Use of Sentinel-1 Multi-Conﬁguration and Multi-Temporal Series for Monitoring Parameters of Winter Wheat

: The present study aims to investigate the potential of multi-conﬁguration Sentinel-1 (S-1) synthetic aperture radar (SAR) images for characterizing four wheat parameters: total fresh mass (TFM), total dry mass (TDM), plant heights (He), and water content (WC). Because they are almost independent on the weather conditions, we have chosen to use only SAR. Samples of wheat parameters were collected over seven ﬁelds (three irrigated and four rainfed ﬁelds) in Southwestern France. We ﬁrst analyzed the temporal behaviors of wheat parameters (He, TDM, TFM and WC) between February and June 2016. Then, the temporal proﬁles of the S-1 backscattering coefﬁcients (VV, VH), the difference (VH − VV), the sum of the polarizations (VH + VV) and their cumulative values are analyzed for two orbits (30 and 132) during the wheat-growing season (from January to July 2016). After that, S-1 signals were statistically compared with all crop parameters considering the impact of pass orbit, irrigation and two vegetative periods in order to identify the best S-1 conﬁguration for estimating crop parameters. Interesting S-1 backscattering behaviors were observed with the various wheat parameters after separating irrigation impacts and vegetative periods. For the orbit 30 (mean incidence angle of 33.6 ◦ ); results show that the best S-1 conﬁgurations (with coefﬁcient of determination (R 2 ) > 0.7) were obtained using the VV and VH + VV as a function of the He, TDM and WC, over irrigated ﬁelds and during the second vegetative period. For the orbit 132 (mean incidence angle of 43.4 ◦ ), the highest dynamic sensitivities (R 2 > 0.8) were observed for the VV and VH + VV conﬁgurations with He, TDM and TFM over irrigated ﬁelds during the ﬁrst vegetative period. Overall, the sensitivity of S-1 data to wheat variables depended on the radar conﬁguration (orbits and polarizations), the vegetative periods and was often better over irrigated ﬁelds in comparison with rainfed ones. Signiﬁcant improvements of the determination coefﬁcients were obtained when the cumulative (VH + VV) index was considered for He (R 2 > 0.9), TDM (R 2 > 0.9) and TFM (R 2 > 0.75) for irrigated ﬁelds, all along the crop cycle. The estimate of WC was more limited (R 2 > 0.6) and remained limited to the second period of the vegetation cycle (from ﬂowering onwards). Whatever parameters were considered, the relative errors never exceeded 23%. This study has shown the importance of considering the agricultural practices (irrigation) and vegetative periods to effectively monitor some wheat parameters with S-1 data. TDM, TFM and the two combined orbits and O132). These relationships


Introduction
An accurate monitoring of winter wheat (usually named Triticum aestivum) is essential since it is one of the most important crops in the world (with an average production of 762.7 Mt for 2020, according to the Food and Agriculture Organization (FAO)) and is the main crop cultivated in France (with a production of 36.9 Mt for the 2018/19 season, according to the US Department of Agriculture [1]). Wheat biophysical parameters need to post-harvest spontaneous regrowth [16], tillering, overwintering, and heading stages [13], shooting and the harvest [20].
Polarimetric indicators derived from S-1 data are not very well investigated over wheat and have shown moderate results for monitoring biophysical parameters compared to VV, VH and the VH/VV [6,7,21]. Nasirzadehdizaji et al. [21] found moderate correlations between polarimetric parameters (entropy, anisotropy and alpha decompositions) and wheat height during the early growth stage. Mercier et al. [6,7] evaluated, for the first time, the potential of polarimetric indicators (Shannon entropy and span) derived from S-1 (with only one orbit) for identifying phenological stages and estimating biophysical crop parameters (GAI, biomass and water content (WC)) of wheat. They found that the Shannon entropy only performed with the WC parameter with R2 = 0.78. They concluded that using Sentinel-2 data were similar or higher to those obtained using S-1 features for estimating crop biophysical parameters of wheat.
To the best of our knowledge, no studies evaluated the potential of using the sum of polarization (VV + VH) over wheat whereas good correlations were found between VH + VV derived from S-1 and biophysical parameters of canola or maize (fresh biomass, plant area index, height and canopy coverage) [21,22].
In this context, the aim of the present study is to identify the best performing S-1 configuration (orbits, polarizations and indexes) and plant condition (vegetation period, irrigation) for accurate wheat parameters monitoring (Fresh and dry total biomass, height and water content) considering different periods of crop development. In this study, all the commonly used SAR indexes are used (VV, VH and VH − VV) completed by one more rare (VH + VV) and one original (temporal cumulative of (VH + VV) indexes). Section 2 describes the study site, satellite images and ground measurement database. Section 3 provides analysis of the temporal evolution of the wheat parameters and of the backscattering S-1 signals. The methodology is detailed in Section 4. Sections 5 and 6 present our results and discussion, respectively, concerning the sensitivities for the different scenarios. Our conclusions are provided in Section 7.

