Spectral subdomains and prior estimation of leaf structure improves PROSPECT inversion on reflectance or transmittance alone

Highlights

• Optimal spectral subdomains improve the retrieval success of PROSPECT constituents.

• Inversion on reflectance or transmittance is enhanced by leaf structure information.

• Leaf structure is well estimated by NIR spectral band ratios.

• Traditional and novel PROSPECT inversion approaches can be readily enhanced.

Abstract

Leaf biochemical and structural traits are vegetation characteristics related to various physiological processes. Taking advantage of the physical relationship between optical properties and leaf biochemistry, field-based spectroscopy has allowed for the rapid estimation of leaf biochemical constituents and repeated non-destructive measurements through time. Leaf constituent retrieval from leaf optical properties following inversion of the physically-based radiative transfer model PROSPECT is now a popular method, but some cases prompt poor retrieval success and this approach requires a strict inversion procedure. We investigated the performances of different inversion procedures for the estimation of leaf constituents, specifically chlorophyll a and b, carotenoids, water (EWT), and dry matter (LMA) from >1400 broadleaf samples, including the definition of optimal spectral subdomains, and the use of leaf reflectance or transmittance alone. We also developed a strategy to obtain prior information on the leaf structure parameter (N) in PROSPECT, when only reflectance or transmittance is measured, and examined the influence of this prior information in combination with different inversion procedures. We found that using the full domain of reflectance or transmittance only systematically leads to suboptimal estimation of chlorophyll a and b, carotenoids, EWT, and LMA, due to either the combined absorption of multiple constituents or inaccurate estimation of the N parameter. Our study confirms that the selection of optimal spectral subdomains leads to improved estimation of all leaf constituents, from 700 to 720 nm for chlorophyll a and b, 520–560 nm for carotenoids, and from 1700 to 2400 nm for EWT and LMA. Prior information on N, computed directly from the spectra, leads to systematic improved estimation of leaf constituents when only reflectance or transmittance is measured, with reductions in normalized root mean square error from 8 to 37%. We strongly recommend using optimal subdomains when inverting PROSPECT to retrieve leaf constituents, and with the availability of only reflectance or transmittance we further recommend the use of prior information on the N parameter.

Introduction

Leaf biochemical and structural traits are physiological indicators of plant functioning, fundamental to multiple fields including environmental monitoring (Ali et al., 2016), agriculture (Faucon et al., 2017; Le Maire et al., 2011), land-use management (Murray et al., 2013), and ecology (Shipley et al., 2016; Maire et al., 2015), and increasingly critical for research in the context of global change.

Photosynthetic pigments are studied in the forms of chlorophyll a and b, and carotenoids (including xanthophylls and carotenes). These pigments dominate light absorption in the visible region of the electromagnetic spectrum, from 400 nm to 750 nm (VIS). Chlorophylls are key molecules for photosynthesis as they absorb light energy and contribute to its conversion into chemical energy. Carotenoids are accessory pigments participating in light energy harvesting, and performing photoprotection from harmful radiation (Zarco-Tejada et al., 2013; Hernández-Clemente et al., 2012). The ratio of chlorophyll a and b to carotenoid content provides information on leaf function, as chlorophyll content (Cab, expressed in mass per unit leaf area) is dynamic throughout a leaf life cycle or under conditions of environmental stress (Féret et al., 2008; Gitelson et al., 2017). Conversely, carotenoid content (Cxc, expressed in mass per unit leaf area) is relatively stable until an advanced stage of senescence (Féret et al., 2017; Chavana-Bryant et al., 2017; Coussement et al., 2018).

