Effective GAI is best estimated from reflectance observations as compared to GAI and LAI: Demonstration for wheat and maize crops based on 3D radiative transfer simulations

Highlights

• Wheat and maize canopy reflectance are simulated with realistic 3D model.

• Effective GAI is best estimated from remote sensing observations.

• 3D model provides the best estimation of effective GAI compared to 1D model and Vis.

Abstract

The definition of LAI (Leaf Area Index) is important when deriving it from reflectance observation for model application and validation. Canopy reflectance and the corresponding quantities of LAI, PAI (Plant Area Index), GAI (Green Area Index) and effective GAI (GAI_eff) are first calculated using a 3D radiative transfer model (RTM) applied to 3D wheat and maize architecture models. A range of phenological stages, leaf optical properties, soil reflectance, canopy structure and sun directions is considered. Several retrieval methods are compared, including vegetation indices (VIs) combined with a semi-empirical model, and 1D or 3D RTM combined with a machine learning inversion approach. Results show that GAI_eff is best estimated from remote sensing observations. The RTM inversion using a 3D model provides more accurate GAI_eff estimates compared with VIs and the 1D PROSAIL model with RMSE = 0.33 for wheat and RMSE= 0.43 for maize. GAI_eff offers the advantage to be easily accessible from ground measurements at the decametric resolution. It was therefore concluded that the most efficient retrieval approach would be to use machine learning algorithms trained over paired GAI_eff and the corresponding canopy reflectance derived either from realistic 3D canopy models or from experimental measurements.

Introduction

Leaf area index (LAI) was defined by Chen and Black (1992) as half the total developed area of leaves per unit horizontal ground area. LAI is directly involved in vegetation functioning and is therefore widely used in agriculture, ecology or global change research and application domains. As leaves represent the main boundary between the plant and the atmosphere, LAI is a key variable used to evaluate the exchanges of mass and energy (Liang, 2004). Furthermore, it reflects the actual plant state and its potential growth (Gonsamo, 2009). However, depending on the targeted traits and processes, several definitions of LAI are used:

• For the aboveground biomass estimation based on allometric relationships (Baret et al., 1989), LAI from the Chen and Black’s definition (1992) is relevant. Note that the Green Leaf Area Index (GLAI) is often used in place of LAI, by considering only the green parts of the leaves.

• For the rainfall interception efficiency of the canopy, all the vegetation elements including leaves, stems, branches and the other aerial organs, either green or senescent should be considered (Domingo et al., 1998, Martello et al., 2015). This leads to using the Plant Area Index (PAI).

• For transpiration and photosynthesis, all the green parts that potentially exchange carbon and water mainly through the stomata should be considered (Wang and Dickinson, 2012). The Green Area Index (GAI) should be used in this case.

• When estimating the radiation interception efficiency, the spatial arrangement of green vegetation elements needs to be considered since leaf clumping may reduce the interception efficiency by the mutual masking of elements, leading to the effective GAI (GAI_eff) definition. GAI_eff may be defined as the GAI value of a turbid medium canopy that would provide the closest green fraction to that of the canopy considered.

These different quantities are closely related, while their relationship will depend on the species, canopy state, and stage. It is therefore mandatory to use the appropriate quantity to ensure a high degree of consistency the targeted application.

Under field conditions, LAI (and GLAI) can be only accessed using direct methods where the (green for GLAI) area of individual leaves is measured for all the leaves present over a given ground area. Similarly, PAI can be measured directly by including the area of all the other elements while only the green parts will be considered for GAI. However, these direct methods are tedious, low-throughput, and generally destructive or at least invasive. This explains why indirect methods are widely used (Gower et al., 1999). Indirect methods are based on instruments measuring canopy gap fraction (the fraction of background sun seen in a given direction) or green fraction (the fraction of green area covered in a given direction) using the same theory that relates the area of canopy elements to the gap (or green) fraction (Jonckheere et al., 2004). The simplest techniques are based on canopy transmittance measurements placed at the bottom of the canopy and used as a proxy of the gap fraction. Hemispherical light sensor (Leblanc et al., 2005), mono-directional sensor (Brede et al., 2018), or multidirectional sensors such as LAI2000 instrument (Campbell and Norman, 1988) or upward looking digital hemispherical photography (Demarez et al., 2008) are widely used. Those techniques where the sensor is put at the bottom of the canopy, are sensitive to the presence of both green and non-green elements without the possibility to separate them. They provide thus a proxy of PAI (Norman and Campbell, 1989). Conversely, techniques based on cameras looking downward from above the canopy allows identifying the green pixels from which GAI is derived. Mono-directional (Baret et al., 2010) or multi-directional (Weiss et al., 2004) views can be used. More recently terrestrial laser scanners (Liu et al., 2017, Soma et al., 2018, Yan et al., 2019) or stereovision (Biskup et al., 2007) have been also used to build a 3D point cloud from which the directional canopy transmittance is computed. This leads to estimates of PAI if no distinction is made between the green and non-green elements, or to GAI when the green points are identified.

