Assessment of Leaf Area Index Models Using Harmonized Landsat and Sentinel-2 Surface Reflectance Data over a Semi-Arid Irrigated Landscape

Abstract

Leaf area index (LAI) is an essential indicator of crop development and growth. For many agricultural applications, satellite-based LAI estimates at the farm-level often require near-daily imagery at medium to high spatial resolution. The combination of data from different ongoing satellite missions, Sentinel 2 (ESA) and Landsat 8 (NASA), provides this opportunity. In this study, we evaluated the leaf area index generated from three methods, namely, existing vegetation index (VI) relationships applied to Harmonized Landsat-8 and Sentinel-2 (HLS) surface reflectance produced by NASA, the SNAP biophysical model, and the THEIA L2A surface reflectance products from Sentinel-2. The intercomparison was conducted over the agricultural scheme in Bekaa (Lebanon) using a large set of in-field LAIs and other biophysical measurements collected in a wide variety of canopy structures during the 2018 and 2019 growing seasons. The major studied crops include herbs (e.g., cannabis: Cannabis sativa, mint: Mentha, and others), potato (Solanum tuberosum), and vegetables (e.g., bean: Phaseolus vulgaris, cabbage: Brassica oleracea, carrot: Daucus carota subsp. sativus, and others). Additionally, crop-specific height and above-ground biomass relationships with LAIs were investigated. Results show that of the empirical VI relationships tested, the EVI2-based HLS models statistically performed the best, specifically, the LAI models originally developed for wheat (RMSE:1.27), maize (RMSE:1.34), and row crops (RMSE:1.38). LAI derived through European Space Agency’s (ESA) Sentinel Application Platform (SNAP) biophysical processor underestimated LAI and provided less accurate estimates (RMSE of 1.72). Additionally, the S2 SeLI LAI algorithm (from SNAP biophysical processor) produced an acceptable accuracy level compared to HLS-EVI2 models (RMSE of 1.38) but with significant underestimation at high LAI values. Our findings show that the LAI-VI relationship, in general, is crop-specific with both linear and non-linear regression forms. Among the examined indices, EVI2 outperformed other vegetation indices when all crops were combined, and therefore it can be identified as an index that is best suited for a unified algorithm for crops in semi-arid irrigated regions with heterogeneous landscapes. Furthermore, our analysis shows that the observed height-LAI relationship is crop-specific and essentially linear with an R² value of 0.82 for potato, 0.79 for wheat, and 0.50 for both cannabis and tobacco. The ability of the linear regression to estimate the fresh and dry above-ground biomass of potato from both observed height and LAI was reasonable, yielding R²: ~0.60.

1. Introduction

One of the most fundamental vegetation biophysical parameters is the Leaf Area Index (LAI), defined as a dimensionless measure of the one-sided leaf area (m²) per unit ground surface area (m²) [1,2]. LAI has long been reported as a good indicator for several agronomic, ecological, and hydrological applications such as vegetation status [3], atmospheric circulation modeling [4], photosynthesis and biomass accumulation [5], evapotranspiration [6], hydrological modeling [6], climate change assessment [7], and predicting rainfall interception [8]. LAI is also crucial in several land surface models [9,10], crop yield models, and yield estimation [11,12].

Remote sensing has proved to be a promising alternative tool for estimating crop LAI quickly over large areas, and without damaging the canopy [13,14]. However, remote sensing requires extensive validation with ground truth data collected over different landcover types [15]. The retrieval of crop biophysical variables from remote sensing falls into two categories: empirical and physical modeling approaches. The simplest method of estimating LAI from remote sensing is by establishing an empirical relationship between the remotely sensed vegetation indices (VIs) and measured LAI, referred to as the LAI-VI approach [16,17]. Vegetation indices are computed based on the reflectance in two or more spectral bands and reflect biophysical characteristics of the plant canopy such as greenness, biomass, and LAI [18,19]. VIs that have shown good correlation with LAI include the normalized difference vegetation index (NDVI) [20], soil adjusted vegetation index (SAVI) [21], enhanced vegetation index (EVI) [22], and enhanced vegetation index 2 (EVI2) [23]. Correlations have been computed using various mathematical forms, such as linear, logarithmic, polynomial, or exponential functions of VIs [5,24].

On the other hand, the physical modeling approach involves the use of radiative transfer models (RTMs) to simulate the canopy spectral reflectance, and the inversion of RTMs to obtain the required parameters [25,26]. Because the inversion of an RTM model can be very computing-intensive, often precomputed look-up-tables (LUTs) are employed for operational use, as in the MODIS LAI product main algorithm [27]. Another modeling technique is the retrieval of LAI biophysical parameters based on neural networks, such as the algorithm implemented in the Sentinel Application Platform (SNAP) biophysical processor tool [28] developed by the European Space Agency (ESA). While SNAP is widely used, the accuracy of the LAI product generated using the SNAP software has not been thoroughly assessed [29,30]. SNAP LAI estimates need to be evaluated over a wide range of crop varieties to assess the general utility of this retrieval approach.

Despite the advances in technology that allow remote sensing to play a vital role in LAI estimation, the trade-off between the temporal and spatial resolution [31] has limited the ability of a single sensor to capture crop LAI dynamics and heterogeneity at the farm level. Several studies pointed out that medium spatial resolution products (e.g., Landsat 30 m spatial resolution) potentially miss observations at critical growth stages due to their long revisit time (16 days) [32,33,34]. Rigorous LAI monitoring, especially during fast-developing crop growth stages, requires daily or near-daily imagery at medium to high spatial resolution (10–30 m) [35,36]. The proven compatibility and good registration between Landsat 8 and Sentinel-2 imaging enable combined LAI estimation at near-daily timesteps and medium resolution [37,38]. In this context, NASA has developed the Harmonized Landsat and Sentinel-2 (HLS) product [39]. HLS consists of surface reflectance (SR) data from the Landsat-8 Operational Land Imager (OLI) and the Sentinel-2 Multi-Spectral Instrument (MSI). The advantage of the HLS product is that it can support near-real-time vegetation monitoring at a medium spatial resolution (<30 m) [39].

THEIA is a French national multi-agency organization that promotes the use of satellite data by public policy actors and scientific community. The THEIA Land Data Center produces and distributes L2A products, including Sentinel-2A and B. S2 L2A data are corrected for atmospheric effects using the MACCS-ATCOR Joint Algorithm (MAJA) [40,41,42,43]. This processor uses multi-temporal information to detect clouds (and cloud shadows) and to estimate the optical properties of the atmosphere. Compared to other S2 atmospheric correction algorithms, MAJA has been shown to achieve better performances for certain land cover types (asphalt, grass, shrubs, pasture, and bare soil) [44]. However, the quality of the S2 images corrected using the MAJA method still needs to be tested over more landcover types and measurement sites.

The present work aims to perform a comparative analysis between LAI generated from three methods: existing vegetation index (VI) relationships applied to Harmonized Landsat-8 and Sentinel-2 (HLS) surface reflectance produced by NASA, the SNAP biophysical model, and L2A THEIA product from Sentinel-2. Evaluation is conducted using ground measurements of LAI conducted in multiple crops in the Bekaa Valley, Lebanon, over two growing seasons (2018–2019). We evaluate whether existing LAI-VI models, initially developed for particular crops, can be applied to the crops sampled in this research irrespective of their limitation to “one place, one time, one equation.” Finally, we establish new LAI-VI site and crop-specific empirical relationships calibrated to local conditions and investigate the crop-specific height and above-ground biomass relationships with LAI.

