Within this framework, we have investigated the sensitivity of 10 parameters including linear polarization backscattering coefficients, H-A-α decompositions, polarization intensity ratios (VH/VV, VV/VH and VV − VH/VV + VH), Radar Vegetation Index (RVI) and intensity arithmetic calculations (VH − VV and VV + VH) derived from multi-temporal C-band Sentinel-1 SAR data, to crop height and Canopy Coverage (CC) of maize, sunflower, and wheat. For this purpose, field measurements were carried out simultaneously with SAR data acquisitions. For backscattering analysis four Sentinel-1 SAR images in descending orbit direction were acquired throughout the same growth season of the study area.

#### 2.2. Field Surveys

In situ measurements were conducted for maize, sunflower and wheat fields in the spring–summer agricultural season of the year 2016. Crop variables and parameters which indicate the growth rate including crop height and CC were collected simultaneously with the SAR data acquisition, and recorded during the field works. Field data collection includes measuring the row and plant cover by still tape in unit area, taking photographs by the camera and recording field characteristics such as soil properties and irrigation status. For calculating CC, photographs were taken in downward position and perpendicular to the ground with 100 cm distance from camera and canopy outmost in the tillering stage when the crop height was less than 100 cm. Considering the study area, 36 test fields that consist of 19 maize, 6 sunflower fields, and 11 wheat fields were dedicated for this research. The variability of development stages for maize, sunflower and wheat has been defined by applying the “Biologische Bundesanstalt, Bundessortenamt, and CHemische” (BBCH) [

20] indicator for each field that generally consist of vegetative and reproductive stages. Seasonal maize, sunflower, and wheat crop calendar of the study area is presented in

Figure 4. According to the defined height and CC thresholds, derived from SAR backscattering and BBCH-scale, we call two stages for crops growth season; the early stage and the later stage.

Four field surveys were conducted to obtain accurate ground measurements in late May–mid June, early July, late July, and late August 2016. General growth stages categories (leaf development, stem elongation, heading and flowering), are defined according to the BBCH-scale (

Table 1). For calculating the crop height of each test site, five height measurements were obtained and their mean value was calculated to represent the crop height of the relevant test field. From the test sites, plant cover and row were measured and also photographs were captured to determine and evaluate the CC percentage. A synopsis of the maize, sunflower and wheat of different growing stages is given in

Figure 5.

In this study site, the BBCH-scale is considered as 53 when the maize height was in range of 120–150 cm. This growth stage of the maize is at the inflorescence emergence and heading stage. When maize height was greater than 220 cm, the BBCH-scale was 69 and represented the end of flowering. Once the sunflower height was greater than 92 cm, the BBCH-scale is found as 79, indicating the end of flowering and the inflorescence reaches full size. The BBCH-scale is considered as 59 after that wheat height reached to 53 cm and inflorescence fully emerged. We observed that different wheat height could have the similar wheat BBCH due to variation of wheat growth conditions which cause to distinction even though they are at the same phenology, in agreement with the study of Liao et al. [

17].

Figure 6 shows the relationship between crop height and the BBCH-scale corresponding to the each crop principal growth stages.

Scatterplots (d–f) in

Figure 6 show SAR response to crop heights. Note that the sensitivity of the SAR backscatter to CC of three different crops has been changed in different height and CC in each crop. For maize, the variation of correlation was determined when the maize CC threshold is 75%. This threshold is 85% and 60% for sunflower and wheat respectively.

#### 2.4. SAR Backscatter

Several studies on the processing of radar data indicate that the phenological stages of the plant have an effect on the backscatter of the signal, and there is a significant correlation between the biophysical parameters of the plants, including height, leaf area index, vegetation mass, plant water content, and radar signal backscatter [

15,

23,

24,

25]. Radar backscattering from vegetation is a function of both wavelengths polarization and frequency. Different frequencies and polarizations enable one to infer various and supplementary information from the single object. In agricultural radar applications, combination of polarizations (co-polarization and cross-polarization) allows analyst to extract extra information about crop characteristics.

The polarization of backscattering microwaves indicates the target structural properties and visualizes scattering characteristics of observed features [

1,

5]. A majority of the space borne radar systems often transmit only one polarization and receives both polarization giving rise to dual polarimetric SAR data (e.g., Sentinel-1 with VH and VV polarizations), while some collecting full polarimetric so-called quad polarization (HH, VV, HV, and VH) imagery (e.g., PALSAR, TerraSAR-X, and RADARSAT-2). Fully polarimetric SAR data is acquired using the H and V polarizations which extracted from SLC data and can be represented by a 2 × 2 scattering matrix S (Equation (1)) including polarimetric information for each individual resolution cell [

26,

27,

28].

