Model-assisted regional forest biomass estimation using LiDAR and InSAR as auxiliary data: A case...

Remote Sensing of Environment 115 (2011) 3599–3614

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Remote Sensing of Environment

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Model-assisted regional forest biomass estimation using LiDAR and InSAR as auxiliarydata: A case study from a boreal forest area

Erik Næsset a,⁎, Terje Gobakken a, Svein Solberg b, Timothy G. Gregoire c, Ross Nelson d,Göran Ståhl e, Dan Weydahl f

a Department of Ecology and Natural Resource Management, Norwegian University of Life Sciences, P.O. Box 5003, NO-1432 Ås, Norwayb Norwegian Forest and Landscape Institute, P.O. Box 115, NO-1431 Ås, Norwayc School of Forestry and Environmental Studies, Yale University, 360 Prospect Street, New Haven, CT 06511-2189, USAd Biospheric Sciences Branch, Code 614.4, NASA-Goddard Space Flight Center, Greenbelt, MD 20771, USAe Department of Forest Resource Management, Swedish University of Agricultural Sciences, SE-90183 Umeå, Swedenf Norwegian Defence Research Establishment, Land and Airsystems Division, P.O. Box 25, NO-2027 Kjeller, Norway

⁎ Corresponding author. Tel.: +47 64965734; fax: +E-mail address: [email protected] (E. Næsset).

0034-4257/$ – see front matter © 2011 Elsevier Inc. Alldoi:10.1016/j.rse.2011.08.021

a b s t r a c t
a r t i c l e i n f o
Article history:Received 27 January 2011Received in revised form 25 August 2011Accepted 27 August 2011Available online 28 September 2011

Keywords:Forest monitoringLaser scanningSARProbability sampling

There is a need for accurate inventory methods that produce relevant and timely information on the forestresources and carbon stocks for forest management planning and for implementation of national strategiesunder the United Nations Collaborative Program on Reduced Emissions from Deforestation and Forest Degra-dation in Developing Countries (REDD). Such methods should produce information that is consistent acrossvarious geographical scales. Airborne scanning Light Detection and Ranging (LiDAR) is among the mostpromising remote sensing technologies for estimation of forest resource information such as timber volumeand biomass, while acquisition of three dimensional data with Interferometric Synthetic Aperture Radar(InSAR) from space is seen as a relevant option for inventory in the tropics because of its ability to “seethrough the clouds” and its potential for frequent updates at low costs. Based on a stratified probability sam-ple of 201 field survey plots collected in a 960 km2 boreal forest area in Norway, we demonstrate how totalabove-ground biomass (AGB) can be estimated at three distinct geographical levels in such a way that the es-timates at a smaller level always sum up to the estimate at a larger level. The three levels are (1) a district(the entire study area), (2) a village, local community or estate level, and (3) a stand or patch level. TheLiDAR and InSAR data were treated as auxiliary information in the estimation. At the two largest geographicallevels model-assisted estimators were employed. A model-based estimation was conducted at the smallestlevel. Estimates of AGB and corresponding error estimates based on (1) the field sample survey were com-pared with estimates obtained by using (2) LiDAR and (3) InSAR data as auxiliary information. For the entirestudy area, the estimates of AGBwere 116.0, 101.2, and 111.3 Mg ha−1, respectively. Corresponding standarderror estimates were 3.7, 1.6, and 3.2 Mg ha−1. At the smallest geographical level (stand) an independent val-idation on 35 large field plots was carried out. RMSE values of 17.1–17.3 Mg ha−1 and 42.6–53.2 Mg ha−1

were found for LiDAR and InSAR, respectively. A time lag of six years between acquisition of InSAR dataand field inventory has introduced some errors. Significant differences between estimates and referencevalues were found, illustrating the risk of using pure model-based methods in the estimation when thereis a lack of fit in the models. We conclude that the examined remote sensing techniques can provide biomassestimates with smaller estimated errors than a field-based sample survey. The improvement can be highlysignificant, especially for LiDAR.

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1. Introduction

The world's forests sequester more carbon than any other terres-trial ecosystem and account for 90% of the annual carbon flux be-tween the atmosphere and the Earth's land surface (Winjum et al.,

1993). Thus, forests play a critical role in the global carbon cycle. Real-izing that tropical deforestation and degradation amount to about 20%of the annual human induced emissions of carbon dioxide (IPCC,2007), there is a broad consensus that measures are required to includemechanisms for protecting the tropical forests in future climate treaties.The United Nations (UN) Collaborative Program on Reduced Emissionsfrom Deforestation and Forest Degradation in Developing Countries(UN REDD) (http://www.un-redd.org) was launched with the aim ofcontributing to the development of capacity for reducing emissions

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3600 E. Næsset et al. / Remote Sensing of Environment 115 (2011) 3599–3614

from loss of forest carbon in developing countries. It is also understoodthat REDD mechanisms must be supported by forest assessment pro-grams that can monitor the carbon stocks. Although national estimateswill be required, many countries are likely to benefit from more localmonitoring programs within the countries as well, gauging the effectsof national policies and local financial mechanisms aimed at reachinggoals for emission control for the nation as a whole. Thus, there willbe a need for systems for forest carbon assessment and monitoring ata broad range of geographical scales, with frequent temporal revisit,and with high accuracy requirements.

The need for local monitoring systems (REDD projects within coun-tries) in particular seems to coincide well with recent developments inforest inventory seen in other parts of the world. Traditionally, groundbased sample surveys have been employed to assess forest resourcesand carbon stocks at a national level. National forest inventory pro-grams have typically served this purpose. At more local scales, samplesurveys and area-based methods have been used separately or in com-bination, with a trend towards area-based methods the smaller the tar-get area is. Sample surveys typically consists of field plots selectedaccording to a given sampling design and distributed across the entiretarget areawhile area-basedmethods typically take a “wall-to-wall” ap-proach where estimates are provided for every unit (e.g. forest stand)across the target area using for example interpretation of aerial photog-raphy and/or intensive field work in every forest stand in question. Inorder to reduce costs and improve accuracy, remote sensing data havebeen used as an integral part of the inventory design.

Airborne Light Detection and Ranging (LiDAR) has emerged as oneof the most promising remote sensing technologies for estimatingabove-ground tree biomass. LiDAR depicts the horizontal and verticaldistribution of biological material with high spatial resolution, andthis depiction can be used to provide estimates of biomass and tree car-bon stocks. In several countries, airborne scanning LiDAR has during thelast decade been used operationally for forest management inventoriesat a typical district level (~50–2000 km2) (Næsset, 2004b; Næsset et al.,2004). Although operational use of airborne LiDAR for forest resourceassessment seems to be most common in boreal and temperate forests(McRoberts et al., 2010), promising results for estimating biomass oftropical forests have also been reported (Clark et al., 2004; Drake etal., 2002, 2003; Lefsky et al., 2002; Nelson, 1997; Nelson et al., 1997;Weishampel et al., 2000). Lately, the potential of airborne LiDAR forREDD monitoring has been emphasized (Angelsen, 2008; Gibbs et al.,2007). Asner (2009) recently proposed a REDDmonitoringmethodolo-gy utilizing airborne scanning LiDAR in combination with other remotesensing data where LiDAR is used in a similar way as the two-stagemethod proposed for wall-to-wall stand-based forest management in-ventory (Næsset, 2002). New Zealand recently started to use LiDAR asa means to estimate carbon stocks of planted forests for reporting onthe Kyoto Protocol (Beets et al., 2010).

Currently, LiDAR data for forest inventory are only available fromairborne platforms, although the planning of space LiDAR missionsis in progress. Thus, the costs of acquiring LiDAR data are currentlyhigh compared to acquisition costs of data from different types of sat-ellite sensors (e.g. optical imaging and radar sensors). As with opticalimaging sensors, LiDAR is hampered by clouds, which limit the oper-ational range of LiDAR in parts of tropical rain forests.

Synthetic Aperture Radar (SAR) operated from satellites is a less ex-pensive and promising technology for biomass assessments over vastgeographical areas. One advantage of SAR is the ability of SAR micro-waves to penetrate clouds, and hence to acquire data under cloudedconditions. SAR biomass models based on backscatter intensity havethe limitation that they saturate far below maximum biomass valuesin forests. The reported saturation levels for the wavelengths currentlyavailable in satellites (X-, C-, and L-band) are about 20–100 Mg ha−1,which represent a typical low biomass situation, although highervalues are occasionally given, partly explained as a result of differencesin the definition of a saturation level (Imhoff, 1995; Kuplich et al.,

2005; Lucas et al., 2007; Mitchard et al., 2009; Santos et al., 2003).There are also problemswith poor accuracy due to variability in weath-er conditions such as moisture, frost, and wind (Eriksson et al., 2007;Ranson & Sun, 1997). A more promising method is interferometricSAR (InSAR), which in combination with a digital terrain model(DTM) (subtracting the DTM from the InSAR elevation) providesradar echo height above ground (InSAR height). InSAR height is strong-ly related to the height of forest canopies (Kellndorfer et al., 2004;Kenyi et al., 2009; Sexton et al., 2009; Weydahl et al., 2007) and alsoto above ground biomass (Gama et al., 2010; Solberg et al., 2010a,b).InSAR data suitable for forest applications are available from bothspaceborne and airborne platforms, in particular the Tandem-X satel-lite mission and airborne combined X- and P-band systems such asthe OrbiSAR. Although InSAR is less accurate than airborne LiDAR dueto coarser geometric resolution than LiDAR and slant angle acquisition(Solberg et al., 2010a), the costs of acquiring satellite SAR data are con-siderably lower than LiDAR. When previous wall-to-wall LiDAR datahave been acquired for topographic mapping purposes as a onetimeoperation for an Area Of Interest (AOI), a highly accurate terrainmodelwill be available as reference surface for subsequent and repeatedInSAR canopy height retrievals, thus facilitating improved estimates ofbiomass. In the absence of detailed LiDAR DTMs, more coarse resolutionDTMs are the only alternative for determination of InSAR canopy heights(Solberg et al., 2010a).

