Accuracy of multitemporal LAI estimates in winter wheat using analytical (PROSPECT+SAIL) and semiempirical reflectance models

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1 Accuracy of multitemporal LAI estimates in winter wheat using analytical (PROSPECT+SAIL) and semiempirical reflectance models Clement ATZBERGER (1), Martine GUÉRIF (2) & Richard DELÉCOLLE (2) (1) University of Trier, Remote Sensing Departement, Trier, Germany (2) INRA-Bioclimatologie, Domaine St Paul, F Avignon, France ABSTRACT: Leaf area index has been estimated from multitemporal ground reflectance measurements using two different appoaches: (i) through the inversion of an analytical canopy reflectance model (PROSPECT+SAIL) and (ii), using a simple semiempirical approach. Calculated statistics revealed that the modeling approach is preferably, althought its use and application is much more difficult and time comsuming than the statistical approach. KEY WORDS: remote sensing, LAI, reflectance model, model inversion, PROS- PECT, SAIL, SPECAN, semi-empirical reflectance model, Camargue, winter wheat, Triticum durum 1 - INTRODUCTION As a fundamental plant parameter leaf area index [LAI=(leaf area)/(ground surface area)] is an important factor in the description of many plant processes, as for example, evapotranspiration and photosynthesis, and a commonly used measure of vegetative development. Since the magnitude and duration of LAI is strongly related to the canopy s ability to intercept photosynthetically active radiation, LAI is also correlated with canopy dry matter production. Moreover, vegetation amount affects radiation exchange with the atmosphere through its effect on albedo, determines the amount of carbon stored in various plant communities and therefore has a strong impact on climate. 1 The LAI is also the main driving variable in many crop growth models, designed for yield prediction. External LAI data may yield information about the actual status of a crop, resulting in an improvement of the modeled crop growth and eliminating the need to aquire detailed varietal, management, meteorologic, hydrologic and pedologic informations for the observed fields (Délécolle et al., 1992). These examples show that the accurate determination of this important plant parameter on different spatial scales is highly recommended. Remote sensing, with its unique synoptic perspective, potentially offers a great improvement over conventional destructive LAI sampling techniques, since it allows the reseacher to analyse agricultural crops quantitatively, instantaneously and, above all, non-destructivley, and even to asses changes in the condition of the same vegetative target with time. In order to estimate LAI remotely, two different approaches have been proposed. In

2 the semiempirical approach, simple statistical techniques are used to obtain a correlation between the target LAI and its spectral reflectance, or some vegetation indices (Asrar et al., 1985; Best and Harlan, 1985; Hatfield et al., 1985). Unfortunally, canopy and observation geometry, as well as leaf and soil optical properties, may greatly affect the (exponential) relationship, making this method rather approximative (Baret and Guyot, 1991). Pinter et al. (1983), for example, have noted that diurnal changes in Sun elevation and azimuth can create significant problems when attempting to estimate LAI from vegetative indices based upon canopy reflectance. Their results further suggest that relationships between LAI and vegetation indices may have a time-of-year dependency, due to the seasonal progression of Sun angles and their influence on the bidirectional reflectance properties of the crop canopy. The above factors are explicitely accounted for when using the canopy modeling approach. This second approach assumes that a model might be developed, which describes accurately the spectral variation of canopy reflectance as a function of canopy, leaf and soil background characteristics, using physical expressions. The model may then be inverted to retrieve canopy properties from observed reflectance data (e.g., Jacquemoud, 1993; Baret and Jacquemoud, 1994). The present work has been intended, (i) to