# Modeling 3D radiative transfer for maize traits retrieval: A growth stage-dependent study on hyperspectral sensitivity to field geometry, soil moisture, and leaf biochemistry

Romain Démoulin, Jean-Philippe Gastellu-Etchegorry, Sidonie Lefebvre, Xavier Briottet, Zhijun Zhen, Karine Adeline, Matthieu Marionneau, Valérie Le Kantec

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Romain Démoulin, Jean-Philippe Gastellu-Etchegorry, Sidonie Lefebvre, Xavier Briottet, Zhijun Zhen, et al.. Modeling 3D radiative transfer for maize traits retrieval: A growth stage-dependent study on hyperspectral sensitivity to field geometry, soil moisture, and leaf biochemistry. Remote Sensing of Environment, 2025, 327, pp.114784. 10.1016/j.rse.2025.114784. hal-05192470

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# Modeling 3D radiative transfer for maize traits retrieval: A growth stage-dependent study on hyperspectral sensitivity to field geometry, soil moisture, and leaf biochemistry

Romain Démoulin<sup>a,b,c ID*</sup>, Jean-Philippe Gastellu-Etchegorry<sup>b ID</sup>, Sidonie Lefebvre<sup>d ID</sup>, Xavier Briottet<sup>c ID</sup>, Zhijun Zhen<sup>b ID</sup>, Karine Adeline<sup>c ID</sup>, Matthieu Marionneau<sup>a</sup>, Valérie Le Dantec<sup>b ID</sup>

## ARTICLE INFO

Edited by Jing M. Chen

**Keywords:**

Maize traits retrieval

Hyperspectral

Radiative transfer model

Plant growth model

Global sensitivity analysis

DART

PROSAIL

## ABSTRACT

This study integrates a dynamic plant growth model with a three-dimensional (3D) radiative transfer model (RTM) for maize traits retrieval using high spatial-spectral resolution airborne data. The research combines the Discrete Anisotropic Radiative Transfer (DART) model with the Dynamic L-System-based Architectural maize (DLAmaize) growth model to simulate field reflectance. Comparison with the 1D RTM SAIL revealed limitations in representing row structure effects, field slope, and complex light-canopy interactions. Novel Global Sensitivity Analyses (GSA) were carried out using dependence-based methods to overcome limitations of traditional variance-based approaches, enabling better characterization of hyperspectral sensitivity to changes in leaf biochemistry, canopy architecture, and soil moisture. GSA provided complementary results to assess estimation uncertainties of the proposed traits retrieval method across growth stages. A hybrid inversion framework combining DART simulations with an active learning strategy using Kernel Ridge Regression was implemented for traits estimation. The approach was validated using ground data and HyPlant-DUAL airborne hyperspectral images from two field campaigns in 2018 and achieved high retrieval accuracy of key maize traits: leaf area index (LAI, R²=0.91, RMSE=0.42 m²/m²), leaf chlorophyll content (LCC, R²=0.61, RMSE=3.89 µg/cm²), leaf nitrogen content (LNC, R²=0.86, RMSE=1.13 × 10⁻² mg/cm²), leaf dry matter content (LMA, R²=0.84, RMSE=0.15 mg/cm²), and leaf water content (LWC, R²=0.78, RMSE=0.88 mg/cm²). The validated models were used to generate two-date 10 m resolution maps, showing good spatial consistency and traits dynamics. The findings demonstrate that integrating 3D RTMs with dynamic growth models is suited for maize trait mapping from hyperspectral data in varying growing conditions.

## 1. Introduction

Maize (Zea mays) is one of the world's most important food crops, serving as a staple in many developing countries (Shiferaw et al., 2011). Beyond human consumption, maize is a key ingredient in animal feed and is extensively used in industrial products, including biofuel production. In the past decades, global maize production has shown consistent growth, reaching 1.2 billion tonnes in 2021 (FAOSTAT, 2023). However, increasing demand and production shortfalls have exacerbated market volatility, contributing to surging global maize prices (Shiferaw

et al., 2011). Growing uncertainties, such as climatic events and the consequent rise in vulnerability to pests and diseases, further make up these challenges. In 2022, maize production decreased by four percent compared to 2021, primarily due to widespread drought affecting several European countries (FAOSTAT, 2023). The cereal industry constantly faces with uncertainties regarding harvest dates, grain quantity and quality. Consequently, it has become essential to monitor crops more accurately, both spatially, temporally and qualitatively. The tracking of biophysical and biochemical metrics of crop physiological

<footnote><sup>a</sup> Hyperplan, 8 Rue de la Madeleine, Bidart, 64210, France</footnote>

<footnote><sup>b</sup> CESBIO, Université de Toulouse, CNES/CNRS/INRAE/IRD/UT3, 18, Avenue Edouard Belin, Toulouse, 31401, France</footnote>

<footnote><sup>c</sup> DOTA, ONERA, Université de Toulouse, Toulouse, 31000, France</footnote>

<footnote><sup>d</sup> DOTA, ONERA and LMA2S, Université Paris Saclay, Palaiseau, 91120, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: romain@hyperplan.fr (R. Démoulin), jean-philippe.gastellu@iut-tlse3.fr (J.-P. Gastellu-Etchegorry), sidonie.lefebvre@onera.fr (S. Lefebvre), xavier.briottet@onera.fr (X. Briottet), zhijun.zhen@outlook.com (Z. Zhen), karine.adeline@onera.fr (K. Adeline), matthieu@hyperplan.fr (M. Marionneau), valerie.le-dantec@univ-tlse3.fr (V. Le Dantec).</footnote>
status has a variety of applications that allows to improve yield antici-
pation capacity, support informed decision-making and ensure global
food security (Weiss et al., 2020). To facilitate the understanding of the
work presented, readers may refer to the table of acronyms in Appendix
Table A.1.

Satellite Remote Sensing (RS) offers great potential for near real-
time monitoring of crops at global scale. Existing multispectral in-
struments such as the Sentinel-2 MSI with high spatial resolution
(10–20 m) and revisit rate (≈5 days) are already used in the agrifood
chain by companies providing crop monitoring to farms and agro-
industries. Thank to its high revisit rate Sentinel-2 allows to monitor
the temporal dynamics of several crop primary variables linked to plant
nutrition and development such as the Leaf Area Index (LAI) (Estévez
et al., 2020) or the Leaf Chlorophyll Content (LCC) (Guo et al., 2023).
However, due to the limited spectral information of Sentinel-2, several
variables (e.g. Leaf dry Matter Content (LMA) and Leaf Water Content
(LWC)) estimations remain challenging. Likewise, proteins, which are
the primary by-products of Leaf Nitrogen Content (LNC), exhibit weak
absorption characteristics in the short-wave infrared (SWIR) region. If
a link is known between LNC and LCC (Berger et al., 2020), the com-
plex interactions existing with crop-endogenous and crop-exogenous
parameters throughout crop development make it difficult to gener-
alize an estimation method on a global scale. However, thanks to
the increased data stream of new spectroscopic instruments, including
continuous narrow bands over the [0.4–2.5] µm range, a better crop
traits retrieval accuracy and absorption patterns discrimination can be
achieved (Hank et al., 2019; Verrelst et al., 2019; Thenkabail et al.,
2018, 2014). Hyperspectral missions with a 30 m spatial resolution
such as PRISMA (Lopinto et al., 2021), EnMAP (Storch et al., 2023)
and Gaofen-5 (Zhong et al., 2021) with a revisit rate from 4 to 29
days are already operational while upcoming global coverage missions
SBG (Thompson et al., 2020) and CHIME (Celesti et al., 2022) are
under preparation. The 30 m resolution of these sensors can however be
limiting for fine-scale surface parameters retrieval. Future 10 m spatial
resolution hyperspectral missions like BIODIVERSITY (Briottet et al.,
2024) and SHALOM (Feingersh and Dor, 2015) will help to estimate
a large panel of primary crop variables with higher spatial resolution.
In this work, hyperspectral airbone RS data has been used rather than
satellite RS data. This reflects the difficulty to access to high quality
satellite data on monitored areas, and allows to work with a higher
spatial resolution to limit crop field boundary effects to validate the
methods described in this publication.

To estimate traits from RS data, a common approach is to per-
form inversion techniques. While a variety of methods exists, hybrid
inversion (HYB) is increasingly being used with spectroscopic data. The
HYB method combines first the use of radiative transfer models (RTMs)
to reproduce the underlying physical processes involved in the mea-
surement, and thereafter the flexibility and computational efficiency
of nonparametric nonlinear machine learning (ML) regression methods
used to retrieve the crop bio-physical properties with a supervised
model training (Verrelst et al., 2019).

Starting to be developed in the 1970s, RTMs play a crucial role in
the analysis and interpretation of RS data for crop monitoring (Hank
et al., 2019). RTMs provide a physically-based framework to simu-
late the complex interactions between electromagnetic radiation and
vegetation in the spectral range of interest for remote sensing obser-
vations, including the [0.4–2.5] µm range. RTMs are used in the HYB
approach for the linkage of spectral reflectance to crop biophysical and
biochemical properties, reducing costly and time-consuming in situ data
collection. One of the earliest canopy RTMs was the SUITS model (Suits,
1971), representing the canopy as a horizontally homogeneous turbid
medium. This was followed by the widely used Scattering by Arbitrarily
Inclined Leaves (SAIL) model (Verhoef, 1984), which improved upon
SUITS by considering Leaf Angle Distribution (LAD). The PROSPECT
leaf optical properties model (Jacquemoud and Baret, 1990), a gen-
eralization of Allen et al. (1969) plate model, is often combined with

SAIL to form the PROSAIL model (Jacquemoud et al., 2009). Thanks
to its ease of use and computational efficiency, PROSAIL has been
extensively used and validated for vegetation characterization (Berger
et al., 2018). 1D models are however limited as they abstract the
canopy as homogeneous layers while vegetation is often heterogeneous
and on sloping terrain. To better represent canopy structure, 3D RTMs
were developed starting in the 1990s with models like the Forest
LIGHT (FLIGHT) model (North, 1996) simulating the reflectance of
3D canopies and the Discrete Anisotropic Radiative Transfer (DART)
model (Gastellu-Etchegorry, 1996), able to simulate RS observations
of complex 3D scenes with topography and atmosphere. DART has
proven its accuracy in various contexts like urban (Gastellu-Etchegorry
et al., 2017) or natural (Widlowski et al., 2015) landscapes for a wide
range of instrumental configurations (e.g., spectral band, observing
direction, field of view, etc.). Comparatively, only few studies tested
3D RTMs to simulate the RS signal of crop field, considered as closer
to the homogeneous medium assumptions. The recent work of Zhen
et al. (2024) comparing 1D and 3D approaches, showed the importance
of maize canopy structure in the simulation of Top-Of-Canopy (TOC)
reflectance. 3D RTMs are more realistic, but require more calculations,
usually more detailed structural information and must be handled with
greater care (e.g., 1D models of row crops have no rows, unlike the
3D models of these crops). The continuous improvements in RTMs effi-
ciency and the increase in computing power have made it more feasible
to use 3D RTMs for large-scale RS applications. For an operational
use of 3D RTMs, Verrelst et al. (2023) highlighted the necessity to
develop automated or semi-automated methods to generate complex
3D scenes. The integration of dynamic plant growth model into 3D
RTMs is increasingly being used for diverse crop applications such as
maize (Jiang et al., 2022), wheat Dong et al. (2024) and rice (Liu et al.,
2024) traits retrieval.

The need for a more accurate representation of canopy architecture
in heterogeneous vegetation canopies has been emphasized by Danner
et al. (2019) and Morcillo-Pallares et al. (2019), who carried out
Global Sensitivity Analysis (GSA) on the PROSAIL and INvertible FOrest
Reflectance Model (INFORM) (Atzberger, 2000) RTMs. GSA is increas-
ingly used in RS to study the influence of one or more input variables on
the output of an RTM. Studies performing GSA (Verrelst et al., 2016b;
Morcillo-Pallares et al., 2019; Gao et al., 2022) often apply variance
decomposition techniques such as Sobol indices (Sobol', 1990). As
the use of a 3D RTM coupled to a crop growth model has not been
extensively used so far, we found essential to perform a GSA to study
the crop trait estimation performances and their systematic uncertainty
sources. This study and its conclusions, complementary to the main
goal of this work, increase the confidence into the proposed method. If
the modeling of maize fields at various growth stages using 3D RTMs
can offer valuable insights into the interactions between hyperspectral
signal and field geometry (e.g., sun-target-sensor configuration), leaf
biochemistry, and soil moisture, commonly used variance-based GSA
methods can however be restrictive for complex 3D RTMs, as they
rely on assumptions of parameter independence that are not always
true. Such assumptions can lead to biased sensitivity estimates when
parameters exhibit correlation or non-linear interactions. Thus, the use
of a novel GSA approaches adapted to the complexity of 3D RTMs is
necessary to improve the accuracy and reliability of sensitivity analyses
in these models.

