Deriving Wheat Crop Productivity Indicators Using Sentinel-1 Time Series

High-frequency Earth observation (EO) data have been shown to be effective in identifying crops and monitoring their development. The purpose of this paper is to derive quantitative indicators of crop productivity using synthetic aperture radar (SAR). This study shows that the field-specific SAR time series can be used to characterise growth and maturation periods and to estimate the performance of cereals. Winter wheat fields on the Rothamsted Research farm in Harpenden (UK) were selected for the analysis during three cropping seasons (2017 to 2019). Average SAR backscatter from Sentinel-1 satellites was extracted for each field and temporal analysis was applied to the backscatter cross-polarisation ratio (VH/VV). The calculation of the different curve parameters during the growing period involves (i) fitting of two logistic curves to the dynamics of the SAR time series, which describe timing and intensity of growth and maturation, respectively; (ii) plotting the associated first and second derivative in order to assist the determination of key stages in the crop development; and (iii) exploring the correlation matrix for the derived indicators and their predictive power for yield. The results show that the day of the year of the maximum VH/VV value was negatively correlated with yield (r = −0.56), and the duration of “full” vegetation was positively correlated with yield (r = 0.61). Significant seasonal variation in the timing of peak vegetation (p = 0.042), the midpoint of growth (p = 0.037), the duration of the growing season (p = 0.039) and yield (p = 0.016) were observed and were consistent with observations of crop phenology. Further research is required to obtain a more detailed picture of the uncertainty of the presented novel methodology, as well as its validity across a wider range of agroecosystems.


Introduction
Time series analysis of satellite remote sensing (RS) images allows detailed crop monitoring, an enhanced understanding of the impact of agricultural practices, and can provide early warnings of low yields [1,2]. There is a wide range of RS data and associate products [3,4], and the most appropriate form will depend on the challenge, such as crop classification, vegetation modelling, and understanding water dynamics such as drought stress and irrigation [5]. Data can also support farming decisions due to the ability to gather and display environmental variables across large areas, providing spatial 662 mm in 2017 to 704 mm in 2018, and 616 mm in 2019. June and July 2018 were particularly dry [48] and the potential soil moisture deficit (PSMD) reached a maximum value of almost 325 mm. The mean annual air temperature was 10.6 °C, ranging from 2.2 °C in February to 19.9 °C in July ( Figure 2).     Table 1).

Figure 2.
Total monthly rainfall (mm) and mean air temperatures ( • C) on the primary axis (left) and maximum potential soil moisture deficit (PSMD; mm) on the secondary axis (right) at Rothamsted farm from September 2016 to August 2019.

Site Ground Measurements of Wheat Development and Yield
In situ observations of phenology were made weekly during the growing season to monitor the wheat development and growth stages. In each field, measurements of grain yield were recorded by the harvest machinery. These data were used as reference points in the methodology to describe the response of the VH/VV ratio to the dynamics of the winter wheat development and growth, and explore the different parameters of the segments with respect to their contribution to yield.

SAR Data to Obtain VH/VV Time Series in Each Wheat Field
The Sentinel-1 SAR data acquired for the Rothamsted Research farm, over the three-year study period were derived from orbit 132 (ascending) with a temporal resolution of six days. One of the reasons for selecting a single orbit is the orientation of the view of the satellite, which plays a significant role in the direction of the emitted beam from the SAR antenna [49,50]. Using the same orbit also had the advantage of a similar incidence angle (range of 5 • ) for adjacent fields on even terrain [49]. The ascending orbit 132, instead of descending 81, was also used to avoid early morning measurements when dew may become a confounding factor [14,45]. Temporal profiles of the S1 VH/VV backscatter ratio were plotted on each field to define the curves' shapes and amplitude, which were related to ground observations of wheat at key growth stages, assisting in the definition of periods defined by the calculated parameters. Figure 3 displays the flow diagram with all the needed steps of the analysis. Remote Sens. 2020, 12, x FOR PEER REVIEW 5 of 22 Figure 3. Flow diagram explaining the steps for the temporal analysis of synthetic aperture radar (SAR) time series, including the data and process.