2. Materials and Methods

2.1. Study Area and Surveyed Crops

The study area is focused on the agricultural scheme of the Bekaa Valley of Lebanon, which is an almost flat plain between two mountain ranges (Figure 1). The total cropland area in the valley is 118,000 ha [45], which accounts for 42% of the total cultivated area in Lebanon [46,47]. The agricultural sector in Lebanon is a key contributor to the country’s agri-food industry. Most of the rural population in the underprivileged regions of Lebanon (Akkar, Dinniyeh, the Northern Bekaa, and the South) rely on agriculture activities, which account for 80% of the local GDP [48]. The study area covers Baalbek (characterized by semi-arid climate) in the 2019 growing season and the North to West Bekaa (characterized by the Mediterranean climate) in the 2018 growing season. Field campaigns were conducted within the study area to acquire ground LAI measurements in several different crop types. In total, 451 fields were surveyed representing a total cultivated area of 5606 ha. A summary of the fields and crops surveyed and measurements collected over the two growing seasons is given in

Table 1. Surveyed crop groups during the 2018–2019 growing seasons, the number of fields and their average areas.

Crop Group	Average Field Area (ha)	Number of Fields	Number of Leaf Area Index Measurements
Herbs	9.3	178	890
(Cannabis: Cannabis sativa,
Mint: Mentha,
Parsley: Petroselinum crispum)
Potato (Solanum tuberosum)	12.4	140	700
Tobacco (Nicotiana tabacum)	5.1	30	150
Vegetables	7.3	66	330
(Bean: Phaseolus vulgaris,
Cabbage: Brassica oleracea,
Carrot: Daucus carota subsp. sativus,
Chickpea: Cicer arietinum,
Corn: Zea mays,
Cucumber: Cucumis sativus,
Lettuce: Lactuca sativa,
Eggplant: Solanum melongena,
Melon: Cucumis melo var. cantalupensis,
Onion: Allium cepa
and Pepper: Capsicum annuum)
Grains	9.9	37	185
(Barley: Hordeum vulgare
and Wheat: Triticum aestivum)
All Crops	9.6	451	2255

. Of the crops studied here, wheat and potato are the two primary strategic cash crops of the Bekaa Valley. In addition, vegetables cover around 20% of the agricultural lands in Lebanon [49]. Due to the involvement of large numbers of people in the cultivation, processing, and trading of tobacco, this crop plays a vital role in the economic and financial sector of the country. Of the total tobacco produced, 43% is produced in the Bekaa and the north of Lebanon [50]. Additionally, cannabis is widely cultivated in Central and Northern Bekaa, with more than 7000 ha planted annually [51]. Cannabis has a high return value compared to other crops representing a major source of income for some farmers in the Bekaa Valley.

2.2. Biophysical Measurements

2.2.1. Leaf Area Index Measurements

In situ measurements of LAI were collected in the 2018 and 2019 growing seasons using the SS1 SunScan Canopy Analysis System (Delta-T Devices). This instrument consists of 64 sensors that measure photosynthetic active radiation (PAR) with an accuracy of ±10%, embedded in a 1 m long portable probe (Figure 2a) with an external beam fraction sensor (BFS) (Figure 2b) [52]. The BFS is used to monitor the light incident on the canopy at the same time as the below-canopy measurements are taken. The SS1 requires several inputs, including the ellipsoidal leaf angle distribution (ELADP), longitude, latitude, and local timing (Figure 2a). Typical ELADP values used in this study are summarized in

Table A1. Typical ELADP values.

Crop	ELADP
Maize	0.76–2.52
Wheat	0.96
Barley	1.2
Cucumber	2.17
Tobacco	1.29–2.47
Potato	1.7–2.47

in Appendix A. LAI measurements were taken during the same day as a Landsat 8 or Sentinel 2 satellite overpass to calibrate and evaluate the relationship between LAI and the vegetation indices to be tested. Some measurements were taken within ±2 h of the overpass, and others continued to the rest of the day.

Two different patterns for data collection strategies were used in 2018 and 2019. In 2018, LAI measurements were collected over the full Bekaa Valley study area in Figure 1. To capture within-field variability, five measurements were taken in each field, and the average value was taken to be representative of the field-scale. For each field, the measurements were acquired at five different locations ~5 m apart following the pattern schematized in Figure 3 (points A, B, C, D, and E), starting from the center of the field. Measurements were collected away from the field boundaries to avoid edge effects.

For the 2019 growing season, extending from April to July, the sampling focus was on monitoring time-series LAI dynamics of three significant crops in the Bekaa regions: wheat, barley, and potato. A total of 42 predefined sampling sites in North Bekaa with recorded GPS coordinates were selected, and LAI was measured at these locations on each Landsat 8 or S2 overpass date. The sampling sites include 21 locations in wheat fields, 12 locations in barley fields, and 9 locations in potato fields.

2.2.2. Canopy Height and Above-Ground Dry and Fresh Biomass Measurements

Measurements of above-ground crop biomass and height were also collected at a subset of the LAI sampling sites in 2018 and 2019. A quadrate (0.5 m² × 0.5 m²) was randomly thrown in the field, and the vegetation within the frame of the quadrate was clipped. Three samples of potato biomass were taken from each field, and the obtained results were averaged. The above-ground plant component was oven-dried at 75 °C for 48 h to a constant weight and then weighed. Above-ground biomass measurements were collected in the potato fields in 2019. Crop height was directly measured for the tobacco and cannabis crops in 2018, and the potato crop in 2019 for the plant samples within the frame. Figure 1 shows the biophysical parameters sampling sites (labeled in dark green) for the 2019 growing season. Crop height and LAI field sampling at different growing stages of a wheat culture studied during the 2019 growing season is shown in Figure 4.

2.3. Surface Reflectance Data

2.3.1. Satellite Datasets

Satellite data were obtained for dates when measurements were collected in the field during the 2018 and 2019 growing seasons. Additional scenes were collected in 2019 to develop the time-series of biophysical retrievals. A total of 17 and 24 HLS images (Tile T36 SYC) were used for the 2018 and 2019 growing seasons, respectively. HLS has adopted the tiling system used by Sentinel-2. The tiles are in the Universal Transverse Mercator (UTM) projection and are nominally 110 km on a side. The tiling system is aligned with the UTM-based Military Grid Reference System (MGRS). The first two numbers of a tile name (such as 36SYC) correspond to the UTM zone, 6° of longitude in width. Each zone is divided into latitude bands of 8°. This is represented by a letter, S in the tile covering the study area. Finally, each 6° × 8° polygon (grid zone) is further divided into 110 km tiles, from west to east, 4th letter (Y in this case), and south to north, 5th letter (C in this case). For further information on the output projection and gridding, readers are referred to the HLS product user’s guide [39]. Figure 5 represents a summary of the satellite data used in the study.

Imagery from the newly released harmonized surface reflectance product (HLS, v1.4) was downloaded for these dates from May to September in 2018 and March to August in 2019. HLS represents a synergy of Landsat-8 (L30) and Sentinel-2 (S30) data with 30 m resolution [39]. This harmonized data product is based on the framework established by Claverie et al. [39], which encompasses several steps: resampling Sentinel-2 to 30 m, a bidirectional reflectance distribution function (BRDF) normalization for both Landsat 8 and Sentinel 2 datasets, a geographical registration for the two products, and a bandpass adjustment using the Landsat-8 band passes as a reference to which the Sentinel-2 spectral bands are adjusted. The resulting data products, S-30 MSI and L-30 OLI consist of surface reflectance data that are consistent in terms of spectral response and spatial resolution. A detailed representation of the HLS processing methodology can be found in [39].

Atmospherically corrected Level 2-A surface reflectance images from Sentinel-2 were also downloaded from the THEIA website at the French Land Data Center (https://www.theia-land.fr/) on the S30 dates listed in Figure 5. These were used to generate LAI with the Sentinel LAI index and SNAP software, designed specifically for use with THEIA SR data products. The goal was to use the LAI biophysical product from Sentinel-2 (using SNAP and S2 index) as a benchmark to compare to the LAI generated using HLS.

