PROSPECT-D: towards modeling leaf optical properties through a complete lifecycle

TL;DR: A new version of the widely-used PROSPECT model is presented, hereafter namedPROSPECT-D for dynamic, which adds anthocyanins to chlorophylls and carotenoids, the two plant pigments in the current version, and outperforms all the previous versions.

About: This article is published in Remote Sensing of Environment.The article was published on 2017-05-01 and is currently open access. It has received 380 citations till now.

Summary

1. Introduction

• This article introduces a new version of the widely-used PROSPECT model, called PROSPECT-D, which for the first time includes all three main pigments that control the optical properties of fresh leaves, i.e., chlorophylls, carotenoids, and anthocyanins.
• The suffix -D stands for "dynamic" because the model makes it possible to simulate leaf optical properties through a complete lifecycle, from emergence, to anthocyanin-expressing stress responses, through to senescence.
• Given the success and widespread use of PROSPECT-5, a major requirement for the development of PROSPECT-D was to preserve, and ideally to improve on, the performance of PROSPECT-5 for pigment estimation in samples containing little or no anthocyanin, while adding support for those that do.
• The authors performed a new calibration of the SAC of each pigment, and updated the refractive index used by the model.
• The authors compared these two criteria for the new and current versions of the model.

2. Calibration of the model

• All of the procedures have points in common, such as the adjustment of one or several optical constants (SAC of leaf chemical constituents, refractive index) over the VIS, near infrared and shortwave infrared (SWIR) domains.
• A standard method consists in determining the optical constants individually or simultaneously at each wavelength by using an iterative procedure (Féret et al., 2008; Li and Wang, 2011) .
• So far, there is no unique method, and adaptations have been proposed to calibrate PROSPECT: Malenovský et al. (2006) adjusted SACs for needle-shaped leaves; Féret et al. (2008) have simultaneously determined the refractive index and SAC of leaf constituents; Chen and Weng (2012) have computed an individual refractive index for each leaf sample.
• The authors provide information about the calibration of PROSPECT-D, including the selection of the calibration dataset, as well as the main steps leading to updated optical constants.

2.2. Data selection for calibration

• While chlorophyll and carotenoids contents are usually highly correlated in mature leaves, ANGERS includes juvenile, stressed and senescent leaves lowering this correlation and allowing the SAC of each of these pigments to be adjusted independently from the others, despite their overlapping domain of absorption.
• Therefore the authors took the decision to include ANGERS in the calibration dataset and to estimate the corresponding 𝐶 𝑎𝑛𝑡ℎ using a spectral index.
• To avoid the associated uncertainty leading to errors in the SACs, the authors combined a subset of ANGERS with a subset of VIRGINIA that included accurate measurements of 𝐶 𝑎𝑛𝑡ℎ obtained by wet chemistry (Merzlyak et al., 2008) .
• Leaves from VIRGINIA were collected in a park at Moscow State University; they contained very high levels of anthocyanin and low to moderate levels of chlorophyll and carotenoids; they displayed the maximum range of anthocyanin among all the available datasets.
• Finally, the authors present a sensitivity study intended to analyze the influence of the expected 𝐶 𝑎𝑛𝑡ℎ uncertainty in ANGERS on the performances of the model.

2.2.a. Estimation of leaf anthocyanin content in ANGERS

• Several nondestructive methods to estimate 𝐶 𝑎𝑛𝑡ℎ from leaf reflectance have been identified and tested on experimental data for which the anthocyanin content has been measured.
• These samples with 𝑚𝐴𝑅𝐼 < 5 correspond to mature green, yellow, and reddish/red leaves with 𝐶 𝑎𝑛𝑡ℎ values less than 12 µg cm 2 .
• In that case, absorptance between 540 nm and 560 nm exceeded 90% and further increases of anthocyanin did not change leaf optical properties.
• A linear model for anthocyanin estimation (Eq. 2) was then derived from the subset excluding the samples with 𝑚𝐴𝑅𝐼 > 5 and 𝐶 𝑎𝑛𝑡ℎ > 12 µ𝑔 cm 2 .
• Relationship between 𝐶 𝑎𝑛𝑡ℎ obtained from wet chemistry and 𝐶 𝑎𝑛𝑡ℎ estimated from reflectance data after application of Eq. 2. Eq. 2 was adjusted only on the black dots.

2.2.b. Selection of the calibration samples

• In order to keep as many samples as possible, the authors decided to build a calibration dataset made of leaf samples selected both in ANGERS and VIRGINIA.
• It should allow capturing the influence of anthocyanins independently from the other pigments.
• In ANGERS the authors discarded at first 14 atypical samples, the spectral behavior of which was incompatible with PROSPECT assumptions.
• The authors removed samples collected on Eucalyptus gunnii and Cornus alba, the overall reflectance of which was very high in the VIS because of the presence of wax (Barry and Newnham, 2012) ; and three samples of Schefflera arboricola displaying uncharacteristic optical properties in the blue (400-450 nm).
• In total, a dataset named CALIBRATION and combining subsets of ANGERS (144 samples) and VIRGINIA (20 samples) was used for the calibration phase.