1.1. Objective

To our knowledge, no study combined 3D RTMs with a dynamic
maize plant growth model to retrieve simultaneously leaf (LCC, LNC,
LMA, LWC) and canopy (LAI) traits with high spatial-spectral resolu-
tion RS. As the availability of satellite hyperspectral data continues to
grow, this study aims to evaluate the advantages of modeling maize
field geometry for trait retrieval across various growth stages and field
topographies. Our approach integrates a maize plant dynamic growth
model into the general purpose 3D RTM DART. The study divides itself
into three key steps:
<table><caption>**Table 1**
List of the biophysical and biochemical traits used in this study with their units, number of samples, average value, standard deviation (Std.) and the method used to derive them.</caption><thead><tr><th>Variable</th><th>Scale</th><th>Unit</th><th>Samples</th><th>Mean</th><th>Std.</th><th>Method</th></tr></thead><tbody><tr><td>LAI</td><td>Canopy</td><td>m<sup>2</sup>/m<sup>2</sup></td><td>87</td><td>1.77</td><td>1.41</td><td>Indirect</td></tr><tr><td>LCC</td><td>Leaf</td><td>µg/cm<sup>2</sup></td><td>87</td><td>43.3</td><td>6.3</td><td>Indirect</td></tr><tr><td>LMA</td><td>Leaf</td><td>mg/cm<sup>2</sup></td><td>31</td><td>4.71</td><td>0.38</td><td>Destructive</td></tr><tr><td>LNC</td><td>Leaf</td><td>mg/cm<sup>2</sup></td><td>31</td><td>0.15</td><td>0.03</td><td>Destructive</td></tr><tr><td>LWC</td><td>Leaf</td><td>mg/cm<sup>2</sup></td><td>31</td><td>12.9</td><td>1.9</td><td>Destructive</td></tr></tbody></table>

(a) To evaluate the limitations of a 1D modeling approach and justify the use of a 3D RTM to simulate maize field reflectance. Simulations using the traditional 1D model SAIL are compared to DART at various maize growth stages and field geometry.

(b) To study the sensitivity of hyperspectral signal to changes in leaf biochemistry, canopy architecture and soil moisture using DART.

(c) To evaluate the retrieval performances of maize field traits from TOC reflectance with high spatial-spectral resolution RS. Our approach combines HYB model with DART simulations for LAI, LCC, LNC, LMA and LWC retrieval using an active learning strategy.

## 2. Material

### 2.1. Study area

In the context of ESA FLuorescence EXplorer (FLEX) (Moreno, 2022) and CHIME preparations, a series of campaigns were carried out from June to July 2018 in a rural area of Tuscany at the north of Grosseto city (42°49'47.02"N 11°04'10.27"E; elev. 2 m a.s.l.), Italy. The study area consists of a diverse flat cultivated area (e.g. wheat, sunflower, tomato). The study focuses on two irrigated maize fields, from Ceccarelli and Le Rogaie farms with different irrigation systems, micro-drop and pivot system respectively. Ceccarelli field, sown in early May, is referred as CEC while Le Rogaie field, subdivided in several parcels was sown from mid to end of June and is referred as PIV in this document. PIV farm is constituted of fields with parallel, clearly visible maize rows oriented with a 201° azimuth and a 0.75 m spacing. The soil structure is ranging from high sand to high clay content. CEC field parallel rows are planted with a 181° azimuth orientation and keep the same 0.75 m spacing as PIV.

### 2.2. Field campaigns

The data collection used in this study was obtained and previously described in detail by Candiani et al. (2022). It consists in a series of biophysical and biochemical traits measurements at different growth stages of CEC and PIV maize fields (see Table 1). In addition, structural traits to characterize field architecture and topsoil reflectance samples were collected in various locations of the site. The field spatial sampling protocol was performed in agreement with international guidelines proposed by Fernandes et al. (2014) and Morisette et al. (2006) on 33 Elementary Sampling Unit (ESU), each covering an area of 20 m × 20 m. ESUs are subdivided into 10 m × 10 m plots with a total of 87 plots where field measurements were performed. The first campaign was carried out in a 5 days timeframe, from July 6 to July 10 on CEC and PIV fields. The second campaign was carried out from July 31 to August 1 on PIV field only.

#### 2.2.1. Biochemical traits

Destructive measurements of nitrogen fraction ($N_{frac}$), LCC, LMA and LWC were measured on a subset of 31 plots by sampling three fully developed leaves within the plot and collecting three 2.2 cm diameter disks per leaf for laboratory analysis. SPAD-502 leafclip chlorophyll meter (Konica Minolta, Japan) non-destructive measurements were

made on a set of fully developed leaves for each of the 87 plots and are used to derive LCC-SPAD relationship (Eq. (1)):

$$LCC = 8.24e^{0.0324 \times SPAD} \left[ \mu g/cm^2 \right] \quad (1)$$

This calibrated relationship revealed a good agreement between our laboratory LCC and SPAD measurements ($R^2 = 0.93$). LNC is derived from $N_{frac}$ and LMA according to Eq. (2):

$$LNC = N_{frac} \times LMA \left[ \mu g/cm^2 \right] \quad (2)$$

An inventory of the collected biochemical traits is presented on Fig. A.1. SPAD-derived LCC was measured in both campaigns while destructive measurements of LNC, LMA and LWC were collected during the first campaign only.

#### 2.2.2. Biophysical and structural traits

At canopy scale, LAI measurements where made with indirect methods on each of the 87 plots. In the case of CEC field, characterized by high canopy fractional cover (CFC), LAI measurements were made with LiCOR LAI-2200 plant analyzer (LI-COR Inc., Lincoln, NE, USA) instrument. In the case of PIV field with low CFC on both campaigns, LAI was measured with digital hemispherical photography (DHP) using a CoolPix 990 4 Megapixel digital camera (Nikon, Tokyo, Japan), equipped with a FE-E8 8 mm fish-eye lens (Nikon, Tokyo, Japan) and mounted on a tripod. LAI-2200 measurements were made following (Morisette et al., 2006) protocol along 10 m transects alternating between below (B) and above (A) canopy measurements following ABBBBA sequence. LAI-2200 canopy transmittance measurements were postprocessed using FV2200 software to derive the LAI. The processing was performed using the 5 concentric rings of the instrument with zenith directions 7°, 23°, 38°, 53° and 68°. The LAI-2200 covers the optical domain below 490 nm, assuming that vegetation elements are black (i.e., the measure does not include light reflected or transmitted by the plants). Under this assumption, transmittance only considers the direct component of sun incoming radiation and can be considered as canopy gap fraction. In the case of DHP, downward pictures were taken on the four corners and at the center of each plot, then postprocessed using Can-Eye v6.4.91 software to generate LAI-2000 5 rings output in order to be consistent with LAI-2200 measurements.

If the canopy is assumed to be a horizontally large, homogeneous volume, where foliage elements are randomly distributed in space, effective LAI ($LAI_{eff}$) can be estimated with indirect optical methods from the directional gap fraction $P(\theta)$ at zenith angle $\theta$ by applying the simplified version of Miller (1967) formula to estimate $LAI_{eff}$ (Eq. (3)):

$$LAI_{eff} = 2 \int_{0}^{\pi/2} -\ln P(\theta) \cos \theta \sin \theta d\theta \quad (3)$$

$LAI_{eff}$ is therefore referred as the LAI value that can be derived from indirect ground measurement assuming a simple random foliage distribution (Chen et al., 2005). However, in real crop canopies, leaves are not randomly distributed in space due to clumping, both at plant scale (fixed row planting) and leaf scale (spatial arrangement on a single plant). The canopy clumping factor ($\Omega$) corresponds to the factor which describes the non-randomness of the leaf foliage distribution linking LAI to $LAI_{eff}$ (Chen et al., 2005) (Eq. (4)):

$$LAI_{eff} = \Omega \times LAI \quad (4)$$

The clumping factor can be estimated with indirect measurements of the non-random distribution of gap fraction using the method proposed by Lang and Xiang (1986) (Eq. (5)):

$$\Omega(\theta) = \frac{\overline{\ln P(\theta)}}{\overline{\ln P(\theta)}} \quad (5)$$

Both LAI indirect measurement methods previously described (LAI-2200 and DHP) rely on this theory to derive LAI from $LAI_{eff}$ and $\Omega$.
Field measurement campaigns cover a diversity of growth stages of PIV and CEC fields. The collected LAI values range from 0.11 to 5.7 m²/m², with heights ranging from 0.23 to 3.23 m and an average density of 7.49 plant/m². The study covers the 3 main growth stages corresponding to PIV field on July 7 with an average LAI of 0.4 m²/m², PIV field on July 30 with an average LAI of 1.13 m²/m² and CEC field on July 7 with an average LAI of 2.97 m²/m². These 3 average growth stages have very different structures and are used to guide the RTM simulation scenarios. An overview of the maize field biophysical and structural traits collected on the study site are shown in Fig. A.2 in Appendix.

## 2.3. Airborne images

Two airborne hyperspectral images were acquired using the HyPlant-DUAL sensor (Siegmann et al., 2019) on July 7 and July 30 under cloud-free sky conditions. HyPlant-DUAL, developed by Forschungszentrum Jülich in collaboration with SPECIM Spectral Imaging Ltd., is a push-broom imaging spectrometer consisting of two modules integrated into a single housing with shared fore optics. The sensor collected data across 626 contiguous spectral bands in the [0.38–2.51] µm range. Spectral resolution varies across the spectrum, with [3–10] nm in the visible and near-infrared (VIS/NIR) domain, and 10 nm in the SWIR domain. Original ground sampling distances (GSD) differ between the two acquisitions with a 1 m GSD for the July 7 flight at 600 m altitude above sea level (ASL) and a 4.5 m GSD for the July 30 flight at 3050 m altitude ASL. The images are both geometrically and atmospherically corrected to derive TOC reflectance from the July 7 acquisition consisting in 6 flightlines and the July 30 acquisition in 4 flightlines. As field campaign measurements did not fit a regular 10 m × 10 m sampling grid, RS signal is extracted and resampled locally on each plot to ensure good agreement between TOC reflectance and in situ vegetation measurements. The signal is extracted and resampled in a 10 m diameter circle centered on each vegetation plot, using a median filter to mitigate sensor noise. Prior to the resampling, field contours are masked using a shapefile to prevent unwanted border effects. The combination of vegetation measurements and corresponding RS signals are used as validation data for the inversion method. Finally, to perform crop traits mapping on the entire fields, both images are spatially resampled on a regular 10 m × 10 m sampling grid in order to preserve the spatial consistency with the resolution of the validation data. A median filter is also used for the image resampling.

## 2.4. Radiative transfer models

At the leaf scale, PROSPECT (Jacquemoud and Baret, 1990) is used to simulate leaf transmittance and reflectance on the [0.4–2.5] µm spectral range. Several versions have been developed (Feret et al., 2008; Féret et al., 2017) to improve precision and consider a wide range of biochemical traits, between others: chlorophyll-a + chlorophyll-b content ($C_{ab}$), carotenes and xanthophylls content grouped under the carotenoids family ($C_{ar}$), dry matter content ($C_{m}$), water content ($C_{w}$) and leaf structure parameter ($N_{struc}$). For this study, we choose the latest version PROSPECT-PRO (Féret et al., 2021) separating $C_{m}$ into carbon-based constituents ($C_{bc}$) and nitrogen-based constituents referred as proteins ($C_{p}$). For this study, $C_{p}$ the main by-product of LNC is converted from PROSPECT-PRO based on the revised factor of 4.43, suggested by Yeoh and Wee (1994).

At the canopy scale, 4SAIL (Verhoef et al., 2007), an improved version of the original SAIL (Verhoef, 1984) model is chosen as the reference 1D RTM. 4SAIL uses the four-stream radiative transfer theory to model the interaction of light with a homogeneous vegetation canopy and simulate the TOC bidirectional reflectance on the [0.4–2.5] µm spectral range.

