determining forest structural attributes using an inverted geometric-optical model in mixed eucalypt...

Determining Forest Structural AttributesUsing an Inverted Geometric-Optical Modelin Mixed Eucalypt Forests, SoutheastQueensland, Australia

Peter Scarth* and Stuart Phinn*

The Montreal Process indicators are intended to pro- sensors for monitoring forest structure and condition.vide a common framework for assessing and reviewing Elsevier Science Inc., 2000progress toward sustainable forest management. The po-tential of a combined geometrical-optical/spectral mixtureanalysis model was assessed for mapping the Montreal INTRODUCTION AND BACKGROUNDProcess age class and successional stage indicators at a

The sustainable utilization of a forested area is depen-regional scale using Landsat Thematic Mapper data. Thedent on management strategies that take into accountproject location is an area of eucalyptus forest in Emuthe functions, structures, and responses to disturbance ofCreek State Forest, Southeast Queensland, Australia. Athe forest at appropriate temporal and spatial scales. Re-quantitative model relating the spectral reflectance of amotely sensed data can contribute to this understandingforest to the illumination geometry, slope, and aspect ofif the mapping and monitoring strategies are consistentthe terrain surface and the size, shape, and density of thewith the space and timescales of the processes and struc-trees was developed. In the model estimates were derivedtures in question (McDonald et al., 1996). Trackingfor crown cover projection, tree density, and canopy size.changes in a forested environment is simplified by theInversion of this model necessitated the use of spectraluse of indicators. Indicators are key measures, or surro-mixture analysis to recover subpixel information on thegates for key measures, that provide useful informationfractional extent of ground scene elements (such as sunlitabout the whole forest system and are based on the bestcanopy, shaded canopy, sunlit background, and shadedscientific understanding of how the environment worksbackground). Results obtained from a sensitivity analysis(ANZECC, 1998). Australia has state, national, and inter-allowed improved allocation of resources to maximize thenational obligations to provide reports on indicators ofpredictive accuracy of the model. It was found that mod-forest sustainability. Montreal Process indicators are in-eled estimates of crown cover projection, canopy size,tended to provide a common framework for assessingand tree densities had significant agreement with fieldand reviewing progress toward sustainable forest man-and air photo-interpreted estimates. However, the accu-agement. The Montreal Process criteria and indicatorsracy of the successional stage classification was limited.provide a basis for the ongoing assessment of the stateThe results obtained highlight the potential for future in-of Australia’s forests and their contribution to societytegration of high and moderate spatial resolution-imagingover time (DPIE, 1998). A technique using Landsat The-matic Mapper (TM) data in conjunction with an invertedGeometric-Optical (GO) model was developed and* Department of Geographical Sciences and Planning, The Uni-

versity of Queensland, Australia tested for assessing two of the most critical MontrealAddress correspondence to S. Phinn, Department of Geographi- Process criteria. These criteria are: (1.1b) the extent of

cal Sciences and Planning, The University of Queensland, Brisbane, area by forest type and by age class or successional stage;Queensland, Australia, 4072. E-mail: [email protected] 5 February 1999; revised 15 June 1999. and (1.1d) the extent of areas by forest type in protected

REMOTE SENS. ENVIRON. 71:141–157 (2000)Elsevier Science Inc., 2000 0034-4257/00/$–see front matter655 Avenue of the Americas, New York, NY 10010 PII S0034-4257(99)00066-8

142 Scarth and Phinn

measured in Landsat TM images. Franklin and Strahler(1988) in West Africa, and more recently Woodcock etal. (1994) in the Stanislaus National Forest in the UnitedStates, have used this approach to estimate tree size anddensity. With the exception of Jupp and Walker (1997),there is a paucity of work within Australian and otherforested environments using this technique.

The Li-Strahler model estimates the proportion ofsunlit and shaded canopy and background for a giventree size and tree density. It is a geometrical-opticalmodel and as such, relies on the three-dimensional struc-ture of the canopy as the primary factor influencing re-flectance from the canopy (Strahler and Jupp, 1990). Themodel assumes that the satellite ground resolution ele-ment (GRE) is much larger than the size of the individ-ual tree crowns but smaller than the size of forest stands,and that the individual trees are randomly (Poisson) dis-Figure 1. Conceptual schema of the Li-Strahler geometric-

optical model, indicating the scene components contributing tributed within the pixel (Woodcock et al., 1994). Hence,to the measured response in each ground resolution element. the signal arriving at the sensor can be modeled as a lin-

ear combination of the response from ground scene ele-ments (sunlit canopy, sunlit background, shaded canopy,

areas defined by age class or successional stage (DPIE, and shaded background) reflecting electromagnetic radi-1998, p. 9). ation (EMR) in each pixel (Fig. 1). However, the data

The spatial extent of Australia’s forest areas con- flow in this model can be inverted. This means that bystrains the exclusive use of conventional air photo inter- knowing the outputs, it is possible to calculate what inputpretation (API) and field assessments to assess indicator conditions were. The inverted Li-Strahler model esti-status for regional and national level reports. Therefore, mates the canopy radii and density of trees from re-use digital remote sensing techniques have been pro- motely sensed images by relating the fraction of shadeposed to introduce speed, reliability, and consistency into within a given picture element (pixel) to the geometrythe monitoring requirements. Medium resolution digital and density of simplified geometric models of trees,imagery (30330 m ground resolution element), such as which are illuminated so that they cast a shadow. Thethat provided by the Landsat satellite’s Thematic Mapper primary tree geometry parameters are h (the height from(TM) sensor, presents a cost-effective option for moni- the ground to midcrown), b (the radii of the crown intoring regional scale ecosystems (Wallace and Campbell, the vertical direction), and r (the radii of the crown in1998). Jupp and Walker (1997) noted that in vegetation the horizontal direction) (Fig. 1). Values of r/b, h/b anddynamics as well as in habitat and resource assessment, the coefficient of variation of r2 must be obtained fromstructure is an essential factor. In this context, structure test stands representing the range of forest types foundis defined as the horizontal and vertical distribution of in the area to be mapped. These test stands can be delin-components within a plant community. Geometric-opti- eated from high spatial resolution digital imagery in com-cal models have been used in a number of forested and bination with maps of air photo-interpreted forest typeswoodland environments to estimate structural properties, and growth stages for sections of the study area. Hence,but have had no application in eucalypt forests of eastern high-resolution digital imagery is only required for aAustralia (Jupp and Walker, 1997; Strahler and Jupp, small part of the study area.1990; Jupp et al., 1986). If r/b, h/b, the solar zenith and azimuth (hi, ui), the

view zenith and azimuth (hv, uv), and the local slope andGeometrical-Optical Models aspect (hs, us) are known, then the remaining variationsLi and Strahler (1985, 1992) modeled a tree canopy as in the Li-Strahler geometrical-optical model can be de-a collection of individual geometric objects that cast scribed in terms of a parameter denoted m. This parame-shadows on a contrasting background (Fig. 1). The geo- ter has often been called the “treeness” and is definedmetrical-optical model with appropriate choices of can- as the ratio of the sum of the squares of the radii of theopy component signatures explains the major portion of trees whose stems are within a GRE to the GRE area.the variance in reflected and absorbed electromagnetic It is a significant parameter in the relationship betweenradiation in a remotely sensed image of forested environ- digital images and forest structure. The mean of m overments. In this study, a similar model is developed as the a forested region is denoted M. This is a stand parameterbasis for analyzing forest structure, in particular the age defined such that p·M5K·A, where K is the stem density

and A is the mean vertically projected area of the crown.class and successional stage from the optical response as