SAR Preprocessing for Field Specific VH/VV Time Series
The SAR data were derived from the Level-1 Ground Range Detected Interferometric Wide Swath (GRD-IW) product from Sentinel-1 satellite. The Sentinel-1 toolbox was used to preprocess the data, including border and thermal noise removal, slice assembly, radiometric calibration, terrain flattening, speckle filtering using refined Lee filter with a 3 × 3 window, and terrain correction to produce gamma naught (γ°) data in VH and VV polarisations. Lastly, each scene was clipped and the γ° VH/VV ratio was calculated. Based on the scale selected for the analysis, a mean value for the whole field (Table 1) was used to minimise the speckle effect, and the area of each field was buffered to minimise the

SAR Preprocessing for Field Specific VH/VV Time Series
The SAR data were derived from the Level-1 Ground Range Detected Interferometric Wide Swath (GRD-IW) product from Sentinel-1 satellite. The Sentinel-1 toolbox was used to preprocess the data, including border and thermal noise removal, slice assembly, radiometric calibration, terrain flattening, speckle filtering using refined Lee filter with a 3 × 3 window, and terrain correction to produce gamma naught (γ • ) data in VH and VV polarisations. Lastly, each scene was clipped and the γ • VH/VV ratio was calculated. Based on the scale selected for the analysis, a mean value for the whole field (Table 1) was used to minimise the speckle effect, and the area of each field was buffered to minimise Remote Sens. 2020, 12, 2385 6 of 20 the influence of surrounding fields. All of the calculations were conducted using untransformed data in a linear form. In the presentation of the results, the initial graphs were developed to allow the reading of both linear and decibel (dB) values, and the final results were presented on decibel axes. In addition, temporal filtering (in the form of smoothing, Savitzky-Golay filter) was used to reduce localised weather patterns, such as heavy rainfall, ice or snow, that can temporarily lower the SAR backscatter. This step avoided the use of additional data (e.g., rainfall used to clean the data) for automation.

Temporal Analysis and Wheat Development Definition
The curve of the VH/VV ratio time series was used to produce indicators that could describe wheat crop growth and development across the season. Smoothing approaches for time series of SAR [51,52] and optical data [42,53] have been used in various studies to reduce noise or fill the gaps of the datasets. Here, the Savitzky-Golay filter was applied over the whole period with a moving window of two months and using a second-order polynomial function [54]. Then the associated first and second derivatives were calculated to define additional wheat growth stages, linked to the SAR temporal characteristics. Key periods of these three curves were identified, as shown as vertical lines in Figure 4, and matched with crop development observed in the field.
influence of surrounding fields. All of the calculations were conducted using untransformed data in a linear form. In the presentation of the results, the initial graphs were developed to allow the reading of both linear and decibel (dB) values, and the final results were presented on decibel axes. In addition, temporal filtering (in the form of smoothing, Savitzky-Golay filter) was used to reduce localised weather patterns, such as heavy rainfall, ice or snow, that can temporarily lower the SAR backscatter. This step avoided the use of additional data (e.g., rainfall used to clean the data) for automation.