DART-Lux (Wang et al., 2022b), a light mode of the DART model (Gastellu-Etchegorry, 1996) developed in CESBIO since 1992 (https:

// dart.omp.eu) is selected as the reference general-purpose 3D RTM. DART-Lux uses Monte Carlo bidirectional ray tracing techniques of the open-source renderer LuxCoreRender (https://luxcorerender.org). Compared to the original DART light mode (Gastellu-Etchegorry et al., 2015), DART-Lux greatly improves computational efficiency, which is a common limitation of 3D RTMs in comparison with their 1D counterparts. This study uses DART version 5-10-2 v1356 released on 2023-11-08.

## 2.5. Plant growth model

DART uses 3D objects as input to create scenes such as maize fields. For accurate RS simulations, it is necessary to have a detailed and precise description of the maize canopy structure. Creating a digital twin of the field (e.g. with LiDAR technologies) is complex and does not scale to large spatial studies. Replicating a single object throughout the entire scene is also too approximate to model the dynamic growth of a maize field. A plant growth model is therefore chosen for its ability to capture the variability of plant architecture at different growth stages and to introduce randomness into the arrangement of leaves. The Dynamic L-System-Based Architectural Maize (DLAmaize) growth model (Zhen et al., 2024) integrates a dynamic maize structure governed by cumulative degree days ($T_d$°) (López-Lozano et al., 2007) and a leaf break model (España et al., 1999) into the Extended L-system (ELSYS) (Goel and Rozehnal, 1992) to simulate maize growth from emergence to male anthesis. In order to accurately parameterize the growth model, prior knowledge of certain architectural features, such as the maximal height ($height_{max}$) and maximal leaf surface area ($area_{max}$), are required. These parameters derived from field measurements are used as input to the growth equations that drive the model's simulations. Additional architectural traits not measured in the field are defined both from literature (Fournier, 1998; López-Lozano et al., 2007) and visual verification.

## 2.6. Maize field 3D scenes

### 2.6.1. Scenes definition

The first step to create a maize field scene is the definition of a 9.86 m × 9.75 m field, the closest to the spatial resolution of the resampled HyPlant images while preventing border effects with scene repetitions. The scene consists in 13 parallel maize rows spaced by 0.75 m each with a 0.17 m distance between each plant along the row, similar as the study site. In total, 754 individual plants compose the field. The plants are selected from 6 individual 3D objects for which the entire growth was simulated using DLAmaize from emergence to maximum height ($height_{max}$ = 3.2 m, $area_{max}$ = 1.01 m²). Each class of maize plant is generated using a different random generation seed. The maximum number of leaves drives the number of development stages and is set to 18 leaves with 50 $T_d$° between each leaf. Considering that middle leaves have a bigger area than first and last leaves, the choice is made to mix different growth stages to have narrower LAI variations at field scale and mitigate repetition patterns. When plant total leaf area is considered too big between leaf(n) and leaf(n-1), half of 754 plants are set to stage leaf(n) and the other half to leaf(n-1). A total of 29 maize field scenes is then created with LAI from 0 to 7 m²/m² and a maximum 0.39 m²/m² difference between two growth stages. Most of vascular plants tend to orient their growth to optimize sun radiation interception leading to both a vertical and horizontal leaf distribution heterogeneity. Similarly to previous work using DART for wheat traits retrieval (Makhloufi and Kallel, 2023), randomness in plants arrangement is used to avoid repetition patterns and optimize canopy space filling. The 6 classes of maize plants are generated with a 5° leaf inclination standard deviation, a 0.03 m standard deviation for leaf base position and a 30° leaf azimuth angle standard deviation. Additional randomness is added into the scene using a 0 to 15° random rotation along the vertical axis and a 50% chance for a 180° flip for each individual plant.
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Color composition (blue, green, red) of the RS data acquired by HyPlant-DUAL on July 7 (left) and July 30 (right) 2018 of PIV and CEC maize fields. Vegetation traits measurements plots are represented as white dots. Topsoil reflectance samples using and ASD FieldSpec 4 spectrometer are represented as cyan triangles. Wet and dry topsoil reflectance samples using the HyPlant-DUAL RS data are represented as red triangles. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

## 2.6.2. Scenes validation

Contrary to DART 3D scene LAI (LAI<sub>3D</sub>) that is physically retrieved by summing all leaves 3D facet areas divided by underneath ground surface area, in situ LAI measurements consists in the previously described indirect methods deriving directional gap fraction. In order to verify the capacity of the described method to accurately retrieve the LAI<sub>3D</sub> of an heterogeneous maize field scene, LAI measurements with the LAI-2200 instrument for each of the 29 growth stages are simulated using DART. For this task, an alternative method is used to calculate the canopy gap fraction with greater accuracy.

Gap fraction is calculated as the transmission of ground thermal emission through the canopy where plant elements have null reflectance, transmittance and thermodynamic temperature. This calculation is done using a wavelength of 12 µm, a ground temperature of 300° K, an atmosphere with a null brightness temperature, and a scene surrounded by similar scenes to avoid edge effects. Actually, any wavelength and ground temperature could be used. The directional gap fraction is the ratio of the radiance exiting the TOC in each upward direction by the ground thermal radiance. The total number of rays is set to 6 480 000. This approach takes advantage of the ray tracing engine of DART-Lux to precisely retrieve the canopy bi-directional transmittance on the entire scene which is equal to the gap fraction when vegetation elements do not reflect or transmit light. The gap fraction is then averaged on the 5 concentric rings (7°, 23°, 38°, 53° and 68°) of the LAI-2200 instrument. Constructor formulas presented at the end of the user manual of this instrument (https://www.licor.com/env/products/leaf-area/LAI-2200C/science) are derived from Eqs. (3)–(5) and are used to compute LAI.

As this indirect method derives the gap fraction of the entire canopy including all plant organs like stems, it is often referred as Plant Area Index (PAI) instead of LAI. The definitions related to LAI however differ between studies. For further detail the reader can refer to the comprehensive work of Fang et al. (2019). Our comparison between simulated

PAI measurements and LAI<sub>3D</sub> as well as other LAI products (see Fig. A.4 in Appendix) showed that under the assumptions that the 3D scenes are representative of the maize fields found on the study site, PAI measured with the LAI-2200 can be considered as equivalent to LAI. Overall LAI-2200 simulation show a minor 4% overestimation compared to LAI<sub>3D</sub>. This observation corroborates the findings of Ryu et al. (2010) showing a tendency of the Ω clumping factor to be overestimated by this type of instrument with a field-of-view not allowing to account for clumping at shoot level. Our 4% difference is however considered acceptable for the LAI-2200 to be used for the validation of LAI<sub>3D</sub> without using correction factors. Another explanation for this low difference between PAI measured with the LAI-2200 and LAI<sub>3D</sub> is the distinctive structure of this type of vegetation with stems usually masked by leaves. While stems have a very low contribution to canopy transmittance, their surface have a much stronger contribution to plant area products. Therefore only leaf area are considered for LAI calculation in the rest of the study. To our knowledge, it is the first time this type of comparison is performed for maize crop from RTM simulations. This highlights the suitability of DART to simulate both airborne/satellite and in the field instrumental observations.

## 3. Method

A general overview of the method presenting the inputs used and the three key steps of this study is shown in Fig. 2.

### 3.1. Selecting a RTM: DART vs. SAIL for different growth stages and field geometry

This section details the method (Fig. A.6) used to compare maize fields reflectances simulated with SAIL and DART. As SAIL and DART use different radiative transfer methods, canopy representations, and as
<figure><img src="image_4.png" /><figcaption>Fig. 2. Flowchart presenting the general method with an overview of the input data used for the different steps of the study.</figcaption></figure>

SAIL does not explicitly simulate the atmosphere, a prior step to match the inputs of these RTMs is necessary. To simulate the TOC reflectance with these models, the 3 average growth stages of the study area (Fig. A.2) are taken as reference. The 3D scenes with the closest LAI values are selected: LAI = 0.47 m²/m² (Fig. 3(a)) for PIV on July 7, LAI = 1.21 m²/m² (Fig. 3(b)) for PIV on July 30 and LAI = 3.11 m²/m² (Fig. 3(c)) for CEC on July 7.

### 3.1.1. SAIL parameterization based on DART inputs

SAIL inputs are defined using DART as a reference. For each maize 3D scene, the corresponding LAI input is applied to SAIL. Accurate modeling of the LAD is also essential. DART explicitly represents leaf orientation, whereas SAIL represents it statistically by a bimodal function LAD<sub>bimodal</sub> (Goel and Strebel, 1984). This function uses two parameters:

* a: controlling the average leaf slope in the canopy

* b: controlling the distribution bimodality magnitude

This approach allows for the reproduction of typical distributions (de Wit, 1965). In the absence of specific LAD information, spherical (Duthoit et al., 2008) or uniform (Widlowski et al., 2007) distributions are usually chosen, though these can be inaccurate for complex canopies. Studies performing inversion techniques (Tagliabue et al., 2022; Candiani et al., 2022) prefer to use the ellipsoidal family LAD defined by Campbell (1990) for its flexibility, using a single parameter: the Average Leaf Inclination Angle (ALIA), ranging from 0° to 90°. The ellipsoidal LAD definition can be adapted to the retrieval of temporal (Propastin and Panferov, 2013) and crop specific (Jiao et al., 2022) variations in ALIA. However, it is limited in its ability to describe the actual structure of the canopy. Often, ALIA is used as an adjustable parameter to compensate for other canopy variables like the LAI to improve inversion performances. In their study, Danner et al. (2019) concluded that ALIA should be treated as a free calibration parameter rather than a physical LAD. In a separate study, Su et al. (2019) demonstrated improved LAI retrieval accuracy by incorporating a LAD derived from terrestrial LiDAR (TLS) data compared to the standard ellipsoidal LAD definition.

For the current work, the choice is made to fit a and b parameters of the LAD<sub>bimodal</sub> function to match the 3D scenes actual LAD (LAD<sub>3D</sub>). To

calculate the LAD, the DART 3D scenes are used to get the area of leaf facets per zenith 1° angular sectors in the [0°–90°] range. Fig. 4 shows the actual LAD<sub>3D</sub> and its corresponding LAD<sub>bimodal</sub>. The LAD<sub>bimodal</sub> has a smooth profile, whereas the LAD<sub>3D</sub> has a discontinuous profile caused by the finite number of leaf facets in the 3D scene.

Contrary to DART, SAIL does not simulate the radiative transfer in the canopy in all possible directions. It computes four radiative transfer fluxes: two directional fluxes in the sun and sensor viewing directions, and two hemispheric fluxes in the upward and downward directions. The downward total flux incident onto the top of the canopy is the sum of a direct sun flux and an atmospheric flux. The ratio “Atmospheric flux/Total flux” is called the SKYL factor. The approximated SKYL defined in François et al. (2002) is sometimes used in SAIL simulations (Danner et al., 2019) although it may lack precision as it is based on an average state of atmospheric conditions aligned to mid-latitudes clear sky and does not consider the SWIR domain. Here, the SKYL is used to represent the atmospheric flux, in order to have consistent representations of the atmospheric flux between DART and SAIL. To do this, the DART atmospheric radiative transfer module computes the SKYL for sun zenith angle (SZA) from 0° to 90° with a 1° step and a 1 nm step over the [0.4–2.5] µm spectral range (see Fig. A.5 in Appendix). Here, we consider the USSTD76 standard rural clear sky gas model and the RURALV23 aerosol model with a 23 km visibility.

### 3.1.2. Scenarios for DART and SAIL intercomparison

Simulations are performed for the 3 predefined growth stages (see Fig. 3). The goal is both to evaluate the inherent effects of light propagation for the two different canopy representations approaches and to quantify the geometrical effects of maize row orientation. While the study site is a flat horizontal cultivated area, the effect of slope is still a major component of the RS signal that cannot be simulated in 1D RTMs. Variations in slope are therefore also considered in this section. For each growth stage, four field geometries are modeled for DART simulations with different sun-to-rows relative azimuth angle (RO) and field slope. RO is used to represent a sun direction that can be perpendicular or parallel to maize rows and the slope is set to a maximum of 10° which is rarely exceeded in western Europe maize fields. Simulations always consider maize fields with rows planted
<figure><img src="image_5.png" /><figcaption>Fig. 3. DART 3D scenes: (a) LAI = 0.47 m²/m², (b) LAI = 1.21 m²/m², (c) LAI = 3.11 m²/m².</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4. LAD<sub>3D</sub> compared with the fitted LAD<sub>bimodal</sub> function for LAI = 0.47 m²/m², LAI = 1.21 m²/m² and LAI = 3.11 m²/m² with respective (a, b) parameters: (a = -0.259; b = -0.245), (a = -0.243; b = -0.311) and (a = -0.182; b = -0.357). For better readability, LAD<sub>3D</sub> is resampled to 3° zenith angular sectors.</figcaption></figure>

perpendicular to the slope, a common farming practice to mitigate surface water runoff. As SAIL does not account for topography or vegetation aggregation, only one SAIL simulation is performed per LAI value. The summary of simulations inputs is presented in Table 2. The soil reflectance is defined using the “loam gravelly brown” reflectance spectra of DART database. This is the sample 87P313 acquired by Klickitat Co., Wa. via USDA Soil Conservation service. PROSPECT-PRO is used to generate a single leaf optical properties (OP) with input parameters in the range of field measurements: C<sub>ab</sub> = 40 [µg/cm²], C<sub>ar</sub> = 10 [µg/cm²], C<sub>w</sub> = 12 [mg/cm²], C<sub>bc</sub> = 9 [mg/cm²], C<sub>p</sub> = 1 [mg/cm²] and N<sub>struc</sub> = 1.5 [-].

