Assessment of Leaf Area Index of Rice for a Growing Cycle Using Multi-Temporal C-Band PolSAR Datasets

: C-band polarimetric synthetic aperture radar (PolSAR) data has been previously explored for estimating the leaf area index (LAI) of rice. Although the rice-growing cycle was partially covered in most of the studies, details for each phenological phase need to be further characterized. Additionally, the selection and exploration of polarimetric parameters are not comprehensive. This study evaluates the potential of a set of polarimetric parameters derived from multi-temporal RADARSAT-2 datasets for rice LAI estimation. The relationships of rice LAI with backscattering coe ﬃ cients and polarimetric decomposition parameters have been examined in a complete phenological cycle. Most polarimetric parameters had weak relationships ( R 2 < 0.30) with LAI at the transplanting, reproductive, and maturity phase. Stronger relationships ( R 2 > 0.50) were observed at the vegetative phase. HV / VV and RVI FD had signiﬁcant relationships ( R 2 > 0.80) with rice LAI for the whole growth period. They were utilized to develop empirical models. The best LAI inversion performance (RMSE = 0.81) was obtained when RVI FD was used. The acceptable error demonstrated the possibility to use the decomposition parameters for rice LAI estimation. The HV / VV-based model had a slightly lower estimation accuracy (RMSE = 1.29) but can be a practical alternative considering the wide availability of dual-polarized datasets. decomposition parameters, as well as their combinations. The relationship between polarimetric SAR variables and rice LAI at di ﬀ erent phenological phases during the whole growing cycle is evaluated. The most suitable polarimetric index or indices for rice LAI estimation can be found to build empirical models. Four RADARSAT-2 datasets acquired during the 2016 rice-growing season in Meishan City, Sichuan, China are analyzed.


Introduction
The staple food for approximately one-half of the global population is rice [1]. The development and health status of the rice crop are of great significance. The leaf area index (LAI) of the crop is crucial in the quantitative description of the canopy structure and photosynthetic processes [2,3]. However, the ground LAI measurements using digital photography [4,5] or integrated sensors [6,7] are time-consuming and laborious, restricting their practical application over a large region. Spaceborne or airborne remote sensing techniques and datasets are a possible alternative for the LAI monitoring at a regional scale [8][9][10]. Several vegetation indices (VIs) are used to estimate the LAI base on the contrast in the reflectance among different spectral bands of optical data [11][12][13][14]. However, the rice The LI-COR LAI-2200 instrument was used to measure the LAI at each site. A 90° view-cap was used to mask the operator. All measured LAI values were called effective LAI, which computed LAI using the gap fraction of the canopy based on Beer's law [39]. A hand-held Trimble GeoExplorer-2008 was used to record the GPS coordinates of the sample sites as well as 11 ground control points (GCPs). The GCPs were used to geo-reference the SAR images and in situ datasets. The cultivation management (transplanting time, planting density, and cultivar), field conditions (field water and weeds), and biophysical parameters (plant height, plant water content, size of leaves and stems, and number of tiller and ear) were recorded. Four principle phenological phases (i.e., transplanting, vegetative, reproductive, and maturity phases) were identified based on the BBCH scale [40] shown in Table 1.  The LI-COR LAI-2200 instrument was used to measure the LAI at each site. A 90 • view-cap was used to mask the operator. All measured LAI values were called effective LAI, which computed LAI using the gap fraction of the canopy based on Beer's law [39]. A hand-held Trimble GeoExplorer-2008 was used to record the GPS coordinates of the sample sites as well as 11 ground control points (GCPs). The GCPs were used to geo-reference the SAR images and in situ datasets. The cultivation management (transplanting time, planting density, and cultivar), field conditions (field water and weeds), and biophysical parameters (plant height, plant water content, size of leaves and stems, and number of tiller and ear) were recorded. Four principle phenological phases (i.e., transplanting, vegetative, reproductive, and maturity phases) were identified based on the BBCH scale [40] shown in Table 1.  Fields were under frequent weed control and inundated with water. The fields were then drained shortly before the harvest. Due to the differences in the timing of the transplanting, the rice varieties, and the selection and use of fertilization, the rice growth status varied at different sample sites. At the first fieldwork carried out on 15 May, rice fields in 67% of the sample sites were in the transplanting phase. On 8 June, all of the sites were in the vegetative phase. On 2 July, about 47% of the sample sites were in the reproductive phase. On the date of the final field trip (26 July), more than one-half of the fields were in the maturity phase.