Temporal Analysis and Wheat Development Definition
The curve of the VH/VV ratio time series was used to produce indicators that could describe wheat crop growth and development across the season. Smoothing approaches for time series of SAR [51,52] and optical data [42,53] have been used in various studies to reduce noise or fill the gaps of the datasets. Here, the Savitzky-Golay filter was applied over the whole period with a moving window of two months and using a second-order polynomial function [54]. Then the associated first and second derivatives were calculated to define additional wheat growth stages, linked to the SAR temporal characteristics. Key periods of these three curves were identified, as shown as vertical lines in Figure 4, and matched with crop development observed in the field.
The next stage was to further parameterise and automate the extraction of these dates and test if they were linked to wheat development. The smoothed VH/VV curve was divided into two periods: i) growth and ii) maturation and senescence to address an observed change in maximum values in the middle of the season. The splitting of the analysis into two periods was also used by Che et al. (2014) [41], who analysed the temporal evolution of the leaf area index (LAI) of vegetation during development and senescence in Shandong Province, China. The breakpoint of two curves occurs during the flowering period (anthesis) when the wheat has reached its full height. The calculation of the breakpoint specifies the start for the VH/VV ratio stabilisation period close to the end of spring.  The next stage was to further parameterise and automate the extraction of these dates and test if they were linked to wheat development. The smoothed VH/VV curve was divided into two periods: (i) growth and (ii) maturation and senescence to address an observed change in maximum values in the middle of the season. The splitting of the analysis into two periods was also used by Che et al. (2014) [41], who analysed the temporal evolution of the leaf area index (LAI) of vegetation during development and senescence in Shandong Province, China. The breakpoint of two curves occurs during the flowering period (anthesis) when the wheat has reached its full height. The calculation of the breakpoint specifies the start for the VH/VV ratio stabilisation period close to the end of spring.

Logistic Curve Fitting
In order to quantify the characteristics of the temporal curve of VH/VV ratio for winter wheat, a logistic model was used during both the growth and maturation phases. Two separate curves, rather than a single double logistic curve, were chosen because the starting value of the VH/VV ratio of the maturation phase (which coincided with flowering) tended to be lower than the finishing point of the growth stage (which coincided with booting) ( Figure 5). In addition, the baseline at the beginning of the season can differ from the end. The two sigmoid logistic curves describing the VH/VV ratio in relation to time t for each stage was characterised by four parameters (Equation (1)): where base is the minimum VH/VV ratio value, Max is the maximum VH/VV ratio value, b is the steepness of the logistic curve, and t o is the x-value of the sigmoid inflexion point. The calculated values are sensitive to a clear definition of the period represented by each sigmoid curve ( Figure 5). The growth period curve was defined from the beginning of the season (Parameter 1 in Figure 5) up to the time of maximum value of the smoothed curve (Parameter 5). The maturation period curve was defined as the period after flowering to the minimum value in the maturation period of the temporally smoothed curve.
where base is the minimum VH/VV ratio value, Max is the maximum VH/VV ratio value, b is the steepness of the logistic curve, and to is the x-value of the sigmoid inflexion point. The calculated values are sensitive to a clear definition of the period represented by each sigmoid curve ( Figure 5). The growth period curve was defined from the beginning of the season (Parameter 1 in Figure 5) up to the time of maximum value of the smoothed curve (Parameter 5). The maturation period curve was defined as the period after flowering to the minimum value in the maturation period of the temporally smoothed curve.  Table 2). All calculations were completed using a linear scale and the secondary y-axis displays the decibel scale for reference.
Combining parameters extracted from the two logistic curves allowed us to derive three additional vegetation development-related parameters (10, 11, and 12 in Figure 5). The period between the two midpoints of the logistic curves (Parameter 10 in Figure 5) was defined as the duration of "full" vegetation, which starts with stem elongation and ends with the reduction of the green canopy and translocation of carbohydrates into the grain during maturation. The difference in baselines is related to the backscatter from the biomass of the crop during tillering. The summary of the extracted parameters and their definitions as well as the associated crop development stage is given in Table 2.  Table 2). All calculations were completed using a linear scale and the secondary y-axis displays the decibel scale for reference.
Combining parameters extracted from the two logistic curves allowed us to derive three additional vegetation development-related parameters (10, 11, and 12 in Figure 5). The period between the two midpoints of the logistic curves (Parameter 10 in Figure 5) was defined as the duration of "full" vegetation, which starts with stem elongation and ends with the reduction of the green canopy and translocation of carbohydrates into the grain during maturation. The difference in baselines is related to the backscatter from the biomass of the crop during tillering. The summary of the extracted parameters and their definitions as well as the associated crop development stage is given in Table 2.

