Journal of Ecology and Environment

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Published online October 29, 2024
https://doi.org/10.5141/jee.24.066

Journal of Ecology and Environment (2024) 48:39

Enhancing leaf area index estimation in tropical vegetation: a comparative study of multivariate linear regression and Sentinel Application Platform-derived leaf area index

Ali Yasin Ahmed1* , Abebe Mohammed Ali2 , Nurhussen Ahmed2 and Birhane Gebrehiwot3

1Department of Geography and Environmental Studies, Jigjiga University, Jigjiga 1020, Ethiopia
2Department of Geography and Environmental Studies, Wollo University, Dessie 1145, Ethiopia
3Department of Land Administration and Surveying, Dilla University, Dilla 419, Ethiopia

Correspondence to:Ali Yasin Ahmed
E-mail alexoy5050@gmail.com

Received: July 2, 2024; Revised: September 11, 2024; Accepted: September 11, 2024

This article is licensed under a Creative Commons Attribution (CC BY) 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ The publisher of this article is The Ecological Society of Korea in collaboration with The Korean Society of Limnology

Background: The leaf area index (LAI) quantifies the total one-sided green leaf area per unit of soil area, making it a crucial parameter in models that simulate carbon, nutrient, water, and energy fluxes within forest ecosystems. This study enhances LAI estimation techniques by employing a multivariate linear regression (MVLR) approach specifically tailored to tropical vegetation. We integrated field-collected LAI data with spectral indices and multispectral bands to develop a robust predictive empirical model. The LAI estimates derived from the MVLR approach are rigorously compared with those obtained from the Sentinel Application Platform (SNAP), a widely utilized tool for remote sensing analysis.
Results: In developing the MVLR model, nine multispectral bands, seven vegetation indices (VIs), and two biophysical variables derived from Sentinel-2 multispectral image were tested to identify efficient predictors for LAI estimation. To determine significant multispectral bands and VIs (ensuring no multicollinearity, high coefficient of determination (R2), low root mean square error (RMSE), and a p-value < 0.05) for the best representative model, stepwise multiple linear regression (SMLR) was employed. Multispectral bands 7 and 8, along with the VIs soil adjusted vegetation index and normalized difference vegetation index, and the fraction of vegetation cover biophysical variable, produced superior outcomes and serve as strong predictor variables for LAI. The accuracy of the MVLR model was validated using 17 directly measured LAI sample plots with the leave-one-out cross-validation method. The estimated LAI using the MVLR model achieved higher accuracy, with an R2 of 0.94, compared to the SNAP toolbox (R2 = 0.71). The RMSE and bias of the MVLR model were 0.18 and 0.006, respectively, while for SNAP-derived LAI, the RMSE and bias were 0.53 and 0.31, respectively.
Conclusions: The improved accuracy and reduced error of the MVLR model are attributed to its adjustment for tropical vegetation types. Future research should focus on comparing the MVLR model with other global LAI products to further validate and enhance its applicability.

Keywords: leaf area index, multispectral bands, multivariate, Sentinel-2, vegetation indices

Leaf area index (LAI) is one of the key biophysical parameters in monitoring various ecological processes. It can be efficiently applied in monitoring vegetation photosynthesis, respiration, transpiration, soil respiration, and the energy exchange of the canopy-atmosphere (Jin and Zhang 2002; Li et al. 2023; Mwangi et al. 2018; Zhang et al. 2020). This demonstrates that LAI is applicable in many fields of study like precision agriculture, vegetation health monitoring, and crop yield estimation (Ma et al. 2022; Sishodia et al. 2020; Xu et al. 2020; Yao et al. 2017). LAI also plays a key role in climate modeling, and biodiversity monitoring; this also points out that LAI is an essential climate variable (Darvishzadeh et al. 2019; Reygadas et al. 2020). It has a strong positive correlation with net primary production, aboveground biomass, and agricultural yield (Eisfelder et al. 2017; Muhe and Argaw 2022). On the other hand, in many instances, it has a negative correlation with climatic variables like surface temperature (Eisfelder 2013; Pizaña et al. 2016).

LAI can be estimated either through direct or destructive sampling or by employing indirect methods that estimate LAI based on the degree of light penetration through the canopy (Ghebremicael et al. 2004). Although direct or destructive measurements of LAI offer precision, collecting such data is labor-intensive and time-consuming, rendering it feasible only for small-scale plots (Vafaei et al. 2021). The availability of freely accessible, high-resolution satellite datasets derived from advanced sensors such as Sentinel-2, coupled with the utilization of sophisticated open-source tools like the Sentinel Application Platform (SNAP), and the growing accessibility of analysis-ready data, presents a remarkable opportunity for the prediction of precise vegetation variables (Kganyago et al. 2020).

In remote sensing, four basic approaches can be used to retrieve or estimate biophysical variables such as LAI from satellite images. First, physical modeling uses radiative transfer models (RTM) to predict the interaction between spectral radiation and vegetation biophysical variables (Cho et al. 2008; Jacquemoud et al. 2000; Myneni 1997; Sikand and Stamnes 2012). Second, empirical or parametric modeling establishes a relationship between vegetation indices (VIs) and the ground measured biophysical variables. Third, machine learning regression algorithm or non-parametric modeling do not require an explicit relationship or specific data distribution, for-example, support vector regression (Durbha et al. 2007). Lastly, hybrid models combine elements from two or more of the aforementioned approaches (Lillesand et al. 2015; Verrelst et al. 2015).

