1. Introduction
Leaf chlorophyll plays a critical role in plant photosynthesis and the conversion of CO2 into stored carbohydrate. Accurate measurements of leaf chlorophyll content over different spatial and temporal extents using remote sensing techniques are needed for monitoring vegetation stress and productivity, and for forest management and precision agriculture applications. As light directly reflected from leaf epidermis does not interact with interior materials, it contains little information on the leaf biochemistry and therefore should be excluded from the remotely sensed leaf reflectance. In the visible spectrum (VIS, 400–750 nm), about 3% to 10% (or higher for some species) of the light striking a leaf surface is directly reflected [1,2], accounting for up to 75% of the total reflected signal in the blue and red bands where light is strongly absorbed by pigments, and up to 25% of the total reflectance in the near infrared spectral region (NIR, 750–1300 nm) [3]. As a result, variations in leaf surface reflectance will introduce uncertainty to the deviation of leaf pigments from reflectance data across a wide range of species and plant functional types [4,5].
Leaf surface reflectance varies greatly with plant species, leaf development and environmental conditions [6,7,8]. It is controlled by epidermal characteristics such as the morphology and density of epicuticular waxes or trichomes [4,9], which can greatly enhance the leaf reflectance in the VIS [10,11]. Waxes also greatly increase the leaf reflectance in the NIR, whilst the effect of trichomes on NIR reflectance can be variable [4]. The magnitude and angular distribution of surface reflectance are dependent on the leaf surface biophysical properties. The highly absorbing visible wavelengths show a strong specular reflection compared to the more diffuse transmitted light [12]. Leaf specular reflectance from a surface is usually considered as wavelength-independent [13], as the leaf cuticle usually contains no pigments [7].
Polarization measurements are classically used to separate leaf surface specular reflectance (polarized) from interior diffuse reflectance (non-polarized) and obtain the optical properties of the leaf epidermis [14]. Leaf bidirectional reflectance measurements are also widely used to differentiate specular and diffuse components and to non-destructively estimate the roughness or refractive index of the epidermis [1,2]. However, these methods are complex and usually need specialized instruments that is not commonly used, precluding widespread measurement for model validation, and are hard to apply at the canopy scale.
Alternatively, efforts have been made to diminish leaf surface reflectance effects on the leaf chlorophyll content retrieval from remote sensing data. Leaf chlorophyll content estimation methods can be categorized into (1) parametric regression, (2) non-parametric regression, (3) physically based, and (4) hybrid methods (reviewed in [15]). Spectral indices, one of the most widely used parametric regression methods, have been modified to use reflectance in the blue wavelengths (~450 nm) to reduce the effects of surface reflectance on leaf pigment retrieval across different species [5]. Derivative spectra have also been found to be relatively insensitive to variations of leaf surface reflectance, especially using red-edge wavelengths [4,16]. However, regression methods suffer in terms of their transferability across temporal and spatial scales [17].
In comparison with regression methods, physically based models are underpinned by scientific theory and therefore have the ability to produce accurate and robust prediction of pigment content across different species and spatial scales. Bousquet et al. [2] proposed a three-parameter model differentiating surface reflectance from bidirectional measurements and retrieved values of cuticle refractive index and roughness parameter for the studied three species, but the model is over-parameterized and impractical for the commonly used leaf directional-hemispherical spectra. The PROSPECT model [18] is the most popular leaf radiative transfer model, due to its widespread validation and ease of inversion [19,20,21]. In PROSPECT, leaf surface reflectance is calculated from the refractive index of the leaf and the maximum incident angle, both of which are fixed values [18]. However, high surface reflectance due to heavy waxes on eucalypts leaves has shown to be a key source of uncertainty in pigment estimation from PROSPECT [22,23,24]. Jay et al. [13] proposed a physical model coupled with PROSPECT (PROCOSINE) to account for leaf surface reflectance and leaf orientation effects on leaf bidirectional reflectance factor (BRF), and successfully applied the model to close range hyperspectral images for retrieving foliar biochemistry. Li et al. [25] optimized the inversion strategies of PROSPECT for alleviating leaf surface reflectance effect, by introducing wavelet coefficient spectra generated after continuous wavelet transform (CWT) in the cost function, and improved the performance for foliar pigments retrieval using BRF spectra. Gerber et al. [26] used an additional layer in PROSPECT to compensate for the surface effects with a refractive index that is different from that of the leaf interior. Nevertheless, it is assumed that the surface layer reflectance does not vary with different leaf samples, despite observations of large variations in leaf surface reflectance across species, growth stages, and environmental conditions [7,27].
In this study, we aim at extending PROSPECT-5 to consider variable leaf surface reflectance and alleviate its effect on leaf chlorophyll content estimation from hyperspectral leaf reflectance data. The objectives of this study are to: (1) introduce an additional surface layer bounded on the N elementary layers in PROSPECT-5, characterized by variable surface refractive index; (2) determine leaf surface and interior refractive indices for each samples and recalibrate the specific absorption coefficients for leaf total chlorophyll and carotenoids; and (3) evaluate the performance and sensitivity of chlorophyll content retrieval and leaf spectra reconstruction.
2. Data 2.1. Datasets
Seven independent datasets are used in this study. The datasets are fresh leaf samples collected and measured by different research groups (Table 1). The ANGERS dataset is downloaded online, shared by its authors. The other six datasets are from our field experiments in China (XS, BM, JTL, and NX) and Canada (Crop_UT and Needle_Zh). There are 922 fresh leaf samples from 56 species in total, including broadleaf and needle, dicotyledon and monocotyledon, trees and herbaceous, and annual and perennial plants, encompassing a wide range of physiological statuses. ANGERS has been widely used for model calibration, as it contains a large number of leaves from different species and a wide range of pigment contents [28]. ANGERS and one-fifth of the leaves in XS, BM, JTL, and NX datasets comprise the calibration dataset, and the rest samples are used as validation data.
2.2. Leaf Spectral Measurements
In the experiments for the seven datasets, leaf samples were transported to a laboratory for spectral measurements immediately after leaf sampling. Leaf directional-hemispherical spectra (<2 nm step over 400–2500 nm) for the upper surface of the leaf samples were measured using a field spectroradiometer coupled with an integrating sphere (Table 1). For needle optical measurements in Needle_Zh, a special carrier was used to hold the needles and to present them to the port of the integrating sphere [32,33]. These measurements include both leaf total reflectance and transmittance but does not discriminate between leaf surface and interior reflectance. The spectra in the ANGERS dataset shared online were already smoothed and processed to 1 nm interval. The measured spectra in the other six datasets were resampled to 1 nm interval and smoothed using the Savizky–Golay approach with a third-order polynomial function using 25 nm bandwidth [34].
