Power Sensitivity Analysis of Multi-Frequency , Multi-Polarized , Multi-Temporal SAR Data for Soil-Vegetation System Variables Characterization

The knowledge of spatial and temporal variability of soil water content and others soil-vegetation variables (leaf area index, fractional cover) assumes high importance in crop management. Where and when the cloudiness limits the use of optical and thermal remote sensing techniques, synthetic aperture radar (SAR) imagery has proven to have several advantages (cloud penetration, day/night acquisitions and high spatial resolution). However, measured backscattering is controlled by several factors including SAR configuration (acquisition geometry, frequency and polarization), and target dielectric and geometric properties. Thus, uncertainties arise about the more suitable configuration to be used. With the launch of the ALOS Palsar, Cosmo-Skymed and Sentinel 1 sensors, a dataset of multi-frequency (X, C, L) and multi-polarization (coand cross-polarizations) images are now available from a virtual constellation; thus, significant issues concerning the retrieval of soil-vegetation variables using SAR are: (i) identifying the more suitable SAR configuration; (ii) understanding the affordability of a multi-frequency approach. In 2006, a vast dataset of both remotely sensed images (SAR and optical/thermal) and in situ data was collected in the framework of the AgriSAR 2006 project funded by ESA and DLR. Flights and sampling have taken place weekly from April to August. In situ data included soil water content, soil roughness, fractional coverage and Leaf Area Index (LAI). SAR airborne data consisted of multi-frequency and multi-polarized SAR images (X, C and L frequencies and HH, HV, VH and VV polarizations). By exploiting this very wide dataset, this paper, explores the capabilities of SAR in describing four of the main soil-vegetation variables (SVV). As a first attempt, backscattering and SVV temporal behaviors are compared (dynamic analysis) and single-channel regressions between backscattering and SVV are analyzed. Remarkably, no significant correlations were found between backscattering and soil roughness (over both bare and vegetated plots), whereas it has been noticed that the contributions of water content of soil underlying the vegetation often did not influence the backscattering (depending on canopy structure and SAR configuration). Most significant regressions were found between backscattering and SVV characterizing the vegetation biomass (fractional cover and LAI). Secondly, the effect of SVV changes on the spatial correlation among SAR channels (accounting for different polarization and/or frequencies) was explored. An inter-channel spatial/temporal correlation analysis is proposed by temporally correlating two-channel spatial correlation and SVV. This novel approach allowed a widening in the number of significant correlations and their strengths by also encompassing the use of SAR data acquired at two different frequencies.


Introduction
A positive impact on hydrology as well as on modern agricultural practices can be achieved by monitoring spatial and temporal dynamics of some land surface variables such as soil water content, m v , and vegetation.Despite the fact that synthetic aperture radar (SAR) allows acquiring in all weather conditions, unassessed strengthenings of the relations among backscattering, σ • , at different frequencies and polarizations and soil-vegetation variables (SVV) are limiting the operational application of SAR.Indeed, SAR configuration controls the wave-target interactions [1,2] and, thus, affects models' assessments depending on its frequency, polarization and acquisition geometry.
The dependence of bare soils σ • , σ • S , on both water content and surface roughness was modeled by several authors [1][2][3][4][5].However, the need of a prior knowledge of the soil surface roughness could reduce the feasibility of SAR techniques [4, [6][7][8].Indeed, reliable roughness measures are hardly achievable: (i) in situ measurements with contact methods (e.g., grid board [9]) are point based and usually not representative at plot scale; (ii) innovative methodologies (e.g., non-contact ultrasonic profiling) are capable of describing wide areas but still economically expensive (i.e., requiring airborne acquisitions).
Over vegetated areas an additional σ • contribution, σ • V , needs to be taken into account.Several authors, investigated σ • V by setting up theoretical models [10][11][12] schematizing the vegetation as simple targets of known geometry (such as plates and cylinders).Simple empirical models, avoiding a rigorous mathematical and geometrical simulation of the canopy, are often based on ratios of bands acquired at different polarizations [13][14][15][16].The need of a priori characterization of vegetation structure (hardly achievable through in situ campaigns) reduces the operational use of SAR in agriculture.
In recent years, several researches focused on m v quantification (over both bare, B, and vegetated, V, soils) explored different SAR configurations and approaches by testing (Table 1): (i) the use of temporal indices; (ii) the integration of passive microwaves and in situ data; (iii) different σ • models; (iv) the conjunct use of complex statistical models (such as Bayesian approach); (v) empirical fitting and ratio methods (refer to the Appendix A for symbols and acronyms).There were several approaches: empirical, EA; semi-empirical, SEA; theoretical, TA; polarimetric, PA; statistical SA, these latter employing Neural Networks, polarimetric indices or, channels ratio.Some authors calibrated σ • models such as: IEM (Integral Equation Model [4]), WC (Water-Cloud model [17]); GO (Geometrical Optics [4]); Dubois [1]; Oh [2,3]; RTM (Radiative Transfer Model); MIMICS (Michigan Microwave Canopy Scattering model [18]).Several authors separated soil and vegetation contributions by exploiting more than two polarizations (single frequency), by parameterizing the WC through in situ data.
All these approaches are usually based on regression analyses among σ • and SVV (i.e., soil roughness, water content, fractional cover and leaf area index).It is well known that SAR configuration (acquisition geometry, frequency and polarization) plays a fundamental role in the σ • vs. SVV relationship; thus it is expected that modifications of some SVV change also the spatial correlation between data acquired with different configurations.
Based on this evidence, this paper firstly aims to quantify the strength of the relation among σ • and four SVV (dynamic and single regression analyses) over bare and vegetated soils, over a wide range of cultivars and for different SAR configurations.These first sections are tailored to address: (i) frequencies and polarizations showing the highest sensitivities of σ • to the dynamic of the selected SVV; (ii) SAR configurations suitable to estimate SVV changes; (iii) frequencies and polarizations carrying redundant information.
Afterwards, the paper shows the effect of SVV changes on the spatial correlation among SAR channels and proposes, as novel approach, the use of temporal regressions of two-channel spatial correlations vs. SVV to explore any improvement achievable compared to the single-channel regression approach.
Table 1.m v retrieval using SAR: overview table on previous studies.Accuracy is reported in terms of: determination coefficient, r 2 ; correlation, r; root mean square error, rmse; average absolute deviation, aad; and mean square error, mse.For detailed notes please refer to Appendix A.