2.3.2. Cloud Masking

Cloud masking is required to identify high-quality land surface reflectance values with low uncertainties. The HLS product contains, in addition to the surface reflectance bands, a level-2-pixel quality assurance band. This band provides information about the cloud status in each pixel (clear, shadow, low, medium, and high confidence), snow/ice, and water pixels. The Landsat-8 cloud mask is derived from both the mask in the USGS Landsat TOA data and the Land Collection 1 Surface Reflectance Code (LaSRC) atmospheric correction tool. However, the Sentinel-2 cloud mask is a union of the Fmask algorithm, which has been adapted from [53] and the LaSRC mask. The quality assessment band (QA) bits of the HLS Landsat and Sentinel-2 were decoded with a loop using simple integer arithmetic, and its output was used to mask cloud shadow, adjacent cloud, cloud, and cirrus from the processed images.

As for the L2A products from THEIA, atmospheric correction, and detection of clouds and cloud shadows are performed using the Multi-sensor Atmospheric Correction and Cloud Screening (MACCS) processor (https://labo.obs-mip.fr/multitemp/?p=6203). The L2A 10-m cloud mask product was downloaded and used from the mask directory.

2.3.3. Vegetation Indices

Vegetation indices (VIs) are widely used in the assessment of several biophysical parameters including the fraction of photosynthetically active radiation absorbed by the vegetation (FAPAR) [54], green vegetation fraction [55], leaf area index (LAI) [56], and canopy chlorophyll content [57]. In this study, we use several indices for the evaluation of LAI, including the soil adjusted vegetation index (SAVI), normalized difference vegetation index (NDVI), enhanced vegetation index 2 (EVI2), and the Sentinel-2 LAI Index (SeLI). SAVI, NDVI, and EVI2 are a combination of visible and near-infrared bands, while SeLI is a combination of near-infrared and the red edge bands of the Sentinel 2 imagery.

NDVI was selected as one of the simplest and earliest VI. Compared to NDVI, both SAVI and EVI2 are less sensitive to soil background [58], and EVI2 is less saturated at high LAI ranges [58]. For SAVI, we use L = 0.5 (USGS, 2017b). SeLI is a new robust LAI_green index developed by Pasqualotto et al. [30] and computed from near-infrared and red edge bands. The red-edge region, between 690 and 750 nm, represents the region between the maximum absorption in the red wavelength and maximum reflection in the near-infrared wavelength by the plant [59,60]. Several researchers emphasize the importance of the red edge band in the estimation of LAI_green. Equations for the VIs used in this study are presented in

Table 2. References and equations of selected VIs to be evaluated in this study.

Index	Acronym	Equation	Reference
Soil adjusted vegetation index	SAVI	$\frac{\left(1+L\right)\left({\rho }_{NIR}-{\rho }_R\right)}{\mathrm{L}+{\rho }_{NIR}+{\rho }_R}$	Huete [21]
Normalized difference vegetation index	NDVI	$\frac{{\rho }_{NIR}-{\rho }_R}{{\rho }_{NIR}+{\rho }_R}$	Rouse Jr., et al. [61]
Enhanced vegetation index 2	EVI2	$2.5[\frac{({\rho }_{NIR}-{\rho }_R)}{({\rho }_{NIR}+2.4{\rho }_R)+1}]$	Jiang et al. [23]
Sentinel-2 LAI	SeLI	$\frac{{\rho }_{NIR2}-{\rho }_{RedEdge1}}{{\rho }_{NIR2}+{\rho }_{RedEdge1}}$	Pasqualotto et al. [30]

, along with primary citations.

In the literature, vegetation indices are often calculated from top-of-atmosphere reflectance. In this study, however, we calculate the VIs (NDVI, SAVI, and EVI2) using the HLS (Harmonized Landsat Sentinel-2) 30-m surface reflectance products derived from both Landsat-8 L1T products and Sentinel-2 MSI L1C data. Furthermore, we calculated SeLI from the L2A THEIA surface reflectance product.

2.4. LAI Models

2.4.1. Existing VI-Based LAI Models

Several existing VI-based LAI models were used to create spatial LAI layers for the study area (

Table 3. A summary of the equations for the selected existing vegetation index-based LAI models evaluated in this study, along with the satellite and reflectance type used in the cited references.

Model #	Relation	Equation of LAI	Studied Crop	Satellite and Reflectance	Reference
1	LAI-NDVI	4.9NDVI − 0.46	Vineyard	Multi-spectral imagery obtained from IKONOS, TOA reflectance	Johnson et al. [62]
2		$0.0287{\mathrm{e}}^{5.081NDVI}$	Wheat and Corn	Surface Reflectance L5 TM	González Piqueras [63]
3		$\begin{array}{cc}\hfill 9.519\times {\mathrm{NDVI}}^3-& 0.104\hfill \\ & \times {\mathrm{NDVI}}^2\hfill \\ & +1.236\hfill \\ & \times \mathrm{NDVI}\hfill \\ & -0.257\hfill \end{array}$	Overall vegetation cover and crops	Surface Reflectance, L5 TM	Myneni et al. [64]
4	LAI-SAVI	$11\times {\mathrm{SAVI}}^3$	Overall vegetation cover, woody trees, and agricultural crops	L5 TM and L7 ETM+, TOA reflectance	Pôçaset al. [65]
5		$\frac{-\ln \left(\frac{0.69-SAVI}{0.59}\right)}{0.91}$
6	LAI-EVI2	${\left(2.92\sqrt{EVI2}-0.43\right)}^2$	Overall crops	Surface Reflectance of L5 TM and L7 ETM+	Kang et al. [58]
7		$(3.16\sqrt{EVI2}-$0.58)2	Row crops
8		${\left(5.3\sqrt{EVI2}-1.66\right)}^{3/2}$	Maize
9		${\left(5.47\mathrm{EVI}{2}^{\frac{3}{5}}-1.03\right)}^{4/3}$	Wheat
10	SeLI (Sentinel-2 LAI index)	5.405 × SeLI − 0.114	Overall crops (potato, artichoke, squash, alfalfa, lettuce, wheat, pumpkin, and others)	Surface Reflectance Sentinel-2	Pasqualotto et al. [30]

). These models were evaluated with the collected LAI measurements to determine the formula with the best performance over the sampled crop types. The models evaluated include relationships with NDVI (linear, exponential, and polynomial of third-order fits), SAVI (third-order polynomial and logarithmic fits), EVI2 (square root fits), and linear fits to SeLI. The relationships between LAI and different studied vegetation indices, as presented in literature, are summarized in Table 3.

2.4.2. SNAP Model

In addition to the VI-based LAI models described in Section 2.4.1, LAI was produced from S2 THEIA surface reflectance data using Sentinel Application Platform toolbox (SNAP) software. SNAP provides a “Biophysical Processor” tool in the thematic land processing pull-down menu, used for the retrieval of several biophysical variables, including LAI. The algorithm is based on neural networks that are trained to estimate the canopy characteristics [66]. LAI can be directly retrieved for each pixel based on a pre-trained neural net. The neural nets are trained using well-known RTM (PROSAIL: PROSPECT [67] + SAIL [26]) as described in [28]. The ANN algorithm requires eight S2 spectral wavebands (B3–B7, B8a, B11, and B12) as input. The eight bands are resampled to 20 m to preserve the red-edge region in the S-2 scenes. LAI, with the quality indicators of the used dataset, were thus automatically obtained with the finest possible resolution.

2.5. Data Analysis

Figure 6 represents a summary of the overall methodological approach that was followed in this study to generate LAI from the studied vegetation indices computed from HLS and the THEIA L2A surface reflectance products and using the SNAP software.