The growth status of rice plants at the four phenological phases are shown in Figure 3. At the transplanting phase, rice plants were small and short. As rice entered the vegetative phase, the plant heights increased, and the number of leaves and stems accumulated. At the reproductive phase, new elements (tassels and ears) began to appear near the plant tops. With the grain ripeness and plant senescence, the geometry of the rice canopy became complicated at the maturity phase. Fields were under frequent weed control and inundated with water. The fields were then drained shortly before the harvest. Due to the differences in the timing of the transplanting, the rice varieties, and the selection and use of fertilization, the rice growth status varied at different sample sites. At the first fieldwork carried out on 15 May, rice fields in 67% of the sample sites were in the transplanting phase. On 8 June, all of the sites were in the vegetative phase. On 2 July, about 47% of the sample sites were in the reproductive phase. On the date of the final field trip (26 July), more than one-half of the fields were in the maturity phase.
The growth status of rice plants at the four phenological phases are shown in Figure 3. At the transplanting phase, rice plants were small and short. As rice entered the vegetative phase, the plant heights increased, and the number of leaves and stems accumulated. At the reproductive phase, new elements (tassels and ears) began to appear near the plant tops. With the grain ripeness and plant senescence, the geometry of the rice canopy became complicated at the maturity phase.
one-half of the fields were in the maturity phase.
The growth status of rice plants at the four phenological phases are shown in Figure 3. At the transplanting phase, rice plants were small and short. As rice entered the vegetative phase, the plant heights increased, and the number of leaves and stems accumulated. At the reproductive phase, new elements (tassels and ears) began to appear near the plant tops. With the grain ripeness and plant senescence, the geometry of the rice canopy became complicated at the maturity phase.

RADARSAT-2 Datasets and Polarimetric Parameters
Four RADARSAT-2 images were obtained on 15 May, 8 June, 2 July, and 26 July 2016. They are quad-polarized and single-look complex (SLC). The spatial resolution in the slant range and azimuth directions is 5.4 m × 7.9 m. The temporal resolution is 24 days. The four acquisition dates are coincidentally within the four principle phenology phases.
The RADARSAT-2 datasets were processed using the Sentinel Application Platform software (SNAP) (http://step.esa.int/main/download/). The analyses include radiometric correction, multilooking, speckle filtering, and geometry reprojection. Multi-looking was implemented in the software with the ground range (GR) square pixel option selected, and the number of looks for azimuth and range direction is 2 and 1, respectively. A 3 × 3 Lee filter was utilized for speckle reduction. For geometry reprojection, Range-Doppler terrain correction was applied using Shuttle Radar Topography Mission (SRTM) 1 arcsec Digital Elevation Model (DEM), and the field measured GCPs were also used for precise geometry correction. The spatial resolution of the processed (ground) images is 10 m × 10 m. The monostatic antenna configuration of RADARSAT-2 gives approximately the same backscattering coefficients for HV and VH polarizations. Thus, only HH, HV, and VV data were used. The combinations of different polarized backscattering coefficients, such as ratios and radar vegetation index (RVI σ , given by 8HV/(HH+VV+2HV)), were calculated because they were sensitive to the morphological structure change of rice plants [41,42].
The Cloude-Pottier and Freeman-Durden decomposition algorithms were performed using the polarimetric decomposition module of the SNAP software. The Cloude-Pottier algorithm decomposed the target coherence/covariance matrix of PolSAR data into eigenvectors and eigenvalues, from which the entropy (H), anisotropy (A), alpha (α), and radar vegetation index (RVI CP ) were obtained [35]. H describes the dominance of the first-contributed scattering mechanism. A represents the power disparity between the second-and third-contributed scattering mechanisms. α is related to the type of the dominant scattering mechanism [43]. RVI CP measures the complexity and randomness of the vegetated area [10,29,44]. The Freeman-Durden algorithm modeled the coherence/covariance matrix as the contribution of three scattering components. The powers of the surface (P S ), double-bounce (P D ), and volume (P V ) scatterings were obtained after the Freeman-

RADARSAT-2 Datasets and Polarimetric Parameters
Four RADARSAT-2 images were obtained on 15 May, 8 June, 2 July, and 26 July 2016. They are quad-polarized and single-look complex (SLC). The spatial resolution in the slant range and azimuth directions is 5.4 m × 7.9 m. The temporal resolution is 24 days. The four acquisition dates are coincidentally within the four principle phenology phases.
