# Using a Vegetation Index-Based Mixture Model to Estimate Fractional Vegetation Cover Products by Jointly Using Multiple Satellite Data: Method and Feasibility Analysis

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## Abstract

**:**

_{v}) and bare soil (V

_{s}) from the MODIS BRDF product via the multi-angle VI method (MultiVI) was feasible to estimate FVC with multiple satellite data. Analyses of the spatial resolution and spectral response function differences for MODIS and other satellites including Landsat 8, Chinese GF 1, and ZY 3 predicted that (1) the effect of V

_{v}and V

_{s}downscaling on FVC estimation uncertainty varied from satellite to satellite due to the positioning differences, and (2) after spectral normalization, the uncertainty (RMSDs) for FVC estimation decreased by ~2.6% compared with the results without spectral normalization. FVC estimation across multiple satellite data will help to improve the spatiotemporal resolution of FVC products, which is an important development for numerous biophysical applications. Herein, we proved that the VI-based mixture model with V

_{v}and V

_{s}from MultiVI is a strong candidate.

## 1. Introduction

_{v}and V

_{s}) are quantitatively derived from publicly available Moderate Resolution Imaging Spectroradiometer (MODIS) Bidirectional Reflectance Distribution Factor (BRDF) products without using any other prior knowledge [18]. By taking the Normalized Difference Vegetation Index (NDVI) as an example, the key end members, NDVI for pure vegetation (V

_{v}) and bare soil (V

_{s}), are two byproducts of this method and can be applied to generate FVC via the VI-based mixture model. The 500 m resolution V

_{v}and V

_{s}from MODIS can be downscaled according to land cover product, which makes it available to generate FVC in various spatial resolutions with multiple satellite data.

_{v}and V

_{s}from MODIS should be discussed, whether they are suitable for all satellite data and capable of the estimation of FVC from multiple satellite data. Research has shown that the spectral response function does influence the band reflectance and VIs [19,20]. Although the difference between the spectral response functions of different satellite sensors has a negligible effect on the estimation accuracy of vegetation structure parameters [19,20], few studies have addressed the uncertainty and feasibility of using information from one satellite (e.g., V

_{v}and V

_{s}from MODIS) to determine vegetation structure parameters (e.g., FVC) from other satellites (i.e., when applying the V

_{v}and V

_{s}from MODIS to other satellite data, does the spectral response function difference affect the accuracy of FVC estimation?).

_{v}and V

_{s}from MODIS via the MultiVI method is capable of estimating FVC by jointly using multiple finer-resolution satellite data (i.e., Landsat 8, GF 1, and ZY 3). We examine the uncertainty and feasibility of the FVC estimation process. Our objectives are:

- (i)
- analyzing the necessity of MODIS V
_{v}and V_{s}downscaling for finer-resolution FVC estimation; and - (ii)
- assessing uncertainty due to spectral response function differences for FVC estimation with different satellite data.

## 2. Materials and Methods

#### 2.1. Study Areas and Field Measurements

^{2}, which is in Hebei Province, China, and consists of 43.2% grassland, 44.0% forest, 9.5% desert and swamp, 3.0% cropland, and 0.3% residential land. The forest is artificial and is dominated by birch and larch. The land cover has a certain heterogeneity but is relatively stable. Field measurements were collected for the primary vegetation types in the SNP.

_{up}is for tree crown FVC while f

_{down}is for FVC underneath the tree crown. Digital images were taken along two diagonals of the plot, and about 20 images were taken for each plot. The digital FVC images were processed by using an automatic and shadow-resistant algorithm (SHAR-LABFVC) with an uncertainty of less than 0.025 [24]. In all, 25 sites with 35 measurements captured from 27 June to 13 September 2015 were used for evaluation herein (i.e., some sites were measured multiple times during this period).

