Estimating leaf biochemical content from laboratory spectral measurements

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Comparison between VI and PROSPECT based methods for CABC and CW estimates

The ranking capacity between cultivars appeared to be very similar using either the VI or the PROSPECT based methods. It should be noticed that ranking did not require any calibration for VIs or bias correction for PROSPECT model inversion. However, in the context of phenotyping, the ranking between genotypes is not always sufficient. Estimates of the absolute values of the biochemical contents will allow using crop models to access functional traits. The results showed that biases were observed for estimates from PROSPECT inversion. This problem could be solved properly at least in two different ways: (1) by recalibrating the specific absorp-tion coefficients for wheat leaves; (2) by changing the formalism of PROSPECT and including heterogeneous distribution of absorbers in the leaf. This will require a recalibration of the specific absorption coefficients over a large range of leaf types. Because of the limited amount of data available, as well as the fact that the only meas-ured optical property was the reflectance over a white background, we did not perform a recalibration of the PROSPECT specific absorption coefficients. Therefore, a simple empirical recalibration of the raw estimates of PROSPECT using the destructive measurements was proposed. Results show that the performances of the veg-etation indices were comparable to those of PROSPECT after this bias correction (Table 5). However, the PROS-PECT model had the capacity to account for the effect of variation in the leaf surface and leaf mesophyll struc-ture. Even though the relationship between Cm and the leaf mesophyll structure was reported in previous stud-ies [41, 69] when considering mixed species including both monocotyledons and dicotyledons, this relationship might not be so strong for a single species like wheat. Therefore, this may be important in the context of pheno-typing experiments where new genotypes with particular surface or mesophyll features may be encountered.

Additional measurements of reflectance and transmittance of both faces

Measurements were made over ten species of plants to represent different optical properties of leaves between upper and lower faces: Fig tree (Ficus Carica), Laurel tree (Laurus Nobilis), Olive tree (Olea Europaea), Lime tree (Tilia Europea), Lemon tree (Citrus Limon), Persimmon tree (Diospyros Kaki), Giant Cane (Arundo Donax), White poplar tree (Populus Alba), Common grape vine (Vitis Vinifera) and Apple tree (Malus Domestica). For each species, five leaves were selected with similar visual aspects. Reflectance and transmittance were measured at three distinct locations over each leaf, avoiding the larger veins. The ASD Fieldspec spectroradiometer was used with a Li‐Cor 1800‐12 integrating sphere to obtain directional‐hemispherical reflectance and transmittance values. The spectroradiometer sampled the 400 to 2200 nm spectral domains with 1‐nm steps and a spectral resolution around 10 nm. The original Li‐Cor lamp system of the integrating sphere was replaced by a lamp powered with a large battery ensuring steady electric power input. The infrared filter placed in front of the original light source was removed as well. The incoming light was almost normal to the leaf sample both for reflectance and transmittance measurements, while the bare fiber of the ASD spectroradiometer (25° field of view) viewed the integrating sphere wall and was perpendicularly to the sample. To reduce possible stray‐light, the experiment was conducted in a darkroom. Lab calibrated Teflon reference surface was used to get absolute directional hemispherical reflectance values of the sample from the absolute reflectance and transmittance of the Teflon (Rref and Tref). To avoid possible changing of the signal over time, the signal values of reflectance and transmittance of the references were acquired before (SRref_bef and STref_bef) and after (SRref_aft and STref_aft) measurements of each leaf. Therefore, the reflectance Ri and transmittance Ti of the leaf sample i were calculated as: ∗ and ∗ (1).
where SRi and STi are the averaged signal values of reflectance and transmittance for each leaf i. Uncertainties were characterized by the averaged RMSE values for each leaf. For the whole wavelength, the uncertainties of reflectance (RMSE≈0.01) are comparatively smaller than that of the transmittance (RMSE≈0.02), which mainly came from different measurement locations (Figure 5).

Leaf described as a four-layer system

A typical dicot leaf is made up of the palisade and spongy mesophyll tissue layers, bounded by two epidermis layers (Figure 7). The epidermis is a single layer of colorless cells with few chloroplasts. Palisade mesophyll is elongated perpendicular to the leaf surface and is arranged into one or a few densely packed layers which contain most of chloroplasts(Govaerts et al. 1996). The spongy mesophyll is made up of irregularly shaped cells and large intercellular air spaces, which facilitate gases circulation inside the leaf. Because of the small amount of absorbing material and much air space in the spongy mesophyll, a large proportion of light coming from the palisade mesophyll is scattered back and is absorbed by chloroplasts within the palisade mesophyll (Raven et al. 2005). This is consistence with measurement results (Figure 6) that absorptance from the upper face is larger than that from the lower face.

