Estimation of chlorophyll content in rice canopy leaves using 3D radiative transfer modeling and unmanned aerial hyperspectral images

Abstract

Background

The chlorophyll content has a strong influence on plant photosynthesis and crop growth and is a key factor for understanding the functioning of farming systems. Therefore, the accurate estimation of chlorophyll content (Cab) is important in precision agriculture. In this study, the three-dimensional radiative transfer model (3DRTM) was used to calculate the radiative transfer and simulate the canopy hyperspectral image of a rice field. Then, a physically based joint inversion model was developed using an iterative optimization approach with penalty function and a priori information constraints to estimate chlorophyll content efficiently and accurately from the hyperspectral curve of a rice canopy.

Results

The inversion model demonstrates that the sparrow search algorithm (SSA) can estimate rice Cab, providing relatively satisfactory Cab estimation outcomes. In addition, the inversion of the SSA method with or without carotenoids content (Car) constraints was compared, and compared to the inversion of Cab without Car constraints [coefficient of determination (R²) = 0.690, root mean square error (RMSE) = 7.677 µg/cm²)], the SSA with constraints was more accurate (R² = 0.812, RMSE = 5.413 µg/cm²).

Conclusions

The Large-Scale remote sensing data and image simulation framework over heterogeneous 3D scenes (LESS) exhibited higher accuracy in estimating the rice Cab compared to the 1DRTM PROSAIL model, which is constituted by coupling the Leaf Optical Properties Spectra (PROSPECT) model and the Scattering by Arbitrarily Inclined Leaves (SAIL) model. The 3DRTM is conducive to precisely estimating Cab from the hyperspectral data of the rice canopy, thereby holding great potential for precise nutrient management in rice cultivation.

Background

Rice is one of the major crops in the world [1], and its efficient production and precise management contribute to a stable global food supply. The effective and accurate acquisition of rice biophysical covariates is the main means to monitor its growth for accurate agricultural management. As a biomolecule of crucial significance in the field of plant physiology, chlorophyll is an important biological covariate for characterizing the photosynthetic capacity of crops [2, 3]. Throughout the entire life cycle of crops, photosynthesis plays a central role, and chlorophyll is a major participant in this process. It is capable of absorbing light energy and converting it into chemical energy, thereby providing an indispensable energy source for the growth, development, and various physiological and metabolic activities of crops [4]. In agricultural production practices, Cab is a key parameter for farm management such as crop yield prediction [5, 6], precision fertilization [7], and disease prevention and control [8, 9], which theoretically guides the efficient management of crops [10]. Therefore, monitoring the spatial distribution of Cab in rice fields over a large area is of great practical significance for smart agriculture and management of agricultural production in the future [11].

The previous method of destructive Cab measurement has the disadvantages of low efficiency and requiring considerable manpower; therefore, it is not suitable for large-area measurement. In contrast, the UAV remote sensing technology enables accurate, nondestructive testing and assessment of vegetation Cab over a wide range of spatial and temporal scales. UAV remote sensing is becoming one of the most popular means of estimating Cab over large areas. The estimation of Cab relies on the reflectance spectral response properties in the red-edge region (680–760 nm) [12]. Additionally, in recent years, studies have shown that multispectral remote sensing images, e.g., those obtained using DJI Phantom 4 [13], Sentinel-2 [14], and Landsat [15], can be used to realize Cab estimation. However, multispectral images with a low spectral resolution are insufficient to accurately quantify canopy Cab. Hyperspectral images provide richer spectral bands and capture more reflectance information than multispectral images [16]. Numerous studies have shown that the estimation accuracy of canopy chlorophyll from hyperspectral images is usually higher than that from multispectral images [17].

Using canopy hyperspectral data to estimate Cab can be broadly classified into two approaches: data-driven decision models and radiative transfer model inversion methods. The data-driven method is usually implemented by extracting characteristic spectra or constructing vegetation indices and then constructing some connection between the reflectance spectral response characteristics of the red-edge region and the chlorophyll content using a regression algorithm or machine learning model. Vegetation index methods have been widely used and rapidly developed due to their advantages of convenience, simplicity, and certain reliability. Liu et al. estimated the Cab of rice using vegetation indices such as Normalized Difference Vegetation Index, Soil-Adjusted Vegetation Index, and Wide Dynamic Range Vegetation Index as feature variables and a random forest approach [18]. Qiao et al. analyzed the relationship between the response of Cab and the spectra using the maximum information coefficient (MIC) method and constructed the relationship between the Cab and the spectra based on the partial least squares regression to construct a model for detecting the canopy chlorophyll content in maize fields [19]. However, the performance of empirical models is limited by the quantity and quality of measured data used and their inability to address the complex coupling effects of physical parameters such as canopy characteristics, forest floor features, and solar observation geometries [20], which usually become unstable when applied to a wide range of spatial scales of vegetation. In contrast, physical mechanism-driven methods are considered reliable in most cases because they follow basic physical mechanisms and are validated by a large amount of data from a variety of scenarios [21].