The accuracy requirements and the geographical level of reportingfor districts or smaller administrative units (counties or municipali-ties) are often similar for forest inventories in developed and devel-oping countries. In the latter case, there currently is great interest inlocal monitoring under a REDD mechanism. Regardless of the setting,there will often be a field sample survey designed for the entire AOI.The smallest unit where estimates are sought might typically be “for-est stand” or “patch” (~0.1–10 ha), where field sample data can hard-ly be expected to be available for every unit. Hence, remotely senseddata must play a crucial role in the estimation. For larger AOIs – onthe order of, say, 10,000–200,000 ha – estimation can be based purelyon sample surveys provided a sufficient sample size, but precisionmay be improved by combining remote sensing data with the samplesurvey. In between these two geographical levels, there might be athird distinct level, typically being an individual forest estate, village,or local community, say, ~100–10,000 ha in size, where some fieldsamples in many cases will be available. However, the number ofsample plots will decline with decreasing size of the target area.Thus, remotely sensed data will most likely improve the precision ofthe estimates if strong relationships exist between the target variableto be estimated and the available remote sensing variables.

When LiDAR or SAR is used for estimation, field plots co-registeredwith these remotely sensed data must be measured in order to developpredictive models of biophysical properties of interest, e.g., biomass, car-bon, or volume. In forest management inventories the field sample sur-veys are sometimes conducted according to systematic designs (with arandom start) (Næsset, 2007) or according to random designs and fre-quently also stratified on the basis of prior information about the forest(Næsset, 2004b). Because of the randomization in the selection of popu-lation units for the field sample, design-based approaches to estimationand inference may be applied and one may take advantage of the richsuite of available design-unbiased or approximately design-unbiased es-timators found in the literature. In some instances, however, the fieldsample is selected by non-probability methods, and variance estimationand subsequent inference based on a presumed model is the only viableoption. Reliance on a model becomes a necessity when there are few,possibly no, field plots available for the AOI (e.g. Breidenbach et al.,2010) or any other geographic level where estimates are sought (e.g. aforest estate or village), and thus estimation has to be based on modelsdeveloped on the basis of training data collected completely or partlyin another region (Næsset et al., 2005). This is a situation faced frequentlyin many developing countries. However, with increased focus on REDD,

3601E. Næsset et al. / Remote Sensing of Environment 115 (2011) 3599–3614

we should expect a rapid growth in the implementationof national forestinventory programs and regional (local) programs adhering to strict de-sign-based principles. Recent examples are Brazil (Freitas et al., 2010)and Tanzania (Tomppo et al., 2010). Thus, estimation and inferencedrawing on design-based principles may be highly relevant for futurewall-to-wall LiDAR- or SAR-assisted inventories.

So far, wall-to-wall LiDAR-assisted forest management inventorieshave focused primarily on estimation at the stand level — a level atwhich the estimation in most cases will lack support from field datafromwithin the stand in question. Further, in operational inventory esti-mates at estate and district (AOI) levels have been obtained by aggregat-ing stand estimates without utilizing data from the local (estate-level)field plots in the estimation. Thus, amodel-based approach has implicitlybeen adopted. Variance estimation has in most cases been ignored. Evenwhen model-based estimators are very precise, they nonetheless can beseriously biased, especially for smaller areas when the applied modelprovides an inapt portrayal of local conditions (Särndal et al., 1992). De-spite the fact that design-based approaches to inferencemay be regardedas relatively mature, such approaches are rare in studies employing re-mote sensing assets (McRoberts et al., 2010). Examples of design-basedapproaches from optical remote sensing can be found in McRoberts etal. (2010). There are recent exampleswith LiDAR, although they have fo-cused mainly on designs where the remote sensing data constitute asample as well (Andersen et al., 2009; Gregoire et al., 2011; Parker &Evans, 2004). To the very best of our knowledge, there are only two stud-ies that have taken a design-based approach utilizing wall-to-wall auxil-iary data from LiDAR or SAR (Andersen & Breidenbach, 2007; Corona &Fattorini, 2008), of which only the latter authors considered varianceestimation.

Further development of forest management inventories based onLiDAR or SAR calls for methods that can provide estimates at all rele-vant geographical levels in a consistent and statistically rigorousmanner. Variance estimation should indeed be a part of this method-ological advance, because it informs the end user of the reliability ofthe biomass estimate. This issue is timely because it coincides withneeds faced under the REDD mechanism. Therefore, realizing theneed to provide estimates at these three distinct geographical levels,i.e., (1) at a district level (AOI) at which the survey often is designed,(2) an estate, local community or village level at which a smaller

Fig. 1.Maps of the 960 km2 study area, 201 sample survey plots (top, right), and 35 large fiel(gray shaded), whereas the map (bottom, right) also shows the three tracts A–C.

fraction of the sample units will be available, and (3) a stand orpatch level at which field observations hardly are available, we artic-ulate the three following objectives for this study:

1. Demonstrate how biomass can be estimated for geographical do-mains (forest estates or local communities) within a larger AOI(district) — and in such a manner that estimates at the smallergeographical level always sum up to the estimate at a larger geo-graphical level, by employing a design-based approach and treat-ing the LiDAR and InSAR data as auxiliary information.

2. Compare such domain estimates and their associated error esti-mates obtained with LiDAR or InSAR as auxiliary informationwith estimates derived from the ground sample survey only.

3. Assess and compare biomass estimates and associated error esti-mates for smaller areas (stands or patches) within domains (e.g.estates) using LiDAR or InSAR data as auxiliary information. Theestimates of the smaller areas should always sum up to the esti-mate of the domains.

In this study we refer to stand or patch as the smallest geograph-ical unit of interest where further subdivision is considered irrelevantfor the purpose of estimating biomass.

At all geographical levels of this study, two different approacheswereapplied for the estimation with InSAR, namely derivation of canopyheight using (i) a highly accurate terrain model derived from airbornescanning LiDAR as reference surface, and (ii) a less accurate terrainmodel derived from the official topographic map series in which theheight information had been produced by photogrammetric methods.

2. Material and methods

2.1. Study area

This study was conducted in the boreal forest in the Aurskog-Høland Municipality (59°50′N 11°30′E, 120–390 m a.s.l) located insouth-eastern Norway, near the Swedish border (Fig. 1). The totalarea was 960 km2. The dominant tree species are Norway spruce(Picea abies (L.) Karst.) and Scots pine (Pinus sylvestris L.). Youngerstands have a larger portion of deciduous species than mature stands.Birch (Betula pubescens Ehrh.) is the dominant deciduous species.

d plots (bottom, right). The map (top, right) also shows the area classified as strata I–IV


The study took advantage of an existing operational stand-basedforest inventory utilizing airborne LiDAR data. The aim of the opera-tional inventory was to provide data for forest planning. Thus, we uti-lized field plot data from a ground-based sample survey, aerialphotographs, and airborne LiDAR data. All three datasets were col-lected for the operational forest inventory. We also collected grounddata in large field plots for assessment and comparison of estimatesfor small areas (objective #3). Finally, Shuttle Radar Topography Mis-sion (SRTM) InSAR data were available.

A major aim of this study was to demonstrate how biomass can beestimated for smaller domains typically being individual estates orlocal communities. In Norway, municipalities are divided into so-calledtracts (Anon., 2010) for production of certain types of public statistics.In this study, we decided to use such tracts as surrogates for domainsrepresenting estates or local communities (Fig. 1). Three tracts wereconsidered, denoted as tracts A, B, and C, respectively.

2.2. Photo interpretation and stratification

Aerial photographs were acquired 28–29 June 2005 using a VexcelUltraCamD aerial camera. Photogrammetry was used to delineate theforest stands and to determine tree species, age, and site productivityof each stand by photo-interpretation. The stands were classified intomultiple predefined strata. Four strata – representing the most valu-able forest in terms of wood quantities and economic values – wereselected to be inventoried by LiDAR. The four strata were defined asfollows:

Stratum I: Mature forest on medium to highly productive sites.Spruce dominated.

Stratum II: Mature forest on medium to highly productive sites. Pinedominated.

Stratum III: Mature forest on poor sites. Spruce and pine dominated.Stratum IV: Young forest on all site types. Spruce and pine

dominated.

The areas of these four strata in the 960 km2 study region were81.8, 66.0, 139.7, and 177.5 km2, respectively, i.e., a total of465.0 km2. These four strata constituted our AOI.

2.3. Sampling design

A field sample plot survey covering the four aforementioned pre-defined strata was conducted during fall 2006. A systematic stratifieddesign was employed. Based on a nominal equal allocation of nh=50plots per stratum, h={I, II, III, IV}, grids were created independentlywithin each stratum. Using Ah to designate the area of stratum h,the spacing of the grid was determined as

lh ¼ffiffiffiffiffiffiAh

nh

sð1Þ

This resulted in field plots located on a square grid at a spacing oflh. A geographical information system (GIS) analysis with the gridslaid atop the stand map revealed that the actual plot numbers wereclose to 50 (Fig. 1, Table 1).

The initial purpose of the field sample survey was to collect data fordevelopment of stratum-specific predictive regression models withLiDAR data as explanatory variables. These models were intended forprediction of biophysical properties at stand level to be used in forestplanning. The tracts into which the study region was divided were ig-nored in the design phase and were thus not a concern in the planningof the survey. However, the systematic design ensured that the sam-pling fraction within a given stratum was fairly stable across tracts.