## 3.2. Global sensitivity analysis with the DART model

This section details the method used to evaluate the hyperspectral sensitivity to maize field parameters at different growth stages. The choice is made to use GSA tools to assess the contributions of DART inputs on the simulated HyPlant-DUAL TOC reflectance of a flat horizontal maize field as on the study site (see Fig. A.7).

### 3.2.1. Hilbert–Schmidt independence criterion

A growth stage-dependent GSA approach is used to quantify the different contributions of leaf biochemical components, canopy architecture, and soil moisture on the RS signal. Commonly used variance decomposition GSA methods like Sobol sensitivity indices (S<sub>i</sub>) require an important number of simulations, up to several tenths of thousands (Morcillo-Pallares et al., 2019), which can be limiting for computationally expensive RTMs like DART. In this study,

<table><caption>Table 2
Input parameters for DART and SAIL intercomparison.</caption><thead><tr><td>Parameter</td><td>Values</td><td>Unit</td></tr></thead><tbody><tr><td>LAI</td><td>0.47, 1.21, 3.11</td><td>m²/m²</td></tr><tr><td>RO<sup>a</sup></td><td>0, 90</td><td>deg</td></tr><tr><td>Slope<sup>a</sup></td><td>0, 10</td><td>deg</td></tr><tr><td>SZA</td><td>45</td><td>deg</td></tr></tbody></table>

the Hilbert–Schmidt Independence Criterion (HSIC) method is preferred (Gretton et al., 2005; Da Veiga, 2015). Contrary to Sobol, HSIC S<sub>i</sub> is a dependence-based method offering significant flexibility to capture complex dependencies between input and output variables. This method accepts discrete and continuous input variables and has already proven its performances against variance-based methods (Marrel and Chabridon, 2021). For enhanced interpretability and to facilitate comparisons across different variables, normalized variant R2-HSIC S<sub>i</sub> are computed using the Squared Exponential covariance kernel as the Reproducing Kernel Hilbert Space (RKHS).

### 3.2.2. GSA simulation plan

DART is used to generate three Look-Up Tables (LUT) for the predefined growth stages representative of the study site (see Fig. 3). Each LUT consists in 5000 simulations covering a wide range of input parameters. For each simulation, the LUT stores the reflectance and the corresponding input parameters. The spectral bands are set to reproduce HyPlant-DUAL sensor (wavelengths and FWHMs). To address border effects, DART 3D scene is repeated one time on each side for a 29.58 m × 29.25 m final scene dimension. In order to reduce computation time for the LUT generation, BOA radiance is calculated using an analytical function instead of the complete radiative transfer (Wang and Gastellu-Etchegorry, 2020). The total number of rays is set to 1 000 000 on the entire scene with a maximum of 30 ray scattering order. Input parameters sets are defined using a Design Of Experiments (DOE). Both the DOE and the GSA rely on OpenTURNS python package (Baudin et al., 2016) available at https://openturns.github.io. The DOE uses Monte Carlo (MC) random sampling with discrete and uniform distributions on defined ranges.

If a link exists between PROSPECT N<sub>struc</sub> parameter and LMA (Jacquemoud and Baret, 1990), the relationship might lack robustness. As N<sub>struc</sub> cannot be physically measured, the range used by Wang et al. (2022a) is preferred for the GSA. In their study on crop specific optimal input distributions for PROSAIL inversion, a broader N<sub>struc</sub> range of [0–3] is best performing for maize GAI estimation. The C<sub>ab</sub> and C<sub>ar</sub> pigments are defined using typical ranges (Candiani et al., 2022; Verrelst et al., 2021). Similarly to Candiani et al. (2022), we use the 0.67 Pearson correlation coefficient from our field measurements to link these two parameters in the DOE. On the other hand, we define C<sub>w</sub>, C<sub>bc</sub> and C<sub>p</sub> parameters according to the variation ranges both from field measurements and from the dataset published by Reichenau et al. (2020), who studied crop traits on an intensively monitored site in Germany. Regarding soil reflectance, Soil Moisture (SM) level is defined with two modalities for a single soil type: wet and dry. The two

<footnote><sup>a</sup> RO and slope are only considered for DART simulations.</footnote>
<caption>**Table 3**</caption>

DART and PROSPECT input parameters used to generate the LUTs for the GSA. LUTs are generated for 3 growth stages representative of the study site: (a) PIV field on July 7, (b) PIV field on July 30, (c) CEC field on July 7. The Design of Experiments (DOE) is generated using uniform and discrete Probability Density Functions (PDF) with a Monte Carlo random sampling.

<table><caption>**Table 4**</caption><thead><tr><th>RTM</th><th>Parameter</th><th>Description</th><th>Range</th><th>Unit</th><th>PDF</th></tr></thead><tbody><tr><td rowspan="4">DART</td><td>SZA</td><td>Sun zenith angle</td><td>22.9, 29.1, 35.3</td><td>deg</td><td>Discrete</td></tr><tr><td>RO</td><td>Rows orientation</td><td>0, 45, 90</td><td>deg</td><td>Discrete</td></tr><tr><td>SM</td><td>Soil moisture level</td><td>dry, wet</td><td>–</td><td>Discrete</td></tr><tr><td>LAI</td><td>Leaf Area Index</td><td>0.47<sup>a</sup>, 1.21<sup>b</sup>, 3.11<sup>c</sup></td><td>m<sup>2</sup>/m<sup>2</sup></td><td>Discrete</td></tr><tr><td rowspan="6">PROSPECT</td><td>N<sub>struc</sub></td><td>Leaf structure</td><td>1–3</td><td>–</td><td>Uniform</td></tr><tr><td>Cab</td><td>Chlorophyll content</td><td>10–80</td><td>µg/cm<sup>2</sup></td><td>Uniform</td></tr><tr><td>Car</td><td>Carotenoid content</td><td>2–15</td><td>µg/cm<sup>2</sup></td><td>Uniform</td></tr><tr><td>Cw</td><td>Water content</td><td>10–45</td><td>mg/cm<sup>2</sup></td><td>Uniform</td></tr><tr><td>Cbc</td><td>Carbon-based constituents</td><td>2–12</td><td>mg/cm<sup>2</sup></td><td>Uniform</td></tr><tr><td>Cp</td><td>Protein content</td><td>0.2–1.5</td><td>mg/cm<sup>2</sup></td><td>Uniform</td></tr></tbody></table>

DART and PROSPECT input parameters used to generate the LUT for the retrieval of maize traits with the HAL method. The Design of Experiments (DOE) is generated using uniform and discrete Probability Density Functions (PDF) with a Monte Carlo random sampling.

<table><thead><tr><th>RTM</th><th>Parameter</th><th>Description</th><th>Range</th><th>Unit</th><th>PDF</th></tr></thead><tbody><tr><td rowspan="3">DART</td><td>(SZA, RO)</td><td>(Sun zenith angle, rows orientation)</td><td>(28.0, 2.1), (28.0, 18.2), (31.3, 12.7), (31.3, 7.6)</td><td>deg</td><td>Discrete</td></tr><tr><td>Soil</td><td>Soil reflectance</td><td>0–9</td><td>–</td><td>Discrete</td></tr><tr><td>LAI</td><td>Leaf Area Index</td><td>0–7</td><td>m<sup>2</sup>/m<sup>2</sup></td><td>Discrete</td></tr><tr><td rowspan="6">PROSPECT</td><td>N<sub>struc</sub></td><td>Leaf structure</td><td>1–3</td><td>–</td><td>Uniform</td></tr><tr><td>Cab</td><td>Chlorophyll content</td><td>10–80</td><td>µg/cm<sup>2</sup></td><td>Uniform</td></tr><tr><td>Car</td><td>Carotenoid content</td><td>2–15</td><td>µg/cm<sup>2</sup></td><td>Uniform</td></tr><tr><td>Cw</td><td>Water content</td><td>5–35</td><td>mg/cm<sup>2</sup></td><td>Uniform</td></tr><tr><td>Cbc</td><td>Carbon-based constituents</td><td>3–6</td><td>mg/cm<sup>2</sup></td><td>Uniform</td></tr><tr><td>Cp</td><td>Protein content</td><td>0–1</td><td>mg/cm<sup>2</sup></td><td>Uniform</td></tr></tbody></table>

corresponding reflectance values are extracted from the HyPlant-DUAL image of July 7 right before and after the rotating irrigation system overpass on a bare soil zone of PIV field. Six samples at 1 m spatial resolution are extracted per modality with a distance of 20 m between samples (see Fig. 1). For each modality, the reference reflectance is calculated as the average of the two median samples. SZA range is defined realistically, according to Sentinel-2 (S2) acquisitions in the study area from May to September. An overview of the DOE input ranges is presented on Table 3.

### 3.3. Vegetation traits retrieval using DART

After quantifying the effects of canopy architecture, soil moisture and leaf biochemistry with the GSA (see Section 3.2), the HYB method using DART to retrieve maize LAI, LCC, LNC, LMA and LWC from HyPlant-DUAL images is detailed in this section (see Fig. A.8).

#### 3.3.1. Hybrid based inversion method using active learning strategy

The first step of the HYB method used in this study consists in simulating a LUT covering a wide range of growth stages, field geometries and biochemical quantities representative of the study area. The LUT is used to train a regression function linking TOC reflectance to maize traits quantities. The trained function is then used to invert reflectance spectra that were not used in the training to retrieve vegetation traits. Kernel-based regression algorithms proved to be one of the best performing methods, especially the Gaussian Process Regression (GPR) and the Kernel Ridge Regression (KRR) (García-Soria et al., 2024; De Clerck et al., 2024; Rivera-Caicedo et al., 2017; Verrelst et al., 2016a). KRR is preferred in this study for its ease of use due to only few hyperparameters compared with other regression functions. In order to optimize the sampling of the LUT for training, an Active Learning (AL) strategy is used in combination with the HYB framework. HYB+AL (HAL) have been demonstrated to outperform models trained on randomly sampled data for crop traits retrieval (Berger et al., 2021; Candiani et al., 2022). The DART simulations, KRR and AL are further detailed in following sections.

#### 3.3.2. Simulation of the training data using DART

DART is used to generate a 5000 simulations training LUT covering the entire growth of a maize field with a LAI ranging from 0 to 7 m²/m². The simulation plan is defined using a randomly sampled DOE. HyPlant-DUAL characteristics, scene dimension and atmospheric conditions are kept identical to Section 3.2.2. As RS images cover two dates with two fields having different row orientation, the definition of 4 illumination configurations (SZA and RO) with accurate sun-target-sensor geometry is necessary for the LUT generation. Simulations are performed for a nadir viewing angle. Computation time is reduced by pre-computing the Bottom Of Atmosphere (BOA) irradiance of the canopy. Indeed, atmospheric conditions (Fig. A.5) are constant. As the work focuses on wide irrigated fields with different soil types and moisture, 10 soil reflectance spectra are used for simulation. When possible (i.e. PIV on July 7), 5 different linear mixing of wet and dry soil extracted from the RS images are calculated, ranging from 0% to 100% dry soil. In addition, 5 reflectance spectra measured *in situ* with the ASD FieldSpec 4 spectrometer at several locations across PIV field are also selected (see Fig. 1). PROSPECT input parameters ranges are defined to capture the validation data. While most leaf target variables have slow evolution over time, $C_w$ can vary in a matter of hours. Moreover, early July measurements were collected in a 5 day time frame. When the data measured in the field are used to define minimum and maximum $C_w$ range for CEC field on July 7 with a dense canopy, a mismatch is observed in the SWIR domain between the RS image and the simulated LUT. The observed patterns are typical from leaf water absorption features. The choice is thus made to increase the maximum range up to 35 mg/cm², allowing for a more robust estimation of LAI, the main structural parameter. An overview of the input parameters ranges used to generate the LUT are listed in Table 4.