2.2.c. Sensitivity of the calibration to the uncertainty associated with 𝑪 𝒂𝒏𝒕𝒉 in ANGERS

• As abovementioned, determining 𝐶 𝑎𝑛𝑡ℎ with a spectral index like 𝑚𝐴𝑅𝐼 leads to uncertainty likely to impact the quality of the calibration.
• The authors performed a sensitivity analysis with the aim of understanding the influence of this uncertainty on the SACs and on the overall performances of the model.

2.3. Selection of the refractive index

• Attempts to obtain a unique refractive index spectrum for all leaves are actually unfounded and inconsistent with the Kramers-Kronig relations that state that the real (refractive index) and imaginary (absorption coefficient) parts of the complex refractive index of a medium are physically linked (Lucarini et al., 2005) .
• These relations allow direct computation of the refractive index of a medium based on its absorption properties on an extended spectral domain.
• Chen and Weng (2012) used the Kramers-Kronig relations to derive an effective refractive index adjusted to each leaf sample, obtaining very promising results.
• Leaf chemical and spectral databases are often incomplete; in particular they cover a limited range of the electromagnetic spectrum, so such a method is impracticable.
• 1) using the refractive index imbedded in PROSPECT-3, and 2) taking the average refractive index derived water (Hale and Querry, 1973), also known as Two options were tested.

2.4. Optimal adjustment of the specific absorption coefficients

• The SAC to be calibrated were then computed by inverting PROSPECT on the 𝑛 = 164 leaves of the calibration dataset.
• The authors minimized the merit function 𝐽 at each wavelength:.

3. Validation: datasets and criteria for the comparison of model performances

• Where 𝑋 𝑚𝑒𝑎𝑠,𝑗 are the measured values and 𝑋 𝑚𝑜𝑑,𝑗 are the values estimated by model inversion for leaf 𝑗.
• As for the quality of the fit, it is appraised by the spectral RMSE which calculates the difference between the measured and simulated reflectance and transmittance spectra on a wavelength-bywavelength basis.

4.1. Selection of a calibration dataset

• Figure 3 shows the pigment distribution corresponding to the calibration and validation samples in ANGERS and VIRGINIA: note that the calibration samples display low to moderate 𝐶 𝑎𝑏 and 𝐶 𝑥𝑐 values, whereas the validation samples encompasses significantly broader pigment contents.
• The calibration samples with high 𝐶 𝑎𝑛𝑡ℎ come from VIRGINIA, for reasons explained earlier.

4.2. Selection of the refractive index

• The refractive index spectra displayed in Figure 2 provide advantages and disadvantages in terms of model accuracy both for the estimation of leaf chemistry and the simulation of leaf optical properties.
• The authors performed calibrations of PROSPECT-D as detailed in Section 3, using either the refractive index of PROSPECT-3 and the one derived by Chen and Weng (2012) .
• Then the authors inverted the two versions of the model on ANGERS, the only dataset covering the SWIR as well as including measurements of 𝐸𝑊𝑇 and 𝐿𝑀𝐴.
• For water and dry matter, results were also very similar.
• Simulated leaf reflectance and transmittance spectra also exhibited very slight differences in the VIS, while they were noticeable in the NIR and SWIR.

4.3. Adjustment of the specific absorption coefficients

• The bold font for numbers indicates the lowest values.
• The substantial improvement in 𝐶 𝑥𝑐 estimation when using PROSPECT-D is a significant result of this article: overall, the RMSE was divided by four compared to the results obtained with PROSPECT-5.
• It is likely that this overestimation of carotenoid content results from the strong absorption of light by anthocyanins in the same wavelength range as carotenoids, and this absorption is not properly modeled by PROSPECT-5.
• In ANGERS, the systematic underestimation of 𝐶 𝑥𝑐 by PROSPECT-5 in leaves containing high amounts of photosynthetic pigments was greatly reduced by PROSPECT-D.
• As explained in Section 4.1, the samples selected for the calibration dataset in ANGERS were marked out by low to medium pigment content, therefore they were not representative of the full range of variation found in this dataset: nevertheless, this did not prevent us from estimating high pigment content with accuracy.

Database

• Estimation of pigment content by inversion of three versions of PROSPECT on six datasets (when relevant).
• Red dots correspond to calibration samples from ANGERS and VIRGINIA.