Study Area
In situ and SAR data have been collected on the 24 km 2 DEMMIN (Durable Environmental Multidisciplinary Monitoring Information Network) test site (Figure 1).The site is hosted by a farm located in Mecklenburg-Western Pomerania in North-Eastern Germany (Görmin farm, 53

Study Area
In situ and SAR data have been collected on the 24 km 2 DEMMIN (Durable Environmental Multidisciplinary Monitoring Information Network) test site (Figure 1).The site is hosted by a farm located in Mecklenburg-Western Pomerania in North-Eastern Germany (Görmin farm, 53°59′33′′N-13°16′40′′E, EPSG 4326).2. Noticeable, these cultivars are characterized by different vegetation architecture.Main soil textures in the Görrmin area were loamy sand and sandy loam.Within this area, the 9 monitored plots are characterized by loamy sand texture.In particular, the soil texture of plots 222, 450 and 140 is predominantly loamy sand; plot 460 is characterized by loamy sand and slightly loamy sand soil; whereas the other plots are characterized by both loamy sand and strong loamy sand soils.

Materials
Data have been collected between April and August 2006 in the framework of the AgriSAR 2006 project (funded by the European Space Agency, ESA) primarily planned to address programmatic needs of Sentinel-1 two-satellite constellation.AgriSAR 2006 campaign was specifically tailored to investigate σ° dynamic throughout the crop-growing season.The dataset includes weekly in situ measures and airborne SAR and optical images.2. Noticeable, these cultivars are characterized by different vegetation architecture.Main soil textures in the Görrmin area were loamy sand and sandy loam.Within this area, the 9 monitored plots are characterized by loamy sand texture.In particular, the soil texture of plots 222, 450 and 140 is predominantly loamy sand; plot 460 is characterized by loamy sand and slightly loamy sand soil; whereas the other plots are characterized by both loamy sand and strong loamy sand soils.In particular, in situ data have been collected by the Leibnitz-Zentrum für Agrarlandschaftsforschung (ZALF) and the University of Kiel (Christian-Albrechts-Universität, Department of Geography) almost simultaneously to SAR and optical flights.Measurements of m v (at 0-5 and 5-10 cm below ground level, b.g.l.), soil surface roughness, fractional cover, F v , and LAI were acquired by the research teams along 16 campaigns.In situ LAI and m v were measured using a LICOR-2000 and a portable IMKO TRIME-FM TDR respectively, root mean square of roughness height, h', was characterized with a laser profiler and a Rollei d7 metric digital stereoscopic system [48].A TDR probe (IMKO TRIME-ES, theoretical accuracy of ±0.01-±0.03m 3 m −3 ) was installed from the Ludwig-Maximilians Universitat München (LMU) and the University of Kiel on fields 102 (sugar beet) and 250 (wheat) providing measures of m v at 5 depths (5, 9, 15, 25 and 47 cm b.g.l.) with a temporal resolution of half an hour.Approximately 1150 measurements were executed, equally spread among plots and acquisition times.In particular, ~24 measurements were carried out for each in situ campaign; for each plot, always the same locations were taken into account; ~36 measurements per plot was carried out during the whole in situ campaign for each SVV.The sugar beet field was completely bare from the first campaign in 19 April until 11 May (F v reached 10% in 7 June); maize field was completely bare until the end of May.Other fields were vegetated until July; rape and barley were harvested during the airborne SAR campaign (Figure 2).
Remote Sens. 2017, 7, 677 5 of 22 In particular, in situ data have been collected by the Leibnitz-Zentrum für Agrarlandschaftsforschung (ZALF) and the University of Kiel (Christian-Albrechts-Universität, Department of Geography) almost simultaneously to SAR and optical flights.Measurements of mv (at 0-5 and 5-10 cm below ground level, b.g.l.), soil surface roughness, fractional cover, Fv, and LAI were acquired by the research teams along 16 campaigns.In situ LAI and mv were measured using a LICOR-2000 and a portable IMKO TRIME-FM TDR respectively, root mean square of roughness height, h', was characterized with a laser profiler and a Rollei d7 metric digital stereoscopic system [48].A TDR probe (IMKO TRIME-ES, theoretical accuracy of ±0.01-±0.03m 3 m −3 ) was installed from the Ludwig-Maximilians Universitat München (LMU) and the University of Kiel on fields 102 (sugar beet) and 250 (wheat) providing measures of mv at 5 depths (5, 9, 15, 25 and 47 cm b.g.l.) with a temporal resolution of half an hour.Approximately 1150 measurements were executed, equally spread among plots and acquisition times.In particular, ~24 measurements were carried out for each in situ campaign; for each plot, always the same locations were taken into account; ~36 measurements per plot was carried out during the whole in situ campaign for each SVV.The sugar beet field was completely bare from the first campaign in 19 April until 11 May (Fv reached 10% in 7 June); maize field was completely bare until the end of May.Other fields were vegetated until July; rape and barley were harvested during the airborne SAR campaign (Figure 2).During the investigation three drying periods occurred; mv varies in the range [0.34-0.06m 3 m −3 ] with some differences among fields.In maize crop, mv was higher than in other fields, probably only due to the root-zone water dynamics of this cultivar (the soil texture was similar to the other monitored plots); mv in barley, wheat, sugar beet and rape fields behaves similarly during the whole period.Finally, temporal trends of h' over barley, rape and wheat fields are quite similar; whereas h' exhibits higher values and different temporal behavior over maize and sugar beet (Figure 3).During the investigation three drying periods occurred; m v varies in the range [0.34-0.06m 3 m −3 ] with some differences among fields.In maize crop, m v was higher than in other fields, probably only due to the root-zone water dynamics of this cultivar (the soil texture was similar to the other monitored plots); m v in barley, wheat, sugar beet and rape fields behaves similarly during the whole period.Finally, temporal trends of h' over barley, rape and wheat fields are quite similar; whereas h' exhibits higher values and different temporal behavior over maize and sugar beet (Figure 3).The SAR dataset includes 120 images acquired in X, C and L bands (central wavelengths: 2, 5, and 21 cm respectively) in dual polarization (HH and VV for X band) and in quad-polarization (HH, VV, VH and HV for C and L bands).Flights were weekly carried out from the 9th of April to the 2nd of August by an airborne E-SAR (Experimental SAR), operated by the German Aerospace Center (Deutsches Zentrum für Luft-und Raumfahrt-DLR).The E-SAR sensor was on board a Do228 aircraft; although a total of 16 radar flights were executed during the AgriSAR 2006 campaign, the 12 performed in the E-W direction were considered in this research.The deployment of corner reflectors of 20 cm × 20 cm during one of the in situ campaigns allowed obtaining multi-look, geo-coded and calibrated σ° products at a raw spatial resolution, RS, of 2 m.During the airborne SAR acquisitions, high variability of mv, Fv and LAI occurred over both bare and vegetated soils, including different cultivars.Thus, AgriSAR 2006 dataset allows investigating (i) how σ° is controlled by changes of SVV and, (ii) how SAR configuration (acquisition geometry, frequency and polarization) rules the relationships between σ° and SVV.

