2.1. AGB
AGB is the main parameter of grassland biomass, and its estimation is the focus of the grassland study with the largest number of publications. It is usually defined as the organic matter produced by the photosynthesis of grassland plants, which can be expressed as the dry weight of grassland plants in the above-ground part of a unit area. It is one of the significant indices of global carbon cycling, reflecting the carbon sink potential of grassland vegetation [
47], and its changes directly reveal the degree of grassland growth and degradation, easily employed to monitor overgrazing [
59].
The estimation models of AGB can be divided into parametric and non-parametric models. Specifically, parametric models mainly include linear [
25], logarithmic [
21], exponential [
33], and other forms of functional models [
60] that belong to statistical regression methods, while non-parametric models mainly involve support vector machine (SVM) [
47], random forest (RF) [
61], and artificial neural network (ANN) [
62], which are primarily machine learning methods. In general, parametric regression models first select variables significantly related to AGB, after which a pre-assumed functional relationship between the variables and AGB is fitted by statistical data. Meanwhile, according to the number of variables, parametric regression models can be further classified as univariate and multivariate models. Except for the abovementioned parametric models that belong to univariate models, the multivariate linear regression (MLR) model is one of the most commonly used multivariate models in this field [
9,
18,
32].
For the selection of variables, due to the significant correlation between vegetation height and biomass, many studies have focused on the inversion of vegetation height, which in turn can be linked to the AGB. These studies share significant methodological similarities in which 3D point cloud data used for inversion were generated from UAV images, while parametric regression models were developed for estimation. Zhang et al. [
21] generated dense 3D point cloud data from UAV RGB images, and vegetation height was generated by calculating the distance between the point cloud data and corresponding ground meshes. The AGB was eventually estimated by a logarithmic regression model using the mean vegetation height, which achieved the coefficient of determination (
) of 0.89 between the estimated and measured AGB. Then, Grüner et al. [
60] also produced 3D point clouds and calculated mean vegetation height based on the difference between digital surface model data and digital elevation model (DEM) data. Then, the AGB was estimated by a reduced major axis regression model whose robustness was demonstrated even under extreme weather conditions (
). In addition, in [
25,
27], the mean vegetation height was also derived from 3D point cloud data, and both of them were utilized to developed linear models for AGB estimation.
Apart from the mean vegetation height, other forms of vegetation height derived from UAV or gound images were also utilized. In [
63], the 90th percentile of vegetation height was derived from UAV images and was adopted for estimation in temperate grasslands by a linear model, but the results indicated that the model worked successfully only at the beginning of the growing season, while at other times, an MLR model combined with the NDVI was necessary. In [
27], the grass volume was derived from UAV images, but its performance was worse than that of mean vegetation height derived from ground images. Then, Xu et al. [
32] adopted ground-based LiDAR data to generate a 3D point cloud, which derived minimum vegetation height and FVC that were utilized to construct an MLR model with the best performance (
). Furthermore, Wijesingha et al. [
31] chose the 75th percentile of vegetation height derived from UAV images or ground-based LiDAR data as the variable in a linear model. Their results showed that the performance based on UAV data was slightly worse than that of LiDAR data. However, these studies are overly dependent on vegetation height, which led to an inability to cope with grasslands made up of complex structures and vegetation. Shi et al. [
22] derived the red-green-blue vegetation index (RGBVI) and the surface bare ratio from UAV RGB images and combined them with ground-measured grazing intensity to create a polynomial regression model achieving
of 0.88. Nevertheless, the above studies should be combined with satellite data to further improve their performance.
