Improving Field-Scale Wheat LAI Retrieval Based on UAV Remote-Sensing Observations and Optimized VI-LUTs

: Leaf area index (LAI) is a key biophysical parameter for monitoring crop growth status, predicting crop yield, and quantifying crop variability in agronomic applications. Mapping the LAI at the ﬁeld scale using multispectral cameras onboard unmanned aerial vehicles (UAVs) is a promising precision-agriculture application with speciﬁc requirements: The LAI retrieval method should be (1) robust so that crop LAI can be estimated with similar accuracy and (2) easy to use so that it can be applied to the adjustment of ﬁeld management practices. In this study, three UAV remote-sensing missions (UAVs with Micasense RedEdge-M and Cubert S185 cameras) were carried out over six experimental plots from 2018 to 2019 to investigate the performance of reﬂectance-based lookup tables (LUTs) and vegetation index (VI)-based LUTs generated from the PROSAIL model for wheat LAI retrieval. The e ﬀ ects of the central wavelengths and bandwidths for the VI calculations on the LAI retrieval were further examined. We found that the VI-LUT strategy was more robust and accurate than the reﬂectance-LUT strategy. The di ﬀ erences in the LAI retrieval accuracy among the four VI-LUTs were small, although the improved modiﬁed chlorophyll absorption ratio index-lookup table (MCARI2-LUT) and normalized di ﬀ erence vegetation index-lookup table (NDVI-LUT) performed slightly better. We also found that both of the central wavelengths and bandwidths of the VIs had e ﬀ ects on the LAI retrieval. The VI-LUTs with optimized central wavelengths (red = 612 nm, near-infrared (NIR) = 756 nm) and narrow bandwidths (~4 nm) improved the wheat LAI retrieval accuracy ( R 2 ≥ 0.75). The results of this study provide an alternative method for retrieving crop LAI, which is robust and easy use for precision-agriculture applications and may be helpful for designing UAV multispectral cameras for agricultural monitoring.

. Summary of LAI retrieval based on LUTs generated from the PROSAIL model.
The objectives of this study were to (1) search for a feasible LUT strategy for field-scale LAI retrieval using multispectral UAV images, and (2) improve the easiness to use, robustness, and accuracy of this method so that it can provide precise agronomic information at field scale. To that purpose, the performance of reflectance-LUT and VI-LUT strategies generated by the PROSAIL model for LAI retrieval were investigated using multispectral UAV images; the central wavelengths and bandwidths of the red and NIR bands for VIs calculations on LAI retrieval were evaluated and further optimized using UAV hyperspectral images.

Study Area and Long-Term Experimental Plots
UAV observations were conducted at the Yucheng Comprehensive Experiment Station (YCES) of the Chinese Academy of Sciences (36.83 • N, 116.57 • E), which is located along the north side of the Lower Yellow River (Figure 1). The study area has a warm temperate and a semi-humid monsoon climate with an approximate annual mean temperature of 13.4 • C and an average annual precipitation of 576.70 mm, concentrated between July and September. The YCES is dominated by a typical cropping system of winter wheat (October-June) and summer maize (July-September).
further optimized using UAV hyperspectral images.

