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Agricultural and Forest Meteorology 150 (2010) 1393–1401

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Agricultural and Forest Meteorology

journa l homepage: www.e lsev ier .com/ locate /agr formet

GAI estimates of row crops from downward looking digital photos takenperpendicular to rows at 57.5◦ zenith angle: Theoretical considerationsbased on 3D architecture models and application to wheat crops

F. Bareta,∗, B. de Solana,b, R. Lopez-Lozanoa, Kai Maa, M. Weissa

a INRA EMMAH UMR1114, Domaine Saint-Paul, Site Agroparc, 84914 Avignon Cedex 9, Franceb ARVALIS – Institut du végétal, Station expérimentale, 91720 Boigneville, France

a r t i c l e i n f o

Article history:Received 15 May 2009Received in revised form 23 February 2010Accepted 20 April 2010

Keywords:Leaf area indexGap fractionDigital photographyRow cropsWheat3D plant architecture model

a b s t r a c t

This study describes a technique to estimate green area index (GAI) of row crops from gap fractionmeasurements at 57.5◦ perpendicular to the row using downward looking digital photos. This particulardirectional configuration makes the gap fraction independent from leaf angle distribution and minimizesleaf clumping when plants overlap within the row and when rows overlap from this particular directionwhich is the case for several crops including wheat, maize, sorghum, sunflower and soybean. This wasdemonstrated from generic row crop canopy architecture models. Additional simulations over realistic3D scenes of wheat crop allowed to calibrate the following equation relating the gap fraction (Po(57.5◦))to GAI for this particular directional configuration: Po(57.5◦) = e−0.824·GAI. This relationship appears veryrobust across development stages, cultivars and variations due to environmental conditions. When com-paring with the situation where leaves are randomly distributed, performances degrade significantly,demonstrating that some residual clumping (˝ = 0.89) has to be accounted for.

Field experiments were conducted over wheat crops using colour digital photos taken at 57.5◦ zenithangle from above in a compass direction perpendicular to the rows. The corresponding gap fractionwas computed after image segmentation based on the three colours. The equation derived from wheatarchitecture model simulations was then used to estimate GAI. Comparison with destructive GAI fieldmeasurements shows very good performances with a relative RMSE of 12%.

GAI values estimated with this technique were also showing a good consistency with LAI2000 PAI(plant area index) estimates. However, systematic biases between the two estimates were observed, dueto canopy elements at the bottom of the canopy not sampled by the instrument because of the height ofthe LAI2000 sensor, as well as accounting for the residual clumping in the proposed method.

These results suggest that this GAI estimation method is very efficient over wheat crops from emergenceup to flowering independently from possible architecture variation due to genotype or environmentalcondition differences. Possible extension to other crops is discussed.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

Leaf area index (LAI) is a key variable involved in several pro-cesses including photosynthesis and transpiration. It is defined ashalf the total developed area of green leaves per unit horizontalground area (Chen and Black, 1992). LAI is considered both as adriver of the future growth of the canopy, and as an integratedindicator of the past development, including the effects of severalpossible stresses. For this reason, LAI is a highly targeted variableboth for the understanding and modeling of canopy functioning,

∗ Corresponding author. Tel.: +33 04 32 72 23 63; fax: +33 04 32 72 23 62.E-mail addresses: frederic.baret@avignon.inra.fr, baret@avignon.inra.fr

(F. Baret).

and for operational applications to adapt to the current state ofthe canopy the decisions that must be taken for crop manage-ment.

LAI may be measured directly through destructive samplingwhich is recognized as the reference method. However, this needsintensive measurements to account for the spatial variability whichmakes these methods tedious, limiting their application to a smallnumber of situations. Indirect methods were developed basedon gap fraction measurements from ground level (Bréda, 2003;Garrigues et al., 2008; Gower et al., 1999; Jonckheere et al.,2004; Weiss et al., 2004). Gap fraction is defined as the fractionof background (respectively sky) seen when looking downward(respectively upward). Several devices were specifically developedfor such measurements, including single detector sensors mainlyusing direct sunlight (TRAC (Chen et al., 1997), DEMON (Lang,

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1986), ceptometers measuring the transmitted light fraction fromincident diffuse and/or the direct illumination (SUNSCAN, ACU-PAR, Decagon. . .), and multidirectional sensors such as LAI2000(Nackaerts et al., 2000) and hemispherical photography (Leblancet al., 2005; Demarez et al., 2008). Single detector devices measur-ing light transmittance from the direct incident sunlight and/or thediffuse one may be difficult to use since the conditions of observa-tions may vary rapidly with time and will impact the performancesof the estimates. Further, estimation of gap fraction from a sin-gle direction or from diffuse conditions requires some additionalassumption on leaf angle distribution that is difficult to get andmay also vary as a function of species, development stages and envi-ronmental conditions. Multidirectional gap fraction measurementsallow accounting implicitly (Miller, 1967) or explicitly (Campbelland Norman, 1988) for the leaf angle distribution. However, thesemeasurements are more accurate under diffuse illumination con-ditions, particularly for LAI2000 or hemispherical photos lookingdownward (Demarez et al., 2008). These illumination conditionsare sometimes difficult to meet? for many locations and time.