On the comparison between measured and simulated reflectance (see Fig. 5), a slight overrepresentation of wet soil in the simulated LUT is observed for PIV field on July 7 characterized a sparse canopy. In the case of PIV field on July 30 and CEC field on July 7, the simulated LUT frames well the measured reflectances. Overall, a good agreement is found between the LUT and the HyPlant-DUAL images.
<figure><img src="image_7.png" /><figcaption>Fig. 5. Simulated Look-Up Tables (LUT) vs. HyPlant image (IMG) for the 3 main growth stages. The displayed LUT is sampled according to in situ measurements having a LAI ranging from 0.14 to 0.81 m²/m² for CEC on July 7, 0.11 to 2.19 m²/m² for CEC on July 7 and 0.85 to 5.7 m²/m² for CEC on July 7.</figcaption></figure>

### 3.3.3. Kernel ridge regression

KRR (Murphy, 2012) is a widely used algorithm in the context of vegetation traits retrieval with hyperspectral remote sensing, owing to its ease of use and ability to account for non-linear relationships between spectral data and vegetation traits (Douak et al., 2012). Notably, KRR has been shown to be one of the best-performing algorithms in this field, consistently delivering accurate predictions of traits such as LAI, canopy chlorophyll content (CCC), and canopy nitrogen content (CNC) (García-Soria et al., 2024; De Clerck et al., 2024; Rivera-Caicedo et al., 2017). KRR incorporates L2 regularization to prevent overfitting, ensuring that the model generalizes well to new, unseen data when trained on simulated data.

Before training the KRR, a preprocessing is performed on the 5000 LUT simulated samples and the HyPlant-DUAL images. A filtering is applied on certain spectral regions by not considering bands below 0.49 µm due to a high sensitivity of the blue bands to aerosols and gas. Bands above 2.35 µm are also removed due to the low sensor signal-to-noise ratio in the image. The two main atmospheric water vapor absorption windows are finally removed: [1.252–1.502] µm and [1.700–2.140] µm. Similarly to Candiani et al. (2022), noise is added to the training data for a better generalization capacity. An artificial additive gaussian white noise is applied to the LUT reflectances with mean of 0 and standard deviation of 0.01 and a 2% random noise is applied on the LUT input parameters. As suggested by Rivera-Caicedo et al. (2017), a spectral dimensionality reduction (DR) technique is applied both to the LUT and the filtered RS images. DR has been shown to speed-up and improve retrieval accuracy of HYB approaches while keeping most of the information of the hyperspectral signal. The choice is made to use a Principal Components Analysis (PCA) DR on the spectral data. PCA latent vectors are first calculated from the reflectances of PIV and CEC fields from HyPlant-DUAL images. RS images and the simulated LUT spectral bands are then reprojected on the first 15 latent vectors of the PCA explaining 99.95% of the images variance. Concerning the KRR hyperparameters, the choice is made to fix to 0.01 the constant α that multiplies the L2 penalty term, controlling regularization strength.

### 3.3.4. Metrics

Our results for the HAL method are expressed in terms of:

*   **Bias:**

$$ \text{bias} = \frac{1}{N} \sum_{i=1}^{N} (y_i - \hat{y}_i) \qquad (6) $$

*   **Coefficient of Determination (R²):**

$$ R^2 = 1 - \frac{\sum_{i=1}^{n} (y_i - \hat{y}_i)^2}{\sum_{i=1}^{n} (y_i - \bar{y})^2} \qquad (7) $$

*   **Root Mean Square Error (RMSE)**

$$ RMSE = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (y_i - \hat{y}_i)^2} \qquad (8) $$

### 3.3.5. Active learning using the Euclidean distance-based diversity

AL is increasingly being used in the context of HYB workflow for vegetation traits retrieval from imaging spectroscopy. The implementation of AL strategy allows for an optimal training samples selection, reducing redundancy in the simulated data. The previous study conducted by Candiani et al. (2022) achieved consistent increase in retrieval accuracy using AL compared to randomly sampled data. The Euclidean distance-Based Diversity (EBD) AL strategy has been shown to be one of the best performing techniques while easy to implement and fast to compute (Berger et al., 2021; Verrelst et al., 2016a). EBD is an iterative sampling strategy used to train the KRR regression algorithm by maximizing the spectral diversity in the training data. The process begins by dividing the LUT into three distinct pools:

*   **A training set**, initialized with a random selection of 50 training samples.

*   **A candidate pool**, containing the remaining LUT samples.

*   **A rejected set**, which starts empty and will contain samples that do not improve model performance.

The first step consists in training the KRR with the training set and calculating the validation RMSE by comparing model's predictions against the validation data (i.e. biochemical and biophysical traits) according to Eq. (8).

**Iterative Sampling:**

*   At each iteration, the candidate pool sample with the largest spectral euclidean distance to the training set is selected using Eq. (9):

$$ d_E = \|x_u - x_i\|_2^2 \qquad (9) $$

where:
<figure><img src="image_8.png" /><figcaption>Fig. 6. Comparison of SAIL and DART simulated maize field reflectance signal for different LAI, field geometries and spectral regions.</figcaption></figure>

- $x_u$ represents a sample from the candidate pool.

- $x_l$ represents a sample from the training set.

• The KRR model is then re-trained on the updated training set, now including the newly selected sample:

- If the RMSE decreases, the new sample is retained in the training set.

- If the RMSE does not improve, the sample is moved to the rejected set.

This iterative process continues until the candidate pool is exhausted. At the end of the procedure, the KRR model is trained on the optimized training set. In this study, 15 different HAL models are trained for each vegetation trait, each initialized with a different random subset of samples. The introduction of variability into the AL

procedure gives access to the associated systematic uncertainties and the final results calculated as the average predictions of the 15 HAL models.

# 4. Results

## 4.1. *Selection of the RTM*

Results obtained from the DART and SAIL reflectance simulations at different growth stages and field geometries are presented on Fig. 6. Four spectral regions are displayed: the visible domain (VIS), near infrared (NIR), shortwave infrared 1 (SWIR 1) and SWIR 2. The reflectance absolute values for associated key wavelengths (i.e. 0.55, 0.68, 1.0, 1.7 and 2.2 µm) are presented in Table 5.

Overall, a good agreement is found between DART and SAIL for a horizontal field (slope = 0°) if SAIL uses a LAD derived from the 3D scene of DART. Then, the absolute difference usually remains below
<caption>**Table 5**</caption>

Maize field reflectance values simulated using DART and SAIL in key wavelengths for different LAI and field geometries.

<table><thead><tr><th rowspan="2">LAI<br>(m²/m²)</th><th rowspan="2">RTM</th><th rowspan="2">RO<br>(°)</th><th rowspan="2">Slope<br>(°)</th><th colspan="5">Reflectance at wavelength (µm)</th></tr><tr><th>0.55</th><th>0.68</th><th>1.00</th><th>1.70</th><th>2.20</th></tr></thead><tbody><tr><td rowspan="6">0.47</td><td rowspan="3">SAIL</td><td>-</td><td>-</td><td>0.06</td><td>0.07</td><td>0.26</td><td>0.30</td><td>0.23</td></tr><tr><td rowspan="3">DART</td><td>0</td><td>0.06</td><td>0.08</td><td>0.26</td><td>0.30</td><td>0.24</td></tr><tr><td>10</td><td>0.06</td><td>0.08</td><td>0.26</td><td>0.30</td><td>0.23</td></tr><tr><td>90</td><td>0.06</td><td>0.07</td><td>0.26</td><td>0.29</td><td>0.22</td></tr><tr><td>90</td><td>0.07</td><td>0.09</td><td>0.29</td><td>0.33</td><td>0.26</td></tr><tr><td rowspan="6">1.21</td><td rowspan="3">SAIL</td><td>-</td><td>-</td><td>0.06</td><td>0.03</td><td>0.30</td><td>0.24</td><td>0.14</td></tr><tr><td rowspan="3">DART</td><td>0</td><td>0.06</td><td>0.04</td><td>0.29</td><td>0.24</td><td>0.15</td></tr><tr><td>10</td><td>0.06</td><td>0.04</td><td>0.30</td><td>0.24</td><td>0.15</td></tr><tr><td>90</td><td>0.06</td><td>0.04</td><td>0.30</td><td>0.24</td><td>0.14</td></tr><tr><td>90</td><td>0.07</td><td>0.05</td><td>0.32</td><td>0.27</td><td>0.17</td></tr><tr><td rowspan="6">3.11</td><td rowspan="3">SAIL</td><td>-</td><td>-</td><td>0.06</td><td>0.01</td><td>0.37</td><td>0.19</td><td>0.08</td></tr><tr><td rowspan="3">DART</td><td>0</td><td>0.07</td><td>0.02</td><td>0.37</td><td>0.20</td><td>0.08</td></tr><tr><td>10</td><td>0.07</td><td>0.02</td><td>0.37</td><td>0.20</td><td>0.08</td></tr><tr><td>90</td><td>0.07</td><td>0.02</td><td>0.38</td><td>0.20</td><td>0.08</td></tr><tr><td>90</td><td>0.08</td><td>0.02</td><td>0.41</td><td>0.22</td><td>0.09</td></tr></tbody></table>

1.0 × 10⁻². On average for RO = 0° and slope = 0°, SAIL tends to provide a lower reflectance with an average absolute difference of 0.006 for LAI = 0.47 m²/m², of 0.005 for LAI = 1.21 m²/m² and of 0.005 for LAI = 3.11 m²/m² (Fig. 6).

For RO = 90° and slope = 10° scenario, DART and SAIL can greatly differ, with a higher reflectance in DART. On average the absolute difference equals 0.023 for LAI = 0.47 m²/m², 0.019 for LAI = 1.21 m²/m² and 0.017 for LAI = 3.11 m²/m². One can notice that the differences between DART and SAIL linked to RO and slope vary differently between growth stages and spectral regions (Fig. 6). The joint effects of RO and slope tend to be higher for sparse canopies (LAI: 0.47 and 1.21 m²/m²) when bare soil is directly visible and decrease for denser canopies (LAI: 3.11 m²/m²). In the case of a sparse canopy, the impact of slope is bigger in longer wavelengths. For a dense canopy, the impact of slope increases in the green and NIR while decreasing in the red and SWIR (see Table 5). Similarly, relative differences between SAIL and DART also depend on the growth stage and spectral region:

* For LAI = 0.47 m²/m², the relative difference equals 7.6%, 17.7%, 8.7%, 10.8% and 13.1% at 0.55, 0.68, 1.00, 1.70 and 2.20 µm respectively.

* For LAI = 1.21 m²/m², the relative difference equals 10.3%, 24.4%, 7.7%, 9.7% and 14.6% at 0.55, 0.68, 1.00, 1.70 and 2.20 µm respectively.

* For LAI = 3.11 m²/m², the relative difference equals 16.9%, 22.2%, 7.9%, 11.0% and 14.4% at 0.55, 0.68, 1.00, 1.70 and 2.20 µm respectively.

As anticipated, the impact of slope when sun illuminates parallel to maize rows (RO = 0°, slope = 10°) is very low, with values comparable to a horizontal field (RO = 0°, slope = 0°). For RO = 0°, a change in slope have a minor impact on the reflectance. Considering the differences observed between these RTMs due to changes in field geometry and development stages, the use of DART is confirmed for the traits retrieval approach.

## 4.2. Global sensitivity analysis

GSA results for the three different growth stages are presented in Fig. 7. First, the GSA of LAI = 0.47 m²/m² growth stage shows that the maize field reflectance is dominated by SM effects. Most of the biochemical traits contribution remain lower than 5%, except for C<sub>ab</sub> with a maximal contribution reaching 5.3% at 0.78 µm. For this growth stage, the GSA method cannot capture a statistical dependence

of the reflectance signal to C<sub>p</sub>. When removing the topsoil moisture contribution and only considering the relative contributions of leaf biochemistry, SZA and RO, the major influence of RO is confirmed with an average relative contribution of 17.6%. Conversely, a low 3.2% SZA contribution is observed.

Second, for the GSA of LAI = 1.21 m²/m² growth stage, SM is still the main contributor to the maize field reflectance. Most of biochemical traits S<sub>i</sub> are higher than 10%. Conversely, a very low C<sub>p</sub> contribution is observed, reaching 0.3% at 1.70 µm and 0.2% at 2.21 µm. For this growth stage, the GSA method is also detecting unrealistic C<sub>p</sub> contributions in regions where no absorption features are known (i.e. 0.1% at 1.00 µm). In the case of leaf biochemistry, SZA and RO relative contributions, a decreasing sensitivity to RO is observed compared to LAI = 0.47 m²/m² growth stage. In the SWIR 2 from 2.00 to 2.40 µm, a 15.1% average relative contribution of RO is still visible. Locally, a peak 28.7% contribution appear in the VIS around 0.68 µm. For this growth stage, SZA has almost no influence on the RS signal.