#### 2.2. Finer-Resolution NDVI

_{v}and V

_{s}from MODIS via MultiVI in finer-resolution FVC estimation, three satellite data were getting involved and compared, being: (i) Landsat 8 OLI surface reflectance product [25]; (ii) Chinese GF 1 satellite wide-field-of-view (WFV; 16 m) data; (iii) Chinese ZY 3 satellite multi-spectral camera (MUX; 5.8 m) data. Table 1 lists the temporal information of these satellite data. An atmospheric correction based on the dark object method was applied to GF 1 data [26]. A 10-day mean temporal composition was applied to GF 1 data to remove outliers. The Fast Line-of-sight Atmospheric Analysis of Hypercubes (FLAASH) module in the Environment for Visualizing Images (ENVI; Exelis, Inc., Boulder, CO, USA) software was used for the atmospheric correction of ZY 3 data. Both GF 1 and ZY 3 surface reflectance were simply averaged aggregated to 30-meter resolution, which was the same as Landsat 8, and NDVI was calculated for FVC estimation.

#### 2.3. Spectral Library

_{v}and V

_{s}from MODIS to the other three finer resolution satellite data. Canopy spectra were simulated based on the three-dimensional (3D) radiative transfer (RT) simulation framework, LESS (large-scale remote sensing data and image simulation framework over heterogeneous 3D scenes) [27]. The RT leaf model, PROSPECT-D [28], built-in LESS was used to simulate different leaves’ spectra. High, middle, and low levels of dry matter (Cm), chlorophyll (Cab), and anthocyanin (Anth) were considered. Table 2 lists the details of the parameters for PROSPECT-D. Canopy structure was defined by Leaf Area Index (LAI), Leaf inclination Angle Distribution (LAD), and crown shape. For canopy spectra simulation, the scene LAI was set at 6, which represented a very dense vegetation scene. The shape of leaf in all scenes was set as disc; details are listed in Table 3. When simulating the canopy spectra, the effects of soil reflectivity were also considered. The soil spectra were from the global spectral libraries [29,30]. In all 486, canopy spectra were simulated and 4439 soil spectra were used for spectral normalization.

#### 2.4. V_{v} and V_{s} Downscaling

_{v}and V

_{s}from MODIS in 500-meter resolution. GlobeLand 30 divides the land surface into 10 types, including 6 vegetation types (i.e., cultivated land, forest, grassland, shrubland, wetland, and tundra) and 4 unvegetated types (i.e., water bodies, artificial surfaces, bare land, and permanent snow and ice). Herein, we combined the wetland, water bodies, and permanent snow and ice into 1 type, all named water bodies, since they all have V

_{s}below 0. As for MODIS, V

_{s}via MultiVI does not consider the water background and it is always greater than 0; this type was considered in the downscaling process, but no FVC estimation was performed. Thus, 8 land cover types (i.e., cultivated land, forest, grassland, shrubland, tundra, artificial surfaces, bare land, and water bodies) were used for V

_{v}and V

_{s}downscaling.

_{v}/V

_{s}for each MODIS pixel is assumed as the combination of V

_{v}/V

_{s}of all land cover types in this pixel area. Take the proportion of each land cover type (k) in the MODIS pixel as the weight (f), 500 m V

_{v}/V

_{s}can be decomposed to 30-meter resolution according to Equation (2).

_{v,modis}and V

_{s,modis}is the V

_{v}and V

_{s}for a single 500 m MODIS pixel, V

_{v,k}and V

_{s,k}is the V

_{v}and V

_{s}for a single 30 m land cover type (k) pixel, m is the number of land cover type in this MODIS pixel area. A 3 × 3 sliding window with 1 MODIS pixel step was used to solve the equation, and the result was set as the solution for all the 30 m land cover type pixels in the center MODIS pixel area. Equation (3) shows an example of how to obtain V

_{v,k}in MODIS pixel (x,y) using a sliding window. For obtaining V

_{s,k}, it is the same as that of V

_{v,k}, except that V

_{v,modis}is replaced by V

_{s,modis}.

#### 2.5. Spectral Normalization

_{v}and V

_{s}from MODIS to match spectral settings of Landsat 8, GF 1, and ZY 3. Canopy and soil spectra described in Sec. II.C was transformed into red and near-infrared (NIR) bands reflectance according to the spectral response functions of each satellite sensor (Figure 2). Normalized coefficients for V

_{v}and V

_{s}were obtained based on canopy and soil NDVI, respectively. A simple linear model (Equation (4)) was performed on Landsat 8 and MODIS, GF 1 and MODIS, and ZY 3 and MODIS, respectively.