Physical mechanism-driven methods are mainly based on the radiative transfer model (RTM), which is a mathematical model that describes the transmission of light within the vegetation canopy. The RTM is capable of calculating the solar radiation within the vegetation canopy based on the radiation characteristics of different frequencies of light and the canopy structure composed of heterogeneous materials such as leaves and the soil background, thereby simulating the canopy reflectance of vegetation [22]. This method provides an important support and basis for vegetation remote sensing applications. The approach based on coupled leaf and canopy RTMs can effectively enable the estimation of leaf biochemical and canopy biophysical parameters. RTMs are categorized into 1DRTMs and 3DRTMs depending on the degree of spatial dimensionality consideration. PROSAIL is the classical 1DRTM model. In the PROSAIL model, the canopy is assumed to be a turbid medium with a random distribution of countless tiny leaf elements. The inversion of the 1DRTM has the advantages of a high computational efficiency, a few inputs, and ease of setting up numerical experiments, and it is widely used in simulating the reflectance of vegetation canopies [23]. However, to simulate canopy reflectance more realistically, many 3DRTMs have been developed that incorporate an explicit 3D description of the canopy structure while considering differences in the optical properties of different vegetation elements [24, 25]. In general, 3DRTMs provide a more realistic spatial description than 1DRTMs, simulate light scattering and reflection more accurately, and are capable of calculating radiation between different media. 3DRTMs, such as Discrete Anisotropic Radiative Transfer (DART) model [26], Radiosity Model Applicable to Porous Individual Objects (RAPID) model [24], and LESS [25], have a high potential and have been used to retrieve the canopy structure and biochemical variables from remotely sensed data. However, the computational effort required to populate the look-up table (LUT) or training dataset when using 3DRTMs is higher than that when using 1DRTMs. Furthermore, a higher number of variables and parameters are required for the 3D description of the canopy structure, and the possible ambiguities among the variables during the inversion process are higher. Therefore, this poses challenges to the estimation of Cab.

Several techniques have been proposed for 3DRTM inversion, including artificial neural networks (ANN) [27], variational techniques [28], and LUT [29]. In recent years, the rapid development of parallel computing and network technology has accelerated the optimization of time-consuming search algorithms. Parameter optimization algorithms are used to find the optimal combination of parameters in the parameter space of a problem to achieve the optimal value of an objective function, and common parameter optimization algorithms include particle swarm optimization, simulated annealing, genetic algorithms, and sparrow search algorithm (SSA). In this study, the SSA was used to construct an inverse model that overcomes the challenges of nonlinear and complex model selection [30]. Furthermore, because 3DRTMs can provide a more accurate description of canopy spectra, the matching results tended to be better in the inversion process, and together with assimilation with high-resolution remote sensing data, the model results were closer to actual observations.

In order to establish a physics-based chlorophyll estimation model and to explore a suitable strategy for estimating Cab, the objectives of this study were as follows:

• (1) The 3D structure of a cluster of rice needs to be simulated and input into the LESS model to simulate the response of Cab to canopy reflectance.

• (2) The performance of the inversion algorithm needs to be evaluated using the SSA in the estimation of Cab in rice.

• (3) The accuracy of the relevant Cab variables needs to be improved by setting the a priori parameter values and penalty function constraints in the joint inversion model.

• (4) The performance of the LESS model needs to be evaluated by comparing the 1DRTM model with the 3DRTM model.

Methods

Experimental region

The test site is located at the Shenyang Agricultural University’s Precision Agriculture Aviation Research Base in Haicheng City, Liaoning Province, within Gengzhuang Town, geographically marked by a latitude of 40° 58’ 45.39” north and a longitude of 122° 43’ 47.00” east, as shown in Fig. 1. Characterized by a warm temperate monsoon climate, the region experiences an average annual temperature of 10.4 °C and an average annual precipitation of 721.3 mm. The rice variety under test, ‘Shennong 9816’, is a popular choice for cultivation in Liaoning. The experimental period spanned from June to August 2023, with the primary objective being to measure the hyperspectral reflectance and to assess the structural and biomass attributes of the rice.

The experimental design encompasses five distinct nitrogen fertilizer treatments, namely N0, N1, N2, N3, and N4. The N0 treatment serves as the control group, with no application of basal fertilizer. The N3 treatment represents the local standard for nitrogen-based fertilizer application. N1 and N2 are designated as low nitrogen fertilization levels, with nitrogen fertilizer applications at 50% and 75% of that in N3, respectively. Furthermore, N4 is set as the high nitrogen application level, with nitrogen fertilizer application at 125% of N3. Phosphorus and potassium fertilizers are applied according to local standards, with the standard application rate for phosphorus fertilizer being 144 kg/hm² and for potassium fertilizer being 192 kg/hm². All other field management practices adhere to local standards. Sampling was conducted weekly, with three samples collected from each plot, resulting in a total of 83 sets of valid samples.