Study Site Description
The study site is located in Southwestern France (43.49 • N; 0.93 • E), over two French regions (Nouvelle-Aquitaine and Occitanie) and covering a footprint of 110 km × 140 km ( Figure 1). The climate is temperate and the area is mainly dedicated to the cultivation of seasonal crops which cover 54% of the land. Soils texture are heterogeneous, depending on the relief and the proximity to large rivers, and dominated by silt or clay in the Eastern parts [19].
The temporal wheat growth evolution is represented between the first of January and July. It is expressed in day of year (DOY) as shown in the Figure 2. This period covers the main phenological stage of the wheat (from the leaf development (LD) to ripening (R)) as detailed in Table 1.  The temporal wheat growth evolution is represented between the first of January and July. It is expressed in day of year (DOY) as shown in the Figure 2. This period covers the main phenological stage of the wheat (from the leaf development (LD) to ripening (R)) as detailed in Table 1.  [23]. The meaning of their acronyms is indicated in Table 1.  The temporal wheat growth evolution is represented between the first of January and July. It is expressed in day of year (DOY) as shown in the Figure 2. This period covers the main phenological stage of the wheat (from the leaf development (LD) to ripening (R)) as detailed in Table 1.  [23]. The meaning of their acronyms is indicated in Table 1.  [23]. The meaning of their acronyms is indicated in Table 1.

Biophysical Parameters
Between February and June 2016, some wheat parameters (crop height, main phenological stages, biomass, dry matter, and water content) were measured at field scale. Samples were collected over seven fields (three irrigated and four rainfed fields) along the wheat cycle from tillering (Ti) to R. Vegetation measurements were composed of 5 samples of 50 cm randomly collected into a 10 by 10 m 2 area, from which the above ground biomass (TFM) was directly weighed in situ for each training field. Then, the total aboveground dry mass (TDM) was measured after crop drying (the samples were put in an oven for 48 h at 65 • C). The water content (WC) was finally derived from the TFM and TDM. Field areas are heterogeneous, and range from 1.8 ha to 16.9 ha. Location and main characteristics of studied fields are summarized in Figure 1 (panels a to d) and Table 2, respectively.

Sentinel-1 Data
From January (DOY = 1) to July (DOY = 210) 2016, 34 S-1 images were acquired ( Figure 3). S-1 is an imaging radar mission launched on April 3, 2014. It provides continuous all weather, day-and-night imagery at C-band, and is freely available from the European Copernicus Services Data Hub.
Cumulative values are also calculated for each polarization and index (VV, VH, VH -VV and VH + VV). They represent the cumulative sum in backscattering signals from the first acquisition to the one performed on the day of interest, with a regular temporal step of 12 days.    The S-1 images were provided in interferometric wide (IW) swath and ground range detected (GRD) modes (Table 3). Mean incidence angles are θ 30 = 33.6 • and θ 132 = 43.4 • in average for the two orbits (30 and 132 respectively) allowing a repetitiveness of six days. The preprocessing of S-1 data was made using the Google Earth Engine website as follows: apply orbit file, GRD border noise removal, thermal noise removal, radiometric calibration, range Doppler terrain correction and resampling at 10 m spacing. Then, the σ 0 (backscattering coefficients) for the two orbits (30 and 132) and the two polarizations (VH and VV) were calculated at each field (noted σ 0 V H and σ 0 VV in the following). Two indexes (ratio and product) are derived from the following equations: Cumulative values are also calculated for each polarization and index (VV, VH, VH − VV and VH + VV). They represent the cumulative sum in backscattering signals from the first acquisition to the one performed on the day of interest, with a regular temporal step of 12 days.    Mean TFM values are higher for irrigated fields (about 9289 g·m −2 against 5788 g·m −2 for rainfed fields) and the considerable discrepancies of TFM values between fields is explained by the difference in the date of sowing and the crop development.
TDM and He parameters increase linearly during the wheat growth cycle for all fields and their values are more homogeneous than those observed for TFM. Nevertheless, higher discrepancies of TDM and He are observed for rainfed fields, especially from the end of the heading (Hg) stage when head starts growing. From this stage, the TDM of irrigated fields continues to increase until H whereas TDM of rainfed fields saturates.
Peak mean heights are about 94 and 84 cm for irrigated and rainfed fields, respectively, during grain heading. For the two kinds of field, similar trends of the WC are observed, they have maximal mean values (about 80%) at the beginning stages then they decrease linearly until the senescence (about 20% a few days before harvest).