In this methodological approach, we first perform a comparative assessment of LAI models (both physical and existing empirical LAI estimation methods) against the ground LAI measurements of the studied crop groups. Particular focus is placed on evaluating the newly embedded biophysical processor, based on the artificial neural network (ANN) method, in the Sentinel Application Platform (SNAP) software, as well as the newly developed S2 LAI algorithm from SeLI index, in comparison with empirically-based VI models applied to HLS data. Next, we generated new empirical fits of the VI data to our ground observations specific to these crop groups. Finally, we see how well LAI (observed and retrieved) correlates with other important crop development variables: canopy height and biomass. To further assess the performance of the studied LAI models against the measured LAI, the measured LAI data were divided into three groups: low (0–2), medium (2–4), and high (>4) LAI ranges.

2.6. Accuracy Assessment

Statistical analysis between observed and remotely sensed LAI was performed for each crop group during the 2018–2019 growing seasons. In 2018, the study was conducted for five crop groups, namely: herbs, grains, potato, tobacco, and vegetables. In 2019, the study was conducted on three major crops, namely: wheat, barley, and potato.

Statistical metrics computed are as follows:

Root mean square error (RMSE) [68]:

$$\mathrm{RMSE}=\sqrt{\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left(\mathrm{Estimated}LA{I}_{\mathrm{i}}-\mathrm{Measured}LA{I}_{\mathrm{i}}\right)}^2}{\mathrm{n}}}$$

(1)

Mean absolute error (MAE) [69]:

$$\mathrm{MAE}=\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left|\mathrm{Estimated}LA{I}_{\mathrm{i}}-\mathrm{Measured}LA{I}_{\mathrm{i}}\right|}{\mathrm{n}}$$

(2)

Mean absolute percentage error (MAPE) [70]:

$$\mathrm{MAPE}=\frac{1}{n}{\sum }_{i=1}^n\frac{\left|\mathrm{Measured}LA{I}_{\mathrm{i}}-\mathrm{Estimated}LA{I}_{\mathrm{i}}\right|}{\mathrm{Measured}LA{I}_{\mathrm{i}}}$$

(3)

Relative RMSE over the average measured LAI, also referred to as coefficient of variation of root-mean square error—CV(RMSE) as in [71]:

$$\mathrm{RRMSE}=\frac{\mathrm{RMSE}}{\overline{\mathrm{Measured}LA{I}_i}}\times 100$$

(4)

Mean bias error (MBE) [72]:

$$\mathrm{MBE}=\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left(\mathrm{Estimated}LA{I}_{\mathrm{i}}-\mathrm{Measured}LA{I}_{\mathrm{i}}\right)}{\mathrm{n}}$$

(5)

Index of agreement (d) [73]:

$$\mathrm{d}=1-\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left(\mathrm{Measured}LA{I}_{\mathrm{i}}-\mathrm{Estimated}LA{I}_{\mathrm{i}}\right)}^2}{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left(\left|\mathrm{Estimated}LA{I}_{\mathrm{i}}-\overline{\mathrm{Measured}LA{I}_{\mathrm{i}}}\right|+\left|\mathrm{Measured}LA{I}_{\mathrm{i}}-\overline{\mathrm{Measured}LA{I}_{\mathrm{i}}}\right|\right)}^2}$$

(6)

We also investigate the relation between the measured LAI and the remotely sensed vegetation indices. For this purpose, we use Pearson’s r, an often-used parametric correlation coefficient given by [74]:

$$\mathrm{r}=\frac{{\sum }_{\mathrm{i}}\left({\mathrm{x}}_{\mathrm{i}}-\overline{\mathrm{x}}\right)\left({\mathrm{y}}_{\mathrm{i}}-\overline{\mathrm{y}}\right)}{\sqrt{{\sum }_{\mathrm{i}}{\left({\mathrm{x}}_{\mathrm{i}}-\overline{\mathrm{x}}\right)}^2\sqrt{{\left({\mathrm{y}}_{\mathrm{i}}-\overline{\mathrm{y}}\right)}^2}}}$$

(7)

The significance of the correlation is computed using the two-tailed t-test with n-2 degrees of freedom:

$$\mathrm{t}=\mathrm{r}\sqrt{\frac{\mathrm{n}-2}{1-{\mathrm{r}}^2}}$$

(8)

3. Results

The performance of the empirical and biophysical models was evaluated using the aforementioned statistical parameters in comparison with field measurements. A table of the derived statistical metrics, along with a summary graphical representation, is shown in Figure 7 and

Table 4. Statistical analysis summary for the studied crops in both 2018 and 2019 growing seasons for the vegetation indices derived from the HLS product models.

HLS VI Models
LAI Model	Statistical Parameter	Herbs	Potato	Tobacco	Vegetables	Grains	Combined Crops
		(n = 178)	(n = 140)	(n = 30)	(n = 66)	(n = 37)	(n = 451)
Model 1 (NDVI, Vineyard)	MAE	0.82	1.28	0.64	0.98	0.74	0.97
	RMSE	1.19	1.60	0.83	1.32	0.94	1.31
	RRMSE	55%	55%	54%	59%	37%	55%
	MAPE	39%	64%	52%	54%	66%	52%
	MBE	−0.43	−0.09	−0.06	−0.11	−0.26	−0.24
	d	0.66	0.50	0.66	0.57	0.69	0.63
Model 2 (NDVI, Wheat and Corn)	MAE	1.76	1.87	1.21	1.65	1.88	1.76
	RMSE	2.07	2.40	1.35	2.09	2.10	2.16
	RRMSE	97%	82%	88%	94%	82%	90%
	MAPE	80%	59%	76%	71%	72%	71%
	MBE	−1.74	−1.81	−1.21	−1.60	−1.86	−1.72
	d	0.45	0.50	0.39	0.47	0.40	0.48
Model 3 (NDVI, Overall agricultural crops)	MAE	1.01	1.56	1.03	1.25	1.41	1.25
	RMSE	1.35	1.95	1.26	1.67	1.77	1.64
	RRMSE	63%	67%	82%	75%	69%	68%
	MAPE	48%	95%	75%	75%	73%	70%
	MBE	−0.66	1.99	−0.34	0.12	0.09	0.05
	d	0.74	0.70	0.75	0.59	0.51	0.71
Model 4 (SAVI, Overall agricultural crops)	MAE	1.75	1.58	1.16	1.50	1.72	1.62
	RMSE	2.06	1.97	1.30	1.95	1.96	1.97
	RRMSE	96%	68%	84%	88%	76%	82%
	MAPE	80%	55%	75%	66%	70%	69%
	MBE	−1.75	−1.39	−1.12	−1.41	−1.70	−1.54
	d	0.47	0.60	0.47	0.48	0.47	0.54
Model 5 (SAVI, Overall agricultural crops)	MAE	0.82	1.68	0.69	1.02	1.82	1.19
	RMSE	1.12	2.09	0.88	1.40	1.97	1.59
	RRMSE	52%	72%	57%	63%	77%	66%
	MAPE	43%	80%	80%	60%	117%	64%
	MBE	−0.13	−0.05	0.34	0.09	−1.58	−0.16
	d	0.63	0.39	0.52	0.55	0.31	0.52
Model 6 (EVI2, Overall agricultural crops)	MAE	0.94	1.55	0.72	1.00	1.59	1.18
	RMSE	1.33	2.08	0.88	1.37	1.76	1.62
	RRMSE	62%	71%	57%	61%	68%	68%
	MAPE	39%	63%	53%	51%	81%	53%
	MBE	−1.46	−0.61	−0.77	−0.38	−1.47	−0.71
	d	0.54	0.35	0.53	0.58	0.42	0.49
Model 7 (EVI2, row crops)	MAE	0.96	1.14	0.77	1.01	0.84	1.00
	RMSE	1.35	1.42	0.92	1.38	1.10	1.34
	RRMSE	63%	49%	60%	62%	43%	56%
	MAPE	41%	57%	55%	52%	52%	49%
	MBE	−0.85	−0.12	−0.38	−0.37	−0.52	−0.5
	d	0.59	0.72	0.52	0.59	0.66	0.70
Model 8 (EVI2, Maize)	MAE	0.94	1.15	0.80	1.02	0.85	1.00
	RMSE	1.31	1.41	0.99	1.38	1.08	1.32
	RRMSE	61%	48%	65%	62%	42%	55%
	MAPE	42%	64%	58%	57%	51%	53%
	MBE	−0.78	0.16	−0.33	−0.21	−0.35	−0.34
	d	0.59	0.76	0.52	0.62	0.68	0.73
Model 9 (EVI2, Wheat)	MAE	0.80	1.29	0.76	1.05	0.85	0.99
	RMSE	1.12	1.56	0.99	1.40	1.03	1.30
	RRMSE	52%	44%	65%	63%	40%	54%
	MAPE	40%	78%	63%	66%	67%	59%
	MBE	−0.33	0.62	0.09	0.23	0.16	0.11
	d	0.66	0.72	0.60	0.64	0.69	0.74

, respectively. The results are explained in the sections below.