Fig. 1

Geographic location of the study site, plot delineation of the experimental field, and distribution of the four nitrogen fertilizer treatments

Data collection

Preprocessing of hyperspectral remote sensing images of rice canopy acquired using unmanned aerial vehicles

Canopy hyperspectral images were acquired using the M600 PRO hexacopter UAV from Shenzhen DJI equipped with the GaiaSky-mini airborne integrated push scanner hyperspectral imaging system from Sichuan Shuanglihepu. The hyperspectral band range was 400–1000 nm, the sampling interval was 3 nm, the effective number of bands was 201, and the spatial resolution of the hyperspectral image was 3.5 cm. Before starting the data collection task, it is necessary to calibrate the hyperspectral sensor first. In this experiment, a 60% diffuse reflectance standard panel calibration was adopted for the radiometric correction of the hyperspectral data to ensure the sensitivity and accuracy of the sensor. Adjust the lens angle to be vertically downward. After the UAV takes off, it flies towards the due north at a flight altitude of 100 m. When it flies above the rice samples, it remains hovering, and the sensor is manually controlled to record the hyperspectral image data, and the hyperspectral data of the rice was obtained from 11 to 12 noon. This period was selected for data acquisition because the sunlight was strong and stable at this time.

The acquired hyperspectral data were preprocessed as follows: First, the ortho-visible remote sensing image captured by DJI Elf 4-RTK drone was used to align the geographic information of the hyperspectral image, and then, ENVI5.6 + IDL tool software was used to extract the hyperspectral data from the plots of the acquired hyperspectral remote sensing image. Then, the spectral angle filling method was used to remove the influence of the spectra of the interfering features, and thereafter, the average spectral data were calculated for each plot of interest. The average spectrum was calculated for the area of interest of each plot, and then, the average spectrum was resampled using the spectral resampling method with a spectral resolution of 3 nm. Finally, the resampled spectrum was denoised using the Savitzky–Golay filter, and the results were used as the hyperspectral information for the experimental plots.

Measurement of biomass of rice leaves

To ensure the leaf activity, during the destructive sampling of the rice, a cluster of rice with the roots was dug out together with the soil on the roots and placed in labeled self-sealing bags. Furthermore, to identify the sampling point position in the hyperspectral image, a handheld RTK instrument was used to locate and record the center of the sampling point. The samples were placed in a low-temperature insulated box and brought back to the laboratory. The chlorophyll and carotenoid contents were obtained using the extraction colorimetric method, detailed as follows: First, fresh rice leaves were washed and dried. A 1 g sample of the plant material was mixed and ground thoroughly with quartz sand to ensure complete homogenization. Then, 95% ethanol solvent was added to the mixture to reach a final volume of 100 ml. Next, the container with these samples was placed in a thermostatic thermostat and heated for 20 min at 60 °C. A blank ethanol solvent sample was used to calibrate the spectrometer, and then, the extract was poured into a cuvette and placed in the spectrophotometer, where the absorbance was measured at specific wavelengths of 663 nm and 645 nm for chlorophyll a and chlorophyll b, respectively, and at 450 nm for carotenoids. Finally, the chlorophyll and carotenoid contents were calculated using the measured absorbance values and the corresponding calculation formula. The determined biochemical parameters are listed in Table 1, with Std representing the Standard Deviation and CV indicating the Coefficient of Variation.

Table 1 Descriptive statistics of canopy Leaf Area Index (LAI), Car, and cab at different days (DAT) after rice transplantation at the Haicheng experimental field

Determination of structural parameters of rice

Three rice plants that were exemplars of healthy growth were selected from each experimental plot. These selected plants were subjected to precise fixed measurements to ensure the accuracy of the data collected. Morphological data of the rice were systematically gathered weekly. This regular data collection was instrumental in tracking the chronological development of the main stem leaves. A ruler, protractor, and vernier calipers were used to determine the morphological indices such as the length of the leaf blade of the main stem, maximum width of the leaf blade, stem–leaf angle, leaf blade height, stem node length, stalk diameter, and plant height. Among them, the leaf blade length is the straight line distance from the bottom of the leaf blade to the tip of the leaf blade when the leaf is laid straight. In addition, the maximum width of a leaf is typically located at its midsection, and the leaf inclination angle is defined as the angle between the leaf and the horizontal plane. Furthermore, the height of the leaf blade is the distance from the ground to the joint between the leaf blade and the stem, and the height of the plant is the distance from the ground to the tip of the tallest leaf of the rice plant.