Gap fraction can be easily transformed into effective LAI values,i.e. the LAI value that would correspond to the measured gap frac-tion while assuming a random distribution of the leaves within thecanopy volume. Obviously, many canopies have leaves which areclumped at several scales: landscape (patches of vegetation), stand(distribution of plants), plant (clumping around the plant), andshoot (clumping around the shoot within the plant). The computa-tion of the corresponding ‘true’ LAI is still an open question that hasalready been addressed by several authors (Chen and Cihlar, 1995;Nilson, 1999; Jonckheere et al., 2006; Lang et al., 1985; Leblanc etal., 2005; Macfarlane et al., 2007). The difference between effectiveand true LAI values depends on canopy architecture, but also onthe directions considered (Kucharik et al., 1999). Andrieu and Baret(1993) and Baret et al. (1993) have demonstrated that maximumdifferences were observed along the row directions over maize,wheat and sugarbeet row crops. Further, gap fraction is mainly sen-sitive to any green or non-green vegetation elements within thecanopy volume, including leaves but also stems and ears. Conse-quently, it is more adequate to relate gap fraction to the plant areaindex (PAI) rather than to LAI as proposed by Demarez et al. (2008),Norman and Campbell (1989), or Chen and Black (1992). Converselyto LAI, PAI is defined as the total developed area of all plant elementsper unit horizontal ground area, i.e. including trunks, branches,stems and reproductive elements independently from their photo-synthetic potentials. The concept of green area index (GAI) appearsas an alternative to LAI and PAI. GAI considers only the photosyn-thetically (green) active plant area with no differences betweenleaves, stems and reproductive organs. GAI has been widely usedin photosynthesis (Leuning et al., 1998), canopy light interception(Thomson and Siddique, 1997) and light use efficiency (Jamiesonand Semenov, 2000) crop models since it is more closely relatedwith the fraction of absorbed photosynthetically active radiation(fAPAR). However, the indirect determination of GAI requires opti-cal devices able to separate green from senescent or wooden partswithin the canopy (Jonckheere et al., 2004).

Digital photography became recently very popular for gap frac-tion measurements since a large number of very high resolutionimages can be acquired with simple commercial cameras and laterprocessed easily with most current computers. Digital photographydoes not need reference incident illumination measurements ascompared to LAI2000 or ceptometer devices. Although hemispher-ical photography proved efficient for LAI estimation, restricting thefield of view around 57.5◦ zenith angle from above the canopywould offer interesting properties: at this angle the relationshipbetween LAI and gap fraction becomes independent from the leafangle distribution (Bonhomme and Ganry, 1976; Weiss et al., 2004).This property comes from the projection function used to compute

gap fraction and corresponding to the average leaf effective cross-section, i.e. the projection of a unit LAI into a given direction. Theprojection function as a function of leaf angle distribution keepsalmost constant and equal to 0.5 for the particular 57.5◦ zenithangle. In addition to this important property, inclined views min-imize the clumping effect at the plant scale. Further, directionsperpendicular to the row minimizes leaf clumping at the standscale for row crops (Lopez-Lozano et al., 2007, 2009). Finally, therestricted field of view provides a spatial resolution far better thanthat corresponding to hemispherical photos, improving thereforethe distinction between the green vegetation and soil or non-greenvegetation elements.

Other measurement configuration features may help gettingbetter LAI estimates: photos taken from above the canopy allowsaddressing very small canopies not accessible with devices put onthe ground due to the finite height of the sensor. Further, tak-ing photos from above the canopy minimizes problems due tothe presence of non-green elements such as senesced leaves andstems generally located at the bottom of the canopy that may maskgreen leaves if photos were taken upward from the bottom of thecanopy allowing the computation of GAI. Finally, the restricted fieldof view and downward looking configuration allow manipulatingillumination conditions through shadowing or flashing, making thetechnique ‘all light conditions’.

The objective of this study is to evaluate the performances of theproposed downward looking digital photography inclined at 57.5◦

perpendicular to the rows for GAI estimates. The method is firstevaluated against simulated 3D scenes covering a large range of rowpatterns. Then, application to wheat canopies which are organizedin rows is analyzed from realistic 3D wheat architecture models andfield experiments where both destructive and LAI2000 measure-ments were acquired along with downward looking digital photosinclined at 57.5◦.

2. Materials and methods

2.1. Simulation of 3D scenes of generic row crops and gapfraction calculation

3D scenes representing a range of row patterns were generated.Plants are approximated by cylinders of diameter �plant. The sow-ing pattern is determined by the plant density N and the distancebetween rows, Drow. The crown cover of the scene, which is oneway of describing leaf clumping, varies with the plant diameterfrom a minimum value close to 0 when �plant equals the size of theleaves, up to 1.0 corresponding to an homogeneous canopy whenthe plants and rows overlap, covering fully the soil.

The plants are filled with leaves represented by equilateral trian-gles with radius Rleaf (distance between triangle centre and vertex)with inclination and azimuth drawn from uniform distributionlaws. The leaf area density in the plants is determined by the canopyLAI when all the other variables are given. For sake of simplicity thevariables N, Drow, �plant, and Rleaf are normalized by the canopyheight (fixed to 1 for all the simulations). Scenes have a squareshape with sides corresponding to 3 rows.

Simulations were generated based on an orthogonal samplingof the variables N, Rleaf and Draw around typical values for severalcrops such as wheat, maize, sorghum, vineyards, sunflower, soy-bean, tomatoes, olive trees, peach trees, lettuce and beets at earlyand mature development stages (Fig. 1). For each of the samplepoints considered described by the triplet [N, Rleaf, Draw], four dif-ferent values of �plant were selected [0, 0.33, 0.66, 1], covering allthe situations between leaves highly clumped around the plant ver-tical axis and leaves homogeneously distributed in the canopy. LAIvalues vary in a geometric progression: [0.25, 0.50, 1, 2, 4, 8].

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Fig. 1. Sampling of input variables N (density of plants), Drow (distance betweenrows) and Rleaf (leaf size) for 3D simulated scenes (crosses) and typical values(circles) for actual crops: Wheat (Wh), Maize (Mz), Sorghum (Sg), Vineyards (Vy),Sunflower (Sf), Soybean (Sy), Tomatoe (To), Olive tree (Ol), Peach tree (Pe), Lettuce(Lt) and Beet (Bt). Variables [N, Rleaf, Drow] are normalized by the canopy height value.

