more detail a reduced sample size of field plots was simulated thatreflects a more applied situation of a real world forest inventory.

3.3 Sampling with regression estimatorsReferring to the signature analysis, the application of regression estimators seemed to be a promising approachfor estimating the terrestrial growing stock. The application of regression estimators is realised under theassumption that the size of the auxiliary variable is known. Generally, it is taken from a full tally, which rendersthe calculation of the true mean of a population possible. In the scope of the present study simple and multiplelinear regression estimators were applied.For a statistically sound application of regression estimators several other assumptions had to be met. Theseassumptions can be found in the literature (e.g. Sachs 1997, Bainbridge 1992, and Leyk 2001) and will not beexplained in detail but to a certain extent be mentioned in different contexts.As for the other sampling approaches, the analysis object to derive the regression model was the sample plot forsampling with regression estimators. Sub-samples of both variables, the backscatter mean and the terrestrialattribute, could be assessed from inside the field plot boundary to calculate the regression functions. The segmentwas used as application object to estimate the growing stock on the basis of the backscatter segment mean andthe developed regression models.

An optimal regression modelSince correlation between radar backscatter and growing stock could be identified in the signature analysis theselection processes could be initialised to find the true relation. Therefore, it was necessary to eliminate thesample plots, which suffered from the SAP.At the end of the selection processes 76 of 114 sample units were considered to match the criterion of beingunbiased and were included in the study.

Simple linear regressionThe bands LHH and LHV were considered for the selection process as they showed the highest sensitivity for theterrestrial growing stock. The correlation coefficients of the resulting regression models were r2=0,632 for LHHand r2=0,584 for LHV. Thus, considerably strong regression estimators could be developed and applied forgrowing stock estimation on the level of segments. The estimation equations for the mean of the variable ofinterest (

lry ), for variance of the mean ( )y(v lr) and for standard error of the mean ( )y(s lr

) were:

)x(byy xlr ��� �

� �

)n(n

)xx(b)yy()y(v

n

iii

lr 2

2

1

�

���

�

��

)lrlr y(v)y(s �

µx: true mean of the auxiliary variable xi a: regression constant

x : Mean of the auxiliary variable xi of the sub-sample )y(v lr: variance of the estimated mean y lr

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b: regression coefficient using the least squared method )y(s lr: standard error of the estimated mean y lr

y : mean of the variable of interest in the sub-sample

Multiple linear RegressionIn some cases regression estimate can be improved by applying multiple linear regressions and thus, includingmore than one band as auxiliary variable. Several band combinations were tested and the calculated correlationcoefficients for multiple-linear regression led to stronger relations than for simple linear regression.An operational problem occurred because of inconstant offsets of the backscatter values of the same or ofdifferent bands to each other at different points in time.

Realisation of a reduced sampleSimilar to stratified sampling a reduced sample was applied to investigate the effect of the combined samplingmethod for a smaller sample size of 57 randomly selected elements. After the selection was done 38 sample plotsremained to be included in regression analysis.Surprisingly, the correlation coefficient for LHH was in the same range as for the total sample above- indicatingthe existence of a truly existing strong relation between backscatter and growing stock on the level of sampleplots.

Approving the regression models for application objectsThe regression estimates obtained (on the level of sample units) were to be applied to the level of segments asapplication objects. Thereby, the Small Area Problem came into focus again. Since the analysis objects (sampleplots) were used to develop regression estimators independently from the application objects (segments) theproperties of both object classes had to be investigated. One precondition for the application of the regressionmodels on the segment level was the transferability. That means, the amount of segment means used for theestimation of segment-wise growing stock had to show the same properties as the amount of sample plot means.Only then the regression functions could be projected to the segment means. Statistically, the distribution, meanand variance of these two populations had to be equal.Practically, the regression model under concern has been applied to all 114 sample plots. Negative estimateswere excluded from further consideration. As negative values do not reflect any realistic values for growingstock, the exclusion was reasonable. For all remaining sample plots the mean and variance of the backscattermeans were calculated.In the second step the same procedure was realised with the amount of segment mean values. Again, the negativeestimated segment-wise growing stock values were excluded and the positives remained for further consideration.The two populations (sample plot mean backscatter and segment mean backscatter) of the remaining values werecompared to each other. After the tests of equality of populations (Kolmogoroff-Smirnoff 2 sample test) and thetest of equality of means (T-Test for two independent samples) have been applied there was no statisticalsignificance between the mean values. The hypothesis of equal means was not rejected, given that equality ofvariances has been proven.The objective of the above described approaches was to solve the Small Area Problem. A major issue was toguarantee the comparability of the sample plot and segment values. The magnitude order of these two objects hasto be similar, statistically, in order to make the projection of the analysis result of one level onto the other levelpossible. After the selection procedure was conducted it became obvious that the properties of the populationcould be maintained and the populations could be considered as equal. Thus, the projection of the regressionestimators to the level of segments results in reliable estimates.