_{vegj,i}is the NDVI of i calculated from canopy spectrum j; NDVI

_{vegj,modis}is the NDVI of MODIS calculated from canopy spectrum j; a

_{v,i}and b

_{v,i}are normalized coefficients for V

_{v}of i. In all 486 canopy spectra were used for a

_{v,i}and b

_{v,i}estimation; thus, n is 486 in Equation (4). The estimation of the normalized coefficients for V

_{s}of i (i.e., a

_{s,i}and b

_{s,i}) are similar to V

_{v}, except for changing the spectra to the soil. When estimating a

_{s,i}and b

_{s,i}, n was 4439, which means 4439 soil spectra. V

_{v}and V

_{s}for Landsat 8, GF 1, and ZY 3 were calculated by applying the normalized coefficients to V

_{v}and V

_{s}from MODIS.

#### 2.6. FVC Production

_{v}and V

_{s}from MODIS with NDVI from Landsat 8, ZY 3, and GF 1. To analyze the necessity of MODIS V

_{v}and V

_{s}downscaling for finer-resolution FVC estimation, FVC (FVC_1 in Figure 3) was estimated with 500-meter and 30-meter endmembers, respectively. To assess uncertainty due to spectral band ranges and spectral response function differences from different satellite sensors, FVC was also estimated with endmembers before (FVC_2 in Figure 3) and after (FVC_3 in Figure 3) spectral normalization. The necessity of MODIS V

_{v}and V

_{s}downscaling, uncertainty of spectral normalization, and consistency of FVC estimation from different satellites were evaluated by comparing with field-measured FVC.

## 3. Results

#### 3.1. Necessity Analysis for V_{v} and V_{s} Downscaling

_{v}and V

_{s}, from MODIS was analyzed by comparing the uncertainty of FVC estimation based on the endmembers at 500 m and 30 m, respectively. Figure 4 shows that FVC from Landsat 8 has lower uncertainty with 30 m V

_{v}and V

_{s}(i.e., RMSD for FVC_2 is 0.124) than with 500 m (i.e., RMSD for FVC_1 is 0.134). However, for ZY 3 and GF 1, the uncertainties are not much different. The RMSDs for FVC_1 and FVC_2 from ZY 3 are 0.117 and 0.119, while for FVC_1 and FVC_2 from GF 1 are 0.094 and 0.102, respectively. The FVC estimation uncertainty of using finer-resolution V

_{v}and V

_{s}depends on the positioning accuracy of the input data (i.e., finer-resolution NDVI). Since the land cover dataset (GlobeLand 30) used for downscaling was produced based on Landsat and HJ satellites [31], the 30 m V

_{v}and V

_{s}have better positioning consistency with FVC from Landsat 8 than ZY 3 and GF 1. As for consistency (R

^{2}), FVC_2 for Landsat 8, ZY 3, and GF 1 all have lower consistency than that of FVC_1. The downscaled endmembers increase the heterogeneity of the estimated FVC results. FVC_1 within the same 500-meter resolution pixel only reflects the difference of the 30 m NDVI from Landsat 8, ZY 3, or GF 1. When downscaled endmembers are used, the FVC_2 differences also include differences in land cover types. This shows that the downscaled endmembers have different accuracy under different land cover types, but the overall trend is good (i.e., RMSD decrease).

#### 3.2. Uncertainty Analysis for Spectral Normalization

_{v}and V

_{s}from MODIS were analyzed by comparing finer-resolution FVC with field measurement (Table 4). We compared situations of no spectral normalization (i.e., original in Table 4), only normalized V

_{s}, only normalized V

_{v}, and normalized both V

_{v}and V

_{s}(i.e., normalized all in Table 4), respectively. Results show that all Landsat 8, ZY 3, and GF 1 have slight improvement after spectral normalization (i.e., on average, the RMSD of FVC estimated with normalized V

_{v}and V

_{s}decreased ~2.6% compared with the FVC estimated with the original V

_{v}and V

_{s}). Since 30 of the 35 field measurements have FVC > 0.5 (Figure 4), which are more sensitive to V

_{v}during production [32], thus only normalized V

_{v}seems to have the lowest uncertainty for Landsat 8 and ZY 3. That is to say when using the VI-based mixture model to estimate consistent finer-resolution FVC products from Landsat 8, ZY 3, and GF 1, a simple spectral normalization of V

_{v}and V

_{s}can be considered.