2.4. Field work

2.4.1. Sample survey plotsHand-held Global Positioning System (GPS) receivers were used

to navigate to the predefined sample plot locations. The area of eachcircular sample plot was 200 m2. The diameter at breast height(dbh) of all trees on the plot exceeding a predefined threshold of4 cmwas callipered and recorded in 2 cm diameter classes. A subsam-ple of tree heights was measured using a Vertex hypsometer; sub-sample trees were selected with probability proportional to stembasal area. Number of height-sample trees per plot ranged between4 and 13 with an average of 9. Lorey's mean height (basal areaweighted mean height) (hL), basal area (G), and number of trees perhectare (N) were computed from the field measurements accordingto procedures outlined by Næsset (2004a). Total above-ground bio-mass (AGB) was estimated as the sum of the individual componentsstump, stem, bark, dead and living branches, and foliage of individualtrees predicted using previously fitted species-specific allometricmodels with single tree dbh and tree height as independent variables(Marklund, 1988) following the procedure outlined in Næsset andGobakken (2008). Because the diameter threshold for the large fieldplots was 5 cm (see below), we also estimated AGBwith a 6 cm diam-eter threshold (2 cm classes) for the sample survey plots to assess theeffect of unequal thresholds for the two datasets. The mean differencein AGB when using 4 and 6 cm thresholds, respectively, was 0.2%.Thus, the effect of using a 4 cm threshold rather than 5 cm is expectedto be b0.1% and will thus not have any serious impact on the results.In the following we will denote the field-based plot-level estimates ofbiomass as “observed biomass” even though the field-based estimateswill be subject to allometric and other errors. A summary of the fielddata is presented in Table 1.

The plot center coordinates (x, y) were determined by differentialGlobal Navigation Satellite Systems (dGNSS), using dual-frequencyreceivers observing pseudorange and carrier phase of the Global Po-sitioning System and Global Navigation Satellite System (GLONASS).The actual plot locations determined by post-processing deviatedsomewhat from the predefined positions that were determined inthe GIS system prior to field work and were used to guide thefield crew to the plots. Single recordings of GPS positions with sim-ple hand-held receivers in navigation mode in a forest environ-ment will frequently exhibit significant errors. Forty-five percentof the plots turned out to be located within a distance of 10 mfrom the predefined positions whereas 82% of the plots were locat-ed within a distance of 20 m. Such errors may sometimes have un-expected consequences. The most extreme effect of erroneouslocation of an individual sample plot in the current study was ex-perienced with plot #132, which had a predefined position in anopening in the forest but was actually established 38.6 m away ina high-biomass location (Fig. 6). Further details are provided inthe discussion.

2.4.2. Large field plotsA total of 35 large field plots (circular, 1000 m2) was measured

during the fall of 2007 and winter of 2008. In this study they wereused as surrogates for stands or patches. Thus, they were used todemonstrate how biomass could be estimated for such units, and toassess and compare error estimates of biomass using LiDAR orInSAR data as auxiliary information. These plots were located alongfive systematically spaced lines, but the exact plot locations withinthe lines were purposefully selected to provide a sample that coveredthe four strata and with a fairly even geographical distribution withinthe study region (Fig. 1). In the mature forest (strata I–III) we aimedfor a uniform distributed of plots dominated by Norway spruce andScots pine. We also aimed for a uniform distribution on differentsite productivity classes for each tree species. A forest map with tree

Table 1Summary of field measurements of sample survey plots and large field plots.

Characteristic Sample survey plots Large field plots

Range Mean St dev Range Mean St dev

Stratum I — Mature forest on medium to highly productive sites. Spruce dominated.No. of plots 50 10hL (m) 14.9–30.0 21.2 3.7 13.6–25.4 18.9 3.7N (ha−1) 500–2400 967 380 480–2340 1291 550G (m2 ha−1) 16.3–55.7 36.9 11.1 18.0–41.3 31.4 7.5AGB (Mg ha−1) 77.0–406.9 214.4 84.4 75.0–258.1 174.1 56.2Tree species distribution by AGB:

Spruce (%) 0–100 78 27 28–98 71 25Pine (%) 0–100 18 27 0–68 19 24Deciduous species (%) 0–40 4 8 1–35 10 11

Stratum II — Mature forest on medium to highly productive sites. Pine dominated.No. of plots 47 5hL (m) 9.4–23.5 16.7 2.8 14.5–18.8 17.1 1.7N (ha−1) 200–3550 940 579 440–850 712 168G (m2 ha−1) 9.4–46.2 26.4 10.1 13.9–29.1 21.7 6.1AGB (Mg ha−1) 20.4–223.4 115.1 54.7 60.9–153.8 102.3 38.2Tree species distribution by AGB:


Stratum III — Mature forest on poor sites. Spruce and pine dominated.No. of plots 50 12hL (m) 12.2–22.6 16.1 2.4 13.2–17.5 15.0 1.4N (ha−1) 200–2200 799 407 510–1110 788 184G (m2 ha−1) 7.8–43.1 26.3 7.1 13.4–29.1 19.7 4.3AGB (Mg ha−1) 36.1–225.4 107.6 41.5 55.7–127.9 83.9 20.8Tree species distribution by AGB:


Stratum IV — Young forest on all site types. Spruce and pine dominated.No. of plots 54 8hL (m) 7.5–20.7 12.7 2.9 11.3–22.8 15.1 3.4N (ha−1) 400–3300 1263 632 900–1710 1203 280G (m2 ha−1) 5.3–41.1 18.5 7.6 13.3–35.5 21.2 7.7AGB (Mg ha−1) 20.0–204.5 77.7 41.7 48.3–222.8 98.6 56.8Tree species distribution by AGB:


hL=Lorey's mean height, N=stem number, G=basal area, AGB=total above-ground biomass.


species, age class, and site productivity information derived by photo-interpretation guided selection of plot locations.

On each plot, dbh was measured for all trees with dbhN5 cm. Forthe dominant tree species the height of two trees in each of five diam-eter classes – covering the entire range of diameters – was measuredusing a Vertex hypsometer. Up to five tree heights were measured ineach secondary species. Secondary species trees were selected withprobability proportional to their stem basal area. The total numberof height measurements per plot ranged from 11 to 20 with an aver-age of 17.

Six nonlinear height–diameter regression models were developed.The models were species (Norway spruce, Scots pine, and deciduousspp.)×site productivity (high, low) specific. Missing tree heightswere predicted via these models. Lorey's mean height (hL) was calcu-lated from the predicted and measured heights. Basal area (G) andnumber of trees per hectare (N) were computed from the diametermeasurements and the tree counts. Total above-ground biomass(AGB) was predicted for every tree using the single-tree allometricmodels for individual components (see above) and aggregated toplot level. In the following we will denote the field-based estimatesof biomass as “observed biomass”. A summary of the field data is

presented in Table 1. The plot center coordinates were determinedaccording to the procedure outlined above.

In the current study, regression models relating observed AGB onthe sample survey plots to the LiDAR data and InSAR data, respective-ly, were fitted, see details below. Thus, these models were referencedto a biomass in the fall of 2006. In order to apply these regressionmodels for prediction of biomass in the large field plots measured in2007–2008, we made a simple adjustment for growth over one grow-ing season. Growth models for AGB are not available, but we assumedthe same proportional growth rate for AGB as for stem volume. Thestem biomass in the current data typically accounts for 60–70%of AGB. The stem volume growth rates were estimated according tospecies-specific stand volume growth models with age, site produc-tivity, and volume as independent variables (Blingsmo, 1988). Meanestimated growth rate for the 35 large field plots was 3.0%. A simplemodel for natural mortality due to competition indicates a loss of0.4% of the stems per year (Braastad, 1982). Since trees lost due tocompetition normally will be trees with a biomass smaller than an av-eraged sized tree, mortality less than 0.4% of the biomass is likely.Thus, in the growth adjustment of the biomass we ignored themortality.


2.5. LiDAR data

Airborne LiDAR data were acquired under leaf-on conditions on 8–10 June 2005 with a supplementary flight conducted on 6 September2005 to fill in a minor gap in the data. A fixed-wing piper PA31-310aircraft was used. LiDAR data were collected with an Optech ALTM3100 laser scanner flying at an altitude of approximately 1850 ma.g.l. The flight speed was 75 m s−1 and the pulse repetition frequen-cy was 50 kHz. The scan frequency was 71 Hz, resulting in a pointdensity on the ground of approximately 0.7 m−2. The maximumscan angle was 15° but pulses emitted at an angle of N13° were dis-carded during subsequent data processing.

Data were initially processed by the contractor (Blom Geomatics,Norway). Planimetric coordinates (x and y) and ellipsoidal heightvalues were computed for all echoes. Ground echoes were foundand classified using the progressive Triangular Irregular Network(TIN) densification algorithm (Axelsson, 2000) of the TerraScan soft-ware (Anon., 2005). A TIN model was created from the planimetriccoordinates and corresponding heights of the LiDAR echoes classifiedas ground points. The heights above the ground surface were calculat-ed for all echoes by subtracting the respective TIN heights from theheight values of all echoes recorded.

The ALTM 3100 sensor is capable of recording up to four echoesper pulse. In this study, we used the three echo categories classifiedas “single”, “first of many”, and “last of many”.

The “single” and “first of many” echoes were pooled into one data-set denoted as “first” echoes, and correspondingly, the “single” and“last of many” echoes were pooled into a dataset denoted as “last”echoes.

The entire study area was divided into grid cells using regulargrids that were laid atop the stand map in a GIS operation. Forevery grid cell, canopy height distributions were derived from theLiDAR echoes within the respective cells. Order statistics from thesedistributions are among the LiDAR metrics we derived, see below. Be-cause order statistics are a monotone increasing function of samplesize and thus spatial scale (Harter, 1970; Magnussen, 1999), it is im-portant that grid cell size and size of the sample survey plots are equalto avoid unequal expectations of the metrics derived from the heightdistributions. Thus, we used a grid cell size of 200 m2.

Separate distributions were created for the first and last echoes,respectively. A threshold value of 2 m above the ground surface wasused to separate the canopy echoes from those below the canopy.From each of these two distributions and for every grid cell weextracted order statistics such as height deciles and maximum heightvalue. Further, we derived multiple measures of canopy density. Thecanopy density measures were derived by dividing the height rangebetween the 2 m threshold and the 95 percentile into 10 equallysized height bins. The densities were then computed as the respectiveratios between number of echoes above a given height bin and totalnumber of echoes (including the below canopy echoes). Thus, thecanopy density measures represent the relative cumulative frequen-cies of echoes at different heights levels in the canopy. These height-and density-related metrics were used as auxiliary information in thesubsequent estimation (see below).