Generation of 3D scenes of rice paddies

Based on the structural data such as the tiller number, leaf length, and leaf inclination angle of rice collected, 83 3D models of different rice structures were drawn by using the Plantfactory software. Moreover, the values of the LAI and leaf inclination angle distribution of these rice plants were calculated. Since the experimental field in this study adopted machine transplanting, the row and column spacing of the rice was consistent, with a row spacing of 0.3 m and a column spacing of 0.25 m. Combining the values of LAI and leaf inclination angle distribution in the experimental field collected by LAI-2200, appropriate rice plants were selected successively in the 3D rice models according to the row and column spacing, and the 3D scene of the rice field was reconstructed, as shown in Fig. 2. Through this method, a rice field scene capable of accurately simulating the spectral response of the rice canopy was constructed.

Fig. 2

3D model and scene of rice used for simulating canopy hyperspectral data in LESS

Canopy reflectance simulation using the LESS model

LESS is a 3DRTM that simulates radiative transfer processes in complex scenes and rapidly generates large-scale remote sensing images [25]. Users can construct simplified or feature-detailed 3D objects and then simulate the BRF of the rice canopy by assigning spectral attributes to the 3D components. Specifically, LESS employs a hemispherical equal-area subdivision method, placing the scene within a virtual hemisphere and dividing it into $\:{N}_{p}$ equal-area microelements. It is assumed that a hyperspectral imager is located within a specific microelement, and then the vegetation canopy reflectance of the microelement where the hyperspectral imager is situated is calculated according to Eq. 1.

$${f_{BR{F_i}}} = {{\pi \sum\limits_P {{Q_{ \in \Delta {\Omega _i}}}} \cdot {P^0} \cdot \Pi _{q = 1}^Q{{\pi f\left( {q,{\omega _i},{\omega _0}} \right)} \over {{p_q}}}} \over {\Delta {\Omega _i} \cdot \cos \theta _i^C \cdot {P_{{\rm{scene }}}}}}$$

(1)

where $\:{f}_{BR{F}_{i}}$ is the reflectance at the facet element 𝑖, $\:\varDelta\:{{\Omega\:}}_{\text{i}}=\frac{2{\uppi\:}}{{\text{N}}_{\text{p}}}\varDelta\:{\varOmega\:}_{i}=\:\frac{2\pi\:}{{N}_{p}}$ is the stereo angle corresponding to each facet element, $\:{\theta\:}_{i}^{c}$ is the central zenith angle of the facet element i, and $\:{P}_{scene}$ is the energy collected by the reference plane at the top of the scene. Furthermore, $\:{P}_{i}^{A}$ is the total photon energy collected by the facet element 𝑖, i.e., $\:{P}_{i}^{A}=\:\sum\:_{{P}^{Q}\in\:\varDelta\:{\varOmega\:}_{i}}{P}^{Q}$, and $\:{P}^{Q}$ denotes the energy of photons corresponding to Q collisions. $\:f(q,{\omega\:}_{i},{\omega\:}_{0})$ indicates the bidirectional scattering distribution function (BSDF) at the 𝑞th intersection point. As is clear from Eq. 1, the basic inputs to the LESS model are the 3D structure of the scene, component spectra, observation geometry, and light parameters, which are simulated by ray tracing to obtain canopy hyperspectral data.

The component spectra of rice leaves can be generated using the PROSPECT model simulation. The model is based on the principle that the reflection, transmission, and absorption of light incident on leaves depend on the chemical and physical properties of these leaves. It is essentially a function of the changes in the spin and angular momentum of photons; the transitions between photon orbital states in Car, Cab, brown pigments, and other accessory pigments; and the vibrational rotational modes within water and biomass [31]. Thus, the simulation of the leaf layer spectra using the modified model can be abstracted as a function of the relevant leaf structural parameters (N), Cab, Car, the equivalent water thickness (Cw), and biomass (Cm). In summary, the link between the Cab and canopy spectra of rice can be established by coupling the LESS and PROSPECT models.

As mentioned earlier, the inputs to the coupled model can be divided into three parts: the 3D structure, the biochemical components in PROSPECT, the light geometry and the observation geometry. The 3D structure is constructed as discussed in Sect. 2.3. The biochemical component parameters have the same range of values as the actual collection data. The light geometry is determined based on the collection time and location, while the observation geometry remains a constant value. This fixed observation geometry is adhered to consistently each time the UAV gathers spectral data. The detailed parameter configuration is shown in Table 2.

Table 2 Configuration of rice parameters in PROSPECT and LESS models

1DRTM canopy reflectance simulation

PROSAIL is a 1DRTM that is a PROSPECT blade scale optical model coupled with a bidirectional reflectance SAIL model of the vegetation canopy, which is commonly used for estimating vegetation canopy parameters at the satellite and UAV scales over large areas. The SAIL model considers the vegetation canopy as a homogeneous, planar surface with attributes such as the tilt angle of the blade and LAI. The model parameters are shown in Table 3.