In recent studies, RTMs are used to derive biophysical variables from satellite images (O’Hagan 2006; Verrelst et al. 2016). These RTMs utilize the full spectrum acquired by multi- to hyperspectral sensors, unlike VIs that use only some of the spectral bands (Verrelst et al. 2016). Additionally, RTMs can exploit the directional signature of multi- angle sensors (Verrelst et al. 2015). However, these models have some weaknesses, including the need for extensive parameterization, as well as requiring more intensive computational skills and time (Richter et al. 2011). On the other hand, most of the empirical models do not require advanced mathematical skills, making them easier to understand and implement (Ali et al. 2019; Magney et al. 2017).

The SNAP biophysical processor, an open-access earth observation analysis tool, estimates biophysical parameters based on two different hybrid models: a physically-based RTM and a robust machine learning algorithm (Upreti et al. 2019; Weiss and Baret 2016). The accuracy of SNAP-deduced LAI from Sentinel-2 data, as well as its consistency with existing LAI products, has been studied (Bochenek et al. 2017; Campos-Taberner et al. 2018; Kganyago et al. 2020). This is crucial since precise and consistent agricultural monitoring strongly hinges on the consistency and inter-comparability of biophysical parameters (Alexandridis et al. 2019).

While numerous studies (Binh et al. 2022; Brown et al. 2019; Chauhan and Lunagaria 2024; Djamai et al. 2019a; Kganyago et al. 2020; Pasqualotto et al. 2019b) have validated LAI estimates derived from Sentinel-2 imagery using the SNAP biophysical variables processor, there remains a gap in comparing these estimates with empirical models that incorporate both multispectral bands and VIs. Our study addresses this gap by developing and validating a multivariate linear regression (MVLR) model that integrates these spectral features, providing a fresh perspective on LAI estimation accuracy. This research, conducted in the Mille watershed of Ethiopia, offers a critical comparison between SNAP-derived LAI and our tailored MVLR model, aiming to enhance LAI estimation techniques, especially in tropical regions with complex vegetation types. The significance of our study lies in its ability to provide more accurate and context-specific LAI estimates, which are essential for improving applications in climate modeling, agricultural management, and forestry practices in regions with similar ecological characteristics. Hence, this study has two main objectives: (1) identify the most efficient predictors of LAI from satellite image reflectance and VIs and develop a MVLR model to estimate LAI and (2) validate and compare LAI derived from SNAP biophysical processor and MVLR model against field-measured LAI.

Description of the study area

The research was conducted in the Millie River basin, located in the Ambasel District of the South Wollo Zone in the Amhara Regional State of Ethiopia, an area predominantly characterized by tropical vegetation types (Fig. 1). Mille River basin is located between 11° 19′ 44″–11° 32′ 37″ latitude and 39° 31′ 44″–39° 40′ 51″ longitude. It has an elevation ranging from 1,427 to 3,635 m above sea level with an average temperature 15°C to 20°C.

Figure 1. Map of the Millie Watershed, located in a tropical climatic region of Ethiopia. The map features a true-color composite of the Sentinel-2 satellite image, utilizing bands 4, 3, and 2. This combination provides an accurate representation of the watershed’s land cover and vegetation, effectively highlighting the key geographical and environmental features pertinent to our study.

The rainfall pattern is bimodal type. The main rainy season is from June to September, while the medium rainy season is from April to June. According to the Kombolcha metrological station, the mean annual rainfall of the study area ranges from 800 to 2,500 mm. The lowest minimum temperature is recorded from August to November (11°C to 12°C) and the highest maximum temperature is recorded during May and June (22°C to 30°C). The livelihood of the study area is mainly mixed agriculture i.e., crop-livestock production, which is mainly rain-fed agriculture.

According to the district statistics, more than 68% of the Mille watershed is covered by agricultural crops and vegetations, while the northern and northwestern parts are dominated by medium-height forest trees, such as Prunus africana, Croton macrostachyus, Cordia africana, and Ficus sur. The study area is characterized by a rich diversity of vegetation and agricultural practices. Economically significant plant species, including Coffea arabica, Mangifera indica, and Catha edulis, play a vital role in the local economy. In addition to these perennial crops, the region also supports various seasonal agricultural crops, such as Zea mays, Sorghum bicolor, Eragrostis tef, and Capsicum annuum, which are particularly abundant during the summer growing season. Vegetation coverage within the watershed varies, with some areas exhibiting dense vegetation, while others are more sparsely covered. The Mille River basin is illustrated using a Sentinel-2 true color composite in Figure 1.

Field LAI measurement

Due to the lack of indirect LAI measurement instruments in the field, the researchers employed direct measurement with minimal disturbance for 17 sample plots. Each field-measured sample plot has a 20 m × 20 m area (Fig. 2B). Before taking measurements, the researchers recorded global positioning system (GPS) coordinates for each plot. The central pixel GPS readings for all plots were verified by overlaying the coordinates with Sentinel-2 image at 20-m resolution.

Figure 2. Location of sample LAI distribution measured in the field. The figure shows 17 sample pixels where LAI was measured using a direct/destructive method with minimal impact on the vegetation. Letter A (black box) indicates a 10 m × 10 m area initially delineated for each sample plots to minimize disturbance during leaf area measurement using the Petiole application. Letter B (red box) marks a 20 m × 20 m area assessed based on the initial measurement in letter A to further reduce disturbance. This method provides accurate ground-truth data for validating the SNAP and MVLR models (Table 1). LAI: leaf area index; SNAP: Sentinel Application Platform; MVLR: multivariate linear regression.