3.1. Evaluation of Existing LAI Models

3.1.1. HLS VI Models

Empirical LAI models that are developed in relation to vegetation indices are considered as one of the most straightforward methods used for predicting LAI. Here we evaluate the efficiency and robustness of LAI models developed from indices that are computed from red and near-infrared HLS surface reflectance bands using the normalized difference ratio: NDVI (Model 1, 2, and 3), soil adjusted vegetation index: SAVI (Model 4 and 5), and enhanced vegetation index 2: EVI2 (Model 6, 7, 8, and 9). Our analysis (Figure 7 and Table 4) shows that Model 7 (EVI2, initially developed for row crops), Model 8 (EVI2, developed for maize), and Model 9 (EVI2, developed for wheat) outperformed other models when LAI observations from all crops sampled in the current study are combined.

On the other hand, models performing relatively poorly can also be identified. Both Model 2 (NDVI, initially developed for wheat, and corn) and Model 4 (SAVI, for overall agricultural crops) underestimated the LAI for all crops. Underestimation was also noticed in Model 5 (SAVI, overall agricultural crops) and Model 6 (EVI2, overall agricultural crops) for grains. Model 8 (EVI2, initially developed for maize) and Model 3 (NDVI, overall agricultural crops) overestimated the LAI for potato. Our analysis shows an apparent underestimation of LAI in all tested models when measured LAI exceeded 4, except for Model 3 and Model 8 which overestimated LAI for potato for observed LAI > 4.

3.1.2. Sentinel-2 LAI Models

For comparison with SNAP and SeLI LAI derived from S2 data only, subsets of HLS model-observation pairs were selected on the S2 dates represented in the THEIA dataset (Figure 8 and

Table 5. Statistical analysis summary for the studied crops in both 2018 and 2019 growing seasons for the HLS VI best-performing models derived from S30, Model 10 (SeLI, overall crops) and SNAP model derived from S2 THEIA products.

S2 Models
LAI Model	Statistical Parameter	Herbs	Potato	Tobacco	Vegetables	Grains	Combined Crops
		(n = 129)	(n = 68)	(n = 24)	(n = 57)	(n = 17)	(n = 295)
Model 10 (SeLI, THEIA S2, Overall agricultural and row crops)	MAE	0.82	1.44	0.69	1.01	0.70	0.98
	RMSE	1.21	1.85	0.86	1.40	0.89	1.38
	RRMSE	55%	56%	59%	59%	35%	59%
	MAPE	36%	52%	58%	55%	51%	46%
	MBE	−0.49	−0.69	−0.11	−0.19	−0.36	−0.44
	d	0.56	0.43	0.42	0.51	0.73	0.58
LAI-SNAP (THEIA S2)	MAE	1.24	1.80	0.93	1.28	0.65	1.32
	RMSE	1.61	2.19	1.08	1.73	0.83	1.72
	RRMSE	73%	66%	73%	73%	33%	70%
	MAPE	52%	63%	61%	59%	37%	56%
	MBE	−1.21	−0.98	−0.75	−0.60	−0.27	−0.95
	d	0.54	0.50	0.37	0.52	0.78	0.59
Model 7 (EVI2, HLS VI, row crops)	MAE	1.00	1.17	0.83	1.10	0.65	1.02
	RMSE	1.39	1.50	0.98	1.46	0.91	1.38
	RRMSE	63%	45%	66%	62%	36%	57%
	MAPE	41%	46%	62%	55%	31%	46%
	MBE	−0.91	−0.43	−0.43	−0.37	−0.47	−0.63
	d	0.56	0.70	0.37	0.55	0.75	0.69
Model 9 (EVI2, HLS VI, Wheat)	MAE	0.79	1.21	0.78	1.14	0.70	0.95
	RMSE	1.14	1.47	1.02	1.49	0.83	1.27
	RRMSE	52%	37%	69%	63%	33%	52%
	MAPE	36%	60%	70%	68%	44%	51%
	MBE	−0.40	0.32	0.003	0.26	0.21	−0.04
	d	0.64	0.73	0.40	0.60	0.79	0.74
Model 8 (EVI2, HLS VI, Maize)	MAE	0.97	1.12	0.86	1.11	0.64	1.01
	RMSE	1.35	1.40	1.04	1.47	0.87	1.34
	RRMSE	62%	42%	71%	62%	35%	55%
	MAPE	42%	50%	65%	60%	27%	48%
	MBE	−0.85	−0.12	−0.41	−0.18	−0.30	−0.48
	d	0.60	0.76	0.37	0.57	0.79	0.73

). The highest performing VI models applied to HLS SR data (7, 8, and 9; Section 3.1.1) outperformed LAI derived from S2 SeLI and the SNAP model (see Section 3.1.2; Table 5 and Figure 8). The HLS VI models had lower RMSE, MAE, RRMSE, and MAPE values than those of Model 10 (SeLI, overall crops), and the SNAP model. Model 9 (EVI2, initially developed for wheat) had the highest index of agreement (d), lowest RMSE, MAE, and MBE, compared to other models, primarily Model 10 (SeLI, overall crops) and the SNAP model. Furthermore, LAI derived from HLS EVI2 outperformed the LAI models derived from the other studied vegetation indices.

3.2. Empirical Relationships between VIs and LAI Observations in Bekaa

Vegetation indices are shown to correlate well with LAI. The studied VIs were evaluated with the multi-crop observed LAI dataset over both 2018 and 2019 growing seasons to devise a new LAI algorithm for crops in the Bekaa Valley. The semi-empirical relationships between the measured LAI and the vegetation indices for all combined crops and different crop groups are given in

Table 6. Statistics obtained using regression equations of the form y = (a × VI + b) × (1 + c × exp (d × VI)) for each of the studied index, for the studied crop groups.