Study Area and Long-Term Experimental Plots
UAV observations were conducted at the Yucheng Comprehensive Experiment Station (YCES) of the Chinese Academy of Sciences (36.83° N, 116.57° E), which is located along the north side of the Lower Yellow River (Figure 1). The study area has a warm temperate and a semi-humid monsoon climate with an approximate annual mean temperature of 13.4 °C and an average annual precipitation of 576.70 mm, concentrated between July and September. The YCES is dominated by a typical cropping system of winter wheat (October-June) and summer maize (July-September).
We selected six types of long-term experimental plots with different tillage treatments, soil water content, and nutrient levels for experiments ( Figure 1 and Table 2). All the experimental plots had been operational for >10 years. Owing to the obvious differences in crop traits caused by the existing gradients of agricultural treatments, the crop LAI dynamic range was large. Thus, the study area was perfect for UAV remote-sensing experiments.   We selected six types of long-term experimental plots with different tillage treatments, soil water content, and nutrient levels for experiments ( Figure 1 and Table 2). All the experimental plots had been operational for >10 years. Owing to the obvious differences in crop traits caused by the existing gradients of agricultural treatments, the crop LAI dynamic range was large. Thus, the study area was perfect for UAV remote-sensing experiments.   Leaves of wheat were collected via destructive sampling for LAI measurements in the laboratory ( Figure 2). The row spacing of all experimental plots was 20 cm. In order to ensure the reasonability and typicality of the study, wheat with relatively uniform canopies outside the border areas of each plot was selected for the experiment. A row of wheat with a length of 0.5 m was cut for LAI measurements. The leaf area was measured using an LI-3000C Leaf Area Meter (Li-COR Biosciences, Lincoln, NE, USA). The average LAI of each plot was calculated according to where TLA (m 2 ) represents the total leaf area of crops within each plot, and a (m) and b (m) represent the width and length of each plot, respectively. Because wheat is row crops, the TLA was calculated according to where LA (m 2 ) represents the measured leaf area of crops harvested within each plot, nrows represents the number of rows for each plot. With UAV flights, three LAI datasets were collected for evaluation of the LAI retrieval accuracy (Table 4). Each dataset exhibited a high coefficient of variation (CV) owing to the wide range of agricultural treatments, which contributed to a good model fit between the measured and simulated LAI. Because the flight coverage of the multispectral UAV observations (all six fields) differed from that of hyperspectral UAV observations (see Figure 1 for the two red rectangles), the number of ground samples for the LAI estimation was different for 15 May 2018.  Leaves of wheat were collected via destructive sampling for LAI measurements in the laboratory ( Figure 2). The row spacing of all experimental plots was 20 cm. In order to ensure the reasonability and typicality of the study, wheat with relatively uniform canopies outside the border areas of each plot was selected for the experiment. A row of wheat with a length of 0.5 m was cut for LAI measurements. The leaf area was measured using an LI-3000C Leaf Area Meter (Li-COR Biosciences, Lincoln, NE, USA). The average LAI of each plot was calculated according to LAI (m 2 /m 2 ) = TLA/(a × b) (1) where TLA (m 2 ) represents the total leaf area of crops within each plot, and a (m) and b (m) represent the width and length of each plot, respectively. Because wheat is row crops, the TLA was calculated according to where LA (m 2 ) represents the measured leaf area of crops harvested within each plot, nrows represents the number of rows for each plot. With UAV flights, three LAI datasets were collected for evaluation of the LAI retrieval accuracy (Table 4). Each dataset exhibited a high coefficient of variation (CV) owing to the wide range of agricultural treatments, which contributed to a good model fit between the measured and simulated LAI. Because the flight coverage of the multispectral UAV observations (all six fields) differed from that of hyperspectral UAV observations (see Figure 1 for the two red rectangles), the number of ground samples for the LAI estimation was different for 15 May 2018.    Figure 3 for the DJ M100 four-rotator UAV (SZ DJI Technology Co., Shenzhen, Guangzhou, China) and DJ M600 Pro six-rotator UAV (SZ DJI Technology Co., Shenzhen, Guangzhou, China) equipped with two sensors (Table 5)-Micasense RedEdge-M multispectral camera (MicaSense, Seattle, WA, USA) and Cubert S185 hyperspectral camera (Cubert GmbH, Ulm, Germany)-were used. The two multispectral flights covered all six fields; the hyperspectral flight covered Field B, D, and E (see Figure 1 for the two red rectangles).  Figure 3 for the DJ M100 four-rotator UAV (SZ DJI Technology Co., Shenzhen, Guangzhou, China) and DJ M600 Pro six-rotator UAV (SZ DJI Technology Co., Shenzhen, Guangzhou, China) equipped with two sensors (Table 5)-Micasense RedEdge-M multispectral camera (MicaSense, Seattle, WA, USA) and Cubert S185 hyperspectral camera (Cubert GmbH, Ulm, Germany)-were used. The two multispectral flights covered all six fields; the hyperspectral flight covered Field B, D, and E (see Figure 1 for the two red rectangles).
The UAV flight time of the three flight missions was from 10:00 to 14:00. For radiation correction, the reflectance of a spectral panel was collected during each flight. The radiation correction, image mosaicking, and orthography of the UAV images were conducted using Agisoft Photoscan (Agisoft LLC, St. Petersburg, Russia) and Pix4D Mapper 3.1.22 (Pix4D, S.A., Lausanne, Switzerland). ENVI 5.1 (ESRI, RedLands, CA, USA) and Python 2.7 were used for further data analyses and programming, respectively.    The UAV flight time of the three flight missions was from 10:00 to 14:00. For radiation correction, the reflectance of a spectral panel was collected during each flight. The radiation correction, image mosaicking, and orthography of the UAV images were conducted using Agisoft Photoscan (Agisoft LLC, St. Petersburg, Russia) and Pix4D Mapper 3.1.22 (Pix4D, S.A., Lausanne, Switzerland). ENVI 5.1 (ESRI, RedLands, CA, USA) and Python 2.7 were used for further data analyses and programming, respectively.