The gap fraction at 57.5◦ perpendicular to the row, Po(57.5◦), wascomputed for each scene based on Lopez-Lozano et al. (2009) usingthe Z-buffer technique (Catmull, 1974). The scene is projected alongthe 57.5◦ zenith angle direction perpendicular to the rows onto aregular grid assigning to each pixel the value of the correspondingscene depth. Po(57.5◦) is computed as the fraction of pixels withdepth equals to that of the soil. To avoid border effects, the sceneswere infinitely replicated as in Chelle et al. (1998).

Finally, LAI was estimated from Po(57.5◦) using the Poissonmodel written for the 57.5◦ direction where the projection functionequals 0.5 (Weiss et al., 2004):

Po(57.5◦) = e0.5·LAI/ cos 57.5◦ ⇔ LAI = − cos 57.5◦

0.5log(Po(57.5◦))

(1)

Note that in this case LAI, PAI and GAI are equivalent since onlygreen leaves are represented.

2.2. Simulations based on the ADEL-wheat 3D architecture modelof wheat crops

Adel-wheat (Fournier et al., 2003; Evers et al., 2007) is adynamic architectural model of wheat, based on the L-system prin-ciples (Lindenmayer, 1968; Prusinkiewicz, 1999; Prusinkiewiczet al., 2000). From a given initial planting pattern of seeds, themodel describes the size, shape, and orientation in space of each

Fig. 2. A typical wheat scene simulated with the ADEL-wheat model.

organ of a plant population as a function of degree days above0 ◦C. The model was calibrated over several experiments. Someof the characteristics such as leaf blade curvature and orien-tation in space are drawn from experimental distribution laws(Fig. 2).

The main variables driving wheat canopy architecture werechanged within their expected range of variation as described inTable 1. The other variables were set to their typical values. Sceneswere made of 4 rows of one metre. A total of 432 scenes were thussimulated covering a large range of GAI values and architecture pat-terns. Note that for these simulations, LAI is different from PAI andGAI since stems are represented for the later stages, while PAI = GAIsince all elements are considered green. The corresponding gapfraction at 57.5◦ perpendicular to the row was then computed usingthe same technique as that described above for the generic 3D rowcrops.

2.3. Experiments and reference LAI and GAI measurements

Three experiments were conducted in Boigneville, France(47.33◦N; 2.38◦E) from 2006 to 2008 resulting in a total of 28measurements. Seven wheat cultivars (Triticum aestivum) and onetriticale cultivar (Triticosecale) were sampled over plots showing awide range of canopy structure at several stages from sowing toearing. The investigated plots were very homogeneous microplotsof about 2 m width by 10 m long.

Destructive LAI was measured by collecting all the plants over50 cm × 50 cm samples for the earlier stages and on 100 cm × 34 cmfor the latter ones. Green leaves were separated from stems andsenesced leaves. Then, specific leaf area was estimated over a sub-sample of 30 g of leaves over which the lamina area was computedby multiplying the product between maximum length and widthby a multiplicative shape correction coefficient depending on cul-tivars. This coefficient ranging between 0.63 and 0.80 was derivedfrom actual leaf area planimeter measurement over a subsample

Table 1Structure parameters for ADEL-wheat model manipulated in the simulated scenes.

Parameters (units) Value levels

Thermal time (◦C d) 400, 600, 800, 900, 1000, 1200Plant density (plant/m2) 150, 300, 500Number of tiller per plant 2, 4Distance between the top of

tiller and main stem (cm)3 or 6

Height of plant Low, medium, highLeaf inclination distribution

(drawn from actualmeasurements)

Plagiophile, erectophile

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collected for each cultivar. The remaining leaves were similarlydried out and weighed. LAI was finally computed by multiplyingthe dry specific leaf area measured on the subsample by the leafmass measured over the whole sample.

The area of stems and ears per unit soil area was also measuredto compute the GAI. Note that in this case GAI was measured sinceonly green elements were considered. However, due to the smallamount of senescent elements, PAI could be approximated as GAI.According to (Lang, 1991) and (Stenberg, 2006), the area index ofnon-flat objects such as stems and ears should be computed as halfthe developed area of the associated convex hull per unit soil area.In the same way as LAI was measured, stem and ear area indiceswere derived by multiplying the specific stem and ear areas by thecorresponding dry weight measurement, and dividing the result bythe area on which the sample was collected. Specific ear and stemarea was taken from Weiss et al. (2001) who found a relatively con-stant value of 0.0034 cm2 g−1. GAI was finally computed by addingthe stem and ear area indices to the measured LAI. After stage ‘ear at1 cm’ where significant stem area appears, LAI/GAI ratio decreasesdown to 0.89 at stem elongation stage and to 0.50 at flowering. ThisLAI/GAI ratio was used to estimate GAI for the 11 measurementsover which only leaf area was available.

To complement the evaluation based on the destructive GAImeasurements, 50 additional measurements were collected usingthe Licor LAI2000 in one experiment including several cultivarsover a range of stages. They were achieved under overcast skyconditions when possible. Measurements were located over the3 centre rows of the microplots by making 1 reading above thecanopy and 4 readings below to sample the row effect. A 180◦ capwas used to mask the observer. PAI values were then computedusing the LAI2000 software based on Miller’s formula (Miller, 1967)as implemented by Welles and Norman (1991). The whole processwas replicated 4 times and averaged to sample the possible vari-ability along the plot. Note that LAI2000 is sensitive to PAI (Demarezet al., 2008) rather than to LAI or GAI.