During field measurement, 10 m × 10 m plot sizes were initially delineated for 17 plots (Fig. 2A). Subsequently, a minimum of five evenly distributed vegetation samples were deliberately selected based on criteria such as height, leaf width, and representativeness. From these chosen plants, typical branches located in the middle of each plant were carefully selected for sampling, ensuring minimal disturbance and efficiency in measurement. The area of each leaf was assessed using a smartphone application called Petiole, which utilizes the smartphone’s camera for individual leaf area measurement.

Before use, the camera was calibrated using a calibration pad provided by Petiole Limited Organization. Petiole, a plant leaf area meter app is a free Android app, which has been published by Petiole Limited on April 05, 2021. It is possible to measure individual leaf area, acquire total leaf area, and save data with the Petiole app. Petiole measures most of the vegetation leaf such as soybean, corn, wheat, potato, coffee, pepper, mango, and others with similar leaf structure as mentioned vegetation type. Petiole Pro, a commercial app, helps to monitor plant health, choose plant phenotype for screening, and understand plant stress faster (Confalonieri et al. 2013; Singh et al. 2021).

It can be downloaded for free from https://cloudapks.com/download/416872/26/. LAI field measurement was conducted on non-needle leaf plants with medium height because it is not advisable to use a mobile app in tinny leave and tall forest trees (Fang et al. 2014; Singh et al. 2021). Lastly, the LAI of each sample plot was computed using Equation 1 (Jonckheere et al. 2004; Stenberg et al. 1994). The statistics of LAI measured in the study plots (n = 17) is provided in Table 1.

Table 1 . Leaf area index estimated from field sample plot (pixel) measurements.

Plot IDLocation (m)Vegetation
(scientific name)
Measured LAI
LatitudeLongitude
001570,2411,267,174Capsicum annuum1.00
002570,1601,267,281Capsicum annuum1.50
003567,9521,267,956Bare-land0.00
004567,8841,267,857Catha edulis0.48
005568,8761,268,594Mangifera indica2.40
006568,7651,268,686Mangifera indica1.80
007569,0971,268,266Mangifera indica2.00
008566,1501,263,929Mangifera indica1.80
009562,9261,267,815Coffea arabica1.85
010568,1101,266,612Mangifera indica2.30
011568,5901,266,774Mangifera indica2.00
012570,1911,266,590Bare-land0.00
013563,4801,268,868Catha edulis1.00
014563,2541,269,081Coffea arabica1.50
015565,9041,268,952Catha edulis1.18
016568,8091,268,310Mangifera indica2.50
017564,8051,266,188Coffea arabica1.40

LAI: leaf area index.



LAI=L×B×TPA

where L represents the total leaf area of the sample branches in square meters (m2), B is the total number of branches on the sample plants, T is the total number of trees in the sample plot, and PA denotes the total area of the sample plot in square meters (m2).

Sentinel-2 data and preprocessing

The remotely sensed data used to estimate LAI was a Level 2A cloud-free (< 10%) satellite image, downloaded from https://scihub.copernicus.eu/. Level-2A’s main output is bottom-of-atmosphere corrected reflectance, which is geometrically and atmospherically corrected (Main-Knorn et al. 2015; Sola et al. 2018).

All 10 m spatial resolution bands were resampled to a 20 m pixel size to ensure consistency across all Sentinel-2 image bands and to match the plot size of the in-situ data. The required Sentinel-2 spectral bands for the SNAP and MVLR models were then extracted for the study area, as the SNAP toolbox requires only eight specific bands.

Methods

SNAP toolbox LAI retrieval

In this study, we used the SNAP biophysical processor to retrieve the LAI from Sentinel-2 satellite images. The process relies on a combination of the PROSAIL (a combination of PROSPECT [leaf optical properties spectra] and SAIL [scattering by arbitrarily inclined leaves]) RTM and an artificial neural network (ANN) algorithm. Specifically, the SNAP biophysical processor uses reflectance data from eight Sentinel-2 bands (B3, B4, B5, B6, B7, B8a, B11, and B12) along with angles related to the sun and satellite to simulate how light interacts with the vegetation (Xie et al. 2019). The ANN, trained on this simulated data, is then used to estimate LAI from the actual Sentinel-2 image (Weiss and Baret 2016).

The ANN training data is created using an RTM, which accurately simulates canopy reflectance within Sentinel-2 bands and across various vegetation types and environmental conditions. The SNAP biophysical processor integrates both quantitative and qualitative quality indicators to evaluate the dependability of the resulting product. These indicators allow us to gauge the data’s confidence level and make informed decisions regarding its application.

This algorithm falls under the classification of “non-specific,” suggesting its ability to provide satisfactory performance across different vegetation types in terms of biophysical variables (Kamenova and Dimitrov 2020; Kganyago et al. 2020; Mourad et al. 2020; Xie et al. 2019). The SNAP toolbox includes three biophysical processors: S2_20 m, S2_10 m, and Landsat 8 (Mourad et al. 2020). In this study, we utilized the S2_20 m biophysical processor.

Vegetation indices retrieval

For this study, eighteen VIs and multispectral bands were selected to assess their effectiveness in estimating LAI for tropical vegetation. The VIs was derived from Sentinel-2 satellite imagery, following a rigorous preprocessing protocol to ensure data quality and accuracy. These indices, known for their ability to capture various aspects of vegetation health and structure, were selected for their potential to effectively assess vegetation condition (Kamenova and Dimitrov 2020; Magney et al. 2017; Xie et al. 2018). The retrieval process involved extracting pixel values from each of the Vis’. This data was then used in subsequent regression analyses to develop a linear regression model tailored for LAI estimation in the study area. The VIs and multispectral bands tested to develop the efficient MVLR model are listed in Table 2.