Finally, we derived the same LiDAR variables for every sample surveyplot as for the grid cells. We also divided the 1000 m2 large field plotsinto 200 m2 sectors and derived these LiDAR variables for every sector.

2.6. SRTM InSAR data

SAR data were acquired by the Endeavour space shuttle during its11 days Shuttle Radar Topography Mission during 12–20 February2000 (Rabus et al., 2003). Operating with a flight inclination angleof 57° the radar beams of the SRTMmission covered the Earth surfacefrom 60° N to 58° S. The X-band StripMap system was among the in-struments carried on this mission. An interferometric data acquisition

was conducted by extending a 60 m mast from the side of the shuttleand having SAR sensors both at the shuttle body and the tip of themast. The X-band SAR data were provided by the German AerospaceCentre (DLR). DLR had produced the Digital Surface Model (DSM)along with a Digital Height Error Model (HEM), which provides a the-oretical estimate of expected height accuracy of every SAR pixel.The X-band SRTM data is delivered as a regularly distributed rastergrid with one sample at every 1 arcsec in a geographical latitude/longitude coordinate system. At our test site close to 60° N, thismeans an effective pixel size of approximately 15×31 m (465 m2).Thus, the size and shape of the pixels deviated from the field plots.Since moisture content has an influence on SAR signal penetration,thorough records of the local weather conditions were made duringthe mission. These observations indicated dry and cold weather dur-ing most of the time of the SRTM mission, with a short period withsome warmer weather and snow fall (Solberg et al., 2010a).

A quality check of the SRTM InSAR DSM was carried out by meansof the LiDAR data. A vertical offset was revealed. This offset was notconstant and it was modeled by fitting a plane through pixels thatwere assumed to be vegetation free at the time of the SRTM mission(2000) as well as at the time of the LiDAR data acquisition (2005).Thus, the modeling was carried out on the basis of a subset of thepixels for which the difference in elevation between the two acquisi-tions was the variable to be modeled. The estimated model indicateda slightly tilted plane with an average offset of 0.82 m. The InSAR DSMwas adjusted accordingly (Solberg et al., 2010a).

Finally, two separate datasets of pixel-level canopy heights wereproduced by (1) subtracting the terrain model derived from LiDARfrom the InSAR DSM (denoted as InSARh_LiDAR), and (2) by subtract-ing the terrain model generated from the official topographic map se-ries with an initial vertical distance between contour lines of 20 mfrom the InSAR DSM (denoted as InSARh_Topo).

2.7. Estimation and inference

2.7.1. Estimation based on the field sample surveyWe find it convenient first to detail the estimation for the tracts,

i.e., the geographical units meant to represent individual forest es-tates or local communities. At this level, the design of this studyallowed estimation based on stratum-specific information. Adoptingthe notation of Särndal (1984), let U be the entire population ofunits [grid cells with size 200 m2 for LiDAR and pixels with size15×31 m (465 m2) for InSAR] in the AOI where U={1, …, k, …, N},i.e., the four forest strata that were included in the current design(see details above). This population is divided into D non-overlappingdomains, i.e., different sized estimation units such as estates or localcommunities. The domains are denoted U⋅d. The sizes of the domainsare N⋅d, where d=1, …, D. We also divide the population into non-overlapping strata, Uh ⋅ with sizes Nh ⋅, where h=1, …, H. Thus, thepopulation is composed of up to H×D unique groups defined by stra-tum and domain. These groups are labeled Uhd with sizes Nhd. In thisstudy, Nhd was always N0.

Now, let bk be the biomass per hectare of the kth unit in the pop-ulation. First, we want to define the parameter mean biomass perhectare (B) within a particular stratum (h) and domain (d) forwhich we later wish to find an appropriate estimator:

Bhd ¼ ∑k∈Uhdbk

Nhd

: ð2Þ

We may estimate the biomass from the field sample alone, i.e.,using a so-called direct estimator. Let sh ⋅ denote a sample of size nh ⋅drawn randomly [i.e., simple random sampling (SRS)] from theunits in Uh ⋅, i.e., from stratum h across all domains. Then shd denotesthe subsample of the plots in Uh ⋅ that falls in domain d. Because thesystematic design provides sizes of nhd close to their respective


expectations the estimators applicable to the population level param-eters apply to the domain level as well (Särndal et al., 1992). Themean biomass per hectare for a particular domain and stratum wasestimated according to

BSRShd¼∑k∈shd

bk.

πk

∑k∈shd1

πk

¼Nh

nh∑k∈shd

bk

Nh

nh∑k∈shd

1¼ ∑k∈shd

bknhd

;, ð3Þ

where πk are the inclusion probabilities. Under SRS πk ¼ nhNh

(Särndal etal., 1992, p. 31). The term following the first equals sign (=) is taken di-rectly from Särndal et al. (1992, p. 185). Note though that we have in-cluded the subscript h to indicate a specific stratum. This estimatorwill be slightly biased since it is a ratio estimator due to the randomsample size. We have included the details in Eq. (3) for the purpose ofillustrating how one can proceed from the general notation in Särndalet al. (1992) to a more commonly known notation.

We will now continue with an estimator of the variance of BSRShd ,and again we will show how we can arrive at a familiar expressionstarting from the general notation. From Särndal et al. (1992) (Eq.(5.8.5)), we have

VBSRShd

� �¼ ∑

k∈shd

1πk

!2

∑k∈shd

∑k0∈shd

πkk0−πkπk

0

πkk0

bk−BSRShdπk

!bk0−BSRShd

πk0

!:

Substituting πk ¼ πk′ ¼nh

Nhand πkk′ ¼

nh nh−1ð ÞNh Nh−1ð Þ (Särndal et al.,

1992, p. 48), this expression, after some arduous algebra reduces tothe somewhat familiar expression

V BSRShd

� �¼ 1− nh

Nh

� �∑k∈shdbk−Bˆ SRShd� �2

nhd nhd−1ð Þ

In this estimator and in all subsequent variance estimators we willignore corrections for finite population [the parenthesized term fol-lowing the equals sign (=)] because the sampling fractions are al-ways very small and a correction would have a negligible influenceon the variance estimates. Thus, the following estimator was used:

V BSRShd

� �¼

∑k∈shdbk−BSRShd

� �2nhd nhd−1ð Þ : ð4Þ

Because a systematic design was adopted for the field survey rath-er than a random design, an overestimation of the variance is a likelyconsequence of ignoring the systematic design (e.g. Särndal et al.,1992).

For a particular stratum h, mean biomass per hectare was estimat-ed according to

BSRSh⋅ ¼∑k∈sh

bknh

ð5Þ

where sh is the sample of size nh drawn from Uh, i.e., from stratum h.The variance was estimated as

V BSRSh⋅

� �¼

∑k∈shbk−BSRSh⋅

� �2nh nh−1ð Þ : ð6Þ

For a particular domain, the survey was conducted according to astratified design. For the estimation we therefore assumed a stratifiedrandom sampling design (STRS). Thus, we estimated the mean bio-mass per hectare for each domain d according to

BSTRS⋅d ¼ ∑h

Nhd

N⋅dBSRShd ð7Þ

with the variance estimator

V BSTRS⋅d

� �¼ ∑

h

Nhd

N⋅d

� �2V BSRShd

� �: ð8Þ

For the entire AOI, we used an estimator following the stratifieddesign. Thus, for the AOI the STRS estimator takes the form

BSTRS ¼ ∑h

Nh

NBSRSh⋅: ð9Þ

It should be noted though that given that the sampling fractionwithin a stratum is equal across all domains, an alternative estimatorfor the AOI is the weighted mean of the domain estimators in Eq. (7).

A variance estimator for BSTRS is

V BSTRS

� �¼ Σ

h

Nh

N

� �2V BSRSh⋅

� �: ð10Þ

2.7.2. Estimation based on the field sample survey and auxiliary LiDARand SAR data

A commonly adopted method for estimation for small domains inLiDAR- and SAR-assisted studies, is simply to aggregate the predictedvalues (of biomass) for all population units within the domain in ques-tion. The predictions are obtained by means of regression models devel-oped from ground samples which in many cases are found only partlywithin or even completely outside the particular domain. This estimatoris known as a synthetic regression estimator (Särndal, 1984; Särndalet al., 1992). As an example, the synthetic regression estimator (SYNT)for biomass per hectare for a particular stratum and domain is

BSYNThd ¼ ∑k∈Uhdbk

Nhd

ð11Þ

where bk is biomass per hectare predicted according to the regressionmodel for the kth unit (grid cell or pixel) in the population (the grid orraster of the entire area). A synthetic estimator depends purely on amodel and typically has low variance but may suffer from severe bias(Särndal et al., 1992, p. 411) if the applied regression model deviatesfrom the true but unknown relationship for the domain in question.

However, because the current survey was designed according to de-sign-based principles, we adopted amodel-assisted regression estimator(Särndal, 1984; Särndal et al., 1992, p. 231, 399). Model-assisted estima-tors use predictions of a fairly large sample of population units (or evenall population units as in the current study) obtained from auxiliarydata (e.g. LiDAR or SAR) to enhance the variance but rely on observations(e.g. field sample plots) for population units selected from a probabilitysample for validity (McRoberts, 2010a).