4.4.b. Spectrum reconstruction

• The authors compared the spectral RMSE between measured spectra and spectra reconstructed by the last three versions of PROSPECT after model inversion on the VALIDATION dataset (Figure 7 ).
• Values obtained with PROSPECT-3 ranged between 2% and 6% over the VIS.
• This model uses a unique SAC to account for total pigment absorption; therefore it solely applies to healthy green leaves.
• The dissociation of chlorophylls from carotenoids in PROSPECT-5 explains the strong decrease in RMSE between 400 nm and 500 nm where carotenoids absorb light.
• The addition of noise to 𝐶 𝑎𝑛𝑡ℎ in ANGERS influences the calibration of the SACs of PROSPECT, as expected, but the variability is limited to the 400-500 nm wavelength range, especially for anthocyanins.

4.5.b. Estimation of pigment content

• The authors estimated pigment content by inverting PROSPECT with the set of SACs derived from noisy 𝐶 𝑎𝑛𝑡ℎ .
• Summarizes the distributions of RMSE from measured and estimated pigment contents for the validation datasets taken separately and for the VALIDATION dataset that group them together.
• The influence is higher on the estimation of carotenoids.
• This version also outperformed all noisy versions when focusing on VALIDATION.
• The results obtained with VALIDATION showed better estimation of 𝐶 𝑎𝑛𝑡ℎ when no noise was added.

5.1. Specific absorption coefficients

• The SAC of carotenoids above 450 nm is very similar in PROSPECT-5 and PROSPECT-D.
• Which highlights the high sensitivity of PROSPECT to very small changes of the SAC, as well as the importance of incorporating anthocyanins into the model even for leaves with low content.
• This improvement in the estimation of 𝐶 𝑥𝑐 was not explained by the differences observed between 400 nm and 450nm: when using all the ANGERS dataset for calibration, the SAC calibrated for 𝐶 𝑥𝑐 showed very similar profile as in PROSPECT-5, but the improvement in the estimation of 𝐶 𝑥𝑐 was still observed.

Figures

Figure 8. Comparison of the SACs obtained for the three pigments when using 𝐶𝑎𝑛𝑡ℎ values directly derived from 𝑚𝐴𝑅𝐼 (dashed lines) and when using 𝐶𝑎𝑛𝑡ℎ values with noise added corresponding to the error of prediction of 𝐶𝑎𝑛𝑡ℎ observed for experimental data (50 repetitions; plain lines and their envelope correspond to mean value ± 1 standard deviation).

Figure 9. Distribution of the RMSE between measured and estimated pigment content after adding noise to the values of 𝐶𝑎𝑛𝑡ℎ of ANGERS used for calibration of PROSPECT and inversion of the model based on the SACs displayed in Figure 8. Colored dots correspond to the RMSE obtained when no noise is added to 𝐶𝑎𝑛𝑡ℎ in ANGERS.

Figure 2. Comparison of the refractive index used in PROSPECT-3 (red dots), PROSPECT-5 (grey diamonds) and corresponding to the mean refractive index proposed by (Chen and Weng, 2012) (blue squares). The grey area corresponds to the range of variation of the refractive index proposed by Chen and Weng, (2012); the plain grey line corresponds to the refractive index for pure liquid water (Hale and Querry, 1973).

Figure 5. Specific absorption coefficients of chlorophylls (green), carotenoids (orange), and anthocyanins (red). The solids line correspond to the SAC of all the pigments in PROSPECT-D, the dashed lines to the SAC of chlorophylls and carotenoids in PROSPECT-5, and to the SAC of anthocyanins measured by Peters and Noble (2014) using thin layer chromatography.

Figure 12. Measured (black dotted line) versus simulated (blue line for PROSPECT-5 and red line for PROSPECT-D) reflectance (lower spectra) and transmittance (upper spectra). (a-b) Acer pseudoplatanus L., (c) Acer platanoides L., (d) Corylus avellana L., (e-f) Parthenocissus quinquefolia (L.) Planch., (g) Corylus maxima 'Purpurea', and (h) Eucalyptus gunnii. Samples (b-e-f) show non-

Figure 11. Comparison of the SAC corresponding to anthocyanins derived from PROSPECT-D calibration (cm2 µg1) and the absorption of pure Cyanidin 3-glucoside at pH 1 and 8.1 (unitless) (after Fossen et al., 1998).

Table 2. RMSE (µg cm2) of the estimation of leaf pigment content using PROSPECT-3 (P-3), 427 PROSPECT-5 (P-5), and PROSPECT-D (P-D) inversion. The bold font for numbers indicates the lowest 428 values. 429

Figure 6. Estimation of pigment content by inversion of three versions of PROSPECT on six datasets

Figure 3. Stacked distribution of pigment content for the calibration and validation samples selected from ANGERS and VIRGINIA. Light colors: calibration (144 samples from ANGERS, 20 Samples from VIRGINIA); dark colors: validation (164 samples from ANGERS, 61 samples from VIRGINIA).