2.4. Digital photo set up and processing

Pictures were taken with a Nikon D40 hosting a23.7 mm × 15.6 mm CCD matrix of 6.24 million pixels, andequipped with a 35 mm focal length lens. A monopod maintainedvertically using a bubble level was bearing a platform inclinedat 57.5◦ zenith angle on which the camera was fixed, lookingdownward. The camera was adjusted at about 1 m above the topof the canopy. Note that the longer focal used decreases the fielddepth, mandating a minimum distance between the first objectseen and the camera (generally between 0.5 and 1 m). Pictureswere sampling the centre of the plot from a compass directionperpendicular to the rows. The distance to the centre of the plot(d) was adjusted so that approximately the same canopy volumewas sampled by the photo and by the destructive method (Fig. 3).The relative homogeneity of the plot associated to the fact thatthe foot-print of both destructive and photographic methods werelargely overlapping (Fig. 3) allowed to compare consistently LAI,PAI or GAI values derived from direct and indirect methods withoutreplications. For the 50 additional measurements used for thecomparison with LAI2000 estimates, 3 replicates of the photoswere made to better capture the spatial variability.

Overcast illumination conditions were preferentially chosen tominimize the shadows where the distinction between soil and veg-etation is more difficult due to the small dynamics of the signal.However, photos were also acquired under direct sun light con-ditions using a separate flash unit (Sigma EF-530 DG ST) with asoftbox diffuser to minimize the shadows. Aperture and speed wereautomatically controlled by the camera without any further correc-tions.

Fig. 3. Description of the geometrical configuration used to acquire the photos (inthe plan perpendicular to the rows).

Only the central part of the photo was extracted for further pro-cessing: the original 25.1◦ vertical field of view was restricted to10◦ to be closer to the targeted zenith angle (57.5◦ ± 5◦) while get-ting enough spatial sampling. Simple simulations (Fig. 5) based onEq. (1) show that the relative uncertainties on LAI estimates due toerrors on the view direction around 57.5◦ is lower than 5% whenthe errors on the 57.5◦ direction are smaller than 2◦. This error islinked to possible deviations from the verticality of the monopodwhich was evaluated to be within this range for each individualphoto. Largest uncertainties are observed for erectophile canopies,while planophile ones are almost insensitive to deviations from the57.5◦ direction (Fig. 5). Note also that the almost linear pattern ofthe impact on LAI estimates of deviations from the 57.5◦ directionfor errors lower than ±5◦ justifies the restricted 10◦ vertical fieldof view used: under these conditions, LAI estimates for positivedeviations from 57.5◦ will be compensated for by the symmetricalnegative deviations (Fig. 5).

The original 37.4◦ horizontal field of view (Fig. 4) was kept,assuming that a tolerance of ±18.7◦ around the direction perpen-dicular to the row was acceptable to minimize clumping effects dueto the row structure.

A binary classification of green elements and gaps (including soiland senescent elements) was then performed to compute the gapfraction at 57.5◦. The Can-eye freeware was used to achieve theclassification (www.avignon.inra.fr/can eye) based on the colourspace. A default classification is first proposed using a greennessindex that may be later fine tuned. The gap fraction is finally com-puted. Note that it corresponds only to the green elements, andwill provide estimates of GAI rather than LAI or PAI although LAIwas (abusively) used above.

Fig. 4. Typical photo showing the part extracted and classified to get the gap fractioncorresponding to soil and senescent vegetation.

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Fig. 5. Relative error on LAI estimates from gap fraction measurements using Eq.(1) when the view direction deviates from 57.5◦ (error on 57.5◦ direction). Resultsderived from simulations based on Eq. (1) for a range of leaf angle distribution: ellip-soidal distributions with average leaf angle varying by 5◦ steps from 15◦ (planophile)to 75◦ (erectophile). The thick solid line corresponds to a spherical distribution.

3. Results

3.1. LAI/PAI/GAI retrieval performances over simulated genericrow crop scenes

For sake of simplicity, the term LAI will be used in this sectionalthough LAI = PAI = GAI as stated earlier for these simulations, sinceonly green leaves were considered. LAI estimated using Eq. (1) fromPo(57.5◦) computed over the simulated scenes was compared tothe actual corresponding LAI (Fig. 5). Eq. (1) assumes that leavesare distributed homogeneously for the direction considered. This isachieved at least when the following two conditions are fulfilled:

(I) There is no space between adjacent plants along the samerow, i.e. the row is continuous which is achieved when theplant diameter, �plant, is equal or larger to the spacing betweenplants, Dpalnt = N/�plant. Many row crops such as olive trees,peach or beets do not verify this assumption.

(II) There is no space between rows as seen from the 57.5◦ direction,i.e. when. �plant + tan 57.5◦ > Drow.

Fig. 6a shows that when both conditions are fulfilled, data pointsalign along the 1:1 line and LAI estimation is relatively accurate.However, some scattering is observed with increasing LAI valuesas a result of the exponential nature of the relationship betweenLAI and Po(57.5◦) that produces inaccurate results when Po(57.5◦)is very close to 0 corresponding to the larger LAI values. Further,some residual clumping due to small variations of leaf area densityin the 57.5◦ direction may slightly impact LAI estimates. This effectis maximum when conditions (i) and (ii) are just verified i.e. when�plant ≈ Dpalnt and/or �plant + tan 57.5◦ ≈ Drow. It explains the slightunderestimation observed in Fig. 6a. These results suggest that theproposed method would perform well over row crops such as mostcereals including wheat, barley, maize or sorghum (Table 2). How-ever, great care should be paid on gap fraction measurements forthe largest LAI values to get more accurate LAI estimates.

Conversely, canopies that do not fulfil one of the conditions (i)(Fig. 6b), or (ii) (Fig. 6c) or none of them (Fig. 6d) achieve very poorLAI estimation performances when Eq. (1) is applied. LAI is sys-

Table 2Characteristics of the fully developed row crops investigated and associated statusof conditions (i) and (ii). Values of the characteristics are relative to canopy height.�plant values are typical values observed in the field.