For mean biomass per hectare within a particular stratum and do-main, a model-assisted regression (MAR) estimator is

BMARhd ¼ ∑k∈Uhdbk

Nhd

þ∑k∈shdek

nhd

; ð12Þ

where ek ¼ bk− bk. This estimator is approximately design-unbiasedirrespective of the model choice when nhd is not too small (Särndal,1984). Firth and Bennett (1998) established that asymptotic design-un-biasedness holds for nonlinear model-assisted regression, as well. It can


be seen that this estimator consists of the synthetic estimator (Eq. (11))with a correction term that adjusts for deviations between the modelpredictions and the observed values in the sample for the domain andstratum in question. An attractive property of this regression estimatoris that the estimator for the population as a whole is consistent withthe weighted mean of the domain estimators (Särndal et al., 1992, p.400).

A variance estimator of BMARhd is (Särndal et al., 1992)

V BMARhd

� �¼

∑k∈shdek−

∑k∈shdek

nhd

� �2

nhd nhd−1ð Þ : ð13Þ

As noted by Mandallaz (2008, p. 120), the synthetic component ofthe estimator for mean biomass, i.e., the first term on the right-handside of the estimator in Eq. (12), does not contribute to the design-based variance, and thus the variance only depends on the samplesize and the goodness of the model for local use (Särndal, 1984).When working with small units such as the H×D groups, there is arisk of fairly small samples. The variance estimator is accurate only as-ymptotically and may not be accurate for very small samples. It hasbeen indicated that samples smaller than five (Thompson, 2002) or10 (Särndal et al., 1992) should be avoided.

For a particular stratum h, mean biomass per hectare was estimat-ed according to

BMARh⋅¼∑k∈Uh

bkNh

þ∑k∈shek

nh: ð14Þ

The variance was estimated as

V BMARh⋅

� �¼

∑k∈shek−

∑k∈shek

nh

� �2

nh nh−1ð Þ : ð15Þ

To obtain estimates for each domain d, the following stratified re-gression estimator was used

BMAR⋅d ¼ ∑h

Nhd

N⋅dBMARhd ð16Þ

with the variance estimator

V BMAR⋅d

� �¼ ∑

h

Nhd

N⋅d

� �2V BMARhd

� �: ð17Þ

Also with the model-assisted approach we estimated biomass forthe entire AOI by ignoring that the population was divided into do-mains. Thus, for the whole AOI we used the stratified estimator

BMAR ¼ ∑h

Nh

NBMARh⋅: ð18Þ

It should be noted that given that the sampling fraction within astratum is equal across all domains, an alternative estimator for theAOI is the weighted mean of the domain estimators in Eq. (16).

A variance estimator of BMAR is

V BMAR

� �¼ ∑

h

Nh

N

� �2V BMARh⋅

� �ð19Þ

2.7.3. Estimation for individual stands or patchesFor estimation at stand (patch) level we did not have any support

from local field sample data for direct estimation or model-assistedestimation as we had for the domains. With a total area of the four

strata considered in this study of 465.0 km2, more than 21,000 standsdid not contain any field plots. None of the stands contained morethan one plot, which means that exactly 201 stands contained oneplot each. For the stand level estimation we used the synthetic esti-mator. Let the unique groups Uhd defined by stratum and domain befurther divided into Phd non-overlapping stands (patches) denotedUhdp with sizes Nhdp, where p=1, …, Phd. The synthetic estimatorwe considered for biomass per hectare at stand level is identical tothe one presented in Eq. (11), i.e.,

BSYNThdp ¼∑k∈Uhdp

bkNhdp

: ð20Þ

However, it is a highly desired property that the area-weightedmean of the estimates at a smaller geographical level (stand) isequal to the estimated mean at a larger level (domain). Because ofthe correction term of the model-assisted regression estimator(Eq. (12)), the weighted mean biomass per hectare over all standswithin a stratum and domain will not be equal to the domain and

stratum-level estimates, i.e.,1Nhd

∑p∈Uhd

Nhdp BSYNThdp≠ BMARhd if

∑k∈shd

ek≠0. To obtain such consistency between stand aggregates

and domain estimates, we adjusted the synthetic stand estimateswith a simple ratio adjustment (Rao, 2003, p. 51).

B�SYNThdp ¼ BMARhd

1Nhd

∑p∈UhdNhdp BSYNThdp

BSYNThdp: ð21Þ

Because we did not have any units from the probability sampleof field plots at hand for the stands, variance estimation drawing ondesign-based principles was not feasible. Model-based inference is aviable option though. However, it was beyond the scope of thisstudy to elaborate any further on model-based variance estimation.Nevertheless, the error of the estimates for a small sample of standswas assessed by independent validation using field observations.

2.8. Analysis

2.8.1. Estimation of LiDAR biomass modelsRegression models that relate the LiDAR and InSAR variables to

above-ground biomass are required for the model-assisted estima-tion. For LiDAR, a large number of variables related to height and can-opy density were derived from the canopy height distributions (seeabove). These variables were available as candidate independent vari-ables for the regression models using the field sample survey plots.Nonlinear models with multiplicative components have quite fre-quently been used in LiDAR biomass studies (e.g. Lim & Treitz,2004; Næsset & Gobakken, 2008).

In the current study, we used nonlinear regression (the Gauss–Newton method; Anon., 2004) to estimate nonlinear models of themean (expected value) function. These models were of the form

E AGB½ � ¼ β0xβ11 xβ2

2 …xβnn ð22Þ

where x1, x2, …, xn are the LiDAR-derived variables and β0, β1, β2, …,βn are parameters to be estimated. Separate models were estimatedfor each of the four strata. However, in order to make a selectionamong the large number of potential candidates as independent vari-ables to be included in the models in Eq. (22), we did a preliminaryestimation of log-transformed models using ordinary least-squares(OLS) regression and took advantage of the stepwise (forward) selec-tion procedure (Anon., 2004). Because many of the LiDAR variablesare highly correlated, there may exist “better” models when using


nonlinear regression than those selected on the basis of the prelimi-nary OLS regression analysis. For example, a given decile of theLiDAR height distribution will often be highly correlated with a neigh-boring decile. This phenomenon occurs also with the density vari-ables among the different vertical layers. We therefore re-estimatedthe nonlinear models in Eq. (22) by replacing each of the initially se-lected independent variables by nearby variables (height deciles werereplaced by deciles below and above the one initially selected; thedensity variables were replaced by density variables for the verticallayers below and above the one initially selected). Thus, several alter-native nonlinear models were estimated. We used the mean squarederror (MSE) as criterion for model selection and finally chose themodel with the lowest MSE within each stratum for the purpose bio-mass estimation.

2.8.2. Estimation of InSAR biomass modelsBased on the sample survey plots and the InSAR heights derived

for the corresponding pixels of the two alternative InSAR height vari-ables, separate regression models were estimated for every stratum.Previous studies have suggested that linear models are appropriate(e.g. Solberg et al., 2010a). Thus, we estimated eight different linearregression models of the form

E AGB½ � ¼ β0 þ β1x ð23Þ

where x is the InSAR height with the topographic (x=InSARh_Topo)and the LiDAR (x=InSARh_LiDAR) terrain models as reference surfaces,respectively. The models were estimated with OLS regression (Anon.,2004).

2.8.3. Estimation of mean biomass and variance of the mean biomassestimates

First, we estimated biomass per hectare for every combination ofdomain and stratum from the field sample only (Eq. (3)), and thensubsequently also for strata (Eq. (5)), domains (Eq. (7)) and the en-tire AOI (Eq. (9)). We also estimated the corresponding standard er-rors (SE), i.e., the square roots of the variances (Eqs. (4), (6), (8),and (10), respectively).

In the model-assisted estimation with LiDAR and InSAR used asauxiliary data, biomass per hectare for every combination of domainand stratum was estimated according to Eq. (12) and then subse-quently for every stratum (Eq. (14)), every domain (Eq. (16)), andthen the entire AOI (Eq. (18)). Corresponding standard errors werealso estimated (Eqs. (13), (15), (17), and (19), respectively). In theestimation, the stratum-specific regression models were used to pre-dict the synthetic (first) part of the respective estimates by providingpredictions for every population unit, i.e., for every 200 m2 grid cellfor LiDAR and for every 15×31 m (465 m2) pixel for InSAR. The de-sign assumes that the field sample survey plots constitute a probabil-ity sample selected among the population units. On the basis of thissample an adjustment of the synthetic estimate is provided by the dif-ferences between the observed biomass value for each individualsample unit and corresponding model predictions. For LiDAR, wetreated every sample survey plot as if it was a sample unit selectedfrom the population of LiDAR grid cells. Thus, the adjustment of thesynthetic estimates was computed as the difference between biomassobserved on each plot and biomass predicted from the LiDAR data onexactly the same plot. For InSAR, we assigned the sample survey plotsto those pixels that the plots fell inside, which is common practice inremote sensing studies (e.g. McRoberts, 2010a). If a plot was split onseveral pixels, it was assigned to the pixel with the largest portion ofthe plot within its borders. For InSAR, the adjustment of the syntheticestimates was thus computed as the difference between biomass ob-served on each plot and biomass predicted from the InSAR data forthe single InSAR pixel with the greatest overlap with the plot.

Finally, biomass was estimated for the large field plots. Althoughthese field plots were only 1000 m2 in size, they were considered sur-rogates for stands or patches, and the pure synthetic estimators wereapplied. For each of the 35 large field plots biomass was predictedaccording to the stratum-specific regression models. For LiDAR, thepredictions were made for every 200 m2 sector of each plot and aver-aged at plot level (Eq. (20)). For InSAR, the predictions were made forall pixels that intersected each plot, and these pixel predictions wereaveraged (weighted by pixel area inside the plot) at plot level(Eq. (20)). Further, we also used the synthetic estimator with ratioadjustment for tract effects (Eq. (21)). All the estimates at plot levelwere compared with the growth-adjusted observed biomass inorder to assess the error. This was done by estimating RMSE andmean difference (D

P) between the observed above-ground biomass

and biomass predicted with the LiDAR and InSAR regression models,i.e.,

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑35

p¼1 Bp− Bp

� �235

vuutð24Þ

and

DP ¼

∑35p¼1 Bp− Bp

� �35

ð25Þ

where Bp is the observed above-ground biomass per hectare for plotp, p=1, 2, …, 35, and Bp is the above-ground biomass per hectare es-timated according to Eq. (20) or Eq. (21). The error was also com-pared within individual strata by estimating RMSE and meandifference strata-wise. Two-tailed one-sample t-tests were performedto assess the statistical significance of the estimated differences.