2.3. Leaf Biochemical Constituent Determination by Destructive Sampling
Four leaf biochemical constituents were measured, including leaf total chlorophyll (Cab, sum of chlorophyll a and b), total carotenoids (Cxc), water (EWT for equivalent water thickness), and dry matter (LMA for leaf mass per area). Right after the leaf spectral measurements, leaf disks were sampled from the same leaf where spectral measurements took place. A cork-borer of known area was used to punch out several leaf disks from the same leaf, avoiding main leaf veins if possible. The sampled needles were scanned on a flatbed scanner for the total projected area. Then the sampled leaf disks or needles were separated into two groups, one for water and dry matter measurements and the other for pigment determination after being frozen.
First, the total fresh weight of one group of disks (Fw, in g) was measured and then dried in an oven at 65 °C for at least 48 h and reweighed until there was little change in the dry weight (Dw, in g). The EWT and LMA was determined as: EWT (in g/m2) = (Fw−Dw)/area of disks and LMA (in g/m2) = Dw/area of disks. The other group of the disks were frozen after sampling, ground or placed in the organic solvents (ethanol, acetone, or dimethylformamide (DMF)) in the dark, until the pigments were fully extracted. After centrifugation, the extracted solution was diluted with the corresponding solvent to a certain volume. The absorbance of the solution was measured using UV–VIS spectrophotometers (UV1800, SHIMADZU Corporation, Japan) and converted to pigment content using specific calibration coefficients for different solvents provided by [29,35,36].
3. Methods 3.1. Addition of a Surface Layer with a Variable Refractive Index
The PROSPECT model simulates leaf directional-hemispherical reflectance and transmittance (400–2500 nm) according to input leaf biochemical contents (Cab, Cxc, EWT, LMA, etc.) and a structure parameter N [18,24,28]. It is based on the plate model [37] that treats a leaf as a stack of N homogeneous elementary layers characterized by an absorption coefficient and a refractive index. When a beam is incident on the boundary of a plate, the transmissivity (tα) and reflectivity (rα) of the surface depend on the effective refractive index (n) and the maximum incidence angle (α) defining the solid angle of the incident beam:
ta=tav(α,n)
ra=1−ta
where tav is the transmissivity of the surface of the top plate.
Due to the undulating shape of the surface of the leaves, the maximum incidence angle for the top layer (αsurf) is different from interior layers (αin = 90°) where the light stream is assumed to be isotropic. The value of αsurf is set to the optimum value 59° in the early versions of PROSPECT and reset to 40° in the versions after PROSPECT-4. The surface effects on leaf optical properties are simplified by using αsurf in all existing versions of the PROSPECT model. Since αsurf is constant and the refractive index (n) is a unique spectrum for all leaves and is identical for the N layers, the surface effects in PROSPECT does not change with leaf samples. The mean reflectance of the upper boundary layer from 400–800 nm (ra) is 0.037. However, leaf surface reflectance could vary greatly with plant species, leaf development, and environmental conditions [6,7,8]. Gerber et al. [26] added an additional non-absorbing surface layer on top of the N elementary layers in PROSPECT to compensate for the surface effects. The refractive index of the surface layer (nsurf (λ)) is different from that of the interior elementary layers (nin (λ)), and their difference determines the surface reflectance as Fresnel coefficients depend on the effective refractive index of the interface. Nevertheless, since nsurf (λ) and nin (λ) in their study were fixed spectra, the surface reflectance did not change with the leaf samples.
Therefore, we add a non-absorbing surface layer similar to that of Gerber et al. [26] in PROSPECT-5, but with variable refractive indices for surface and interior layers. The surface layer is bound to the first of the N elementary layers without any interspace filled by air. According to Gerber et al. [26], this additional surface layer can be considered as an equivalent layer compensating surface effects rather than a true representation of leaf cuticle. Figure 1 shows the basic structure of the modified model (denoted as PROSPECT-Rsurf).
When light incidents on top of the surface layer, the maximum incidence angle (αsurf) is assumed to be 40° and becomes isotropic after transmission through this layer, following the principles in PROSPECT-5 [28]. The reflectance (RL1) and transmittance (TL1) of the first elementary layer coated with the surface layer are calculated as,
RL1=r01+t01⋅t10⋅r1201−r10⋅r120
TL1=t01⋅t1201−r10⋅r120
with r120=r12+t12⋅t21⋅r20⋅θ21−r20⋅r21⋅θ2
and t120=t12⋅t20⋅θ1−r20⋅r21⋅θ2
where the subscript 0 corresponds to the air, 1 to the surface layer, and 2 to the leaf interior; r120 and t120 are reflectance and transmittance when light emerges from the surface layer and passes through the first elementary layer; θ is the transmission coefficient of the elementary layer; and rij and tij (i, j = 0, 1, 2) are the reflectivity and transmissivity at the interface when light emerges from medium i into j, respectively, defined by the maximum incident angle (α) and effective refractive index (n′) as:
tij=tav(α,n′)
rij=1−tij
where n′=nj/ni . The reflectance ρ90 and transmittance τ90 of the other N-1 elementary layer follow Equations (1) to (6) in [18]. The total reflectance (R) and transmittance (T) of a leaf is calculated by stacking the first layer group (a plate coated with surface layer) and the N-1 layers according to [18].
Leaf surface reflectance is specified by the multiple scattering between the surface layer and the first elementary layer, characterized by the two refractive indices nsurf (λ) and nin (λ). Reflectance of the additional surface layer (Rs) is defined based on the calculation of the reflectance of the first group layer (RL1) using Equations (3) to (8), by assuming the transmittance of the first elementary layer (θ) to be 0:
Rs=r01+t01⋅t10⋅r121−r10⋅r12
The transmittance of the surface layer is:
Ts=1−Rs
Based on the definition, the surface layer reflectance in PROSPECT-Rsurf is the surface directional-hemispherical reflectance, consistent with leaf reflectance and transmittance simulated in the model. It is the integration of leaf surface reflectance over the hemisphere from the leaf upper surface which includes the leaf specular reflectance as well as multiple scattering between the surface and interior layers.