Temporal
Evolution of the Backscattering Signals Acquired at Two Polarizations (VV and VH) and Two Orbits (30 and 132) over All Fields associated with weak direct ground scattering. This absorption is more pronounced on the VV + VH signal (about 10 dB). Brown et al. [14] and Mercier et al. [7], demonstrated that for a very well developed wheat cover, backscatters at VV polarization were more influenced by wheat growth than VH, especially at a high incidence angle. These results are confirmed with the increase of VH-VV in time. Our result also showed that this difference is attenuated when the incidence angle decreases (orbit 30).
• Finally, from 50 days before H, the backscattering coefficients increase by approximately 2.2 dB and 3.5 dB for both VV and VH at 132 and 30 orbits, respectively, as observed in [15,20,24]. From the end of June, the backscattering is less absorbed by the vegetation due to the vegetation drying (Figure 5; [19]). The SAR signal penetrates more into the vegetation layer and is more affected by the soil moisture variations. This phenomenon is much more important for VV + VH whereas the signal VH -VV is quite stable until harvest. Figure 5c,d show the temporal evolution of the cumulative (VV, VH, VH-VV and VH+VV) indexes for orbit 30 and 132, respectively. It can be seen that the cumulative indexes linearly decrease as a function of time with an important slope during the first growing cycle until the DOY = 150. These behaviors could be related to the high absorption of the radar signals by the vegetation canopy for both VV and VH polarizations. We can show clearly that the behaviors of the cumulative (VV, VH, VH-VV and VH+VV) are practically not affected by the wheat phenological stages.  Table 1); the yellow lines represent the harvest period.

Methodology
Our methodology, presented in Figure 6, consists in estimating empirical relationships between radar signals (VH, VV, VV + VH, VV -VH and their cumulative sum) and crop parameters. Consecutive scenarios were proposed: the first one (A) consisted of combining all S-1 data orbits 30 and 132 (O30 and 132) all along the crop-growing period.  Table 1); the yellow lines represent the harvest period.
The general trend can be divided into three different periods: • During LD to Ti (approximatively until the DOY = 53), the backscattering coefficients show only a few variations whatever the polarization. At these stages, the crop . During this period, the soil contribution becomes negligible inducing an increase of the volume scattering mechanisms, which could be justified by the rise in TFM values over all wheat fields ( Figure 5). According to Mattia et al. [11] and El Hajj et al. [17], the decrease in SAR signals is due to the high absorption of the incident SAR wave produced by the vertical stems and leaves associated with weak direct ground scattering. This absorption is more pronounced on the VV + VH signal (about 10 dB). Brown et al. [14] and Mercier et al. [7], demonstrated that for a very well developed wheat cover, backscatters at VV polarization were more influenced by wheat growth than VH, especially at a high incidence angle. These results are confirmed with the increase of VH − VV in time. Our result also showed that this difference is attenuated when the incidence angle decreases (orbit 30). • Finally, from 50 days before H, the backscattering coefficients increase by approximately 2.2 dB and 3.5 dB for both VV and VH at 132 and 30 orbits, respectively, as observed in [15,20,24]. From the end of June, the backscattering is less absorbed by the vegetation due to the vegetation drying ( Figure 5; [19]). The SAR signal penetrates more into the vegetation layer and is more affected by the soil moisture variations. This phenomenon is much more important for VV + VH whereas the signal VH − VV is quite stable until harvest. Figure 5c,d show the temporal evolution of the cumulative (VV, VH, VH − VV and VH + VV) indexes for orbit 30 and 132, respectively. It can be seen that the cumulative indexes linearly decrease as a function of time with an important slope during the first growing cycle until the DOY = 150. These behaviors could be related to the high absorption of the radar signals by the vegetation canopy for both VV and VH polarizations. We can show clearly that the behaviors of the cumulative (VV, VH, VH − VV and VH + VV) are practically not affected by the wheat phenological stages.

Methodology
Our methodology, presented in Figure 6, consists in estimating empirical relationships between radar signals (VH, VV, VV + VH, VV − VH and their cumulative sum) and crop parameters. Consecutive scenarios were proposed: the first one (A) consisted of combining all S-1 data orbits 30 and 132 (O30 and 132) all along the crop-growing period. In the second case (B), we separated the S-1 images into two datasets of orbit 30 (O30) and 132 (O132) to analyze the influence of the orbit pass directions. The third one (C) took into account the irrigation practices, each orbit dataset is further divided into irrigated and rainfed fields. Finally (D), two vegetative periods (P [1] and P [2]) were considered for irrigated and rainfed dataset separately. The range of DOY adopted for the two vegetative periods were defined based on the sampling dates of wheat parameters. They are presented in Figure 7 by blue and yellow colors for irrigated and rainfed fields, respectively.
In the second case (B), we separated the S-1 images into two datasets of orbit 30 (O30) and 132 (O132) to analyze the influence of the orbit pass directions. The third one (C) took into account the irrigation practices, each orbit dataset is further divided into irrigated and rainfed fields. Finally (D), two vegetative periods (P [1] and P [2]) were considered for irrigated and rainfed dataset separately. The range of DOY adopted for the two vegetative periods were defined based on the sampling dates of wheat parameters. They are presented in Figure 7 by blue and yellow colors for irrigated and rainfed fields, respectively. Figure 6. Methodological flowchart used to identify the best synthetic aperture radar (SAR) configuration as a function of wheat parameters (He, TDM, TFM and WC). O30 and O132 represent the two orbits 30 and 132 respectively. P [1] and P [2] are the two considered vegetative periods.