Methods
For bare soils, h' and mv were included in the analysis; whereas, over vegetation the behavior of σ° was assessed under a wide range of mv for different cultivars with varying h', LAI, and Fv.
Different data analyses were carried out: (i) dynamic analysis of both σ° and SVV over all fields and over a selected plot; (ii) single regressions between σ° and SVV; (iii) single regression analysis between inter-channel spatial correlation and SVV at plot scale.

Data Aggregation
As a preliminary step, images were spatially averaged to reduce the speckle.Although several filters have been proposed to this aim [49][50][51][52][53] a simple spatial averaging technique was preferred.Indeed, the spatial aggregation limits inaccuracies in the comparison between σ° and in situ data due to georeferencing errors and GPS positioning uncertainties, respectively.The more appropriated RS was selected based on the values assumed by the Moran index IM [54] and the speckle index, IS [55].During the airborne SAR acquisitions, high variability of m v , F v and LAI occurred over both bare and vegetated soils, including different cultivars.Thus, AgriSAR 2006 dataset allows investigating (i) how σ • is controlled by changes of SVV and, (ii) how SAR configuration (acquisition geometry, frequency and polarization) rules the relationships between σ • and SVV.

Methods
For bare soils, h' and m v were included in the analysis; whereas, over vegetation the behavior of σ • was assessed under a wide range of m v for different cultivars with varying h', LAI, and F v .
Different data analyses were carried out: (i) dynamic analysis of both σ • and SVV over all fields and over a selected plot; (ii) single regressions between σ • and SVV; (iii) single regression analysis between inter-channel spatial correlation and SVV at plot scale.

Data Aggregation
As a preliminary step, images were spatially averaged to reduce the speckle.Although several filters have been proposed to this aim [49][50][51][52][53] a simple spatial averaging technique was preferred.Indeed, the spatial aggregation limits inaccuracies in the comparison between σ • and in situ data due to georeferencing errors and GPS positioning uncertainties, respectively.The more appropriated R S was selected based on the values assumed by the Moran index I M [54] and the speckle index, I S [55].