Leaf water content, here defined as equivalent water thickness (EWT, expressed in mass per unit leaf area), and leaf dry matter content, also known as leaf dry mass per unit area (LMA, expressed in mass per unit leaf area), the reciprocal of specific leaf area (SLA), are two important leaf traits related to tissue density which in turn influence other leaf functional traits. EWT, the difference between fresh mass and dry mass per unit area, influences dehydration resiliency (Kattenborn et al., 2017). Due to the biophysical constraints imposed by the leaf economic spectrum, LMA is systematically correlated with assemblages of other plant traits as it represents the compromise between the cost of leaf construction and the resultant light interception area (Asner et al., 2014). LMA is related to leaf life-span, and inversely related to individual plant water conductance, photosynthetic capacity, root system, nutrient uptake, turnover and growth rate (Gara et al., 2019; Reich et al., 1997; Maréchaux et al., 2016). LMA can thus capture a large portion of functional variation in ecosystems. LMA also allows conversion between mass-based and area-based constituent quantities, bridging the gap between different Modeled approaches. The ratio of EWT to LMA is used to calculate fuel moisture content for fires, as both together influence fire ignition and propagation (Qi et al., 2014; Riano et al., 2005).

Several destructive and non-destructive techniques can be used to measure leaf traits. Destructive methods require the collection and transportation of leaf samples, followed by analysis of leaf constituents using wet chemistry techniques (Jacquemoud and Baret, 1990; Lichtenthaler, 1987). Destructive techniques are thus time consuming, expensive, and in the case of remote sites logistically restricting due to the light and heat-sensitive nature of pigment and moisture analyses (Asner et al., 2015). Alternatively, non-destructive techniques based upon leaf spectroscopy, have been successful in retrieving leaf traits. Leaf spectroscopy is relatively cost-effective, with the benefit of repeatability, and remote application, and has been adopted as a common approach to the study of leaf traits (Hill et al., 2019; Féret et al., 2019; Féret et al., 2017; Chavana-Bryant et al., 2017; Sun et al., 2018; Nunes et al., 2017; Le Maire et al., 2004, Le Maire et al., 2008). Leaf spectroscopy takes advantage of the relationship between leaf optical properties (including reflectance, transmittance and absorptance) and their structural and biochemical properties.

A variety of approaches have been developed to estimate Cab, Cxc, EWT, and LMA from leaf spectra (Hill et al., 2019; Sun et al., 2018; Cheng et al., 2014; Le Maire et al., 2008; Goetz et al., 1990). They can be grouped into three categories: statistical, physical, and hybrid approaches (Verrelst et al., 2015; Verrelst et al., 2012). Statistical approaches involve the collection of a calibration dataset of leaf constituents concurrent with optical measurements from which regression models are established to estimate leaf constituents from reflectance and/or transmittance spectra. The most direct models correspond to spectral indices involving combinations of optical properties at a reduced number of relevant wavelengths. For example, Cab can be estimated from leaf reflectance data with various spectral indices (Chavana-Bryant et al., 2017; Le Maire et al., 2004). Partial least square regression (PLSR) and machine learning algorithms have also been applied to estimate quantities of biochemical constituents (Féret et al., 2019; Hill et al., 2019; Martin et al., 2018). Statistical approaches are computationally very efficient, and have been successful in the retrieval of a large number of leaf traits based on spectral data at both leaf and canopy scale. The two main disadvantages of statistical and machine learning approaches however are the need for comprehensive training datasets, and the lack of generalization ability, leading to limited applicability to the retrieval of leaf traits from different sites and species (Féret et al., 2019; Jiang et al., 2018; Sun et al., 2018; Wang et al., 2015). However recent studies have shown that improvements in instrumental design, data calibration, methods and algorithms now enable more robust data driven predictive models applicable to larger and more diverse areas and vegetation types (Hill et al., 2019, Serbin et al., 2019).