Determining Forest Structure Attributes 143

In the case of Poisson-distributed stems, this value of M end-member is the spectral response of pixels having thecan be related to the vertical crown cover projection closest approximation to pure conditions (i.e., pure cover(CCP) by Eq. (1) (Jupp and Walker, 1997): types) that are found in the image. In most cases, an

end-member spectrum is obtained from field measure-CCP512e2p·M (1)ments with a spectrometer, or is taken from a spectral

The Li-Strahler model assumes that the reflectance of library. Alternatively, pure (unmixed) pixels can be lo-the sunlit and shadowed components is uniform and in- cated on imagery with sufficiently high spatial resolutiondependent of varying crown, background, and atmo- that has been field-validated.spheric parameters, with negligible multiple scattering The general equations that govern SMA are outlined(Gerard and North, 1997). The chief difficulty in modelin Eq. (2) and Eq. (3).ing is finding an analytical solution to the area of overlapbetween illumination and viewing shadows, particularly Sb5o

m

i51Kirib1dSb (2)

in dense forest where large illumination and viewingangles create mutual shadowing of the crowns (Li and 1.05o

m

i51Ki (3)

Strahler, 1992). Additionally, the assumption of Lam-bertian reflectance is made in this study. Other methods, where Sb is the reflectance of a pixel in band b; Ki is thesuch as nested modeling where leaves are treated as dis- fractional abundance (the area of the pixel occupied bycrete objects within the crown envelope (Strahler and a cover type) of end-member i in a single GRE (from aJupp, 1990), and radiative transfer methods, such as the total of m end-members); rib is the reflectance of bandLi et al. (1995) model, have shown some success, al- b of end member i; and dSb is the residual error in bandthough these methods are computationally intensive for b of the model fit.regional scale analysis. This study evaluates the model If the matrix of end-member spectra r are known,compatibility with Australian forest types, in particular then a simple least squares inversion can be used to findSoutheast Queensland eucalypt forests that are dissimilar the vector K, the fractional abundance vector for eachfrom the North American conifer forests used in the pixel. The most difficult step in this approach is the se-Woodcock et al. (1994) study and the semiarid shrub lection of suitable end-member spectra. Once the end-used by Franklin and Strahler (1988). members have been found, it is possible to determine

To determine the tree size and density it is neces- the percentage abundance of the ground cover types forsary to find the relative abundance of the scene compo-input into an inverted geometrical-optical model.nents that produce the measured response at the sensor,

and then invert the model to derive the forest parame-ters. It is therefore essential to develop a method that DATA AND METHODStakes the TM sensor responses and estimates the relative

Study Areaabundance of the sunlit and shaded scene componentsThe Emu Creek State Forest is located approximatelyfor individual ground resolution elements. An approach100 km southwest of Brisbane in Southeast Queensland,such as spectral mixture analysis can be used to produceon the western side of the Great Dividing Range atfour fraction images that indicate the percentage of the1528269 E, 288119 S (Fig. 2). Emu Creek bisects theground resolution element occupied by the sunlit andstudy area, forming the headwaters to the Condamineshaded, canopy, and background scene elements. The so-River and consequently is part of the Murray Darlinglar irradiance for each ground resolution element is alsocatchment. Altitude of the study site varies from aboutrequired. The output fraction images then provide input660 m to 1,200 m, with thin and rocky soils due to theto a geometrical-optical model for estimating the canopysteep topography (Fig. 3). Vegetation varies from rainradii and tree density.forest and tall, open forest communities in moist shel-tered areas to open forest and woodland on more ex-Spectral Mixture Analysisposed, drier sites. The overstory consists of a number ofLinear spectral mixture analysis (SMA), or spectral un-Eucalyptus species, growing up to 30 m in height: E. mi-mixing theory, has been widely used to compute thecrocorys Tallow-wood, E. propinqua Small-fruited Greyabundance or percentages of cover types that make upGum, E. acmenioides White Mahogany, and E. eugeni-a GRE (Wessman et al., 1997; Adams et al., 1993). Pechoides Narrow-leaved Stringybark. The understory andet al. (1985) pioneered early Australian work on mixtureground cover was a mix of regenerating overstory smalleranalysis as a formal framework for analyzing reflectancetree species (Casuarina torulosa Forest Oak, Acacia sp.),data from multicomponent surfaces, with particular ref-grasses (Themeda triandra Kangaroo Grass, Lomandraerence to the effects of shadowing as an interaction be-sp., and Senecio sp.), and ferns. The climate is temperatetween landscape components. SMA relies on the selec-with average annual rainfall of 900 to 1,000 mm withtion of end members that closely represent and maximize

the difference between pure surface cover types. An marked seasonal distribution.


Figure 2. Location of the study site, Emu Creek,southeast Queensland, Australia (developed fromERSIS data, 1993).

Sequence of Processing Operations Land and Trees Study (SLATS) (Collett et al., 1998). ANormalized Difference Vegetation Index (NDVI) wasA discrete sequence of processing operations was appliedadded as an additional information band to provide ato process field and image data acquired for the studymeans for reducing the differences between reflectancesite (Fig. 4). This sequence involved: (1) modifying thevalues of surfaces subject to different illumination levelsLi and Strahler (1992) geometric-optical model; (2) con-and to provide additional discrimination between vege-ducting a sensitivity analysis to determine which inputtated and nonvegetated regions. A minimum noise frac-parameters should be focused on to obtain the most ac-tion (MNF) transform was applied to the seven bandscurate data; (3) parameterizing and implementing a spec-to reduce the dimensionality of, and diminish the noisetral unmixing routine to estimate the sunlit and shadedinherent in, the data (Green et al., 1988). Examinationcanopy and ground sections of a pixel; (4) integrating the

unmixing results into the geometric-optical model to esti- of the transformation eigenvalues showed that the firstmate tree density and canopy width; and (5) quantita- three MNF components explained 87% of the variancetively assessing the accuracy of tree density, crown cover in the data. Visual inspection of the MNF data showedprojection, successional stage, and canopy size maps us- significant noise in bands four to seven. Based on thising field and air photo data. result, only the first three MNF bands were retained for

further analysis.Data Preprocessing Ancillary data were used for a number of applica-

tions, including a digital elevation model (DEM) with 50The Landsat TM scene used in this project was acquiredm spatial resolution, 1 m vertical resolution, and subpixelon June 29, 1995 and had been processed to eight-bit

“at-sensor” reflectance values for use in the Statewide geometric registration. The DEM was used to calculate

Figure 3. Distribution of slopes over theEmu Creek study site: (left) Graph ofstudy site area as a function of slope and(right) slope map indicating the locationof the field quadrats.