N Drow �plant Rleaf Cond. (i) Cond. (ii)

Wheat (Wh) 325 0.153 0.176 0.082 + +Sorghum (Sg) 40.5 0.389 0.443 0.083 + +Maize (Mz) 25.3 0.368 0.421 0.131 + +Vineyards (Vy) 3.07 1.562 0.625 0.063 + −Sunflower (Sf) 16.6 0.375 0.125 0.094 + +Soybean (Sy) 40.0 0.400 0.150 0.070 + +Tomatoe (To) 9.00 0.467 0.200 0.067 − +Olive tree (Ol) 1.23 1.143 0.572 0.010 − +Peach (Pe) 2.08 0.800 0.400 0.030 − +Lettuce (Lt) 0.15 3.332 1.332 1.00 − −Beet (Bt) 0.14 5.000 2.000 1.50 + −

tematically underestimated due to leaf clumping in the projectiondirection. This is the case for some row crops simulated where rowspacing is large compared to plant height and radius such as verti-cally trained vineyards (Table 2). Apart from the large bias observedover cases corresponding to Figure 6b, when spaces are observedbetween plants, the scatter of points is significant, requiring specificcalibration for such situations. For cases corresponding to Fig. 6cand d when spaces are observed between rows along the directioninclined at 57.5◦ and perpendicular to the row, the sensitivity of gapfraction to LAI is minimal because of the highly clumped nature ofthese canopies. In such conditions, it is questionable whether LAIcould be accurately retrieved from Po(57.5◦).

3.2. GAI retrieval performances evaluated over synthetic 3Dwheat scenes

In this section, GAI will be used rather than LAI since the ADEL-wheat model represents not only green leaves but also green stemsand ears. Note that in this case GAI = PAI since no senescent ele-ments were simulated. The gap fraction computed over the 432simulated wheat canopies were related to the corresponding GAIvalues. Results confirm (Fig. 7) that the measurement configurationproposed minimizes all the sources of variability of canopy archi-tecture introduced in the simulated scenes according to Table 1.Very small scatter is observed around the best fit curve adjustedwith the simplex optimization method (R2 = 0.97; RMSE = 0.014):

Po(57.5◦) = e−0.931·GAI (2)

Closer inspection of the residuals did not allowed to identify aparticular factor explaining the differences. When Eq. (2) is used toestimate LAI from the Po(57.5◦) gap fraction value, a RMSE = 0.39 isobserved. Conversely, using the theoretical relationship describedby Eq. (1) (Po(57.5◦) = e−0.931·GAI) degrades the GAI estimation per-formances with RMSE = 0.51. The ratio between the two extinctioncoefficients corresponds to a small clumping effect characterizedby a clumping index ˝ = 0.824/0.931 = 0.89. It may be explained bysmall variation of the leaf area density in the view direction, eithervertically linked to residual row effects, or horizontally, linked toclumping around the main plant axis.

3.3. Validation against destructive measurements on actualwheat crops

Results obtained over the 28 experimental points show thatestimates of GAI from gap fraction measured at 57.5◦ using Eq. (2)derived from the 3D ADEL-wheat model simulations are stronglycorrelated to destructive LAI up to the stem elongation phase(Fig. 8right), with a RMSE of 0.20 (Table 3): there is almost nobias between GAI estimation and LAI measurements. After stemelongation, LAI is strongly overestimated (Fig. 6left, empty squares)

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Fig. 6. LAI estimated for simulated generic row canopies from Po(57.5◦) as compared to the actual LAI. Results are presented in a boxplot format. Solid line is 1:1 line. (a)Canopies that do not present space between plants and between rows in the projection direction (condition i and ii verified), (b) canopies that present only space betweenplants (condition ii only verified), (c) canopies that present only space between rows (condition i only verified), and (d) canopies that present space between plants and rows(none of conditions i and ii are verified).

from Po(57.5◦) measurements because of the increasing light inter-ception by stems and then ears. When destructive LAI is replacedby destructive GAI measurements, i.e. accounting for green stemsand ears, all the points including those observed after stem elon-gation are close to the 1:1 line as expected and RMSE value is

Fig. 7. Relationship between gap fraction at 57.5◦ and GAI observed over the ADEL-wheat canopy architecture simulations. The thin solid line corresponds to the bestexponential fit Po(57.5◦) = e−0.824·GAI . The thick solid line corresponds to the theoret-ical relationship of Eq. (1): Po(57.5◦) = e−0.931·GAI .

minimum (Table 3). This highlights the importance of using theproper definition when comparing quantities derived from differ-ent measurement systems.

The goodness of the relationship between GAI values measuredby destructive sampling, and those estimated from the photosindirectly confirms that the method used for destructive and pho-tographic GAI estimates were accurate. Note that the uncertaintiesof GAI estimates appear to be proportional to the GAI value asdiscussed earlier for the simulated scenes. Subsequently, largerabsolute GAI errors are expected for the highest GAI values, requir-ing thus great care for the spatial sampling, image quality andclassification process in those situations. Further, the several culti-vars included in the experiment were expressing large differencesin canopy architecture including leaf orientation and grouping ofstems on the row. These architectural differences did not show offin Po(57.5◦) estimates, demonstrating that the method is mainlyindependent from cultivar architecture peculiarities.

When assuming a random distribution of vegetation elementsusing Eq. (1) valid for 1D turbid medium, performances for GAI esti-mation degrade significantly (Table 3). This clearly demonstrates

Table 3RMSE values associated to the comparison between estimates of PAI from Po(57.5◦)measurements and destructive LAI or GAI measurements. GAI estimates are achievedeither using Eq. (2) adjusted over 3D ADEL-wheat model simulations or Eq. (1)derived for random distribution of leaves in the canopy, i.e. 1D turbid medium.Values in parenthesis correspond to RMSE computed only for stages earlier thanstem elongation (22 points over the 28 total data points).

