Combination of Linear Regression Lines to Understand the Response of Sentinel-1 Dual Polarization SAR Data with Crop Phenology— Case Study in Miyazaki, Japan

: This study investigated the relationship between backscattering coe ﬃ cients of a synthetic aperture radar (SAR) and the four biophysical parameters of rice crops—plant height, green vegetation cover, leaf area index, and total dry biomass. A paddy rice ﬁeld in Miyazaki, Japan was studied from April to July of 2018, which is the rice cultivation season. The SAR backscattering coe ﬃ cients were provided by Sentinel-1 satellite. Backscattering coe ﬃ cients of two polarization settings—VH (vertical transmitting, horizontal receiving) and VV (vertical transmitting, vertical receiving)—were investigated. Plant height, green vegetation cover, leaf area index, and total dry biomass were measured at ground level, on the same dates as satellite image acquisition. Polynomial regression lines indicated relationships between backscattering coe ﬃ cients and plant biophysical parameters of the rice crop. The biophysical parameters had stronger relationship to VH than to VV polarization. A disadvantage of adopting polynomial regression equations is that the equation can have two biophysical parameter solutions for a particular backscattering coe ﬃ cient value, which prevents simple conversion from backscattering coe ﬃ cients to plant biophysical parameters. To overcome this disadvantage, the relationships between backscattering coe ﬃ cients and the plant biophysical parameters were expressed using a combination of two linear regression lines, one line for the ﬁrst sub-period and the other for the second sub-period during the entire cultivation period. Following this approach, all four plant biophysical parameters were accurately estimated from the SAR backscattering coe ﬃ cient, especially with VH polarization, from the date of transplanting to about two months, until the mid-reproductive stage. However, backscattering coe ﬃ cients saturate after two months from the transplanting, and became insensitive to the further developments in plant biophysical parameters. This research indicates that SAR can e ﬀ ectively and accurately monitor rice crop biophysical parameters, but only up to the mid reproductive stage.


Introduction
Rice is a staple food, feeding approximately half of the world's population. Estimates indicate that, by the mid-twenty first century, one of the biggest challenges will be to feed the nine billion people Kurosu et al. [20]. They used the C-band VV (i.e., vertical transmitting, vertical receiving) polarization data from the European Remote Sensing (ERS-1) satellite. However, few studies investigated using C-band SAR data. These studies have mainly focused on the relationship between the backscatter coefficients from rice fields and rice growth parameters. Moreover, HH (i.e., horizontal transmitting, horizontal receiving) or VV and the ratio of HH/VV backscattered coefficients are frequently used data sets in the past studies that indicate high correlations with rice growth stages [18,21]. In all these studies, the cross polarized HV (i.e., horizontal transmitting, vertical receiving) or VH (the reverse of HV) backscatter was rarely focused on, possibly because of the limited availability of SAR data in terms of time series and polarization. Sentinel-1 radar platform lunched by the European Space Agency is able to provide timely and precise high-resolution data [22]. Le Toan et al. reported that, for X-band SAR data of HH and VV polarization, both HH and VV increased because of the increment in the vegetation cover vertical structures, but VV is more sensitive to changes in vegetation cover during the vegetative stages [23]. This idea is further supported by Mansaray et al.-even though VV polarization produces higher backscatter coefficients values, VH polarization constantly increases and is more sustained compared with VV, where saturation is reached during the tillering stage [24].
In this study, we introduce the monitoring of rice growth parameters using multi-temporal Sentinel-1 VH and VV polarization SAR images. Plant height, green vegetation cover, LAI, and the total dry biomass were acquired by fieldwork, and the coefficient of determination (R 2 ) between the parameters and the backscattering coefficient derived from SAR data were investigated. While previous studies typically analyzed the relationship between plant biophysical parameters and the SAR backscattering coefficients using a single linear or polynomial regression line, this study attempts to express the relationship using the combination of two linear-regression lines, which is unique to this study. The two-linear-line approach taken in this study helps to clarify the turning-point of the response of SAR backscattering signals to rice plant phenology. Also, the approach has the potential to easily estimate the plant biophysical parameters by SAR backscattering coefficients.

