Comparison of different polarimetric decompositions for soil moisture retrieval over vegetation covered agricultural area

Remote Sensing of Environment 199 (2017) 120–136

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Comparison of different polarimetric decompositions for soil moisture retrieval over vegetation covered agricultural area☆ Hongquan Wang ⁎, Ramata Magagi, Kalifa Goita Centre d'Applications et de Recherches en Télédétection (CARTEL), Département de Géomatique Appliquée, Université de Sherbrooke, Sherbrooke, Québec J1K2R1, Canada

a r t i c l e

i n f o

Article history: Received 14 November 2016 Received in revised form 26 June 2017 Accepted 10 July 2017 Available online xxxx Keywords: Soil moisture Vegetation Agricultural fields Ground measurements Polarimetric decompositions Retrieval Performance SMAPVEX12 UAVSAR

a b s t r a c t This study investigates and compares the potential of three model-based polarimetric decompositions, namely those developed by Freeman-Durden (1998), Hajnsek et al. (2009) and An et al. (2010), for soil moisture retrieval over agricultural fields covered by several crops. The volume scattering component was first removed from the full coherency matrix. Then, in order to reduce the effect of the incidence angle on the retrieval results, a normalization process at a reference incidence angle was conducted for the first time, on the dominant surface or dihedral scattering component from which the soil moisture was retrieved. The time series of Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR) data and the ground measurements of soil and vegetation characteristics collected during the Soil Moisture Active Passive (SMAP) Validation Experiment in 2012 (SMAPVEX12) were used to compare the three decomposition methods with respect to the scattering mechanisms and the soil moisture retrieval performances. The results show that the performance of each decomposition method for soil moisture retrieval depends on the crop types and the crop phenological stages. Indeed, Freeman-Durden model provided the best results for corn and wheat, Hajnsek decomposition performed well for canola, while better results were obtained for soybean using An decomposition. At the early growth stage, both the surface and dihedral scattering components contributed to retrieve the soil moisture, while at a later crop development, the surface scattering component is almost the only scattering mechanism from which soil moisture was retrieved. Thus, the best performance for soil moisture retrieval was obtained a) at the early crop development stage from Hajnsek decomposition which better integrated the dihedral component and b) at a later growth stage from An decomposition which enhanced the surface scattering. Finally, an overall soil moisture underestimation with RMSE of 0.06–0.11 m3/m3 was observed from the three decompositions, and the highest retrieval rate of 33%–39% was obtained from An decomposition as a result of the enhanced surface scattering. © 2017 Elsevier Inc. All rights reserved.

1. Introduction Soil moisture is a crucial parameter for studying the hydrological processes, and is considered as an essential climate variable by the Global Climate Observing System (Bojinski et al., 2014; GCOS107, 2006). Remote sensing technique provides a powerful way to estimate the soil moisture at several high spatial and temporal resolutions. In contrast to optical remote sensing, Synthetic Aperture Radar (SAR) is independent of sun light, and the generated microwave signal can penetrate the soils, allowing the estimation of soil moisture and its timely monitoring. Furthermore, the polarimetric SAR increases the observation space, leading to a potential enhancement of soil moisture retrieval by ☆ Manuscript received November, 2016. This work was supported in part by the Canadian Space Agency Class Grant and Contribution Program as part of the Canadian plan to spatial missions of soil moisture, and in part by the Natural Sciences and Engineering Resources Council of Canada. ⁎ Corresponding author. E-mail addresses: [email protected] (H. Wang), [email protected] (R. Magagi), [email protected] (K. Goita).

http://dx.doi.org/10.1016/j.rse.2017.07.008 0034-4257/© 2017 Elsevier Inc. All rights reserved.

considering the multiple signatures and their consistency (Cloude, 2010; Cloude and Pottier, 1997). Over bare soils, successful retrieval performances may be obtained by either theoretical scattering models (Allain et al., 2004; Allain et al., 2002; Fung and Chen, 2004; Fung and Li, 1992; Shi et al., 1997; Ulaby et al., 1982) or empirical approaches (Baghdadi et al., 2012a; Baghdadi et al., 2012b; Baghdadi et al., 2006; Dubois et al., 1995; Oh, 2004; Oh et al., 1992, 2002; Sahebi and Angles, 2010; Wang et al., 2016a; Wang et al., 2015; Zribi and Dechambre, 2002). However, for the agricultural areas which are seasonally covered by different crops, the backscattering from vegetation and soils are coherently superimposed in the SAR signature, complicating thus the soil moisture retrieval. In order to obtain the ground scattering components associated with the soil moisture, many efforts were devoted in the past decades. For instance, the water cloud model (Attema and Ulaby, 1978; Gherboudj et al., 2011; Kumar et al., 2012; Kumar et al., 2015) assumes the vegetation layer as an uniform cloud composed of water particles with random spatial distribution. Consequently, the canopy backscattering coefficient is modeled as an incoherent summation of the scattering contribution