The surface refractive index nsurf(λ) changes with different epidermal materials with various morphology and density, while nin(λ) is determined by the internal structure and the organization and composition of internal leaf tissues and air spaces. According to Kramers–Kronig (K–K) relations [38], the real (refractive index) and imaginary (absorption coefficient) part of the complex refractive index are physically linked. Chen and Weng [39] used the K–K relations to derive the effective refractive index with promising results and demonstrated variations of the leaf refractive index for different leaf samples. They found that the leaf refractive index decreases almost monotonically with the wavelength (400–2500 nm), confirming the refractive index spectrum used in PROSPECT-3 (nP3(λ)). However, since the K–K relations require complete electromagnetic spectrum of the biochemical absorption coefficient which are difficult to obtain so far, it is impracticable for most of the commonly used leaf spectral databases covering a limited range of the spectrum [24]. In the latest version PROSPECT-D, nP3(λ) is adopted instead of the one used in PROSPECT-5 in order to avoid artifacts resulting from numerical optimization [24]. Since direct measurements of the leaf surface and internal refractive indices are difficult and the variation of the leaf tissue refractive index with wavelengths remains unclear, the following two assumptions are made in this study, (1) the spectral variation patterns of nsurf(λ) and nin(λ) follow the pattern of nP3(λ); and (2) nsurf(λ) is higher than nin(λ). The two refractive indices nsurf (λ) and nin(λ) are defined by
nsurf(λ)=fsurf⋅nP3(λ)
nin(λ)=fin⋅nP3(λ)
where fsurf and fin are fractions of the surface and interior refractive indices, respectively, which are independent of wavelengths but vary with leaf samples. In this way, we can focus on the variations of the surface and interior refractive indices between different leaves using only two parameters for each sample, while the spectral variation characteristics of the two refractive indices are unaltered. In order to keep nsurf (λ) higher than nin(λ) in the model, nsurf (λ) is expressed as
nsurf(λ)=fsurf′⋅nin(λ)
with f′surf higher than 1. The factor f′surf is the relative refractive index between the leaf surface and the interior. Therefore, we have two variables f′surf and fin in addition to the structure parameter N and biochemical contents (Cab, Cxc, EWT, and LMA) in PROSPECT-Rsurf. The main symbols used in this study and their meanings are listed in Table A1. Considering that leaf pigments absorb light in the VIS domain and effects of the leaf surface reflectance on leaf spectra are significant in the VIS, we make the above modifications in PROSPECT-Rsurf in the range from 400 to 800 nm in this study.
3.2. Model Calibration
After adding the new surface layer and the two refractive indices in PROSPECT-Rsurf, the specific absorption coefficient (SAC) of leaf constituents can be recalibrated from wavelength to wavelength. Since absorption by leaf dry matter and water is low in the VIS, only the SAC of total chlorophyll (kCab(λ)) and carotenoids (kCxc(λ)) are recalibrated. The structure parameter N and the refractive index fractions f′surf and fin change from leaf to leaf and are assumed to be wavelength independent. Since N, f′surf, and fin cannot be directly measured, they are determined in the recalibration process. In order to avoid unfeasibly large computation introduced by concurrently optimizing all the parameters (N, f′surf, fin, kCab(λ), and kCxc(λ) at each wavelength λ from 400–800 nm), the recalibration process is split into two steps. First, the wavelength-independent N, f′surf, and fin are determined, and then kCab(λ) and kCxc(λ) are determined wavelength by wavelength. Due to the possible interaction between the two steps, we performed a cross calibration iteratively until the optimized values of these parameters remain almost unchanged. Detailed descriptions are as follows.
3.2.1. Determination of N, f′surf and fin
The variables N, f′surf, and fin are estimated for each leaf individually from the measured spectra (400–800 nm) with measured Cab, Cxc, EWT, and LMA as input through a numerical optimization process, by finding the best combination of variables that minimizes the merit function:
J(N,fsurf′,fin)=∑λ=400800[(Rmeas,λ−Rmod,λ(N,Cab,Cxc,EWT,LMA,fsurf′,fin))2+(Tmeas,λ−Tmod,λ(N,Cab,Cxc,EWT,LMA,fsurf′,fin))2]
where Rmeas,λ and Tmeas,λ are the measured leaf total reflectance and transmittance at wavelength λ, respectively, and Rmod,λ and Tmod,λ are simulated by PROSPECT-Rsurf. The bound-constrained optimization package FMINSEARCHBND.M [40] in the Matlab software is used. The initial values of N, f′surf, and fin are 1.5 (1–5), 1.1 (1.0001–3), and 1 (0.7–3), respectively, with constrained values given in brackets. The ranges of f′surf and fin are set according to the measurements and simulation of the leaf refractive index in previous studies in [1,2,26,39,41].
3.2.2. Adjustment of the Specific Absorption Coefficients
After determining N, f′surf, and fin, the SAC of total chlorophyll and carotenoids are adjusted through optimization using all leaves comprising the calibration dataset. Similar to the process described in [28], the SAC values of chlorophyll (kCab,λ) and carotenoids (kCxc,λ) at each wavelength are obtained by minimizing the merit function:
J(kCab,λ,kCxc,λ)=∑i=1m(Rmeas,λi−Rmod,λi(kλi))2+(Tmeas,λi−Tmod,λi(kλi))2
where m is the total sample number, kλi is the total absorption coefficient of the elementary layer at wavelength λ for sample i, which is calculated from the structure parameter N and the biochemical contents as follows:
kλi=kCab,λ⋅Cabi+kCxc,λ⋅Cxci+kEWT,λ⋅EWTi+kLMA,λ⋅LMAiNi
where kEWT,λ and kLMA,λ are SAC of EWT and LMA in PROSPECT-5 at λ, respectively, Ni is the structure parameter of sample i; and Ciab, Cixc, EWTi, and LMAi are the measured four biochemical contents of sample i. The initial values of kCab,λ and kCxc,λ are 0.05 and 0.2, respectively. During the inversion, their values were limited in the range of 0–0.1 and 0–0.5, respectively.
3.2.3. Cross Calibration
After step (2), the adjusted SACs are used for recalculating the values of N, f′surf, and fin (step (1)). Then the SAC values of Cab and Cxc are re-adjusted (step (2)) and new sets of N, f′surf, and fin can be subsequently determined (step (1)). We repeat steps (1) and (2) in this way for several times until the optimized N, f′surf, and fin values for each sample and the kCab,λ and kCxc,λ spectra from 400 nm to 800 nm remain nearly unchanged (changes less 0.1%).