4.0 RESULTSIn the following the main results are presented briefly for the example of growing stock estimates. The userrequirements for desired precision of growing stock estimations were assumed to be roughly 15m3/ha for themean and 10000m3 for the total growing stock. Estimations of required sample sizes were referred to theseassumptions.

Both combined methods showed a gain in statistical efficiency. The most efficient sampling method for the totalsample size was the stratified sample whereas regression estimators led to a higher efficiency applying thereduced sample size.

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114 57

136,38 125,48

8,75 10,62

134,28 125,57

7,22 7,91

r² 0,63 0,66

130,64 129,54

7,50 7,418

Sampling with Regression Estimators

sample size

Stratified Sampling

1-phase Sampling

)y(vs Sty St�

)y(vs lry lr�

)y(vsy

�

]ha/³m[y

]ha/³m[y St

]ha/³m[y lr

114 57

8,75 10,62N requ. (prop) 149 110N requ. (ney) 156 114

4,66N requ. (prop) 44N requ. (ney) 33,60

Deff 0,28

7,25 7,91N requ. (prop) 110 67N requ. (ney) 100 58

Deff 0,69 0,55

7,22 7,94N requ. (prop) 122 69N requ. (ney) 105 62

Deff 0,70 0,58

sample size

Stratification with terrestrial pre-information

Stratification without terrestrial pre-information

Poststratification

1-phase Sampling

)y(vs Sty St�

)y(vsy

�

)y(vs Sty St�

)y(vs Sty St�

Table 1: Results of 1-phase-samplingand different stratified sampling methods(nrequ.=required sample size;prop=proportional; ney=Neyman-allocated; Deff= Design effect)

For 1-phase sampling the estimated mean growing stock was136.38m3/ha (see table 2), the total growing stock 97172.69 m3.Considering the obtained standard errors of the mean (8.75m3/ha)and the total value (6232.44m3) growing stock was estimated with aconsiderably high accuracy and thus small variances. The requiredsample sizes for above mentioned accuracy were n=149 (see table1) and N=171.As expected, the values for standard errors and required samplesize increased for the reduced sample to simulate a more realisticapproach for combined sampling methods (see table 1 and 2).

To evaluate the gain in efficiency for stratified sampling compared to SRS the Design effect (DEFF) was used.The DEFF is given by the ratio of the variance of the considered complex sample to the variance of SRS of thesame number of elements (Rosander 1977).More than 20 stratification rules were tested for both approaches with and without a-priori-information. Aspresented in table 1, there was almost no difference in relation to standard errors between these two scenarios.The variance could be reduced only to a certain level. The Design effects were around 0.7. The more efficientmethod was the stratification without terrestrial a-priori-information since the effort to reach the same result hasbeen smaller than for stratification with terrestrial a-priori-information.Applying the reduced sample size, a higher gain in efficiency was calculated through stratification. Hereby, thereduction of the total variance was obtained to a higher degree (see Table 1).As presented in Table 1, these results are emphasized by considering the required sample sizes for the abovegiven accuracies using the proportional allocation (nreq(prop)). For the reduced sample size, an even morepronounced reduction of the required sample size compared to SRS could be observed (see Table 1).Additionally, the Neyman-allocation was applied. An even higher reduction of the sample size (nreq(ney))succeeded, including simulated information about the within strata variance (see Table 1).As a third method a post-stratified sample was applied for evaluation purposes. Since in post-stratification theterrestrial sample is assessed before the stratification process, it is not possible to reduce the sample sizeaccording to strata characteristics but the total variance (Shiver/ Borders 1996). As this method led to a reductionof total variance, the existence of true homogeneous subpopulations became evident. As presented in Table 1, thevariance could even be more reduced than for any other stratification rule. Thus, a problem in achievinghomogeneous subpopulations in pre-stratification became obvious.