#### 3.3. Accuracy Analysis for FVC by Comparing with Traditional VI-Based Linear Mixture Model

_{v}and V

_{s}after spectral normalization were used for the process of FVC production in this study (i.e., FVC_3 was used for comparison). V

_{v}and V

_{s}for the traditional VI-based model were obtained based on the statistic method provided by Zeng et al. [14]. According to Zeng et al. [14], V

_{v}is the NDVI value at the 75th percentile of the cumulative distribution histogram for cultivated land, forest, and grassland, and 90th percentile for shrubland and artificial land, while V

_{s}is the constant value, 0.05, for all land cover types. Considering that Landsat 8 has the highest recognition among all and is the best data match with the GlobeLand 30 land cover product, Landsat 8 on 31 July 2015 was selected for this comparison. Figure 5 shows the FVC map estimated by the proposed method (Figure 5a) and the traditional VI-based linear mixture model (Figure 5b), respectively. The spatial distribution of FVC in both Figure 5a,b is very similar, except that the texture of Figure 5a is clearer. The accuracy of Figure 5a,b was checked by using the field measurements around 31 July 2015. The result (Figure 6) shows that the FVC estimated by the process in this study has less uncertainty (RMSD = 0.110) than the traditional VI-based model (RMSD = 0.149). The lower consistency (R

^{2}) is also caused by the heterogeneity of downscaled V

_{v}and V

_{s}.

## 4. Discussion

#### 4.1. Applicability of the V_{v} and V_{s} Downscaling Method

_{v}and V

_{s}downscaling method used herein, Figure 7 shows the distribution of pixel heterogeneity in the SNP area. The number of different land cover types in each 500-meter MODIS pixel was used to represent the heterogeneity. Herein, most pixels have over two kinds of land cover types but less than six, which makes Equation (3) solvable.

_{v}and V

_{s}(FVC_2) was used (Figure 4b). The uncertainty was also presented by absolute error (FVC_2—field-measured FVC). The land cover heterogeneity was grouped into three groups: (1) the number of land cover types is less than three but equal to or greater than two (2 ~ 3); (2) the number of land cover types is less than four but equal or greater than three (3 ~ 4); (3) the number of land cover types is equal or greater than (>4). In Figure 8, the red median marks for both Landsat 8 and ZY 3 FVC are all above the dark red dash zero line in all three groups, which means that they both overestimated the FVC. Due to the small image width of ZY 3, areas with high heterogeneity (>4) are not covered. While for GF 1, both the median and mean are below zero, which means that it underestimated the FVC. The differences in the uncertainty of the estimated FVC hardly change with the heterogeneity (Figure 8), which shows that the surface heterogeneity does not affect the accuracy of the process.

_{v}, V

_{s}, and finer-resolution NDVI accurately, or land cover product matching the finer-resolution NDVI is not available, particularly in areas that have undergone rapid land cover changes, the coarse-resolution V

_{v}and V

_{s}which represent the average situation of a wide range (herein 500 m × 500 m) and have the closest observation time is better for FVC estimation based on VI-based model. In this study, the positioning accuracy between Landsat 8 and finer-resolution V

_{v}and V

_{s}was less than one pixel, while ZY 3 and GF 1 were worse based on visual interpretation (i.e., within 2~3 pixels).

