Leaf area index estimation from the time-series SAR data using the AIEM-MWCM model

Figures & data

Figure 1. Location of the study region and distribution of sampling points. (a) Location of Xiangfu area in Henan Province; (b) location of leaf area index sampling points.

Figure 2. Flowchart of leaf area index inversion by AIEM-MWCM.

Table 1. Value ranges of the advanced integral equation model (AIEM) parameters.

Parameter	Unit	Lower boundary	Upper boundary
$SM$	m^3m^−3	0.02	0.4
$s$	cm	−11	−10
$l$	cm	10	30

Table 2. The range of all parameters in generating look up table.

Name of parameter	Unit	Lower limit	Upper limit	Sources
$\mathrm{LAI}$	m^2/m^2	0.1	7	Ground measurement
${\sigma }_{\mathrm{mod}}$	dB	−11	−9	AIEW-MWCM acquisition
${\sigma }_{\mathrm{mod}}$	dB	−12	−10	Dubois-MWCM acquisition
${\sigma }_{\mathrm{obs}}$	dB	−12	−10	Image acquisition
${\mathrm{f}}_{\mathrm{VI}}$	No unit	0.15	0.45	Image acquisition

Figure 3. Image filtering results obtained by (a) Frost filter; (b) Kuan filter; (c) SAR-BM3D filter; and (d) improved SAR-BM3D filter.

Table 3. Objective and quantitative comparison of filtering results of different methods.

Methods	The evaluation index
	ENL	EPI
Frost filter	1.3756	0.4395
Kuan filter	1.5210	0.3758
SAR-BM3D	1.3244	0.5133
Modified SAR-BM3D	1.7856	0.6988

Figure 4. LAI Inversion by the RVI_Freeman model. (a–e) are from the jointing, booting, heading, filling, and maturing stages, respectively.

Table 4. Accuracy evaluation of the backscattering coefficient model of Dubois-MWCM.

Growth Stage	Model	R^2	RMSE	Growth Stage	Model	R^2	RMSE
Jointing	HH	0.1863	0.8896	Booting	HH	0.1763	0.9324
	VV	0.1563	0.9324		VV	0.1432	0.9423
Heading	HH	0.1768	0.9236	Filling	HH	0.1769	0.9155
	VV	0.1325	0.9411		VV	0.1399	0.9356
Maturing	HH	0.1832	0.9153
	VV	0.1455	0.9367

Table 5. Accuracy evaluation of the backscattering coefficient model of AEIM-MWCM.

Growth Stage	Model	R^2	RMSE	Growth Stage	Model	R^2	RMSE
Jointing	HH	0.1986	0.8769	Booting	HH	0.2156	0.8632
	VV	0.1758	0.9125		VV	0.1866	0.9125
Heading	HH	0.1892	0.8963	Filling	HH	0.1856	0.9011
	VV	0.1639	0.9243		VV	0.1745	0.9586
Maturing	HH	0.1936	0.8936
	VV	0.1745	0.9314

Figure 5. Correlation analysis of Dubois-MWCM and LAI. (a–e) are from the jointing, booting, heading, filling, and maturing stages, respectively.

Table 6. Model parameters at HH polarizations.

Polarization	Growth Stages	Model Parameters
		A	B
HH	Jointing	0.046	0.198
	Booting	0.037	0.210
	Heading	0.057	0.186
	Filling	0.048	0.132
	Maturing	0.036	0.185

Figure 6. Correlation analysis of AEIM-MWCM and LAI. (a–e) are from the jointing, booting, heading, filling, and maturing stages, respectively.

Table 7. Model parameters at HH polarizations.

Polarization	Growth Stages	Model Parameters
		A	B
HH	Jointing	0.027	0.143
	Booting	0.038	0.135
	Heading	0.024	0.187
	Filling	0.049	0.203
	Maturing	0.036	0.189

Figure 7. The AEIM-MWCM model and LAI verification analysis. (a–e) are from the jointing, booting, heading, filling, and maturing stages, respectively.

Figure 8. Correlation analysis between GF-3 LAI and MODIS LAI. (a–e) are from the jointing, booting, heading, filling, and maturing stages, respectively.

Figure 9. LAI images inverted by AEIM-MWCM. (a–e) are from the jointing, booting, heading, filling, and maturing stages, respectively.

Data availability statement

The code used in this study are available by contacting the corresponding author.