Among various satellite data, most researchers preferred to directly select some vegetation indices highly correlated with vegetation growth and status. Therefore, the NDVI has always been popular in studies [
9,
38,
64,
65,
66]. In addition, EVI, SAVI, and LSWI were utilized in some studies [
18,
26,
39]. For example, Li et al. [
39] estimated peak AGB of alpine grasslands by an EVI-based linear model, and they further focused on the temporal variability of precipitation on the AGB so that a new index was developed through the principal component analysis (PCA) and an MLR model to quantify this variability. Kong et al. [
9] selected VI2 (normalization value of green peak reflectance and red valley reflectance) and the NDVI as driving variables through correlation analysis and developed an MLR model for alpine grasslands, gaining
of 0.87. Wang et al. [
18] developed an MLR model, which combined optical and radar data as variables. However, these above-vegetation indices are easily disturbed by soil background. On this basis, Ren et al. [
26] introduced a negative soil adjustment factor into SAVI to remove the effect of soil background and estimated the AGB in desert grasslands through a linear model, which demonstrated that the performance of the improved SAVI far exceeded that of the NDVI. However, their experiments were conducted on the ground using ASD hyperspectral images alone, requiring further validation on satellite images. Wang et al. [
38] modified several typical vegetation indices according to the changes of FVC in different phenological periods to eliminate the effect of soil background in semiarid grasslands and then compared them on different regression models, demonstrating the logarithmic model based on the modified NDVI achieved the best performance (
).
Apart from soil background, the low spatial and temporal resolution of some satellite images also limits the accuracy of estimation. To improve the temporal continuity of the estimation results, Clementini et al. [
64] integrated NDVI data from SPOT, MODIS, and Landsat satellites to generate a long time series of the AGB for grazing grasslands using a power function regression model. Then, for the improvement of spatial resolution, Pang et al. [
67] proposed a satellite-scale simulated spectra method, which scaled up ASD hyperspectral images to the satellite level with high spatial resolution by a mixed pixel decomposition model. Then, a multi-granularity spectral segmentation algorithm was adopted to extract spectral segmentation features that were used in an MLR model, achieving
of 0.95. Furthermore, to obtain NDVI data with both high temporal and spatial resolution, Zeng et al. [
68] built a rule-based piecewise regression tree model to fuse MODIS and Landsat images and generated averaged the NDVI time series with 30m resolution that were finally employed in an exponential model to estimate the AGB. In addition, some other factors have also been studied. KarakoÇ et al. [
66] investigated the spectral properties of grasslands at different altitudes and with different biomass densities in the Mediterranean region. The performance of linear and exponential models based on various forms of the NDVI and simple ratio (SR) were compared, which indicated that the spectral saturation effect due to high biomass densities severely degraded the estimation accuracy, while the selection of indices depending on the spectral characteristics of grasslands was more crucial than the choice of regression models. In addition, Braun et al. [
15] explored the possibility of using satellite radar data alone. PCA was applied to integrate SAR data and passive brightness temperature data from radar satellites, which showed that the radar-based exponential regression model performed better in a savanna with low biomass but could not cope with high biomass, only achieving the
of 0.52. Bao et al. [
69] adopted the wavelet-PCA to fuse SAR images and multispectral images and estimated the AGB by a linear model using fused bands, which significantly outperformed the models based on vegetation indices or SAR images alone. Similarly, in [
18], the results showed that the combination of SAR data could dramatically boost the model performance. Thus, the combination of optical and radar data is a feasible option for improvement.
However, the improvement of the above optimization strategies is limited. Parametric estimation models generally do not perform well, especially in the case of high spatial heterogeneity and complex grass species. Compared to parametric models, non-parametric models also require the selection of variables, but they can freely learn from statistical data without any pre-assumed functional relationships. John et al. [
70] developed a rule-based Cubist model, which belongs to the regression tree approach in which driving variables mainly include vegetation indices, satellite products, topographic and climatic variables. Then, Yin et al. [
71] adopted the consistent adjustment of the climatology to actual observations method to fill the temporal gaps in Landsat images, generating a series of high temporal resolution images that were subsequently utilized to train a Gaussian process regression model, which achieved a relatively high accuracy (
) compared to univariate regression models. Naidoo et al. [
61] developed an RF model using various forms of the NDVI and SR and some spectral bands as variables. Although their best results were obtained by using only the WorldView data due to its higher spatial resolution, the Sentinel optical data could also achieve comparable performance when combined with their SAR data. Finally, Zheng et al. [
72] combined vegetation indices, meteorological data, and topographical data to drive an RF model gaining the
of 0.76.