3. Results

The estimated regression models for LiDAR contained two (strata Iand II) or three (strata III and IV) independent variables (Table 2). AllLiDAR models contained at least one variable representing a fairlyhigh height decile and at least one canopy density metric. Rootmean square error ranged between 14.6 and 41.9 Mg ha−1 and R2 be-tween 0.76 and 0.89. The relative magnitude of RMSEwas quite stableacross strata (18.9–20.8%). Linear regression models with InSARheight estimated separately for each of the four strata revealedRMSE values ranging between 41.4 and 77.4 Mg ha−1 (InSARTopo)and between 35.7 and 74.7 Mg ha−1 (InSARLiDAR), with correspond-ing R2 values of 0.03–0.18 and 0.13–0.28 (Table 2). Scatter plots of ob-served versus predicted biomass for strata I–IV are displayed in Fig. 2.

The overall estimated mean above-ground biomass for the entire AOIbased on the stratified field sample survey was 116.0 Mg ha−1

(SE=3.7 Mg ha−1) (Table 3). The model-assisted estimate with LiDARdata as auxiliary information was 101.2 Mg ha−1 (SE=1.6 Mg ha−1).When using InSAR heights as auxiliary information the estimates were112.8 (SE=3.5 Mg ha−1) and 111.3 Mg ha−1 (SE=3.2 Mg ha−1) whentopographic and LiDAR data were applied as reference terrain models,respectively.

For the three tracts, the estimated mean above-ground biomassranged from 110.1 to 127.4 Mg ha−1 (SE=5.5–8.2 Mg ha−1) for thefield survey (Table 3). When using LiDAR as auxiliary data the corre-sponding tract estimates ranged between 97.6 and 104.9 Mg ha−1

(SE=2.5–3.7 Mg ha−1). Thus, the LiDAR-assisted estimates wereconsistently lower than the field estimates and none of the LiDAR-assisted tract estimates were within the 95% confidence intervals ofthe corresponding field estimates and vice versa (Fig. 3). Themodel-assisted estimates based on InSAR with topographic andLiDAR terrain models as reference surfaces were 106.4–121.8(SE=5.3–8.1 Mg ha−1) and 104.8–118.1 Mg ha−1 (SE=4.7–

100 200 300 400

100

200

300

400

100

200

300

400

Obs

erve

d bi

omas

s (M

g

)

ha

-1

Predicted biomass Mg ha-1

Stratum IStratum IIStratum IIIStratum IV

0 100 200 400

0Obs

erve

d bi

omas

s (M

g

)

ha

-1

Predicted biomass Mg ha-1

0 100 200 400

010

020

030

040

0

Obs

erve

d bi

omas

s (M

g h

)a

-1

1300

-

( )

( )300

Table 2Selected regression models used in the model-assisted estimation.

Stratum Model RMSE(Mg ha−1)

RMSE(%)

R2

LiDARStratum I cAGB ¼ 11:4043pf 1:232650 dl0:64710 41.9 19.5 0.76a

Stratum II cAGB ¼ 4:7065pf 1:381680 df 1:36550 23.9 20.8 0.82a

Stratum III cAGB ¼ 11:1982pf 2:471590 pl−1:502660 df 0:82876 20.7 19.2 0.77a

Stratum IV cAGB ¼ 12:0330pf 1:094070 df 0:52451 dl0:37462 14.6 18.9 0.89a

InSARTopoStratum I cAGB =143.077+6.933 InSARh_Topo 77.4 36.1 0.18Stratum II cAGB =81.364+4.318 InSARh_Topo 52.1 45.3 0.12Stratum III cAGB =97.348+1.376 InSARh_Topo 41.4 38.5 0.03Stratum IV cAGB =69.847+1.672 InSARh_Topo 41.4 53.3 0.03

InSARLiDARStratum I cAGB =106.086+10.244 InSARh_LiDAR 74.7 34.8 0.23Stratum II cAGB =71.658+6.976 InSARh_LiDAR 51.6 44.8 0.13Stratum III cAGB =70.775+6.05 InSARh_LiDAR 37.4 34.8 0.21Stratum IV cAGB =49.842+7.749 InSARh_LiDAR 35.7 46.0 0.28cAGB =predicted total above-ground biomass; pf50, pf70, pf80, pf90=50th, 70th, 80th and

90th height percentiles of the first echo canopy height distribution, respectively;pl60=60th height percentile of the last echo canopy height distribution; df0, df1,df6=relative cumulative canopy height densities above the 0th (2 m), 1st, and 6thvertical height layer of the first echo height distribution, respectively; dl0,dl2=relative cumulative canopy height densities above the 0th (2 m) and 2ndvertical height layer of the last echo height distribution, respectively; InSARh_Topo,InSARh_LiDAR=canopy height derived from InSAR data with topographic map dataand LiDAR data as terrain reference surfaces, respectively.

a Computed as the square of Pearson correlation coefficient between observed andestimated AGB.


7.4 Mg ha−1), respectively. The large differences in the overall esti-mates and for the tracts between the field survey and the model-assisted alternatives — and for LiDAR in particular, were mainly dueto large differences for strata I and III. Detailed results for individualstrata and for strata within tracts can be found in Table 3.

In the estimation of mean above-ground biomass for the 35 largefield plots with the synthetic estimator and without any adjustmentfor local tract effects (Eq. (20)), a mean difference between estimatedand observed biomass of −4.6 Mg ha−1 (p=0.115) was found whenusing LiDAR data (Table 4, Fig. 4). The corresponding mean differ-ences were −20.6 Mg ha−1 (p=0.019) and −21.0 Mg ha−1

(p=0.003) for the estimates based on InSAR with topographic andLiDAR terrain references, respectively. RMSE values were17.3 Mg ha−1 for LiDAR and 53.2 and 44.1 Mg ha−1 for the InSARestimates.

When adjusting the synthetic estimates for local tract effects(Eq. (21)), the mean differences were somewhat reduced, althoughthe changes were not statistically significant. For LiDAR and InSAR(with topographic and LiDAR references) the mean differences were−4.1 Mg ha−1 (p=0.172), −19.6 Mg ha−1 (p=0.025), and−18.4 Mg ha−1 (p=0.009), respectively, with corresponding RMSEvalues of 17.7, 52.7, and 42.6 Mg ha−1. Detailed results for individualstrata reveal that there are large discrepancies among strata-level es-timates. This is most pronounced for the InSAR estimates (Table 4).

Predicted biomass (Mg h a )

Fig. 2. Scatter plots of observed biomass on the sample survey plots versus predictedbiomass for strata I–IV. Biomass predictions based on regression models (Table 2) forLiDAR (top), InSARTopo (middle), and InSARLiDAR (bottom).

4. Discussion

This study has demonstrated how one may combine data from aprobability sample of field plots and data with full areal coveragefrom airborne LiDAR and InSAR to achieve precise biomass estimatesfor an area of interest. Precise estimates can even be achieved forminor regions of the area. This statistical framework is highly relevantin forest management inventories as well as for implementation andverification of local REDD strategies within a country. We focused inparticular on consistency between estimates obtained at the variousgeographical levels.

The empirical results indicated standard errors for individualtracts when using LiDAR data as auxiliary information with a magni-tude of 41–45% of the errors obtained when using the field sampleonly, and 43.2% for the entire AOI. If for the sake of simplicity we ig-nore the stratified design and assume that the field sample constitut-ed a random and not a systematic sample, we would in this specificcase need a field sample of 201(1/0.432)2=1077 plots to obtain the

image of Fig.�2

Table 3Estimated mean above-ground biomass and associated standard error estimates basedon the field sample survey only and by using auxiliary data from LiDAR and InSAR, re-spectively (Mg ha−1).

Region andstratum

Numberof fieldsamplesurvey plots

Fieldsample

LiDAR InSARTopo InSARLiDAR

B SE B SE B SE B SE

Tract A 51 127.4 8.2 104.9 3.7 121.8 8.1 118.1 7.4Stratum I 12 237.0 25.0 170.2 16.1 218.1 24.4 209.5 25.4Stratum II 9 128.4 18.7 118.4 6.5 123.4 16.6 129.4 17.8Stratum III 16 112.8 12.6 88.0 4.2 111.2 12.4 100.6 10.5Stratum IV 14 78.0 13.0 78.6 3.6 75.8 13.4 78.1 10.3

Tract B 76 110.1 5.5 97.6 2.5 106.4 5.3 104.8 4.7Stratum I 14 223.8 21.9 161.6 7.7 201.6 20.6 207.8 17.2Stratum II 21 116.6 12.5 117.7 4.4 116.8 11.7 119.5 10.9Stratum III 14 106.9 11.1 88.2 6.8 107.3 10.8 99.8 9.1Stratum IV 27 74.0 6.5 76.8 2.8 73.1 6.3 70.8 5.9

Tract C 74 115.2 6.5 101.5 2.7 112.7 6.1 112.8 5.6Stratum I 24 197.7 17.3 174.9 8.2 194.7 15.3 187.5 14.8Stratum II 17 106.1 12.8 112.3 6.9 100.5 12.3 104.4 12.5Stratum III 20 103.9 7.8 81.3 4.0 101.7 7.8 102.5 7.8Stratum IV 13 85.3 14.1 75.4 4.2 84.5 13.2 85.9 11.2

Entire AOI 201 116.0 3.7 101.2 1.6 112.8 3.5 111.3 3.2Stratum I 50 214.4 11.9 169.3 5.8 202.7 10.8 198.9 10.5Stratum II 47 115.1 8.0 117.1 3.4 113.0 7.5 117.9 7.5Stratum III 50 107.6 5.9 85.4 2.8 106.3 5.8 101.3 5.2Stratum IV 54 77.7 5.7 77.1 1.9 76.5 5.6 76.4 4.8

B=estimated mean above-ground biomass, SE=estimated standard error of meanabove-ground biomass.


same precision as we achieved with support of the LiDAR data. This ismore than five times the current sample of 201 plots. Thus, the valueof the LiDAR data is substantial for increasing precision and, in addi-tion, it produces a map.