Dynamic Analyses
This section is focused on the investigation of σ • temporal behavior.In the first subsection, σ • dynamic was evaluated at different frequencies and polarizations during the whole period for varying SVV.Subsequently, the σ • temporal dynamic is qualitatively compared to SVV changes for two selected plots.4.2.1.Dynamic Analysis: All Plots Firstly, it was analyzed the σ • dynamic at different frequencies and polarizations (hereinafter referred to as channel) during the whole period, in which variations of m v , h', LAI and F v occurred.
For each plot the σ • range of variability, ∆σ • plot , was evaluated.Then, for each channel, metrics such us the average of ∆σ • plot , ∆σ • avg , and standard deviation of ∆σ • plot , ∆σ • stdev , were quantified.The higher ∆σ • avg the more the channel sensitivity to SVV changes, the higher ∆σ • stdev the more heterogeneity among plots.The corresponding metrics computed on ∆h', ∆m v , ∆F v and ∆LAI are discussed within the corresponding result Section 5.2.1.Backscattering varies with the dielectric and geometric properties of the soil-vegetation system.In particular, dielectric properties are ruled by m v (for the soil layer) and canopy water content; whereas, the geometric properties are ruled by h' (for the soil layer) and by both vegetation biomass (F v and LAI) and canopy structure (this latter has not been parameterized during the campaign).

Dynamic Analysis: Two Selected Plots
This analysis was performed for two selected plots: the first displayed soil drying over both bare and vegetated stages (plot 460, sugar beet); the second (plot 450, barley) was fully vegetated from April to July, then, it was harvested and thus, was bare during the last two SAR acquisitions.The analysis allows understanding how σ • behaves with m v over changing SVV.Outcomes over the first plot allow evaluating which channels have the higher sensitivity to vegetation growth.The dynamic of σ • over the second selected plot allows evaluating which channels have higher sensitivity to m v when the soil is beneath a vegetation canopy.

Temporal Single Regression Analysis
Because of the speckle noise affecting SAR images at raw resolution, operational applications are to be preferred using spatially aggregated images by averaging both in situ measures and the corresponding aggregated σ • values.Thus, temporal single regressions among σ • and SVV were analyzed to address the application of semi-empirical models over bare and vegetated plots; m v and h' were analyzed over bare soil, whereas, F v and LAI were also explored over vegetated areas.

Inter-Channel Spatial/Temporal Correlation
A target is expected exhibiting different dielectric and geometrical properties if sensed with distinct SAR configurations.Thus, a pixel based spatial correlation image, r sp , was evaluated for each plot using a moving kernel.A plot representative spatial correlation, r s , was obtained by averaging values of r sp co-localized to in situ measures.The calculation is extended to all available channel pairs and acquisition times, thus, generating an r s domain cube.Because the moving kernel is applied on spatially aggregated images, a minimum kernel size (3 × 3) was chosen to avoid exceeding plots' dimensions.A total of 45 channel pairs were analyzed; the r s cube was evaluated for each of the 9 monitored plots.
The dynamic between r s and SVV was analyzed via a single regression over 9 selected pairs of channels.The analysis determines in what extent r s could be useful to assess SVV changes; thus, results are shown in terms of plot temporal correlation coefficients, r t , out-coming from the r s vs. SVV regressions (Figure 4).

Data Aggregation
The IM first derivative suggests almost the same aggregation level for co-polarized, σ°pp, and cross-polarized, σ°pq, channels.Whereas, RS suggested by the IS analysis are higher at σ°pp than those at σ°pq with highest values shown by XHH, and lowest value exhibited by LHV.The RS equal to 20 m, as suggested by IS analysis, although even coarser then the value suggested by IM analysis (≈10 m), remains suitable to characterize the average plot size (~280 m).

Dynamic Analysis: All Plots
L bands show the highest ∆σ°avg values especially at cross-polarized channels.This suggests that σ° at L band could be highly influenced by SVV dynamics.The higher values of ∆σ°stdev also highlight that σ° is influenced by SVV depending on the cultivar; contrarily, lower ∆σ°stdev exhibited by Xpp and Cpp bands implies a weaker influence of the cultivar (Figure 5, left panel).

Data Aggregation
The I M first derivative suggests almost the same aggregation level for co-polarized, σ • pp , and cross-polarized, σ • pq , channels.Whereas, R S suggested by the I S analysis are higher at σ • pp than those at σ • pq with highest values shown by X HH , and lowest value exhibited by L HV .The R S equal to 20 m, as suggested by I S analysis, although even coarser then the value suggested by I M analysis (≈10 m), remains suitable to characterize the average plot size (~280 m).

Data Aggregation
The IM first derivative suggests almost the same aggregation level for co-polarized, σ°pp, and cross-polarized, σ°pq, channels.Whereas, RS suggested by the IS analysis are higher at σ°pp than those at σ°pq with highest values shown by XHH, and lowest value exhibited by LHV.The RS equal to 20 m, as suggested by IS analysis, although even coarser then the value suggested by IM analysis (≈10 m), remains suitable to characterize the average plot size (~280 m).

Dynamic Analysis: All Plots
L bands show the highest ∆σ°avg values especially at cross-polarized channels.This suggests that σ° at L band could be highly influenced by SVV dynamics.The higher values of ∆σ°stdev also highlight that σ° is influenced by SVV depending on the cultivar; contrarily, lower ∆σ°stdev exhibited by Xpp and Cpp bands implies a weaker influence of the cultivar (Figure 5, left panel).
Bare soils exhibited lower ∆σ • avg (particularly at L frequency) compared with those observable during the whole investigation period (where both bare and vegetated conditions occurred).
Over vegetation, the highest ∆σ • avg at L frequency was found for sugar beet, which is characterized by a broad-leaf structure; whereas X channels exhibited highest ∆σ • avg for barley and wheat; finally C channels exhibited highest ∆σ • avg for rape, barley and wheat.These differences confirm that vegetation structure determines the geometric properties of the target.