Crop Group	VI	Regression Coefficients				p-Value	RMSE	R2
		a	b	c	d
Grains (n = 36)	EVI2	4.5	−0.6	15.0	−6.23	<0.0001	0.34	0.82
	SAVI	−0.02	2.9	−5.5	−12.57	<0.0001	0.34	0.81
	NDVI	−0.3	3.1	−5.4	−7.93	<0.0001	0.37	0.78
	SeLI	−0.4	3.0	−4.8	−11.47	0.001	0.43	0.77
Potato (n = 158)	EVI2	−2.7	2.5	0.009	9.63	<0.0001	1.25	0.59
	SAVI	−3.4	2.7	0.003	12.36	<0.0001	1.25	0.59
	NDVI	−3.8	3.7	0.0001	14.10	<0.0001	1.35	0.52
	SeLI	0.01	0.004	306.3	0.00	0.03	1.59	0.06
Herbs (n = 136)	EVI2	−1.1	0.8	0.3	7.34	<0.0001	0.69	0.34
	SAVI	1.1	0.2	1.6	1.30	<0.0001	0.74	0.23
	NDVI	1.6	2.4	−0.9	−1.67	<0.0001	0.73	0.29
	SeLI	1.0	0.3	1.3	1.12	<0.0001	0.69	0.32
Tobacco (n = 25)	EVI2	0.01	0.0020	383.4	0.00	0.00036	0.40	0.43
	SAVI	0.01	0.0022	347.7	0.00	0.00116	0.43	0.37
	NDVI	0.01	0.0020	302.0	0.00	<0.0001	0.37	0.49
	SeLI	0.01	0.0022	369.9	0.00	0.006	0.35	0.39
Vegetables (n = 70)	EVI2	4.0	0.5	0.0007	9.39	<0.0001	0.74	0.53
	SAVI	0.02	0.004	143.9	0.88	<0.0001	0.79	0.47
	NDVI	0.1	0.022	20.8	0.21	<0.0001	0.85	0.38
	SeLI	0.0002	0.000	19,210.5	0.00	<0.0001	0.90	0.35
All Crops (n = 425)	EVI2	2.9	0.8	0.01	5.46	<0.0001	0.94	0.63
	SAVI	3.2	0.7	0.003	7.93	<0.0001	0.97	0.61
	NDVI	1.0	1.1	0.01	5.72	<0.0001	1.07	0.51
	SeLI	1.1	0.032	4.94	−0.56	<0.0001	1.10	0.27

. The different types of fitting functions with the crop group-specific LAI-VI relationships are summarized in Table 6 for the two satellites combined (L30 and S30), and in

Table 7. Regression coefficients obtained by regressing LAI against EVI2 using the equation of the form y = (a × VI + b) × (1 + c × exp (d × VI)), for the studied crop groups, separated by satellite type, L30, and S30.

Crop Group	VI	L30				S30
		Regression Coefficients				Regression Coefficients
		a	b	c	d	a	b	c	d
Grains	EVI2	0.00	0.01	123.21	0.26	1.28	0.30	1.57	0.47
Potato		−1.81	1.61	0.01	10.36	−3.56	3.26	0.00	10.41
Herbs		7.52	−0.51	0.00	0.00	4.98	0.47	0.00	0.00
Tobacco		4.13	0.37	0.00	0.00	3.08	0.91	0.00	0.00
Vegetables		4.34	0.22	0.01	6.77	4.04	0.50	0.00	9.39
Combined Crops		4.07	0.35	0.00	7.93	1.34	0.99	0.11	3.63

for the two satellites separated.

The R² for each index obtained with different fittings ranged between 0.27 and 0.63 for the crops combined, with SeLI index having the lowest R² in all fittings (0.27). However, the p-value was <0.0001 in all cases. Results for Pearson’s r shows a strong correlation between the measured LAI and EVI2 (r = 0.7), followed by SAVI (r = 0.67) and NDVI (r = 0.6) and SeLI (r = 0.5) with the lowest correlation. Each index was represented as a function of the measured LAI for the different crop groups and the combined crops (Figure 9). However, EVI2 herein can be identified as a best-suited index for a unified algorithm for the crops combined.

To evaluate the significance of combining both Landsat-8 and Sentinel-2A in determining the LAI-EVI2 for each crop group, we fitted modeled LAI from L30, from S30, and from both satellites combined using the regression coefficients from Table 6 and Table 7 and then extracted the modeled LAI on the observed days. The summary of comparisons between the modeled and observed LAI is shown in

Table 8. Statistical comparison between modeled and observed LAI separated by satellite type: L30, S30, and L30 and S30 combined, the modeled LAI is obtained using the LAI-EVI2 empirical relationships displayed in Table 6.

Crop Group	Statistical Parameter	L30	S30	L30 and S30
Grains (n = 36)	RMSE	1.46	0.60	0.32
	MAE	1.41	0.48	0.25
Potato (n = 158)	RMSE	1.30	1.23	1.20
	MAE	0.99	0.99	0.94
Herbs (n = 136)	RMSE	0.76	0.71	0.69
	MAE	0.61	0.58	0.55
Tobacco (n = 25)	RMSE	0.46	0.41	0.40
	MAE	0.37	0.32	0.31
Vegetables (n = 70)	RMSE	0.74	0.71	0.71
	MAE	0.58	0.59	0.59
Combined Crops (n = 425)	RMSE	1.05	0.92	0.89
	MAE	0.80	0.71	0.66

. Our results show that combining both satellites allowed us to achieve lower RMSE and MAE for the crops combined and for each crop group. The use of L30 separately produced higher RMSE and MAE values than those obtained from L30-S30 combined, whereas the use of S30 yielded a lower RMSE and MAE values than L30. Overall, these results demonstrate the benefits of the combined use of Landsat-8 and Sentinel-2A satellites comparing to the single-satellite usage in defining the LAI-EVI2 relationship.

3.3. LAI-Crop Height Relationships

3.3.1. Crop Height

In addition to LAI, crop height is often used to monitor crop development [75,76,77,78,79] and is an essential variable in many land-surface modeling systems—governing surface turbulence and transport of wind and radiation through the canopy to the soil surface [80,81,82,83]. LAI vs. height relationships are unique to specific crop types due to the vast diversity of canopy structure among crop types [84,85,86,87]. In this study, a linear regression analysis was conducted to obtain the relationship between the crop height, the measured LAI, and the best performing LAI models for potato, cannabis, and tobacco. Figure 10, Figure 11 and Figure 12 indicate that an increase in leaf area is associated with an increased height due to leaf extension as the crop develops. Our analysis shows that the relation between the ground measured LAI and the measured height of the potato crop is essentially linear with an R² value of 0.82, greater than that obtained when regressing the crop height to LAI obtained from Model 7 (EVI2, row crops; R² = 0.48) (Figure 10). A similar crop height-LAI linear relationship was obtained for the wheat crop against measured LAI with a higher R² (0.79) compared to Model 9 LAI (EVI2, wheat)-height relation (R² = 0.61) (Figure 11). Furthermore, a good relationship exists between the measured height and the measured LAI for the cannabis and tobacco crops with R²: 0.489 and 0.495, and between the modeled LAI (model 10 derived from SeLI), with R²: 0.384 and 0.494 for both cannabis and tobacco, respectively (Figure 12).

To evaluate the importance of combining both L30 and S30 in defining the LAI-h relationship, we applied the L30, S30, and L30 and S30 regression equations obtained between the modeled height and observed LAI for each crop group at each observation day. Statistical comparison between separated and combined satellite datasets is shown in

Table 9. Statistical comparison between modeled and observed height (h(m)) separated by satellite type: L30, S30, and L30 and S30 combined, modeled height is obtained from equations displayed in Figure 10, Figure 11 and Figure 12 as a function of observed LAI.

Crop Group	Statistical Parameter	L30	S30	L30 and S30
Wheat	RMSE	0.104	0.113	0.101
(n = 38)	MAE	0.085	0.092	0.084
Potato	RMSE	0.065	0.053	0.052
(n = 52)	MAE	0.051	0.045	0.044
Cannabis	RMSE	0.194	0.193	0.185
(n = 128)	MAE	0.163	0.161	0.157
Tobacco	RMSE	0.167	0.146	0.145
(n = 18)	MAE	0.135	0.118	0.116

. This relationship is better defined when both L30 and S30 are combined, where slightly lower RMSE and MAE values were obtained when the LAI based height relationship was determined using both L30 and S30, than those obtained with S30 or L30, separately.

3.3.2. Potato Dry and Fresh Weight

Potato crop biomass is an essential indicator of crop development, and the availability of this information during the growing season can help in decision-making processes for optimal crop production [88,89]. Reflectance-based VI response to canopy variables such as LAI largely determines potato growth, and VIs are widely used in biomass prediction models [11,12]. Here, we regressed the above-ground dry and fresh weight of the potato crop studied in 2019 against each of the measured LAI, LAI obtained from Model 7 (EVI2, row crops), and the measured height. The relationship between above-ground fresh and dry weights as a function of both the measured LAI and modeled LAI shows that an increase in the leaf area index is associated with an increase in biomass (Figure 13). No saturation in the measurement of biomass from LAI was noticed. Fresh and dry above-ground biomass of potato could be derived from the modeled LAI using a linear relation was with good accuracy (R²: 0.7 for fresh biomass) and with moderate accuracy (R²: 0.4 for dry biomass).