Table 2 . Sentinel-2 multispectral bands and vegetation indices tested for the estimation of leaf area index.

Band No.FunctionCentral wavelength (nm)Spatial resolution (m)
B3Green56010
B4Red66510
B5Red-edge70520
B6Red-edge74920
B7Red-edge78320
B8Near infrared84210
B8aNear infrared86520
B11Short wave IR1,61020
B12Short wave IR2,19020
VIsVegetation indicesFormula
IRECIInverted red-edge chlorophyll index(Band 7 – Band 4)/ (Band 5/ Band 6)
NDVINormalized difference vegetation index(Band 8 – Band 4)/ (Band 8 + Band 4)
TNDVITransformed normalized difference vegetation index12NIRREDNIR+RED+1+1
NDVI45Normalized difference vegetation index with bands 4 and 5(Band 5 – Band 4)/ (Band 5 + Band 4)
SAVISoil adjusted vegetation index[(NIR – Red)/ (NIR + Red + 0.5)] × (1 + 0.5)
REPRed-edge position705 + 35 × [(B4 + B7)/2 – B5]/ (B6 – B5)
MSAVIModified soil-adjusted vegetation index22×NIR+1(2×NIR+1)28×(NIRRED)2
BPVsBiophysical variables
FAPARFraction of absorbed photosynthetically active radiation
FVCFraction of vegetation cover

IR: infrared.



Extraction of predictor variables pixel values

Pixel values for each variable derived from the Sentinel-2 image were extracted using ArcGIS 10.8 software. The geographical coordinates (latitude and longitude) of the field plots served as reference points for aligning the pixels, as illustrated in Figure 2. The extracted pixel values for each predictor variable are presented in Tables 3 and 4. These values were then exported in comma-separated values format for further correlation and regression analysis using R studio.

Table 3 . Pixel values extracted from selected bands of Sentinel-2 image.

Plot IDLocation (m)B3B4B5B6B7B8B8aB11B12
LatitudeLongitude
001570,2411,267,1740.1880.1810.2410.3490.3810.3880.3930.3000.237
002570,1601,267,2810.1850.1800.2380.3650.4010.3890.4190.2880.223
003567,9521,267,9560.2120.2280.2390.2520.2570.2500.2650.2500.226
004567,8841,267,8570.1760.1920.2130.2470.2600.2780.2740.2700.244
005568,8761,268,5940.1750.1570.2230.3960.4390.4460.4550.2810.209
006568,7651,268,6860.1920.1690.2330.3610.3930.4380.4140.2830.219
007569,0971,268,2660.1740.1550.2130.4040.4700.4900.4910.2740.197
008566,1501,263,9290.1690.1530.2040.3850.4400.4620.4650.2810.199
009562,9261,267,8150.1620.1660.2090.2980.3380.3680.3590.2580.198
010568,1101,266,6120.1800.1590.2310.4300.4790.5050.5020.2960.215
011568,5901,266,7740.1910.1740.2450.3770.4110.4420.4440.3150.234
012570,1911,266,5900.2170.2340.2470.2530.2570.2460.2570.2530.233
013563,4801,268,8680.1700.1690.2260.3110.3370.3320.3580.2980.222
014563,2541,269,0810.1710.1730.2150.3040.3310.3720.3530.2820.214
015565,9041,268,9520.1680.1690.2290.3300.3580.3610.3780.2920.227
016568,8091,268,3100.1990.1680.2160.3550.3980.4800.4080.2660.211
017564,8051,266,1880.1620.1470.2060.3800.4360.4310.4650.2730.196

The abbreviation is shown in Table 2.



Table 4 . Pixel values of vegetation indices extracted from Sentinel-2 image.

Plot IDLocation (m)SAVIREPNDVINDVI45MSAVIIRECIFVCFAPAR
LatitudeLongitude
001570,2411,267,1740.3590.7190.5540.2430.3160.3430.4380.432
002570,1601,267,2810.3530.7190.5550.2430.3090.4260.5350.531
003567,9521,267,9560.0480.7140.0910.0460.0390.0420.1190.130
004567,8841,267,8570.1710.7190.3210.1020.1400.0920.1640.187
005568,8761,268,5940.4470.7200.6870.3350.4010.6470.6050.602
006568,7651,268,6860.4010.7180.6170.2880.3560.4330.5210.508
007569,0971,268,2660.5170.7240.7290.2930.4790.9060.7110.727
008566,1501,263,9290.4870.7230.7220.2980.4440.7860.6360.647
009562,9261,267,8150.3470.7230.5890.2240.2980.3600.4630.497
010568,1101,266,6120.5670.7230.7610.3700.5371.0160.7500.753
011568,5901,266,7740.5600.7230.7510.3430.5281.0370.7420.743
012570,1911,266,5900.0440.6990.0810.0510.0360.0270.0880.082
013563,4801,268,8680.2960.7180.5230.2570.2500.2750.3970.400
014563,2541,269,0810.3320.7210.5430.2100.2870.2810.3910.413
015565,9041,268,9520.3370.7190.5660.2600.2900.3310.4320.452
016568,8091,268,3100.4790.7240.6880.2530.4380.7060.6360.647
017564,8051,266,1880.4600.7230.7100.3370.4140.6760.6150.636

The abbreviation is shown in Table 2.