Figure 6.
Methodological flowchart used to identify the best synthetic aperture radar (SAR) configuration as a function of wheat parameters (He, TDM, TFM and WC). O30 and O132 represent the two orbits 30 and 132 respectively. P [1] and P [2] are the two considered vegetative periods.

Results
In this section, we present the results of our statistical analysis of radar measurements as a function of the wheat parameters: He (cm), TFM (g.m −2 ), TDM (g.m −2 ) and WC (%) for all of the studied fields. Mean backscattering coefficient values (VH, VV), the difference of the polarizations (VH -VV), the sum of the polarizations (VH + VV) and their cumulative values are estimated for each field and their correlations with the wheat parameters were analyzed, according to scenarios A, B, C and D presented in the method. Table 4 provides correlations determined for the different backscattering parameters (VV, VH, VH -VV and VH + VV) and their cumulative indexes as a function of the He, TDM, TFM and WC for the two combined orbits (O30 and O132). These relationships are based on 136 measured points. It can be seen that no correlations (R 2 < 0.15) are obtained with all the backscattering parameters. Strong improvements are achieved when we use the cumulative indexes for all the crop parameters. For He and TDM, an increase greater than 70% was obtained after considering the cumulative (VV, VH and VH + VV) indexes.

Results
In this section, we present the results of our statistical analysis of radar measurements as a function of the wheat parameters: He (cm), TFM (g·m −2 ), TDM (g·m −2 ) and WC (%) for all of the studied fields. Mean backscattering coefficient values (VH, VV), the difference of the polarizations (VH − VV), the sum of the polarizations (VH + VV) and their cumulative values are estimated for each field and their correlations with the wheat parameters were analyzed, according to scenarios A, B, C and D presented in the method. Table 4 provides correlations determined for the different backscattering parameters (VV, VH, VH − VV and VH + VV) and their cumulative indexes as a function of the He, TDM, TFM and WC for the two combined orbits (O30 and O132). These relationships are based on 136 measured points. It can be seen that no correlations (R 2 < 0.15) are obtained with all the backscattering parameters. Strong improvements are achieved when we use the cumulative indexes for all the crop parameters. For He and TDM, an increase greater than 70% was obtained after considering the cumulative (VV, VH and VH + VV) indexes. Regarding TFM and WC parameters, improvements were lower, at about 40%, using cumulative indexes. In the following sections, only the best indexes are considered for the scenarios B, C and D: VH + VV and its cumulative values. Figure 8 shows the correlations and the relative errors of the VH + VV and its cumulative index as a function of He, TDM, TFM and WC before and after taking into account the impact of the orbit pass (30 and 132). As observed in scenario A, no correlation was obtained combining the two orbits with all the crop parameters. Similarly, weak correlations (R 2 < 0.2) were observed after separating the data according to orbit pass (O30 and O132). Compared to scenario A, the performances remained better using the cumulative index (VH + VV) with all the crop parameters particularly with TDM and He (R 2 > 0.7 and rRMSE < 50%). Figure 9 represents the results obtained by considering the impact of irrigation on the two-orbit dataset (Irrigated, O132; Rainfed, O132; Irrigated, O30 and Rainfed, O30 respectively). Weak correlations are observed between VH + VV and all wheat parameters for rainfed and irrigated fields (R 2 < 0.2). The use of the cumulative (VH + VV) index significantly improves the estimate of all parameters, especially the TDM and TFM (for irrigated fields) compared to the scenario A (Figure 8b). In these best cases, the rRMSE are lower than 33% for all the parameters of irrigated fields. Relative errors exceed 50% only for the estimate of TFM of non irrigated fields. count the impact of the orbit pass (30 and 132). As observed in scenario A, no correlation was obtained combining the two orbits with all the crop parameters. Similarly, weak correlations (R 2 < 0.2) were observed after separating the data according to orbit pass (O30 and O132). Compared to scenario A, the performances remained better using the cumulative index (VH + VV) with all the crop parameters particularly with TDM and He (R 2 > 0.7 and rRMSE < 50%).  Figure 9 represents the results obtained by considering the impact of irrigation on the two-orbit dataset (Irrigated, O132; Rainfed, O132; Irrigated, O30 and Rainfed, O30 respectively). Weak correlations are observed between VH+VV and all wheat parameters for rainfed and irrigated fields (R² < 0.2). The use of the cumulative (VH + VV) index significantly improves the estimate of all parameters, especially the TDM and TFM (for irrigated fields) compared to the scenario A (Figure 8b). In these best cases, the rRMSE are lower than 33% for all the parameters of irrigated fields. Relative errors exceed 50% only for the estimate of TFM of non irrigated fields.