#### 4.2. Spectral Analysis for Multiple Satellite Sensors

_{v}and V

_{s}from MODIS to make it match the NDVI from Landsat 8, ZY 3, and GF 1, since V

_{v}and V

_{s}in the VI-based model determine the benchmark and boundary of the FVC estimation [2]. Table 5 lists the original and normalized V

_{v}and V

_{s}. The average V

_{v}for Landsat 8 and ZY 3 are larger than MODIS since the slope of normalized coefficients is less than 1 (Figure 9a). This may be due to the wider high NIR response range of Landsat 8 and ZY 3 than MODIS; the spectral band range (width) with response > 0.9 is 854~875 (21) nm for Landsat 8, 775~871 (96) nm for ZY 3, and 847~864 (17) nm for MODIS (Figure 2). Although GF 1 also has a wide spectral band range, the peak of the NIR spectral response for GF 1 (i.e., 774 nm) is less than others (MODIS: 857 nm, Landsat 8:859 nm, ZY 3: 807 nm; Figure 2). The normalized V

_{v}for GF 1 is less than MODIS. For V

_{s}, all normalized V

_{s}are less than MODIS. There is less difference in the change rate and reflectivity of soil spectra between red and NIR than vegetation. The difference in V

_{s}is mainly caused by the spectral band range.

#### 4.3. Prospect of FVC Estimation by Joint Using Multiple Satellite Data

## 5. Conclusions

_{v}) and bare soil (V

_{s}) from MODIS via the MultiVI method. It is supposed to be able to produce high-frequency and high-temporal FVC products, since multiple finer-resolution satellite data (i.e., Landsat 8, ZY 3, GF 1) can be used to achieve high frequency. The inconsistent spatial resolution between V

_{v}and V

_{s}from MODIS and finer-resolution satellite data and the difference in spectral band range and spectral response function are analyzed. Results shows that FVC from Landsat 8 (RMSD = 0.121), ZY 3 (RMSD = 0.117), and GF 1 (RMSD = 0.099) has uncertainty ~0.11 with downscaled and spectral normalized V

_{v}and V

_{s}. The necessity of V

_{v}and V

_{s}downscaling depends on the positioning accuracy of the finer-resolution satellite data. When the positioning accuracy is worse (i.e., greater than one pixel herein), the coarse-resolution V

_{v}and V

_{s}have less uncertainty during FVC estimation. After spectral normalization, the uncertainty (RMSD) for FVC estimation decreases by ~2.6%.

_{v}and V

_{s}from MODIS via MultiVI is flexible in producing FVC at finer resolution and shows potential for the generation of high-frequency large-area products.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Land cover map in the SNP area (50 km × 60 km) from 30 m GlobeLand30 product in 2010. Yellow stars present the 25 site locations.

**Figure 3.**Flowchart of finer-resolution FVC production. Herein, 30 m NDVI was from Landsat 8, GF 1, and ZY 3.

**Figure 4.**Analysis of FVC estimation using the V

_{v}and V

_{s}of different spatial resolutions. (

**a**) FVC_1: used V

_{v}and V

_{s}at 500 m resolution; (

**b**) FVC_2: used V

_{v}and V

_{s}at 30 m resolution.

**Figure 5.**FVC map in the SNP area on 31 July 2015. (

**a**) FVC_3 from Landsat 8, which means V

_{v}and V

_{s}are estimated via MultiVI; (

**b**) FVC from Landsat 8 with V

_{v}and V

_{s}from statistic results. The black areas represent no data.

**Figure 6.**Analysis of FVC estimation in the SNP area on 31 July 2015. The blue line and circles are for FVC_3 from Landsat 8 with V

_{v}and V

_{s}from MultiVI; the green line and circles are for FVC from Landsat 8 with V

_{v}and V

_{s}from statistic results.

**Figure 7.**The land cover heterogeneity of each 500 m MODIS pixel in the SNP area. The heterogeneity was described by the number of different 30 m land cover types from GlobeLand 30 in 2010.

**Figure 8.**The error of FVC estimation under different land cover heterogeneity. FVC error is the difference between estimated FVC and field-measured FVC (FVC_2-field-measured FVC). The heterogeneity was described by the number of different 30 m land cover types from GlobeLand 30 in 2010. On each box, the central red mark indicates the median, the number at the top indicates the mean, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually using the red ‘+’ marker symbol. The dark red dash line is the zero line, which means no error. LT 8 is short for Landsat 8.

**Figure 9.**Spectral normalization between finer-resolution satellite NDVI and MODIS NDVI. (

**a**) is for vegetation; (

**b**) is for soil.

**Table 1.**The temporal information for satellite data. All data were captured in 2015 which match the field measurements.