Retrieving LAI from UAV Data Using PROSAIL Model
The PROSAIL model, along with the UAV remote-sensing data, was used to retrieve wheat LAI [42]; it is derived from the combination of the PROSPECT blade model and the SAIL canopy structure model [43]. The PROSPECT model simulates the optical properties of leaves, from 400 to 2500 nm, with four inputs: leaf structure parameter (N), chlorophyll content (Chl), leaf water mass per area (LMA), and blade equivalent thickness (EWT). The SAILH model is a radiative transfer model on the canopy scale, in which vegetation is treated as a mixed medium with an assumption that the blade azimuth distribution is uniform [44]. In total, fourteen parameters (N, Chl, EWT, LMA, LAI, leaf carotenoid content (caro), brown pigment content, soil brightness parameter (psoil), hot-spot size parameter (hot spot), solar zenith and azimuth angles, view zenith and azimuth angles, and average leaf angle (ALA)) are required for running the PROSAIL model, most of which are difficult to obtain (Table 6) (e.g., ALA, caro, and hot spot). High-dimensional LUTs are often generated to retrieve LAI because most PROSAIL inputs are difficult to reach in practice [11,24]. The computation processes for high-dimensional LUTs are slow and complex, which may hinder the application of LUTs to parameter inversion. Sensitivity analysis of models is an alternative way to solve this issue. It can identify the sensitive model inputs and evaluate their sensitivity levels; the changes of these sensitive inputs in a certain range will lead to obvious variations of model outputs. Thus some unessential PROSAIL variables can be set as constants so that the dimension of the LUTs decreases [12]. Sensitivity analysis includes local and global analyses. The global analysis can reveal the effects of each input and interaction among inputs on model outputs. In this study, the extended Fourier amplitude sensitivity test (EFAST) was used for global sensitivity analysis. The EFAST is a quantitative method based on variance [45]. The variance produced by the change of model outputs reveals the sensitive values or levels of model inputs [12].
LAI retrieval from the UAV data comprised three steps ( Figure 4). Firstly, select appropriate VIs for LAI retrieval based on the (EFAST) global sensitivity analyses of the PROSAIL model; secondly, generate reflectance-LUTs and VI-LUTs by running the PROSAIL model; thirdly, retrieve LAI through cost functions (see Section 2.3.3 for the formula of cost functions) based on the LUTs. In step 3, both of the multispectral and hyperspectral UAV datasets were used. The multispectral datasets were used to investigate the robustness of LUT strategies for LAI retrieval (step 3.1); the hyperspectral dataset was used to improve the LAI retrieval robustness and accuracy (step 3.2).

Selecting Optimal VIs for LAI Retrieval (Global Sensitivity Analysis)
The global sensitivity analyses were conducted to select VIs for LAI retrieval. First, 5000 model input datasets (Range (EFAST), Table 6) with uniform distributions were generated using the Simlab 2.2.1 software (JRC, Italy). These generated datasets were the simulated inputs of the PROSAIL model. Second, the PROSAIL model was run in a forward mode to obtain model outputs (spectral reflectance) using the PyProSAIL package of Python 2.7 (http://teledetection.ipgp.jussieu.fr/prosail/, accessed on 24 June 2019). Then VIs (Table 7) were calculated using the PROSAIL outputs-spectral reflectance. Thirdly, datasets of the PROSAIL inputs and outputs were used to conduct the EFAST global sensitivity analysis using Simlab 2.2.1.
The reflectance values of the blue (B), green (G), red (R), red-edge (E), and NIR bands were denoted as ρB, ρG, ρR, ρE, and ρNIR, respectively. We selected some VIs that were used for the estimation of crop traits in previous studies (Table 7, where ρ1 = ρNIR). These VIs were divided into three groups: R-VIs (calculated using ρR and ρNIR), G-VIs (calculated using ρG and ρNIR), and E-VIs (calculated using ρE and ρNIR). In this study, variables of VIs were changed; thus VIs with the same formula but different variables were denoted as m-VIs (e.g., modified atmospherically resistant vegetation index (m-ARVI) represents R-ARVI (ρ2 = ρR), G-ARVI (ρ2 = ρG), and E-ARVI (ρ2 = ρE) in the R-VI, G-VI, and E-VI groups, respectively). The global sensitivity analyses were conducted to select VIs for LAI retrieval. First, 5000 model input datasets (Range (EFAST), Table 6) with uniform distributions were generated using the Simlab 2.2.1 software (JRC, Italy). These generated datasets were the simulated inputs of the PROSAIL model. Second, the PROSAIL model was run in a forward mode to obtain model outputs (spectral reflectance) using the PyProSAIL package of Python 2.7 (http://teledetection.ipgp.jussieu.fr/prosail/, accessed on 24 June 2019). Then VIs (Table 7) were calculated using the PROSAIL outputs-spectral reflectance. Thirdly, datasets of the PROSAIL inputs and outputs were used to conduct the EFAST global sensitivity analysis using Simlab 2.2.1.

Generating Reflectance-LUTs and VI-LUTs
Since sensitivity analysis can identify sensitive inputs of a model and evaluate their sensitivity levels, some unessential inputs can be set as constant values for decreasing the dimension of LUTs. For simplifying the LAI retrieval to fulfill the requirement of practical application, we generated two-dimensional (2D) LUTs for LAI retrieval, as previous studies have done [12], which set chlorophyll content and LAI as variables while other parameters in PROSAIL model as constants.
The ranges of the model inputs were determined for wheat according to ground measurements, previous studies [23], and the LOPEX'93 database (http://opticleaf.ipgp.fr/index.php?page=database, accessed on 29 November 2018) (Value (LUT), Table 6). We generated two types of LUTs: the reflectance-LUTs and VI-LUTs, which retrieved the LAI through spectral reflectance and VIs, respectively.