Impact of Phenological Periods (Scenario D)
According to the SAR signal behavior ( Figure 5), the impact of two vegetative periods are considered in the analysis of VH + VV and its cumulative values as a function of crop parameters for two orbits (30 and 132) and irrigation practices (irrigated and rainfed). Figures 10 and 11 illustrate the bar plots of the R 2 and rRMSE computed for VH + VV and its cumulative indexes as a function of all the crop parameters for the P [1] and P [2], respectively. Significant performance improvements of the VH + VV are observed by taking into account the impact of the vegetative periods, for all the fields compared to the other scenarios. These improvements depend on the orbit pass otherwise on the incidence angle and they are generally better over irrigated fields than rainfed ones.
Concerning the second vegetative period P [2], the statistical performances (R 2 > 0.65 and rRMSE < 20%) indicate marked correlations of the VH + VV with He, TDM and WC for the orbit 30 (with θ30 = 33.6°) and over irrigated fields. The change in the temporal WC behaviors between the two vegetative periods P [1] and P [2] led to the improvements of the correlation between the VH + VV and the WC parameter during the second wheat period (Figure 4). For the two orbits 30 and 132, the results show that responses of the VH + VV to the wheat TFM are weak (R 2 < 0.2) at the P [2]. These relationships could be jus-

Impact of Phenological Periods (Scenario D)
According to the SAR signal behavior (Figure 5), the impact of two vegetative periods are considered in the analysis of VH + VV and its cumulative values as a function of crop parameters for two orbits (30 and 132) and irrigation practices (irrigated and rainfed). Figures 10 and 11 illustrate the bar plots of the R 2 and rRMSE computed for VH + VV and its cumulative indexes as a function of all the crop parameters for the P [1] and P [2], respectively. Significant performance improvements of the VH + VV are observed by taking into account the impact of the vegetative periods, for all the fields compared to the other scenarios. These improvements depend on the orbit pass otherwise on the incidence angle and they are generally better over irrigated fields than rainfed ones.
Concerning the second vegetative period P [2], the statistical performances (R 2 > 0.65 and rRMSE < 20%) indicate marked correlations of the VH + VV with He, TDM and WC for the orbit 30 (with θ 30 = 33.6 • ) and over irrigated fields. The change in the temporal WC behaviors between the two vegetative periods P [1] and P [2] led to the improvements of the correlation between the VH + VV and the WC parameter during the second wheat period (Figure 4). For the two orbits 30 and 132, the results show that responses of the VH + VV to the wheat TFM are weak (R 2 < 0.2) at the P [2]. These relationships could be justified by the high TFM discrepancies observed between fields especially after F stage. Considering the cumulative (VH + VV) index, stronger correlations are observed during the first period P [1] with R 2 equal to 0.93, 0.92 and 0.87 for the He, TDM and TFM respectively at the two orbits (30 and 132). Strong relationships are also obtained with He (R 2 about 0.7) and TDM (R 2 = 0.9) parameters for the second period P [2], particularly for irrigated fields. Whatever the period, the rRMSE are always lower than 35% when R 2 exceeds 0.7. The sensitivities of the cumulative (VH + VV) index and the TFM are lower during the P [2] than the P [1]. For WC, we note the considerable impact of the vegetative period with the best correlations obtained for the second period P [2] and for irrigated fields (R 2 about 0.73 and 0.62 for the orbit 30 and 132, respectively). Over rainfed fields, we observe important improvements of this parameter during the P [2] with approximately R 2 = 0.5 for the two orbits (30 and 132). This behavior could be explained by the linearly decrease of the WC during the last wheat stages. Finally, Figure 12 shows the scatter plot of the best correlations obtained for irrigated fields with linear sensitivities with all the crop parameters. The relationships between the three parameters (TDM, TFM and He) and the cumulative (VH + VV) index show strong dependence between them with R 2 > 0.87 and with rRMSE < 19% whatever the field and the orbit. Lower performances are obtained for the estimate of WC during P  Finally, Figure 12 shows the scatter plot of the best correlations obtained for irrigated fields with linear sensitivities with all the crop parameters. The relationships between the three parameters (TDM, TFM and He) and the cumulative (VH + VV) index show strong dependence between them with R 2 > 0.87 and with rRMSE < 19% whatever the field and the orbit. Lower performances are obtained for the estimate of WC during P [2] (R 2 = 0.68) despite the low rRMSE of 11%. The sensitivity of the cumulative (VH + VV) index and TDM is approximately −0.16 dB/g·m −2 , −3.7 dB·cm −1 with He, −0.03 dB/g·m −2 with TFM and 2.68 dB/% with WC. tween the three parameters (TDM, TFM and He) and the cumulative (VH + VV) index show strong dependence between them with R 2 > 0.87 and with rRMSE < 19% whatever the field and the orbit. Lower performances are obtained for the estimate of WC during P [2] (R² = 0.68) despite the low rRMSE of 11%. The sensitivity of the cumulative (VH + VV) index and TDM is approximately −0.16 dB/g.m −2 , −3.7 dB.cm −1 with He, −0.03 dB/g.m −2 with TFM and 2.68 dB/% with WC.