Data | Landsat 8 | GF 1 | ZY 3 |
---|---|---|---|

Product Time | 19 June; 5 and 21 July; 6 August; 7 and 23 September | 30 June; 10 and 30 July; 8 September | 5 August; 3 September |

**Table 2.**Leaf biochemical parameters for PROSPECT-D. N: structure coefficient; Cm: dry matter; Bp: brown pigments; Car: carotenoids; Cab: chlorophyll; Anth: anthocyanin; Cw: water thickness.

Parameters | N | Cm (g/cm ^{2}) | Bp | Car (μg/cm ^{2}) | Cab (μg/cm ^{2}) | Anth (μg/cm ^{2}) | Cw (cm) |
---|---|---|---|---|---|---|---|

Values | 1.5 | 0.005; 0.01; 0.015 | 0 | 10 | 25 50 75 | 10 20 30 | 0.025 |

**Table 3.**Canopy structure information of the simulated dataset. SZA: solar zenith angle; HOM: homogeneous scene; HET: a heterogeneous scene with spherical crowns; UNI: uniform distribution; SPH: spherical distribution.

Scene | Object | Object Radius | Object Height | LAD | Number of Soil Types | SZA |
---|---|---|---|---|---|---|

HOM | Leaf | 0.05 m | 0~15 m | UNI; SPH | 3 | 0°; 20°; 40° |

HET | Sphere | 4 | 10~19 m | UNI; SPH | 3 | 0°; 20°; 40° |

**Table 4.**Uncertainty (RMSD) analysis for spectral normalization by comparing finer-resolution FVC (FVC_3) with field measurement. Original: no spectral normalization; Normalized V

_{s}: only did spectral normalization for V

_{s}; Normalized V

_{v}: only did spectral normalization for V

_{v}; Normalized All: did spectral normalization for both V

_{v}and V

_{s}.

Satellite | Original | Normalized V_{s} | Normalized V_{v} | Normalized All |
---|---|---|---|---|

Landsat8 OLI | 0.124 | 0.126 | 0.119 | 0.121 |

ZY3 MUX | 0.119 | 0.122 | 0.114 | 0.117 |

GF1 WFV | 0.102 | 0.099 | 0.101 | 0.099 |

**Table 5.**V

_{v}and V

_{s}statistic over the field sites in SNP in 2015. V

_{v}and V

_{s}for Landsat 8, ZY 3, and GF 1 are the values after spectral normalization. Ave: average; Std.: standard deviation.

Title 1 | MODIS | Landsat 8 | ZY 3 | GF 1 | |
---|---|---|---|---|---|

V_{v} | Ave. | 0.879 | 0.885 | 0.884 | 0.869 |

Std. | 0.041 | 0.039 | 0.039 | 0.042 | |

V_{s} | Ave. | 0.151 | 0.139 | 0.127 | 0.130 |

Std. | 0.032 | 0.032 | 0.025 | 0.025 |

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## Share and Cite

**MDPI and ACS Style**

Song, W.; Zhao, T.; Mu, X.; Zhong, B.; Zhao, J.; Yan, G.; Wang, L.; Niu, Z. Using a Vegetation Index-Based Mixture Model to Estimate Fractional Vegetation Cover Products by Jointly Using Multiple Satellite Data: Method and Feasibility Analysis. *Forests* **2022**, *13*, 691.
https://doi.org/10.3390/f13050691

**AMA Style**

Song W, Zhao T, Mu X, Zhong B, Zhao J, Yan G, Wang L, Niu Z. Using a Vegetation Index-Based Mixture Model to Estimate Fractional Vegetation Cover Products by Jointly Using Multiple Satellite Data: Method and Feasibility Analysis. *Forests*. 2022; 13(5):691.
https://doi.org/10.3390/f13050691

**Chicago/Turabian Style**

Song, Wanjuan, Tian Zhao, Xihan Mu, Bo Zhong, Jing Zhao, Guangjian Yan, Li Wang, and Zheng Niu. 2022. "Using a Vegetation Index-Based Mixture Model to Estimate Fractional Vegetation Cover Products by Jointly Using Multiple Satellite Data: Method and Feasibility Analysis" *Forests* 13, no. 5: 691.
https://doi.org/10.3390/f13050691