Retrieving LAI through Cost Functions
The cost function was used to find the optimal LAI estimate where p represents the number of input variables (the number of bands for reflectance-LUTs/p = 1 for VI-LUTs). R m represents the measured spectral reflectance/VIs, and R s represents the simulated reflectance/VIs from the PROSAIL model. When the cost-function value reaches the minimum in a given reflectance-LUT/VI-LUT, the simulated LAI is considered to be the optimal estimate. In this section, both of the multispectral and hyperspectral UAV data were used for LAI retrieval; the multispectral data were used for investigating the robustness of LAI retrieval strategies. However, the hyperspectral data were further used for improving LAI retrieval accuracy and robustness. For clear statements, the optimization of LAI retrieval is explained in detail in Section 2.3.4.

Optimizing LAI Retrieval Using Hyperspectral Datasets
The hyperspectral UAV data were used for optimizing LAI retrieval. The central wavelengths and bandwidths of the R and NIR bands for LAI retrieval were assessed to optimize the construction of four UAV-based VIs (m-NDVI, m-MCARI2, m-ARVI, and m-NRI selected by global sensitivity analysis; see Section 3.1); the central wavelengths of the B, G, and E bands were set to constant values of 475, 560, and 717 nm, respectively, according to the specifications of the Micasense RedEdge-M (Table 5).
For evaluating the effects of the central wavelengths and bandwidth on LAI retrieval, four simulated datasets were generated as Table 8 shows. The bandwidths of Datasets 1 and 2 were broad; those of Datasets 3 and 4 were narrow (4 nm). The central wavelengths of R and NIR bands were optimized in Datasets 2 and 4.  Table 10 for the selection of optimal central wavelengths. ** The central wavelengths of NIR bands were 752 nm for m-NDVI, m-NRI, and m-ARVI, and 756 nm for m-MCARI2. Please see Table 10 for the selection of optimal central wavelengths.
The optimal central wavelengths of the NIR and R bands were determined via three steps. First, an autocorrelation analysis was performed between any two hyperspectral bands among 88 bands (600-950 nm, Cubert S185). We set p > 0.05 to find uncorrelated bands since the p value of correlated variables was < 0.05. Second, four selected m-VIs (m-NDVI, m-MCARI2, m-ARVI, and m-NRI; see Section 3.1) were calculated from the combinations of reflectance data determined above. Third, the optimal central wavelengths were determined by the highest Pearson correlation coefficient (r values) between the calculated VIs and the measured LAI.
Then, for evaluating the effects of the bandwidth on the LAI retrieval, the narrow bandwidths of the hyperspectral data were resampled into broad bandwidths (Table 8). Because the spectral resolution of the hyperspectral data (Cubert S185) was relatively coarse (4 nm), we only compared the LAI retrieval accuracy of VIs with a narrow bandwidth (4 nm) and broad bandwidths (equal to those of the RedEdge-M camera; see Table 5).

Statistical Analysis
Python 2.7 was used for statistical analyses, including four statistical indicators for evaluation of the LAI retrieval accuracy: the Pearson correlation coefficient (r), coefficient of determination (R 2 ), root-mean-square error (RMSE), and mean relative error (MRE). The equations for calculating the R 2 , RMSE, and MRE were calculated according to where i represents the sequence number of the array, M i represents the LAI value of the measured LAI array, E i represents the LAI value of the estimated LAI array, M represents the average value of the measured LAI array, and E represents the average value of the estimated LAI array.

Optimal VIs Selected through Global Sensitivity Analyses
Results of the global sensitivity analyses indicate that the B, R, and NIR bands were more sensitive to LAI, whereas the G and E bands were more sensitive to Chl (Figure 5a). Additionally, E and NIR bands were quite sensitive to the average leaf angle (ALA), with values of 0.26 and 0.19, respectively; B and R were quite sensitive to soil-brightness parameter (psoil), with values of 0.35 and 0.27, respectively; G and E were partially sensitive to leaf-structure parameter (N), with values of 0.17 and 0.11, respectively. Compared with the multispectral bands, the average sensitivity values of the VIs to psoil and N decreased to 0.02 and 0.03, respectively. Thus, the LAI, Chl, and ALA were the three most sensitive PROSAIL inputs to the 39 VIs, with average sensitivity values of 0.72, 0.21, and 0.10, respectively. The average sensitivity values of the R-VIs to the LAI, Chl, and ALA were 0.86, 0.03, and 0.13, respectively. Those of the E-VIs were 0.60, 0.39, and 0.06, respectively, and those of the G-VIs were 0.71, 0.22, and 0.10, respectively. The foregoing results indicate that the R-VIs were the most sensitive to the LAI, the least sensitive to the Chl. Therefore, R-VIs were selected for LAI retrieval.

LAI Retrieval Based on Two LUT Strategies Using Multispectral UAV Data
For assessment of the LAI retrieval performance of two LUT strategies, two-year UAV multispectral observations and were used. For reflectance-LUT, the R 2 values were 0.42 and close to zero in 2018 and 2019, respectively, remarkably lower than those for the VIs-LUT (R 2 > 0.74) ( Table 9)  Within the R-VI group, the total sensitivity values of the following six R-VIs to the LAI reached 0.90: nitrogen ratio index in the R-VI group (R-NRI, 0.93), normalized difference vegetation index in the R-VI group (R-NDVI, 0.93), wide dynamic range vegetation index in the R-VI group (R-WDRVI, 0.91), modified improved chlorophyll absorption ratio index in the R-VI group (R-MCARI2, 0.91), atmospherically resistant vegetation index in the R-VI group (R-ARVI, 0.91), and optimized soil adjusted vegetation index in the R-VI group (R-OSAVI, 0.90). R-NDVI, R-WDRVI, and R-OSAVI were calculated using only the R and NIR bands, while R-NDVI was more commonly used and more sensitive to the LAI than R-WDRVI and R-OSAVI. Therefore, R-NDVI, R-NRI, R-MCARI2, and R-ARVI were selected for LAI retrieval. For simplicity, R-NDVI, R-NRI, R-MCARI2, and R-ARVI are denoted as NDVI, NRI, MCARI2, and ARVI, respectively.