Apart from the combination of satellite data, some recent studies have combined ground survey data and remote sensing data [
47,
73,
74]. In detail, Lyu et al. [
74] combined the NDVI and the EVI with meteorological and soil variables to construct an ANN model achieving superior performance (
). Meng et al. [
47] compared various statistical regression models with machine learning models driven by six indices from both ground and satellite data. They verified that the RF model achieved the best results with
of 0.78. Finally, Zhou et al. [
73] combined ground data with the NDVI and selected seven indices to drive an RF model whose results were subsequently taken as the driving field for the simulations of high accuracy surface modeling, which not only achieved better results (
) than machine learning models but also accurately reproduced the spatial distribution characteristics of the AGB. In their further analysis, they concluded that warm and humid climates, overgrazing, and population growth are the main factors to drive the AGB changes.
In summary,
Table 2 shows more details about the above methods. The
values between the estimated and actual AGB have been extracted according to their best experimental results, which can be used to evaluate the conformance between estimated and actual values.
2.2. Primary Productivity
The main parameters involved in this field are GPP and net primary productivity (NPP). GPP is generally defined as the amount of organic carbon fixed by photosynthesis in unit time by green plants, which is the biggest carbon flux of terrestrial ecosystems, while NPP is equal to GPP minus autotrophic respiration, which reflects the efficiency of plants in fixing and converting photosynthetic products and also determines the material and energy available to heterotrophic organisms. Therefore, the accurate estimates of GPP and NPP and the precise tracking of their spatial and temporal changes are the basis for understanding ecosystem dynamics and studying regional carbon uptake and cycling.
It is worth noting that traditional specialized estimation methods in this field mainly include the process-based biogeochemical approach and the light-use efficiency (LUE) approach. The process-based biogeochemical approach, mainly including the Biome-BGC model and the boreal ecosystem productivity simulator model, simulates the physiological processes in plants such as the photosynthesis and the decomposition of organic matter. The LUE approach is generally founded on the absorption and conversion of incident solar radiation by plants, including the vegetation photosynthesis model (VPM) and the CASA model. Recently, with the widespread use of remote sensing technology, most studies have combined remote sensing data with traditional methods for estimation and monitoring at large scales. Among these methods, the CASA model is the most popular and widely used [
75,
76,
77,
78]. Based on it, NPP can be estimated by:
where
is the actual LUE and
is the absorbed photosynthetically active radiation.
where
is the total solar radiation,
is the fraction of photosynthetic active radiation absorbed by vegetation canopy, and the coefficient of 0.5 is the proportion of vegetation utilizing active incoming solar radiation, which is a frequently used empirical value.
where
is the ideal maximum LUE,
and
are the environmental stress coefficients of temperature, and
is the environmental stress coefficients of water. It is worth noting that
,
, and
reflect the restriction of LUE.
Some satellites can directly provide NPP and GPP products. For example, MOD17 is a set of NPP and GPP products provided by MODIS. Their estimation algorithms are based on the LUE approach. However, the reliability of MODIS GPP products is still a challenge, especially with extreme or highly variable climates and high levels of human activities. Zhu et al. [
45] evaluated the performance and robustness of MODIS GPP products in tropical, temperate, and alpine grasslands, demonstrating the products generally underestimate the actual GPP by approximately 32%. They attributed this problem to the bias of
and the uncertainty of
. Ye et al. [
34] applied a GLOPEM-CEVSA model that belongs to the LUE approach for NPP estimation and adopted a defoliation formulation model to calculate the carbon consumed by grazing. Their results showed that grazing would cause an underestimation of NPP by about 29% in semiarid and arid grasslands. Thus, rather than directly adopting satellite products, researchers prefer to develop specific models for the study area to obtain more robust estimates. These models mainly belong to the above approaches and require numerous parameters to drive and calibrate [
79,
80,
81,
82,
83]. However, similar to the problems in [
45], most parameters are uncertain and sparse and are difficult to obtain by same measuring methods.