3.3. Model Validation: Criteria for the Comparison of Model Performance
We performed model inversions on the validation datasets separated into broadleaf and needle leaf samples with PROSPECT-5 and PROSPECT-Rsurf. The performances of the two models are compared in terms of Cab estimation and leaf spectral fit. PROSPECT-Rsurf is inverted on the validation datasets using the following merit function:
J(N,Cab,Car,EWT,LMA,f′surf,fin)=∑λ=400800[(Rmeas,λ−Rmod,λ(N,Cab,Car,EWT,LMA,f′surf,fin))2+(Tmeas,λ−Tmod,λ(N,Cab,Car,EWT,LMA,f′surf,fin))2]
where Rmeas,λ and Tmeas,λ are the measured leaf total reflectance and transmittance at wavelength λ, respectively, Rmod,λ and Tmod,λ are the ones simulated by PROSPECT-Rsurf.
Standard deviation (σ) and coefficient of variability (CV) are calculated to characterize the distribution of variables. Pearson’s correlation coefficient (r), root mean square error (RMSE), and bias (BIAS) between the retrieved and measured variables are calculated to evaluate the differences between the measured and estimated variables (such as pigment content, leaf reflectance, or transmittance):
CV(%)=σy¯j×100
RMSE=∑j=1n( y′j−yj)2n
BIAS=∑j=1n( y′j−yj)n
where yj is the measurements, yj their mean, y′j the modeled values, and n the sample numbers.
3.4. Model Sensitivity
Since there are no direct measurements of leaf surface and interior refractive indices in this study, the uncertainty in determining f′surf and fin (corresponding to nsurf and nin) from model inversion using the experimental data and the effect of such uncertainty on the quality of the calibration should be evaluated. We perform several steps of sensitivity analysis to understand the influence of noise in the measured spectral data on surface and interior refractive indices determination, and their uncertainty on the adjustment of SACs and on the overall model performances.
3.4.1. Global Sensitivity Analysis
A global sensitivity analysis was set up to evaluate the contribution of the variability in each input variable (N, f′surf, fin, Cab, Cxc, EWT, and LMA) to output reflectance or transmittance from PROSPECT-Rsurf. Sobol’s sensitivity analysis was implemented using a Matlab software tool (GAST) [42]. A dataset of 5000 random parameters was generated using the data range in Table 2 according to measurements and model inversion results.
3.4.2. Sensitivity of Model Calibration
We first investigate the sensitivity of N, f′surf, and fin estimation to noise in spectral measurements. Randomly generated Gaussian noises with standard deviation (σ) set to be 2% of the measured R or T (the mean value μ = 0) are added to measured R and T, respectively, at each wavelength from 400–800 nm. Then N, f′surf, fin, and biochemical parameters are derived from the calibrated PROSPECT-Rsurf model inversion following the procedure described in step (1) of Section 3.2. The operation is repeated 100 times for each sample in the validation datasets.
Second, randomly generated Gaussian noises (σ = 0.009 and 0.039, σ of f′surf and fin derived from inversion, respectively) are introduced to f′surf and fin, respectively, and the noisy datasets are used to determine kCab,λ and kCxc,λ following the method described in step (2) of Section 3.2 in order to investigate the uncertainty introduced by noise in f′surf and fin determination.
3.4.3. Sensitivity of Model Performance
In order to evaluate the influence of uncertainty in f′surf and fin estimation on leaf chlorophyll content retrieval, we add Gaussian noises (σ = 0.009 and 0.039) to f′surf and fin derived from inversion, respectively. Then the noisy f′surf and fin (denoted as f′surf-noise and fin-noise) are used as input parameters when retrieving N and the biochemical parameters using the following merit function:
J(N,Cab,Cxc,EWT,LMA)=∑λ=400800(Rmeas,λ−Rmod,λ(N,Cab,Cxc,EWT,LMA,f′surf−noise,fin−noise))2+(Tmeas,λ−Tmod,λ(N,Cab,Cxc,EWT,LMA,f′surf−noise,fin−noise))2
where Rmeas,λ and Tmeas,λ are the measured leaf total reflectance and transmittance at wavelength λ, respectively, Rmod,λ and Tmod,λ are the ones simulated by PROSPECT-Rsurf. The retrieved groups of biochemical contents are compared with measurements to evaluate the performance of the model for both validation and calibration datasets.
4. Results 4.1. Validation of Model Performances
4.1.1. Recalibrated Specific Absorption Coefficients
Figure 2 displays the SACs of total chlorophyll (kCab,λ) and carotenoids (kCxc,λ) in PROSPECT-Rsurf (P-Rs) and PROSPECT-5 (P-5). The differences between the two models are subtle, with a little higher difference between 500 and 550 nm. In P-Rs between 500 and 550 nm, kCab,λ is slightly higher and kCxc is slightly lower than those in P-5. Considering the variation of leaf surface reflection does not introduce large changes in the SACs of pigments.
4.1.2. Chlorophyll Content Estimation
Figure 3 compares the performances of chlorophyll content estimation for PROSPECT-Rsurf (P-Rs) to PROSPECT-5 (P-5). The color of the points in Figure 3 corresponds to the surface layer reflectance (Rs). The results are demonstrated in three groups: the calibration, broadleaf samples in validation, and needle leaves in validation datasets. Estimation of Cab using P-Rs is improved for the broad leaves in validation datasets (Figure 3b), with RMSE decreasing from 11.12 to 8.87 µg/cm2, r increasing from 0.81 to 0.88, and BIAS adjusted from −3.31 to 0.65. For some of the broadleaf validation samples with high Rs, the underestimation of Cab using P-5 due to the underestimation of Rs is alleviated in P-Rs with BIAS close to 0 (0.65). Furthermore, the overestimation of extremely low Cab samples is corrected.