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from the vegetation, the underlying soil and the multiple scattering between the vegetation and soil surface. Furthermore, polarimetric decomposition (Cloude and Pottier, 1996) was established to isolate the individual scattering mechanism (e.g. surface, dihedral and volume scattering) from the polarimetric SAR signature. Among several types of polarimetric decomposition techniques (e.g. coherent decomposition using scattering matrix and Eigen-based incoherent method), the model-based incoherent decomposition especially has potential for the soil moisture retrieval over vegetation covered area, since each scattering component is physically interpreted. In this sense, Freeman and Durden (1998) model-based decomposition simulates i) the surface scattering component using Bragg scattering from relative smooth surface (ks b 0.3, with wavenumber k and surface root mean square height s), ii) the dihedral scattering component as the backscattering from two orthogonal surfaces with different dielectric constants, and iii) the volume scattering using dipoles with a random orientation. Thus, once the volume scattering is removed from the total signal, the soil moisture information is contained in the remaining surface and dihedral scattering components. The appropriate modeling of the volume component is crucial for the polarimetric decomposition, and consequently for the application in soil moisture estimation (Cui et al., 2014; van Zyl et al., 2011). However, prior the polarimetric decomposition, An et al. (2010) applied the deorientation process to the coherency matrix in order to remove the disturbance of stochastic orientation angles on the polarimetric scattering in each pixel. The deorientation process minimizes the cross-polarized scattering power and maximizes the co-polarized scattering power, which is expected to benefit to soil moisture retrieval from the ground scattering component. Nevertheless, so far, the Freeman-Durden decomposition and its modified formulation which accounts for the deorientation (An et al., 2010) are widely used for image classification and the identification and interpretation of the scattering mechanisms (Adams et al., 2013; Cui et al., 2012; Singh et al., 2013; Zhang et al., 2015). Very few efforts focused on quantitative soil moisture retrieval. Indeed, a pioneer study of Hajnsek et al. (2009) and others investigations presented great advances in the potential of model-based decomposition for soil moisture retrieval over vegetation covered agricultural fields. Therefore, based on the current progress in polarimetric decompositions and considering the encouraging results previously obtained, the objective of this study is to investigate and compare the potential of Freeman and Durden (1998), Hajnsek et al. (2009) and An et al. (2010) decompositions for quantitative soil moisture retrieval. It is understood that each algorithm has its advantage and limitation. Nevertheless, considering the spatiotemporal variability of crop characteristics with the crop types and the phenological development stages, we assumed a possibility to appropriately remove the volume scattering from the decomposition algorithms, and use resulting surface or dihedral scattering component for soil moisture retrieval. In this paper, Section 2 describes the time series of the Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR) data and ground truth measurements of interest collected in the framework of Soil Moisture Active Passive Validation Experiment in 2012 (SMAPVEX12). The three polarimetric decomposition methods for soil moisture retrieval are described in Section 3. The results are analyzed and discussed in Section 4 and the main conclusion is presented in Section 5. 2. Study site and dataset description