Table 2: Comparison of samplingresults from stratified sampling andsampling with regression estimators(represented are the standard errorsof the means and mean values; for

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Linear regression for growing stock

y = 4,9139x - 711,63r2 = 0,6317

-50

50

150

250

350

100 120 140 160 180 200

LHH-backscatter inside field plots boundaries

grow

ing

stoc

k m

³/ha

regression the correlation coefficient)As already mentioned, the most sensitive bands for terrestrial growing stock were LHV and LHH. Various simpleand multiple linear regression models were tested and the standard error of the mean value could be calculated.The smallest standard errors obtained were 7.5m3/ha and even 7.4m3/ha for the reduced sample as presented inTable 2. These results indicate very robust regression models resulting in higher efficiencies than stratificationfor the reduced sample and a significant gain in efficiency compared to 1-phase-sampling. The true populationparameters were underestimated by approximately 5 percent (see Table 2). The saturation point of the radarsignal was obtained between 120 and 130m3/ha. Saturation is the point where the change of the variable ofinterest does no longer explain changes of the auxiliary variable. This procedure seemed to be the mostpromising method for a forest inventory under boreal conditions although the growing stock of small patchescould not be estimated with high precision.

5.0 CONCLUSIONSThe objective of the presented study was to examine the efficiency gains of a forest inventory for growing stock.Therefore, the combined methods stratified sampling and sampling with regression estimators on the basis ofSAR were applied and compared to each other under constant conditions.For both combined methods, an increase of efficiency was found. While for the total terrestrial sample thestratification led to a slightly higher efficiency than regression, the results for a reduced sample were different.The regression estimators appeared to result in strong relationships and represented the highest increase ofefficiency for the reduced sample.

The limited gain in efficiency for Stratified Sampling was due to the Small Area Problem. Since sample plots forwhich biased backscatter signals were observed were maintained in the analysis to keep the equal selectionprobability, a certain portion of elements was wrongly classified. Therefore, the needed homogeneity inside thestrata after the application to the level of segments could not be achieved and the reduction of total variancepartially failed. Thus, the true quality of stratification could not be presented.The explanation for the suitability of regression estimators for LHH and LHV under the presented conditionscan be found considering illustration 4. The saturation point approximately corresponded to the terrestrialgrowing stock mean. Thus, the overestimations in the range of small growing stock and the underestimations inthe range of high values of growing stock equalized approximately over the whole range. Consequently, thesuitability of the method seems to be dependent on the mean growing stock over the inventory area and on the

saturation point of the backscatter. For areas with similarconditions as the presented research area, regressionestimators seem to be the optimal design for a forestinventory of growing stock since small sample sizes led to asignificant gain in efficiency.

Illustration 4: Linearregression estimator for LHHto estimate the growing stock

To overcome the Small Area Problem for stratification the properties of sample units and segments have to bestudied. One possibility to modify the object properties would be the reduction in size of the segment and at thesame time the enlargement of the sample plots (see illustration 5). For this situation, the mean values of bothobjects are comparable and the transfer of analysis results from sample plots to segments would lead to asuccessful subdivision into homogeneous subpopulations. Consequently, the variance of the sample could befurther reduced and a more efficient sampling approach could be designed. The limitations in relation to thecritical size of segments and to the optimal sample plot size and number had to be discussed.

Illustration 5: Exemplarymodification principlesto approach thebackscatter mean

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properties of segments and field plotsUnfortunately, the potential of the new introduced index value could not be proven since the stratificationsuffered extremely from the Small Area Problem. But the application of such artificial measures with a highsensitivity to radar backscatter should be further investigated.Stratified sampling as well as a combined approach of both combined sampling methods after the mentionedmodifications are made, seem to be promising for operational applications and should be focused in furtherinvestigations. Thus, sampling methods with a higher flexibility could be established and studied under differentconditions.The results presented should encourage continuing investigation of SAR data in relation to more efficient forestinventory designs to conform to current demands.

ACKNOWLEDGEMENTSSpecial thanks should be concerned to the Infoterra GmbH. for giving the opportunity to conduct this study.For the availability of the field survey data, assessed by the project “BART”, special thanks go to KonstantinOlschofsky, Dresden University of Technology. Furthermore, we gratefully acknowledge the kind support of theStora Enso Forest Consulting Ltd and the German Aerospace Center, DLR, Bonn.

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