For needle leaves, the Cab estimated using P-Rs is highly correlated with the measurements (r = 0.89), and much higher than those from P-5 (r = 0.72). However, Cab estimated using P-Rs is systematically overestimated, resulting in high RMSE and BIAS compared to those using P-5 (Figure 3c,d). According to [33], the main reason for the overestimation is that the assumption in the PROSPECT model that a leaf is horizontally infinite may not hold for needle leaves since the needle width is comparable to the needle thickness. The amount of light that escapes from needle edge could be large, leading to the overestimation of leaf reflectance (R) and transmittance (T) using both P-Rs and P-5. Consequently, the overestimation of leaf R and T in VIS leads to increases in Cab in order to lower R and T to fit measured spectra during P-Rs model inversion. However, the overestimation of Cab using P-5 is minor, since the abovementioned overestimation of R and T caused by needle edge effects is partially offset by the underestimation of leaf surface reflectance. As illustrated in Figure 3c, Cab estimation using P-5 for samples with high Rs (red points) is better than those with relatively lower Rs (blue points). For samples with high Rs, the underestimation of Rs using constant leaf surface reflectance in P-5 is higher than that of the sample with low Rs, resulting in higher offset effect on Cab estimation.
In order to further investigate the ability of the improved model for estimating needle chlorophyll content, we incorporated the edge effects of needles using the methods proposed in [33] in the modified model PROSPECT-Rsurf. According to [33], needle width and thickness, were introduced into the model to take into account the effects of leaf morphology on Cab retrieval. The performance of Cab estimation was improved by considering the edge effects in PROSPECT-Rsurf (P-Rs-edge), as demonstrated in Figure 4. The overestimation of Cab is alleviated compared to PROSPECT-Rsurf in Figure 3f. The RMSE using P-Rs-edge decreases from 8.98 to 6.08 µg/cm2, with r increasing from 0.72 to 0.77, and BIAS adjusted from 4.39 to −1.61, compared to that of PROSPECT (P-5). Cab estimated using P-Rs-edge is also better than the results of incorporating the edge effects without considering the variation of leaf surface reflectance demonstrated in [33] (RMSE = 6.32 µg/cm2, r = 0.77), with the scattered points closer to the 1:1 line.
4.1.3. Spectra Reconstruction
We compared the spectral RMSE and r between the measured spectra and spectra reconstructed by PROSPECT-5 (P-5) and PROSPECT-Rsurf (P-Rs) after model inversion on calibration and validation datasets (Figure 5). RMSE for broadleaf validation leaves obtained with P-5 ranges from 0.01 to 0.03 over 400–800 nm, while for needle leaves RMSE (P-5) is between 0.01 and 0.05 over the VIS and is much higher (>0.06) over the NIR. P-Rs outperforms P-5 over 400-800 nm for both broad and needle samples, with RMSEs decline to lower than 0.015. P-Rs greatly improve R simulation over the VIS for broad leaves. For needle leaves, RMSEs for both R and T decline greatly over 400-800 nm, while the improvement over NIR for needle leaves is predominant with RMSE decreased from over 0.06 to less than 0.01. There are great increases in r for R from 400–700 nm especially over 400–500 nm, whereas the improvements of r for T is minor. The reconstructed R is highly correlated to measurements with r close to 0.9.
To further illustrate the ability of PROSPECT-Rsurf to simulate leaf optical properties, we selected samples with a large range of Cab and relatively high Rs values (Figure 6). For the samples with Cab ranging from 0.9 to 80.9 µg/cm2, R and T simulated values using P-Rs are quite close to the measured ones. In most cases, the fit using P-Rs is better than that using P-5, especially where Rs values are high. For example, the measured reflectance spectra of Cornus alba ‘Elegantissima’ and Eucalyptus gunnii leaves (Figure 6c,e) are high compared to other leaves with similar Cab values, probably due to the high surface reflectance. R of the two leaves is substantially underestimated by P-5 over 400–700 nm and T is also underestimated around 550 nm. The underestimation is greatly reduced using P-Rs for both R and T.
4.2. Estimated Leaf Surface Reflectance and Refractive Indices
Leaf surface layer reflectance estimated during the inversion process for all the leaves derived from Equation (9) is illustrated in Figure 7. The nearly flat lines of Rs indicate that spectral variation of the estimated Rs is minor, with the mean standard deviation of 0.0025 over 400–800 nm. The histogram (Figure 7b) shows that Rs values at 550 nm for most samples range from 0.03 to 0.07, with a mean value of 0.0527. Rs can account for a large proportion of leaf total reflectance in VIS. Distributions of the ratio of Rs to leaf total reflectance at 550 nm (R550) and 680 nm (R680), respectively, for all the samples are shown in Figure 7c. The average proportion of Rs to R550 is 39.8%, and for more than 90% samples the proportion of Rs to R550 is between 15% and 65%. The proportion of Rs to R680 is even higher than that of Rs to R550, with an average proportion to be 86.3% and more than 75% samples having the Rs-to-R680 ratio higher than 80%.
Statistics of the mean values of estimated Rs at 550 nm (Rs,550) for each species are shown in Figure 8 and Table A2. About 93% of all 56 species under study have mean Rs,550 in the range from 0.03 to 0.05. The mean reflectance of the upper boundary layer in PROSPECT-5 from 400–800 nm (ra = 0.037) is also in this range. Among these species, mean Rs,550 of leaves of cider gum (Eucalyptus gunnii), black spruce (Picea mariana (Mill.)), and red-barked dogwood (Cornus alba ‘Elegantissima’) are much higher than others, at 0.112, 0.082, and 0.080, respectively. The high Rs can be ascribed to the presence of epicuticular wax that reflects a large amount of incident light [11,22,24]. Further investigation into the surface characteristics of leaves with high Rs reveals that leaves with heavy wax on the surface, or leathery or hard leaves with glabrous surfaces (Table A2 and Figure A1 in the Appendix A) usually have high Rs. Leaves of leatherleaf arrowwood (Viburnum rhytidophyllum) are lustrous but the estimated surface reflectance is not very high (mean Rs,550 = 0.042), probably due to the deeply veined surface which increases the surface roughness and reduces surface specular reflectance. The estimated Rs of some pubescence leaves is also high, although not as high as waxy leaves. These results demonstrate that the estimated Rs is able to represent the main reflectance characteristics of leaf surfaces.
The estimated Rs is found to be strongly correlated to leaf reflectance around 445 nm (R445), except for broad leaves with extremely low Cab (<2 µg/cm2, black cross in Figure 9). There is a slight difference in the R445 and Rs relationship between broad and needle leaves.