The analyses include radiometric correction, multi-looking, speckle filtering, and geometry reprojection. Multi-looking was implemented in the software with the ground range (GR) square pixel option selected, and the number of looks for azimuth and range direction is 2 and 1, respectively. A 3 × 3 Lee filter was utilized for speckle reduction. For geometry reprojection, Range-Doppler terrain correction was applied using Shuttle Radar Topography Mission (SRTM) 1 arcsec Digital Elevation Model (DEM), and the field measured GCPs were also used for precise geometry correction. The spatial resolution of the processed (ground) images is 10 m × 10 m. The monostatic antenna configuration of RADARSAT-2 gives approximately the same backscattering coefficients for HV and VH polarizations. Thus, only HH, HV, and VV data were used. The combinations of different polarized backscattering coefficients, such as ratios and radar vegetation index (RVI σ , given by 8HV/(HH+VV+2HV)), were calculated because they were sensitive to the morphological structure change of rice plants [41,42].
The Cloude-Pottier and Freeman-Durden decomposition algorithms were performed using the polarimetric decomposition module of the SNAP software. The Cloude-Pottier algorithm decomposed the target coherence/covariance matrix of PolSAR data into eigenvectors and eigenvalues, from which the entropy (H), anisotropy (A), alpha (α), and radar vegetation index (RVI CP ) were obtained [35]. H describes the dominance of the first-contributed scattering mechanism. A represents the power disparity between the second-and third-contributed scattering mechanisms. α is related to the type of the dominant scattering mechanism [43]. RVI CP measures the complexity and randomness of the vegetated area [10,29,44]. The Freeman-Durden algorithm modeled the coherence/covariance matrix as the contribution of three scattering components. The powers of the surface (P S ), double-bounce (P D ), and volume (P V ) scatterings were obtained after the Freeman-Durden decomposition, as seen in Figure 4 [36], as well as the ratios of different scattering mechanism, and the radar vegetation index (RVI FD , given by P V /(P S + P D + P V )) [45]. For vegetation area, surface scattering is the scatter from the ground. Double-bounce scattering describes the interaction between the plants and ground. Volume scattering comes from the plant canopy [37,46,47]. The derived images (backscatter and decomposition images) were registered and stacked. Because the processed images had a pixel size of 10 m × 10 m while each sample site was 50 m × 50 m, all pixels inside the sample site area were extracted and averaged.  The red, green, and blue bands correspond to P D , P V , and P S , respectively.

Method of Data Analysis and Model Construction
The different transplanting dates of 30 rice sample sites resulted in various phenological phases on the SAR imaging dates. SAR variables obtained from the multi-temporal datasets associated with the ground measurements were regrouped into four collections corresponding to the four phenological phases. For each phase, the data were partitioned into the training dataset (3/4 of the total) and validation dataset (1/4). The training dataset was used in statistical analyses including data visualization, regression analysis, and model development. The validation dataset was used for the accuracy assessment of the model.
The multi-temporal polarimetric parameters and their combinations during the rice phenology succession were analyzed using boxplots. To better understand the time-varying responses of the polarimetric parameters to LAI, we conducted the regression analyses not only for the entire growth cycle but also under different phenological phases. For each phenological phase, the optimal relationship between rice LAI and each polarimetric parameter was identified according to the highest coefficient of determination (R 2 ) of the linear, logarithmic, and exponential regression relationships. For the entire growth cycle, the polynomial (quadratic and cubic) regression fits were additionally performed considering the complicated variation of polarimetric parameters during the phenology sequence. The Statistical Product and Service Solutions (SPSS) software (https://www.ibm.com/analytics/spss-statistics-software) was used for the regression analyses. Regression models are expressed respectively as . The red, green, and blue bands correspond to P D , P V , and P S , respectively.

Method of Data Analysis and Model Construction
The different transplanting dates of 30 rice sample sites resulted in various phenological phases on the SAR imaging dates. SAR variables obtained from the multi-temporal datasets associated with the ground measurements were regrouped into four collections corresponding to the four phenological phases. For each phase, the data were partitioned into the training dataset (3/4 of the total) and validation dataset (1/4). The training dataset was used in statistical analyses including data visualization, regression analysis, and model development. The validation dataset was used for the accuracy assessment of the model.