Development of the FASPECT model

In original PROSPECT model, only one layer of the leaf was considered and the radiative transfer process within the leaf was ignored. This allowed little flexibility to describe particular surface features and would result in some bias for the simulation of leaf optical properties. Based on the built system of leaf (Figure 8), the FASPECT model is proposed to consider the leaf as four layers. Radiative transfer terms of each layer are showed in Table 3.
In FASPECT, epidermis layers are assumed to be very thin with negligible absorption, so transmittance of epidermis can be described by 1 minus the corresponded reflectance. As it was explained in Section 3.1, ↓ from the incoming collimated light is larger than ↑ from the multiple scattered lights within the leaf, so ↓ is smaller than ↑ and the ratio between two reflectance of upper epidermis would be smaller than 1 (α1 = ↓/ ↑ <1). Similarly, ↑ is smaller than ↓, so α2 = ↑/ ↓ <1. According to several converging observations(Jacquemoud and Baret 1990; Bousquet et al. 2005), the wavelength dependency of the refraction index was assumed negligible in the 400‐2500 nm spectral domain. Therefore, epidermis reflectivity was considered independent on wavelength. The leaf structure parameter (N) is sum of the structure parameter of palisade mesophyll (N2) and spongy mesophyll (N3). The parameter p = N2 / N is used to characterize the gradient between two mesophyll layers. In original PROSPECT model, p was set to be 0.5 for all kinds of leaves. Even though the proportion of palisade and spongy parenchyma is comparatively average, p should be slightly smaller than 0.5 for leaves with well‐developed spongy mesophyll or around 0.5 for monocotyledonous leaves.
The total absorption coefficient (K) is the sum of the pigment contents multiply by the corresponding SACs. For chlorophyll and carotenoids, they are manly existed in palisade mesophyll and spongy mesophyll. The distribution of them is computed using parameter d, which represents the ratio between chlorophyll or carotenoids content in palisade mesophyll (Cab2 or Cc2) and the total chlorophyll content (Cab or Cc). So the chlorophyll or carotenoids content in spongy mesophyll (Cab3 or Cc3) can be computed as Cab (1‐d) or Cc (1‐d). In previous versions, chlorophyll was assumed to be uniform distributed within the leaf (d = 0.5). However, since palisade mesophyll contains most of chloroplasts, d should ranges from 0.5 to 1. For water and dry matter contents, they are assumed to be distributed proportionally as the distribution of N in mesophyll layers. So water or dry matter content in palisade mesophyll (Cw2 or Cm2) are computed as p Cw or p Cm and those in spongy mesophyll (Cw3 or Cm3) are computed as (1‐p) Cw or (1‐p) Cm.
As compared to previous versions of PROSPECT model, the description of differences between faces is achieved at the expense of 6 additional parameters that do not vary with wavelength: d, p, r1, α1, r4 and α4.

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Selection of calibration dataset