Parameter Optimisation
The calculation of the logistic curve fitting parameters in Table 2 was based on a weighted least squares (WLS) estimator, which considers the uncertainty of each point by minimising the sum of the squared difference divided by the respective standard deviation (σ) in each point (Equation (2)). The incorporation of the standard deviation in the estimator was used to minimise the outlier effects. The VH/VV ratio points were selected as the observation values in each defined period.

Automatic Curve Extraction and Correlation Analysis
By scripting the SAR processing using Python, it was possible to automatically derive a smoothed VH/VV ratio curve and two logistic curves. Then the 12 parameters were derived for each field site across three years. A Pearson correlation coefficient (r) was calculated for each pair in a matrix. This approach allows the illustration of the interactions between the parameters and the direct effect on final crop yield. A significant test of the r was performed and highlighted in the plots.

Annual Analysis of VH/VV Ratio Curve Parameters, 2017 to 2019
Two logistic curves for the nine fields selected in 2017 (Figure 6), the five fields selected in 2018 (Figure 7), and the four fields selected in 2019 (Figure 8), were plotted. The smoothed time series were used to identify the start and end of (i) the growth (start of the year to red line) and (ii) the maturation periods (purple to min senescence value). Then the midpoints were calculated by fitting the logistic curves in these periods, creating the time parameters shown in Figures 6-8.      The timing of the mean maximum VH/VV ratio (TZ max ) was relatively consistent varying from day-of-year (DOY) 129 in 2017, to DOY 140 in 2018, and DOY 131 in 2019 (Table 3). The mean values (Table 4) of the three parameters of the logistic curve for the growth period were also relatively consistent from year to year: G_base (range 0.13-0.15), G_steep (range: 0.08-0.11), and G_midP (range: DOY 99 to 109). There was greater variation in G_max, which ranged from a mean of 0.31 in 2017 to 0.40 in 2019. The mean values of two of the parameters of the logistic curve for the maturation period were also relatively similar across the three years: S_base (range: 0.10-0.13), and S_midP (range: DOY 199 to DOY 208). By contrast, the mean values of S_max (range: 0.23-0.30) and S_steep (range: -0.12 to -0.21) showed greater interannual variation ( Table 4).
The root mean square error (RMSE) of the growth (G) and maturation (S) logistic curves are shown in the last two columns of Table 3 for the seasons 2017, 2018, and 2019. Statistical comparison between the parameters of different years showed that TZmax (p = 0.042), the G_midP (p = 0.037), S_base (p = 0.030) are significantly different at 95% confidence using ANOVA or the Kruskal-Wallis H-test if there was a non-normal distribution. There was also a significant interannual variation in the Duration (p = 0.039) and Yield (p = 0.016).