The multi-temporal polarimetric parameters and their combinations during the rice phenology succession were analyzed using boxplots. To better understand the time-varying responses of the polarimetric parameters to LAI, we conducted the regression analyses not only for the entire growth cycle but also under different phenological phases. For each phenological phase, the optimal relationship between rice LAI and each polarimetric parameter was identified according to the highest coefficient of determination (R 2 ) of the linear, logarithmic, and exponential regression relationships. For the entire growth cycle, the polynomial (quadratic and cubic) regression fits were additionally performed Remote Sens. 2019, 11, 2640 7 of 16 considering the complicated variation of polarimetric parameters during the phenology sequence. The Statistical Product and Service Solutions (SPSS) software (https://www.ibm.com/analytics/spss-statisticssoftware) was used for the regression analyses. Regression models are expressed respectively as where SAR para is the polarimetric parameter. b i (i = 0, 1, . . . , 12) coefficients in the regression equations. Parameters with the strongest relationship of the rice LAI for the entire growth cycle were used to construct the inversion models. The difference between the modeled and measured LAI values was plotted and the linear regression analysis was conducted to quantify the relationship. The inversion accuracy was quantified by the Root Mean-Square Error (RMSE) using the validation dataset.

Phenological Variation of Ground Measured Rice LAI and Polarimetric SAR Variables
The succession of rice LAI (training dataset) of four phenological phases is shown in Figure 5. The ranges of LAI values at each phase were illustrated by the boxplots. The trend was illustrated with the connection of median values at four phases. The LAI increased monotonously during the growth cycle. In particular, from the transplanting to reproductive phases, a significant increase and narrow overlaps between phases were observed due to the rapid plant development and consequent increase of canopy density. As rice plants completed the vegetative growth and entered the reproductive phase, panicle (later rice heads) emerged from the flag leaf sheath then anthers appeared at the top of panicle. The basal leaves gradually turned yellow and withered when most of the spikelets completed flowering. The effect of canopy development on the LAI growth weakened since the growth of stems and leaves almost stopped. Thus, the increase rate significantly slowed after the reproductive phase. where SAR para is the polarimetric parameter. bi (i = 0, 1, …, 12) coefficients in the regression equations. Parameters with the strongest relationship of the rice LAI for the entire growth cycle were used to construct the inversion models. The difference between the modeled and measured LAI values was plotted and the linear regression analysis was conducted to quantify the relationship. The inversion accuracy was quantified by the Root Mean-Square Error (RMSE) using the validation dataset.

Phenological Variation of Ground Measured Rice LAI and Polarimetric SAR Variables
The succession of rice LAI (training dataset) of four phenological phases is shown in Figure 5. The ranges of LAI values at each phase were illustrated by the boxplots. The trend was illustrated with the connection of median values at four phases. The LAI increased monotonously during the growth cycle. In particular, from the transplanting to reproductive phases, a significant increase and narrow overlaps between phases were observed due to the rapid plant development and consequent increase of canopy density. As rice plants completed the vegetative growth and entered the reproductive phase, panicle (later rice heads) emerged from the flag leaf sheath then anthers appeared at the top of panicle. The basal leaves gradually turned yellow and withered when most of the spikelets completed flowering. The effect of canopy development on the LAI growth weakened since the growth of stems and leaves almost stopped. Thus, the increase rate significantly slowed after the reproductive phase.  