Scattering matrix which depends on incident and the scattered field, has four components, each representing the received and transmitted polarizations [

29,

30]. The scattering matrix consists of information on the nature and characteristic of the observed media and features. Full polarimetric SAR data set which is described as scattering matrix is foundation for several coherent polarimetric decomposition and analysis. For polarimetric analysis an alternative procedure is derived from a covariance matrix (C

_{3}) that represents the average polarimetric information extracted from a set of neighboring pixels to produce the mean polarimetric response. The covariance matrix C

_{3}, (Equation (2)), is determined from the outer element of the vector form of the scattering matrix with its Hermitian conjugate, KC [

17,

27]. The averaged target vector (covariance matrix) for fully polarimetric data is given by Equation (3).

where ensemble averaging is shown by the | | represents the modulus, the * indicates complex conjugation and the complex conjugate transpose shown by superscript H. For natural targets, in case of monocratic radar, S

_{HV} ≈ S

_{VH} when Srt indicates the complex scattering amplitude for received and transmitted polarization (r, t ∈ {h, v}) for horizontal and vertical polarization and the scattering matrix is defined by three-element complex target vector, K

_{C} =

${\left[{S}_{HH}\sqrt{2}{S}_{HV}{S}_{VV}\right]}^{T}$, where superscript T indicates the matrix transpose [

29,

30]. In the covariance matrix, diagonal elements (C

_{11} = σ

^{0}_{HH}, C

_{22} = σ

^{0}_{HV}, and C

_{33} = σ

^{0}_{VV}) define backscattering coefficients and the upper or lower triangular components represent complex numbers. The backscattering coefficients have correlation with the structural characteristics of the features [

17,

31].

In comparison to the quad polarization, dual polarimetric SAR sensors collect a fraction of total (precisely half of the scattering matrix components) polarimetric information involved in fully polarimetric imagery [

27]. It means that each resolution cell at each time point is defined by a 2 × 2 covariance matrix (C

_{2}) that is obtained from C

_{3}. The resulting covariance matrix which is for dual polarization (e.g., Sentinel-1) is represented by Equation (4).

Since dual polarization has only diagonal elements, the matrix with off-diagonal components are set to zero and do not follow a complex Wishart distribution; however, the two diagonal blocks (1 by 1) do [

30,

32].

Polarimetric Synthetic Aperture Radar (PolSAR) technique has resulted many different investigations and improvements in crop growth monitoring, yield estimation, crop disaster prediction and prevention and in more general terms providing accurate information for precision farming. PolSAR products, such as Entropy (H), Alpha (α) and Anisotropy (A) decompositions are calculated from the covariance matrix. The H-α-A decompositions are used to extract average parameters from experimental data suggested by Cloude and Pottier [

33]. This approach is based on second-order statistics using a smoothing algorithm [

34]. Natural measure of the inherent reversibility of the backscattering data is defined by entropy (H), and indicates the randomness of the scatter, while the underlying average scattering mechanisms, scattering type (surface, double-bounce and volume scattering) can be identified using Alpha parameters. The relative power the second and third eigenvectors is described by Anisotropy (A), which represents being of different properties in different directions when measured along different axes [

33,

35]. The Entropy (H) decomposition parameter has more sensitivity to the crop parameters and the density and randomness of some vegetation canopy than Alpha and Anisotropy [

28,

36].

In agricultural radar monitoring, Radar Vegetation Index (RVI) is a method for observation of the level of the vegetation growth in time series data analysis as an alternative to NDVI (Normalized Difference Vegetation Index) method used in optical image processing studies [

37]. Ranging between 0 and 1, RVI is used for measuring the randomness of scattering in microwave signal [

38]. It is close to 0 for a smooth bare surface and as vegetation grows the value increases till the crop reaches to the end of growth cycle and it is affected by vegetation water content and sensitive to the biomass [

39]. RVI calculation needs quad-polarized data, thus for full polarization, RVI is retrieved by the Equation (5).

where σ

^{0}_{HH} and σ

^{0}_{VV} are co-polarized backscattering coefficients and σ

^{0}_{HV} is cross-polarized backscattering coefficient in power units. According to the Charbonneau et al. [

40] the assumption that supposes σ

^{0}_{HH} ≈ σ

^{0}_{VV} then Equation (5) can be reduced to the form as Equation (6).

Melanie et al. [

41] studied the RVI and concluded that RVI

_{HH} is useful when just two polarizations are available and can be an appropriate approximation of the surface scattering if the interaction between the surface plane and vegetation is insignificant.

Since Sentinel-1 is dual polarization and has VH and VV polarizations, following Charbonneau et al. [

40] assumption of possibility to modification of RVI in case of availability of two polarizations we assume an alternative to RVI for dual polarization as shown in Equation (7).

The index is about the contribution of volume scattering which is indicated by cross-polarized response. Pre-processing steps of satellite images were carried out using open source tools of Sentinel Application Platform (SNAP) software [

42]. Mean backscatter values and temporal variation of backscatter for each field for three different crop types relying on backscatter statistic results are extracted using

rasterstats zonal statistics and interpolated point queries function with a Python module [

43]. The module is used to summarize geospatial raster datasets to extract information based on vector geometries [

44]. Quantum GIS [

45], an open source GIS software is applied to draw the region of interest (ROI) polygons as vector geometries used in

rasterstats zonal statistics function. To decrease the effects of mix of the classes, the polygons are set at proper interval from the edges of the field boundary and homogeneous pixels are selected for the evaluation.

Figure 7 shows the flowchart of Sentinel-1 dual polarimetric SAR data processing.