Study Area
The study field is in the Kibana Agricultural Science Station of the University of Miyazaki, in the Miyazaki prefecture of Japan ( Figure 1). The study area lies at a base elevation of approximately 21 m above sea level and it is located at 31 • 50 14" north and 131 • 23 56" east. The climate of Miyazaki is humid subtropical, with hot and humid summers and cool winters. The average annual temperature is 17.1 • C, and annual precipitation is 2550 mm. Figure 2 shows the monthly average air temperature and rainfall in Miyazaki. The primary rainy season is from early June to mid-July. The season is called as "plum rain" and a large amount of the precipitation is a result of the East Asian monsoon system. In 2018, more than half of the days in June had recorded precipitation around the study area. The monsoon rain is a fundamental water resource for paddy rice cultivation in this area. Another peak of monthly precipitation appears in August to September, which is typically from short-term heavy rains brought by typhoons. Rice is the major staple food in Japan. Popular Japanese rice varieties, Oryza sativa 'Koshihikari' and 'Hinohikari', are most commonly cultivated around the study area. The first variety, which was planted in the study field, is typically planted in early season (transplants in late March to early April and harvest in late July) for the purpose of avoiding the risk of damage by typhoons in late summer; the later variety is planted in normal season (transplants in June and harvest in October). Figure 3 represents the rice development stages in the study area during 2018, determined by actual field surveys, following the framework of rice development stages used by Wu et al. [25]. The vegetative stage lasts for about 45 days, while the reproductive and flowering stages last for 45 and 20 days, respectively. The number of days slightly changes by year and farmer, depending on the weather conditions and cultivation practices.

Data Acquisition and Analysis
This study compares Sentinel-1 VH and VV backscattering coefficients with ground-measured biophysical parameters of a rice crop, to investigate the potential and limitations in estimating the biophysical parameters used by satellite SAR monitoring. Table 1 summarizes the data used in this study. Ten Sentinel-1A time series images of the study area were acquired for the entire cultivation season from April to July 2018. The dates of the image acquisitions are given in Table 1. Sentinel-1 ground range detected (GRD) data of dual polarization (VH and VV polarization), acquired with interferometric wide (IW) mode, were used in this study. The GRD image products with the IW mode are provided by 10 m × 10 m pixel size, but the reference spatial resolution is 20 m × 22 m (range and azimuth directions, respectively), because the product is created by the multi-look procedure of IW images [26]. The acquired SAR images were preprocessed using ESA's open source Sentinel-1 Toolbox [21]. The process includes radiometric calibration, terrain flattening, and geometric correction. Topographic variations can dominate the radiometric backscatter signal strongly because of the local area illuminated within each azimuth and slant range [27]. The reference area used within the beta naught (β 0 ), sigma naught (σ 0 ), and gamma naught (γ 0 ) backscatter conventions is described by Small [28]. Each convention differs in their choice of definition. The β 0 convention is the slant range plane itself [27]. The contents of images conforming to its convention are not subjected to modifications based on ellipsoid or terrain Earth models [28]. σ 0 is the ground as modeled by an ellipsoidal Earth. For γ 0 , the area is the projection in the plane perpendicular to the slant range direction [29]. In our study, first, the radiometry of the SAR backscatter product was transformed into β 0 backscatter convention, as is also recommended by Small et al. [30]. Secondly, the range Doppler terrain correction was applied. In this process, once the DEM integration was completed, the normalization was performed by converting β 0 to γ 0 . In this study, the averages of VH and VV polarization backscatter signals read by four pixels from the center of the crop sampling field were