The transformation of the measured directional gap or green fraction into PAI or GAI is generally based on some assumptions on canopy structure, particularly regarding leaf arrangement. One of the main assumptions considers that leaves are randomly distributed within the canopy volume. A distinction is thus made between the true PAI or GAI and the corresponding “effective” values that are derived from gap or green fraction measurements assuming that leaves are randomly distributed (Fang et al., 2018, Nilson, 1999).

PAI and GAI can also be retrieved from reflectance observations using empirically or physically based methods. Empirical methods consist in calibrating relationships between a combination of reflectance in several wavebands and ground measured LAI. The most common method is the use of spectral vegetation indices (VIs) (Broge and Leblanc, 2001, Broge and Mortensen, 2002, Liu et al., 2012, Richardson et al., 1992). While in the past, empirical methods were calibrated, and thus, applicable over very restricted experiments and environmental conditions, recent developments have shown that robust and accurate estimates can be assessed with machine learning techniques providing that the data used to train the algorithms represents well the domain of application (Camacho-Collados et al., 2017). Conversely, physically based methods consist in inverting a Radiative Transfer Model (RTM) that simulates the physical processes involved in the photon transport within the canopy (Strahler, 1997). Inversion techniques such as optimization (Jacquemoud et al., 2000), Look-Up-Tables (LUT) (Duan et al., 2014, González-Sanpedro et al., 2008) or machine learning (Verrelst et al., 2012, Weiss et al., 2002) are used to estimate the RTM input variables including PAI or GAI from the measured reflectances. The accuracy of such methods depends on the ability of the model to simulate realistically the reflectance of the targeted canopy given a description of the architecture of the canopy and the optical properties of its elements. The 1D RTMs such as PROSAIL (Jacquemoud et al., 2009) assume that the canopy is a horizontally homogeneous layer of randomly distributed leaves. Inverting 1D RTMs has the advantage of being computationally efficient and characterized by a low number of inputs, which eases the setting of numerical experiments and constrains the possible ambiguities between variables during the inversion process (Baret and Buis, 2008). However, several 3D radiative transfer models were developed to get more realistic simulations of canopy reflectance: they combine an explicit 3D description of the canopy architecture while accounting for the differences in optical properties of the several vegetation elements. 3D RTMs such as FLIGHT (North, 1996) based on Monte Carlo ray tracing methods or DART (Gastellu-Etchegorry et al., 2004) based on the discrete ordinate methods have already been used to retrieve canopy structure and biochemical variables from remote sensing data (Banskota et al., 2015, Gascon et al., 2004, Hernández-Clemente et al., 2017, Malenovský et al., 2013). Such 3D models are inverted using LUT or machine learning techniques. However, compared to 1D RTMs, the large computation effort required to populate the LUT or the training dataset, combined with the high number of variables and parameters required for the 3D description of the canopy architecture mainly explain why the space of canopy realization is generally poorly sampled, resulting into possibly less robust PAI or GAI estimates.

The objective of this study is to evaluate the retrieval performances from top of canopy reflectance observations of the different xAI (PAI, LAI, GLAI, GAI and GAI_eff) state variables of interest. To circumvent the influence of instrument difference and associated measurement errors, the retrieval performances were evaluated with RTM simulations over realistic 3D wheat and maize scenes. To mimic satellite observations using RTM simulations, SENTINEL-2 satellite data which is widely applied in recent crop monitoring applications (Segarra et al., 2020) was selected as an example. We consider a range of phenological stages for wheat and maize crops. We compared the performances of several retrieval methods including VIs combined with a semi-empirical model, and a machine learning based RTM inversion approach using the raw reflectance as inputs and trained with 1D or 3D RTM simulations.