Linear constraints on carotenoids

Carotenoids and chlorophyll have a strong linear relationship in the early and middle growth stages of many plants. Linear regression analysis was performed on the collected calcium and carbon values of rice. A strong linear relationship was observed between Car and Cab in this experiment [coefficient of determination (R²) = 0.902; root mean square error (RMSE) = 24.638 µg/cm²)], as shown in Fig. 3. Therefore, the linear constraint of chlorophyll and carotenoids can be added to the objective function of the SSA in the form of a penalty function, as shown in the following equations:

$$\:\widehat{f}\left(x\right)=f\left(x\right)+\varnothing\:g\left(x\right)$$

(2)

$$\:g\left(x\right)=\:\left\{\begin{array}{c}0,\:5.928*Car-3.517\\\:\:\:\:\:\:\:\:\:\:\:\:\le\:Cab\le\:\\\:\:\:\:\:\:\:\:\:\:\:\:\:\:6.826*Car+0.717\\\:1,\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:other\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\end{array}\right.$$

(3)

Table 3 Configuration of rice parameters in PROSAIL models

Fig. 3

Relationship between Cab and Car

Strategies for estimating cab in rice

The main methods used to estimate the Cab of vegetation through a physically based RTM include machine learning methods and LUT methods. This study simulates the spectral response of rice canopies based on a 3DRTM and inverts Cab using an optimization algorithm based on actual collected canopy spectra. The flowchart of the work done in this study is shown in Fig. 4:

Fig. 4

Strategy flowchart for estimating Cab using a joint inversion model

• Step 1: LESS coupled with the PROSPECT model to simulate canopy spectra: The main inputs to the LESS model were environmental covariates, leaf spectra, and rice 3D structure. The establishment of the link between Cab and canopy reflectance spectra is not possible. To establish a mathematical model that links canopy spectra to chlorophyll content, the PROSPECT-5 model was coupled with the LESS model. The PROSPECT-5 model simulates the spectral response of plant leaves by inputting biochemical variables such as Cab and Car. The LESS model simulates the spectral response of plant canopies by inputting parameters such as 3D structure, leaf spectra, and light geometry. By coupling the PROSPECT-5 model with the LESS model, a connection between Cab and canopy spectra was established.

• Step 2: SSA inversion model: Some parameters of the LESS model coupled with the PROSPECT joint inversion model, such as the rice leaf structure N, rice 3D structure, and environmental covariates, were selected as known variables whose types were measured or fixed, while Car, Cab, and Cw were optimized iteratively. In each iteration, the joint inversion model simulated the canopy reflectance with these variables. After reaching the maximum number of iterations, the values of Car, Cab, and Cw are determined by minimizing the sum of squared errors (SSE) between the simulated and measured spectra, as follows:

$$\:SSE={\sum\:}_{\lambda\:=400}^{700}{\left({\rho\:}_{\lambda\:}-{\rho\:}_{\lambda\:}^{{\prime\:}}\right)}^{2}$$

(4)

where λ is the wavelength between 400 nm and 1000 nm, and and $\:{\rho\:}_{\lambda\:}^{{\prime\:}}$ are the reflectance values at λ for the simulated and measured spectra, respectively. To optimize the parameters, we used a swarm intelligence optimization technique, the SSA.

• Step 3: Performance optimization of joint inversion models: Based on the idea that Cab and Car have a strong positive correlation, an a priori equation was proposed. Moreover, the results of the sensitivity analysis of the system showed that in the 400–700 nm band, Cw and Cm contributed very little to the spectral reflectance. Then, the optimal N value of rice was selected through the analysis of the canopy spectra results with different N values. Thus, the problem of different spectral characteristics for the same object can be solved, thereby improving the inversion accuracy.

To test the predictive effectiveness of the method, R² and RMSE were used. The minimum RMSE and maximum R² to evaluate the performance of the proposed method are calculated as follows:

$$\:{R}^{2}=1-\frac{{\sum\:}_{i=1}^{n}{\left({y}_{i}-\widehat{{y}_{i}}\right)}^{2}}{{\sum\:}_{i=1}^{n}{\left({y}_{i}-\stackrel{-}{{y}_{i}}\right)}^{2}},$$

(5)

$$\:RMSE=\sqrt{\frac{{\sum\:}_{i=1}^{n}{({y}_{i}-\widehat{{y}_{i}})}^{2}}{n}},$$

(6)

where $\:{y}_{i}$ is the true value of the sample, $\:\widehat{{y}_{i}}$ is the predicted outcome value, and n is the total number of samples.