develop a methodology for the calibration and inversion of an analytical canopy reflectance model (PROSPECT+SAIL) in SPOT RED and NIR channels; (ii) to compare the specific accuracy of the semiempirical and analytical approach in estimating the LAI; (iii) to evaluate the accuracy of both approaches when segregating the data set into two phenological phases and according to their variety, and (iv) to evaluate the accuracy of six different vegetation indices in comparison to the reflectance data (only for the semiempirical model) DATA COLLECTION The study took place in the Camargue (France), which corresponds to the Rhône delta (43 24 N latitude, 4 19 E longitude). Data were acquired on nine commerical wheat plots of four common wheat varieties (i.e., ARCOUR, CAPDUR, CRESO and OLINTO). The above-ground biomass was measured on 10 random sample sites of 0.25 m 2 area within every field. LAI was determined using an optical scanning area meter and interpolated to the moments of radiometric measurements. The ground reflectance measurements have been performed using SPOT simulation radiometers which simultaneously measure the radiance and irradiance in SPOT RED ( nm) and near-infrared ( nm) channels (Jappiot, 1987). The radiometer was mounted on a support 2.5 m high, vertically orientated, viewing a circle 52 cm in diameter. Ten radiometric readings were taken in each field for up to 13 different dates covering the entire cycle of the crop. In order to work in standardized conditions, the measurements were performed around solar noon (20 θ z 34 ), with a clear sky and with no wind. A total number of 36 coincident LAI and (2*36=72) reflectance measurements were finally available. 3 - METHODOLOGY The semiempirical model We named semiempirical model the commonly known exponential relationship between the target LAI and its spectral reflectance/vi (e.g., Baret and Guyot, 1991): ρ = ρ + ( ρ ρ ) e Canopy Soil ( k LAI ) (3.1) This description is likely to oversimplify the radiation problem, since the predicted reflectances depend only on three parameters besides LAI: the reflectance of the underlying soil (ρ soil ), the reflectance of a fully developed

3 (LAI ) vegetation canopy (ρ ), and the attenuation coefficient for radiation in the canopy (k). The coefficients ρ soil, ρ, and k can be determined simultaneously using the error expression (summation over data points): 2 = [ρ measured -ρ modelled ] 2 (3.2) where ρ mesured is the measured reflectance and ρ modelled is given by Eq.3.1 using measured values of LAI. If ρ soil, ρ and k are all known at a particular wavelength, then a single reflectance measurement permits inference of LAI, expect for saturation at large LAI. Saturation occurs at all wavelengths for large LAI, effectively limiting the sensitivity of all spectral measurements/vi s for dense vegetation cover. In order to minimize the effect of the underlying soil a great number of mathematical formulas using visible and NIR reflectances, here called VI s, have been proposed. Among these, we used six vegetation indices: NDVI (Rouse et al., 1974), TSAVI (Baret et al., 1989), GEMI (Pinty and Verstraete, 1991), RATIO (Pearson and Miller, 1972), PVI (Richardson and Wiegand, 1977) and GEO (Malet and Baret, 1992). However, one has always to consider, that it is not physically possible to eliminate soil reflectance variations, either explicitly or implicitly, from such formulas because soil reflectance does affect observed radiances (Verstraete, 1994). Beside these six vegetation indices, we used RED and NIR reflectances as predictors and calculatd also a mean value (labelled MEAN) of the two spectral estimates. Table 1 gives solution values for the 8 predictors (six VI s + two reflectances) for: (a) all data pooled together, (b) data segregated into two phenological periods (i.e., from emergence up to maximum LAI and from maximum LAI to maturity), and (c) data segregated according to their variety. 