The estimated leaf interior refractive index (nin) is demonstrated in Figure 10. For most of the samples, nin values are in the range from 1.2 to 2.0. The refractive index used in PROSPECT-3 and PROSPECT-5 are in the range of the estimated leaf interior refractive indices. Similar to the refractive index used in PROSPECT-3 and PROSPECT-D, spectral variation of the estimated leaf interior refractive index is minor. The estimated spectra of nin conform with the leaf refractive indices derived from K–K relations [39].
4.3. Sensitivity to the Uncertainty Associated with Rs
4.3.1. Global Sensitivity Analysis
The results of Sobol’s sensitivity analysis for the total reflectance (R) and transmittance (T) simulated using PROSPECT-Rsurf are shown in Figure 11. Leaf chlorophyll content (Cab) mainly influences R and T in the range over 500 to 750 nm, while N mainly affects the NIR spectrum (750–800 nm). The effects of leaf carotenoids content (Car) on R and T are minor, mainly over 450 to 550 nm, while leaf dry matter content (LMA) mainly contributes to the absorption in NIR. The internal refractive index (represented by fin) can be considered as another variable influencing the leaf internal structure and contributes to R and T mainly over NIR. Leaf surface reflectance (Rs), represented by the ratio of the refractive index of leaf surface layer to that of interior layers (f′surf), is the main factor contributing to R at blue wavelengths (400–500 nm), and has little contribution to T. In the red-edge region over 690–720 nm, Cab and N are the two main contributors, while the influence of Rs (i.e., f′surf) on R is low. The red edge reflectance is more sensitive to variations in Cab and N rather than in Rs.
4.3.2. Sensitivity of Model Calibration
After adding groups of noise to the measured spectra, group values of N, nsurf, and nin and the corresponding Rs are obtained for each sample. The distributions of the coefficient of variability (CV) of N, nsurf, nin, and Rs are shown in Figure 12. Most CV values of N are lower than 2.5%, with a mean value of 1.0%. The max CV of nsurf and nin are lower than 1.5%, and the mean values are less than 0.5%. The CV values of the corresponding Rs calculated from nsurf and nin are between 0.4% to 1.4%.
The variability in SACs of chlorophyll (kCab) derived from noisy f′surf and fin (corresponding to nsurf and nin, respectively) is limited to the 400–450 nm wavelength range, while that of carotenoids (kCxc) is in 400–480 nm (Figure 13). The influence of introducing noises to noisy f′surf and fin on kCab is lower than that on kCxc. The mean standard deviation (σ) of kCab and kCxc over 400–450 nm is 0.0016 (CV = 4.6%) and 0.0052 (CV = 14.2%), respectively.
4.3.3. Chlorophyll Content Retrieval
Cab retrieved using PROSPECT-Rsurf with the noisy f′surf and fin (corresponding to nsurf and nin, respectively) are illustrated in Figure 14. For the calibration dataset, the performance of PROSPECT-Rsurf (P-Rs) and PROSPECT-5 (P-5) are comparable, and it introduces slight uncertainty in Cab estimation after adding noise to f′surf and fin. For broadleaf validation samples (V(b) in Figure 14), the uncertainty in Cab estimation using P-Rs with noise added is small. RMSE changes from 8.90 to 10.81 µg/cm2 with a mean value of 9.63 (8.6% increase comparing to that of P-Rs), and r varies from 0.85–0.88 (mean = 8.71). Nevertheless, Cab retrieval using P-Rs with noises introduced is still better than that of P-5 (RMSE = 11.12 µg/cm2, r = 0.81), with lower RMSE and higher r values. It proves that P-Rs is effective and better than P-5 in Cab estimation for tested broadleaf samples. For black spruce needles (V(n)) with relatively high surface reflectance, wide variations in RMSE are found, indicating that Cab estimation for needles is sensitive to the noise added to f′surf and fin. However, the estimated Cab using P-Rs is better correlated with measurements than that using P-5, no matter noise is introduced or not. As mentioned before there is an overestimation of leaf spectra since the edge effects are ignored, leading to systematic overestimation of retrieved Cab. This systematic error in Cab can explain the higher RMSE by P-Rs than by P-5.
5. Discussion 5.1. Effects of Leaf Surface Reflectance on Chlorophyll Estimation
The existing versions of PROSPECT were proved to be effective for retrieving foliar biochemical contents for the majority of the tested samples. However, the spectral fit and pigments retrieval using PROSPECT models are poor for leaves with extremely high surface reflectance [22,24]. In this study, we incorporate variable leaf surface reflectance in PROSPECT-Rsurf to improve chlorophyll content (Cab) retrieval and spectral reconstruction, especially for samples coated with heavy wax or hard cuticle leading to high leaf surface reflectance. Leaf surface reflectance can occupy over 40% of the total reflectance at around 550 nm, and large variations across different species and plant functional types are observed, indicating the important influence of leaf surface reflectance on leaf chlorophyll content retrieval.
PROSPECT-5 and PROSPECT-Rsurf performed similarly in Cab retrieval for leaves with lower Rs, since the slight differences between the leaf surface reflectance used in the two models were compensated by adjusting the structure parameter N during model inversion. However, when the actual leaf surface reflectance is much higher than the surface reflectance used in PROSPECT-5, the error in spectral simulation probably cannot be compensated by adjusting N during inversion, leading to error in Cab estimation. Notwithstanding the compensating effects of N adjustment on Cab estimation using PROSPECT-5, PROSPECT-Rsurf shows notable improvements in Cab estimation as well as spectral simulation over 400–800 nm. Two new variables representing leaf surface and interior refractive indices are introduced in PROSPECT-Rsurf. The inversion procedure may consequently increase the computing time and the applicability of the model at the canopy scale is limited as the additional parameters may increase the ill-posed problem of model inversion. However, we demonstrate that the leaf surface reflectance effect on chlorophyll content retrieval can be alleviated by introducing variable leaf surface layer reflectance.
Sensitivity analysis shows that leaf reflectance at the red-edge region (690–720 nm) is found to be less sensitive to the variation of Rs than that at other VIS wavelengths (Figure 11), suggesting that the red-edge reflectance can be used to build spectral indices that is less sensitive to leaf surface reflectance variation. This agrees with the spectral indices for Cab estimation developed from empirical data in previous studies [4,16]. The difference between the reflectance at two VIS bands reduced the effect of surface reflectance, since surface reflectance was considered as wavelength independent. Sims and Gamon [5] found that modified spectral indices incorporating reflectance at 445 nm (R445) is able to eliminate the effect of surface reflectance and is better correlated with chlorophyll content. The high correlation between leaf surface layer reflectance and R445 found in this study provides support for these spectral indices from the perspective of a radiative transfer model.