Figure 6 shows the phenological variation of the basic polarimetric parameters (training dataset) obtained from the four SAR acquisitions. Different parameters should reflect the characteristics of plant morphological structure change. Some parameters were dominated by the same physical characteristics and consequently had similar phenological trends, such as HV and P V (increased monotonously), and HH and P D (peaked at vegetative phase then decreased). Among quadpolarized backscattering coefficients, HV backscatter had the lowest values (lower than −17 dB) and increased continuously with the phenology sequence. HH backscatter peaked at the vegetative phase (higher than −10 dB), then decreased gradually. VV backscatter had comparable amplitudes with HH backscatter and declined from the vegetative to reproductive phases. For the Cloude-Pottier decomposition parameters, the entropy (H) kept the values higher than 0.65 and consistently increased to 0.82, while the anisotropy (A) sharply dropped from 0.62 to 0.33. The alpha angle (α)  Figure 6 shows the phenological variation of the basic polarimetric parameters (training dataset) obtained from the four SAR acquisitions. Different parameters should reflect the characteristics of plant morphological structure change. Some parameters were dominated by the same physical characteristics and consequently had similar phenological trends, such as HV and P V (increased monotonously), and HH and P D (peaked at vegetative phase then decreased). Among quad-polarized backscattering coefficients, HV backscatter had the lowest values (lower than −17 dB) and increased continuously with the phenology sequence. HH backscatter peaked at the vegetative phase (higher than −10 dB), then decreased gradually. VV backscatter had comparable amplitudes with HH backscatter and declined from the vegetative to reproductive phases. For the Cloude-Pottier decomposition parameters, the entropy (H) kept the values higher than 0.65 and consistently increased to 0.82, while the anisotropy (A) sharply dropped from 0.62 to 0.33. The alpha angle (α) climbed to the maximum (up to 55 • ) at the reproductive phase and was generally within an interval from 45 • to 50 • at the last three phases. As for the Freeman-Durden decomposition parameters, the volume scattering power (P V ) rose from −11 to −6 dB during the growing cycle, while the surface scattering power (P S ) fell significantly from −10 to −17 dB. The double-bounce scattering power (P D ) increased slightly from the transplanting phase (−15.2 dB) to the vegetative phase (−14.8 dB) then slowly decreased to −18 dB at the maturity phase. The ratios of the polarimetric parameters and radar vegetation indices (RVI σ , RVI FD , and RVI CP ) are plotted in Figure 7. Monotonic trends were observed for most of the ratios, such as HV/HH and P D /P V . Radar vegetation indices derived from different algorithms responded positively to rice growth and showed similar trends.

Regression Analyses between Rice LAI and Polarimetric Parameters
R 2 values of regression analyses are summarized in Table 2. The numbers of samples (training dataset) used were 15, 42, 18, and 15, respectively, for the transplanting, vegetative, reproductive, and maturity phases. As shown in the table, for the entire growth cycle, several tested polarimetric parameters exhibited moderate relationships (R 2 > 0.50) with the rice LAI, such as HV/VV, P V /P S , and RVIs. In comparison with the results obtained with the basic polarimetric parameters, the use of parameter combinations (ratios and radar vegetation indices) might achieve higher R 2 values, suggesting that LAI was related to multiple scattering mechanisms produced by the complex physical structure of the scattering elements. Because rice LAI increased monotonously during the growth cycle, the ratios of two parameters that changed monotonously but moved inversely would enhance the sensitivity of SAR signatures to the biophysical development of rice plants, such as the P V /P S . Among all polarimetric descriptors, HV/VV and RVI FD data showed relatively strong relationships (R 2 > 0.80).
For the four segmented phenological phases, the strongest relationships between polarimetric parameters and rice LAI were found at the vegetative phase, during which the HV/VV and RVI FD values were the most sensitive variables to the LAI variation, as evidenced by high R 2 values (0.75 for the HV/VV data and 0.68 for RVI FD data). At the transplanting and reproductive phases, weak relationships (R 2 < 0.30) were observed except for parameters such as HH and VV. At the maturity phase, polarimetric descriptors lost sensitivity for high LAI values having negligible relationships (R 2 < 0.15).

Model Development and Validation
Because the HV/VV and RVI FD data were the most relevant to the rice LAI for the entire growth cycle, the scatterplots and trends of rice LAI (training dataset) as a function of these two parameters are shown in Figure 8. LAI increased exponentially as the HV/VV or RVI FD increased. In comparison with the RVI FD data, the HV/VV values were relatively dispersed for LAI higher than 5. Exponential equations of the best fits for the rice LAI and HV/VV or RVI FD were derived using the training dataset of all phenological phases and SPSS software. They were LAI = 39.7 × e (0.41×HV/VV) , R 2 = 0.81 (6) On the basis of the validation dataset, the modeling RMSE was 1.29 for (6) and 0.81 for (7).