Figure 4. Outline of the modeling methodology used to derive forest structural parametersfrom Landsat TM and DMSV data (input data5light gray boxes, output products5darkgray boxes).

slope and aspect surfaces along with a topographic mod- sites were identified based on analysis of image data col-lected from the Specterra Digital Multi-Spectral Videoeling error image. Air photo-interpreted growth stage

maps for 1996 were supplied by the Queensland Depart- (DMSV) at 2.0 m pixel size. Quadrat one was located atan altitude of 765 m on a 158 easterly slope with thin,ment of Natural Resources as ArcInfo polygons, with at-

tribute tables indicating the area covered by tree crowns, rocky, moist dark loam soils. Quadrat two was located ona level 780 m high ridge 100 m west of quadrat one onsuccessional stage, and presence of disturbance. This

coverage had been assessed as having below-average ac- moderately deep loam soils with a high organic content.This quadrat was markedly more open than quadrat onecuracy (Jones, 1998).

Fieldwork within the Emu Creek State forest was with smaller trees of a similar species composition toquadrat one. There was no evidence of logging in quad-completed in June 1998 to collect data for calibration

and validation of the Geometric-Optical modeling pro- rats one and two, though cattle grazing appeared inten-sive. The area had been burnt within the last 10 years.cess. Three distinct forest structural types and reference


Quadrat three was located on a NW slope at an elevationof 660 m, on rocky loam soils with high organic content.

h9s 5p2

2arctan3tan1p22hs2r/b 4 (8)There was no evidence of disturbance by fire, logging,

or grazing at this site. These reference sites were sur-veyed using a differential GPS and total survey station h9i 5arctan1tan hi

r/b 2 (9)within the 40340 m quadrats. 156 eucalypt stems above100 mm diameter were identified and recorded, together

h9v5arctan1tan h9sr/b 2 (10)with an estimate of their height, crown diameter, and

relative spatial position.Incorporating the topographic transformations of Schaffet al. (1994) gives Eq. (11):Geometrical-Optical Model Development andh″i 5arccos(cos(h9i )cos(h9s )1sin(h9i )sin(h9s )cos(ui2us)) (11)Sensitivity Analysis

The Li and Strahler (1992) model was derived from the and Eq. (12)assumption that the Bidirectional Reflectance Distribu-

h″v 5hs (12)tion Function (BRDF) is a purely geometric phenome-non resulting from a scene of discrete three-dimensional

Eqs. 6 through 12 were used to find the value of Mobjects being illuminated and viewed from different loca-from the solar zenith and azimuth, the slope and aspecttions. The reflectance or response from each of the fourof the surface, and the proportion of sunlit backgroundscene components (sunlit canopy, sunlit background,kg. The sensitivity of m to noise in kg and errors in theshaded canopy, and shaded background) in this simpli-estimation of r/b, h/b, hs, and us can be shown by takingfied model is a function of the size and density of thethe partial derivative of m with respect to these variables.canopies present. Hence, it was not necessary to obtainThe equations for ]m/](r/b), ]m/](h/b), ]m/]hs, and ]m/an expression for the BRDF of each scene component]us were used to calculate and visualize the susceptibilitythroughout the image. The solution for one componentof the model to small changes in input parameters.(sunlit background) is sufficient to invert the model to

derive the size and density terms. Li and Strahler (1992)Spectral Mixture Analysis Modelmodeled the sunlit background component (KG) as theThe inversion of the Li-Strahler model requires an esti-proportion of the area of background within a groundmate of kg, the sunlit background fraction. This must beresolution element that is both illuminated and viewed,a quantitative value, representing the actual proportionusing the Boolean model (Serra 1982) as seen in Eq. (4):of sunlit background in each image pixel ranging from 0

Kg5e2p·M·[sec(h9i)1sec(h9v)2O(h

i,h

v,φ)] (4) to 100 percent. This condition disallows the use of

matched filtering and related approaches. Consequently,where the term O(hi,hv,φ) is the overlap function be- a linear spectral mixture model where the reflectance oftween viewing and illumination shadows as projected a pixel (s) was applied is given by Eq. (13):onto the background. Li and Strahler (1992) and Wanner

s5kgG1kcC1ktT1kzZ (13)et al. (1995) give the exact solution of this function inthe principle plane as shown in Eq. (5): where k5end member fraction for sunlit background (g)

and canopy (c) and shaded background (t), and canopyO(hi,hv,φ)5

1p

(sec h″i 1sec h″v )(t2sin t cos t) (5) (z); and G, C, T, Z5end member reflectance spectra forsunlit background (G) and canopy (C) and shaded back-ground (T) and canopy (Z).where for the nadir-viewed case [see Eq. (6)]:

Note that this requires spectral knowledge of all thefour sunlit and shaded, canopy, and background endcos t5min11,h/b

|tan h″i 2tan h″v cos φ|sec h″v 1sec h″i 2 (6)

members in a pixel. In this simplified model, there areonly the four ground scene elements (G, C, T, and Z) inIf the GRE is large with respect to the individual cano-a ground resolution element and the identity Eq. (14) ispies then it is possible to substitute for O(hi,hv,φ) in Eq.also assumed to hold true:4 and solve for m, as seen in Eq. (7):

kg1kc1kt1kz51 (14)m≈ 2ln(kg)

