**4. Discussion**

In contrast with previous studies that mostly used images acquired under fixed or within narrow ranges of incidence angles, the correction derived in this study facilitates the use of imagery acquired under all typical geometrical conditions. By applying simple transformations to Sentinel-1 imagery acquired under a wide range of incidence angles, the dependency of σ0 and β0 on the local incidence angle decreased, and the empirical modeling of several crop properties was improved. This achievement is remarkable because

monitoring crops using the full temporal resolution of SAR imagery is much more useful than using imagery acquired at a narrow range of angles. Moreover, vegetation variable estimation models calibrated in one region using the proposed methods can be applied to other areas.

The improvement in the R<sup>2</sup> and RMSE of the models following the local incidence angle normalization procedure was found to be significant in many of the models: wheat height and LAI models; β0-based processing tomato LAI, height, and Kc models; σ0-based cotton Kc and height models; and β0-based cotton height model. Since the statistical significance of the difference between correlations is dependent on the number of images used for model development, some of the models yielded a difference that was not significant (wheat Kc model, processing tomato σ0-based LAI, height, and Kc models, and cotton Kc β0-based model). However, the trend of improvement following the proposed normalization procedures is clear, and the practical usefulness of the proposed methods can be better represented by the RMSE improvements because RMSE represents the vegetation variable estimation accuracy. The RMSE improvement was found to be significant in the following models: processing tomato σ0-based LAI and Kc models; and cotton Kc σ0 and β0-based models. The RMSE improvement was not significant in the following models: wheat, processing tomato σ0-based LAI, and processing tomato β0-based models, and cotton height σ0- and β0-based models. The R<sup>2</sup> and RMSE of all the models calibrated in the present study improved following incidence angle normalization. The range of RMSE improvements varied from model to model (Table 3), from 5 to 52%. Moreover, the performance of the newly developed β0-based local incidence angle normalization method shows potential for overcoming the limitations of σ0-based modeling for agricultural purposes. The use of β0 to improve vegetation variable estimation is particularly useful in fields with a rough soil surface geometry. Using β0 is not common for Sentinel-1 imagery, and the users' community could benefit from adopting this approach.

The models presented here for wheat and processing tomatoes were calibrated based on measurements taken throughout the entire duration of growing seasons and can, therefore, be applied at any time during crop development without restrictions. Nevertheless, the RMSE of LAI and height estimations was slightly higher at the peak of the season compared to the rest of the season. The relatively high accuracy of the models calibrated in this study and their independence from the incidence angle following the new normalization methods are advantageous compared to previous studies [47,55,60,61,64], in which the images used were limited to a narrow range of incidence angles. In addition, in contrast to [48] that presented models that can only be reliably applied to certain vegetation heights, the wheat and processing tomato models presented here are applicable to any height within the range measured in our experiments: 34–95 cm (wheat) and 24–77 cm (processing tomatoes). A comparison between several studies that used C-band SAR to estimate vegetation height and LAI is shown in Tables 5 and 6.

The models for LAI estimation show a better performance than previous studies. Previous estimation based on imagery acquired under a narrow range of incidence angles and dual-polarization [47] only achieved R<sup>2</sup> = 0.25. Moreover, the models in this study performed similarly to quad-polarization RADARSAT-2-based models for corn and soybean LAI estimation that utilized imagery acquired under a narrow range of incidence angles [39] and achieved R<sup>2</sup> = 0.66 and RMSE = 0.75 and R<sup>2</sup> = 0.64 and RMSE = 0.63, respectively. Another study [60] presented a wheat LAI estimation model, which has better prediction performance than the models obtained in the present study (RMSE = 0.4), but as in other previous models, it was based on images acquired under only one incidence angle. Unlike the LAI estimation based on optical imagery, the wheat and processing tomato LAI models developed in this study were not saturated even at the peak of vegetation development (wheat LAImax = 7.7, processing tomato LAImax = 9.1). Therefore, the LAI models in this paper might be applied throughout the whole season duration, which is useful because the LAI is a proxy for many vegetation variables [23], including crop productivity [105].


**Table 5.** Comparison of vegetation height estimation models based on Sentinel-1 and RISAT-1 C-band SAR.

**Table 6.** Comparison of vegetation LAI estimation models based on Sentinel-1 and RISAT-1 C-band SAR.


The use of SAR for agricultural purposes has also been significantly enhanced by this study. While several previous studies used SAR to estimate the wheat LAI and crop height, processing tomatoes were not studied enough. Moreover, estimating Kc of wheat, processing tomatoes, and cotton by SAR, to the best of our knowledge, was not previously conducted. Previously, the crop water requirement estimation of maize, soybean, pasture, and bean using SAR imagery acquired under a narrow range of incidence angles was conducted [49]. Another study showed a non-crop-specific region-wise correlation between only one Sentinel-1 image and the crop water stress index derived through the LANDSAT-8 image [106]. Finally, [107] used smoothed time series of Sentinel-1 backscatter values in different polarization combinations to estimate Kc in vineyards. Therefore, the wheat and processing tomato Kc estimation models derived in this study pave the way to accurate Kc estimation using all available SAR imagery. This study stands out by overcoming the limits imposed by the range of incidence angles typical for SAR imagery. As a result, the newly developed normalized wheat and processing tomato Kc estimation models can be used with confidence during the entire duration of a growing season.