Dynamic Analysis: Two Selected Plots
The dynamic analysis for the plot 460 revealed that σ • pq exhibits lower values if compared to σ • pp at the same frequency.Peaks of σ • occur contextually to m v maxima (Figure 6, drying period I).As expected, σ • over bare soil (until the 11th of May) is linearly correlated to m v at all channels.With the growth of the vegetation two different σ • behaviors were observed: σ • at L (both σ • pp and σ • pq ) and C (σ • pq only) is highly related to m v until F v is lower than 3%.Whereas σ • pp at X and C frequencies were still influenced by m v dynamics until F v is lower than 10% (Figure 6, drying period II).
Remote Sens. 2017, 7, 677 9 of 22 Bare soils exhibited lower ∆σ°avg (particularly at L frequency) compared with those observable during the whole investigation period (where both bare and vegetated conditions occurred).
Over vegetation, the highest ∆σ°avg at L frequency was found for sugar beet, which is characterized by a broad-leaf structure; whereas X channels exhibited highest ∆σ°avg for barley and wheat; finally C channels exhibited highest ∆σ°avg for rape, barley and wheat.These differences confirm that vegetation structure determines the geometric properties of the target.

Dynamic Analysis: Two Selected Plots
The dynamic analysis for the plot 460 revealed that σ°pq exhibits lower values if compared to σ°pp at the same frequency.Peaks of σ° occur contextually to mv maxima (Figure 6, drying period I).As expected, σ° over bare soil (until the 11th of May) is linearly correlated to mv at all channels.With the growth of the vegetation two different σ° behaviors were observed: σ° at L (both σ°pp and σ°pq) and C (σ°pq only) is highly related to mv until Fv is lower than 3%.Whereas σ°pp at X and C frequencies were still influenced by mv dynamics until Fv is lower than 10% (Figure 6, drying period II).The difference between σ° collected on 19 April and 21 June is prevalently a measure of the vegetation biomass change; indeed, σ° at these two times were acquired at almost similar h' and mv conditions.It is noticeable that high positive σ° differences occur at cross-polarization, thus confirming outcomes of several other studies (e.g., [56]).
The dynamic analysis for the plot 450 (barley) revealed that all σ° at L frequency behave similarly to mv; σ° at C and X frequencies is less influenced by mv dynamics, thus highlighting that σ° at L frequency partially penetrated the canopy cover (Figure 7, drying periods I to III).In particular, σ°L,HH vs. mv was characterized by r 2 ≈ 0.27, whereas lower r 2 characterized regressions with other frequencies (r 2 ~ 10 −4 for both σ°C,HH and σ°X,HH vs. mv).Conversely, L frequencies were not linked to Fv (r 2 ~ 0.05); whereas, slightly higher r 2 (~0.15) characterized σ° vs. Fv at C frequency; finally, X channels were completely uncorrelated with Fv (r 2 ~ 10 −6 ).The difference between σ • collected on 19 April and 21 June is prevalently a measure of the vegetation biomass change; indeed, σ • at these two times were acquired at almost similar h' and m v conditions.It is noticeable that high positive σ • differences occur at cross-polarization, thus confirming outcomes of several other studies (e.g., [56]).
The dynamic analysis for the plot 450 (barley) revealed that all σ • at L frequency behave similarly to m v ; σ • at C and X frequencies is less influenced by m v dynamics, thus highlighting that σ • at L frequency partially penetrated the canopy cover (Figure 7, drying periods I to III).In particular, σ • L,HH vs. m v was characterized by r 2 ≈ 0.27, whereas lower r 2 characterized regressions with other frequencies (r 2 ~10 −4 for both σ • C,HH and σ • X,HH vs. m v ).Conversely, L frequencies were not linked to F v (r 2 ~0.05); whereas, slightly higher r 2 (~0.15) characterized σ • vs. F v at C frequency; finally, X channels were completely uncorrelated with F v (r 2 ~10 −6 ).

Temporal Single Regression Analysis
A first analysis was applied on bare soils having different h'.Single regressions among σ° vs. mv and h' were calculated separately for two plots (IDs 460 and 222) that remained bare until the first week of May; h' values ranged between 0.93-1.77and 1.42-2.05cm, for plots 460 and 222 respectively (Table 3).Correlations, r, are classified according to Evans, 1996 [57]; slopes, m, and intercepts, q, values could be employed to apply empirical or semi-empirical models (e.g., the WC model [17]).No significant correlations characterized the σ° vs. h' regressions (not shown).Noticeable, very strong and significant σ° vs. mv correlations were found for XVV (plot 460), CHH and for L frequencies (plot 222); while, strong (i.e., 0.6 < r < 0.8) correlations were not significant (p-value > 0.1).
For plot 460 two quasi-significant correlations were found at XHH and LVV, respectively.The highest σ° vs. mv correlations were found at L frequency (≈0.99).
A second analysis was applied on vegetated plots (Table 4).Noticeable, σ° vs. h' returned no significant correlations (not shown).Regarding σ° vs. mv, only moderate to strong correlations (0.4 < r < 0.8) were found as the capability of the signal of perceiving the mv is attenuated by the vegetation cover.Most significant σ° vs. mv correlations were found at L frequency, highlighting that the longer the wave the better the canopy penetration.A limited number of quasi-and significant correlations were found at C and X frequencies even if these were characterized by lower r values.