LAI Retrieval Based on Two LUT Strategies Using Multispectral UAV Data
For assessment of the LAI retrieval performance of two LUT strategies, two-year UAV multispectral observations and were used. For reflectance-LUT, the R 2 values were 0.42 and close to zero in 2018 and 2019, respectively, remarkably lower than those for the VIs-LUT (R 2 > 0.74) ( Table 9 The foregoing results indicate that the VI-LUT strategy was more robust and accurate than the reflectance-LUT strategy, which offers an alternative method for LAI retrieval. The LAI retrieval from four VI-LUTs corresponded to ground-based measurements ( Figure 6 and Table 9). The R 2 , RMSE, and MRE values for LAI retrieval ranged between 0.74-0.83, 0.33-0.51, and 0.22-0.31, respectively. Overall, the LAI estimation accuracy was similar among the four VI-LUTs, although the NDVI-LUT and MCARI2-LUT performed slightly better. In 2018, the R 2 values of the MCARI2-LUT and NDVI-LUT were close to 0.75, and the RMSE and MRE of MCARI2-LUT were 0.38 and 0.22, respectively (the lowest among the four VI-LUTs), which was consistent with the comparison between the regression line and the 1:1 line (Figure 6c). In 2019, the R 2 value of the MCARI2-LUT was 0.83, higher than the other three VI-LUTs. The RMSE and MRE values of MCARI2-LUT were 0.33 and 0.30, respectively, which were the lowest among the four VI-LUTs. For ARVI-LUT and NRI-LUT, LAI values were slightly underestimated both in 2018 and in 2019. The foregoing results indicate that the VI-LUTs had different characteristics of LAI estimation. Figure 7a shows the results of the autocorrelation analyses (Pearson correlation analysis between any two bands). Figure 7b is the uncorrelated band ranges under the conditions of r < 0.20 and p > 0.05 (n = 89, see Table 4). As the wavelength that located in NIR ranges increases, the signal-noise ratio gradually becomes low and the reflectance will be more easily affected by the absorption of water [50].

Optimization of Central Wavelengths for VI Calculation
Thus, the band ranges over 850 nm were excluded in this study. We selected two appropriate regions: 740-760 nm (ρ 1 bands) and 600-723 nm (ρ 2 bands), along with 740-850 nm (ρ 1 bands) and 703-725 nm (ρ 2 bands).   Figure 7a shows the results of the autocorrelation analyses (Pearson correlation analysis between any two bands). Figure 7 b is the uncorrelated band ranges under the conditions of r < 0.20 and p > 0.05 (n = 89, see Table 4). As the wavelength that located in NIR ranges increases, the signal-noise ratio gradually becomes low and the reflectance will be more easily affected by the absorption of water [50]. Thus, the band ranges over 850 nm were excluded in this study. We selected two appropriate regions: 740-760 nm (ρ1 bands) and 600-723 nm (ρ2 bands), along with 740-850 nm (ρ1 bands) and 703-725 nm (ρ2 bands).

Optimization of Central Wavelengths for VI Calculation
Then, m-NDVI, m-MCARI2, m-ARVI, and m-NRI were calculated using the combinations of ρ1 bands and ρ2 bands within the above-determined ranges. The central wavelengths of the ρ1 and ρ2 bands were refined via Pearson correlation analysis between the calculated VIs and the measured LAI ( Figure 8). The specific bands of ρ1 and ρ2 were determined for four VIs by identifying the highest r value from the correlation plots in Figure 8. As shown in Table 10     Then, m-NDVI, m-MCARI2, m-ARVI, and m-NRI were calculated using the combinations of ρ 1 bands and ρ 2 bands within the above-determined ranges. The central wavelengths of the ρ 1 and ρ 2 bands were refined via Pearson correlation analysis between the calculated VIs and the measured LAI ( Figure 8). The specific bands of ρ 1 and ρ 2 were determined for four VIs by identifying the highest r value from the correlation plots in Figure 8. As shown in Table 10, m-NDVI, m-MCARI2, and m-ARVI exhibited significantly positive correlations with the measured LAI (r > 0.86, p < 0.01, n = 89), while m-NRI was significantly negatively correlated with the measured LAI (r m-NRI = −0.86, p < 0.01, n = 89). Correspondingly, the optimal central wavelengths of m-NDVI, m-ARVI, and m-NRI were all located at 752 nm (ρ 1 band) and 672 nm (ρ 2 band), while the values for m-MCARI2 were located at 756 nm (ρ 1 band) and 612 nm (ρ 2 band).