Physical approaches based on RTMs such as the PROSPECT model at the leaf scale (Jacquemoud and Baret, 1990) are theoretically robust, as they are built upon fundamental relationships between light and leaf tissues, relying on well-defined equations of optics involving scattering and absorption interactions which are site and species-independent (Jacquemoud and Baret, 1990; Féret et al., 2008). PROSPECT assumes a relatively simple representation of plant leaves and simulates their optical properties based upon the generalized plate model. The plate model, first developed by Allen et al. (1969), calculates the diffuse reflectance and transmittance of acompact leaf assuming that the refractive index and specific absorption of leaf constituents are known. The generalized plate model (Allen et al., 1970; Breece and Holmes, 1971; Stokes, 1862) establishes a system of equations corresponding to N uniform compact layers separated by N-1 air spaces, in order to obtain reflectance and transmittance of the series of layers. The PROSPECT model is based on this generalized plate model for real values of N which is defined as the structure parameter, allowing representation of leaf internal structure for dicotyledon as well as monocotyledon species. In forward mode PROSPECT simulates leaf directional-hemispherical reflectance and transmittance from 400 nm to 2500 nm (Schaepman-Strub et al., 2006) based upon a limited number of input biochemical and structural components (Jacquemoud and Baret, 1990). Successive versions of PROSPECT have included more constituents (Féret et al., 2008). The latest version, PROSPECT-D, accepts as input parameters Cab, Cxc, anthocyanins, brown pigments, EWT, LMA, and the N structure parameter, allowing accurate simulation of leaf optical properties for a broad range of leaf morphologies and development stages (Coussement et al., 2018; Jiang et al., 2018; Féret et al., 2017). The inversion of PROSPECT allows the retrieval of leaf biochemical constituents from leaf directional-hemispherical reflectance and transmittance data by searching the input parameters which allow the best fit between simulated and measured spectra. Several algorithms have been used in the literature to perform this inversion, including look-up-table (LUT) methods (Ali et al., 2016) and iterative optimization based on minimization algorithms (Jacquemoud et al., 1996). PROSPECT was applied for the first time at the canopy level to remotely retrieve canopy-level foliar traits in combination with the canopy bidirectional reflectance model, Scattering by Arbitrary Inclined Leaves (SAIL), in 1992, in a coupled model known as PROSAIL (Baret et al., 1992). PROSAIL has since been utilized for a variety of applications, including the remote quantification of foliar constituents for both homogeneous and heterogeneous canopies, the development and improvement of vegetation indices, the correction of imaging spectroscopy, phenotyping, and others (Jay et al., 2019; Berger et al., 2018). While PROSAIL is regarded as the most widely used canopy level RTM (Jacquemoud et al., 2009), both PROSPECT and SAIL are continuously evolving due to advancements in understanding at both the canopy level and leaf level. Finally, hybrid approaches combine statistical and physical approaches, such as the establishment of spectral indices or machine learning regression models based on simulated optical data generated in forward mode (Brown et al., 2019; Hill et al., 2019; Berger et al., 2018; Verrelst et al., 2015).

Traditionally, the PROSPECT model is inverted upon directional-hemispherical reflectance and transmittance data across the VIS and infrared (IR) domains from 400 nm to 2500 nm. However, this approach has prompted poor retrieval success for some constituents, in particular LMA (Jiang et al., 2018). Imperfections in both the PROSPECT model and optical measurements as suggested by Féret et al. (2019), uncertainty in the PROSPECT model's representation of the light absorption properties of molecules, such as those associated with LMA (Sun et al., 2018; Li et al., 2016), as well as inherent spectral shadowing effects all likely contribute to the poor retrieval success of some constituents. To alleviate these problems, multiple studies suggest prior selection of optical subdomains for the estimation of specific constituents. Li and Wang (2011) defined a multistep iterative inversion procedure estimating PROSPECT parameters individually based on optimal spectral domains, and obtained improved estimation of Cab, EWT and LMA. However, they only used reflectance data and did not test their approach on publicly available datasets. Moreover, the iterative procedure is computationally intensive. Wang et al. (2015) obtained improved retrieval of cellulose and lignin by inverting PROSPECT from 2100 nm to 2300 nm. However, they focused on specific biochemicals of dry matter, and did not investigate the parameters used in the publicly available version of PROSPECT. More recently, Féret et al. (2019) evidenced that PROSPECT inversion based on the spectral subdomain from 1700 nm to 2400 nm led to dramatic improvement in the retrieval of LMA and EWT. However, they focused on the IR domain and did not investigate the generalization of optimal spectral subdomains in the VIS domain for the estimation of leaf pigments.