Third, for the GSA of LAI = 3.11 m²/m² with a dense canopy, SM contribution is low compared to leaf biochemistry. The GSA method captures almost no dependence to C<sub>p</sub>, remaining below 0.1% in the SWIR domain dominated by C<sub>w</sub>. The comparison of leaf biochemistry, SZA and RO relative contributions, confirm an average 99.7% leaf biochemistry contribution to the reflectance signal with no significant sensitivity to RO and SZA.

## 4.3. Crop traits retrieval

Maize traits retrieval accuracies with the HAL method are summarized in Table 6 comparing *in situ* validation data to the HAL model estimates. Retrieval accuracies are expressed in terms of bias, RMSE and R² (see Section 3.3.4). For each variable, the best performing model is compared to the average prediction of the 15 trained HAL models. These results show a good capacity of the HAL method to retrieve maize traits both at canopy and leaf scale with a very low bias for every variable of the study. The decrease in accuracy of the average model predictions compared to the best model is considered acceptable for all the variables while providing valuable information on the AL strategy uncertainties.

At canopy scale, almost no differences in LAI predictions are observed between the average and the best model, showing the AL strategy to converge towards an optimal sampling. Retrieval accuracy are the highest on average with R² = 0.91 and RMSE = 0.42 m²/m² (see Fig. 8(a)). Errors however appear to increase with LAI, potentially linked to saturation effects.

At leaf scale, lower LCC and LWC retrieval accuracies are observed with R² = 0.61, RMSE = 3.89 µg/cm² and R² = 0.78, RMSE = 0.88 mg/cm² respectively (see Table 6). For these variables, a higher prediction standard deviation of the 15 HAL models reveal an important variability in the AL sampling strategy (Figs. 8(b) and 8(e)). Conversely, LNC and LMA estimates have a lower variability (Figs. 8(c) and 8(d)) and a high accuracy with R² = 0.86, RMSE = 1.13 × 10⁻² mg/cm² and R² = 0.84, RMSE = 0.15 mg/cm² respectively (Table 6). The validation of the retrieval method at leaf scale reveal no evident link between higher HAL uncertainty and low LAI values.

LAI estimation maps (see Fig. 9) are highly heterogeneous with defined spatial patterns. Overall on July 7, low LAI values are observed for PIV field and high LAI for CEC field. For PIV field on July 30 the vegetation has significantly developed in agreement with the different sowing dates of the sub-parcels. For CEC field, a consistency in LAI spatial distribution between the beginning and end of July is noted. However, a noticeable drop in LAI is visible in CEC field areas that were already well developed during the first campaign. The decrease in LAI is in agreement with a 10% Normalized Difference Vegetation Index (NDVI) drop at field scale going from 0.88 to 0.78. Sensor striping noise also appears to affect the signal in crucial wavelengths for LAI predictions. This translates into a line shaped underestimation for CEC
<figure><img src="image_9.png" /><figcaption>**Fig. 7.** GSA for 3 growth stages. The upper graphs corresponds to the stacked R2-HSIC S<sub>i</sub> normalized index calculated from the DART simulated LUT. The lower graphs merges the upper S<sub>i</sub> of leaf biochemical traits under “Leaf” and removes the joint effects and the soil moisture. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<table><caption>**Table 6**
Summary of retrieval accuracy metrics expressed as absolute bias, Root Mean Squared Error (RMSE) and coefficient of determination (R<sup>2</sup>). Results are shown for both the best of the 15 trained HAL models and the average prediction of the 15 trained HAL models.</caption><thead><tr><th rowspan="2">Variable</th><th rowspan="2">Unit</th><th colspan="3">Best model</th><th colspan="3">Average model</th></tr><tr><th>Bias</th><th>RMSE</th><th>R<sup>2</sup></th><th>Bias</th><th>RMSE</th><th>R<sup>2</sup></th></tr></thead><tbody><tr><td>LAI</td><td>m<sup>2</sup>/m<sup>2</sup></td><td>&lt;1 × 10<sup>-2</sup></td><td>0.41</td><td>0.91</td><td>&lt;1 × 10<sup>-2</sup></td><td>0.42</td><td>0.91</td></tr><tr><td>LCC</td><td>µg/cm<sup>2</sup></td><td>0.15</td><td>3.59</td><td>0.67</td><td>0.32</td><td>3.89</td><td>0.61</td></tr><tr><td>LNC</td><td>mg/cm<sup>2</sup></td><td>&lt;1 × 10<sup>-3</sup></td><td>6.91 × 10<sup>-3</sup></td><td>0.95</td><td>&lt;1 × 10<sup>-5</sup></td><td>1.13 × 10<sup>-2</sup></td><td>0.86</td></tr><tr><td>LMA</td><td>mg/cm<sup>2</sup></td><td>&lt;1 × 10<sup>-2</sup></td><td>0.14</td><td>0.86</td><td>&lt;1 × 10<sup>-2</sup></td><td>0.15</td><td>0.84</td></tr><tr><td>LWC</td><td>mg/cm<sup>2</sup></td><td>0.03</td><td>0.68</td><td>0.87</td><td>0.08</td><td>0.88</td><td>0.78</td></tr></tbody></table>

field on July 30 and a higher prediction standard deviation of the HAL method on July 30. Overall, prediction standard deviation usually stay below 0.10 m²/m² except for CEC field on July 30 where no field measurements of the LAI were available to orient the AL training. This results in an increased prediction variability.

LCC estimation maps (see Fig. 10) reveal a relatively stable LCC for PIV field between the two campaigns with values ranging mostly from 40 to 55 µg/cm² except for small local spots dropping around 30 µg/cm². CEC field display a higher spatial heterogeneity on July 7 with LCC reaching 20 µg/cm² in certain areas. While LCC typically increases as leaves develop, high LAI prediction is not always linked with a high LCC. For CEC field on July 30, LCC has globally decreased with a varying intensity in different areas. The LCC prediction standard deviations are spatially heterogeneous while remaining usually below 4 µg/cm², both for PIV and CEC fields on July 7 and for PIV field on July 30. Conversely, for CEC field on July 30 where no field measurement is available, the standard deviation is ranging from 6 to 8 µg/cm². Higher standard deviation appear to be usually linked to lower LCC estimates. For PIV field on July 30 the presence of a striping noise increase the predictions variability while not being visible on the average predictions.

LNC estimation maps (see Fig. 11) appear for PIV field on July 7 with low LAI to be sensitive to soil type and soil moisture. For this growth stage (Fig. 3(a)), previous GSA results showed a null sensitivity

of the hyperspectral signal to C<sub>p</sub> (the main bi-product of LNC). For PIV and CEC fields on July 30 an important striping noise pattern is present. On the East part of PIV field, a linear pattern is also visible due to the pivot irrigation system overpass. This lead to higher LNC estimations below the irrigation edge corresponding to a dryer soil. The sensitivity of LNC predictions to topsoil moisture and sensor noise for PIV field on July 30 is in agreement with the GSA results showing minor signal contribution of C<sub>p</sub> and a SWIR domain dominated by water absorptions from leaf and soil. For CEC field with high LAI on both campaigns, LNC estimates are spatially heterogeneous, often correlated with LCC and display a good consistency between the two campaigns. However an important LNC increase is observed at the end of July. The prediction standard deviations show a higher standard deviation on July 30, partially due to the absence of field measurements to orient the AL training. For this date, the standard deviation is ranging between 0.02 and 0.03 mg/cm².

Similarly to LNC estimations, LMA maps (see Fig. 12) are sensitive to soil type, soil moisture and striping noise. These effects are however less pronounced than for LNC thank to a higher C<sub>bc</sub> spectral contribution (the major constituent of LMA). For PIV on July 30 low LMA is estimated, usually around 4 mg/cm². For CEC field having a high LAI on both campaigns, LMA is estimated with a lower spatial heterogeneity and a good spatial consistency between the two dates. On average LMA is increasing which is in agreement with crop maturation. Identically
<figure><img src="image_10.png" /><figcaption>Fig. 8. Scatter plots of the measured values against the average predictions of the 15 trained KRR models for (a) LAI, (b) LCC, (c) LNC, (d) LMA and (e) LWC variables. Prediction standard deviation is represented as error bars.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 9. LAI estimation maps on July 7 and July 30. The upper maps represent the average prediction of the 15 trained KRR models while the lower maps represent the prediction standard deviation. Grayscale background image corresponds to NDVI vegetation index from 0 (white) to 1 (black).</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 10. LCC estimation maps on July 7 and July 30. The upper maps represent the average prediction of the 15 trained KRR models while the lower maps represent the prediction standard deviation. Grayscale background image corresponds to NDVI vegetation index from 0 (white) to 1 (black).</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Fig. 11.** LNC estimation maps on July 7 and July 30. The upper maps represent the average prediction of the 15 trained KRR models while the lower maps represent the prediction standard deviation. Grayscale background image corresponds to NDVI vegetation index from 0 (white) to 1 (black).</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Fig. 12.** LMA estimation maps on July 7 and July 30. The upper maps represent the average prediction of the 15 trained KRR models while the lower maps represent the prediction standard deviation. Grayscale background image corresponds to NDVI vegetation index from 0 (white) to 1 (black).</figcaption></figure>

to LNC, LMA estimations have a higher standard deviation, around 0.4 mg/cm² on July 30 where no field measurements are available.

<figure><img src="image_15.png" /><figcaption>**Fig. 13.** LWC estimation maps on July 7 and July 30. The upper maps represent the average prediction of the 15 trained KRR models while the lower maps represent the prediction standard deviation. Grayscale background image corresponds to NDVI vegetation index from 0 (white) to 1 (black).</figcaption></figure>

LWC estimation maps (see Fig. 13) are less consistent than the other variables estimated with the HAL method. Estimations have an important spatial heterogeneity on both campaigns and are sensitivity to soil type, soil moisture and striping noise. For CEC field on July 7, LWC tends to be negatively correlated with LAI while positively correlated with LAI on July 30. The negative correlation between LWC and LAI is also observed in validation data with LWC measurements not exceeding 20 mg/cm². This variable has a high prediction standard deviation, between 4 and 5 mg/cm² on July 30 where no LWC field measurements were carried out. Lower confidence is therefore given to LWC estimation.

A growth stage-dependent analysis of maize traits prediction distributions is presented with the HAL method in Fig. 14. These results reveal a great variability between the different fields and dates. Some variables such as LMA and LNC seem to be generally correlated. Identically for LCC and LNC and for LMA and LAI, usually positively correlated. The rest of the covariances does not reveal evident relationships.

## 5. Discussion

To our knowledge, no study combined 3D RTMs with a dynamic plant growth model to retrieve maize traits with high spatial-spectral resolution RS. In this work, our approach aimed to be as generic as possible through a semi-automatic 3D scene generation approach, but was tested on a flat horizontal cultivated area as constrained by our available datasets. This section examines the limitations of the 1D RTM SAIL to accurately simulate maize field reflectance and some of the implications for crop traits retrieval. The relationship between traits retrieval accuracy and phenological stages is also discussed.

### 5.1. Limitations of the 1D field representation to model heterogeneous row crops

Concerning the comparison of simulated maize field reflectance between DART and SAIL, the field slope revealed to have an important
<figure><img src="image_16.png" /><figcaption>**Fig. 14.** Distributions and covariances of crop traits predicted for PIV and CEC maize fields on July 7 and July 30 are displayed in the lower left corner. *In situ* measured vegetation traits are represented as circles. Density functions are displayed diagonally. Correlation coefficients between predicted traits are displayed in the upper right corner. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

impact in certain configurations. Typically, when SAA is perpendicular to maize rows and parallel to the slope (RO = 90°, slope = 10°), the effect is the highest. Contrarily, when SAA is parallel to maize rows and perpendicular to the slope (RO = 0°, slope = 10°), low differences are observed, usually less than 0.01. This result highlights the importance of combined effects of sun illumination and slope directions that cannot be modeled with a simple model like SAIL. Second, it is also shown that the differences between DART and SAIL due to the slope can be significant and are not constant across growth stages and spectral regions.