Relationship Between SAR-Derived Parameters and Yield
The interactions between each of the parameters and yield were further displayed using a correlation matrix (Figure 9). There were various significant correlations between parameters. As would be expected, the inflorescence indicator (D_max = G_max -S_max) was correlated with the two parameters used in the calculation (G_max and S_max), with r values of 0.76 and −0.75, respectively. At the same time, significant correlations were found between D_max and G_steep (r = −0.54), S_midP (r = 0.68), and Duration (r = 0.49). By contrast, D_base displayed no significant correlations with the other parameters, with the exception of G_base (r = 0.65) that was used for its calculation. The definition of D_base is G_base minus S_base, where S_base represents the VH/VV ratio value on bare soil (that should remain relatively consistent) and the value of G_base is determined by the combination of soil and low vegetation during the tillering period.
Starting from the first row in Figure 9, the baseline of growth (G_base) shows a significant positive correlation (r = 0.58) with the baseline of maturation (S_base). This is because G_base depends on the shift of the VH/VV ratio during the initial bare/sparse/small vegetation period and the soil background (S_base). In the second row, the slope of the midpoint of growth (G_steep) has a negative correlation with the VH/VV ratio at G_max value (r = −0.68). In the third row, the midpoint of growth (G_midP) is highly correlated with the timing of the max (TZmax) smoothed VH/VV ratio value (r = 0.69), highlighting the interaction of stem elongation and booting stage. G_midP was also correlated with the calculated Duration (r = −0.68) and the maturation midpoint (S_midP; r = 0.78). This is because the Duration value is defined by the difference between these two time indicators. The value of TZmax, the timing of the maximum value of VH/VV, was positively correlated with S_max (r = 0.50), but negatively correlated with low Duration values (r = −0.64).
During the maturation period, S_max was negatively correlated with the midpoint S_midP (r = −0.72) and Duration (r = −0.80). The only correlation shown by the steepness of the curve in this period was with the yield. The value of S_midP was positively correlated with Duration (r = 0.76) and D_max (r = 0.68). The value of S_base was not significantly correlated with any of the indicators except G-base.   As illustrated by the matrix (Figure 9), multiple correlations exist among the individual parameters and between individual parameters and yield (last column). The results suggest that the two parameters, G_midP and TZmax (which are correlated), had the strongest association with grain yield, i.e., r = −0.45 and r = −0.56, respectively, after Duration (r = 0.61). The negative correlation suggests that earlier growth, i.e., lower values of G_midP and TZmax were associated with higher end-of-season grain yields. Figure 10 displays the two most significant parameters that are sensitive to yield.
Remote Sens. 2020, 12, x FOR PEER REVIEW 17 of 22 As illustrated by the matrix (Figure 9), multiple correlations exist among the individual parameters and between individual parameters and yield (last column). The results suggest that the two parameters, G_midP and TZmax (which are correlated), had the strongest association with grain yield, i.e, r = −0.45 and r = −0.56, respectively, after Duration (r = 0.61). The negative correlation suggests that earlier growth, i.e., lower values of G_midP and TZmax were associated with higher end-of-season grain yields. Figure 10 displays the two most significant parameters that are sensitive to yield.

Discussion
Using the example of winter wheat over three growing seasons, it was possible to derive fieldspecific annual coefficients of a generalised two-component empirical model of crop productivity from the SAR VH/VV ratio. Due to the ubiquitous and high-frequency availability of S1 data, this approach could offer new opportunities for monitoring and predicting productivity in areas affected by frequent cloud cover. The characterisation of VH/VV response over a season used three stages: i) the creation of a smooth VH/VV time series for each field; ii) the definition of the timing of the maximum value using temporal characteristics of the time series, growth, and maturation period using first and second derivatives; and iii) the creation of two logistic curves using the observation in the predefined periods of growth and maturation [41]. The results are discussed as follows: first, in terms of the robustness of our mathematical method over three seasons to consider multiple factors of variation; second, the gain of biophysical understanding using this method; and finally, the agronomic potential of our results.

Technical and Statistical Process, the Goodness of Fit, Robustness, and Uncertainty
Since 2016, SAR data from Sentinel-1 have become twice as frequent as data used in previous studies [2,20], which improves the robustness of the possible analysis. However, to reduce the variability of SAR data we chose to use imagery from only the ascending satellite passing as images from the descending orbit were often affected by morning dew. Similar observations have been made in other studies [14,45], indicating greater certainty when using the ascending rather the descending phase of the satellite for predicting crop state variables in this area. Even so, the results demonstrate substantial variation of SAR backscatter, which can be due to differences in topography affecting the incidence angle or changes in canopy architecture [49,50].
As pointed out in an earlier review [5], SAR variability is also connected to diurnal variation in plant-soil-water relations, which can affect the erectness of the crop canopy and the dielectric properties of the system. To reduce the effect of such fluctuations in the SAR time series, our approach used a step of smoothing the data, which resulted in a set of relatively consistent dynamic curves for winter cereals [20], and limited the extreme values of the VH/VV ( Figure 6). The subsequent logistic