LAI GAI

3D ADEL-wheat Eq. (2) 1.28 (0.20) 0.28 (0.22)1D Turbid medium Eq. (1) 1.01 (0.21) 0.36 (0.39)

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Fig. 8. Comparison between destructive LAI (left) and GAI (right) measurements with estimates of GAI from Po(57.5◦) measurements and Eq. (2). Filled circles correspond tostages before stem elongation while empty circles represent measurements at flowering stage.

that some residual clumping has to be accounted for, confirmingthe previous ADEL-wheat simulations.

3.4. Comparison with LAI2000 estimates on actual wheat crops

Results obtained over the 50 experimental points show thatPAI values estimated from LAI2000 were well correlated (R2 = 0.97)with GAI values estimated from digital photos at 57.5◦ (Fig. 9left).Little scatter is observed for the low GAI/PAI values as expected.Small scatter is observed for the highest PAI values while morescatter was expected due to the non-linear nature of the GAI/PAIrelationship with Po(57.5◦). However only 2 points were available(Figure 9). Conversely, some scatter is observed over the mediumGAI/PAI values resulting from the uncertainties both in LAI2000 andphotographic methods yielding an overall RMSE = 0.25. It corre-sponds to a reasonably low value in terms of relative accuracy (9%),confirming a posteriori the consistency of the sampling design forboth measurements.

However, GAI estimated from the photos, GAI3DPo(57.5◦), is system-

atically higher than that estimated from LAI2000 measurements,PAILAI2000, as observed in Fig. 9 left and from the best linear fitequation:

GAI3DPo(57.5◦) = (1.02 ± 0.04) · PAILAI2000

+ (0.65 ± 0.08) (R2 = 0.97; RMSE = 0.25) (3)

The higher GAI values estimated from the Po(57.5◦) method areexplained by a significant offset (0.65 ± 0.08) mainly due to thevegetation elements placed at the bottom of the canopy that arenot seen by the LAI2000 device because of its significant height(3–4 cm). In addition, the slightly higher slope (1.02 ± 0.04) maybe explained by the fact that leaf clumping is accounted for in thePo(57.5◦) method, while LAI2000 estimates assume randomly dis-tributed elements. However, a higher slope around 1/˝ = 1.12 wasexpected if the leaf clumping index of ˝ = 0.89 computed previ-ously from the 3D wheat scenes was accounted for. The differencemay come from a significant senescent fraction associated to thehigher PAI values. It was accounted for with LAI2000 PAI estimates,while photos were mostly sensitive to the green elements (GAI). Thepoints with higher PAI values have a strong contribution to the slopeof the linear regression. The overall RMSE = 0.74 corresponds to 25%relative uncertainty between PAILAI2000 and GAI3D

Po(57.5◦) confirms thesignificant differences between the two area estimates.

When using Eq. (1) rather than Eq. (2) in computing GAI1DPo(57.5◦)

from Po(57.5◦) values, i.e. assuming random distribution of canopyelements, the goodness of the fit is obviously very similar to theprevious one (Eq. (3)):

GAI1DPo(57.5◦) = (0.90 ± 0.03) · PAILAI2000

+ (0.58 ± 0.07) (R2 = 0.98; RMSE = 0.22) (4)

Fig. 9. Comparison between PAI estimates derived from LAI2000 measurements and GAI estimates derived from Po(57.5◦) measurements using either Eq. (2) (left) or Eq. (1)(right).

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1400 F. Baret et al. / Agricultural and Forest Meteorology 150 (2010) 1393–1401

However, the overall RMSE = 0.45 (16% relative) value decreasedsignificantly, showing a closer agreement between GAI1D

Po(57.5◦) andPAILAI2000 (Fig. 9) as expected since both estimates are based on theturbid medium assumption. However, the discrepancies are stillobserved for the lower PAI values, related to the significant off-set (0.58 ± 0.07) due to the elements placed at the bottom of thecanopy and not viewed by the LAI2000 system. Note that this off-set is slightly lower than that corresponding to Eq. (3), probably inrelation with the residual clumping ˝ = 0.89 as noted previously:1.02·0.89 = 0.89 = 0.90. The slope of Eq. (4) is significantly differ-ent from the expected unit value (no clumping accounted both forGAI1D

Po(57.5◦) and PAILAI2000.) for the same reason as explained pre-viously: LAI2000 instrument includes both senescent and greenelements in PAI estimates, while downward looking photos aremainly sensitive to the green elements (GAI). The importance ofsenescent elements was the highest for the two points with thehighest PAI values which have a strong influence on the slope ofthe linear regression.

4. Conclusion

These results highlighted first the importance of clearly definingthe variables of interest that are accessible through indirect mea-surement techniques. As a matter of fact, the method describedhere based on downward looking photos is directly related to thegreen area index, GAI, that includes all green elements and not onlyleaves as for leaf area index, LAI, while excluding all non-green ele-ments in opposition to the plant area index, PAI. GAI is probablythe most pertinent variable for several key processes involved incanopy functioning. This is therefore a very important advantageof such downward looking photographic technique as comparedto upward looking systems such as LAI2000 that generally do notallow separating green from non-green vegetation elements andaccesses directly PAI.

This study demonstrated that gap fraction derived from digitalphotos acquired at 57.5◦ zenith angle in a compass direction per-pendicular to the rows provided good estimates of GAI over rowcrops when rows are continuous and when no gaps between rowsare seen from the 57.5◦ direction. This will be the case for severalcrops such as wheat, maize, sorghum sunflower or soybean. How-ever, simulations on realistic 3D scenes for the case of wheat cropsshow that a residual clumping effect (˝ = 0.89) should be accountedfor. This indicated that specific relationships for such row cropsshould be calibrated. This specific calibration could be also veryefficient for crops presenting gaps between plants or gaps betweenrows as seen from the 57.5◦ direction. Such an approach was alreadyproposed successfully by Lopez-Lozano et al. (2009) for vineyards.However, the generic row crop simulations indicate also that whenleaf clumping is too high, GAI retrieval might be very inaccurate.