On the basis of the validation dataset, the modeling RMSE was 1.29 for (6) and 0.81 for (7). Modeled and measured rice LAIs are plotted (validation dataset) in Figure 9. Overestimates appeared using both models during the seedling period, when ground observed values ranged from 0 to 2. The heterogeneity of water depth and soil roughness could deteriorate the relationship Modeled and measured rice LAIs are plotted (validation dataset) in Figure 9. Overestimates appeared using both models during the seedling period, when ground observed values ranged from 0 to 2. The heterogeneity of water depth and soil roughness could deteriorate the relationship between the rice LAI and polarimetric parameters [25]. Uncertainty might occur for the models when the ground observed LAI shows a saturation near 5. The leaf density of rice canopy peaked in this period. The plant moisture content, seed plumpness, and the randomness of plant canopy gradually changed and affected the SAR backscatter. Modeled and measured rice LAIs are plotted (validation dataset) in Figure 9. Overestimates appeared using both models during the seedling period, when ground observed values ranged from 0 to 2. The heterogeneity of water depth and soil roughness could deteriorate the relationship between the rice LAI and polarimetric parameters [25]. Uncertainty might occur for the models when the ground observed LAI shows a saturation near 5. The leaf density of rice canopy peaked in this period. The plant moisture content, seed plumpness, and the randomness of plant canopy gradually changed and affected the SAR backscatter. In a comparison of both models, the RVI FD -based model offered promising results with a small RMSE of 0.81 and the ability to estimate LAI at high values well. Intuitively, the RVI FD was the most suitable index for the rice LAI inversion. Possible causes for the best performance included that In a comparison of both models, the RVI FD -based model offered promising results with a small RMSE of 0.81 and the ability to estimate LAI at high values well. Intuitively, the RVI FD was the most suitable index for the rice LAI inversion. Possible causes for the best performance included that RVI FD was calculated as P V /(P S + P D + P V ). The development of rice canopy led to a continuous increase in P V while (P S + P D + P V ) integrated the signal from all polarizations and reflected the total power scattered from the rice fields.
The HV/VV-based model had a slightly larger RMSE of 1.29 in the rice LAI estimation. The increase in error in comparison with the RMSE for the RVI FD -based model was probably due to the fact that only amplitude information of the SAR data was considered. Without the polarimetric phase difference information that relates to the physical structure and dielectric properties of the underlying surface and vegetation components, the complex microwave scattering process could not be adequately revealed by the amplitude data alone. Nevertheless, HV/VV is a suitable alternative to RVI FD for monitoring the rice LAI because dual-polarization SAR data such as the Sentinel-1 SAR are widely-accessible.

Discussion
The changes in quantity, geometry, and distribution of leaves, stems, and ears had significant effects on the SAR backscatter. The responses of backscattering coefficients and decomposition parameters to the rice plant growth were further interpreted. At the transplanting phase, rice plants were sparsely distributed in the fields, with the measured LAI ranged from 0.35 to 1.42. The water in the fields resulted in strong surface scattering, and the backscatter characteristics of rice fields were mainly affected by the water [48]. In this period, VV backscatter was moderate, with −13 dB on the average. HV backscatter was low and with −22 dB on the average. HH backscatter started at relatively low values, with an average of −11.5 dB as shown in Figure 6a. Moderate entropy (about 0.68) and anisotropy (about 0.62) are observed in Figure 6b, indicating two strong scattering components existed [49]. Due to the small rice plants, the amount of scattering attenuation was small. The median value of the alpha angle was 38 • , suggesting that the surface scattering contributed significantly to the total backscatter [49,50]. The strong surface scattering power (−10 dB on average) and weak double-bounce scattering (−15 dB on average) supported this assessment, as seen in Figure 6c. The sparse rice canopy also resulted in relatively weak volume scattering (−11 dB on average), which predicted low HV backscatter values [34]. Strong surface scattering contributed to moderate VV values [51]. Weak double-bounce scattering resulted in low HH values [49,50]. The weak relationship between polarimetric parameters and rice LAI at transplanting phase was mainly due to the disturbance caused by the diversity of field conditions such as field water depth and soil roughness.