LAI Retrieval Based on Two LUT Strategies Using Hyperspectral UAV Data
A comparison between the measured and simulated LAI indicates that the VI-LUT strategy with UAV hyperspectral observations was more robust than the reflectance-LUT strategy ( Table 11). The R 2 values for the reflectance-LUTs (≤0.32) were significantly lower than those for the VIs-LUTs (≥0.75), and the RMSE and MRE values for the reflectance-LUTs (RMSE > 2.57, MRE ≥ 2.22) were higher than those for the VIs-LUTs (RMSE ≤ 0.66, MRE ≤ 0.40). Furthermore, among the four proposed VIs, the

LAI Retrieval Based on Two LUT Strategies Using Hyperspectral UAV Data
A comparison between the measured and simulated LAI indicates that the VI-LUT strategy with UAV hyperspectral observations was more robust than the reflectance-LUT strategy ( Table 11). The R 2 values for the reflectance-LUTs (≤0.32) were significantly lower than those for the VIs-LUTs (≥0.75), and the RMSE and MRE values for the reflectance-LUTs (RMSE > 2.57, MRE ≥ 2.22) were higher than those for the VIs-LUTs (RMSE ≤ 0.66, MRE ≤ 0.40). Furthermore, among the four proposed VIs, the MCARI2-LUT was the most robust and accurate strategy for wheat LAI retrieval (R 2 = 0.82, RMSE = 0.37, and MRE = 0.26). Table 11. R 2 , RMSE, and MRE for linear regression between simulated LAI and estimated LAI based on reflectance-LUTs/VI-LUTs using hyperspectral UAV data in 2018 (n = 89).

Evaluation of Optimized VI-LUTs Using Hyperspectral Data for LAI Retrieval
Firstly, we compared datasets with the same bandwidths to reveal the effects of central wavelengths on LAI retrieval. For datasets with a broad bandwidth (Datasets 1 and 2, the dots; see Figure 9), the LAI retrieval robustness for the MCARI2-LUT was improved slightly after optimizing the central wavelengths of the VIs, as its RMSE decreased by 0.22. However, those of ARVI-LUT did not. For datasets with a narrow bandwidth (Datasets 3 and 4, the crosses), after optimizing central wavelengths, R 2 increased obviously by 0.12, 0.10, 0.12, and 0.09 for the NDVI-LUT, ARVI-LUT, MCARI2-LUT, and NRI-LUT, respectively. RMSE decreased by 0.04 and 0.06, and MRE decreased by 0.03 and 0.06 for NDVI-LUT and MCARI2-LUT, respectively. Although RMSE of ARVI-LUT and NRI-LUT slightly increased by 0.02 and 0.01, respectively, overall, optimizing the central wavelengths of datasets with narrow bandwidths could improve the robustness of VI-LUTs for LAI retrieval.
Secondly, we compared datasets with the same central wavelengths to show the effects of bandwidth on LAI retrieval. For datasets with the optimized central wavelengths (Datasets 2 and 4, in red, see Figure 9), overall, the LAI retrieval for datasets with narrow bandwidths was more robust than datasets with broad bandwidths. However, for VIs without optimization of the central wavelengths (Datasets 1 and 3, in black; see Figure 9), overall, the effects of bandwidth on LAI retrieval remained unclear according to the results of this study. These foregoing results indicate that both of the central wavelength and bandwidth affected LAI retrieval.
MCARI2-LUT, and NRI-LUT, respectively. RMSE decreased by 0.04 and 0.06, and MRE decreased by 0.03 and 0.06 for NDVI-LUT and MCARI2-LUT, respectively. Although RMSE of ARVI-LUT and NRI-LUT slightly increased by 0.02 and 0.01, respectively, overall, optimizing the central wavelengths of datasets with narrow bandwidths could improve the robustness of VI-LUTs for LAI retrieval.
Secondly, we compared datasets with the same central wavelengths to show the effects of bandwidth on LAI retrieval. For datasets with the optimized central wavelengths (Datasets 2 and 4, in red, see Figure 9), overall, the LAI retrieval for datasets with narrow bandwidths was more robust than datasets with broad bandwidths. However, for VIs without optimization of the central wavelengths (Datasets 1 and 3, in black; see Figure 9), overall, the effects of bandwidth on LAI retrieval remained unclear according to the results of this study. These foregoing results indicate that both of the central wavelength and bandwidth affected LAI retrieval.

Discussion
Our research indicates that low-dimensional VI-LUTs along with UAV multispectral images were feasible for wheat LAI retrieval, and more robust than reflectance-LUTs. The MCARI2-LUT and NDVI-LUT are recommended for LAI retrieval owing to their better performance. Furthermore, the central wavelengths and bandwidths of a commonly used multispectral camera (Micasense RedEdge-M), can be modified for specific applications. Regarding the LAI retrieval accuracy with two-year multispectral UAV images, the R 2 values of the VI-LUT strategy were >0.74. The R 2 values of the reflectance-LUT strategy were 0.42 in 2018 and close to zero in 2019. In wheat LAI retrieval with four simulated datasets, a dataset with central wavelengths of 756 nm for the NIR band and 612 nm for the R band and a narrow bandwidth (~4 nm) performed the most robustly; the R 2 value of the MCARI2-LUT increased by 0.06, and the RMSE and MRE decreased by 0.18 and 0.10, respectively.