Different performances of PROSPECT inversion have also been reported when using both leaf reflectance and transmittance spectra together, leaf reflectance spectra only, or leaf transmittance spectra only. Sun et al. (2018) reported better retrieval accuracy for LMA when using only reflectance or only transmittance than when using reflectance and transmittance combined. Added to improved estimation of leaf constituents, the measurement of only reflectance or only transmittance may save significant time. However, Hill et al. (2019) reported a strong bias in the estimation of carotenoids and EWT from PROSPECT-D inversion when using reflectance only. Contrarily, Asner et al. (2011) found that transmittance spectral information is sufficient to accurately estimate Cab as well as Cxc, using PLSR models. In light of these contradictory results, an assessment of PROSPECT inversion performance when using only reflectance or only transmittance from publicly available datasets, along with traditional comprehensive inversion procedures, is needed to inform future research.

One source of uncertainty and potentially error in the estimation of leaf chemistry when using PROSPECT inversion with reflectance or transmittance only is the N parameter. The N parameter is usually inferred based on information from both reflectance and transmittance in the near infrared domain (NIR, 750 nm to 1400 nm) (Jacquemoud and Baret, 1990; Allen et al., 1970), though can also be estimated throughout the full spectral domain alongside constituents. The N parameter is the only model parameter not based upon a quantifiable leaf physiological trait. The performance of partially-informed PROSPECT inversion, with either reduced subdomains excluding NIR information, or only reflectance or transmittance, in estimating the N parameter has yet to be explored. The N parameter is the main factor influencing leaf optical properties in the spectral domains dominated by scattering effects, such as the NIR domain and part of the short wave infrared (SWIR, 1400 nm to 3000 nm) domain. As a result, uncertainty in N can directly lead to uncertainty in simulated leaf optical properties, and in the constituents estimated from PROSPECT inversion relying on these domains (Qiu et al., 2018).

Qiu et al. (2018) reported a strong correlation of 0.82 between the N parameter and the ratio between reflectance and transmittance measured in the NIR at 800 nm. Taking advantage of this correlation to estimate N requires measuring both leaf reflectance and transmittance, in line with the original method used to compute N from leaf optical properties, used during PROSPECT calibration and described by Jacquemoud et al. (1996). However, absorptance in the NIR domain is usually very low: Merzlyak et al. (2004) even suggested that absorptance in the domain ranging from 750 nm to 800 nm can be neglected. Qiu et al. (2019) reported the N parameter having a dominant influence on reflectance and transmittance from 750 to 800 nm over other PROSPECT parameters, as well as leaf surface reflectance. Thus assuming light in the NIR is primarily either reflected or transmitted as a function of leaf structure, information about reflectance only or transmittance only might be sufficient to accurately estimate the N parameter with moderate uncertainty, following the hypothesis that absorptance is negligible. The estimation of N prior to PROSPECT inversion may therefore lead to improved estimation of leaf constituents when using optimal spectral subdomains with only reflectance or transmittance.

Our primary objective is to identify the optimal method for the estimation of leaf constituents based on PROSPECT inversion, including Cab, Cxc, EWT and LMA. Multiple recent studies proposed different alternatives to this problem, and our study compares these approaches when taken individually or combined. These approaches include i) use of reflectance, transmittance, or the combination of both, ii) definition of optimal spectral subdomains for specific leaf constituents, and iii) prior estimation of the N parameter from reflectance or transmittance only.