Multi-collinearity test

The presence of multi-collinearity between bands and VIs was tested using tolerance and variance of inflation factor (VIF) using R. Tolerance less than 0.1 and VIF greater than 10 indicates multi-collinearity between variables (Alin 2010; Daoud 2017; Joseph et al. 2012). To remove variables that have multi-collinearity with other variables, we have used the olsrr package in R studio (Kim 2019). This test is important to exclude variables which has the same impact on the dependent variable.

Multivariate linear regression model

In this study, we employed a MVLR model to estimate the LAI using Sentinel-2 multispectral bands and VIs. The MVLR model was developed and analysed using R Studio, chosen for its computational efficiency and its ability to handle multiple predictor variables simultaneously, which is crucial for accurately estimating vegetation characteristics from remotely sensed data.

We developed empirical models by establishing relationships between LAI and the selected VIs and multispectral bands. The Sentinel-2 bands and VIs used in this analysis are listed in Table 2. These variables were chosen based on their relevance in previous studies, which have demonstrated that incorporating multiple VIs can significantly enhance prediction accuracy (Ali et al. 2019; Middinti et al. 2017; Zhang et al. 2021).

The process involved first extracting the spectral bands and VIs from the Sentinel-2 imagery. These extracted features were then input into the MVLR model within R Studio to establish a predictive relationship with the ground-truth LAI measurements. The regression coefficients were derived to optimize the model for LAI estimation, ensuring that the model provided accurate and reliable outputs for the specific tropical vegetation characteristics of the Mille watershed.

Validation of the model

The estimated LAI was passed through a validation process using direct/destructive field-measured LAI values. Accuracy assessment of all individual VI models and MVLR derived model-derived LAI was executed using a cross-validation technique. Due to the limited sample size of field-measured LAI values, it was not feasible to divide the data into separate training and testing datasets for the empirical models. Therefore, the training and the testing data were the whole data sets i.e., seventeen sample plots.

The best cross-validation method to use the whole data sets for training and testing is the leave-one-out cross-validation (LOOCV) (Cawley 2006). To validate the empirical model using the LOOCV method, we used the Caret package in R software. The root mean square error (RMSE), bias and coefficient of determination (R2) were used to validate the MVLR model using the LOOCV technique. The corresponding estimated LAI from SNAP was validated with the in-situ measured LAI. The highest R2, lowest RMSE, and a bias close to zero were considered to be the best-estimated value of the derived LAI.

R2=1(yiy'i)2(yiyi¯)2
RMSE=(yiy'i)2ny¯×100
Bias=(yiy'i)n

where yi and yi are the actual and predicted values for sample i and n is the number of samples considered.

Relationship between multispectral bands and measured LAI

The response of LAI to Sentinel-2 bands reflectance was assessed by fitting a linear regression model. The relationship between measured LAI and Sentinel-2 band reflectance was examined before applying VIs. As shown in Figure 3, the reflectance of several Sentinel-2 bands exhibits a statistically significant correlation with LAI variation.

Figure 3. Association between observed LAI and Sentinel-2 band reflectance. Among the red-edge bands, band 6 (R2 = 0.67) and 7 (R2 = 0.69), the near-infrared band 8 (R2 = 0.86) and 8a (R2 = 0.70), and band 4 (R2 = 0.67) shown a strong correlation. From short wave IR spectrum band 12 has a medium association with observed LAI with an R2 value of 0.35. Bands 3, 5, and 11 show a weak correlation with LAI measured at the field. Bands 3, 4, 5, and 12 show a negative association whereas bands from 6–11 show a positive relationship with that of observed LAI. LAI: leaf area index; IR: infrared.

Relationship between VIs and measured LAI

The result of the correlation analysis between LAI measured at the field and the VIs revealed that there is a strong association between the observed LAI and most of the VIs with R2 values ranging from 0.54 to 0.83. Among the predictor VIs, transformed normalized difference vegetation index (R2 = 0.82), soil adjusted vegetation index (SAVI) (R2 = 0.83), red-edge position (R2 = 0.54), normalized difference vegetation index (NDVI) (R2 = 0.83), NDVI with bands 4 and 5 (R2 = 0.72), and inverted red-edge chlorophyll index (IRECI) (R2 = 0.68) were strongly correlated with LAI (Fig. 4). Since almost all VIs were similarly correlated with LAI, we have investigated the multi-collinearity of predictors for both VIs and multispectral bands of Sentinel-2 image to exclude predictor variables that have multi-collinearity with the other variables. In addition to performing a multicollinearity test, we used stepwise multiple linear regression (SMLR) to identify significant single bands and VIs that exhibit high R2, low RMSE, and a p-value < 0.05 for the best representative model.

Figure 4. Association between observed LAI and VIs computed from Sentinel-2 imagery. LAI: leaf area index; VIs: vegetation indices. The abbreviation is shown in Table 2.

The performance of VIs in estimating LAI from Sentinel-2 bottom-of-canopy reflectance was validated with seventeen field LAI measurements. Based on the fitted linear regression (Fig. 4), the LAI of the study area was estimated. Accuracy and correlation of the VIs models in contrast to in-situ LAI were validated using LOOCV (R2cv), and RMSEcv. VIs models with higher accuracy include SAVI, MSAVI, NDVI, and TNDVI. Relative to the other VIs, REP has a lower correlation and accuracy (Table 5).

Table 5 . The performance of vegetation indices and biophysical variables to estimate leaf area index.

NoVIsR2RMSEBias
1IRECI0.590.48–0.00002
2MSAVI0.700.41–0.00009
3NDVI0.690.41–0.000029
4NDVI450.680.43–0.000049
5S2REP0.360.81–0.006
6SAVI0.720.39–0.000028
7TNDVI0.630.450.00006
8FVC0.730.39–0.000029
9FAPAR0.730.39–0.000029
10MVLR0.940.190.0006
11SNAP0.710.530.31

The abbreviation is shown in Table 2.