(sec h″i 1sec h″v )(p2t1cos t sin t)(7) The MNF transform reduced the six input Landsat TM

bands and the calculated NDVI to three bands with largeFor the nadir-viewed case, the illumination, viewing, and eigenvalues and coherent eigenimages. With reliable esti-slope angles corrected for the spheroidal shape of the mates of the end-members, Eqs. (13) and (14) represent

four equations in four unknowns. This was formulated ascrown are shown in Eqs. (8), (9), and (10):


the linear system [see Eq. (15)]: the surface, the canopy end members should not change.The major change will be to the background end mem-q·K5R (15)bers due to the irradiance change within the IFOV at

where q denotes the matrix of end members, the pure the default viewing geometry. The method of correctionreflectance values of the sunlit and shaded, canopy and was to calculate the actual irradiance over the study areabackground, including the sum to one constraint; K is at the time of scene acquisition by the sensor using athe unknown proportions of the sunlit and shaded, can- model based on Collares-Pereira and Rabl (1984). Theopy, and background ground cover types; and S is the model outputs per-pixel estimated beam (eB) and diffusereflectance of the pixel in the three MNF bands. Equa- (eD) components of irradiation for the time of acquisition.tion (15) was solved on a per-pixel basis using the singu- The total irradiation is calculated by eT5eB1eD. If E islar value decomposition (SVD) of the matrix q. The SVD the mean total irradiance over the study site, then theof q was also used to calculate the two-norm condition correction in Eq. (19) can be used to modify G, the re-number, j(q), as an indication of the accuracy of the reflectance of a sunlit background surface as viewed by asults from matrix inversion and the linear equation solu- sensor, on a per-pixel basis when unmixing (Pellikka,tion. The relationship between errors in the measure- 1998), as shown in Eq. (19):ment of the reflectance (dS) and the consequent errorsin the ground scene element fractions (dK) is expressed G(corrected)5

G·eT

E(19)

in Eq. (16):

Because the operation was performed in MNF space, itidKiiKi

<j(q)idSiiSi

(16) was necessary only to modify the band one componentof G. MNF band one is usually related to the overall

The sensor noise dS is related to the covariance-variance scene brightness (Green et al., 1988), which in turn is anoise matrix N by dS·dST5N (Settle and Drake, 1993). function of the scene irradiance. The second and third

Substituting this into Eq. (16) gives Eq. (17): components were not altered, as the remaining MNFbands were mutually orthogonal to the first MNF band

idKi<j(q)√iNi·iKi

iSi(17) and as such are not related to the scene irradiance.

End-Member OptimizationThis relationship demonstrates the importance of con-The initial set of end-members obtained from the man-ducting an MNF transform before conducting spectralual delineation of pixel purity index (PPI) spectra (Re-unmixing. The MNF transform reduces data dimension-search Systems, 1998; Kruse, 1998), while representativeality and results in data with unit noise such that √iNi5of the extreme pixels in the Landsat TM image, may still1.0 (Green et al., 1988). Since √iNi calculated from thecontain mixtures of the “ideal” sunlit and shaded canopyestimated Landsat TM noise was 9.9, Eq. (17) demon-and background end-members (Fig. 5). Since a priori in-strates that the MNF transform produced unmixing re-formation from three field-sampled quadrats was avail-sults with a potential error almost an order of magnitudeable, along with the location of a bare field, expected ge-lower than unmixing with raw Landsat TM data.ometric-optical model results for these pixels were

Nonnegativity Constraint computed and compared to the precise values obtainedEquation (15) fails to take into account the constraint by fieldwork. By slightly perturbing the q matrix, it isthat the proportions of the scene elements must always possible to reduce the error between the expected andbe positive [see Eq. (18)]: actual values of tree density and move the values in the

q matrix closer to being true representative end mem-K>0 (18)bers. This process matches the geometric-optical model

In practice, given reasonably representative and separa- output to field values and determines suitable end-mem-ble end members it is unlikely that the condition in Eq. ber values for use in the spectral-unmixing model. This(15) will be violated. However, it was found that this iterative minimization process was based on the calcula-constraint was necessary during the end member optimi- tion of the least squared error between the field-deter-zation process. mined CCP for the three quadrats and an open paddock,

and the values obtained from the geometrical-opticalIrradiance Correctionmodel. The mean of the closest four model pixels thatThe component spectral signatures of each end membersurround each field quadrat was used for the evaluation.are influenced by their topographic slope and aspect, af-The objective of the process was to force the geometri-fecting both direct and diffuse irradiance of each scenecal-optical model output to equal the field-calculatedcomponent. To enable the assumptions of SMA to beCCP through small perturbations of the end-members inmet in the Emu Creek scene, it was essential to mini-an iterative process. Initially the model underestimatedmize or remove these effects and focus on canopy geom-

etry. Since trees grow vertically in spite of the slope of the CCP for all of the calibration points by up to 25%.


Figure 5. Initial end members in (a) MNF bands and (b) original Landsat TM bands, andoptimized end members in (c) MNF bands and (d) original Landsat TM bands.

Upon termination, the error for the quadrats was less(1985), where R2< V(m)

(11w)·Mwas shown to give errors ofthan 3%, with the model still overestimating the CCP for

a bare field by 10%. Figure 5 shows the optimized spec- up to 5 m in the determination of crown diameters dur-tra, demonstrating that although the values have changed ing the initial modeling process using extreme values ofslightly, the forms of the end members are cognate with M and V(m) and thus was not used. Eq. 21 relates the

squared crown diameter to the mean and variance of thethe initial end members.“treeness” parameter (m), given the coefficient of vari-ability of the squared crown diameter (w). A squareInverting the Model Using the Variance of m“stand” was delineated around each pixel and used to cal-Li and Strahler (1985) demonstrated how the variance of culate the mean and variance of m about that pixel.

the “treeness” parameter (m) within a stand could beused to estimate the values of K and R2. If M5KR2 is Determining Stand Size and Successional Stagethe mean value of m for a stand, then the variance of m from R2

within a stand is given by the formula for independentTo determine the size of a stand, the semivariance of mproducts (Li and Strahler, 1985), as shown in Eq. (20):was estimated by an interactive semivariogram plottingtool developed in ENVI. The relationship between theV(m)5V(k·R2)5(R2)2·V(k)1K2·V(R2)1V(k)·V(R2) (20)range of the semivariogram derived from the DMSV im-

Since k is a Poisson function, it can be shown that [see age and the spatial extent of a vegetation community wasEq. (21)]: used as an estimator to define a stand (Jupp et al., 1988;

Phinn et al., 1996). The characteristic range of the semi-R2<√(11w)2·M214·V(m)·w2(11w)·M

2w(21) variogram in both the horizontal and vertical directions

in forested areas was 13 pixels, or 325 m. This value wasused to define a neighborhood of 13313 pixels (10.5 ha)The additional approximation used by Li and Strahler


Table 1. Geometrical-Optical Model Calibration Parameters muth, respectively. At this point with the value of m at0.31 (CCP of 62%), the apportioned error in m is equalParameter Meanto 0.94 times the error in the slope calculation in radians,

r/b 0.7560.27 or 0.016 times the error in degrees. Given that the maxi-h/b 2.6160.65mum RMS error in the topographic modeling was 30%,