3 When the data have been segregated into two phenological periods (b) only parameters ρ soil and k were allowed to vary between the two periods. When the data have been segregated according to their variety the parameters ρ and ρ soil have been fixed to their fitted values from the pooled data set (i.e., the coefficients given in table 1-a) since the number of observations has been to small. Therefore, in this case, only the extinction coefficient is adjusted. Once the parameters of Eq.3.1 have been adjusted, the estimation of LAI from measured reflectance data/vi (ρ) is straightforward: LAI estimated =-ln((ρ-ρ )/(ρ soil -ρ ))/k (3.3) The analytical model (PROSPECT+SAIL) Contrary to the above described semiempirical model, analytical canopy reflectance models provide a logical connection between the botanical features of the canopy, the geometry of the radiometric interaction and the resulting alteration of the reflected radiation using physical expressions (for an excellent review of existing canopy reflectance models see Goel, 1988). However, to get a model that might be simple enough to be manipulated and even inverted, the number of input parameters must be small. The SAIL model (Verhoef 1984, 1985) is a good compromise between simplicity and predictive performance. Leaves are supposed to be lambertian, with no finite dimensions and a random spatial distribution. Leaf inclination is approximated by an ellipsoidal distribution (Campbell, 1986), characterized by the average leaf inclination angle (θ l ). Canopy reflectance is expressed as (Baret and Jacquemoud, 1994): ρ (λ) =ρ(ρ l(λ),τ l(λ),ρ s(λ),lai, θ l,θ z,θ v,φ,skyl) (3.4)

4 Input variables required to compute canopy reflectance are: ρ l(λ),τ l(λ) ρ s(λ) θ l θ z θ v,φ skyl respectively leaf reflectance and transmittance soil reflectance average leaf inclination angle solar zenith angle view geometry (respectively zenith and azimuth angles) fraction of diffuse incoming radiance (assumed isotropic and independent of λ; skyl=0.1) Notice from (3.4) that leaf optical properties and soil reflectance variables depend on wavelength. To simplifiy the model, soil reflectances in RED and NIR spectral channels were assumed to be lineary related through: ρ soil (NIR)= ρ soil (RED) (3.5) For further reduction of model parameters, the spectral variation of leaf reflectance and transmittance is described using a model of leaf optical properties (PROSPECT; Jacquemoud and Baret, 1990), which requires only 2 input parameters to compute leaf reflectances and transmittances in the visible and near infrared spectral domain: (i) the number N of thin layers separated by thin slices of air (N is not necessarilly an integer; here set to 1.5), and (ii) the chlorophyll concentration expressed per unit leaf area (C ab ). Coupling SAIL canopy reflectance model to leaf optical properties model (PROSPECT) results thus finally in: variables θ l, C ab, and ρ soil (RED) have been fitted (a) for the pooled data set, (b) for the data set segregated into two phenological periods (i.e., from emergence up to maximum LAI and from maximum LAI to maturity), and (c) for the data set segregated into four varieties. The fitted parameter values are given in table 2. Notice, that when the data have been segregated into four varieties (c), only the mean leaf angle inclination parameter θ l has been allowed to vary. The two other parameters (ρ soil (RED) and C ab ) have been fixed to their fitted values from the pooled data set (a), because of a too limited number of measurements. In order to avoid time comsuming computer calculations we have simplified the inversion process by the following steps: given the fitted coefficients of table 2, simulate spectral reflectances in SPOT RED and NIR channels for 0 LAI 9 and six different solar zenith angles (10, 20,..., 60 ), labelled ρ(λ) θz from ρ(λ) θz calculate the appropriate parameter values ρ (λ) and k(λ) (ρ soil (λ) is allready given) according to the semiempirical model in Eq.3.1, labelled ρ (θz,λ) and k (θz,λ) calculate four functions describing ρ (θz,λ) and k (θz,λ) as a function of θ z, labelled f1 (θz,red), f1 (θz,nir), f2 (θz,red) and f2 (θz,nir) The observed reflectances in SPOT RED and NIR channels (ρ (i) ) may then be easily inverted according to Eq.3.3 when f1 (θz,λ) is used instead of ρ (λ) and f2 (θz,λ) instead of k(λ). This approach yields LAI estimates for both SPOT channels. The final LAI is calculated as the mean of the two spectral estimates. ρ (λ) =ρ(n,c ab,ρ s (RED),LAI, θ l,θ z,θ v,φ,skyl) (3.6) Given the field measured LAI s and the appertaining values for observation and illumination geometry the three independent RESULTS When all data were pooled together (table 3- a) the smallest standard deviation has been achieved with the PROSPECT+SAIL model (std=±0.62 LAI). The accuracy of the semiempirical predictors varied between 0.66