On this basis, the combination of ground and remote sensing data is fully utilized in many studies to calibrate the process-based biogeochemical models and LUE models. Nanzad et al. [
79] combined satellite products and meteorological data to drive a boreal ecosystem productivity simulator model. You et al. [
80] introduced NDVI-driven phenological indices to improve the Biome–BGC model and obtained an increase of 0.08 in
compared to the original model (
). Biudes et al. [
81] adopted vegetation indices and products from MODIS data to drive multiple models for GPP estimates in tropical savanna, demonstrating the VPM model performed best. Irisarri et al. [
82] also utilized the NDVI to drive a LUE method and quantified the effects of temperature, precipitation, and human activity on NPP in arid grasslands. Yu [
83] developed a LUE–VPM model based on satellite products for GPP estimation in alpine grasslands, which achieved a large decrease of 36.21 in the root mean square error (RMSE) metric compared to MODIS GPP products.
Meanwhile, Zhao et al. [
75] optimized a CASA model for NPP estimation in temperate grasslands, which simulated
based on meteorological data, estimated
based on the NDVI and the ratio vegetation index (RVI), and derived
based on temperature and LSWI. Their results demonstrated that the optimized model outperformed MODIS NPP products with 0.06 improvement in
. Then, the CASA model was also improved by Luo et al. [
77], who modified the calculation of
by LSWI, achieving an increase of 0.04 in
and a decrease of 0.11 in RMSE compared to original model. Zheng et al. [
76] also constructed a CASA model, which estimated
based on the NDVI and proved a strong correlation between spring phenology and NPP in alpine grasslands. In addition, the NDVI time series were built by Blanco et al. [
84] using MODIS data to estimate
by a linear model, and NPP was calculated by a LUE method. Gaffney et al. [
85] constructed the NDVI time series with high spatial and temporal resolution by fusing Landsat and MODIS data to fit the
for semiarid rangelands, and the above-ground NPP was estimated by a linear model similar to Equation (
1). Their results pointed out the potential confounding effect of dead vegetation biomass on
, especially in grasslands with a long growing season. Similarly, Liu et al. [
86] also fused Landsat and MODIS data to construct the NDVI time series for
estimates and then calculated
according to Equation (
2). They assumed that annual grassland production is equal to
accumulated during the growing season and obtained
of 0.83 on California grasslands. In addition, the selection of
is also crucial for a CASA model; many studies usually just rely on an empirical value [
76,
77], which is not suitable for all grasslands. Thus, Jin et al. [
78] modified the calculation of
based on the least error criterion between the estimated and ground-measured NPP and established the quadratic u-curve functions of
for different types of grasslands, which achieved a boosting of 0.09 in
compared to the original model based on empirical values.
There are also some studies that have developed statistical regression models such as linear [
40,
87], exponential [
88,
89], power function [
48], and MLR [
28,
90]. Most of these studies focused on the selection of driving variables for their models. In [
40], the performance of the red-edge and non-red-edge vegetation indices was compared, which showed that the red-edge chlorophyll index could improve GPP estimation at large scales. In [
88], the performance of several vegetation indices was also contrasted, which indicated that MSAVI based on an exponential model worked best. Sakowska et al. [
87] adopted various vegetation indices from satellites and airplanes with linear models to investigate the scale dependency of NPP estimation, which showed that the near-infrared difference index (NIDI) performed best, and they further proved the potential of Sentinel multispectral images for large-scale estimation. Matthew et al. [
91] applied a piecewise function between the maximum NDVI and the NPP considering the asymptotic and saturated nature of the NDVI to estimate the long-term annual production in the Great Plains, achieving
of 0.79. Cerasoli et al. [
28] simulated satellite images from ASD hyperspectral images and constructed an MLR model for GPP estimation in the Mediterranean. Unlike previous studies that only focused on vegetation indices, spectral band was also considered in [
28] and proved to be as essential as vegetation indices. Then, Xu et al. [
90] constructed an MLR model based on phenological variables and the maximum of GPP, both of which were derived from the EVI and land surface temperature products. In addition, Dieguez et al. [
92] applied a harmonic oscillation function based on the obtained maximum and minimum NPP data from satellite products to fit the NPP dynamic curve for Uruguayan grasslands considering the effects of climate and grazing. Meroni et al. [
93] estimated GPP by the assimilation of MODIS NDVI into a crop growth model that was driven by meteorological variables. The results showed that the assimilation method outperformed MODIS products with a 0.14 improvement in
.