Even InSAR with terrain data derived from LiDAR as reference sur-face showed improved precision over the pure field sample. Follow-ing the above reasoning the estimated precision of the InSARestimate corresponded to what one would expect with a field sampleof approximately 270 plots. It should be noted that the InSAR dataavailable for this study were not ideal. There was a time lag between

Fig. 3. Estimated mean above-ground biomass (horizontal lines) and associated 95%confidence intervals for the three tracts A, B and, C based on the field sample surveyonly and by using auxiliary data from LiDAR and InSAR, respectively.

the SRTM InSAR data acquisition in 2000 and the field survey in 2006of almost seven full growing seasons. The fact that the estimated re-gression models related the InSAR (and LiDAR) data to the time ofthe field survey, does not compensate for the varying growth ratesfor different parts of the forest area and natural mortality and distur-bances which will introduce significant errors in the estimatedmodels.

We adopted the regression estimators in Eqs. (12) and (16) be-cause it assures that biomass estimates for sub-populations (domain,tract) always sum up to the estimate for the population as a whole. Ifthis particular property is of less importance, e.g. if estimates for thesmall domains are of primary interest, other estimators may be pre-ferred. For example, the modified regression estimator (Hidiroglou& Särndal, 1985) and the dampened modified regression estimator(Särndal & Hidiroglou, 1989) both have the same basic structure asthe general regression estimator, with one term due to the syntheticregression estimator and another adjustment term that dampenspossible domain-specific local bias caused by an improper model.The two latter estimators are known to be more precise because ofslightly different corrections for bias. Both were used in a previousLiDAR study by Andersen and Breidenbach (2007). Other estimatorsfor small domains are available and may be suitable, depending onthe objectives of the study and the properties of the survey designand the data, see e.g. Särndal et al. (1992), Köhl et al. (2006), or Rao(2003) for further details and references.

The LiDAR-based estimates of mean above-ground biomass of the35 large field plots following the synthetic estimator (Eq. (20))showed only minor mean differences from the observed biomass(statistically non-significant), in general smaller than 8–9% of themean value for the various strata (Table 4). When the synthetic esti-mates were adjusted for local effects to make them consistent withthe tract estimates (Eq. (21)), the mean differences were hardly af-fected. These results are well in line with previous accuracy assess-ments of LiDAR-based stand estimates of similar variables (e.g.timber volume). The RMSE values of around 12–17% of mean biomassagree with previous findings. A review of previous studies conductedin boreal forest conditions with particular emphasis on timber vol-ume, basal area and other biophysical properties which are correlatedwith biomass can be found in Næsset (2007). In general, synthetic es-timators have been shown to be very precise, albeit with possiblylarge biases (McRoberts et al., 2010). Synthetic estimation does notprovide any means for controlling potential bias and depends entirelyon correctly specified models. It is therefore recommended that a“representative” sample is used for model development to reducethe risk of bias (Särndal, 1978), although the main objective of thedata collection in conjunction with synthetic estimation is model de-velopment and not validity of the estimation. In this particular studyas well as in most other LiDAR-studies where probability sampleshave been employed, the application of a pure model-based approachwas rather successful.

For InSAR, the differences between estimated and observed meanAGB for the 35 large field plots were larger. For individual strata thesedifferences were of a magnitude up to around 33% (Table 4), andtended to be somewhat lower when the LiDAR terrain data wereused as reference surface. There was a general trend towards overes-timation of AGB. Someminor and insignificant reductions in these dif-ferences could be achieved by the adjustment of local effects(Eq. (21)). RMSE values typically ranged from around 40 to 55% ofthe mean observed biomass, with a tendency of lower RMSE valuesfor InSAR data with LiDAR data used as reference surface. The RMSEvalues for the individual strata for the various InSAR estimates werelarger than for the LiDAR estimates, as one would expect. However,as noted above, there were additional errors inherent in the appliedInSAR data that may not be present in future acquisitions. Neverthe-less, the differences between estimated and observed mean AGB forthe 35 large field plots using InSAR as auxiliary data illustrates the

Table 4Mean of estimated mean above-ground biomass and associated accuracies for the 35 large field plots using the unadjusted (Eq. (20)) and adjusted (Eq. (21)) synthetic estimatorswith LiDAR and InSAR data, respectively (Mg ha−1).

Estimator LiDAR InSARTopo InSARLiDAR

BP

RMSE DP

p-value BP

RMSE DP

p-value BP

RMSE DP

p-value

Unadjusted 116.7 17.3 −4.6 0.115 133.0 53.2 −20.6 0.019 133.4 44.1 −21.0 0.003Stratum I 182.6 23.4 −13.7 0.058 214.0 74.4 −44.7 0.051 207.3 59.0 −38.0 0.032Stratum II 106.5 12.2 −7.0 0.229 115.4 32.0 −15.6 0.325 122.1 33.1 −22.4 0.141Stratum III 87.1 14.3 −4.8 0.261 110.1 34.9 −27.6 0.001 105.6 27.4 −23.2 b0.001Stratum IV 85.2 15.0 8.6 0.109 77.1 54.8 16.9 0.420 89.8 48.3 4.2 0.823

Adjusted 116.2 17.7 −4.1 0.172 132.0 52.7 −19.6 0.025 130.8 42.6 −18.4 0.009Stratum I 182.9 23.6 −14.0 0.055 210.7 74.0 −41.4 0.073 199.6 56.3 −30.3 0.087Stratum II 106.7 14.7 −7.2 0.323 114.0 37.2 −14.3 0.453 121.2 40.1 −21.4 0.274Stratum III 85.6 13.8 −3.3 0.426 109.4 34.1 −27.0 0.001 103.8 26.4 −21.4 b0.001Stratum IV 84.8 15.9 9.0 0.113 78.8 52.2 15.2 0.447 91.2 44.0 2.8 0.870

B=mean of estimated mean above-ground biomass, RMSE=root mean square error between estimated and observed mean above-ground biomass (Eq. (24)),DP

=meandifference between estimated and observed mean above-ground biomass (Eq. (25)).


risk of using pure model-based methods in the estimation when themodels are poorly specified or subject to errors that sometimes canbe hard to detect. This will be the case regardless of which remotesensing technique is used.

A final source of error in the InSAR regression models is a potentiallack of geographical correspondence between the sample surveyplots and the SAR pixel assigned to each plot. The SAR data have cer-tain limitations in the precision of their coordinates, they are largerthan the sample survey plots (465 versus 200 m2), they have a differ-ent shape than the plots (15×31 m pixels versus circular plots), andthe SAR pixel structure is not perfectly aligned with the systematiclayout of the sample survey plots so that plots may be split on severalpixels. All these factors introduce errors in the field-to-InSAR rela-tionships. However, this is a common problem in remote sensingwhen the data have a pixel structure and medium to low resolution.

When such problems arise in design-based applications, the de-sign unbiasedness as well as the reliability of the variance estimatesmay be compromised since the population is defined to be the entirecollection of pixels from which a probability sample is selected, i.e.,the sample survey plots. Clearly, the field plots do not constitute atrue probability sample of the population of pixels due to the geo-graphical mismatch of sample plots and pixels. Although it is com-mon practice to relate field plots to image pixels for modeldevelopment as well as estimation and inference, it is important toevaluate to what degree these departures from the preconditions ofdesign-based estimation have influenced the results. In the currentstudy, we therefore re-estimated the InSAR regression models assum-ing that the second closest pixel to each sample plot was assigned to

0

10

20

30

40

50

60

RM

SE

, Mg

ha-1

Unadjusted Adjusted

Fig. 4. Root mean square error (RMSE) (left) and mean difference (right) between estimatedjusted (Eq. (20)) and adjusted (Eq. (21)) synthetic estimators with LiDAR and InSAR data,

the plot rather than the closest ones. The re-estimation showed onlyminor shifts in the regression parameter estimates, indicating thatthe model-assisted estimates were fairly robust against errors causedby geographical mismatch. This result was not surprising, given thefact that a managed boreal forest will be fairly homogenous withinshort distances as long as one stays within the same managementunit (forest stand). Tropical forests may often be less homogenousthan seen in this case study. In the current study, the positions ofthe field plots were accurately measured with GPS+GLONASS. Inmany applications field positions will be subject to substantial errorsand in fragmented forests in particular such errors may have seriousconsequences for the accuracy of the estimates (McRoberts, 2010b).Data from future InSAR missions with pixel sizes and shapes corre-sponding better with the size and shape of typical field plots may im-prove regression models as well as errors of model-assisted estimatesas compared to those obtained in the current study. For the LiDAR es-timation these problems can be overcome since the basic nature andflexibility of the data (point data) allow us to compute the auxiliaryinformation (the LiDAR metrics) within the plot borders (Gregoireet al., 2011).

A striking pattern in this study is the trend to higher estimatedvalues for above-ground biomass based on the field sample surveycompared to the model-assisted estimates using LiDAR and InSARdata as auxiliary information. In particular, the differences weremost pronounced between the field-based and LiDAR-assisted esti-mates with the InSAR-assisted estimates somewhere in between.These differences at tract level and even for the entire AOI, were mainlydue to large discrepancies for strata I and III (Table 3). It is likely that

-25

-20

-15

-10

-5

0

5

10

15

20

25

Mea

n di

ffere

nce,

Mg

ha-1

LiDAR

InSAR_Topo

InSAR_LiDAR

Unadjusted Adjusted

and observed mean above-ground biomass for the 35 large field plots using the unad-respectively.


the current sample of field plots for these two strata is somewhat out inthe (upper) tail of the sampling distribution and thus above averagewithrespect to AGB. Because the remotely sensed data capture the auxiliaryvariables for the whole population, the model-assisted estimates willbe lower than the direct estimate when a probability sample is in theupper tail of the sampling distribution.