On the other hand, the regression of above-ground dry and fresh biomass (AGDB and AGFB, respectively) of potato against crop height showed that an increase in the above-ground fresh and dry weight of the potato crop is associated with an increase in the crop height (Figure 13). The ability of the linear regression to estimate the fresh and dry above-ground biomass of potato from crop height was with a good accuracy level (R²: app. 0.6), with lower RMSE and MAE values obtained as a result of combining both L30 and S30 compared to the single-use of L30 in defining the AGFB and LAI relationship (

Table 10. Statistical comparison between modeled and observed above-ground dry biomass (AGDB) and above-ground fresh biomass (AGFB) for potato separated by satellite type: L30, S30, and L30 and S30 combined, modeled fresh and dry above-ground biomass is obtained from equations displayed in Figure 13 as a function of observed LAI.

Biophysical Parameter	Statistical Parameter	L30	S30	L30 and S30
Potato AGDB	RMSE	0.026	0.026	0.026
(n = 146)	MAE	0.020	0.020	0.020
	RRMSE	29%	29%	29%
Potato AGFB	RMSE	0.424	0.390	0.390
(n = 146)	MAE	0.348	0.337	0.338
	RRMSE	35%	32%	32%

).

3.3.3. Seasonal Co-Variability in Observed and Modeled Biophysical Variables

This analysis shows that changes in both observed and modeled parameters (LAI, crop height, and biomass) are proportional to changes in EVI2 (Figure 14 and Figure 15). Continuous capture of the biophysical variables’ time-series was obtained when combining both L30 and S30 as compared to single sensor use. Modeled LAI derived from the LAI-VI models established in Section 3.2 was used to derive the height and biomass for potatoes on the LAI-height and LAI-biomass equations generated in Section 3.3. We further investigated the seasonal co-variability in the biophysical variables for wheat and potato crops sampled in the Bekaa Valley during the 2019 growing season (Figure 14 and Figure 15). Fresh and dry biomass weight was also evaluated for potato. Measurements of potato crop development were collected regularly during the 2019 growing season, whereas wheat biophysical parameter measurements were conducted at the end of the growing season.

The phenological differences between both potato and wheat were captured for three potato and wheat farms. Typically, the potato had a higher peak of both modeled and measured LAI during the middle of the growing season, where the average maximum measured LAI for all studied potato fields was found to be 6–8 m²/m² in the mid-season stage (DOY 180). The average minimum measured potato LAI was about 2–3 m²/m² during the beginning of the growing season (DOY 140). Similarly, modeled LAI evolution was observed for the three potato farms. On the other hand, the measured wheat LAI ranged between 2 and 3 m²/m². Lower wheat LAI values were observed since wheat was monitored during the end of the season, where LAI tends to decrease.

The measured crop height increases as the crop develops. The average minimum measured potato crop height was about 0.4 m during the beginning of the growing season (DOY 140). The maximum average crop height for all studied potato fields was found to be around 0.6 m in the mid-season stage (DOY 180). The measured wheat crop height was found to be approximately 1 m during the end of the season (DOY 135–140). Similar modeled crop height evolution was observed for the three wheat farms.

Similarly, the above-ground fresh and dry biomass increased with crop growth. The above-ground biomass was the lowest at the beginning of the growing season, and it increases to reach its maximum during the middle of the growing season with a value of 2 kg/m² and 0.2 kg/m², for the above-ground fresh and dry biomass, respectively.

Different temporal LAI, crop height, and biomass dynamics were noticed in both potato and wheat crops (Figure 14 and Figure 15). Both crop type and management practices affect the dissimilarity of the temporal biophysical parameters of these crops. Furthermore, the same crop types, but different fields, diverged in their biophysical temporal profiles. These deviations can be attributed to the variation of farming conditions, agronomic, and management practices among the farms with the same crops.

3.3.4. Spatial Biophysical Parameter Patterns

Figure 16 shows the time development of the LAI, crop height, and above-ground fresh and dry biomass of a potato crop surveyed during the 2018 season. The modeled LAI maps are derived from the exponential LAI-EVI2 fit established in Section 3.2. These LAI maps were used to derive the height and biomass for potatoes on the LAI-height and LAI-biomass equations generated in Section 3.3. The spatial variability of the canopy conditions throughout the growing season is considerable, reflecting differences in soil conditions, planting dates, and cultivation practices. Note that fields 10 and 11 have depressed growth patterns coinciding with the L30 satellite overpass (DOY: 167). Furthermore, fields 9, 10, 11 and half of 8 reached senescence earlier than the other fields. The fact that fields 10 and 11 lag behind other potato-fields in terms of crop development is probably due to soil moisture stress that could be an insufficient amount of water available for irrigation or that irrigation was delayed. However, moisture stress was not high enough to completely inhibit crop growth.

Other factors yielding the variation in the magnitude of biophysical parameters estimation include the crop’s susceptibility to unfavorable growth conditions, crop variety, differences in planting and harvest dates, crop management, weed control, planting density, and irrigation management. Overall, HLS products present good spectral and temporal resolution allowing for visual inspection of error estimates in time series maps of LAI and other biophysical variables.

4. Discussion

4.1. Uncertainties in -LAI Assessment

Uncertainties associated with LAI assessment can be grouped into two categories: the uncertainty of remote sensing methods and the errors in the LAI observation techniques.

LAI can be retrieved using a physical radiative transfer model or a simple empirical model based on a vegetation index. Any physical model is a simplification of the complex world. There are uncertainties associated with the physical model itself, and in the surface reflectance data used as input. The uncertainty of atmospheric correction of the satellite images is a major factor affecting the accuracy of LAI estimation by remote sensing [58]. Atmospheric correction also affects LAI-VI relationships. The use of vegetation indices to generate LAI products is subject to several uncertainties. First, studies have shown that due to VI saturation effects, LAI values that are greater than 4 m²/m² are beyond the prediction power of the studied vegetation indices [5,24,60]. Thus, issues with VI saturation over dense canopies remain an issue to be addressed [58,90]. Second, different vegetation indices respond differently to the crop leaf optical properties defined by the leaf chlorophyll, dry mass, and water content [67]. Third, the leaf inclination, solar angle, and sensor bandwidth and calibration affect the vegetation spectral reflectance [91]. Therefore, LAI-VI relationships usually are only good for the local area where model was developed, while physical models could, in theory, be used more generally.

Regarding errors in the LAI measurement method, the underestimation of LAI in the high range of measured LAI can be attributed to the SS1 equipment limitations under high vegetation cover (LAI range > 4 m²/m²). LAI that is calculated using light transmission theory, such as the SS1 method, is underestimated because SS1 does not correct for canopy clumping effects [92]. Generally, when the canopy is clumped, the leaves hide each other, leaving a gap in between, and thus allow for more light to reach the ground as compared to randomly distributed leaves. The underestimation of LAI with SS1 was also observed in previous studies due to the lack of clumping correction [93,94]. Another type of error that falls in the second uncertainty category is that the leaf angle distribution (ELADP) is a fixed constant that is predefined by the user according to the crop. However, the chosen ELADP values may not be accurate throughout the growing season since the canopy leaves change throughout the entire season [95]. The assumption of a constant leaf absorption constant of 0.85 adds uncertainty to the LAI measurements. Moreover, row spacing, crop height, and time of measurement can affect the LAI values.

Scaling up field observations to match satellite pixel footprint is another challenge. Field LAI is a point measurement. Even through many points can be measured within a satellite pixel, the summary of the point measurements is still an approximation of the area. In addition, satellite pixels have geolocation errors and their footprints may vary from date to date, which is always a challenge for remote sensing data product validation [96].

