## 3 Results
### Empirical-Based Models  
One of the commonly used remote sensing methods of deriving LAI from spectral data is the empirical-based approach [38]. In this approach, regression models are used to study the relationship that exists between the target variables; for example, LAI and its spectral reflectance. Empirical methods also use derived metrics and machine-learning methods to derive LAI. The number of studies exploring newly developed vegetation indices and models increased for forest, crop and grassland LAI estimations.  
The R\({}^{2}\) of empirical models ranged from 0.14 to 0.99 and the RMSE ranged from 0.01 to 2.41 (Table 2). This indicates that the performance of empirical models was variable. Machine learning methods performed relatively consistently for forest in terms of the R\({}^{2}\) (0.85-0.93). Unlike forests, crops and grasslands had a highly variable performance in terms of R\({}^{2}\) (0.44-0.98). The use of machine-learning algorithms for estimating LAI showed positive results in a number of studies; examples include [32; 33; 39; 40]. A study conducted by [39], using WorldView-2 imagery, demonstrated that machine-learning algorithms such as support vector machines (SVMs) and artificial neutral networks (ANN) can accurately predict LAI at tree species level. The SVM model which was based on validation data achieved an R\({}^{2}\) of 0.75. There was an overall increase in machine learning methods, especially for big data calculations.  
There were more than 150 vegetation indices that were developed for mapping and estimating biomass, either using space borne, airborne and ground-based sensors [41]. Of the 150 vegetation indices, only a few were tested and validated [42]. Ref. [43] estimated LAI and other plant structural attributes using satellite images. This study used traditional vegetation indices such as the normalized difference vegetation index (NDVI) and found that NDVI had a strong correlation of R\({}^{2}\) = 0.83 with biomass and R\({}^{2}\) = 0.70 with LAI. Although different vegetation indices showed positive results for estimating LAI, there  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & & **Forest** & & & **Crop** & & & **Grassland** & \\ \hline
**Model** & **Sensors** & **N** & **R** & **RMSE** & **N** & **R** & **RMSE** & **N** & **R** & **RMSE** & **Method** \\ \hline  & PROSAIL & 5 & 0.63–0.92 & 0.26–1.12 & 9 & 0.58–0.96 & 0.3–1.16 & 5 & 0.67–0.98 & 0.27–1.13 & \\ \hline  & PARAS & 2 & 0.83–0.93 & 0.71–0.85 & 0 & & & 0 & & & \\ \hline Hybrid Models & 4-Scale BRD & 2 & 0.43–0.68 & 0.31–1.08 & 1 & 0.86 & 0.43 & 0 & & & Regression and ML algorithms \\ \hline  & Other models & 5 & 0.21–0.99 & 0.20–1.86 & 1 & 0.89 & 0.5 & 1 & 0.78 & 0.64 & \\ \hline  & & & & & & & & & & & Regional \\ Other models & & 6 & 0.41–0.096 & 0.01–0.92 & 3 & 0.43–0.97 & 0.42–0.98 & 1 & 0.67–0.099 & 0.01–1.94 & 0.01–1.94 & 0.01–1.94 & 0.01–1.94 \\  & & & & & & & & & & & distribution \\  & & & & & & & & & & model, etc. \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Number of Papers** & **Example** \\ \hline Reflectance based & 38 & [PERSON] et al. [30] \\ \hline Vegetation index based & 47 & [PERSON] et al. [31] \\ \hline Derived metrics & 29 & [PERSON] et al. [32] \\ \hline Machine learning models & 11 & [PERSON] et al. [33] \\ \hline
4-Scale bidirectional & 14 & [PERSON] et al. [34] \\ \hline PROSPECT + DART & 29 & [PERSON] et al. [35] \\ \hline PROSAIL & 23 & [PERSON] et al. [36] \\ \hline Other models & 14 & [PERSON] et al. [37] \\ \hline \hline \end{tabular}
\end{table}
Table 3: Most used model types.  
was no vegetation index that is generic and can be applied consistently and continuously to estimate LAI regionally and globally.