There are several indications of the current sample having suchproperties. First, the field crews were instructed to use hand-held GPSreceivers to navigate to the predefined positions of the sample plotsand then measure the actual plot locations accurately with survey-grade GPS+GLONASS receivers. We did a pair-wise comparison of bio-mass predicted bymeans of the LiDAR data using the regressionmodels(Table 2) for the predefined locations of the 201 sample survey plotswith the corresponding LiDAR-predicted biomass values for the actualplot locations. The predicted biomass for the actual plot locations wason average 8.8 Mg ha−1 higher than for the predefined locations(Fig. 5). For stratum I the difference was 19.8 Mg ha−1. Thus, the cur-rent sample tended to have a higher biomass than at least the samplethat was intended to be collected. In Fig. 5 it can be seen that one plotin particular (plot #132) has a large difference in biomass(262.5 Mg ha−1). As an example, Fig. 6 gives further details regardingplot #132. It shows that theplot had a predefinedposition in anopeningin the forest with a predicted biomass of 3.7 Mg ha−1 but was actuallyestablished 38.6 m in the NE direction where the predicted biomasswas 266.2 Mg ha−1. The conditions on the predefined and actual loca-tions of the plot are also illustrated by the LiDAR canopy height distribu-tions from those locations.

Second, assuming that the sample is located somewhat out in the tailof the sampling distribution, it is reasonable to expect a shift in the aux-iliary variables between the sample and the population as well. Wecompared the mean values of the auxiliary variables included in the se-lected LiDAR regression models for the sample and the population(Table 5). For stratum I, the two selected auxiliary LiDAR variableswere consistently higher in the sample than in the population (6.2and 18.7% higher). For stratum III this trendwas evenmore pronounced(8.3–36.2% higher). As a comparison, the differences in means of the

Fre

quen

cy

-200 -100 0 100 300

020

4060

8010

0

Difference in biomass (Mg ha -1)200

Fig. 5. Frequency distribution of differences in biomass for 201 sample survey plots be-tween their actual and predefined positions. Biomass values for actual and predefinedpositions, respectively, were predicted from the LiDAR data using the regressionmodels in Table 2. The mean of the distribution was 8.8 Mg ha−1.

sample and the population were between−0.4 and−0.6% for stratumII and between−1.1 and 3.7% for stratum IV.

Third, we had the large field plots at hand for an independent val-idation of the regression models. The large field plots did not consti-tute a probability sample. However, to the extent that a validationof the regression models against these plots gives fairly unbiased re-sults, it is reasonable to expect that the regression models performfairly well for the remaining part of the population as well and thusthat the model-assisted estimates based on the LiDAR data are trust-worthy. This would in particular be a strong argument if the indepen-dent validation would show only minor discrepancies and the meanobserved AGB values of the sample survey plots and the large fieldplots at the same time would differ significantly. In the following, itis our intention to pursue this argument.

Errors in the explanatory variables will affect the parameter esti-mates of the regressions, and in particular deflate the value of the pa-rameter estimate for the explanatory variable subject to errors. In thecurrent study, several types of errors (mentioned above) were inher-ent in the InSAR heights in particular. Thus, the InSAR models willtend to become ‘flat’ and will thus to a larger degree than more ap-propriate models like the LiDAR models, tend to reflect the meanvalue of the data used for model estimation (the sample surveydata). As a matter of fact, for each of the four strata the meanInSAR-estimated biomass of the 35 large field plots was fairly similarto the mean observed biomass of the sample survey plots, despite thefact that mean observed field values of the sample survey plots andlarge field plots deviated by 11–22%. For the poorest InSAR models,i.e., the models for InSAR height with topographic terrain data usedas reference, the mean estimated biomass for the large field plots de-viated less than 3% from the mean observed value of the sample sur-vey plots. For LiDAR however, the estimated biomass for the largefield plots showed only minor and statistically non-significant devia-tions from the observed values, as noted above. The fact that themodel-assisted estimates were lowest using LiDAR as auxiliarydata – and with the InSAR-assisted estimates in between the directestimates and the model-assisted LiDAR estimates – is consistentwith the results of the independent validation and the assumptionthat the current probability sample is located somewhat in theupper tail of the sampling distribution.

In this study, a probability sample of circular field plots with size200 m2 was used in the estimation. Although not reported here, forstrata I–III these plots were the inner circles of two concentric circularplots, of which the larger plot has an area of 400 m2. Because ofboundary effects (trees with stem locations outside the plot andthus not measured in field but with crowns partly inside the plotsand thus measured by the laser, and vice versa) and GPS positioningerrors, larger plots are often preferred in operational forest manage-ment inventories with LiDAR (Gobakken & Næsset, 2009). We did apreliminary estimation of biomass for the three mentioned stratausing the 400 m2 plots and the estimators presented in this study.The results showed a reduction in estimated standard errors byaround 25%, and the relative improvement in precision was largerthan what we experienced for the pure field survey (the direct esti-mate) when increasing the plot size from 200 to 400 m2. Thus, ouranalyses indicate there is a potential for improved estimates bychoosing plot sizes better suited for model development. However,the best suited plot sizes will depend on the characteristics of the for-est to be inventoried and available resources.

Finally, one should keep in mind that the design-based estimatorsof variance do not account for the uncertainty, whether manifest asbias or variance, in the allometric prediction of the biomass on theground plot. Although this is a commonly accepted practice globallywhen estimating biomass with previously fitted models of AGB, it isa practice that both vitiates design unbiasedness of estimators of bio-mass and likely results in an underestimation of its design-based var-iance (Gregoire & Stehman, 2011).

0.0 0.1 0.2 0.3 0.4

05

1015

2025

3035

Density

LiD

AR

hei

ght (

m)

Fig. 6. Left: Predefined position (red) and actual position where field measurements were conducted (blue) for sample survey plot #132. Plot size is 200 m2. Right: CorrespondingLiDAR canopy height distributions (kernel density) for plot #132 at the predefined position (red) and the actual position (blue). The distance between the predefined and actualpositions is 38.6 m. Biomass for actual position predicted from LiDAR data was 266.2 Mg ha−1 whereas biomass predicted from LiDAR data for predefined position was 3.7 Mg ha−1.


5. Conclusions

The simple model-assisted estimators demonstrated in this studyare relevant for a number of practical inventory applications encoun-tered in developed countries as well as in tropical countries where ef-ficient and timely methods for inventory and monitoring are requiredfor local REDD activities. The strengths of the demonstrated estima-tors are the consistency obtained between various geographical levelsand the attractive property of (approximate) design-unbiasedness.Although the present study only focused on a current inventory, theadopted estimators and procedures can easily be adapted to estima-tion of temporal changes. The empirical results indicated a consider-able improvement in precision of the biomass estimates when

Table 5Mean values of the auxiliary variables used in the selected LiDAR regression models(Table 2) for the population and for the sample.

Variable Population Sample

n Mean n Mean

Stratum I 408,851 50pf50 (m) 13.41 15.93dl0 0.44 0.47

Stratum II 329,888 47pf80 (m) 14.86 14.81df0 0.65 0.65

Stratum III 698,366 50pf90 (m) 14.14 15.31pl60 (m) 12.07 13.67df6 0.33 0.45

Stratum IV 887,698 54pf70 (m) 10.05 9.94df1 0.63 0.65dl2 0.29 0.30

pf50, pf70, pf80, pf90=50th, 70th, 80th and 90th height percentiles of the first echocanopy height distribution, respectively; pl60=60th height percentile of the last echocanopy height distribution; df0, df1, df6=relative cumulative canopy height densitiesabove the 0th (2 m), 1st, and 6th vertical height layer of the first echo heightdistribution, respectively; dl0, dl2=relative cumulative canopy height densities abovethe 0th (2 m) and 2nd vertical height layer of the last echo height distribution,respectively.

LiDAR data were used as auxiliary information. The results also dem-onstrated an improvement for the more crude InSAR, in particularwhen an accurate terrain model was used as reference surface. Accu-rate terrain models will only occasionally be available in tropicalcountries, however, if the relationship between biomass and InSARheight is linear, a temporal change in biomass might be estimatedeven without terrain model. Other errors inherent in the currentInSAR data, such as the time lag between the acquisitions of the var-ious datasets, suggest that we have underestimated the potentialbenefits of InSAR. Hence, InSAR may be a useful alternative to LiDARin situations where LiDAR data are unavailable because of highcosts, extensive areas, or cloud problems. For REDD applications inparticular it becomes imperative to conduct similar and detailed stud-ies under tropical forest conditions. Availability of relevant and effi-cient data for stratification, as well as the strength of regressionsmodels will deviate from what we have experienced in our borealstudy. In this study, we only conducted an independent validationto assess the quality of the biomass estimates at the lowest geograph-ical level (stands, patches) where we had to rely on the synthetic es-timator. It would be highly relevant to provide error estimates even atthis geographical level. Methods for such estimation should be sub-ject to further studies.

Acknowledgments

This research has been funded by the Research Council of Norway(project #184636/S30: “Effects of changing climate on the alpine treeline and mountain forest carbon pools along 1500 km N–S and eleva-tion gradients”). We wish to thank Viken Forest Owners Associationfor giving access to stand maps and data collected in the field samplesurvey, and to Blom Geomatics for collecting and processing the air-borne laser scanner data. We are also grateful to our colleagues atthe Norwegian University of Life Sciences, Dr. Ole Martin Bollandsås,Mr. Marius Hauglin, and Mr. Vegard Lien for collection and estimationof field data at the large sample plots, and to Dr. Johannes Breiden-bach for valuable comments on an early draft of this article. Finally,we wish to thank the four anonymous reviewers who all providedcomprehensive and relevant comments which significantly improvedthe manuscript.


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