When considering a horizontal flat field as for our study site, the differences between DART and SAIL are less important. In this scenario (RO = 0°, slope = 0°), a maximal 0.012 absolute difference is reached for LAI = 0.47 m²/m² at 2.2 µm. It appears that the impact of RO is higher for low LAI and is most of the time below 0.01 absolute difference. Even in the case of a dense canopy (LAI = 3.11 m²/m²) with no clear visible rows, a 0.008 difference can be observed in chlorophyll sensitive wavelengths at 0.55 µm. Such a subtle change in reflectance can be confounded with a 12.5% C<sub>ab</sub> overestimation for a target 40 µg/cm² concentration. For the same growth stage with a 10° slope and the same biochemical quantities, the difference between DART and

SAIL is even higher, reaching 0.013 corresponding to a potential 17.5% C<sub>ab</sub> overestimation. This example highlights the benefits of considering a 3D field representation both for horizontal and sloping terrain, even in the presence of a dense canopy. Actually, an accurate simulation of the reflectance signal can be crucial for crop traits retrieval, especially for variables with a low spectral contribution and during early development stages.

Most DART and SAIL comparisons rely on independent parameterization or on canopies represented as turbid volumes with typical LAD definitions. To our knowledge, our study is the first to perform a comparison using consistent parameters across both models by adapting SAIL parameters to match DART ones, particularly by performing a growth stage-dependent fitting of the LAD function to the actual canopy geometry. In their study, Zhen *et al.* (2024) also compared the reflectance of DART and SAIL at nadir view with a 45° SZA using the same growth model for a horizontal flat field. In their study, SAIL was parameterized using a spherical LAD by default. For a Green Area Index (GAI) of 3 m²/m² using DART as reference, they observed a 0.08 absolute difference at 0.8 µm in the NIR, corresponding to a 26.36% relative difference. Similarly, when a spherical LAD was used in our study for SAIL simulations instead of the fitted LAD (Fig.
4), a 0.03 absolute difference was observed at 0.8 µm for a LAI of 3.11 m²/m², corresponding to a 6.87% relative difference. This higher precision compared to Zhen et al. (2024) can be explained by a more realistic 3D scene parameterization considering less leaf clumping and a larger 3D scene area. Finally when testing our approach relying on a growth stage-dependent LAD modeling in SAIL, a <1.0 × 10⁻³ absolute difference is observed, corresponding to a 0.17% relative error. This highlights that SAIL is able to simulate the reflectance of a maize field with improved accuracy when a realistic LAD is modeled using physical knowledge from the 3D field scenes. This is especially true for dense horizontal maize field with no significant slope or rows orientation effect.

In the perspective of crop traits retrieval we therefore recommend to use a 3D modeling approach, particularly when simulating the reflectance of a maize field during the early vegetative phase and for diverse topographies. The benefits of a 3D modeling approach for maize traits retrieval however depend on several factors: the topography, the growth stage and the spectral sensitivity to the estimated trait.

## 5.2. Hyperspectral sensitivity to maize field parameters

While GSA are usually conducted on generic 1D models like PROSAIL by simulating a wide range of input parameters, the originality of our approach is to be crop-specific and growth stage-specific. The HSIC GSA results highlight the sensitivity to soil moisture level at the beginning of the vegetative phase. For sparse canopies (LAI: 0.47 and 1.21 m²/m²) and using a single soil type, the canopy reflectance is mainly sensitive to soil moisture. Similar study have been carried out by Gao et al. (2022) who studied the sensitivity of Vegetation Indices (VIs) to soil reflectance using variance-based GSA method with PROSAIL. In this study, various soil types and soil moisture levels were considered. Results show that soil type has the highest impact of these two parameters. They also conclude that soil reflectance variability is critical to accurately estimate C<sub>ab</sub> and LAI with VIs. Our results confirm that a precise characterization of soil reflectance is essential for the retrieval of leaf traits in a sparse canopies.

Focusing on the C<sub>p</sub> biochemical trait linked to LNC, our GSA results show no spectral sensitivity to this variable at canopy level for LAI = 0.47 m²/m². Overall, the C<sub>p</sub> contribution remains below 1.0%, even for a dense canopy. Similarly, at leaf level Féret et al. (2021) showed a very low C<sub>p</sub> signal contribution. In their study, a broad [0 - 3.0] mg/cm² input range was defined for various plant species including deciduous trees. Our narrower maize-specific [0.2–1.5] mg/cm² C<sub>p</sub> input range partially explains the quasi null sensitivity to C<sub>p</sub> at canopy scale. The broad [10 - 45] mg/cm² C<sub>w</sub> input range used for our GSA is also one explanation due to high leaf water absorptions in the SWIR, in C<sub>p</sub> sensitive wavelengths. In their study, Berger et al. (2020) highlighted the Chlorophyll-Nitrogen linear relationship during the vegetative phase, confirmed by our field measurements showing a 0.89 Pearson correlation coefficient linking LCC to LNC (see Fig. A.3 in Appendix). For LAI = 0.47 m²/m² and contrary to C<sub>p</sub>, C<sub>ab</sub> reaches a much higher 5.3% sensitivity index at 0.55 µm. We therefore recommend for future studies to consider this existing relationship to improve LNC monitoring during the early vegetative phase of maize instead of relying purely on the C<sub>p</sub> spectral signature in the SWIR. This suggestion is consistent with previous work performed on more complex canopies (i.e. forest ecosystems) that suggests using reflectance spectra in the sensitivity domain only do not lead to robustly retrieve leaf-level variables. Additional information is needed because variations in canopy structure (i.e different phenological stages) can lead to similar reflectance spectra at the canopy scale (Knyazikhin et al., 2013b; Ollinger et al., 2013; Knyazikhin et al., 2013a). Since moderate to strong plant-specific relationship exist between nitrogen and chlorophyll, (Homolová et al., 2013) also supported the use of RS derived chlorophyll content as a proxy to estimate nitrogen. For LAI = 1.21 m²/m², C<sub>p</sub> reaches a maximal 0.3% contribution at 1.7 µm, which is less than the 0.8%

row orientation contribution. These results corroborate the comparison of DART and SAIL for the horizontal flat field scenario, especially the importance of row orientation at the beginning of the vegetative phase. We therefore recommend to accurately model the 3D rows orientation in order to simulate a canopy reflectance having the level of precision necessary to retrieve LNC from C<sub>p</sub> spectral signature.

To our knowledge, only one other study conducted a GSA to assess C<sub>p</sub> contribution at canopy scale (Wang et al., 2018). This work using variance-based GSA focuses on mixed forest with high LAI. They observed a 2%–4% PROSPECT+INFORM canopy reflectance sensitivity to C<sub>p</sub> particularly in the SWIR domain dominated by leaf water absorptions. Using our HSIC-based GSA in this context is the first of its kind and would require further investigation. Typically, when a null contribution would be expected according to PROSPECT-PRO specific absorption coefficients, extremely low sensitivity index is sometimes observed (e.g. 0.17% C<sub>p</sub> at 0.7 µm for LAI = 1.21 m²/m²). Such observations can be linked to the presence of Monte Carlo noise in our simulations due to the ray tracing light mode used in DART. Using a single 3D scene repetition in DART simulations might also lead to bias in S<sub>i</sub> estimates due to rays escaping the scene. Another limitation of our GSA relies in the band specific approach, which contrary to VIs approaches, does not consider relationships between bands nor spectral pattern. As mentioned before, further investigation on the sensitivity of various VIs to crop traits and their robustness to topsoil moisture and geometry should be performed similarly to Gao et al. (2022).

Overall, HSIC-based GSA demonstrated to be a robust framework for quantifying the importance of field geometry, canopy structural and biochemical traits across different phenological stages. This novel application of HSIC to 3D RTM simulations enables a more comprehensive understanding of how various factors influence canopy reflectance, potentially improving the accuracy of crop traits retrieval from hyperspectral RS data. A more detailed analysis of slope effects with our method should be investigated.

## 5.3. Crop traits retrieval

As we have already mentioned, the recovery of leaf variables from a reflectance spectrum measured at canopy level remains a controversial subject, particularly with regard to the impact of forest canopy structure (Knyazikhin et al., 2013b; Ollinger et al., 2013; Knyazikhin et al., 2013a). However, our study, performed on a canopy with a less complex structure (maize crop), demonstrates the ability of the HAL method to retrieve both canopy-level (LAI) and leaf-level (LCC, LNC, LMA, LWC) variables with high accuracy. Leaf-level traits mapping can however be challenging for variables with low spectral contribution in low LAI conditions, when a precise description of canopy architecture is essential. On the evaluation of our inversion method without the active learning procedure (results not shown), retrieval accuracies were not sufficient at leaf level, confirming the observations of Candiani et al. (2022) using the same dataset and employing PROSAIL with a GPR model. This lower leaf-level performances can be attributed to a sub-optimal sampling of the training data as well as canopy structure effects. An other potential source of error is the use of a fixed LAD in 3D scenes via the plant growth model, which might not match exactly the LAD of our study area. Candiani et al. (2022) used the ellipsoidal LAD function in PROSAIL with the ALIA parameter sampled according to a gaussian distribution with a mean of 49.0° and a 4.9° standard deviation. The absence of senescent leaves or reproductive organs (panicles or ears) in our 3D simulations is also a potential source of errors.

Candiani et al. (2022) tested various dimension reduction and active learning techniques. Their best LCC results (R² = 0.72 and RMSE = 3.31 µg/cm²) have similar performances to our model reaching R² = 0.67 and RMSE = 3.59 µg/cm². However, their LCC retrieval performances significantly declined when using the EBD active learning strategy with a 15 principal components dimension reduction (R² = 0.41 and RMSE
= 4.80 µg/cm²). Overall, a substantial variability between trainings is observed in their study for leaf-scale variables. Conversely, our training approach performing HAL-KRR method on a LUT generated with uniform distributions revealed to be relatively robust to dimension reduction and active learning strategies.

On LNC retrieval compared to the results of Candiani et al. (2022) ($R^2$ = 0.56 and RMSE = 0.02 mg/cm²), our study achieved a major improvement in the retrieval accuracy reaching $R^2$ = 0.95 and RMSE = $6.91 \times 10^{-3}$ mg/cm². In addition to the 3D modeling approach, this improvement can be partly explained in the case of variables with low signal contribution, by the active learning sampling method's ability to select a training set of samples with correlated parameters. For instance, in some trainings, a 0.31 correlation coefficient between $C_{ab}$ and $C_p$ emerged after the active learning sampling (i.e. 1340 samples), despite not being specified in the DOE. The LNC mapping on PIV field with low LAI appears to be sensitive to soil moisture level and RS noise, which is in agreement with the GSA results for sparse canopies. A possible source of error is the modeling of soil moisture level with a linear mixing of dry and wet modalities. Given that changes in soil reflectance do not respond linearly to variations in moisture levels, an enhanced characterization of soil reflectance could be achieved using a dedicated RTM such as MARMIT-2 (Dupiau et al., 2022) or BSM (Verhoef et al., 2018). Concerning the mapping of LNC on CEC field with high LAI across both campaigns, the results appear to be spatially and temporally consistent. The important LNC increase between the two dates is partly attributed to dry matter accumulation during leaf maturation. The presence of senescent material with low water content also reduces SWIR absorptions, increasing $C_p$'s signal contribution compared to fresh green leaves dominated by water absorption.

Considering the importance of non-photosynthetic vegetation elements, for CEC field on July 30 where no field measurement was conducted, a decrease in LAI and LCC is observed which is in alignment with a 10% NDVI drop between the two campaigns. As highlighted by Candiani et al. (2022), the lower LAI prediction can result from the presence of reproductive organs (panicles and ears) and an increased amount of senescent vegetation during the reproduction and maturation phases. Similarly, the study of Li et al. (2021) demonstrated that the presence of maize panicles can cause a significant 3% NDVI drop leading to a potential 0.7 m²/m² GAI underestimation. For the monitoring of maize crop during the reproduction and maturation stages, we recommend to include senescent leaves and panicles in the 3D scenes modeling.

On LWC retrieval, further analysis revealed discrepancies between the validation data and the fitted values necessary to simulate reflectances consistent with the RS images. Field measurements typically range from 10 to 20 mg/cm² while the optimal simulation values are between 20 and 30 mg/cm² to get a matching reflectance in the SWIR domain. Possible sources of error are the rapid LWC diurnal and between-days variations of this irrigated crop under hot and stressful climatic conditions as well as the measurement method. First, field measurements were acquired in a 5-day timeframe (July 6, 7, 8 and 10) for only one airborne acquisition flight. Secondly, this variable was measured using leaf disc samples representing a small amount of plant biomass sensitive to evapotranspiration. In their study (Tagliabue et al., 2022) also referred to LWC as the most challenging variable to estimate. They observed skewed LWC measurement distribution between 5.8 and 12.3 mg/cm². These LWC field measurements ranges seem low for irrigated maize fields when compared with the data of Reichenau et al. (2020) on an intensively monitored site in Germany for which values usually vary between 20 and 35 mg/cm² and reach up to 45 mg/cm² in rare cases. While consistent spatial patterns are observed at leaf scale for LCC, LNC, and LMA prediction maps for moderate to high LAI (>1.5 m²/m²), LWC remains challenging with high prediction standard deviations of the HAL method.