Temporal Single Regression Analysis
A first analysis was applied on bare soils having different h'.Single regressions among σ • vs. m v and h' were calculated separately for two plots (IDs 460 and 222) that remained bare until the first week of May; h' values ranged between 0.93-1.77and 1.42-2.05cm, for plots 460 and 222 respectively (Table 3).Correlations, r, are classified according to Evans, 1996 [57]; slopes, m, and intercepts, q, values could be employed to apply empirical or semi-empirical models (e.g., the WC model [17]).No significant correlations characterized the σ • vs. h' regressions (not shown).
For plot 460 two quasi-significant correlations were found at X HH and L VV , respectively.The highest σ • vs. m v correlations were found at L frequency (≈0.99).
A second analysis was applied on vegetated plots (Table 4).Noticeable, σ • vs. h' returned no significant correlations (not shown).Regarding σ • vs. m v , only moderate to strong correlations (0.4 < r < 0.8) were found as the capability of the signal of perceiving the m v is attenuated by the vegetation cover.Most significant σ • vs. m v correlations were found at L frequency, highlighting that the longer the wave the better the canopy penetration.A limited number of quasiand significant correlations were found at C and X frequencies even if these were characterized by lower r values.
Table 4. r of σ • vs. m v for plots covered by vegetation.Quasi-significant correlations (i.e., 0.05 < p-value < 0.1) are outlined; significant correlations (i.e., p-value < 0.05) are highlighted in light-grey; strong and significant correlations are also bolded; very weak correlations (r < 0.19) are not reported.Several very strong and significant σ • vs. F v correlations (Table 5) were found over maize (at C HV , L HH and L HV ) and sugar (all channels except L HH and L HV ).These plants are both characterized by bigger leaf dimensions compared to those characterizing other cultivars.Noticeable, σ • vs. F v regressions showed higher r than those characterizing σ • vs. m v (best r ~0.95 for σ • vs. F v at L HV over maize plot), thus confirming that: (i) σ • is mainly controlled by geometric and dielectric properties of the vegetation; (ii) the canopy limits the assessment of the properties of the underlying soil.Although several significant correlations were found for other cultivars, these were characterized by weak (0.2 < r < 0.4) or moderate (0.4 < r < 0.6) r values.The highest and significant σ • vs. LAI correlations were found again for sugar beet and maize; whereas, no significant correlations were found at X and C HH channels.Several significant correlations were found for other cultivars; diversely than σ • vs. F v , most of these exhibited a strong correlation (Table 6).For some channels, σ • resulted significantly correlated with both LAI and F v .Although σ • at L HH resulted also correlated to m v the higher p-value indicates a weaker significance of this correlation.This section discusses and analyzes r s domains for the two selected plots (see Sections 4.2.2 and 5.2.2).For the plot 460, r s domains were analyzed for increasing vegetation cover (for bare to vegetated) and decreasing m v (Figure 8).In particular, three different dates were selected: (i) 19

Inter-Channel Spatial/Temporal Correlation at Plot Scale
This section discusses and analyzes rs domains for the two selected plots (see Sections 4.2.2 and 5.2.2).For the plot 460, rs domains were analyzed for increasing vegetation cover (for bare to vegetated) and decreasing mv (Figure 8).In particular, three different dates were selected:  On 19 April the rs domain highlights that strong to very strong correlation occurred among σ° at L and X channels, weak to very strong correlations were observed among σ° at C channels.On 7 June, when mv slightly decreased and sugar beet started growing (Fv ~ 0.1); rs between σ° at some channels slightly increased (e.g., σ° at CHH and CVV).Finally, on the 26th of July σ° of most of the bands were strongly correlated (rs > 0.8).Whereas, lower correlations were observed among some σ° at CHV and σ°pq at L frequency (rs ~ 0.8).The decreasing of mv caused a noticeable increasing of rs for all channel pairs.For the field 450 (Figure 9) rs domains were analyzed at three selected times: (i) on 13 June, when Fv ~ 0.  On 13 June, the higher correlations among channels of the same frequency are observable.More specifically, moderate to very strong correlations occur among X, C and L frequency channels.Conversely, very weak to weak correlations characterized inter-frequency channels (e.g., C vs. L On 19 April the r s domain highlights that strong to very strong correlation occurred among σ • at L and X channels, weak to very strong correlations were observed among σ • at C channels.On 7 June, when m v slightly decreased and sugar beet started growing (F v ~0.1); r s between σ • at some channels slightly increased (e.g., σ • at C HH and C VV ).Finally, on the 26th of July σ • of most of the bands were strongly correlated (r s > 0.8).Whereas, lower correlations were observed among some σ • at C HV and σ • pq at L frequency (r s ~0.8).The decreasing of m v caused a noticeable increasing of r s for all channel pairs.For the field 450 (Figure 9) r s domains were analyzed at three selected times: (i) on 13 June, when F v ~0.9 and m v ~0.06 m 3 m −3 ; (ii) on 21 June, when F v slightly increased (F v ~0.95) and m v considerably increased to ~0.22 m 3 m −3 ; and, (iii) on 26 July, when both F v and m v considerably decreased to ~0.3 and ~0.06 m 3 m −3 respectively.bands were strongly correlated (rs > 0.8).Whereas, lower correlations were observed among some σ° at CHV and σ°pq at L frequency (rs ~ 0.8).The decreasing of mv caused a noticeable increasing of rs for all channel pairs.For the field 450 (Figure 9) rs domains were analyzed at three selected times: (i) on 13 June, when Fv ~ 0.9 and mv ~ 0.06 m 3 m −3 ; (ii) on 21 June, when Fv slightly increased (Fv ~ 0.95) and mv considerably increased to ~0.22 m 3 m −3 ; and, (iii) on 26 July, when both Fv and mv considerably decreased to ~0.3 and ~0.06 m 3 m −3 respectively.On 13 June, the higher correlations among channels of the same frequency are observable.More specifically, moderate to very strong correlations occur among X, C and L frequency channels.Conversely, very weak to weak correlations characterized inter-frequency channels (e.g., C vs. L frequencies).On 21 June, m v considerably increased (with almost constant F v ) causing a radical change in the C vs. L region; indeed, positive weak became negative weak correlations.On 26 July the m v and F v decreased to their minimum values causing the considerably increase of all r s values.
Based on the above mentioned evidences, it could be hypnotized that r s and SVV time series are correlated (temporal).
Thus, for 9 selected channel pairs the r s vs. SVV were computed over both bare soil (Table 7) and vegetated plots (Tables 8-11) to explore the determinability of SVV through r s .Results are shown in terms of correlation coefficients, r t .