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The landscape is characterized by an extremely flat topography, and the main crops over the agricultural area are canola (13.2% of the area), corn (7%), soybean (6.7%) and wheat (32.2%). 2.2. UAVSAR time series In the framework of SMAPVEX12, the polarimetric UAVSAR image acquisitions covered 14 dates between June 17 and July 17, 2012, a nominal swath of 21 km and 25°–65° incidence angle. In this study, the multi-look product (MLC) of flight line #31606 with spatial resolution of 5.0 m in range and 7.2 m in azimuth is used. This flight line covers all the investigated agricultural fields. The coherency matrix [T] was extracted using the PolSARpro5.0 software and a boxcar filter with 7 × 7 window size is applied to reduce the speckle effect (Lee and Pottier, 2009). As the terrain is flat, no topographic correction was implemented. 2.3. Ground measurements In coincidence with the UAVSAR acquisitions, the SMAPVEX12 ground campaign was carried out over 55 agricultural fields between June 6 and July17 2012 to measure both the soil and vegetation parameters. More details about these measurements can be found in McNairn et al. (2015) and in SMAPVEX12 website (https://smapvex12. espaceweb.usherbrooke.ca/). 1) Volumetric soil moisture was measured at 6 cm depth using calibrated hand-held Hydra probes. For each field, sixteen points were sampled with three replicate measurements at each point in order to obtain a representative soil moisture value. The daily rainfall was also recorded to understand the soil moisture variability. As shown in Fig. 2, there is an agreement between the temporal evolution of the mean value of soil moisture measurements and the rainfall amount. A peak of mean soil moisture value usually follows a rain event, then the lack of precipitation and/or evaporation process leads to the decreasing trend of soil moisture (Fig. 2). 2) On each field, the surface roughness was measured at two locations using a digital camera and a 1-m long profilometer installed in the look direction of UAVSAR. At each location, the roughness parameters RMS height s and autocorrelation length l were determined from the digitized pictures of 3-m profiles. The mean values of s and l are 1.22 cm and 9.25 cm for canola field, 1.21 cm and 9.75 cm for corn field, 0.91 cm and 11.66 cm for soybean field, 1.12 cm and 11.75 cm for wheat field. The observed surface roughness variability over different fields was mainly caused by the tillage and sowing practices. 3) Crop growth parameters such as height and biomass were measured in order to account for the vegetation effect on soil moisture retrieval from UAVSAR signature. For instance, Fig. 3 shows the temporal variation of measured crop height, which can be successfully fitted to the classical logical growth equation (Yin et al., 2003): f (x) = Hmax / (1 + e−n(x − m)), with maximum height (Hmax), sigmoid midpoint day (m) and growth speed indicator (n). It also proves the robustness of SMAPVEX12 ground measurements on vegetation growth. In addition, for a given crop type especially canola, there is a variability between different fields due to the difference in soil and plant growth status.

2.1. Study site 3. Methods The study site is the SMAPVEX12 experimental area (Fig. 1) which covers 15 km × 70 km (49°20′–50°0′N, 97°40′–98°30′W) and is located at the bottom of the Red River watershed in Winnipeg, Canada. The area experiences a humid continental climate with an average annual precipitation of approximately 505 mm (http://www.winnipeg. climatemps.com/). It consists of pasture, forests and agricultural areas.

The interest in the model-based decompositions for soil moisture retrieval relies on the physical interpretation of each scattering components. In this context, the present study aims to compare the suitability of three model-based polarimetric decomposition algorithms, namely Freeman and Durden (1998), Hajnsek et al. (2009)

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Fig. 1. SMAPVEX12 study area and the location of the ground measurement points.

and An et al. (2010) decompositions for soil moisture retrieval over several agricultural crops with different phenological development stages. These models are referred as Freeman-Durden, Hajnsek and An decomposition, respectively in the paper. In the following, the modeling processes of surface, dihedral and volume scattering components were considered in the three decomposition algorithms. Then, the soil moisture retrieved from the different methods were compared using SMAPVEX12 data.

[T3] into three submatrices associated to three uncorrelated scattering mechanisms: 2

T 11 ½T3 ¼ 4 T 12 0

T 12 T 22 0

2 2 2 3 3 0 1 β 0 jα j 0 5 ¼ f s 4 β jβ j 2 0 5 þ f d 4 α  T 33 02 0 03 0 2 0 0 fv 4 þ 0 1 05 4 0 0 1

α 1 0

3 0 05 0 ð1Þ

3.1. Model-based polarimetric decompositions Freeman-Durden decomposition: Based on the reflection symmetry assumption for natural media, this model expands the coherency matrix

The first term corresponding to surface scattering mechanism is modeled by the surface scattering amplitude (fs) and β which is the normalized difference of Bragg scattering between horizontal (HH) and