The improvement in chlorophyll estimation and spectral reconstruction using PROSPECT-Rsurf is important for the study of the interaction between photosynthetic pigments and solar radiation. Given that leaf chlorophyll content can drive about 60% of the canopy reflectance variation in VIS [43], the effects of variable leaf surface reflectance on canopy reflectance in VIS cannot be ignored. Future studies by coupling PROSPECT-Rsurf with canopy models are needed to explore the influence of leaf surface reflectance on canopy reflectance and therefore canopy chlorophyll content retrieval.
5.2. Improvements on Needle Leaf Chlorophyll Content Retrieval
When applying PROSPECT-5 to needle leaves, the amount of light that escapes from needle edges cannot be ignored. In PROSPECT-5 inversion the overestimation of leaf R and T caused by the edge effects is partially compensated by the underestimation of leaf surface reflectance. Therefore, Cab estimation using PROSPECT-5 appears good with low BIAS. When leaf surface reflectance is adjusted in PROSPECT-Rsurf, the edge effects show up, leading to the overestimation in Cab but higher correlation coefficients compared to measurements. Zhang et al. [33] introduced needle width and thickness in a scheme to adjust measured leaf total reflectance and transmittance for considering the edge effects on chlorophyll content retrieval, and showed that Cab estimation is improved compared to that of PROSPECT-3. Based on this study, we incorporated the edge effects of needles in PROSPECT-Rsurf. The performance of Cab is improved after considering both leaf edge and surface effects, compared to both PROSPECT-5 and the results in [33]. The result indicates that appropriate representation of needle structure is required in order to estimate needle chlorophyll content with good accuracy. There are still large uncertainties in the estimated Cab compared to measurements. This necessitates further model refinements specific for the morphology and internal structure of needle samples, as well as accurate measurements of needle spectra.
5.3. Leaf Surface Reflectance and Refractive Indices
The estimated Rs differs widely for leaves with different surface features. Our results show that some leaves with heavy wax or hard cuticle, or white trichomes, usually have high leaf surface reflectance. Leaf surfaces coated with heavy waxes or hard cuticle reflect large amounts of light, most of which is specular, while trichomes increase the ability to scatter light [11]. However, due to the variety of the morphology and density of epicuticular waxes or trichomes, quantitative evaluation of the effects of waxes and trichomes on leaf total reflectance is difficult and needs further exploration.
The surface layer reflectance (Rs) is characterized by the refractive indices of the additional surface layer (nsurf) and the interior layers (nin) in PROSPECT-Rsurf. The leaf surface layer and interior refractive indices derived from model inversion are comparable to the leaf refractive index obtained by Kramers–Kronig (K–K) transformations [39]. The derived leaf surface and interior layer refractive indices should not be considered as true representations of leaf surface and interior refractive indices but as equivalent parameters compensating for leaf surface reflectance and internal multiple scattering, respectively. The spectral variations of nsurf and nin are minor, resulting in relatively flat leaf surface layer reflectance spectra in 400–800 nm, which are consistent with the findings that leaf specular reflectance from a surface is usually considered as wavelength-independent [13], as the cuticle and cell walls of leaf epidermis usually contain no pigments [7].
The improvements in spectral reconstruction and chlorophyll content retrieval using PROSPECT-Rsurf suggest that the leaf surface reflectance obtained in this study is a better estimate of the actual surface reflectance than the original reflectance spectrum used in PROSPECT-5. The derived surface layer reflectance is effective in revealing the variations in leaf surface reflectance features across different species, functional types and growing stages. Therefore, although a certain degree of uncertainty exists in the estimated Rs, we believe that the surface layer reflectance estimated in this study is reasonably accurate. Measurements on the surface reflectance and quantitative evaluation of the two refractive indices are needed to further validate our modified model and develop methods to nondestructively estimate the surface reflectance more accurately for pigments retrieval.
6. Conclusions
In this study, we demonstrated that incorporating variable leaf surface layer reflectance in the PROSPECT-Rurf model is effective in improving the leaf chlorophyll content retrieval as well as spectral simulation, especially for leaves with high surface reflectance. The root mean square error (RMSE) of Cab estimates decreased from 11.1 µg/cm2 to 8.9 µg/cm2 and the Pearson’s correlation coefficient (r) increased from 0.81 to 0.88 (p < 0.01) for broadleaf samples in validation datasets, compared to PROSPECT-5. For needle leaves, r increased from 0.71 to 0.89 (p < 0.01), but systematic overestimation of Cab was found to be due to the edge effects of needles. After incorporating the edge effects in PROSPECT-Rsurf, the overestimation of Cab was alleviated and its estimation was improved. The result indicates that accurate representation of needle structure is required in order to appropriately estimate Cab.
Although a certain degree of uncertainty exists, the estimated Rs is able to capture the variation of leaf surface reflection features across different plant species. Sensitivity analysis indicated that the influence of the uncertainty in estimation of Rs on chlorophyll content retrieval is small (8.6% increase on average). The estimated leaf surface reflectance was found to be highly correlated with leaf total reflectance at 445 nm (R445), providing evidence for using R445 in spectral indices to eliminate the effect of surface reflectance on Cab estimation. We also found that the red-edge leaf reflectance is less sensitive to variation in leaf surface reflectance, confirming the usefulness of red-edge wavelengths for chlorophyll retrieval.
The coupling of PROSPECT-Rsurf with canopy models will allow exploration of the influence of leaf surface reflectance on canopy reflectance and therefore canopy chlorophyll content retrieval, for the purpose of monitoring plant physiological statuses and vegetation productivity across different spatial and temporal scales.