Data Acquisition and Analysis
This study compares Sentinel-1 VH and VV backscattering coefficients with ground-measured biophysical parameters of a rice crop, to investigate the potential and limitations in estimating the biophysical parameters used by satellite SAR monitoring. Table 1 summarizes the data used in this study. Ten Sentinel-1A time series images of the study area were acquired for the entire cultivation season from April to July 2018. The dates of the image acquisitions are given in Table 1. Sentinel-1 ground range detected (GRD) data of dual polarization (VH and VV polarization), acquired with interferometric wide (IW) mode, were used in this study. The GRD image products with the IW mode are provided by 10 m × 10 m pixel size, but the reference spatial resolution is 20 m × 22 m (range and azimuth directions, respectively), because the product is created by the multi-look procedure of IW images [26]. The acquired SAR images were preprocessed using ESA's open source Sentinel-1 Toolbox [21]. The process includes radiometric calibration, terrain flattening, and geometric correction. Topographic variations can dominate the radiometric backscatter signal strongly because of the local area illuminated within each azimuth and slant range [27]. The reference area used within the beta naught (β 0 ), sigma naught (σ 0 ), and gamma naught (γ 0 ) backscatter conventions is described by Small [28]. Each convention differs in their choice of definition. The β 0 convention is the slant range plane itself [27]. The contents of images conforming to its convention are not subjected to modifications based on ellipsoid or terrain Earth models [28]. σ 0 is the ground as modeled by an ellipsoidal Earth. For γ 0 , the area is the projection in the plane perpendicular to the slant range direction [29]. In our study, first, the radiometry of the SAR backscatter product was transformed into β 0 backscatter convention, as is also recommended by Small et al. [30]. Secondly, the range Doppler terrain correction was applied. In this process, once the DEM integration was completed, the normalization was performed by converting β 0 to γ 0 . In this study, the averages of VH and VV polarization backscatter signals read Remote Sens. 2020, 12, 189 6 of 17 by four pixels from the center of the crop sampling field were used. The locations of the sampling pixels are shown in Figure 4. The study area was composed of five paddy rice fields that were all managed similarly. Considering the 20 × 22 m effective resolution of Sentinel-1A GRD images, the sampled SAR backscatter signals used in this study are not affected by surface conditions outside of the study area.
Remote Sens. 2020, 12, x FOR PEER REVIEW 6 of 17 used. The locations of the sampling pixels are shown in Figure 4. The study area was composed of five paddy rice fields that were all managed similarly. Considering the 20 × 22 m effective resolution of Sentinel-1A GRD images, the sampled SAR backscatter signals used in this study are not affected by surface conditions outside of the study area.

Ground Measurements of Plant Biophysical Parameters
Field surveys were conducted simultaneously with the dates of satellite image acquisitions, to obtain ground-measured plant height, green vegetation cover, LAI, and total dry biomass of rice crop. The actual field conditions during the cultivation period are shown in Figure 5. Representative plant height for an image date was determined by averaging the measurements at ten different locations in the study field. The standard deviations for the 10 samples, indicating the spatial variation of the plant height, were small (1 to 4 cm) in the vegetative and reproductive stages, and large (7 to 10 cm) in ripening stage. The spatial heterogeneity of plant height in the ripening stage was the result of different degrees of rice ears hanging. For green vegetation cover, ten photo image samples were taken from 70 cm above the top of the plant canopy, and the average fractional green canopy cover of rice plant was analyzed by a smartphone application, Canopeo [31]. The fractional green canopy cover is a key variable for determining canopy development, light interception, and evapotranspiration. The average standard deviation of 10 samples was 6%. In each observation, four plant hills that represent the average conditions of the field were sampled for measurements of LAI and dry biomass. ImageJ software [32] was used to compute LAI values by sampled leaves after scanning.

Ground Measurements of Plant Biophysical Parameters
Field surveys were conducted simultaneously with the dates of satellite image acquisitions, to obtain ground-measured plant height, green vegetation cover, LAI, and total dry biomass of rice crop. The actual field conditions during the cultivation period are shown in Figure 5. Representative plant height for an image date was determined by averaging the measurements at ten different locations in the study field. The standard deviations for the 10 samples, indicating the spatial variation of the plant height, were small (1 to 4 cm) in the vegetative and reproductive stages, and large (7 to 10 cm) in ripening stage. The spatial heterogeneity of plant height in the ripening stage was the result of different degrees of rice ears hanging. For green vegetation cover, ten photo image samples were taken from 70 cm above the top of the plant canopy, and the average fractional green canopy cover of rice plant was analyzed by a smartphone application, Canopeo [31]. The fractional green canopy cover is a key variable for determining canopy development, light interception, and evapotranspiration. The average standard deviation of 10 samples was 6%. In each observation, four plant hills that represent the average conditions of the field were sampled for measurements of LAI and dry biomass. ImageJ software [32] was used to compute LAI values by sampled leaves after scanning.