Table 3 lists more details of most studies mentioned above. The values of
are from the best experimental results of the involved studies. In addition, it is necessary to take environmental and human factors into account if we want to obtain highly accurate estimates. Many of the above studies have focused on the spatial and temporal variation of primary productivity and exploring the factors that cause changes. Gómez et al. [
94] adopted MODIS GPP products to quantify the contribution of climate factors, sunshine, and nitrogen deposition for GPP estimation in alpine grasslands using MLR models. The results demonstrated that precipitation and temperature were the first and second most important variables, while nitrogen deposition also had a significant impact. The results in [
84] also demonstrated that the temporal variability of NPP could be largely explained by the precipitation during growing seasons. Many others studies have also pointed out that precipitation and temperature directly affect the distribution and accumulation of primary production [
48,
75,
79,
82,
92,
94]. Apart from climate factors, the impact of grazing [
34,
77,
82], fertilization treatment [
28], beginning of growing season [
76], and grassland policies [
48] were also investigated. In addition, the influence of dead vegetation biomass and below-ground biomass should also be considered, especially in grasslands with long growing seasons [
85,
95]. In [
95], the significant underestimation of NPP using peak live biomass alone was experimentally demonstrated, particularly in tropical grasslands, due to the neglect of dead vegetation and below-ground biomass. Therefore, adding some appropriate variables to the estimation process, depending on the characteristics of the grassland under study, can help improve the accuracy of the results.
2.3. FVC
FVC is defined as the percentage of the vertical projection of green vegetation over the entire calculated area, which is the basic parameter for describing the characteristics of the grassland ecosystem and for obtaining the condition of grassland vegetation with its changes. Its accurate estimation is of great practical significance for regional grassland environment evaluation, management, and degradation monitoring.
The commonly used ground measurement methods of FVC for the accurate verification in most estimation methods are different from those of the previous parameters. Although sampling methods for ground measurements exist, the most commonly used method is the threshold-based photographic method that usually employs digital cameras or spectrometers to shoot the ground. Some studies focused on FVC estimation at near-surface and proved the validity of the photographic method [
24,
96,
97]. In [
24], the excess green index was calculated based on UAV RGB images for each pixel with a threshold to distinguish vegetation and non-vegetation pixels through an iterative algorithm. Then, the effect of the degree of vegetation fragmentation on the number of required sample images for validation was also investigated in [
24]. Xu et al. [
96] adopted ground-based RGB images, which set thresholds for the pixel difference values between different bands of RGB images to distinguish photosynthetic vegetation and senescent vegetation and then estimated the coverage. In addition, Kim et al. [
97] also utilized ground-based RGB images but transformed them into three types of color spaces, and the histogram algorithm based on HIS color space achieved the best performance for arid and semiarid grasslands with
of 0.97. However, their estimates failed on the regional scale with a very large RMSE, which might be due to the disturbance of both soil background and vegetation types and the mismatch of data at different scales.
For larger scale estimates, one of the most classic approaches is the mixed pixel decomposition method supported by the assumption that each pixel of an image may consist of multiple components such as bare ground, shrubs, and grassland. Thus, the information in the pixels can be decomposed to distinguish the different components, and FVC can be considered as the proportion of vegetation. Among various mixed pixel decomposition methods, the most classical and commonly used method is the linear pixel dichotomy, which supposes that the pixels are only composed of vegetation and bare soil components. Since the NDVI has proven to have a strong correlation with FVC, this method can be expressed as:
where
represents the NDVI value of the whole vegetation cover pixel, and
is the NDVI value of the whole soil cover pixel. Generally, the values of
and
should be verified by ground measurements for different types of grasslands. In addition, in specific studies, the NDVI can also be replaced by other vegetation indices or spectral bands that prove to be more closely related to FVC than the NDVI.