Discussion
This section presents the discussion of the results obtained using VH + VV and its cumulative index with wheat parameters because these configurations lead to the best performances as demonstrated in Section 5.1. As for the result section, three scenarios are considered: B, C and D.

Impact of the Orbit Pass (Scenario B) and Irrigation (Scenario C)
Results presented in Section 5.2 ( Figure 8) show that performances are not dependent on the orbit pass and the geometrical configuration of the SAR sensor following their incidence angles (θ30 = 33.6° and θ132 = 43.4°), especially when cumulative indexes are considered and performances are high (R 2 > 0.7 and rRMSE < 50%). This could be explained by the similar temporal linear trend of TDM, He and cumulative values of VH + VV. This phenomenon is particularly interesting since previous studies demonstrated that the non-cumulated radar backscatters acquired at C band are angular-sensitive over wheat [11,14,25]. According to them, the sensitivities of non-cumulated radar backscatters are affected by the soil scattering, attenuated by the wheat canopy at low incidence angles (θ < 40°). Beyond 40° incidence angle, the dominant mechanism changes to the direct volume scattering from the canopy. The lower angular sensitivity of cumulated VH + VV signals open new perspective for merging radar signal independently of incidence angle or orbit pass.
The interest of using cumulative index is confirmed when plots are spitted into irrigated and rainfed fields. In this case, as observed in Pageot et al. [26] for irrigation mapping, the results of Figure 9 demonstrated that the cumulative indexes derived from S-1 data (VV and VH) are sensitive to the impact of irrigation on vegetation development.

Discussion
This section presents the discussion of the results obtained using VH + VV and its cumulative index with wheat parameters because these configurations lead to the best performances as demonstrated in Section 5.1. As for the result section, three scenarios are considered: B, C and D.

Impact of the Orbit Pass (Scenario B) and Irrigation (Scenario C)
Results presented in Section 5.2 ( Figure 8) show that performances are not dependent on the orbit pass and the geometrical configuration of the SAR sensor following their incidence angles (θ 30 = 33.6 • and θ 132 = 43.4 • ), especially when cumulative indexes are considered and performances are high (R 2 > 0.7 and rRMSE < 50%). This could be explained by the similar temporal linear trend of TDM, He and cumulative values of VH + VV. This phenomenon is particularly interesting since previous studies demonstrated that the non-cumulated radar backscatters acquired at C band are angular-sensitive over wheat [11,14,25]. According to them, the sensitivities of non-cumulated radar backscatters are affected by the soil scattering, attenuated by the wheat canopy at low incidence angles (θ < 40 • ). Beyond 40 • incidence angle, the dominant mechanism changes to the direct volume scattering from the canopy. The lower angular sensitivity of cumulated VH + VV signals open new perspective for merging radar signal independently of incidence angle or orbit pass.
The interest of using cumulative index is confirmed when plots are spitted into irrigated and rainfed fields. In this case, as observed in Pageot et al. [26] for irrigation mapping, the results of Figure 9 demonstrated that the cumulative indexes derived from S-1 data (VV and VH) are sensitive to the impact of irrigation on vegetation development.