Data Analysis
The ground-based biophysical parameters were compared with VH and VV polarization backscattering coefficients of Sentinel-1A, to analyze the relationship between plant biophysical parameters and the SAR backscattering coefficients. The relationships were analyzed using two types of regressions. The first approach describes the relationship with a single polynomial regression equation determined by the least-square method, which is a traditional method of statistical analysis popularly used in this type of study. Another method attempts to describe the relationship by the combination of two linear regression lines. The concept of the two-linear-lines method is illustrated in Figure 6. The basic assumption of this approach is that the SAR backscattering coefficients first linearly increases as the rice plant develops (first period in Figure 6), and then the backscattering coefficient reaches a saturation level at a specific date termed the "turning point" during the cultivation season. In this research, the turning point is defined as the point where the R 2 of the linear regression Remote Sens. 2020, 12, 189 7 of 17 for the first period reaches its maximum. The R 2 of the linear regression for the second period ( Figure 6) is expected to be a small value, because the SAR backscattering coefficient is saturated in the second period, and thus the backscattering coefficients no longer explain the further changes in plant biophysical parameters.
Remote Sens. 2020, 12, x FOR PEER REVIEW 7 of 17 Figure 5. Photos of study field during the study period.

Data Analysis
The ground-based biophysical parameters were compared with VH and VV polarization backscattering coefficients of Sentinel-1A, to analyze the relationship between plant biophysical parameters and the SAR backscattering coefficients. The relationships were analyzed using two types of regressions. The first approach describes the relationship with a single polynomial regression equation determined by the least-square method, which is a traditional method of statistical analysis popularly used in this type of study. Another method attempts to describe the relationship by the combination of two linear regression lines. The concept of the two-linear-lines method is illustrated in Figure 6. The basic assumption of this approach is that the SAR backscattering coefficients first linearly increases as the rice plant develops (first period in Figure 6), and then the backscattering coefficient reaches a saturation level at a specific date termed the "turning point" during the cultivation season. In this research, the turning point is defined as the point where the R 2 of the linear regression for the first period reaches its maximum. The R 2 of the linear regression for the second period ( Figure 6) is expected to be a small value, because the SAR backscattering coefficient is saturated in the second period, and thus the backscattering coefficients no longer explain the further changes in plant biophysical parameters.

Temporal Changes in Plant Biophysical Parameters
Figure 7 shows ground-measured biophysical parameters of the rice crop (plant height, green vegetation cover, LAI, and total dry biomass) in the study field. Plant height ( Figure 7A) constantly increased until around 72 days after transplant (middle of reproductive stage). The green vegetation cover ( Figure 7B) gradually increased in the early vegetative stage, and then rapidly increased during the late vegetative stages. The green vegetation cover maintained at maximum during the  Figure 7 shows ground-measured biophysical parameters of the rice crop (plant height, green vegetation cover, LAI, and total dry biomass) in the study field. Plant height ( Figure 7A) constantly increased until around 72 days after transplant (middle of reproductive stage). The green vegetation cover ( Figure 7B) gradually increased in the early vegetative stage, and then rapidly increased during the late vegetative stages. The green vegetation cover maintained at maximum during the reproductive stage, and then rapidly dropped during the ripening stage when the leaves turned yellow. LAI ( Figure 7C) had a similar trend as the green vegetation cover, with some delays in the timing. The total dry biomass ( Figure 7D) did not significantly increase during the vegetative stage, and constantly increased during the reproductive and ripening stages.  Figure 7 shows ground-measured biophysical parameters of the rice crop (plant height, green vegetation cover, LAI, and total dry biomass) in the study field. Plant height ( Figure 7A) constantly increased until around 72 days after transplant (middle of reproductive stage). The green vegetation cover ( Figure 7B) gradually increased in the early vegetative stage, and then rapidly increased during the late vegetative stages. The green vegetation cover maintained at maximum during the reproductive stage, and then rapidly dropped during the ripening stage when the leaves turned yellow. LAI ( Figure 7C) had a similar trend as the green vegetation cover, with some delays in the timing. The total dry biomass ( Figure 7D) did not significantly increase during the vegetative stage, and constantly increased during the reproductive and ripening stages.  Figure 8 shows the temporal variation in VH-and VV-bands' backscattering coefficients. The numbers are the averages of four pixels from the center of the study field (Figure 4). Throughout the cultivation season, VV is higher than VH. Both VH and VV backscattering coefficients were the lowest during the initial period of rice cultivation. During this period, green vegetation cover was low ( Figure 7B), and the dominant surface observed by satellite is the water surface flooded in the paddy field. The backscattering coefficients increased during the late vegetative stage, and became stable after 48 days (VV) or 60 days (VH). This trend in the backscattering coefficients agrees with those in previous studies [2,25,33]. cultivation season, VV is higher than VH. Both VH and VV backscattering coefficients were the lowest during the initial period of rice cultivation. During this period, green vegetation cover was low ( Figure 7B), and the dominant surface observed by satellite is the water surface flooded in the paddy field. The backscattering coefficients increased during the late vegetative stage, and became stable after 48 days (VV) or 60 days (VH). This trend in the backscattering coefficients agrees with those in previous studies [2,25,33].