Different from PROSPECT model which assumes biochemical contents are homogenous distributed within the leaf, the FASPECT model treats each variable proportionally distributed in different layer. So it is necessary to recalibrate the SACs of biochemical variables. As explained in Section 3.2, the distribution of chlorophyll and carotenoids are more centered in palisade mesophyll while the distribution of water and dry matter content within leaf is comparatively homogenous. Therefore, the SACs of chlorophyll and carotenoids should be recalibrated and the SACs of water and dry matter content are kept the same as PROPSECT‐5. For anthocyanin, since it is distributed in different leaf cell layers for different species, phylogeny and environmental conditions (Lee 2002), it is difficult to determine its distribution with one or two parameters. As simplification, anthocyanin is assumed to be evenly distributed and the SAC was from PROSPECT‐D. According to the comparison from (Féret et al. 2017), the refractive index from PROSPECT‐3 which was computed from an albino maize leaf provided the best performance, while the refractive index from PROSPECT‐5 would induce artifices in leaf optical properties because of the strong spectral variation. So the refractive index from PROSPECT‐3 is applied to FASPECT model.
Therefore, the calibration dataset should include both the measured reflectance and transmittance ranging from 400 nm to 2400 nm and the measured biochemical variables including pigment contents (chlorophyll, carotenoid and anthocyanin), water and dry matter contents. Considering the accuracy problem from LOPEX (Feret et al. 2008), the ANGER dataset which meets those criterions is chosen as the calibration dataset. ANGER was also used to calibrate PROSPECT‐4, PROSPECT ‐5 and PROSPECT –D. It includes leaves with different states like albino or etiolated leaves which play a vital role to eliminate the strong correlation between chlorophyll and carotenoid in mature leaves (Feret et al. 2008). From (Féret et al. 2017), the anthocyanin contents (Cant) of each sample from ANGER were estimated using spectral index with good accuracy when Cant < 11 µg/cm‐2, so the estimated Cant was also included and samples with low Cant (< 5 µg/cm‐2) were kept to reduce the influence from estimated anthocyanin. To eliminate redundancy of calibration dataset, samples with little impact on calibrated SACs of chlorophyll and carotenoids were removed. Finally, totally 120 samples from ANGER were selected as the calibration dataset and the remaining (188 samples) were used as the validation dataset. It is notice that only optical properties from one face were available in ANGER, so all reflectance and transmittance used to adjust SACs in the next section were considered as optical properties from upper face.

Adjustment of specific absorption coefficients

As calibration algorithm proposed in (Feret et al. 2008), the calibration of SACs was conducted  using iteration optimization methods with two‐steps. Firstly, the structure parameter N was determined with three selected bands in NIR where absorption was smaller. Then, each SAC was calibrated wavelength by wavelength with the whole calibration dataset. However, in FASPECT model, six additional parameters which are independent with wavelength are added. So, more bands covering the whole wavelength are needed to define wavelength invariant parameters. For the first step, different combinations of bands were traversed to fit the spectral curve using smoothing spline function from Matlab2016. The sum of the root‐mean‐square error (RMSE) between measured and simulated spectrum from calibration dataset were used to evaluate the fitting results. In this way, 30 most representative bands were selected from 400 nm to 2450 nm with the curve fitting methods (Figure 9).

LuxCoreRender ray tracing model implementation

LuxCoreRender is a physically based and unbiased rendering engine. It is derived from the Physically Based Radiative Transfer project (Pharr et al. 2016) and is an open source software for ray tracing model simulations (Coubard et al. 2011). It computes the radiation fluxes according to physical equations describing the interaction between light and materials. It produces realistic images of photographic quality with a reasonable computation time (LuxCoreRender 2018).
The path tracing was selected as the ray-tracing integrator. The path tracing allows the path integrator to shoot rays from the camera into the scene and continues reflecting the ray off objects until it finds a light or the search is terminated (LuxCoreRender 2018). Even though it is usually slower than bidirectional or photon map integrator, it can provide unbiased simulation results. For each pixel, 128 rays were generated including direct and diffuse scattering. Leaves were assumed lambertian both for reflectance and transmittance. Stems had the same reflectance as the leaf but no transmission. The soil was set to be flat and lambertian. The scene illumination was simulated with only one directional light source.

Table of contents :

1 Introduction
1.1 Nitrogen fertilization problemAbstract
1.2 Estimation of leaf and canopy characteristics: from leaf measurements to satellite data
1.2.1 Methods to estimate the chlorophyll content at the leaf level The boilogical material
1.2.2 Methods to estimate the chlorophyll content and GAI from satellite data
1.3 Study objective and outlook
2 Estimating leaf biochemical content from laboratory spectral measurements
2.1 The current limits of the PROSPECT model to estimate leaf biochemical content
2.2 Improving the PROSPECT model to retrieve leaf biochemical content
2.3 Conclusion of the chapter
3 Estimates of canopy characteristics from satellite data
3.1 LuxCoreRender: validation and solutions to speedup simulations
3.2 In-silico comparison between turbid medium and 3D realistic based radiative transfer models to estimate GAI of wheat and maize canopies: impact of leaf clumping
3.3 The use of 3D realistic models reduce the bias in GAI and chlorophyll estimates from satellite data: the case of wheat and maize crops under a wide range of conditions
3.4 Conclusion of the chapter
4 Conclusion and perspectives

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