Discussion
Using the example of winter wheat over three growing seasons, it was possible to derive field-specific annual coefficients of a generalised two-component empirical model of crop productivity from the SAR VH/VV ratio. Due to the ubiquitous and high-frequency availability of S1 data, this approach could offer new opportunities for monitoring and predicting productivity in areas affected by frequent cloud cover. The characterisation of VH/VV response over a season used three stages: (i) the creation of a smooth VH/VV time series for each field; (ii) the definition of the timing of the maximum value using temporal characteristics of the time series, growth, and maturation period using first and second derivatives; and (iii) the creation of two logistic curves using the observation in the predefined periods of growth and maturation [41]. The results are discussed as follows: first, in terms of the robustness of our mathematical method over three seasons to consider multiple factors of variation; second, the gain of biophysical understanding using this method; and finally, the agronomic potential of our results.

Technical and Statistical Process, the Goodness of Fit, Robustness, and Uncertainty
Since 2016, SAR data from Sentinel-1 have become twice as frequent as data used in previous studies [2,20], which improves the robustness of the possible analysis. However, to reduce the variability of SAR data we chose to use imagery from only the ascending satellite passing as images from the descending orbit were often affected by morning dew. Similar observations have been made in other studies [14,45], indicating greater certainty when using the ascending rather the descending phase of the satellite for predicting crop state variables in this area. Even so, the results demonstrate substantial variation of SAR backscatter, which can be due to differences in topography affecting the incidence angle or changes in canopy architecture [49,50].
As pointed out in an earlier review [5], SAR variability is also connected to diurnal variation in plant-soil-water relations, which can affect the erectness of the crop canopy and the dielectric properties of the system. To reduce the effect of such fluctuations in the SAR time series, our approach used a step of smoothing the data, which resulted in a set of relatively consistent dynamic curves for Remote Sens. 2020, 12, 2385 16 of 20 winter cereals [20], and limited the extreme values of the VH/VV ( Figure 6). The subsequent logistic fitting approach enabled the calculation of a specific backscatter value and time-specific parameters from the VH/VV ratio data ( Figure 5). Accounting for the standard deviation during the fitting of the logistic curves made it possible to give lower weight to data with high uncertainty and improved the precision of the derived curves. The average RMSE values of the logistic curve fitting in growth (G) and senescence/maturation (S) periods were 0.05 and 0.07, respectively.
The creation of the fitted curves allowed the derivation of 12 parameters that can be related to the development, growth, and yield of winter wheat. Two temporal parameters from the analysis (TZmax and Duration) were significantly correlated with yield ( Figure 9). Further analysis could focus on the opportunity of using a combination of parameters or a combination of VV and VH/VV values. The approach was effective in each of three years that were characterised by different environmental conditions and yields. In 2018, there was minimal rainfall in June and July, and the grain yields obtained in 2018 (4.09-7.01 t ha −1 ) were substantially lower than in 2017 (5.04-9.59 t ha −1 ) and 2019 (7.99-10.17 t ha −1 ).