Relationship between Backscatter and Rice Biophysical Parameters Expressed with Polynomial Regression
The relationship between VH or VV and the plant biophysical parameters, with single polynomial regression lines, is shown in Figures 9-12. Our results from the polynomial regression agree with the results reported by Chakraborty et al. [19], where they studied rice crop biophysical parameters, that is, crop height, using SAR data obtained by Radarsat. They found that polynomial relationships are the most appropriate to link plant height and SAR backscattering coefficients. They obtained coefficients of determination between backscatter and plant height, where R 2 = 0.694, 0.693, 0.527, and 0.947 for beam S-1, S-5, S-6, and S-7, respectively, while in our case, R 2 = 0.952 and 0.874 for VH and VV, respectively (Figure 9). In a similar type of study, Le Toan et al. studied the relationship between backscatter and rice crop parameters, that is, plant height and biomass, using ERS-1 data [34], demonstrating a high-performance description by polynomial regression. R 2 values shown in Figures 9-12 indicate that VH is superior to VV. Compared with VV, VH backscattering coefficients have a much stronger relationship to all of the tested biophysical parameters, where plant height, green vegetation cover, and LAI versus VH had an R 2 greater than 0.9 (Figures 9-11). Compared with these three biophysical parameters, total dry biomass had a weaker relationship to backscattering coefficients ( Figure 12). Total dry biomass is constantly low during the vegetative stage, but the backscattering coefficients change significantly during the period (Figures 7D and 8). In the following reproductive and ripening stages, total dry biomass increases significantly, but the backscattering coefficients values are stable. Therefore, it is difficult to correlate the total dry biomass and backscattering coefficients.

Relationship between Backscatter and Rice Biophysical Parameters Expressed with Polynomial Regression
The relationship between VH or VV and the plant biophysical parameters, with single polynomial regression lines, is shown in Figures 9-12. Our results from the polynomial regression agree with the results reported by Chakraborty et al. [19], where they studied rice crop biophysical parameters, that is, crop height, using SAR data obtained by Radarsat. They found that polynomial relationships are the most appropriate to link plant height and SAR backscattering coefficients. They obtained coefficients of determination between backscatter and plant height, where R 2 = 0.694, 0.693, 0.527, and 0.947 for beam S-1, S-5, S-6, and S-7, respectively, while in our case, R 2 = 0.952 and 0.874 for VH and VV, respectively (Figure 9). In a similar type of study, Le Toan et al. studied the relationship between backscatter and rice crop parameters, that is, plant height and biomass, using ERS-1 data [34], demonstrating a high-performance description by polynomial regression. R 2 values shown in Figures 9-12 indicate that VH is superior to VV. Compared with VV, VH backscattering coefficients have a much stronger relationship to all of the tested biophysical parameters, where plant height, green vegetation cover, and LAI versus VH had an R 2 greater than 0.9 (Figures 9-11). Compared with these three biophysical parameters, total dry biomass had a weaker relationship to backscattering coefficients ( Figure 12). Total dry biomass is constantly low during the vegetative stage, but the backscattering coefficients change significantly during the period (Figures 7D and 8). In the following reproductive and ripening stages, total dry biomass increases significantly, but the backscattering coefficients values are stable. Therefore, it is difficult to correlate the total dry biomass and backscattering coefficients. Remote Sens. 2020, 12, x FOR PEER REVIEW 10 of 17

Relationship between Backscattering Coefficients and Rice Biophysical Parameters Expressed by Two Linear Regression Lines
Even though the polynomial regression reasonably expresses the relationship between backscattering coefficients and the biophysical parameters, except the total dry biomass, the polynomial approach has an operational inconvenience for rice crop monitoring by satellite SAR. The polynomial equation accepts two solutions for a specific backscattering coefficient value. For example, VH = −13 dB can either take LAI = 1.6 or 2.5 (Figure 11), which is inconvenient when estimating LAI by satellite-observed backscattering coefficients. As a unique attempt by this study,  show the relationship between VH or VV and plant biophysical parameters by a combination of two linear regression lines. The regression equations shown in the figures are for the linear regressions of the first periods, where the first period is defined in Figure 6. Data plot by triangles, appearing in Figures 14 and 15, are the data for the last day of ground observation, where some reductions of green vegetation cover and LAI were confirmed by plant senescence (Figure 7B,C). Such data were treated as the data for second period.