Results

LESS model sensitivity analysis and input parameter optimization

We analyzed the sensitivity of the reflectance spectra simulated using the LESS model from 400 nm to 1400 nm to different input parameters, and the results are shown in Fig. 5. The response characteristics of the spectra were analyzed by increasing the number of selected input parameters to a specific number while keeping the number of other parameters fixed. The results showed that Cab values had a strong effect on the simulated spectra from 400 to 700 nm, especially in the green light band from 500 to 560 nm; the smaller the Cab value was (10–50), the larger the value of the spectral reflectance was (Fig. 5A), a result that is in accordance with the optical properties of chlorophyll. The Prospect-D leaf structural parameter N affected the simulated spectra of the canopy from 400 to 1400 nm (Fig. 5B), reflecting a positive correlation between the value of N (1–2) and the canopy reflectance. Car also affected the canopy reflectance (Fig. 5C). Furthermore, Car mainly affected the spectral reflectance from 500 to 550 nm. From 400 nm to 700 nm, the effects of Cm and Cw on the spectral reflectance were almost negligible (Fig. 5D and E). The influence of the rice structure on canopy spectral properties was analyzed by controlling the 3D structure inputs of rice at different growth stages. For ease of analysis, the LAI was considered to study the structure of rice at each stage. The results indicated that the rice structure significantly contributed to the canopy spectra from 400 to 1400 nm. As the rice stems and leaves grew continuously during the tillering and nodulation stages, the LAI increased, which in turn led to an increase in the reflectance of the rice canopy.

In conclusion, only Cab, leaf structural parameter N, Car and rice 3D structure contributed in the 400–700 nm spectral band. Therefore, to realize the accurate inversion of rice Cab, the accurate leaf structural parameter N needs to be selected; in addition, the problem of different spectral characteristics with the same object caused by different parameter combinations of Car and Cab needs to be solved.

Fig. 5

Effects of different parameter values on spectra: (A) Cab, (B) N, (C) Car, (D) Cw, (E) Cm, and (F) LAI

Due to the fact that the data collected in this study originates from a single type of rice, the leaf structural parameter N is consistent. In this study, several groups of measured physicochemical parameters were selected and input with different values of N into the model. The simulated spectra of the output were compared with the measured values of the canopy spectra to select the simulated spectra that had the smallest error with the measured spectral values. The corresponding N value was used as a constant model input parameter. As shown in Fig. 6, the minimum error was obtained when N = 1.5. The corresponding SSE was 0.000415.

Fig. 6

Measured spectra and the simulated spectra obtained with different input values of N

LESS simulation of canopy hyperspectral accuracy assessment

The SSA can be used to iteratively optimize the LESS model according to a cost function over a prespecified parameter range to provide the set of variables for which the minimum SSE is considered to be the solution of the inversion. According to Eq. 4, the accuracy of the LESS model in simulating the spectra will have a direct effect on the accurate estimation of Cab. To assess the performance of the forward model, four sets of actual parameters, including rice structure, chlorophyll content, and biomass, were input into the model to generate corresponding simulated canopy reflectance spectra. These simulated spectra were then compared with the actual canopy spectra obtained from field trials. As shown in Fig. 7, the simulated spectra align with the measured spectra in trend, and the differences between them are relatively small across the wavelengths from 400 nm to 700 nm. In addition, the average error value between the 81 measured canopy spectra and the simulated canopy spectra was calculated. The fluctuation of the average error values between different spectral bands is shown in Fig. 8: the average error values in the violet region, that is, the narrow band region of approximately 400–450 nm, were relatively high.

The wax layer and micro-surface structure of the leaves have a greater impact on the reflection and scattering of light in the ultraviolet and blue light bands compared to other bands. When simulating transmitted light using the Monte Carlo method, under the same computational resource conditions, the simulation accuracy for multiple scattering calculations of short-wavelength light is lower than that for other bands [32]. Overall, the SSE between the canopy spectra simulated using the LESS model and the spectra actually collected by drones is small. Therefore, the LESS simulation framework is suitable to be applied to the canopy spectral response in rice fields.

Fig. 7

Comparison between simulated canopy reflectance spectra and real measured spectra

Fig. 8

Average absolute error between canopy spectra and simulated spectra

Evaluating canopy cab retrieval performance of SSA

To evaluate the performance of the SSA in solving the hyperspectral search problem, it was designed to randomly generate 40 sets of parameters as defined in Table 2 according to different rice structures, Cab, Car, Cm, and Cw as simulated real values to be inputted into the LESS model to obtain the 400–700 nm rice canopy hyperspectra and to form a simulated dataset, wherein the input Cab values meet the linear constraints of Car as shown in Eq. 3. The population size of the SSA and the number of iterations were set to 20 and 15, respectively, to optimize the model based on the simulated spectral values. Notably, to accelerate the model optimization process, only Cab and Car were optimized as shown in Eq. 2, while Cm and Cw were inputted as fixed values. Although the simulated datasets had different values of Cm and Cw, the accuracy of the inversion was not affected, and the rate of convergence was much higher than that when these four values were used as parameters at the same time. As shown in Fig. 9, the simulated values were very similar to the optimized values, which again verifies that the inversion of Cab in the 400–700 nm spectral band does not need to take into account the effect of the values of Cm and Cw. The SSA can obtain a high inversion accuracy (R² = 0.996, RMSE = 1.053 µg/cm²), indicating its high quality and potential for hyperspectral optimal value search.