4.2. S2 Model Results in Comparison to Previous Studies

We also assessed the performance of the newly developed SeLI-based LAI algorithm. Pasqualotto et al. [30] showed that LAI derived SeLI could be used as a generic model for LAI_green of different crop types. Our results agree with the conclusions obtained by Pasqualotto et al. [30] and Sharma, et al. [97], who pointed out that the S2 red-edge bands are critical for the estimation of biophysical variables, mainly the LAI. Following the HLS VI models, Model 10 (SeLI, developed for overall agricultural crops) ranked next in terms of low RMSE, MAE, MBE, RRMSE, and MAPE values for all crops sampled in the study area. However, the S2 LAI algorithm significantly underestimates high LAI compared to other LAI-HLS derived models.

Our assessment shows that LAI derived from SNAP performed best for grain crops. The results demonstrate the potential of using SNAP to derive more uniform LAI estimates for both wheat and barley (possibly due to the good performance of the radiative transfer model for homogenous conditions). A clear underestimation of the SNAP-LAI product was noticed for herbs, potato, vegetables, and tobacco (Figure 8). Pasqualotto et al. [30] showed that LAI estimated from the Sentinel-2 product using the SNAP software underestimated LAI of potato, artichoke, squash, alfalfa, lettuce, wheat, pumpkin, and others. Compared to HLS VI and S2 SeLI models, SNAP provided less accurate estimates of LAI (Table 5 and Figure 8). These results are not in agreement with Kganyago et al. [98] who showed that SNAP-derived LAI values were overestimated for maize and sunflowers during the 2019 peak growing time in South Africa. This shows that the LAI estimation using SNAP software is highly location and crop type dependent.

S2 and HLS models outperforming the SNAP model confirm the suitability of S2 models applications to the small geographical scale (field level) of our study. The authors of the SNAP (personal communication) mentioned that the biophysical processor lacks the ancillary information from which some vegetation architecture features could be derived. Hence, the absence of reliable and regularly updated land cover maps at a spatial resolution, like that of S2, prevents tailoring of specific algorithms for each of the land cover classes. Consequently, the algorithm may provide reasonably good estimates over all the cases, but certainly poorer performances as compared to algorithms specific to a given surface type [28]. Thus, the poor performance of SNAP-derived LAI suggests that it is not suitable for precision agriculture and may be useful for large-area applications.

4.3. HLS VI Models Validation Challenges

The major challenge encountered while validating existing vegetation index relationships applied to HLS SR product is the uniqueness and diversity of the site-specific LAI-VI relationships. Site-specific properties such as the crop type [5], biochemical properties of the leaf canopy [99], biophysical properties of the leaf canopy [100], as well as sensor characteristics and the atmospheric scattering and absorption [101], have yielded unique local LAI-VI relationships that are ideally applicable only under unique conditions. This work shows that the existing LAI-VI models, initially developed for particular crops from different sensors, can be applied to some crops sampled in this research irrespective of their limitation to “one place, one time, one equation.” As shown in Results, the LAI models originally developed for wheat (RMSE: 1.27), maize (RMSE: 1.34), and row crops (RMSE: 1.38) worked well for the combined crops of the study area. However, these relationships cannot replace the locally established relationships in this work, as the local relationships account for the site-specific conditions affecting the LAI-VI relationships.

4.4. Empirical Relationships Establishment between VIs and LAI Observations Challenges

The major challenge of establishing the empirical relationship between the observed LAI and vegetation indices is the difficulty of finding one index with a sufficiently general character that can be used to estimate LAI for a wide variety of crop types. In this work, the established indices do not present this general character, as each index performed differently in different crop types. The most robust relation between ground measured LAI and vegetation indices appears in SeLI for cannabis, SAVI and EVI2 for potato, NDVI for tobacco, and EVI2 for vegetables. However, EVI2 outperformed other vegetation indices for all crops combined, and therefore it can be identified as an index that is best suited for a unified algorithm for crops in semi-arid irrigated regions with heterogeneous landscapes.

As more remote sensing and field measurements become available, machine learning approaches may be used to investigate the complex relationships between LAI and remote sensing spectral features. Surface reflectance provides information about land covers and structures, which could be used to build the relationship directly [102].

5. Conclusions and Recommendations

This study reconfirms the limited ability of Landsat as an isolated sensor to capture the full time-series at the farm level. L30 missed biophysical observations at critical growth stages due to the smaller number of images available. Few L30 images were used due to its long revisit time and cloud coverage. Our results also demonstrate the importance of higher observation frequency achieved with the combination of Landsat-8 and Sentinel-2A satellites compared to the single use of L30 in both crop monitoring and modeling efforts, where stronger LAI-based crop biophysical parameters relationships were achieved with L30 and S30 combined, as compared to L30 separately. LAI and other crop growth variables are appropriately monitored and modeled in this work, especially during fast-developing phenomena. Multi-satellite data normalization is crucial, and this was addressed through crop biophysical variables time-series generated for monitoring wheat and potato crops in the Bekaa Valley. Time series of crop growth parameters are essential for detecting changes in crop cover, and the combination of data from different ongoing satellite missions provides this opportunity. Thus, the recent availability of high temporal frequency high-resolution images (HLS product) provides the ability to conduct and utilize more site-based biophysical variables measurements for crops other than the two studied strategic crops (wheat and potato) by providing more time-matched surface reflectance products.

Using the combined Landsat 8 and Sentinel-2 data at a 30-m spatial resolution, we focused in this work on the estimation LAI at the field scale in a semi-arid irrigated heterogeneous landscape. Unlike most existing approaches utilizing vegetation indices derived from non-normalized satellite data to estimate LAI, we derived the LAI from three methods, namely: existing vegetation index (VI) relationships applied to Harmonized Landsat-8 and Sentinel-2 (HLS) surface reflectance produced by NASA, the SNAP biophysical model, and L2A THEIA product from Sentinel-2. The EVI2 index surpassed any other index in predicting LAI, and it is the best for modeling LAI of various crops. This study also shows that LAI derived from the artificial neural network through ESA’s SNAP biophysical processor is underestimated but yielded a good accuracy level for wheat and barley LAI estimation. Hence, the poor performance of SNAP dictates further improvement to support precision agriculture [98]. Future studies should investigate the discrepancy in the disagreement of LAI-SNAP accuracy in the cited research work. While the LAI derived from the SeLI algorithm produces an acceptable accuracy level compared to HLS-EVI2, a significant underestimation at high LAI was observed. The normalizing satellite data in crop monitoring and modeling is crucial to eliminate the bias due to sensor and bandwidth variability and atmospheric correction techniques. We encourage the scientific community to validate new crop and site-specific LAI-VI, LAI-height, and LAI-above-ground biomass empirical relationships developed in this work.

We recommend exploring improved hemispherical LAI estimation techniques that can provide information on the canopy clumping and leaf angle inclination, measure the LAI at different heights, and differentiate between leaves and woody parts through the integration of infrared techniques [103,104]. The use of other vegetation indices, such as the normalized difference water index (NDWI), derived from near- and shortwave-infrared reflectance, may be less susceptible to saturation problems [105]. Ingestion of multiple spectral bands within a machine learning approach may be useful for large-area applications [102]. Future work may also focus on the effects of soil moisture on the retrieval of LAI. More studies on the use of other vegetation indices that correct for soil background, such as the Weighted Difference Vegetation Index (WDVI) [106], could be explored (here we found that EVI2, which corrects for both atmosphere and soil background, gave good results). Additionally, future studies should consider quantifying the effect of various atmospheric correction approaches such as Sen2Cor, FORCE, iCor, and MAJA on biophysical parameters retrieval, since atmospheric correction performance varies by different spectral bands of Sentinel-2 [98].