Relationship between Backscattering Coefficients and Rice Biophysical Parameters Expressed by Two Linear Regression Lines
Even though the polynomial regression reasonably expresses the relationship between backscattering coefficients and the biophysical parameters, except the total dry biomass, the polynomial approach has an operational inconvenience for rice crop monitoring by satellite SAR. The polynomial equation accepts two solutions for a specific backscattering coefficient value. For example, VH = −13 dB can either take LAI = 1.6 or 2.5 (Figure 11), which is inconvenient when estimating LAI by satellite-observed backscattering coefficients. As a unique attempt by this study, Figures 13-16 show the relationship between VH or VV and plant biophysical parameters by a combination of two linear regression lines. The regression equations shown in the figures are for the linear regressions of the first periods, where the first period is defined in Figure 6. Data plot by triangles, appearing in Figures 14 and 15, are the data for the last day of ground observation, where some reductions of green vegetation cover and LAI were confirmed by plant senescence (Figure 7B,C). Such data were treated as the data for second period. Backscattering coefficients as a function of total dry biomass, expressed by polynomial regressions.

Relationship between Backscattering Coefficients and Rice Biophysical Parameters Expressed by Two Linear Regression Lines
Even though the polynomial regression reasonably expresses the relationship between backscattering coefficients and the biophysical parameters, except the total dry biomass, the polynomial approach has an operational inconvenience for rice crop monitoring by satellite SAR. The polynomial equation accepts two solutions for a specific backscattering coefficient value. For example, VH = −13 dB can either take LAI = 1.6 or 2.5 (Figure 11), which is inconvenient when estimating LAI by satellite-observed backscattering coefficients. As a unique attempt by this study, Figures 13-16 show the relationship between VH or VV and plant biophysical parameters by a combination of two linear regression lines. The regression equations shown in the figures are for the linear regressions of the first periods, where the first period is defined in Figure 6. Data plot by triangles, appearing in Figures 14  and 15, are the data for the last day of ground observation, where some reductions of green vegetation cover and LAI were confirmed by plant senescence (Figure 7B,C). Such data were treated as the data for second period. second period (p-values > 0.05) except the combination of LAI monitored by VV (p = 0.045). In the first period, p-values are smaller (i.e., more significant) in VH than VV for all biophysical parameters, indicating that VH is superior to monitor the rice crop. Compared with the polynomial approach, the two linear regression approach better described the relationship between biophysical parameters and SAR backscattering coefficients, especially with VH. The lines visually fit well to the scatter plot, even for total dry biomass, which was difficult to describe with the polynomial line.  first period, p-values are smaller (i.e., more significant) in VH than VV for all biophysical parameters, indicating that VH is superior to monitor the rice crop. Compared with the polynomial approach, the two linear regression approach better described the relationship between biophysical parameters and SAR backscattering coefficients, especially with VH. The lines visually fit well to the scatter plot, even for total dry biomass, which was difficult to describe with the polynomial line.      16 show the backscattering coefficients as the y-axis, which is a typical format in similar studies. However, backscattering coefficients should be the explanatory variable and the biophysical parameters should be the objective variables when estimating plant biophysical parameters by satellite-SAR monitoring. Figure 17 shows the relationship between VH and the By the analysis of R 2 values, the "turning point" for all combinations of biophysical parameters and VV was 48 days after transplant, which is the beginning of the reproductive stage. The turning point is later in most combinations with VH and was 60 days after transplant (the mid-reproductive stage). Compared with VV, VH has higher R 2 values, and has a later turning point (meaning that VH has higher tolerance to saturation), indicating that VH is superior to monitor the rice crop. The nearly horizontal regression lines in the second stages indicated that both VH and VV backscatter coefficients were saturated after passing the turning point. Further changes in biophysical parameters after the turning point cannot be described by SAR monitoring. Table 2 shows the summary of significant test for the regression lines with the R 2 values of the lines. The linear regression lines are statistically significant (p-value < 0.05) for all combinations during the first period, but not in the second period (p-values > 0.05) except the combination of LAI monitored by VV (p = 0.045). In the first period, p-values are smaller (i.e., more significant) in VH than VV for all biophysical parameters, indicating that VH is superior to monitor the rice crop. Compared with the polynomial approach, the two linear regression approach better described the relationship between biophysical parameters and SAR backscattering coefficients, especially with VH. The lines visually fit well to the scatter plot, even for total dry biomass, which was difficult to describe with the polynomial line.  16 show the backscattering coefficients as the y-axis, which is a typical format in similar studies. However, backscattering coefficients should be the explanatory variable and the biophysical parameters should be the objective variables when estimating plant biophysical parameters by satellite-SAR monitoring. Figure 17 shows the relationship between VH and the biophysical parameters for the first period, where the biophysical parameters are plotted as the y-axis. A caution to use with the regression equation (shown in Figure 17), for predicting plant biophysical parameters in operation, is that the minimum number of the biophysical parameters should be limited as zero, because negative numbers of these parameters do not have any physical meaning. The linear regression accurately reproduced the biophysical parameters for the first period, with a root mean square error (RMSE) = 0.039 m for plant height, 4.05% for green vegetation cover, 0.065 for LAI, and 0.013 kg m −2 for total dry biomass. However, this approach is not applicable after about 60 days from transplant, owing to saturation of the backscattering coefficients of VH in late cultivation season. Rice crop biophysical monitoring by SAR is very effective, but only up to mid reproductive stages. axis. A caution to use with the regression equation (shown in Figure 17), for predicting plant biophysical parameters in operation, is that the minimum number of the biophysical parameters should be limited as zero, because negative numbers of these parameters do not have any physical meaning. The linear regression accurately reproduced the biophysical parameters for the first period, with a root mean square error (RMSE) = 0.039 m for plant height, 4.05% for green vegetation cover, 0.065 for LAI, and 0.013 kg m −2 for total dry biomass. However, this approach is not applicable after about 60 days from transplant, owing to saturation of the backscattering coefficients of VH in late cultivation season. Rice crop biophysical monitoring by SAR is very effective, but only up to mid reproductive stages.
While this study demonstrated the potential and the limitation in applicability of the combination of linear regression lines, sensitivity of the calibrated constants in the estimation equation to a variation of field conditions (e.g., different field, year, region, variety of rice crop) has not been evaluated. Future study topics include the application of the suggested methodology to different years and/or locations to investigate how the relationship between SAR backscatter coefficients and the rice biophysical parameters are sensitive to the field management and yearly change of the weather condition. Enhancing the number of ground sampling is another future topic to better stabilize the data for analysis.  While this study demonstrated the potential and the limitation in applicability of the combination of linear regression lines, sensitivity of the calibrated constants in the estimation equation to a variation of field conditions (e.g., different field, year, region, variety of rice crop) has not been evaluated. Future study topics include the application of the suggested methodology to different years and/or locations to investigate how the relationship between SAR backscatter coefficients and the rice biophysical parameters are sensitive to the field management and yearly change of the weather condition. Enhancing the number of ground sampling is another future topic to better stabilize the data for analysis.