95% confidence intervals. r/b is the crown horizontal to vertical radii then the upper limit for the error in m from this sourceratio, h/b is the ratio of tree midcrown height to the vertical canopy radius.is equal to 0.13. Whilst this is approaching almost 50%of the actual value of m, the error in most cases will bemuch less. This is due to the maximum error in topo-about a given pixel that circumscribed the limits of thegraphic modeling being concentrated in areas of high“stand.” This “stand” was then used to determine theslope, where the sensitivity of m is much less. For reli-mean and variance of m for inversion of the geometrical-able extraction of biophysical data, a higher spatial reso-optical model using Eq. (21).lution digital elevation model would be required to miti-Gates et al. (1983) studied the distribution of treegate these errors (Jensen, 1996).sizes in plantations of Pinus radiata and found that the

The sensitivity of m to errors in the tree geometrytree height distribution was negatively skewed for aparameters r/b and h/b is demonstrated in Fig. 7. Here,young forest, normally distributed for a mature forest,contours represent the value of ]m for different h/b andand positively skewed for a senescent forest. In thisr/b values when the sunlit background fraction equalsstudy, the Pearson mode skewness was used as a basis to20% with a slope of 08. Clearly, the geometrical-opticalclassify successional stage in eucalypt forests [Eq. (22)].output is sensitive only to change in r/b when h/b ex-ceeds a value of approximately 1.75. This is illustratedb5

mean(r)2mode(r)rr

(22)using KG520% and the values of r/b and h/b determinedfrom the field data (Table 1). At this point, ]m/](r/b)5The calculation of b was used produce nominal scale suc-0.12 while ]m/](h/b)50. This demonstrates the impor-cessional stage maps for the study site by classifying pix-tance of accurate r/b calibration, even though h/b is anels in the output image from the geometric-opticaleasier ratio to measure. Obviously, time and resourcesmodel (canopy radius) with b,20.2 as regeneration,are better spent on the accurate determination of the r/b20.2,b,0.2 as mature and b.0.2 as senescent.parameter rather than on the h/b parameter.

Sensitivity to the Sunlit Background FractionRESULTS AND DISCUSSIONThe sensitivity of the relationship between m and the

Field Data sunlit background fraction is explored in Fig. 8. The par-tial derivative of m with respect to the sunlit backgroundThe field data set was manipulated to provide the geo-is plotted against the sunlit background fraction. Whenmetrical-optical model calibration parameters and to pro-the sunlit background fraction is 9%, ]m/]KG is equal tovide data for validation of output. Table 1 summarizes21.0, indicating that the error in the determination m isthe tree geometry parameters and Table 2 summarizesequal to the error in determining the sunlit backgroundstatistics on the height and squared crown radius, includ-fraction. However, when the sunlit background fractioning the coefficient of variation. Information on the meanis 1%, ]m/]KG is 29.1, meaning that any error in thecanopy radii, tree height, tree density, and the crownmeasurement of the sunlit background fraction is magni-cover projection calculated for each quadrat is outlinedfied to a nine-fold error in the determination of m. Thein Table 3.accurate determination of the sunlit background compo-nent in areas of high CCP is a critical issue when highGeometric-Optical Model Development andoutput precision is necessary.Sensitivity Analyses

The sensitivity of m to the calculation of slope and aspectSpectral Mixture Analysisis illustrated in Fig. 6, where the height indicates the

value of the partial derivative of m with respect to the Initial End-Membersslope and aspect. The greatest sensitivity occurs when The initial end-members are shown in Fig. 5. Note thethe slope and aspect equal the solar altitude and azi- high standard deviation of the sunlit background end

member in bands four and five. The band four variationis due to the sunlit background consisting of both leaf

Table 2. Mean, Standard Deviation, and Coefficient of litter and bare soil with low near-infrared reflectance andVariability of the Squared Horizontal Canopy Radii (r2)grasses or other understory vegetation with high near-

Mean 12.13 m2 infrared reflectance. The variation in band five is mostStandard deviation 14.76 m2

probably related to moisture irregularities across the site.w 1.22 The optimization process resulted in the end-members


Table 3. Field Determined Crown Radii, Tree Height, Tree Density, and Crown Cover Projection

StandardMean Deviation Standard

Canopy of Canopy Mean Tree Deviation of Tree Density CCPSite Radii (m) Radii Height (m) Tree Height (Trees/Ha) (%)

Quadrat 1 7.4 2.7 19.8 6.2 9.0 74Quadrat 2 7.0 4.2 14.8 6.2 8.0 58Quadrat 3 6.0 2.6 10.3 3 6.0 31Open Field N/A N/A N/A N/A N/A 0

displayed in Fig. 5. Note the similarity with the original Predicted ErrorAdditional information on the maximum RMS error re-end-member signatures. The major changes have been asulting from the unmixing process can be drawn fromreduction of the band four reflectance and a correspond-the results from Eq. (17). This indicates the uppering increase in the band five reflectance of the sunlitbound of the error in the unmixing of all the groundbackground component. Figure 9 shows the resultingscene elements, calculated from the spectral conditionfour fraction images from the optimized end-members.number of q. This indicated that for a result expected to

Infeasible Areas range between zero and one (0% to 100% ground sceneThere are some areas where the linear unmixing process element fraction), there is a large area where the poten-delivered a negative sunlit background fraction. These tial error is greater than one. This is an important result,areas indicate a result that is both intuitively and numeri- and underlines the significance of more sophisticated un-cally infeasible, since the logarithm of a negative number mixing algorithms that incorporate additional a prioriis complex. Visual interpretation of the DMSV image knowledge of the scene to further constrain the unmixingshowed these areas generally, but not always, corre- process. Another way to reduce this potential source ofsponded with areas that are in topographic shadow. Sun- error is to concentrate on reducing the values of thelit background fractions below zero outside of the topo- spectral condition number of q, which ranges from 20 tographic shadow zones indicate either the presence of 28 in this study. This entails producing a q matrix withground scene elements other than sunlit and shaded can- greater linear independence, preferably with a conditionopy and background or the use of unrepresentative end value close to the minimum of one. In this application,members in the unmixing process. These areas were re- this is equivalent to increasing the spectral separabilitycoded as infeasible in the output images and no output of the sunlit and shaded canopy and background end

members. This would not appear to be possible withfraction estimates were provided.

Figure 6. Model sensitivity plot de-picting variations in ]m (treeness), as afunction of variable topographic slopeand aspect conditions for a constantlevel of sunlit background (KG520%).


mixing process in the modeling structure. There are rela-tively few places where the unmixing model has failed orhas very high errors, indicating that the assumption ofrepresenting a complex forested environment by fourground scene elements (sunlit and shaded canopy andbackground) accounts for the majority of the spectralvariance within the Emu Creek subscene. However, thepotential errors in the unmixing process, calculated usingthe two-norm condition number of the matrix of end-members, exceed the ground scene element fraction val-ues in many locations. This error can only be mitigated byincreasing the information input to the unmixing model.