Fig. 9

Comparison between optimized values of Cab and simulated true values

Five measured spectra were randomly selected for optimization in the simulated dataset, the selected population size was 20, and the number of iterations was 20 to trace the convergence process. Figure 7 shows that for the number of iterations between 2 and 15, RMSE values were very low. As shown in Fig. 10, when the number of iterations was between 15 and 20, the SSE of the five spectral curves no longer decreased with the increase in the number of iterations, and the Cab estimation accuracy reached a high value. Therefore, in the case of a population size of 20, when the maximum number of iterations was set to 15, the Cab estimation accuracy met the requirements for practical applications and reduced the time for optimization. Notably, the reduction in the number of input parameters in this experiment was helpful for the SSA to search the optimal values of target variables quickly.

Fig. 10

SSE values of different spectra for different number of iterations

Estimating canopy cab with a car-constrained SSA inversion model

Equation 1 shows that numerous parameters need to be introduced in the process of mimicking the real scene, but too many parameters lead to issues such as more time needed for convergence in the iterative inversion and different spectral characteristics with the same object. The relationship between rice Cab and Car was used as a constraint, which improved the efficiency and accuracy of the inversion process. The Cab was estimated using a joint inversion model driven by the SSA coupled with LESS, with the input variables of the rice 3D structure, canopy spectra, and environmental parameters, and the number of SSA iterations and population size were set to 15 and 20, respectively. Furthermore, the 400–700 nm canopy spectra were selected, and the fixed values of Cw and Cm, which were the input parameters of the LESS model, were optimized according to Eq. 4. In addition, Cab and Car were optimized. Figure 11 shows that the joint inversion model driven by the SSA coupled with LESS can effectively estimate Cab. In particular, the relationship between the content of Car and Cab in rice was utilized as a constraint to effectively enhance the estimation accuracy of the model for Cab. Without the constraint, the model’s estimation accuracy was R² = 0.690, RMSE = 7.677 µg/cm². With the constraint, the model’s estimation accuracy improved to R² = 0.812 and RMSE = 5.413 µg/cm². Compared to the model without constraints, the estimation accuracy with constraints showed an improvement in both R2 and RMSE metrics. Overall, the joint inversion model developed in this study improved Cab estimation in rice.

Fig. 11

Comparison of Cab estimation with and without Car constraints

Moreover, all the studies in this experiment were based on rice at the tillering and nodulation stages. Table 1 shows that from 30 DAT to 63 DAT, when rice was at the tillering and nodulation stages, Cab had a good linear relationship with Car and LAI, and the model exhibited a good performance in estimating Car. At 80 DAT, when the tasseling stage began, Cab exhibits a decreasing trend, while Car shows an increasing trend, and the correlation between Cab and Car is no longer significant. Additionally, the structure of rice becomes more complex, which reduces the accuracy of estimating Car.

Estimation of cab using the 1DRTM

The rice canopy exhibits a complex structure, and its hyperspectral characteristics can be more accurately represented using a 3DRTM as opposed to a 1DRTM. The inaccurate representation of the 3D structure of rice may result in the same Cab value corresponding to different canopy structures and different radiative responses, which will affect the accurate estimation of Cab, as shown in Fig. 5. To verify the superior performance of the 3DRTM in inverting rice Cab, in this study, the capabilities of the 3DRTM LESS and the 1DRTM PROSAIL to estimate Cab accurately were compared based on the turbid medium assumption. In addition, the parameter settings in PROSAIL were consistent with those in LESS, and both used the SSA. The R² and RMSE results showed that the Cab estimation accuracy of the 3DRTM (R² = 0.812, RMSE = 5.413 µg/cm², as shown in Fig. 11) was higher than that of the 1DRTM (R² = 0.728, RMSE = 6.914 µg/cm², as shown in Fig. 12).

Fig. 12

Measured Cab and PROSAIL estimated Cab

Discussion

Inversion accuracy analysis of SSA and constraint methods for multisolvability problems

The SSA has characteristics such as high stability, strong global search capability, and fast convergence speed. As shown in Fig. 10, the algorithm converges with a population size of 20 and an iteration count of 15. As the optimization outcomes approach convergence, the performance of the optimization algorithm is fully realized. Nevertheless, due to the complexity of the RTM, describing its process requires numerous parameters, inevitably leading to the problem of multiple solutions, which limits the inversion accuracy [33].

To further improve the accuracy of the model inversion, the issue of multiple solutions was first addressed using a prior information. The algorithm is highly sensitive to errors in these parameters, and the accuracy of the inversion model is directly influenced by the model’s precision and the accuracy of a prior information introduced [34]. In addition, by analyzing the effect of different chemical component contents on the spectrum from 400 nm to 1400 nm and selecting the bands that are sensitive to changes in Cab and insensitive to changes in Cw and Cm, it was found that the spectral bands in the range of 400 nm to 700 nm satisfy the above conditions. Finally, utilizing the strong correlation between Cab and Car, this relationship is employed as a penalty function to constrain the values of Cab., which significantly limited the multiple-solution problem of the inversion model, as shown in Fig. 11. Clearly, using the correlation of rice biochemical parameters as constraint information in the inversion model can improve the SSA based inversion model by limiting the multiple-solution problem.