Environmental and Biophysical Understanding
The sensitivity of SAR backscatter to surface changes in the structure and the soil and crop water content means that SAR can be an effective tool to monitor crop development [5,24] starting from early growth, to the increase in the water volume of the crop through stem elongation, and its decrease during maturity. In this paper, we assigned two separate logistic curves during the cropping season to examine whether the resulting parameters were correlated with observations in the field. A specific feature of creating two curves is the derivation of the D_max value, which would not be captured by assuming a single curve. Our interpretation is that the change in the VH/VV value at flowering is a real effect, which equates to a change in the structure of the crop (Figure 6) during the inflorescence period, as mentioned by other authors [2,14,18]. Even so, the value of D_max was variable, ranging from -0.13 to 0.38 for an individual field and year (Table 3). Additional research, including perhaps data focused on structure, is required to further understand this variability.
The correlation analysis ( Figure 9) was able to identify two time-based parameters, one derived from the growth period (G_midP) and one derived from the smoothed VH/VV curve (TZmax), which were negatively associated with the final grain yield (r = −0.45 and −0.56, respectively). This means that a delayed occurrence of the midpoint of the growth curve and the timing of the maximum VH/VV ratio was associated with lower grain yields. The late or slow growth of the crop canopy is likely to result in a reduced capacity of the crop to intercept solar radiation and use photosynthesis to produce assimilates required for final yield. For example, in 2018, the late occurrence of G_midP and TZmax was associated with an unusually dry period in June and July 2018 (Figure 2), which reduced canopy growth and photosynthesis and resulted in substantially lower grain yields than in the other two years.
The analysis also showed that the duration of the period of "full" vegetation (Duration) was positively related to grain yield (r = 0.61). This can be explained by the yield benefitting from a longer period of photosynthesis and a longer grain-filling period when assimilates are transferred from green tissue to the grain [55,56]. These results suggest that using the VH/VV ratio to identify the timing of specific crop periods, which are related to the structural change of the wheat canopy [2,14], may be a more useful determinant of yield than the actual values of the VH/VV ratio, per se.

Opportunities for Agronomic Management and Modelling
The analysis raises two questions for crop management. First, what can be learnt about crop dynamics from monitoring satellite-based SAR data, dynamics, and amplitude? Second, is there potential for a farmer or agronomist to use SAR-derived indicators for spatially varying crop management and inputs between fields? The growth and development of a wheat crop depends on the interaction between the weather (e.g., solar radiation, rainfall, and temperature), crop genetics, field characteristics (e.g., aspect and soil type), and field management (e.g., previous cropping history and the timing, type of cultivation, and drilling). The results from the SAR data analysis indicates that it is possible to identify seasonal differences in the timing of crop growth, and this may be useful in identifying the most appropriate schedule of fertilizer and agrochemical application between fields. The analysis also suggests that it may be possible to improve the prediction of the eventual crop yield from an analysis of SAR characteristics.
A potential limitation with the method is that some of the parameters are determined retrospectively from a full temporal dataset, for example, the calculation of TZmax, the timing of the maximum value of VV/VH, requires data that occur after TZmax. Likewise, the value of S_steep, which occurs during the maturation of the crop, requires data that occur after that point. Developing a really effective predictive tool that can be used to modify field management instantaneously will require parameters that can be estimated in real-time. Further work is needed to improve the estimation of parameters, as well as the application of the methodology on other farms to validate the robustness of the method. The correlation of the productivity indicators with field measurements also has the potential to assist in better model simulations of crop development and growth. At the same time, temporal characteristics, as well as connection with the biophysical properties of the field, could be examined to improve the calibration and its incorporation into a data assimilation framework to estimate more efficiently the field production [1,7,8].

Conclusions
This paper describes a new methodology to derive wheat productivity indicators from Sentinel-1 VH/VV time series. The temporal curves, their first and second derivatives, and logistic curve fitting for growth and maturation periods were used to define 12 phenomorphological parameters. These provide information about the growth, development, and yield of wheat crop at field scale, offering an alternative approach to ground survey or yield estimation.
The analysis of the VH/VV ratio time series and the correlation matrix indicates that the time-based parameters appear to be related to biophysical changes in the field. In particular, the time period of "full" vegetation (Duration) was positively correlated with yield (r = 0.61), and a delay in the timing of the maximum VH/VV value (TZmax) was negatively correlated with yield (r = −0.56).
Automation of the SAR image analysis was possible, as the only inputs required were backscatter data from VH and VV polarisations. Future work will explore the use of this method to estimate commercial wheat production in other farming landscapes in the UK. It could also be adapted to monitor growth and development, as well as yield prediction for other arable crops, potentially allowing the remote quantitative assessment of environment and management impacts.