MVLR: multivariate linear regression; SNAP: Sentinel Application Platform.



Selection of efficient predictors for MVLR model

When fitting a linear regression model to multispectral bands and VIs for estimating the LAI of the study area, we found that many bands and VIs are strongly correlated with the observed LAI. However, most of the tested predictors have a multi-collinearity. Then, only two bands and three VIs were selected and the remaining variables were excluded from the MVLR model because of lower R2 and the presence of multi-collinearity. Table 6 shows correlation coefficient matrix between Sentinel-2 multispectral bands and VIs derived from Sentinel-2 imagery. In addition to performing a multicollinearity test, we used SMLR to identify significant single bands and VIs that exhibit high R2, low RMSE, and a p-value < 0.05 for the best representative model.

Table 6 . Correlation between Sentinel-2 multispectral bands and vegetation indices derived from Sentinel-2 imagery.

VariablesB7B8B8aSAVINDVINDVI45MSAVIIRECIFVCFAPAR
B71.00
B80.901.00
B8a0.980.901.00
SAVI0.860.900.901.00
NDVI0.790.870.850.881.00
NDVI450.850.790.880.900.921.00
MSAVI0.860.920.900.980.920.881.00
IRECI0.850.830.830.870.740.720.901.00
FVC0.900.920.920.860.900.880.960.901.00
FAPAR0.880.920.920.940.920.860.960.900.981.00

It shows correlation coefficient matrix.

The abbreviation is shown in Table 2.



Table 7 presents the variables selected for developing the MVLR model, including specific bands and VIs, along with their statistical parameters. The variables listed are band 7, band 8, SAVI, NDVI, and fraction of vegetation cover (FVC). The intercept of the model is –0.9812. The overall model summary includes the R2, adjusted R2, and the model’s p-value, indicating a strong fit with R2 of 0.94, adjusted R2 of 0.91, and a significant p-value of 3.313e-06.

Table 7 . Statistical parameters of selected bands and vegetation indices for multivariate linear regression model development.

PredictorsR2EstimateStandard errort-valuep-value (> |t|)
(Intercept)-–0.98120.7583–1.2940.22220
B80.7213.16323.54483.7130.00342
B70.68–10.52143.3703–3.1220.00972
SAVI0.72–8.84944.2009–2.1070.05893
FVC0.734.98222.31062.1560.05405
NDVI0.693.63701.60952.2600.04511
Model summary

Model typeR2Adjusted R2F-statisticsp-value
MVLR0.940.9132.133.313e-06

The abbreviation is shown in Table 2.

MVLR: multivariate linear regression.



Therefore, using the selected variables’ correlation with field-measured LAI, and the intercept and slope of the regression, the MVLR model was developed (Equation 5).

LAI=(10.52×B7)+(13.1632×B8)  (8.8494×SAVI)+(3.6370×NDVI)+  (4.9822×FVC)0.9812

Validation and comparison of MVLR model and SNAP toolbox derived LAI

The correlation result demonstrated that the selected VIs showed an excellent performance in predicting the LAI of the study area. Even though each predictor performs well individually, the combination of band 7, band 12, IRECI, and SAVI outperforms all of them. The MVLR model was cross-validated with 17 field-measured LAI using the LOOCV technique. The RMSE and the R2 show a superior performance than the SNAP-derived LAI. The developed MVLR model has an R2 of 0.94 (Fig. 5). In contrast, the SNAP toolbox-derived LAI achieves an R2 of 0.71 (Fig. 6). Tables 8 and 9 provide a detailed comparison of observed and predicted LAI values from both the MVLR model and SNAP toolbox across various plot locations.

Table 8 . Comparison of multivariate linear regression model and Sentinel Application Platform derived leaf area index.

ModelsR2BiasRMSE
MVLRM derived LAI0.940.00060.19
SNAP toolbox derived LAI0.710.310.53

RMSE: root mean square error; MVLRM: multivariate linear regression model; LAI: leaf area index; SNAP: Sentinel Application Platform.



Table 9 . Comparison of observed LAI with predicted LAI values from the multivariate linear regression model and SNAP toolbox.

Plot IDLocation (m)Observed LAIPredicted LAI
(MVLR) model
Predicted LAI
(SNAP toolbox)
LatitudeLongitude
001570,2411,267,1741.001.141.28
002570,1601,267,2811.501.491.57
003567,9521,267,9560.000.110.30
004567,8841,267,8570.480.420.93
005568,8761,268,5942.401.832.45
006568,7651,268,6861.801.932.54
007569,0971,268,2662.002.143.52
008566,1501,263,9291.801.962.03
009562,9261,267,8151.851.681.55
010568,1101,266,6122.302.102.68
011568,5901,266,7742.001.992.58
012570,1911,266,5900.000.100.20
013563,4801,268,8681.001.111.51
014563,2541,269,0811.501.421.26
015565,9041,268,9521.181.231.39
016568,8091,268,3102.502.592.14
017564,8051,266,1881.401.682.04

LAI: leaf area index; MVLR: multivariate linear regression; SNAP: Sentinel Application Platform.



Figure 5. Validation of MVLR model-derived LAI using ground-measured LAI. MVLR: multivariate linear regression; LAI: leaf area index.

Figure 6. Validation of SNAP toolbox-derived LAI using ground-measured LAI. SNAP: Sentinel Application Platform; LAI: leaf area index.