Geometrical-Optical Model Outputand ValidationThe calibrated geometrical-optical model, incorporating ir-radiation correction and linear spectral unmixing, wascompiled as an IDL program designed to integrate with

Figure 7. Model sensitivity plot depicting variations in the ENVI image-processing package. The model outputs a]m (treeness) contours as a function of variations in for- number of georeferenced products that include (Fig. 10):est structural properties r/b and h/b for a constantlevel of sunlit background (KG520%). • fraction and infeasibility images;

• an image of the “treeness” parameter (m);• a crown cover projection image;

Landsat TM data due to the limited number and width • a mean crown diameter image;of spectral bands. “Next-generation” satellite sensors • a mean tree density image; andsuch as the Australian Resource Information and Envi- • a stand diameter skewness index.ronment Satellite (ARIES) (Harkness et al., 1998) prom-

The infeasibility image is used to mask from further anal-ise a larger number of spectral bands to improve groundyses those locations where the model has not producedscene element end member separability, and hence im-an output.prove the q matrix condition.

The hypothesis that the predicted CCP is related toAccurate determination of the percentage cover ofand not significantly different than the API CCP waseach ground scene element within a pixel proved to betested by rank correlation of the forest classes derivedthe single most difficult task in this work. The difficultyfrom the model and API classes. This hypothesis was ac-stems from two fundamental problems in mixture analy-cepted with 99.8% confidence and with a 0.0% possibil-sis: (1) finding representative end-members and account-ity of type II error (Table 4). Evidently, the geometrical-ing for their change due to viewing geometry and irradi-optical model outputs reliable estimates of the treenessance variations across the scene; and (2) incorporation of

assumptions about the ground scene elements and the parameter m to compute the CCP value, and the as-

Figure 8. Model sensitivity plot depicting variationsin ]m/]KG (i.e., variations in the treeness parameterassociated with changes in sunlit background levels).


Figure 9. Gray-scale fraction images produced by thespectral unmixing process, representing the fraction ofeach ground resolution element occupied by sunlit can-opy, sunlit background, shaded canopy, and shaded back-ground, from the Emu Creek Landsat TM scene, 29June 1995.

sumption of a Poisson distribution of crown centers that The hypothesis that the measured tree density wasequal to the model tree density was tested using linearunderpins the m to CCP conversion is valid [Eqs. (16)

and (17)]. This is in agreement with work by Franklin et correlation through the origin. As in the previous section,the problems of small sample size and use of the fieldal. (1985), who concluded that in Californian conifer for-

ests, with sensor instantaneous field of views (IFOV) of data for model calibration apply. The high correlation of0.94 could be expected, given the good results for crown20 to 50 meters, counts of trees within the IFOV do not

differ much from those expected from a Poisson model. diameter. Since m5k·R2 and m is known to be accuratein these regions, it follows that a good crown diameterThe hypothesis that the predicted crown diameter

was equal to the field diameter was tested using linear estimation should give a good density estimation. The hy-pothesis is accepted at the 89% significance level with acorrelation through the origin. The testing of this hy-

pothesis is limited by the use of only three samples, al- 7% chance of a type II error (Table 6).In this study, the Pearsons mode skewness of thethough each sample mean is calculated from a minimum

of 40 trees in the quadrat. There was a very high correla- crown diameter within a moving window was used as anestimator for the successional stage of the forest [Eq.tion between the measured and predicted mean crown

diameter values (Table 5). However, the small sample (18)]. The data values were assigned to one of three suc-cessional stage classes. Table 7 outlines the results of asize only allows acceptance of this hypothesis at the 93%

significance level, with the probability of type II error of Spearman rank correlation used to test the hypothesisthat the skewness of crown diameter values is related to6.0%. Time limitations in this study prevented the collec-

tion of independent calibration and validation data sets, API successional stage. Although a moderate correlationwas observed, the hypothesis can only be accepted at theso the quadrats used in this analysis were also used to

calibrate the unmixing end members through iterative 80% significance level.It was evident that there is some pattern of associa-optimization using CCP values at these points. This re-

sulted in very accurate m values for these areas, which tion between the crown diameter skewness and the APIgrowth stage in eucalypt forests, which is similar to thatin effect means that this analysis is primarily testing the

applicability of model inversion using the spatial variabil- observed in pine forests by Gates et al. (1983). Althoughthis is a promising result, additional investigations areity of m.


Figure 10. Forest structure parameter maps derived for Emu Creek on 29 June 1995, from pro-cessing of the geometric-optical model output: (a) crown cover projection; (b) mean crown diame-ter; (c) successional stage; (d) mean tree density.

necessary to quantify and extricate the true nature of KHAT statistic of 25.7%. Comparison with the 535modal smoothed classes, excluding areas where there isthis relationship.

The combined CCP and successional stage classes a low confidence in the model output, dramatically im-proves accuracy. The overall accuracy is improved towere evaluated by comparison with the management unit

classes derived from the API data. The overall mapping 67.4% with a significant j statistic of 47.0% (Table 8).This result highlights the complications involved in usingaccuracy (or average error level) is low at 39.3%, with a


Table 6. Simple Linear Correlation: Tree Density withTable 4. Spearman Rank Correlation: Model Crown CoverProjection with API Data Field Data

Correlation coefficient r 0.94Spear rank correlation rs 0.75Student’s t-test 4.25 Student’s t-test 2.89

a (type I error) 0.11a (type I error) 0.002b (type II error) 1.00 b (type II error) 0.93

a secondary data source for validation. The API delin- the geometrical-optical model should concentrate onproducing accurate measurements of the crown dimen-eates homogeneous areas of forest attributes into distinct

polygons (Jones, 1998). Although mapped at a higher sions. It was noted that the need to evaluate the loga-rithm of the sunlit background fraction in the modelingresolution than the Landsat TM data, the qualitative API

data may contain significant smoothing, with the most process emphasizes the effects of other errors in regionswhere the sunlit background fraction is close to zero.frequently occurring management class ascribed to the

polygon attribute. The modal smoothing of the original This result may limit the applicability of this model inareas of high crown cover projection. It is possible how-geometrical-optical model classes imitated this smoothing

process, resulting in a higher overall accuracy. ever, to use the sunlit canopy fraction instead of the sun-lit background fraction if additional terms to approximateIndividual class accuracy is highly variable in both