Exploration of other means of inverting cab constraints during the late growth period of rice

In the late developmental stages of rice, the physiological state of rice plants undergoes significant changes, and the metabolic activities in the leaves provide more nutrients to the grains. Under these circumstances, the metabolic rates and pathways of chlorophyll and carotenoids are no longer synchronized, resulting in a weakened correlation between the two [35]. Clearly, in the heading stage of rice growth and development, Car can no longer be used as a penalty function to constrain the estimation of Cab in the inversion of Cab. As shown in Fig. 13A and B, the values of Cab and Car change asynchronously with the growth and development of rice, which predicts that the accuracy of chlorophyll inversion will decrease. The rice plants collected in the experiment were affected by different N concentrations of fertilizer. The in-depth exploration of the physical and chemical parameters of the samples revealed significant differences in LAI, Cab, and Car between low- and high-nitrogen-concentration treatments, as shown in Fig. 13. For all concentrations, the values of Cab and Car continuously increased between 30 and 60 DAT, and these values for the different concentrations differed substantially at 81 DAT. This could be due to the slower growth and development of rice at low nitrogen concentrations. However, at high nitrogen concentrations, the rapid growth and development of rice led to a decrease in Cab, consistent with previous research findings [36]. In contrast, Car continued to increase under high nitrogen concentrations, showing a significant negative correlation with Cab under high nitrogen concentrations. As shown in Fig. 13A and C, for low and medium nitrogen concentrations, Cab and LAI exhibited the same trends. The nitrogen fertilizer treatment significantly affected leaf chlorophyll values and altered the canopy structure. Therefore, the quantitative simulation of canopy leaf chlorophyll values should consider fertilization levels and different growth stages. For late rice, the relationship between Car and LAI and Cab can be considered separately for different N fertilizers.

Fig. 13

The variations in rice parameters under different nitrogen fertilizer contents at various DAT: (A) Cab, (B) Car, (C) LAI

Novelty and limitations of inversion models

In this research, a 3DRTM was innovatively applied to chlorophyll estimation in rice fields. The LESS model was used to simulate the canopy spectra of rice, and the inverse model of Cab was established based on SSA. A 3D structure of the rice field was also constructed for the 3DRTM, and the accuracy of the structure was adequate for the estimation model. The inversion of RTMs based on search algorithms is essentially an ill-conditioned problem because various combinations of canopy parameters may produce similar spectra [37]. The use of a priori information is an effective strategy to solve this problem and improve the accuracy of canopy parameter inversion. In this study, a priori information was used to construct the joint inversion model by taking N, Cw, and Cm as model constant inputs based on the sensitivity analysis results; furthermore, the strong linear relationship between Car and Cab was used to constrain the estimates throughout the estimation process. The successful application of the joint inversion model proposed in this study gives us confidence in the accurate monitoring of Cab in rice. The RTM method provides high accuracy and portability for estimating canopy variables, but the existence of complex and diverse environments still poses challenges to the model’s portability. This study focuses on the performance of ‘Shennong 9816’ rice and does not involve other rice varieties, which may limit the generalizability of the conclusions. Adjustments to key parameters may be necessary under different conditions [38]. Further research on multiple rice varieties is needed to explore the versatility of the model. Additionally, in the construction of 3DRTMs for rice, the influence of stems on canopy spectra has not been considered. The stems of rice play a role in the optical processes of reflection, refraction, and absorption of light, thereby altering the characteristic representation of canopy spectra. The existing construction schemes have omitted this crucial aspect, resulting in a certain deviation between the constructed three-dimensional radiation scenarios and the actual rice growth environment. Therefore, to improve the construction of rice 3DRTMs, more effort should be invested in further detailed and systematic research on the impact of stems on canopy spectra.

Conclusions

This study has evaluated the performance of the RTM to simulate the spectral characteristics of rice canopies and the accuracy of inverting rice Cab using the SSA. The study found that the problem of multiple solutions is inevitable during the inversion process, but the introduction of constraints can effectively optimize the outcomes. The findings indicated that the constrained 3DRTM and SSA coupled model can achieve a relatively good estimation of Cab. The appropriate range of the target variables for rice can, in principle, be applied to data obtained at different growth stages. Future studies should construct models for estimating chlorophyll content in different rice varieties using radiative transfer models to verify the generalization of the RTM method. Parameter search methods can offer an alternative approach for inverting crop remote sensing radiative transfer models and hold significant potential in the numerical optimization for inverting radiative transfer models. Finally, the joint inversion model developed in this study shows potential for estimating rice Cab. Future research should focus on estimating Cab across large areas of different types of rice fields using multiple remote sensors. Moreover, further exploration is needed to simplify the representation of rice field scenarios and their effect on Cab estimation.