Analyses of LAI Retrieval Performance for Reflectance-LUTs and VI-LUTs
Results of the global sensitivity analyses for PROSAIL model indicate that the LAI was the dominant factor affecting B, R, and NIR bands and VIs, in agreement with previous studies [43,51]. The Chl and ALA were two additional variables that the spectral bands and VIs were sensitive to (see Figure 5). In this study, the VIs were divided into three groups to identify the optimal VI group for LAI retrieval. The results indicate that the R-VIs were the most sensitive to the LAI and could reduce the influences of other PROSAIL variables. The E-VIs and G-VIs were sensitive to the Chl but less influenced by the ALA. This study selected the R-VIs for LAI retrieval. However, E-VIs have also been widely applied in LAI retrieval owing to their capabilities of reducing the impact of the ALA of different crops [17]. But the interactions between crop biophysical (e.g., LAI, ALA) and biochemical parameters (e.g., Chl) may introduce uncertainties in parameter retrieval [28]. Additionally, the red-edge bandwidth is narrow, with a low signal-to-noise ratio and uncertainties in its spectral response [51]. Therefore, in UAV remote-sensing, replacing the traditional red bands (ρ 2 = ρ R ) with red-edge bands (ρ 2 = ρ E ) for VIs calculation on LAI retrieval must be considered in future studies.
The results based on two-year multispectral data indicate that the VI-LUT strategy was able to accurately estimate the crop LAI, and performed more robustly than the reflectance-LUT. In this study, UAV multispectral images were acquired during the wheat grain filling period in different years, which might be an effective way to demonstrate the robustness of LUT method for LAI retrieval. We speculate that because the VIs were expressed as a nonlinear mathematical combination of different bands (Table 7), the differences among sensed objects identified only by G, B, or R reflectance observations would be increased by VI calculations [52]. Previous studies have suggested that VIs can provide information on vegetation phenotyping and reduce some interferences from the soil, atmosphere, and shadows [17,51]. Accordingly, the VI-LUT performed more accurately and robustly than the reflectance-LUT for LAI retrieval. However, the reflectance-LUT strategy is also suitable for LAI retrieval when the spectral bands are not limited [11,18]. Most of the multispectral cameras applied in agriculture, such as the multiSPEC-4C and Micasense RedEdge-M cameras which are commonly used, only include three to six bands; thus, they do not provide sufficient information on spectral reflectance or reduce influences of environmental noises. Therefore, the VI-LUT strategy is a fine alternative method for LAI retrieval and is particularly recommended for precision-agriculture applications with multispectral cameras having limited bands.

Analyses of LAI Retrieval Performance for Different VI-LUTs
In this study, the differences in LAI retrieval among the four VI-LUTs were not obvious. This is because most of the bands used for the VI calculation were the same, leading to a strong correlation between the VIs. However, the VI-LUTs had specific characteristics regarding LAI estimation. The MCARI2-LUT and NDVI-LUT performed slightly better than the other VI-LUTs in this study (Tables 9  and 11). We cannot explain the superiority of NDVI and MCARI2 for LAI retrieval based on the results of this study. However, previous studies have indicated that MCARI2 involving the G band is sensitive to vegetation coverage and types, as the G band can indicate canopy chlorophyll content that is strongly related to the LAI [53,54]. Therefore, MCARI2 is a robust index for LAI estimation [48]. Moreover, in order to make the issue-the better performance of NDVI and MCARI2 for LAI retrieval-more convincing, future studies can further investigate the different formulas and the characteristics of different bands for the calculations of VIs.
Moreover, some VIs, such as NDVI, tend to be saturated for high-density vegetation [14,55]. However, as shown in Figure 6, the saturation problem of VIs was not significant in this study. We speculate that the foregoing results were related to the LAI measurements. In this study, the LAI values were relatively low, compared with previous studies in which the LAI was measured using an LAI-2200, LAI-2000, or digital hemispherical photography (DHP) [56,57]. The LAI measured using an LAI-2200, LAI-2000, and DHP included leaves and other green parts such as stems and ears, whereas the LAI measured using an LI-3000C only includes leaves (no other green parts). We compared the LAI values for the LI-3000C and LAI-2200. The results indicated that the LAI measured using the LAI-2200 was higher than using the LI-3000C. The R 2 value of the regression model was 0.82, indicating that the LAI measurements in this study were feasible. In this study, if the LAI was measured using an LAI-2200, VIs may have underestimated the LAI (with an increased RMSE and MRE); thus, the saturation problem of VIs might occur when the canopy achieves middle-to-high coverage.