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| ANGERS | XS | BM | JTL | NX | Crop_UT | Needle_Zh | |
|---|---|---|---|---|---|---|---|
| Year | 2003 | 2014 | 2015 | 2015 | 2014 | 2013 | 2003–2004 |
| Number of samples | 276 | 175 | 54 | 35 | 140 | 152 | 90 |
| Number of species | 43 | 2 (a) | 8 (b) | 1 (c) | 1 (d) | 2 (e) | 1 (f) |
| Spectral measurement devices | ASD FieldSpec
Integrating sphere (IS) | ASD FieldSpec 3
ASD RTS-3ZC IS | ASD FieldSpec Pro FR
Li-COR 1800 IS | ASD FieldSpec Pro FR
Li-COR 1800 IS | |||
| Spectral sampling | 1.4 nm (400–1000 nm), 2 nm (1000–2500 nm) | ||||||
| Solvent for pigments | Ethanol 95% | Acetone 100% | DMF * | DMF | |||
| Method for pigments | [29] | [29] | [30] | [31] | |||
| Chlorophyll (µg/cm2) | |||||||
| Max | 106.7 | 93.8 | 80.8 | 83.9 | 71.7 | 92.5 | 62.6 |
| Min | 0.8 | 16.8 | 1.4 | 30.1 | 20.1 | 0.4 | 12.0 |
| Mean | 33.9 | 50.9 | 40.1 | 56.1 | 44.0 | 43.6 | 29.3 |
| SD ** | 21.7 | 15.5 | 15.5 | 15.9 | 11.2 | 20.3 | 9.1 |
| Carotenoids (µg/cm2) | |||||||
| Max | 25.3 | 17.2 | 16.7 | 15.2 | 12.8 | \ | 10.3 |
| Min | 0.0 | 3.8 | 4.4 | 6.8 | 3.9 | \ | 3.2 |
| Mean | 8.7 | 9.9 | 9.9 | 10.7 | 8.0 | \ | 6.3 |
| SD | 5.1 | 2.9 | 2.7 | 2.3 | 1.9 | \ | 1.6 |
| Water (g/m2) | \ | ||||||
| Max | 340.0 | 144.8 | 206.1 | 312.0 | 168.8 | \ | \ |
| Min | 43.9 | 59.0 | 65.0 | 143.8 | 84.4 | \ | \ |
| Mean | 116.2 | 102.9 | 115.3 | 213.6 | 117.2 | \ | \ |
| SD | 48.6 | 15.9 | 29.1 | 47.0 | 16.1 | \ | \ |
| Dry matter (g/m2) | \ | ||||||
| Max | 331.0 | 166.2 | 145.6 | 185.9 | 56.1 | \ | \ |
| Min | 16.6 | 55.4 | 49.0 | 67.0 | 8.7 | \ | \ |
| Mean | 52.4 | 100.9 | 81.8 | 122.6 | 33.2 | \ | \ |
| SD | 36.7 | 24.7 | 21.8 | 26.9 | 6.0 | \ | \ |
(a) Species including Liquidambar formosana L. and Quercus acutissima L.; (b) Species including Koelreuteria paniculata L., Sapium sebiferum L., Malus spectabilis L., Lagerstroemia indica L., Cerasus serrulata L., Liquidambar formosana L., Populus nigra L., and Cyclocarya paliurus L.; (c) Ligustrum lucidum L.; (d) Zea mays L.; (e) Zea mays L. and Triticum aestivum L.; (f) Picea mariana (Mill.). * Dimethylformamide. ** Standard Deviation
| Variable | Range of Sobol Set |
|---|---|
| N | 1–3 |
| f′surf | 1–1.1 |
| fin | 0.76–1.15 |
| Cab | 0–120 (µg/cm2) |
| Cxc | 0–3 (µg/cm2) |
| EWT | 40–345 (g/m2) |
| LMA | 17–330 (g/m2) |
Author Contributions
Conceptualization, F.Q.; formal analysis, F.Q.; funding acquisition, W.J.; investigation, F.Q., H.C., J.L., Q.Z. and Y.Z.; methodology, F.Q.; supervision, J.C.; writing-original draft, F.Q.; writing-review and editing, J.C., H.C., Q.Z., Y.Z. and W.J.
Funding
This research was funded by the National Key R&D Program of China, grant number 2016YFA0600202; National Natural Science Foundation of China, grant number 41701393; Natural Science Foundation of Jiangsu Province for Youth, grant number BK20170641; and China Postdoctoral Science Foundation, grant number 2018T110477 and 2017M621698.
Acknowledgments
We thank Luc Bidel, Christophe François and Gabriel Pavan who collected and shared the ANGERS dataset. We are indebted to Jun Wang, Meihong Fang, and some other group members at Nanjing University who are not listed here, for their great help in the leaf biochemical and spectral measurements.
Conflicts of Interest
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
Appendix A
Table
Table A1.List of symbols used in this study.
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Table
Table A2.Estimated Rs at 550 nm and leaf surface characteristics of species with high Rs.
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Figure A1.Pictures of leaves of species with high estimated surface reflectance (Rs-vi). The species of leaves in each picture numbered with letters from (a) to (o) correspond to the species ID in the first column of Table A2.
Figure A1.Pictures of leaves of species with high estimated surface reflectance (Rs-vi). The species of leaves in each picture numbered with letters from (a) to (o) correspond to the species ID in the first column of Table A2.
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1International Institute for Earth System Science, Nanjing University, Nanjing 210023, China
2Department of Geography and Planning, University of Toronto, Toronto, ON M5S 3G3, Canada
3Department of Biological Sciences, Delta State University, Cleveland, MS 38733, USA
*Author to whom correspondence should be addressed.
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Abstract
[...]variations in leaf surface reflectance will introduce uncertainty to the deviation of leaf pigments from reflectance data across a wide range of species and plant functional types [4,5]. The surface effects on leaf optical properties are simplified by using αsurf in all existing versions of the PROSPECT model. Since αsurf is constant and the refractive index (n) is a unique spectrum for all leaves and is identical for the N layers, the surface effects in PROSPECT does not change with leaf samples. In the latest version PROSPECT-D, nP3(λ) is adopted instead of the one used in PROSPECT-5 in order to avoid artifacts resulting from numerical optimization [24]. Since direct measurements of the leaf surface and internal refractive indices are difficult and the variation of the leaf tissue refractive index with wavelengths remains unclear, the following two assumptions are made in this study, (1) the spectral variation patterns of nsurf(λ) and nin(λ) follow the pattern of nP3(λ); and (2) nsurf(λ) is higher than nin(λ). [...]randomly generated Gaussian noises (σ = 0.009 and 0.039, σ of f′surf and fin derived from inversion, respectively) are introduced to f′surf and fin, respectively, and the noisy datasets are used to determine kCab,λ and kCxc,λ following the method described in step (2) of Section 3.2 in order to investigate the uncertainty introduced by noise in f′surf and fin determination. 3.4.3.
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