Zhang et al. [
98] developed a linear pixel dichotomy model for the grasslands in Qaidam basin and compared its performance with that of an NDVI-based linear regression model, demonstrating that both had similar results in the evaluation of metrics but that the linear pixel dichotomy model suffered from a significant underestimation problem. Therefore, some studies attempted some other assumptions and utilized different remote sensing data. He et al. [
99] assumed each pixel was composed of vegetation, bare soil, and water components, and they utilized the ground-based hyperspectral images to select the most relevant spectral bands to these components in semiarid grasslands, which achieved
of 0.86. Recently, Vermeulen et al. [
100] assumed that pixels were composed of grassy, woody, and bare soil components, and multiple vegetation indices and bands were combined to drive the model, which achieved the lowest RMSE value for FVC estimation of grassy components.
Meanwhile, models based on statistical regression or machine learning have also emerged in many studies. For statistical regression models, Zhang et al. [
36] compared them with pixel decomposition methods and gradient difference methods for alpine, temperate, and desert grasslands, which showed that the logarithmic regression model obtained the best results on all types of grasslands, but all models were performed with low accuracy for alpine grasslands. Jansen et al. [
101] studied the effect of different phenological periods on FVC estimation in grazing grasslands through linear regression models and found that the optimal driving variable of linear models was varied for each phenological period so that they further integrated the NDVI and set thresholds for it to automatically identify phenological periods and select variables. For machine learning methods, Meng et al. [
102] evaluated the effectiveness of both statistical regression and machine learning methods in alpine grasslands, and all the machine learning methods were driven by both satellite and ground data. The results showed that the accuracy of machine learning models far exceeded that of statistical regression models, with the RF model achieving the best performance but suffering from poor stability. Then, Ge et al. [
103] developed a SVM model for alpine grasslands, which significantly outperformed both linear pixel dichotomy models and statistical regression models in terms of
, RMSE, and F-test. Gao et al. [
104] established an RF model by combining satellite and ground data as variables. Meanwhile, to validate the reliability of MODIS NDVI, a linear regression model was developed between MODIS NDVI and ground-based NDVI, and the NDVI finally adopted in the model was the mean value of them. Lin et al. [
105] compared regression methods, linear pixel dichotomy method, and machine learning methods, which proved that the RF model outperformed others. The original RF model in [
105] was driven only by vegetation indices achieving
of 0.86, and the model was further optimized by adding spectral bands and topographical data to the driving variables, achieving a 0.06 improvement in
. Liu et al. [
106] also adopted an RF model that was driven by vegetation indices, meteorological data, and topographical data, which obtained results with
of 0.92 for grasslands.
Table 4 shows the details of the above methods with their best
values. In addition, in terms of long-term monitoring, Yang et al. [
107,
108] focused on the spatiotemporal distribution of FVC in Chinese grasslands. In [
107], they estimated and mapped the distribution for grasslands in western China over 300 years. They first simulated FVC without human disturbance, and then added this disturbance based on an historical cropland dataset and an empirical model built from modern land use data. Then, the same approach was adopted in [
108] and was further combined with historical forest data to estimate FVC for grasslands in eastern China from 1700 to 2000. In addition, they also mapped its spatiotemporal changes and investigated the causes that mainly included population growth, agricultural expansion, and deforestation.
Finally, apart from [
96], some studies also concentrated on the FVC of senescent vegetation [
109,
110,
111]. Chai et al. [
109] simulated MODIS spectral bands from ground-based hyperspectral images and then calculated eight vegetation indices, demonstrating that a linear model driven by the dead fuel index (DFI) performed best with
of 0.62. Then, Yu et al. [
110] combined the DFI with the NDVI from MODIS in a linear mixed pixel decomposition model that supposes each pixel is composed of photosynthetic vegetation, senescent vegetation, and bare soil components. The results in [
110] demonstrated that their proposed model achieved the best performance for FVC estimation of both photosynthetic vegetation and senescent vegetation at regional scales. Finally, based on their previous study [
109], Chai et al. [
111] directly derived DFI from MODIS data and introduced the NDVI to set thresholds for DFI to distinguish growing and non-growing periods of grasslands. They developed a DFI-based linear model for non-growing periods to estimate FVC of senescent vegetation at regional scales achieving
of 0.6.
2.4. LAI
LAI is normally defined as half of the total green leaf area per unit surface area, which is closely related to plant photosynthesis, vegetation productivity, and ecosystem carbon accumulation. It is one of the key indices to reflect the growth status of grassland vegetation, as well as one of the most fundamental characteristic parameters in many ecosystem modeling processes.