Figure 1 .
Figure 1.LHV diachronic composition of the DEMMIN test-area (R: 24 May; G: 21 June; B: 26 July).Labels indicating crop IDs and cultivars are over-imposed.Nine crops were monitored over one or more plots (the plot identifier is reported between brackets): wheat (IDs 230 and 250), rape (IDs 101 and 140), barley (IDs 440 and 450), maize (ID 222) and sugar beet (IDs 102, 460).Sowing and harvesting dates are reported in Table2.Noticeable, these cultivars are characterized by different vegetation architecture.Main soil textures in the Görrmin area were loamy sand and sandy loam.Within this area, the 9 monitored plots are characterized by loamy sand texture.In particular, the soil texture of plots 222, 450 and 140 is predominantly loamy sand; plot 460 is characterized by loamy sand and slightly loamy sand soil; whereas the other plots are characterized by both loamy sand and strong loamy sand soils.

Figure 2 .
Figure 2. Temporal photo sequence of some Görmin's fields.Pictures were collected during the investigation periods by ZALF and LMU institutes; the white gridded panel (1 m × 1 m size, 10 cm × 10 cm grid resolution) allows estimating the vegetation height evolution.

Figure 2 .
Figure 2. Temporal photo sequence of some Görmin's fields.Pictures were collected during the investigation periods by ZALF and LMU institutes; the white gridded panel (1 m × 1 m size, 10 cm × 10 cm grid resolution) allows estimating the vegetation height evolution.
includes 120 images acquired in X, C and L bands (central wavelengths: 2, 5, and 21 cm respectively) in dual polarization (HH and VV for X band) and in quad-polarization (HH, VV, VH and HV for C and L bands).Flights were weekly carried out from the 9th of April to the 2nd of August by an airborne E-SAR (Experimental SAR), operated by the German Aerospace Center (Deutsches Zentrum für Luft-und Raumfahrt-DLR).The E-SAR sensor was on board a Do228 aircraft; although a total of 16 radar flights were executed during the AgriSAR 2006 campaign, the 12 performed in the E-W direction were considered in this research.The deployment of corner reflectors of 20 cm × 20 cm during one of the in situ campaigns allowed obtaining multi-look, geo-coded and calibrated σ • products at a raw spatial resolution, R S , of 2 m.Remote Sens. 2017, 7, 677 6 of 22

Figure 3 .
Figure 3. Temporal dynamic of spatially averaged mv, h', Fv and LAI.Blue bars mark mv peaks separating consecutive drying periods occurred at all crops except for maize in which the second drying period was shorter (see the dashed bar).

Figure 3 .
Figure 3. Temporal dynamic of spatially averaged m v , h', F v and LAI.Blue bars mark m v peaks separating consecutive drying periods occurred at all crops except for maize in which the second drying period was shorter (see the dashed bar).

Finally, errors 22 Figure 4 .
Figure 4. Flow-chart of the inter-channel spatial/temporal correlation analysis.The flow-chart is applied to each plot and for all four SVV (mv, h', LAI and Fv).The 9 selected channel pairs are bounded in red within the rs domain cube.

Figure 4 .
Figure 4. Flow-chart of the inter-channel spatial/temporal correlation analysis.The flow-chart is applied to each plot and for all four SVV (m v , h', LAI and F v ).The 9 selected channel pairs are bounded in red within the r s domain cube.

5. 2 .
Dynamic Analyses 5.2.1.Dynamic Analysis: All Plots L bands show the highest ∆σ • avg values especially at cross-polarized channels.This suggests that σ • at L band could be highly influenced by SVV dynamics.The higher values of ∆σ • stdev also highlight that σ • is influenced by SVV depending on the cultivar; contrarily, lower ∆σ • stdev exhibited by X pp and C pp bands implies a weaker influence of the cultivar (Figure 5, left panel).Remote Sens. 2017, 7, 677 8 of 22

Figure 4 .
Figure 4. Flow-chart of the inter-channel spatial/temporal correlation analysis.The flow-chart is applied to each plot and for all four SVV (mv, h', LAI and Fv).The 9 selected channel pairs are bounded in red within the rs domain cube.