With a 95% confidence interval, LAI derived from the SNAP toolbox and the MVLR model exhibit similar outliers. RMSE for the SNAP and MVLR model-derived LAI were 0.53 and 0.19, respectively. When investigating the bias of both models, the SNAP toolbox had a bias of 0.31, whereas the MVLR model had a bias of 0.0006. The positive bias indicates overestimation in the model (Fig. 7).

Figure 7. Comparison of MVLR model and SNAP toolbox: The figure illustrates the comparative analysis of LAI values derived from the MVLR model and SNAP Toolbox methods. The graph highlights the variations in metrics and the relative performance of each method. MVLR: multivariate linear regression; SNAP: Sentinel Application Platform; LAI: leaf area index.

In this study, we investigated the efficacy of two distinct methodologies—MVLR model and SNAP-derived LAI—for estimating LAI in tropical vegetation. Our results demonstrated that both methods could effectively estimate LAI; however, there were notable differences in their accuracy and reliability under varying conditions. The availability of fine Sentinel-2 bands in the red-edge region of the electromagnetic spectrum, combined with their high spatial resolution, facilitates better-quality and simpler calculations of LAI using multispectral bands and VIs. This enhanced capability allows for more accurate and detailed assessments of vegetation characteristics, which are crucial for various ecological and environmental applications.

While some VIs saturate when the LAI increases (Baret and Guyot 1991; Pasqualotto et al. 2019a), this study demonstrates that such saturation does not impact our estimates. The maximum LAI of 3.52 observed in the study area, though likely overestimated by the SNAP toolbox, falls below the saturation threshold (Baret and Guyot 1991). This suggests that the selected VIs and multispectral bands effectively capture LAI variations within the observed range, ensuring reliable and accurate measurements.

The results of the MVLR model demonstrate the effectiveness of empirical models that utilize combinations of multispectral bands and VIs for accurately estimating green LAI. Such models offer simplicity and speed. The findings show that LAI strongly correlates with most of the multispectral bands and VIs derived from Sentinel-2 satellite image. Each of the tested bands and VIs has a statistically significant correlation with the field-measured LAI. However, the presence of multicollinearity among several of the tested variables complicates the development of the MVLR model.

Predictor variables with multi-collinearity and weak association were excluded as they cause high variance in regression analysis (Muhe and Argaw 2022). The green band, band 5 from the red-edge region, band 11 and 12 from the shortwave infrared region exhibit a weak association with field-measured LAI. The combination of the above-listed bands is important in leaf dry matter content investigation rather than green LAI (Ali et al. 2019).

The estimation of LAI demonstrates promising accuracy through the utilization of individual reflectance and VIs. While each VI independently exhibits a satisfactory level of predictive capability for LAI, the incorporation of multiple VIs significantly enhances the prediction accuracy. This highlights the importance of a multifaceted approach that leverages diverse VIs to enhance LAI estimation accuracy (Middinti et al. 2017).

Multi-collinearity between the variables, assessed through tolerance and variance inflation factors, is a critical consideration in this analysis. The strong associations observed among most Sentinel-2 bands and VIs suggest that the formulation of commonly used VIs, which often rely on similar spectral bands, inherently contributes to this multi-collinearity. Specifically, the high correlations found between bands 4 and 6, as well as bands 8 and 8a, and their associations with certain VIs, are likely due to the similar reflectance characteristics of vegetation in the red and red-edge (bands 4, 6, and 7) and NIR (bands 8 and 8a) regions. These findings underscore the importance of carefully selecting input variables to minimize redundancy and enhance model performance (Zheng and Moskal 2009).

Based on the association of spectral bands with actual measured LAI and their multicollinearity statistics, the importance rankings of spectral bands for predicting LAI were as follows: NIR (band 8), red-edge (bands 6 and 7), red (band 4), SWIR (band 12), and NIR (band 8a). These results align with the findings of Chrysafis et al. (2020), who investigated LAI retrieval in a mixed Mediterranean forest area using multispectral bands derived from Sentinel-2 imagery.

The combination of band 7, band 8, SAVI, NDVI, and FVC achieved excellent accuracy in predicting LAI (Fig. 5). This result agrees with the findings of Middinti et al. (2017), who demonstrated that utilizing multiple VIs yields a more efficient and accurate prediction of LAI compared to a single VI. The enhanced accuracy can be attributed to the complementary information provided by different spectral bands and indices, which capture various aspects of vegetation characteristics and reduce the impact of individual index limitations. By integrating multiple VIs, the model benefits from a broader and more nuanced dataset, leading to improved predictive performance and robustness in LAI estimation. This multi-faceted approach allows for better handling of the complexities and variations within the vegetation canopy, thus providing a more reliable assessment of LAI.

The analysis confirms that combining multiple spectral bands and VIs significantly enhances LAI prediction accuracy. The superior performance of the MVLR model, as evidenced by the high R2cv of 0.94, emphasizes the effectiveness of integrating diverse independent variables. This model’s high accuracy can be attributed to the complementary information captured by different bands and indices, which provide a more comprehensive representation of the vegetation canopy. This result is highly consistent with the findings of Middinti et al. (2017), who predicted LAI using reflectance and VIs from Landsat 8 OLI (Operational Land Imager) in Indian tropical forests (R2 = 0.83, RMSE = 0.78), though our study achieved a slightly higher R2 and lower RMSE.