5 (GEO) and 1.05 (XS2). The three best semiempirical predictors have been GEO, GEMI and PVI. Reflectances in RED and NIR spectral channels accounted only for 63 % of the LAI-variance thus leading to high standard deviations (1.05 and 0.80, respectively). However, when the mean value form both spectral estimates has been calculated (MEAN), the standard error reduced drastically to about ±0.76 LAI (table 3-a). When the data were segregated into two distinct phenological phases (table 3-b) (i.e., one from emergence up to maximum LAI the second from maximum LAI to maturity), the standard deviations of all semiempirical predictors reduced markedly, whereas the accuracy of the analytical model remained practically constant. This feature might be explained by the fact that the analytical model explicitly considers the solar zenith angle, whereas in the semiempirical model this parameter is only implicitly accounted for when distinguishing two periods. For example, from table 1-b (TSAVI) it can be seen that in the relationship between LAI and TSAVI neither the reflectance of the underlying soil (ρ soil ), nor the (fixed) reflectance of the dense vegetation (ρ ), could explain the better predictions of the piecewise exponential model, but only the varying extinction coefficients (k). As expected, we found for the first phenological period up to maximum LAI greater solar zenith angles and therefore higher extinction coefficients than for the second period. This finding is consistent with all analysed VI s (table 1-b). The three best semiempirical predictors in the piecewise exponential model have been MEAN, TSAVI and GEO with standard deviations as good as the PROSPECT+SAIL model (std ±0.60 LAI). When the data were segregated according to their variety (table 3-c) the PROS- PECT+SAIL model achieved the smallest standard deviation at all (std=±0.50 LAI). This rather strong reduction from 0.62 (table 3-a) to 0.50 (table 3-c) could be attributed to 5 the fact that now existing varietal differences in the canopy architecture (i.e., different mean leaf inclination angles, θ l ) could be explicitly accounted for. In fact, fitted θ l varied from 53 (ARCOUR) up to 62 (CRESO) (table 2-c). The standard errors of the semiempirical predictors (table 3-c) were in general also better compared to the pooled data (table 3-a), but the changes were not as drastically since the effect of solar zenith angle apparently dominates over the effect of changing canopy architecture. The three best semiempirical predictors have been GEO, RATIO and PVI. Notice that GEO was in every case (table 3-a to 3-c) among the three best semiempirical predictors, PVI in two out of the three cases; the commonly used NDVI always among the atleast accurate predictors. 5 - CONCLUSION The PROSPECT+SAIL model has been successfully calibrated on a multitemporal wheat data set. Adjusted plant parameters (i.e., reflectance of the underlying soil, mean leaf inclination angle, and chlorophyll a+b concentration) have been with reasonable values, althought direct independent measurements have not been available to verify their fitted values. The inversion process of the PROS- PECT+SAIL model has been successfully simplified in order to permit an analytical solution of the inverse problem as a prerequisite of the analysis of large satellite data sets. Compared to the simpler semiempirical approach, the PROSPECT+SAIL model proved in any case to be more accurate in estimating the LAI. Using the PROSPECT+SAIL model, the LAI has been estimated from the pooled data set (n=36) with an accuracy of ±0.62 LAI (std). A further error reduction to ±0.50 LAI has been achieved when segregating the data set into four different wheat varieties.