error matrixes, with the best result occurring in the non- the mutual shadowing effect of tree crowns are includedin the model. This may alleviate errors in these regions.forest class. The high accuracy coupled with the large

number of points in this class will tend to weight the This study has demonstrated the utility of geometri-cal-optical modeling for the extraction of forest biophysi-overall accuracy. This is particularly evident in the modal

smoothed table, where over 50% of the sample points cal attributes in Australian eucalyptus forests. In particu-lar, the ability to estimate the extent of area by forestare in the nonforest class. The mature forest classes gen-

erally have a high mapping accuracy. These classes are type and by age class or successional stage in correspon-dence with Montreal process indicators 1.1b and 1.1dmore widespread than the regeneration and senescent

classes, and in the context of this study are areas where was demonstrated. The ability to reliably estimate foreststructural dimensions (tree height, diameter, and den-there is low crown diameters skewness. As noted in the

previous sections, the geometrical-optical model provides sity) is important due to its association with ecologicalprocesses and the species associated with these processesbetter estimates of CCP than successional stage informa-

tion, so this result could be anticipated. (DPIE, 1998).Geometrical-optical models incorporating radiative

transfer techniques, such as the Li et al. (1995) model,CONCLUSIONS offer potential for improved performance, particularly inareas of high crown cover projection. Furthermore, thisThe geometric-optical model used in this study has

proven reliable in estimating eucalyptus canopy cover in study has only considered the sunlit background fractioncomponent of the Li and Strahler (1992) model. Thisthe Emu Creek State forest. It has also proven reliable in

extracting biophysical data on crown diameter and tree study confirms results established by Woodcock et al.(1997): (1) The underling assumptions of canopy shapedensity, although further field evaluation is necessary to

assuage the low sample size used in this study. The rela- and tree size are valid; and (2) The estimates of CCP arereliable. In addition it addresses a limitation identifiedtionship between the skewness of the canopy size distri-

bution and the API-determined successional stage is by Woodcock et al. (1997) through the use of multiscaleimage spatial statistics to calibrate the model and definepromising, but further research is necessary to develop

a more accurate association between these variables. the extent of a forest stand. Additional research incorpo-rating the sunlit canopy and shaded canopy and back-Sensitivity analysis of the geometric-optical model indi-

cates the importance of obtaining accurate estimates of ground offers the potential for improved modeling per-formance. Techniques for spectral mixture analysis,the topographic slope and aspect, and the crown geome-

try parameter (r/b). The field effort required to calibrate although becoming widespread, need rigorous evaluation

Table 5. Simple Linear Correlation: Mean Crown Table 7. Spearman Rank Correlation: Model SuccessionalStage with API DataDiameter with Field Data

Correlation coefficient r 0.98 Spearman rank correlation rs 0.48Student’s t-test 1.43Student’s t-test 4.91

a (type I error) 0.07 a (type I error) 0.20b (type II error) 1.00b (type II error) 0.94


Tab

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analysis of density dependant pattern in coniferous forestin a variety of environments to determine the reliabilitystands. Vegetation 64:29–36.of their output. In particular, issues of nonlinear mixing,

Franklin, J., and Strahler, A. H. (1988), Invertible canopy re-the number of fractions to be determined verses theflectance modelling of vegetation structure in semiarid wood-number of measurements, the stability of the final solu-land. IEEE Transact. Geosci. Remote Sens. 26:809–825.tion, and the computational efficiency of the algorithm

Gates, D.J., McMurtrie, R., and Borough, C.J. (1983), Skew-need to be addressed. ness reversal of distribution of stem diameter in plantations

It is noted that the greatest improvement in geomet- of Pinus radiata. Austr. For. Res. 13:267–270.rical-optical modeling accuracy would be obtained using Gerard, F. F., and North, P. R. J. (1997), Analysing the effectboth higher spatial resolution digital elevation models of structural variability and canopy gaps on forest BRDF us-and higher spectral resolution sensors. The development ing a geometrical-optical model. Remote Sens. Environ. 62:

46–62.of next-generation imaging platforms allows an opportu-Green, A. A., Berman, M., Switzer, P., and Craig, M. D.nity for multiple scale analysis of biophysical processes,

(1988), A transformation for ordering multispectral data inwith the opportunity to use high spatial and hyperspec-terms of image quality with implications for noise removal.tral resolution data to calibrate combined geometrical-IEEE Transact. Geosci. Remote Sens. 26:65–74.optical/spectral mixture analysis models. However, the

Harkness, L., Ptzner, L., and Rutten, D. (1998), The electro-integration of multiple scale data requires techniques to optical design of the ARIES hyperspectral remote sensingaddress both up- and downscaling problems in the spatial satellite. In Proceedings of the 9th Australasian Remoteand spectral domains to provide a coherent modeling Sensing and Photogrammetry conference, University offramework. NSW, Sydney, CD ROM: Causal Productions.

Jensen, J. R. (1996), Introductory Digital Image Processing,2nd ed., Prentice Hall, New Jersey.The authors acknowledge The Queensland Department of Natu-

Jones, K. (1998), Mapping disturbance in Southeast Queens-ral Resources, Forest Ecosystems, Assessment and Planningland eucalypt forests from 1:25000 aerial photography. Inteam for the air photo-interpreted forest disturbance andProceedings of the 9th Australasian Remote Sensing andgrowth stage data and the Digital Multispectral Video data;

The Queensland Department of Natural Resources, Comprehen- Photogrammetry conference, University of NSW, Sydney.sive Regional Assessment branch for the Digital Elevation Jupp, D. L. B., Strahler, A. H., and Woodcock, C. E. (1988),Model; The Queensland Department of Natural Resources, Autocorrelation and regularisation in digital images I. BasicStatewide Landcover and Trees Study and the Australian Cen- Theory. IEEE Transact. Geosci. Remote Sens. 26:463–473.tre for Remote Sensing for the Landsat Thematic Mapper data; Jupp, D. L. B., and Walker, J. (1997), Detecting structural andand Dave Mitchell from the Australian Koala Foundation for growth changes in woodlands and forests: The challenge forthe initial field data. remote sensing and the role of geometric-optical modelling.

In The Use of Remote Sensing in the Modelling of ForestProductivity (H. L. Gholz, K. Nakane, and H. Shimoda,REFERENCESEds.), Kluwer Academic Publishers, The Netherlands, pp.75–108.