Figure 1. Relationship between 𝐶𝑎𝑛𝑡ℎ obtained from wet chemistry and 𝐶𝑎𝑛𝑡ℎ estimated from reflectance data after application of Eq. 2. The black dots correspond to the 137 leaf samples with 𝑚𝐴𝑅𝐼 < 5 (R2 = 0.90) and the grey dots correspond to the 76 leaf samples with 𝑚𝐴𝑅𝐼 > 5 (R2 = 0.37). Eq. 2 was adjusted only on the black dots.

Figure 10. Spectral RMSE between measured and estimated leaf reflectance and transmittance obtained for the VALIDATION dataset after model inversion using PROSPECT-D calibrated with (grey lines) and without (red lines) uncertainty added to 𝐶𝑎𝑛𝑡ℎ.

Figure 7. Spectral RMSE between measured and estimated leaf reflectance and transmittance obtained for the VALIDATION dataset after model inversion using PROSPECT-3, PROSPECT-5, and PROSPECT-D.

Table 1. Description of the leaf datasets used in this study. * The ANGER dataset is available online http://opticleaf.ipgp.fr/index.php?page=database. 181

Figure 4. Spectral RMSE between measured leaf optics and simulated reflectance (left), and transmittance (right) obtained after model inversion with the refractive index used in PROSPECT-5 (black dotted line), PROSPECT-3 (red), and derived from Chen and Weng (2012) (light grey).

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Prospect-d: towards modeling leaf optical properties through a complete lifecycle" ?

Gatelson et al. this paper proposed a method for modeling leaf optical properties through a complete lifecycle. 

Q2. What is the reason for the broadness of the absorption peak?

The broadness of the absorption peak may be caused by calibration artifacts 408 related to residual correlations between the pigments. 

Q3. What is the rse's role in predicting green LAI 699?

Hyperspectral vegetation indices and novel algorithms for predicting green LAI 699 of crop canopies: Modeling and validation in the context of precision agriculture. 

Q4. What is the way to measure leaf and canopy chlorophyll?

the availability of physical models including chlorophyll as input parameters allowed 92 investigating and better understanding its influence on the signal measured by satellite sensors, 93 leading to improved predictive models for leaf and canopy chlorophyll content in a more systematic 94 way than experimental data collection would have permitted. 

Q5. What is the reason for the improvement of Cxc estimation accuracy?

The improvement of 𝐶𝑥𝑐 estimation accuracy upon incorporation of 530 anthocyanins into PROSPECT-D may stem from the inherent correlation between anthocyanin and 531 flavonoid content. 

Q6. What is the reason why the calibration samples were discarded from the 449 dataset?

Samples showing underestimated 𝐶𝑥𝑐 in ANGERS were discarded from the 449 calibration dataset due to unusual optical properties (surface effects) or very high 𝑚𝐴𝑅𝐼. 

Q7. What is the reason for the increasing absorption closer to the UV-526 A?

The increasing absorption closer to the UV-526 A may be explained by the presence of flavonols in some leaves: these molecules, which are 527 biosynthetically associated with anthocyanins in plant secondary metabolism, are also optically 528 active in this domain. 

Q8. How many SACs were found in the calibration of PROSPECT-D?

Preliminary calibration tests using part or all of these datasets led to 191 SACs with strong discrepancies and poor performances for the estimation of pigment content. 

Q9. What is the optimum adjustment of the specific absorption coefficients for each group of pigments?

The adjustment of the SAC for each group of pigments is based on numerical optimization 303 routines applied to experimental data. 

Q10. What is the case of the combined 95 PROSPECT leaf optical properties model?

This is the case of the combined 95 PROSPECT leaf optical properties model (Jacquemoud and Baret, 1990) and SAIL canopy bidirectional 96 reflectance model (Verhoef, 1984; Verhoef et al., 2007), also referred to as PROSAIL, which has been 97 used for more than 25 years (Jacquemoud et al., 2009). 

Q11. What is the spectral RMSE between measured and estimated canth?

Spectral RMSE between measured and estimated leaf reflectance and transmittance 859 obtained for the VALIDATION dataset after model inversion using PROSPECT-D calibrated with (grey 860 lines) and without (red lines) uncertainty added to 𝐶𝑎𝑛𝑡ℎ. 

Q12. Why are the wavelength domains narrower than in vitro?

These ranges are broader than in vitro due to the 314 detour effect: the lengthening of the optical path-length within the leaf results in substantial 315 flattening of the absorption spectrum in vivo (e.g., Rühle and Wild, 1979; Fukshansky et al., 1993).