6 The semiempirical approach yielded results of roughly 0.10 LAI units less accurate than the analytical modeling approach. The GEO vegetation index proved in any case to be among the three best semiempirical predictors; PVI in two out of three cases. NDVI was in every case among the at least accurate semiempirical predictors. The accuracy of either ρ(red) and ρ(nir) was less than any of the six analysed vegetation indices. However, when the spectral LAI-estimates have been used to calculate a mean value (MEAN) than results have been as accurate as those from the vegetation indices. The next step will be to apply the developed methodology to a multitemporal SPOT data set with five images aquired by the INRA- Montfavet (France) during the same perid as the ground reflectance measurements. An image based methodology for the accurate atmospheric correction of these SPOT images has already been developed and verified (Atzberger, 1995). ACKNOWLEDGEMENTS: This study wasn t feasible without the outstanding help from the french collegues at INRA-Montfavet. Special thanks must be given to S. Jacquemoud and F. Baret for the computer codes of the SAIL and PROSPECT models and to R. Délécolle and M. Guérif for their continious and amicable help. I have greatly appreciated the aid from Magda Chelfaoui (Université de Bourgogne). REFERENCES Asrar, G. et al. (1985): Estimtes of leaf area index from spectral reflectance of Wheat under different cultural practices and solar angle.- in: Remote Sens. Environ., Vol.17, S.1-11 Atzberger, C. (1995): The spectral correlation concept: An effective new image-based atmospheric correction methodology over land surfaces.- in:parlow (Ed.): Proc. 15th 6 EARSeL Symp. on Progress in Environmental Research and Applications, Basel, Switzerland, 4-6 Sept. 1995, Baret, F. and Guyot, G. (1991): Potentials and limits of vegetation indices for LAI and APAR assessment.- in: Remote Sens. Environ., Vol.35, S Baret, F. und Jacquemoud, S. (1994): Modeling canopy spectral properties to retrieve biophysical and biochemical characteristics.- in: Hill und Mégier (Ed.): Imaging Spectrometry - A Tool for Environmental Observations. ECSC, EEC, EAEC, Brüssel und Luxemburg, S Baret, F. et al. (1989): TSAVI: A vegetation index which minimizes soil brightness effects on LAI and APAR estimation.- in: 12th Canadian Symp. Rem. Sensing and IGARSS 90, Vancouver, Canada, 4 p. Best, R.G. und Harlan, J.C. (1985): Spectral estimation of green leaf area index of Oats.- in: Remote Sens. Environ., Vol.17, S Campbell, G.S. (1986): Extinction coefficients for radiation in plant canopies calculated using an ellipsoidal inclination angle distribution.- in: Agric. and Forest Meteorology, Vol.36, p Délécolle, R. et al. (1992): Remote sensing and corp production models: present trends.- in: ISPRS Journal of Photogrammetry and Remote Sensing, Vol.47, S Goel, N.S. (1988): Models of vegetation canopy reflectance and their use in estimation of biophysical parameters from reflectance data.- in: Remote Sensing Reviews, Vol.4, S Hatfield, J.L. et al. (1985): Leaf-area estimates from spectral measurements over various planting dates of Wheat.- in: Int. J. Remote Sens., Vol.6(1), S Jacquemoud, S. (1993): Inversion of the PROSPECT+SAIL canopy reflectance

7 model from AVIRIS equivalent spectra: Theoretical study.- in: Remote Sens. Environ., Vol.44, S Jacquemoud, S. and Baret, F. (1990): PROSPECT: A model of leaf optical properties spectra.- in: Remote Sens. Environ., Vol.34, S Jacquemoud, S. and Baret, F. (1993): Estimating vegetation biophysical parameters by inversion of a reflectance model on hight spectral resolution data.- in: Varlet- Grancher et al. (Ed.): Crop structure and light microclimate: Characterization and application, Meeting held at the Chateau de Saumane, Vaucluse, France, INRA- Editions, S Malet, P. and Baret, F. (1992): Canopy geometry characterisation from temporal evolution of red and near infrared re- flectances.- Pearson, R.L. and Miller, L.D. (1972): Remote mapping of standing crop biomass for estimation of the productivity of shortgrass Prairie, Pawnee National Grasslands, Colorado.- in: 8th Int. Symp. Rem. Sensing of Environm., ERIM Ann Arbour, MI, p Pinter, P.J. et al. (1983): Diurnal patterns of wheat spectral reflectance.