Conclusions
The objectives of this research were to study the relationship between SAR backscattering coefficients and rice crop biophysical parameters using Sentinel-1 satellite imagery, and to suggest an approach to evaluate plant biophysical parameters of rice crop using a combination of linear regression lines. Setting a study area in paddy rice fields in Miyazaki, Japan, ground measurements were conducted for plant height, green vegetation cover, LAI, and the total dry biomass of rice crop, every 12 days, simultaneously to the Sentinel-1A satellite SAR observations. Relationships between the plant biophysical parameters and SAR backscattering coefficients (VH and VV polarization) were analyzed. The results indicated that SAR backscattering coefficients linearly increase as plant biophysical parameters develop, until the "turning point," which is 48 (VV) or 60 (VH) days after transplant. The timing corresponds to the beginning of the mid reproductive stages. During the period from transplant to the turning point, plant height, green vegetation cover, LAI, and total dry biomass were precisely described by SAR monitoring, especially with VH polarization. The performance of crop monitoring by SAR was very high during the period; RMSE in estimations of these four biophysical parameters by VH backscattering coefficients were 0.039 m for plant height, 4.05% for green vegetation cover, 0.065 for LAI, and 0.013 kg m −2 for total dry biomass. However, backscattering coefficients saturate after the day of the turning point, and become insensitive to further developments of the plant biophysical parameters. Specifically, this research indicates that rice crop monitoring of biophysical properties by SAR is very effective, but only up to mid reproductive stages. Future study includes a sensitivity analysis of regression equations for field management.