At the vegetative phase, the measured rice LAI had a 0.87-5.81 range. The wide range of LAI values implied the marked temporal and spatial variation of rice vegetative growth. As the plants grew, HV backscatter increased by 3 dB, as seen in Figure 6a. HH backscatter increased by 3.5 dB due to the increase in the plant size. As a result, volume scattering and double-bounce scattering increased, as seen in Figure 6c. VV backscatter increased slightly by~0.4 dB because it was attenuated by the strong extinction caused by the vertical orientated stems and leaves as well as possibly the Brewster angle effect [18,49,52]. The alpha angle was mostly within an interval from 44 • to 48 • , even reaching 52 • , together with increased entropy and decreased anisotropy, as seen in Figure 6b. Lopez-Sanchez et al. [49,50] and Koppe et al. [52] attributed these to the presence of adequate double-bounce scattering, which was on par with the surface scattering. At the vegetative phase, the radar signal responded to the accumulation of leaves and stems, resulting in the moderate to high relationships (R 2 > 0.50) for several parameters (e.g., HV/VV, P V /P S , and RVI FD ). For most of the polarimetric parameters, the R 2 value at the vegetative phase had the dominant influence on the overall R 2 . One reason was that the radar signal responded clearly to the obvious biophysical changes of rice plants in this period. In addition, the vegetative phase not only went through from the tillering stage to the booting stage but also was the longest phenological phase (almost accounted for one-half of a growth cycle). Thus, there were a greater number of LAI measurements for the vegetative phase within a long time span.
At the reproductive phase, rice completed its vegetative growth, and the LAI ranged from 4.33 to 7.59. Emerged tassels and ears were new scatterers in the upper portion of the canopy. A slight increase (about 0.5 dB) was observed in the HV backscatter, as seen in Figure 6a. The dense canopy attenuated the microwave energy penetrated the plants and bounced off the ground, as seen in Figure 6c [53]. Accordingly, HH backscatter decreased by 1.5 dB. The predominantly vertical orientation of most of the stems and leaves led to the attenuation in the VV polarization. The alpha angle increased, to a maximum of 55 • , and the median value of anisotropy fell to 0.35 (Figure 6b), indicating an enhancement of volume scattering along with the rice phenology advancement. The weak relationship between LAI and the polarimetric parameters this time mainly suffered from a saturation trend of LAI values. Rice ears and the changes in plant structure and moisture were attributed to the polarimetric parameter variation. The relationship between LAI and the polarimetric parameters was less straightforward.
At the maturity phase, the rice LAI ranged from 4.84 to 6.92. The augmentation of rice grain produced strong backscattering, which contributed to the increase (about 1 dB) in HV backscatter, as shown in Figure 6a. HH backscatter further decreased by almost 0.5 dB. The reduction was mainly due to a large amount of rice canopy attenuation. The orientation of the plants became random and the moisture content of the plants reduced. Therefore, less attenuation occurred in the VV polarization [52]. High entropy (0.82 on average) and low anisotropy (0.33 on average) denoted the almost random volume structure of the rice plants, as seen in Figure 6b. The dominant scattering mechanism transformed into volume scattering (Figure 6c). Despite the attenuation caused by the dense canopy, the C-band RADARSAT-2 microwave energy could still penetrate the rice plants and reveal the changing information, while the LAI reached saturation. Therefore, the dependence of the polarimetric parameters on the LAI was further weakened.
Although the relationships of the rice LAI to RVI FD and HV/VV were empirically established, uncertainty remained during the rice-growing cycle. The uncertainty could be attributed to the diversity of the cultivation management and field circumstances [54]. To improve the predictive accuracy, physical model should be used to elucidate the effects of plant and field properties on the polarimetric parameters [29,55].

Conclusions
We estimated the LAI of rice using the multi-temporal quad-polarized RADARSAT-2 datasets. Polarimetric parameters including backscattering coefficients, the Cloude-Pottier and Freeman-Durden decomposition parameters, and their combinations were analyzed. The relationship between the rice LAI and polarimetric parameters as well as the phenology evolution was explored. HV/VV and RVI FD showed strong relationships (R 2 > 0.80) with the rice LAI for the entire growth cycle. Both were used to develop two empirical models, respectively. The strongest relationship (R 2 = 0.84) and lowest error (RMSE = 0.81) were achieved when the RVI FD was used in the modeling. The model was simple but had satisfactory results in the rice LAI inversion. The HV/VV-based model had a slightly lower estimation accuracy (RMSE = 1.29) but could be a practical alternative considering that fully polarimetric data is expensive. Thus, it should be possible to assess rice LAI timely using multi-temporal C-band PolSAR datasets.