On the covariance of estimated traits (Fig. 14), the bivariate matrix of LAI and LWC estimations suggest a bias in the HAL model to fit LWC

validation data, especially for CEC field on July 7 with a -0.75 negative correlation between LWC and LAI, while a positive 0.69 correlation coefficient is observed for PIV on July 30. LMA is much more consistent between fields and dates showing a positive correlation with LAI which is usually the case during crop development. A saturation pattern of this variable is observed for high LAI (>2 m²/m²), except for CEC on July 30 for which LAI is probably underestimated, as already mentioned due to the effect of non-photosynthetic elements such as panicles. A consistent correlation between LMA and LNC between fields at dates is also observed. The relationship is stronger for the CEC field with higher LAI (usually LAI > 2 m²/m²). This observation can be explained by a higher contribution of LNC and LMA to the reflectance for dense vegetation. A positive correlation is also visible between LCC and LNC, especially during the vegetative phase of CEC field on July 7 with a 0.64 correlation coefficient. The relationship between LMA and LCC is not as evident, revealing a bigger spread between dates and fields indicating possible interactions.

Only few studies have estimated multiple crop traits from hyperspectral data. Tagliabue et al. (2022) focused on mixed crops using PRISMA spaceborne data at 30 m spatial resolution to accurately retrieve leaf and canopy traits using a HAL-GPR model: LNC with $R^2$ = 0.87 and RMSE = $1.3 \times 10^{-2}$ mg/cm², LCC with $R^2$ = 0.67 and RMSE = $5.88$ µg/cm², LWC with $R^2$ = 0.63 and RMSE = $3.34$ mg/cm², LAI with $R^2$ = 0.82 and RMSE = $0.57$ m²/m². Our 3D maize-specific approach achieved higher retrieval accuracies comparatively and was successfully used to generate 10 m spatial resolution maps. This method appears promising to exploit the upcoming increased high spatial-spectral resolution RS data stream (Feingersh and Dor, 2015; Briottet et al., 2024), but also to better understand the results obtained at 30 m spatial resolutions for the large majority of ongoing and foreseen hyperspectral satellite missions such as EnMAP, CHIME or SBG (Storch et al., 2023; Celesti et al., 2022; Thompson et al., 2020).

Finally, while PROSAIL is easy to use thanks to a limited number of input parameters and computational demand, its main limits rely in the assumptions of an homogeneous vegetation canopy that may not capture all real canopy complexities as noted by Liang et al. (2016). Our approach demonstrated the feasibility and accuracy of combining a plant growth model with a 3D RTM to estimate multiple maize crop traits under varying conditions and growth stages. In their study using PROSAIL, Tagliabue et al. (2022) showed overall good temporal transferability of their HAL-GPR approach to other year for most investigated traits. This suggests the method has potential for operational use across different growing seasons. Similarly, an evaluation of our method's transferability to new sites with different rows orientations, topography and soil types should be conducted. In addition, future work can include to study the transferability of our developed approach to other crop types than maize. Dong et al. (2024) successfully combined ADEL wheat growth model (Abichou et al., 2013; Fournier et al., 2003) with the LESS 3D RTM (Qi et al., 2019) to accurately retrieve GAI from multispectral satellite data. Other growth models such as rice are being developed (Liu et al., 2025) and could be further investigated in the framework of crop traits retrieval.

## 6. Conclusions

This study highlights the potential of combining a 3D radiative transfer model and a dynamic plant growth model to accurately retrieve maize traits from hyperspectral remote sensing data using hybrid inversion based on machine learning techniques and active learning. The key findings demonstrate the importance of using 3D models to accurately simulate and analyze the reflectance of heterogeneous maize fields at different growth stages, with the 3D DART model outperforming the 1D SAIL model in capturing the effects of field geometry, especially for sloping terrain and low LAI conditions where the row orientation has a significant impact. A growth stage-dependent global sensitivity analysis revealed the varying importance of different factors
influencing canopy reflectance and identified topsoil moisture as a critical factor, particularly during early growth stages. The proposed Hybrid-Active Learning method using DART simulations and machine learning demonstrated improved retrieval accuracy for several crop traits compared to previous studies using 1D models, successfully mapping multiple maize traits across different growth stages with high spatial and spectral resolution, showing consistent spatial patterns for most variables in moderate to high LAI conditions, except leaf water content. Future research should focus on further investigating slope effects, incorporate senescent leaves and reproductive organs into the 3D modeling approach and evaluate the transferability of the proposed method to new sites and different crop types. As future high spatial resolution hyperspectral satellite missions become operational, validating and adapting this methodology for spaceborne data will be crucial for large-scale crop monitoring. Overall, this research underscores the benefits of using 3D RTMs for crop trait retrieval, especially in heterogeneous canopies and varied topographies, and demonstrates the potential of integrating these models with advanced machine learning techniques to exploit the rich information content of hyperspectral data for improved crop monitoring and management. The advancement of satellite imaging spectroscopy will enhance existing multispectral technologies by combining the hyperspectral instrument's capability to detect subtle biochemical changes with the high revisit rate and efficient coverage of multispectral missions.

### CRediT authorship contribution statement

**Romain Démoulin:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Conceptualization. **Jean-Philippe Gastellu-Etchegorry:** Writing – review & editing, Supervision, Software, Methodology, Conceptualization. **Sidonie Lefebvre:** Writing – review & editing, Software, Formal analysis. **Xavier Briottet:** Writing – review & editing, Supervision, Methodology, Conceptualization. **Zhijun Zhen:** Software. **Karine Adeline:** Writing – review & editing, Supervision, Software, Methodology, Conceptualization. **Matthieu Marionneau:** Writing – review & editing, Supervision, Software, Resources, Methodology, Conceptualization. **Valérie Le Dantec:** Writing – review & editing, Supervision, Methodology, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

This work received support from the French National Agency for Research and Technology (ANRT) under the CIFRE grant of Romain Démoulin (agreement n° 2022/1370), cofunded by Hyperplan. The authors would like to thank all the people who contributed to the data acquisition, both in the field and remotely sensed, in particular Mirco Boschetti and Gabriele Candiani from the Natural Resources Lab of CNR-IREA (support unit of Milano) and Cinzia Panigada and Giulia Tagliabue from the Department of Earth and Environment Science (DISAT) – University of Milano – Bicocca. The authors are also grateful for the comments and guidance of the anonymous reviewers. Most of the color maps used in this study prevent the exclusion of readers with impaired color vision (Crameri et al., 2020).

### Appendix

#### A.1. List of abbreviations

See Table A.1.

<table><caption>**Table A.1**
List of abbreviations (abbrev.).</caption><thead><tr><td>Abbrev.</td><td>Description</td></tr></thead><tbody><tr><td>ASL</td><td>Above Sea Level</td></tr><tr><td>AL</td><td>Active Learning</td></tr><tr><td>ALIA</td><td>Average Leaf Inclination Angle</td></tr><tr><td>BOA</td><td>Bottom-Of-Atmosphere</td></tr><tr><td>CEC</td><td>Ceccarelli farm irrigated with micro-dropping</td></tr><tr><td>CFC</td><td>Canopy Fractional Cover</td></tr><tr><td>DR</td><td>Dimensionality Reduction</td></tr><tr><td>DHP</td><td>Digital Hemispherical Photography</td></tr><tr><td>DOE</td><td>Design Of Experiments</td></tr><tr><td>EBD</td><td>Euclidean distance-Based Diversity</td></tr><tr><td>ESU</td><td>Elementary Sampling Unit</td></tr><tr><td>FWHM</td><td>Full Width at Half Maximum</td></tr><tr><td>GAI</td><td>Green Area Index</td></tr><tr><td>GPR</td><td>Gaussian Process Regression</td></tr><tr><td>GSA</td><td>Global Sensitivity Analysis</td></tr><tr><td>HAL</td><td>Hybrid model with active learning</td></tr><tr><td>HYB</td><td>Hybrid model</td></tr><tr><td>KRR</td><td>Kernel Ridge Regression</td></tr><tr><td>LAD</td><td>Leaf Angle Distribution</td></tr><tr><td>LAI</td><td>Leaf Area Index</td></tr><tr><td>LAI<sub>eff</sub></td><td>Effective Leaf Area Index</td></tr><tr><td>LCC</td><td>Leaf Chlorophyll Content</td></tr><tr><td>LMA</td><td>Leaf Mass per Area</td></tr><tr><td>LNC</td><td>Leaf Nitrogen Content</td></tr><tr><td>LUT</td><td>Look-Up Tables</td></tr><tr><td>LWC</td><td>Leaf Water Content</td></tr><tr><td>NDVI</td><td>Normalized Difference Vegetation Index</td></tr><tr><td>NIR</td><td>Near Infrared</td></tr><tr><td>PAI</td><td>Plant Area Index</td></tr><tr><td>PCA</td><td>Principal Component Analysis</td></tr><tr><td>PIV</td><td>Le Rogaire farm irrigated with pivot system</td></tr><tr><td>RO</td><td>Sun direction to maize rows relative azimuth angle</td></tr><tr><td>RTM</td><td>Radiative Transfer Model</td></tr><tr><td>RS</td><td>Remote Sensing</td></tr><tr><td>SAA</td><td>Sun Azimuth Angle</td></tr><tr><td>S<sub>i</sub></td><td>Sensitivity index</td></tr><tr><td>SM</td><td>Soil Moisture</td></tr><tr><td>SWIR</td><td>Short Wave Infrared</td></tr><tr><td>SZA</td><td>Sun Zenith Angle</td></tr><tr><td>T<sup>a</sup></td><td>Cumulative degree days</td></tr><tr><td>TOC</td><td>Top-Of-Canopy</td></tr><tr><td>VI</td><td>Vegetation Index</td></tr><tr><td>VIS</td><td>Visible</td></tr></tbody></table>

#### A.2. Supplementary data

##### A.2.1. Biochemical traits inventory

See Fig. A.1.

##### A.2.2. Biophysical traits inventory

See Fig. A.2.

##### A.2.3. Correlations among collected maize traits

See Fig. A.3.

#### A.3. Radiative transfer models parameterization

##### A.3.1. LAI<sub>3D</sub> vs. simulated LAI-2200 measurements

See Fig. A.4.

##### A.3.2. Atmosphere modeling with DART

See Fig. A.5.

#### A.4. Supplementary method

See Figs. A.6–A.8.
<figure><img src="image_17.png" /><figcaption>Fig. A.1. Histograms representing biochemical traits measurements from the two campaigns on CEC and PIV fields with their associated mean (μ) and standard deviation (σ).</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Fig. A.2.** Histograms representing biophysical and structural traits measurements from the two campaigns on CEC and PIV fields with their associated mean (μ) and standard deviation (σ).</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Fig. A.3.** Correlation matrix of the validation data with associated number of samples (n) used to compute Pearson correlation coefficients.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>Fig. A.4. Licor LAI-2200 measurement derived from the DART simulated gap fraction against the actual LAI of the DART 3D scene at different growth stages.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>Fig. A.5. SKYL factor computed by DART for clear sky conditions on the [0.4–2.5] µm range with sun zenith angle between 0° and 90°.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>Fig. A.6. Flowchart of the method used to compare the reflectance of a maize field simulated by SAIL and DART RTMs for different growth stages and topography as described in Section 3.1.</figcaption></figure>
<figure><img src="image_23.png" /><figcaption>**Fig. A.7.** Flowchart of the HSIC-based GSA method used to assess the contributions of DART inputs on the simulated HyPlant-DUAL signal at different growth stages as described in Section 3.2.</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>**Fig. A.8.** Flowchart of the maize traits retrieval method as described in Section 3.3. This method uses DART to generate training data for a ML algorithm. Before the generation of maize traits maps, predictions are validated against field measurements in the framework of an active learning strategy.</figcaption></figure>

## Data availability

The authors do not have permission to share data. To access to the dataset, request must be addressed to Mirco Boschetti from the Natural Resources Lab of CNR-IREA (support unit of Milano) and Cinzia Pani-gada from the Department of Earth and Environment Science (DISAT) - University of Milano - Bicocca.

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