Although the cotton models calibrated in this study showed good performance, they are based on the data recorded from the middle to late stages of growing seasons. Therefore, future studies should improve upon this by including the early stages of the growing seasons. In addition, we did not calibrate an LAI model for cotton in this paper, but this should be feasible given good field measurements. Therefore, additional field experiments should be carried out to calibrate models for crop variables throughout the growing season. Even though the cotton models developed in this study might have only limited use, all four cotton models showed a sizeable improvement in the R<sup>2</sup> and RMSE over the nonnormalized models. This result confirms the effectiveness of the novel angle normalization approach suggested in the present study.

The performance of models based on the new transformation was favorable compared to models based on the dual-polarized RVI. Although the RVI-based models in the present study were calibrated under the most favorable conditions possible, using only ascending overpass imagery acquired under only one incidence angle, the new models based on local incidence angle normalization methods outperformed them: the RMSE of RVI-based models was 40–203% higher. It should be noted that the assumption σ0VV ≈ σ0HH underlying the dual-polarized RVI is in contradiction to previous findings that show a typical difference of 5 dB between σ0VV and σ0HH in the intermediate range of incidence angles in the C band [91,108,109]. Therefore, we conclude that the dual-polarized RVI is not recommended where the assumption of the equality of backscatter in the two polarizations cannot be made.

Unlike previous studies that used only fields with rows perpendicular to the SAR beam [110], in this study, all the fields were used in model calibration. While this row geometry is less noticeable in wheat fields, particularly in the middle and later stages of the season, it should be noted that cotton and processing tomatoes are planted in rows of earth mounds with furrows between them. In addition, the spatial orientation of the rows in the fields in this study was not uniform between the locations. For example, in the processing tomato fields in Gadash, the rows were oriented from west to east, while in Gadot, the orientation was from west-southwest to east-northeast. This difference in the spatial orientation of rows affects the backscatter because the target's radar crosssection depends on its angle relative to the satellite [111], and even minimal changes in the target aspect significantly affect the RCS [112,113]. Nevertheless, the processing tomato models were not sensitive to the crop row orientation because they showed a similar RMSE (Tables S5 and S7) when they were applied to different fields. Therefore, the proposed models seem to be insensitive to the row orientation and could likely be used in other fields with different row orientations relative to the satellite orbit. However, this should be further tested in future studies.

Despite the overall reliable performance of the newly developed models, it should be pointed out that winter images in descending orbits have much weaker correlations with the vegetation height, LAI, and Kc compared to images from ascending orbits. Consequently, SAR images acquired in descending orbits could not be used for the development of the wheat model. In the summer crops tested in this study, this phenomenon did not occur, rendering the imagery acquired from descending orbits usable for the modeling of crop variables.

A likely explanation for the weaker performance of wheat models based on imagery from descending orbits might be related to the higher relative humidity in the early morning (descending images were acquired around 03:40 GMT) compared to the relative humidity in the evening (ascending images were acquired around 15:40 GMT). This observation is confirmed by our meteorological measurements in Saad and Kvutsat Yavne, which showed a regular diurnal pattern of a decrease in relative humidity following sunrise: from up to 100% in early morning hours to 40–60% in the afternoons. At night and in the early morning, the relative humidity is very high, and the formation of fog and dew, along with increased topsoil moisture, causes increased scattering and attenuation of the SAR beam [114,115]. Additionally, the SAR beam can be affected by common atmospheric inhomogeneities in the morning hours over Israel that create radar echoes [116] and increase the atmospheric reflectance and attenuation of the transmitted energy [117]. In previous studies, datasets affected by these effects were binned. For example, [61] omitted a dataset that was affected by dew. The issue of the relatively lower performance of descending orbit-based models is an interesting direction that can be studied by analyzing data from other regions and coupling them with the complementary ground and atmospheric measurements.

Although the newly proposed local incidence angle normalization methods were tested on the typical incidence angle range of Sentinel-1 and most other spaceborne SAR

missions, they are not expected to be effective for very steep incidence angles near to the "nadir hole" region [118] or for very shallow angles because of the non-linear dependence of the radar backscatter on the incidence angle in these ranges [90,91].

The proposed σ0 local incidence angle normalization method can be used not only for agricultural purposes but also for other SAR applications. Additional studies need to be carried out to determine if this method is ideal for general use. The β0 local incidence angle normalization method might be used for the vegetation variable estimation of crops other than processing tomatoes and cotton grown on rough soil surfaces. Future studies should pursue this.