In our study, we validate the SNAP-derived LAI with an R2 of 0.71, a bias of 0.31, and an RMSE of 0.53. These results demonstrate a good correlation between observed and predicted LAI values, aligning well with findings from previous studies. For instance, our R2 value closely matches that of Djamai et al. (2019b), who reported an R2 of 0.70, though our RMSE (0.53) is significantly lower than their RMSE of 0.98, indicating better performance in our case. Compared to Chauhan and Lunagaria (2024), who also achieved an R2 of 0.70 but with higher bias, our study shows improved accuracy with a lower bias (0.31). Moreover, while Binh et al. (2022) reported a lower R2 of 0.45 and a higher RMSE of 2.19, highlighting challenges in LAI estimation for mangroves, our study’s higher R2 and lower RMSE demonstrate better reliability and precision in LAI retrieval. Similarly, our findings surpass those of Brown et al. (2019), who reported an R2 of 0.54 and an RMSE of 1.55 in forest environments. Lastly, our results are consistent with Pasqualotto et al. (2019b), who found an R2 greater than 0.70 and an RMSE below 0.86, further supporting the strength of LAI retrieval using SNAP in tropical regions.

However, the comparative analysis of R2, RMSE, and bias underscores the robustness of the MVLR model in predicting LAI. The significantly lower RMSE (0.19) of the MVLR model, compared to the SNAP toolbox’s RMSE (0.53), underscores the superior precision of the MVLR model’s predictions. Moreover, the minimal bias observed in the MVLR model (0.0006) suggests a reduction in systematic errors, thereby enhancing the reliability of its LAI estimates. In contrast, the positive bias observed in the SNAP- derived LAI (0.31) indicates a tendency towards overestimation, suggesting that while the SNAP toolbox is useful, it may benefit from further calibration or adjustment for specific applications. This finding supports the conclusions of Kganyago et al. (2020), who validated SNAP-derived LAI using field-measured LAI data for two different crop types—sunflower and maize. Their study identified overestimation at different growth stages of these crops, suggesting that SNAP’s performance is contingent upon both crop type and growth stage, which is consistent with our findings. This indicates that the VIs and multispectral bands-based MVLR model can predict LAI with greater accuracy than the SNAP biophysical processor.

According to Kganyago et al. (2020), the overestimation of LAI and major biases perceived from SNAP-derived LAI may be as a result of prior rules made from global LAI retrieval models which cannot be adjusted to local environments. This overestimation can impact the interpretation of vegetation health and density, making it crucial to consider the model biases when using these tools for ecological and environmental research. The findings emphasize the importance of model validation and the integration of multiple data sources to achieve accurate and reliable LAI predictions. However, the performance of SNAP-derived LAI, in this study, is slightly better than the Kganyago et al. (2020) research findings (R2 = 0.6 to 0.70).

The superior accuracy of the MVLR model in our study is attributed to its adjustment for the specific vegetation types found in the study area. This tailored approach enables more precise estimation of LAI, particularly in the context of tropical climatic regions where diverse vegetation types and seasonal variability are prevalent. In contrast, the lower accuracy of the SNAP-derived LAI highlights the challenges of applying global models to local environments without customization. The effectiveness of the estimated LAI extends beyond mere accuracy; it plays a crucial role in assessing vegetation health, monitoring ecosystem dynamics, and informing sustainable agricultural practices in tropical regions. To further enhance the accuracy of the MVLR model, incorporating additional field-measured LAI data would be beneficial, providing a stronger foundation for training the model and improving its predictive capabilities across various tropical landscapes.

This study provides a comprehensive comparison between the MVLR model and the SNAP biophysical processor for estimating LAI in tropical vegetation. The findings demonstrate that while both methods are capable of estimating LAI, the MVLR model offers superior accuracy and reliability, particularly due to its incorporation of multispectral bands and VIs tailored to the specific characteristics of tropical vegetation. The MVLR model’s high R2, minimal bias, and lower RMSE compared to SNAP-derived LAI underscore its effectiveness in providing precise LAI estimates, which are critical for applications in ecological monitoring and sustainable agricultural practices. The study also highlights the limitations of using global models like SNAP in local environments, where adjustments for specific vegetation types and climatic conditions are necessary. The observed overestimation in SNAP-derived LAI, aligned with findings from other studies, suggests that further calibration or adjustment is needed to improve its accuracy for local applications.

Overall, the MVLR model has demonstrated superior performance in estimating LAI in tropical region, highlighting its potential as a robust and reliable tool. Future research should focus on incorporating additional field-measured LAI data to further refine the model and expand its applicability across diverse tropical landscapes. Additionally, comparing the MVLR model with other global LAI products will be crucial for further validation and to enhance its effectiveness in diverse environments.

We are thankful to the members of the Department of Geography and Environmental Studies at Wollo University who assisted with field data collection. We also extend our gratitude to the anonymous reviewers and the academic editor for their valuable and insightful feedback.

LAI: Leaf area index

MVLR: Multivariate linear regression

SNAP: Sentinel Application Platform

VIs: Vegetation indices

RMSE: Root mean square error

SMLR: Stepwise multiple linear regression

SAVI: Soil adjusted vegetation index

NDVI: Normalized difference vegetation index

RTM: Radiative transfer models

ANN: Artificial neural network

VIF: Variance of inflation factor

LOOCV: Leave-one-out cross-validation

IRECI: Inverted red-edge chlorophyll index

FVC: Fraction of vegetation cover

AYA, AMA, and NA designed methodology, AYA collected field data. AYA, and AMA conceived the study, and designed the research framework, AYA performed statistical analysis and prepared the manuscript, AMA, and NA provided supervision throughout the study, AYA writing original drift, NA, AMA, BG Validation, AMA, NA, and BG reviewing and editing. All authors read and approved the final manuscript.

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