Experimental results show that application to wheat crops con-firm accurate LAI estimation performances for the first stages ofthe vegetative part of the growth cycle, while after stem elonga-tion, the contribution of stems and then ears have to be included toproduce similarly accurate estimations. The resulting GAI estimatesfrom Po(57.5◦) showed great consistency with destructive GAI mea-surements from sowing up to flowering. It demonstrated thatthis particular geometrical configuration effectively reduces thevariability due to canopy architecture observed either due to phe-nological stages, cultivar or environmental conditions. Moreover,comparison with PAI values derived from LAI2000 measurementsshows also good consistency with however, larger values estimatedfrom the photographic method. This was explained by a significantamount of elements placed at the bottom of the canopy and notseen by the LAI2000 device because of its height, inducing an offsetclose to 0.6. Further, leaf clumping was taken into account explicitly

when deriving GAI values from the photos by specific calibration on3D wheat crop scenes, while LAI2000 provides effective PAI values,assuming random distribution of canopy elements. However, partof the increase of GAI values due to the clumping effect may be com-pensated by not accounting for the non-green elements converselyto the PAI estimates from LAI2000 measurements.

Although the accuracy of GAI estimates was high within ourexperimental results (RMSE = 0.28, or 12% in relative value), theexponential nature of the relationship between GAI and Po(57.5◦)would yield more scatter for the highest GAI values because ofthe non-linearity of the relationship inducing a well known sat-uration effect. Great attention should therefore be paid to get thebest quality photographs for dense canopies. This includes properillumination to clearly distinguish soil and senescent materialsfrom green photosynthetically active vegetation organs. Finally,the comparison between indirect and destructive methods for GAIestimates was achieved successfully over a very consistent spa-tial support without replications. Characterization of the averageGAI values over a plot will require replications of individual pho-tos to capture the actual spatial heterogeneity. The smaller field ofview reducing the individual foot-print of the photo may be com-pensated by an increase of the distance between the camera andthe canopy. The experience acquired here when comparing withLAI2000 measurements using photos taken from 1m above the topof the canopy, indicates that 3 replications yielded accurate andconsistent estimates for wheat crops.

This study was partly achieved using 3D model simulations ofcanopy scenes. Generic 3D models yield already efficient results.However, improvement of the accuracy with which canopy struc-ture characteristics are retrieved largely depends on the realismof the simulations. Effort should therefore be directed towards thedescription of the 3D canopy architecture through plant modeling.Sensitivity analysis would then allow screening between factorsand observational configurations to design accordingly the retrievalalgorithm based on calibration of dedicated relationship over these3D model simulations.

References

Andrieu, B., Baret, F., 1993. Indirect methods of estimating crop structure from opti-cal measurements. In: Varlet-Grancher, C., Bonhomme, R., Sinoquet, H. (Eds.),Crop Structure and Microclimate: Characterization and Applications. INRA,Paris, France, pp. 285–322.

Baret, F.B., Andrieu Folmer, J.C., Hanocq, J.F., Sarrouy, C., 1993. Gap fraction mea-surement from hemispherical infrared photography and its use to evaluatePAR interception efficiency. In: Varlet-Grancher, C., Bonhomme, R., Sinoquet,H. (Eds.), Crop Structure and Microclimate: Characterization and Applications.INRA, Paris, France, pp. 359–372.

Bonhomme, R., Ganry, J., 1976. Mesure de l’indice foliaire du bananier par photogra-phies hémisphériques faites “in situ”. Fruits 31 (7/8), 421–425.

Bréda, N.J.J., 2003. Ground-based measurements of leaf area index: a review of meth-ods, instruments and current controversies. Journal of Experimental Botany 54(392), 2403–2417.

Campbell, G.S., Norman, J.M., 1988. The description and measurements of plantcanopy structure. In: Russell, B.M.A.P.G.J.G. (Ed.), Plant Canopies: Their Growth,Form and Function. Cambridge University Press, pp. 1–19.

Catmull, E., 1974. A Subdivision Algorithm for Computer Display of Curved Surfaces.University of Utah.

Chelle, M., Andrieu, B., Bouatouch, K., 1998. Nested radiosity for plant canopies. TheVisual Computer 14, 109–125.

Chen, J.M., Black, T.A., 1992. Foliage area and architecture of plant canopiesfrom sunfleck size distributions. Agricultural and Forest Meteorology 60, 249–266.

Chen, J.M., Cihlar, J., 1995. Quantifying the effect of canopy architecture onoptical measurements of leaf area index using two gap size method anal-ysis. IEEE Transactions on Geoscience and Remote Sensing 33 (3), 777–787.

Chen, J.M., Rich, P., Gower, S.T., Norman, J.M., Plummer, S., 1997. Leaf area indexof boreal forests: theory, techniques and measurements. Journal of GeophysicalResearch 102 (D24), 29429–29443.

Demarez, V, Duthoit, S., Weiss, M., Baret, F., Dedieu, G., 2008. Estimation of leaf areaindex (LAI) of wheat, maize and sunflower crops using digital hemisphericalphotographs. Agricultural and Forest Meteorology 148, 644–655.

Author's personal copy

F. Baret et al. / Agricultural and Forest Meteorology 150 (2010) 1393–1401 1401

Evers, J.B., Vos, J., Fournier, C., Andrieu, B., Chelle, M., Struik, P.C., 2007. An architec-tural model of spring wheat: Evaluation of the effects of population density andshading on model parameterization and performance. Ecological Modelling 200(3–4), 308–317.

Fournier, C., Andrieu, B., Ljutovac, S., 2003. ADEL-wheat: a 3D architectural model ofwheat development. In: Hu, B.-G., Jaeger, M. (Eds.), Plant growth modeling andapplications: proceedings-PMA03: international symposium on plant growthmodeling, simulation, visualization and their applications. Tsinghua UniversityPress, Beijing, China, pp. 54–66.