Adams, J. B., Smith, M. O., and Gillespie, A. R. (1993), Im- Jupp, D. L. B., Walker, J., and Penridge, L. K. (1986), Inter-aging spectroscopy: Interpretation based on spectral mixture pretation of vegetation structure in Landsat MSS imagery:analysis. In Remote Geochemical Analysis: Elemental and A case study in disturbed semiarid and Eucalypt woodlands.Mineralogical Composition (C. M. Pieters and P. A. Englert, Part two. Model based analysis. J. Environ. Man. 23:35–57.Eds.), Cambridge University Press, Cambridge, 145–166. Kruse, F. A. (1998), Advances in Hyperspectral Remote Sens-

Australian and New Zealand Environment and Conservation ing for Geologic Mapping and Exploration. In ProceedingsCouncil (ANZECC), State of the Environment Reporting of the 9th Australasian Remote Sensing and Photogramme-Task Force (1998), Core Environmental Indicators for Re- try conference, University of NSW, Sydney, CDROM:porting on the State of the Environment—Discussion paper Causal Productions.for public comment, ANZECC Secretariat, Canberra. Li, X., and Strahler, A. H. (1985), Geometric-optical modelling

Collares-Pereira, A., and Rabl, J. (1984), Solar radiation calcu- of a conifer forest canopy. IEEE Transact. Geosci. Remotelations. Solar Energy 22:158–160. Sens. GE-23:705–721.

Collett, L. J., Goulevitch B. M., and Danaher, T. J. (1998), Li, X., and Strahler, A. H. (1992), Geometrical-optical bidirec-SLATS radiometric correction: A semi-automated, multi- tional reflectance modelling of the discrete-crown vegeta-stage process for the standardisation of temporal and spatial tion canopy: Effect of crown shape and mutual shadowing.radiometric differences. In Proceedings of the 9th Austral- IEEE Transact. Geosci. Remote Sens. GE-30:276–292.asian Remote Sensing and Photogrammetry conference [CD- Li, X., Strahler, A. H., and Woodcock, C. E. (1995), A hybridROM], University of NSW, Sydney, Causal Productions. geometric optical-radiative transfer approach for modelling

Department of Primary Industries and Energy (DPIE). (1998), surface albedo and directional reflectance of discontinuousA Framework of Regional (Sub-National) Level Criteria and canopies. IEEE Transact. Geosci. Remote Sens. 33:466–480.Indicators of Sustainable Forest Management in Australia, McDonald, E. R., Jupp, D. L. B., and Walker, J. (1996), Re-Department of Primary Industries and Energy MIG Secre- mote sensing as the basis of an integrated forest assessment.tariat, available at http://www.dpie.gov.au/agfor/forests/mon- In Proceedings of the 8th Australasian Remote Sensing andtreal/framework.html. Photogrammetry conference, available at http://www.rfa.gov.

au/documents/rs/rspaper.html.Franklin, J., Michaelson, J., and Strahler, A. H. (1985), Spatial


Pech, R. P., Davis, A. W., and Graetz, R. D. (1985), Reflec- tional reflectance of forests and woodlands using Booleanmodels and geometric optics. Remote Sens. Environ.tance modelling and the derivation of vegetation indices for

an Australian semi-arid shrubland. Int. J. Remote Sens. 7: 34:153–178.Wallace, J., and Campbell, N. (1998), Evaluation of the Feasi-389–412.

Pellikka, P. (1998), Development of correction chain for multi- bility of Remote Sensing for Monitoring National State ofthe Environment Indicators in Australia, State of the envi-spectral airborne video camera data for natural resource as-

sessment. Fennia 176:1–110. ronment technical paper series (Environmental indicators),Department of Environment, Canberra.Phinn, S., Franklin, J., Hope, A., Stow, D., and Huenneke, L.

(1996), Biomass distribution mapping using airborne digital Wanner, W., Li, X., and Strahler, A. H. (1995), On the deriva-tion of kernels for kernal driven models of bidirectional re-video imagery and spatial statistics in a semi-arid environ-

ment. J. Environ. Man. 47:139–164. flectance. J. Geophys. Res. 100:21077–21089.Wessman, C. A., Bateson, C. A., and Benning, T. L. (1997),Research Systems (1998), ENVI Users Guide, Research Sys-

tems Inc., Boulder, Colorado. Detecting fire and grazing patterns in tallgrass prairie usingspectral mixture analysis. Eco. App. 7:493–511.Schaaf, C. B., Li, X., and Strahler, A. H. (1994), Topographic

effects on bidirectional and hemispherical reflectances cal- Woodcock, C. E., Collins, J. B., Gopal, S., Jakabhazy, V. D.,Li, X., Malcomer, S., Ryherd, S., Harward, V., Levitan, J.,culated with a geometric-optical canopy model. IEEE

Transact. Geosci. Remote Sens. 32:1186–1193. Wu, Y., and Warbington, R. (1994), Mapping forest vegeta-tion using Landsat TM imagery and a canopy reflectanceSerra, J. (1982), Image Analysis and Mathematical Morphology,

Academic Press, New York. model. Remote Sens. Environ. 50:240–254.Woodcock, C. E., Collins, J. B., Jakabhazy, V. D., Li, X., Mal-Settle, J., and Drake, N. A. (1993), Linear mixing and the esti-

mation of ground cover proportions. Int. J. Remote Sens. comer, S. A., and Wu, Y. (1997), Inversion of the Li-Strahler canopy reflectance model for mapping forest struc-14:1159–1177.

Strahler, A. H., and Jupp, D. L. B. (1990), Modelling bidirec- ture. IEEE Transact. Geosci. Remote Sens. 35:404–414.

Appendix 1. Symbols Used

Nomenclature Description

S The reflectance of a pixel as viewed by a sensorC The reflectance of a sunlit crown surface as viewed by a sensorG The reflectance of a sunlit background surface as viewed by a sensorT The reflectance of a shaded crown surface as viewed by a sensorZ The radiant spectral response of a shaded background surface as viewed by a sensorkc The proportion of the area of the crown surface within the ground resolutuion element that is both illuminated and viewedkg The proportion of the area of background within the ground resolution element that is both illuminated and viewedkt The proportion of the area of crown surface within the ground resolutuion element that is not illuminated but viewedkz The proportion of the area of background within the ground resolution element that is not illuminated but viewedR2 The mean horizontal squared radius of crowns in a standhv The zenith angle of view directionhi The zenith angle of illumination directionhs The slope of the ground resolution elementus The aspect of the ground resolution elementφ The relative azimuth of illumination and view directionsn The number of trees in a pixelk The density of spheroid centres in the ground resolution element, or the Poisson parameterK The mean of k in a standm;kr2 The “treeness” parameterM The mean of m in a standh The mean height to midcrownr The horizontal radius of a crownb The vertical half axis of the crownrr The standard deviation of r within a standw The coefficient of variation of r2

b The Pearson mode skewness of r within a standet The total irradiation on a pixel at the time of scene acquisitionE The mean total irradiation over the study site

determining forest structural attributes using an inverted geometric-optical model in mixed eucalypt...

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