Apart from direct destructive measurements, researchers can use ground-based optical sensors such as LAI-2200C and AccuPAR for non-destructive measurements. In addition, the radiative transfer models founded on physical principles are another approach for indirect measurements, which simulate radiative transfer processes in vegetation and describe canopy spectral changes as a function of canopy, leaf, and soil background characteristics. Among these models, the PROSAIL model, which is a combination of the SAIL canopy reflectance model and the PROSPECT leaf optical properties model, is the most popular and widely used. The construction of a PROSAIL model requires more than a dozen parameters including the LAI. Some of them are the physiological and biochemical parameters of the vegetation canopy and soil indices that can be obtained from satellite data and ground measurements, while other parameters usually do not have appropriate physical meanings and are hard to measure, so they are often assumed as empirical values based on prior knowledge in practice [
112,
113,
114].
Many studies have focused on the radiative transfer models using both ground and satellite images. Punalekar et al. [
114] adopted the PROSAIL model and estimated the LAI in grazing grasslands. Both ground and satellite images were adopted; the ground-based hyperspectral images were used to simulate multispectral images from satellites. The results showed that the simulated images could provide great accuracy at small scales (
), while the actual satellite images only offered relatively low accuracy (
) due to the overestimation problem in the case of high vegetation density. Pacheco-Labrador et al. [
115] developed the soil-canopy observation photosynthesis and energy fluxes (SCOPE) model, which is the combination of radiative transfer model and soil-vegetation-atmosphere transfer models, and they introduced multiple constraints to the model for different parameter estimation using ground images. As for the LAI, the model constrained by GPP and sun-induced fluorescence provided the best performance (
). Finally, Klingler et al. [
116] developed PROSAIL models based on both simulated and actual satellite images, and the model based on actual satellite images provided the lowest RMSE value compared to the ground-based sensors. Pu et al. [
112] applied a 3D radiative transfer model to investigate and quantify the uncertainty of MODIS LAI products caused by algorithms and input parameters, proving a significant underestimate problem of the products for grasslands with a low LAI.
Apart from the above methods, statistical regression and machine learning have also been applied in this field. Imran et al. [
113] established a linear regression model to verify the strong correlation between ground measured LAI and the normalized difference index (NDI). In [
113], ground-based hyperspectral images were adopted for the calculation of NDI and for the simulation of satellite-based NDI, and a PROSAIL model was also utilized to demonstrate that the grassland structural heterogeneity significantly affected the accuracy of the LAI estimation. Wang et al. [
18] compared the performance of MLR, SVM, and RF models, which demonstrated that the MLR model driven by optical and radar data had the best performance with the lowest RMSE value, and the combination of radar data could further reduce RMSE value compared to using optical data only. For machine learning models, Karimi et al. [
35] developed an RF model driven by the NDVI and meteorological data, which obtained highly accurate estimated results (
) in several grassland sites. Furthermore, in [
117], the RF models driven by variables from different sources were compared, which showed that the model driven by optical variables could obtain a good accuracy (
) in semiarid grasslands, while the combination of SAR and DEM data could achieve a certain promotion (
). However, the promotion proved to be limited by the heterogeneity of studied grasslands. Schwieder et al. [
118] also constructed an RF model driven by spectral bands and vegetation indices from satellites, and they compared the model with an improved PROSAIL model. The results showed that the RF model is slightly superior with an advantage of less than 0.01 for
.
In addition, Zhou et al. [
119] constructed an ANN model driven by spectral bands from satellites and gained great performance for grasslands (
). Then, the model was combined with an assimilation model and MODIS LAI products to generate time-continuous LAI data with 30 m resolution. Recently, Danner et al. [
120] combined the PROSAIL model with four machine learning models. Specifically, in [
120], the PROSAIL model was adopted to simulate absent data from ground measurements so that a complete dataset could be provided for the training of machine learning methods. Then, these models were further trained with hyperspectral bands, and the results showed that although the ANN model outperformed others for the estimation of simulated LAI (
), its performance in real estimation did not significantly differ from that of other models. Finally,
Table 5 shows the details of the above methods with their best
values.