Garrigues, S., Garrigues, S., Shabanov, N.V., Swanson, K., Morisette, J.T., Baret, F.,Myneni, R.B., 2008. Intercomparison and sensitivity analysis of Leaf Area Indexretrievals from LAI-2000, AccuPAR, and digital hemispherical photography overcroplands. Agricultural and Forest Meteorology 148, 1193–1209.

Gower, S.T., Kucharik, C.J., Norman, J.M., 1999. Direct and indirect estimation of LeafArea Index, fAPAR, and net primary production of terrestrial ecosystems. RemoteSensing of Environment 70 (1), 29.

Jamieson, P.D., Semenov, M.A., 2000. Modelling nitrogen uptake and redistributionin wheat. Field Crops Research 68, 21–29.

Jonckheere, I., Jonckheere, I., Fleck, S., Nackaerts, K., Muys, B., Coppin, P., Weiss,M., Baret, F., 2004. Review of methods for in situ leaf area index determination.Part I: Theories, sensors and hemispherical photography. Agricultural and ForestMeteorology 121, 19–35.

Jonckheere, I., Nackaerts, K., Muys, B., van Aardt, J., Coppin, P., 2006. A fractaldimension-based modelling approach for studying the effect of leaf distribu-tion on LAI retrieval in forest canopies. Ecological Modelling 197 (1–2), 179–195.

Kucharik, C.J., Norman, J.M., Gower, S.T., 1999. Characterizing the radiation regime ofnon-random forest canopies: theory, measurements, modeling and simplifiedapproach. Tree Physiology 19, 695–706.

Lang, A.R.G., 1986. Leaf area and average leaf angle from transmission measurementof direct sunlight. Australian Journal of Botany 34, 349–355.

Lang, A.R., 1991. Application of some of Cauchy’s theorems to estimation of sur-face areas of leaves, needles, and branches of plants, and light transmittance.Agricultural and Forest Meteorology 55, 191–212.

Lang, A.R.G., Xiang, Y., Norman, J.M., 1985. Crop structure and the penetration ofdirect sunlight. Agricultural and forest Meteorology 35, 83–101.

Leblanc, S., Chen, J., Fernandes, R., Deering, D.W., Conley, A., 2005. Methodologycomparison for canopy structure parameters extraction from digital hemispher-ical photography in boreal forests. Agricultural and Forest Meteorology 129,187–207.

Leuning, R., Dunin, F.X., Wang, Y.P., 1998. A two-leaf model for canopy conduc-tance, photosynthesis and partitioning of available energy. II. Comparison withmeasurements. Agricultural and Forest Meteorology 91 (1–2), 113–122.

Lindenmayer, A., 1968. Mathematical models for cellular interactions in develop-ment I. Filaments with one-sided inputs. Journal of Theoretical Biology 18 (3),280–292.

Lopez-Lozano, R., Baret, F., Chelle, M., Rochdi, N., Espana, M., 2007. Sensitivity of gapfraction to maize architectural characteristics based on 4D model simulations.Agricultural and Forest Meteorology 143 (3/4), 217–229.

Lopez-Lozano, R., Baret, F., García de Cortázar-Atauri, I., Bruguier, N., Casterad, M.A.,2009. Optimal geometric configuration and algorithms for LAI indirect estimatesunder row canopies. The case of vineyards. Agricultural and Forest Meteorology149 (8), 1309–1316.

Macfarlane, C., Macfarlane, C., Hoffman, M., Eamus, D., Kerp, N., Higginson, S.,McMurtrie, R., Adams, M., 2007. Estimation of leaf area index in eucalypt forestusing digital photography. Agricultural and Forest Meteorology 143, 176–188.

Miller, J.B., 1967. A formula for average foliage density. Australian Journal of Botany15, 141–144.

Nackaerts, K., Coppin, P., Muys, B., Hermy, M., 2000. Sampling methodology for LAImeasurements with LAI-2000 in small forest stands. Agricultural and ForestMeteorology 101, 247–250.

Nilson, T., 1999. Inversion of gap frequency data in forest stands. Agricultural andForest Meteorology 98, 437–448.

Norman, J.M., Campbell, G.S., 1989. Canopy structure. In: Pearcy, R.W., Ehleringer,J.R., Mooney, H.A., Rundel, P.W. (Eds.), Plant Physiological Ecology: Field Meth-ods and Instrumentation. Chapman and Hall, New York, New York, USA, pp.301–325.

Prusinkiewicz, P., 1999. A look at the visual modeling of plants using L-systems.Agronomie 19, 211–224.

Prusinkiewicz, P., Hanan, J., Mech, R., 2000. An L-System-Based Plant Modeling Lan-guage, Applications of Graph Transformations with Industrial Relevance, pp.258–273.

Stenberg, P., 2006. A note on the G-function for needle leaf canopies. Agriculturaland Forest Meteorology 136 (1/2), 76.

Thomson, B.D., Siddique, K.H.M., 1997. Grain legume species in low rainfallMediterranean-type environments II. Canopy development, radiation intercep-tion, and dry-matter production. Field Crops Research 54 (2–3), 189–197.

Weiss, M., Troufleau, D., Baret, F., Chauki, H., Prévot, L., Olioso, A., Bruguier, N., Bris-son, N., 2001. Coupling canopy functioning and canopy radiative transfer modelsfor remote sensing data assimilation. Agricultural and Forest Meteorology 108(2), 113–128.

Weiss, M., Baret, F., Smith, G.J., Jonckheered, I., Coppin, P., 2004. Review of methodsfor in situ leaf area index determination, part II: estimation of LAI, errors andsampling. Agricultural and Forest Meteorology 121, 37–53.

Welles, J.M., Norman, J.M., 1991. Instrument for indirect measurement of canopyarchitecture. Agronomy Journal 83 (5), 818–825.