Impact of Phenological Periods (Scenario D)
The results presented in Section 5.4 ( Figure 10) show that performances are strongly dependent on the vegetative period. The good results obtained during the period P [1] could be explained by the linear increase of the He, TDM and TFM parameters especially until the F wheat stage (Figure 4). It confirms and expands those observed by Nasirzadehdizaji et al. [21] who found that the sensitivity of the (VH + VV) derived from S-1 data is relatively good with wheat height (with R 2 = 0.61) at the beginning stage (for He < 53) and no significant correlation is observed at the later growing stage (He ≥ 53 cm). Regarding the WC parameter, the correlation is very weak in the P [1], when WC is constant around 80% (Figure 4). The relationships estimated between radar index and WC are strongly improved during the P [2] (Figure 11). This phenomenon could be attributed to the lower radar attenuation in the vegetation layer during senescence when vegetation dries and WC decreases.
The significant correlations of the VH + VV and physical parameters that we obtained during P [1] at the orbit 132 and not at the orbit 30 are mainly related to the influence of the incidence angle ( Figure 10). In fact, the orbit 132 is acquired at a higher incidence angle than the orbit 30. The sensitivities of the radar signals to vegetation canopy increase at a high incidence angle, which could explain the best correlations that we observed between backscattering coefficients and crop parameters at orbit 132. Several studies have analyzed the behavior of the backscattering signals of wheat crops as a function of incidence angles and phenological stages [11,14,15,25,27]. They demonstrated that the backscattering signals are mainly affected by the dominance of the direct canopy backscattering after heading stage (DOY = 124) for high incidence angles (θ > 37 • ). El Hajj et al. [17] explained these behaviors by the inability of the radar signals to penetrate into wheat for the well-developed vegetation cover particularly after heading at a high incidence angle.
To reduce discrepancies between fields during the first vegetative period, the mean signals recorded between DOY = 1 and the LD stage of wheat (DOY = 31) were taken as references σ 0 mean to eliminate the effect of surface soil parameters (roughness, moisture, topography) and keep only the vegetation variations on measured signals. Then, the backscattering measurements σ 0 measured were corrected by the mean backscattering (σ 0 mean ) considering the bias between them for each date and field. Figure 13 illustrates temporal evolution of the VH + VV and its cumulative index for each training field at 132 orbit (same results are observed for orbit 30, not shown here). Visually, the differences between fields observed during the first period of the temporal backscattering signals are reduced taking into account the bias correction for the VH + VV and the cumulative index ( Figure 13). However, a few improvements are obtained in the statistical coefficients (R 2 ) especially with TDM and He for some cases. Figure 14 represents the enhanced correlations obtained after considering bias for orbit 132. For example, we can note an increase of 22% and 8% over rainfed fields for He and TDM parameters, respectively, after bias correction. Despite these improvements, the best results remain those obtained using the cumulative indexes (for which no gain has been observed after the removal of the influence of surface soil properties).
Despite previous studies having demonstrated high sensitivities of the VH − VV to wheat parameters [7,[15][16][17][18]20,21], our results (Table 5) revealed that the VH + VV are clearly better than the VH − VV for almost all wheat parameters. Among all the considered configurations, the VH + VV allowed better estimations of the wheat parameters than those obtained using either ratios [20,21] or polarimetric parameters [7,21]. The new empirical approach proposed in this study, notably the cumulative indexes, provides even better correlations than the VH + VV with all crop parameters.
( Figure 13). However, a few improvements are obtained in the statistical coefficients (R ) especially with TDM and He for some cases. Figure 14 represents the enhanced correlations obtained after considering bias for orbit 132. For example, we can note an increase of 22% and 8% over rainfed fields for He and TDM parameters, respectively, after bias correction. Despite these improvements, the best results remain those obtained using the cumulative indexes (for which no gain has been observed after the removal of the influence of surface soil properties).  Despite previous studies having demonstrated high sensitivities of the VH -VV to wheat parameters [7,[15][16][17][18]20,21], our results (Table 5) revealed that the VH + VV are clearly better than the VH -VV for almost all wheat parameters. Among all the considered configurations, the VH + VV allowed better estimations of the wheat parameters than those obtained using either ratios [20,21] or polarimetric parameters [7,21]. The new empirical approach proposed in this study, notably the cumulative indexes, provides even better correlations than the VH + VV with all crop parameters.   Despite the lack of recent ground campaign data, our approaches are also discussed according to further S-1 images acquired during 2017, 2018 and 2019 using S1-A data (to be comparable with the year 2016). For each year, we selected eight fields of wheat located closest to the studied fields used in 2016 (<10 km). Figure 15 illustrates the temporal evolution of the VH + VV configuration and its cumulative values from the first of January to the end of July for each year, at orbit 30. The general trends of these behaviors are similar whatever the year to those obtained during 2016 (Figure 5c). The results presented here confirm that our approaches could be reliably extended to other years to accurately estimate wheat parameters using the cumulative indexes.
Remote Sens. 2021, 13, x FOR PEER REVIEW 18 of 20 evolution of the VH + VV configuration and its cumulative values from the first of January to the end of July for each year, at orbit 30. The general trends of these behaviors are similar whatever the year to those obtained during 2016 (Figure 5c). The results presented here confirm that our approaches could be reliably extended to other years to accurately estimate wheat parameters using the cumulative indexes.