Figure 5 .
Figure 5. Observed ∆σ • avg and corresponding ∆σ • stdev (dashed lines) for all available channels are shown on the left panel; ∆m v , avg , ∆F v,avg (dark-grey vertical bars, primary axis), ∆LAI avg and ∆h' avg (bright-grey vertical bars, secondary axis), and corresponding ∆SSV stdev (dashed lines) are shown on the right panel.

Figure 6 .
Figure 6.SVV (mv and Fv) and σ° temporal dynamics for the plot 460 (sugar beet); co-polarized σ° are shown in the upper left panel, whereas cross-polarized σ° are in the upper right panel.Vertical blue bars mark mv peaks separating three consecutive drying periods; the green vertical bar marks the time in which the increase of Fv began.

Figure 6 .
Figure 6.SVV (m v and F v ) and σ • temporal dynamics for the plot 460 (sugar beet); co-polarized σ • are shown in the upper left panel, whereas cross-polarized σ • are in the upper right panel.Vertical blue bars mark m v peaks separating three consecutive drying periods; the green vertical bar marks the time in which the increase of F v began.

Figure 7 .
Figure 7. SVV (mv and Fv) and σ° temporal dynamics for the plot 450 (barley); co-polarized σ° are shown in the upper left panel, whereas cross-polarized σ° are in the upper right panel.Vertical blue bars mark mv peaks separating three consecutive drying periods.

Figure 7 .
Figure 7. SVV (m v and F v ) and σ • temporal dynamics for the plot 450 (barley); co-polarized σ • are shown in the upper left panel, whereas cross-polarized σ • are in the upper right panel.Vertical blue bars mark m v peaks separating three consecutive drying periods.

Figure 8 .
Figure 8. rs domain for plot 460 at three selected dates: 19th April (left panel), 7th June (central panel) and 26th July (right panel).The dichromatic color ramp describes very strong negative to very strong positive correlations (from blue to grey).Values of rs rounded to first decimal place are also reported.

Figure 9 .
Figure 9. rs domain for plot 450 three selected times: 13 June (left panel); 21 June (center panel) and 26 July (right panel).The dichromatic color ramp describes very strong negative to very strong positive correlations (from blue to grey).Values of rs rounded to first decimal place are also reported.

Figure 8 .
Figure 8. r s domain for plot 460 at three selected dates: 19 April (left panel), 7 June (central panel) and 26 July (right panel).The dichromatic color ramp describes very strong negative to very strong positive correlations (from blue to grey).Values of r s rounded to first decimal place are also reported.

Figure 9 .Figure 9 .
Figure 9. rs domain for plot 450 three selected times: 13 June (left panel); 21 June (center panel) and 26 July (right panel).The dichromatic color ramp describes very strong negative to very strong positive correlations (from blue to grey).Values of rs rounded to first decimal place are also reported.On 13 June, the higher correlations among channels of the same frequency are observable.More specifically, moderate to very strong correlations occur among X, C and L frequency channels.Conversely, very weak to weak correlations characterized inter-frequency channels (e.g., C vs. L frequencies).On 21 June, mv considerably increased (with almost constant Fv) causing a radical Figure 9. r s domain for plot 450 three selected times: 13 June (left panel); 21 June (center panel) and 26 July (right panel).The dichromatic color ramp describes very strong negative to very strong positive correlations (from blue to grey).Values of r s rounded to first decimal place are also reported.

Table 2 .
Sowing and harvesting dates for main crops during the investigation period; plots IDs are reported within brackets.

Table 2 .
Sowing and harvesting dates for main crops during the investigation period; plots IDs are reported within brackets.Data have been collected between April and August 2006 in the framework of the AgriSAR 2006 project (funded by the European Space Agency, ESA) primarily planned to address programmatic needs of Sentinel-1 two-satellite constellation.AgriSAR 2006 campaign was specifically tailored to investigate σ • dynamic throughout the crop-growing season.The dataset includes weekly in situ measures and airborne SAR and optical images.

Table 5 .
r of σ • vs. F v for plots covered by vegetation.Quasi-significant correlations are outlined; significant correlations are highlighted in light-grey; very strong and significant correlations are highlighted in dark-gray with values in bold; very weak correlations are not reported.

Table 6 .
r of σ • vs. LAI for plots covered by vegetation.Significant correlations are highlighted in light-grey; strong and significant correlations are also bolded; very strong and significant correlations are highlighted in dark-grey with values in bold; very weak correlations are not reported.

Table 7 .
r t , over bare soils occurring during the study period; quasi-significant correlations (i.e., characterized by 0.05 < p-value < 0.1) are outlined; very weak correlations (r < 0.19) are not reported.

Table 8 .
r t vs. h' temporal correlations, r t , over the whole period for different crops; significant strong correlations (p-value < 0.05, 0.6 < r < 0.8) are in light-gray highlighted with values in bold; quasi-significant correlations (0.05 < p-value < 0.1) are outlined; very weak correlations (r < 0.19) are not reported.