Other Issues Regarding LAI Retrieval Accuracy
Both the VIs and LAI could characterize the functional traits of vegetation canopies, but the relationships between the LAI and VIs were nonlinear and varied between the different vegetation types [58]. The LAI retrieval accuracy for maize was lower than that for wheat for both two-year multispectral observations (please see Appendix A Figure A1 and Appendix A Table A1) and one-year hyperspectral observations (please see Appendix A Table A2). The main reason for this might be the different canopy structures. The remotely sensed LAI implicitly refers to green parts that could be either leaves or other green elements of a vegetation canopy [51]. Thus, the LAI is sensitive to plant structure, such as the clump level, leaf angle, and crop height [59,60]. The PROSAIL model was successfully used for various vegetation types. It treats the canopy as a collection of absorbing and scattering tissues randomly distributed in a horizontal layer. Hence, the PROSAIL model is recommended for application to homogenous crops [11,61]. Both maize and wheat are row crops. When they are at the early stage of growth, they have incomplete coverage and strong leaf clumping, and the background reflectance dominates the spectral signal and affects LAI retrieval [43]. At the middle and later growth stages, their canopies tend to be homogenous. Therefore, the PROSAIL retrieval performance was limited for hyperspectral observations of maize at the early stage of growth (R 2 ≤ 0.39) (please see Appendix A Table A2), in agreement with previous studies [62]. Furthermore, the biophysical and biochemical characteristics of vegetation change during different stages. In this study, we did not focus on the effects of phenology on the LAI retrieval. However, continuous UAV observations of critical crop growth periods are required for further validations of the robustness and accuracy of VI-LUTs for LAI retrieval.
Statistical regression models (e.g., a simple linear regression model between vegetation parameters and VIs) and machine-learning models (e.g., random forest models and support vector models) have been widely employed for the retrieval of crop biophysical and biochemical parameters. However, one of the main drawbacks is that their applications are valid only in the areas for which they have been calibrated [63]. The PROSAIL model, as one of the radiative transfer models, can overcome this disadvantage and does not require field measurements in conjunction with remote observations for calibration and validation. Because various combinations of canopy parameters may yield similar spectral reflectance, the ill-posed retrieval problem of the PROSAIL model hinders LAI retrieval. Therefore, a priori information, i.e., ranges of model inputs for model parameterization, is essential. The a priori information is related to many factors, such as the crop types, canopy structure, and growth period of the crops. Thus, the low-dimensional VI-LUT should be modified according to the specific vegetation and growth periods.

Analyses of Optimization for LUT Strategies
In this study, the VI formula structure may also have affected VI calculation in LAI retrieval. Additionally, the central wavelength and bandwidth of VIs affected LAI retrieval. LAI retrieval with four simulated datasets indicate that the VI-LUTs with optimized narrow bands (4 nm) had the highest accuracy. However, the effects of different bandwidths on the accuracy of crop parameter estimation remain unclear. Some hyperspectral narrow bands are sensitive to certain crop parameters, but they might be insensitive to other crop parameters, which may increase the computational loads and distort the accuracy of LAI retrieval [41]. Observational data with broad bands can yield strong reflectance signals, which may reduce the influence of the surrounding environment. Therefore, when selecting the bandwidth in practice, it is essential to achieve a tradeoff between the retrieval sensitivity and the signal-noise ratio.
In summary, this study demonstrates that the VI-LUT strategy based on the PROSAIL model is an alternative method for LAI retrieval with higher accuracy and robustness than the reflectance-LUT strategy. It is valuable for monitoring the crop growth status in precision-agriculture owing to its advantages of simplicity, robustness, accuracy, and saving time and labor. Moreover, the optimization of the central wavelengths and bandwidths of VIs may be helpful for designing multispectral cameras according to specific applications.

Conclusions
The objective of this study was to develop a crop LAI retrieval strategy with accuracy, robustness, and ease of use for UAV remote sensing applications in precision-agriculture at the field scale, which would assist the design of UAV multispectral cameras for agronomic monitoring. The study was conducted using UAV remotely sensed images (two-year multispectral data and one-year hyperspectral data) and the PROSAIL model simulation approach. It was concluded that the low-dimensional VI-LUTs were easy to use and more robust (R 2 ≥ 0.74, RMSE ≤ 0.51, MRE ≤ 0.31 for multispectral datasets) than reflectance-LUTs (R 2 ≤ 0.42, RMSE ≥ 0.94, MRE ≥ 0.70 for multispectral datasets) in crop LAI retrieval based on UAV data. The differences in LAI retrieval among four VI-LUTs were not obvious. However, the MCARI2-LUT and NDVI-LUT performed slightly better than the other VI-LUTs and thus are recommended for crop LAI retrieval. Moreover, both the central wavelengths and bandwidths of the VIs affected LAI retrieval. The hyperspectral UAV data with central wavelengths of 756 nm for the NIR band and 612 nm for the R band and a narrow bandwidth (~4 nm) improved the performance of the MCARI2-LUT for LAI retrieval.
The VI-LUT strategy based on the PROSAIL model, as an alternative method for LAI retrieval at the field scale, is recommended for crop growth monitoring with multispectral cameras having limited bands. The optimized central wavelengths and bandwidths of VIs, as well as corresponding methods of VI optimization, might contribute to improving the design of multispectral cameras onboard UAVs for retrieving vegetation traits in precision-agriculture.