- in: IEEE Trans. Geoscience and Remote Sensing, 21, p Pinty, B. and Verstraete, M.M. (1991a): Extracting information on surface properties from bidirectional reflectance measurements.- in: Journal of Geophysical Research, Vol.96(D2), S Pinty, B. and Verstraete, M.M. (1991b): GEMI: A non-linear index to monitor global vegetation from satellites.- Richardson, A.J. und Wiegand, C.L. (1977): Distinguishing vegetation from soil background information.- in: Photogrammetric Engineering and Remote Sensing, Vol.43(2), S Rouse, J.W. et al. (1974): Monitoring the vernal advancement of natural vegetation.- NASA/GSFC Final Report, Greenbelt, MD, 371 pp. Verhoef, W. (1984): Light scattering by leaf layers with application to canopy reflectance modeling: The SAIL model.- in: Remote Sens. Environ., Vol.16, S Verhoef, W. (1985): Earth observation modeling based on layer scattering matrices.- in: Remote Sens. Environ., Vol.17, S Verstraete, M.M. (1994): Retrieving canopy properties from remote sensing measurements.- in: Hill und Mégier (Ed.): Imaging Spectrometry - A Tool for Environmental Observations. ECSC, EEC, EAEC, Brüssel und Luxemburg, S

8 TABLES Table 1: Fitted coefficients of the semiempirical model (Eq.3.1). (a) all data pooled together, (b) data segregated into two phenological periods, and (c) data segregated according to their variety. The numbers (1) and (2) in (b) refer to the first period (1) from emergence up to maximum LAI, respectively, to the second period (2) from maximum LAI to maturity. The abbreviations Ac, Cd, Cr, and Ol in (c) refer to wheat varieties ARCOUR, CAPDUR, CRESO, and OLINTO, respectively. (For further details refer to the text) (a) pooled data (b) two periods (c) four varieties ρ ρ soil k ρ ρ soil (1) ρ soil (2) k(1) k(2) k (Ac) k (Cd) k (Cr) k (Ol) ρ RED ρ NIR NDVI TSAVI GEO GEMI RATIO PVI Table 2: Fitted coefficients of the analytical PROSPECT+SAIL model. (a) all data pooled together, (b) data segregated into two phenological periods, and (c) data segregated according to their variety.θ l is the mean leaf inclination angle, ρ soil is the reflectance of the underlying bare soil in the RED channel, and C ab is the leaf chlorophyll concentration. (For further details refer to table 1) (a) pooled data (b) two periods (c) four varieties θ l ρ soil C ab θ l (1) θ l (2) ρ soil (1) ρ soil (2) C ab (1) C ab (2) θ l (Ac) θ l (Cd) θ l (Cr) θ l (Ol) Table 3.: Accuracy with which the LAI has been estimated from ground reflectance measurements in SPOT RED and NIR channels using the semiempirical model (first block containing lines 1 to 9) and the analytical model (second block). (a) all data were pooled together; (b) data were segregated into two phenological phases; (c) data were segregated according to their variety. The three best semiempirical predictors are with asterisk (*).(For further details refer to the text) (a) pooled data (b) two periods (c) four varieties std r 2 slope cept std r 2 slope cept std r 2 slope cept ρ RED S ρ NIR E MEAN * M NDVI I TSAVI * E GEO * * * M GEMI * P. RATI O * PVI * * SAIL ρ

9 Accuracy of multitemporal LAI estimates in winter wheat using analytical (PROSPECT+SAIL) and semiempirical reflectance models Clement ATZBERGER (1), Martine GUÉRIF (2) & Richard DELÉCOLLE (2) (1) University of Trier, Remote Sensing Departement, Trier, Germany (2) INRA-Bioclimatologie, Domaine St Paul, F Avignon, France ABSTRACT: Leaf area index has been estimated from multitemporal ground reflectance measurements using two different appoaches: (i) through the inversion of an analytical canopy reflectance model (PROSPECT+SAIL) and (ii), using a simple semiempirical approach. Calculated statistics revealed that the modeling approach is preferably, althought its use and application is much more difficult and time comsuming than the statistical approach. KEY WORDS: remote sensing, LAI, reflectance model, model inversion, PROS- PECT, SAIL, SPECAN, semi-empirical reflectance model, Camargue, winter wheat, Triticum durum The original version of this text appeared in : Guyot, Gerard (Ed.) (1995): Assessment of remote sensing tools for the estimation of photosynthesis and primary production. Present and future potential. Proceedings of the international colloquium on photosynthesis and remote sensing. EARSeL. ISPRS. Montpellier, France, Impressions Dumas, F Saint-Etienne,