Conclusions
This work has presented new empirical approaches for monitoring some wheat parameters (TFM, TDM, He, WC) from S-1 SAR data. We proposed the use of polarized backscatters (VV, VH, VH -VV and VH + VV) and their cumulative values to assess wheat parameters for two orbits (30 and 132). Various scenarios were considered: • Scenario A demonstrated that among all the evaluated radar backscatters (VV, VH, VH -VV and VH + VV), the highest correlations are obtained using the sum of VH and VV backscatters or their cumulative values. The cumulative VH + VV index is more correlated with all crop parameters (0.46 < R² < 0.89), than non-cumulative backscatters (0.01 < R² < 0.13), regardless of their agricultural practices, vegetative periods and even by combining all S-1 data orbits (30 and 132) all along the crop-growing period.

•
The second scenario (B) highlighted the weak influence of the orbit pass (incidence angle) on the crop parameters retrieval all along the crop cycle whatever the considered backscatters.

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The impact of irrigation is particularly visible on scenario C. Whereas the performance are not significantly affected from the previous scenarios (A or B) considering VH + VV backscatters, strong relationships are obtained between cumulative values of VH + VV and two biophysical parameters (TDM and He) (R 2 > 0.92 and rRMSE < 20%) whatever the orbit pass.

•
The importance of considering two vegetative periods is shown in scenario D. This is the only scenario where non-cumulated backscatters are significantly correlated with in situ wheat parameters. During the first period (growing period), the highest dynamic sensitivities (R 2 > 0.8 and rRMSE < 30%) were observed with (He, TDM and TFM) over irrigated fields for the orbit 132 (with an average incidence angle of 43.4°). The results obtained during the second vegetative period allowed us to estimate He, TDM and WC over irrigated fields with high correlation (R² > 0.7), using

Conclusions
This work has presented new empirical approaches for monitoring some wheat parameters (TFM, TDM, He, WC) from S-1 SAR data. We proposed the use of polarized backscatters (VV, VH, VH − VV and VH + VV) and their cumulative values to assess wheat parameters for two orbits (30 and 132). Various scenarios were considered: • Scenario A demonstrated that among all the evaluated radar backscatters (VV, VH, VH − VV and VH + VV), the highest correlations are obtained using the sum of VH and VV backscatters or their cumulative values. The cumulative VH + VV index is more correlated with all crop parameters (0.46 < R 2 < 0.89), than non-cumulative backscatters (0.01 < R 2 < 0.13), regardless of their agricultural practices, vegetative periods and even by combining all S-1 data orbits (30 and 132) all along the cropgrowing period.

•
The second scenario (B) highlighted the weak influence of the orbit pass (incidence angle) on the crop parameters retrieval all along the crop cycle whatever the considered backscatters.

•
The impact of irrigation is particularly visible on scenario C. Whereas the performance are not significantly affected from the previous scenarios (A or B) considering VH + VV backscatters, strong relationships are obtained between cumulative values of VH + VV and two biophysical parameters (TDM and He) (R 2 > 0.92 and rRMSE < 20%) whatever the orbit pass.

•
The importance of considering two vegetative periods is shown in scenario D. This is the only scenario where non-cumulated backscatters are significantly correlated with in situ wheat parameters. During the first period (growing period), the highest dynamic sensitivities (R 2 > 0.8 and rRMSE < 30%) were observed with (He, TDM and TFM) over irrigated fields for the orbit 132 (with an average incidence angle of 43.4 • ). The results obtained during the second vegetative period allowed us to estimate He, TDM and WC over irrigated fields with high correlation (R 2 > 0.7), using data acquired in the orbit 30 (with an average incidence angle of 33.6 • ). Regarding cumulative index, we also note the relevant effect of considering the vegetative period. The best sensitivities of the cumulative (VH + VV) index and the He, TDM and TFM were obtained during the first vegetative period with R 2 > 0.78 and 0.7 for irrigated and rainfed fields, respectively. For WC, the best correlations were obtained for the second period (when vegetation starts drying from flowering) with R 2 > 0.6 and 0.5 for irrigated and rainfed fields, respectively. Whatever the considered parameters, the relative errors were low and ranged from 6.2% to 23%.
Results of this paper highlight the strong potential of the cumulative index (VH + VV) for the monitoring of the crop parameters, particularly the TFM, He, TDM and WC. Despite the lack of recent ground campaign data, results presented in the discussion section demonstrated that our approaches could be reliably extended to other years (2016 to 2019). In future studies, it will be interesting to assimilate this index in agricultural crop models. This would certainly improve the accuracy of crop growth simulations and enhance subsequently yield estimations. In addition, it would be recommended to validate our findings with more recent data and to extend our approach to other cereal crops (corn, soybean etc.). Funding: This research was funded by IRT Antoine de Saint-Exupéry Foundation STAE for the POMME-V project (R056).