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vertical (VV) polarizations. The parameters fs and β depend on the soil dielectric constant (εs) and the signal incidence angle (θ); in addition, fs is also influenced by surface roughness. However, Bragg model is only valid for limited surface roughness conditions, and the depolarization due to high surface roughness values is neglected. The second term corresponds to the dihedral scattering mechanism, and is modeled by the dihedral scattering amplitude (fd), and α which is the normalized difference of Fresnel coefficients in HH and VV polarizations for a pair of orthogonal surfaces with different dielectric materials. Consequently, the parameters fd and α depend on soil (εs) and vegetation (εt) dielectric constants, and on incidence angle (θ). Like fs, the dihedral intensity fd is also influenced by surface roughness. The third term corresponding to volume scattering mechanism is modeled as a unique scattering contribution from a cloud of randomly orientated dipoles, with a volume scattering amplitude (fv). Hajnsek decomposition: Considering the reflection symmetry, the coherency matrix [T3] is also decomposed into three scattering components: 2 3 1 β  sincð2δÞ 0 3 T 11 T 12 0 6 7 1 2 6 7 0 ½T3 ¼ 4 T 12 T 22 0 5 ¼ f s 6 β sincð2δÞ 2 jβ j ð1 þ sincð4δÞÞ 7 4 5 1 2 0 0 T 33 0 0 jβj ð1− sincð4δÞÞ 2 2 2 3 2 3 V 11 V 12 0 jα j α 0 þf d jLs j2 4 α  1 0 5 þ f v 4 V 12 V 22 0 5 0 0 V 33 0 0 0 2

ð2Þ The surface scattering mechanism, represented by the first term, is modeled by the X-Bragg model which considers a wider surface roughness validity range (ks b 1, with k and s, the wavenumber and the surface rms height, respectively) than the Bragg model (ks b 0.3) used in the Freeman-Durden method. The depolarization of surface roughness was introduced into the surface scattering component by rotating the Bragg surface coherency matrix around the Line Of Sight (LOS). The distribution width of the rotation angle is denoted as δ which governs both the depolarization effect and the cross polarization power. The dihedral scattering component represented by the second term includes the

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attenuation effect of surface roughness through the dihedral scattering correction factor Ls. The volume scattering mechanism represented by the third term is extended from dipoles with only one fixed random orientation in Freeman-Durden method (Eq. (1)) to dipoles oriented horizontally, vertically and randomly (Eq. (3)). The volume coherency matrices [Tvh, Tvv, Tvr] associated to these three spatial orientations are given as 2

3 0 V 11 V 12 ½Tvvol  ¼ fv4 V 12 V 22 0 5 03 V 33 2 0 2 0 0 f ½Tvr  ¼ v 4 0 1 0 5; 4 0 0 1

2 15 5 fv 4 5 7 → ½Tvv  ¼ 30 0 0 2 15 −5 f ½Tvh  ¼ v 4 −5 7 30 0 0

3 0 0 5; 83 0 05 8

ð3Þ

An decomposition: to restrict the negative powers found in the scattering components, a deorientation method is proposed by An et al. (2010) for more accurate polarimetric decomposition. The full coherency matrix [T] is rotated around LOS by an angle ϕ, which minimizes the cross polarization scattering powers and maximizes the co-polarization scattering powers. After applying the deorientation process, identical scatterers with different orientation angles result in similar coherency matrix [T3](ϕ). 2

1 0 cosð2ϕÞ ½T3ðϕÞ ¼ 4 0 02 − sinð2ϕÞ 1 0  4 0 cosð2ϕÞ 0 sinð2ϕÞ

32 0 T 11 sinð2ϕÞ 54 T 12 cosð2ϕÞ 3 0 0 − sinð2ϕÞ 5 cosð2ϕÞ

T 12 T 22 0

3 0 0 5 T 33 ð4Þ

Then the rotated [T3](ϕ) is assumed to satisfy the reflection symmetry and is modeled as an incoherent summation of three scattering mechanisms: the surface and dihedral scattering mechanisms of An decomposition are similar to those of Freeman-Durden, but the volume scattering component is modeled using a pure random volume

Fig. 2. Temporal evolution of mean values of soil moisture measurements and rainfall.

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Fig. 3. Temporal evolution of measured crop (canola, corn, soybean and wheat) height.

coherency matrix with equal eigenvalues and an entropy value of 1. 2

T 11 ½T3ðϕÞ ¼ 4 T 12 0

T 12 T 22 0

2 2 2 3 3 0 1 β 0 jα j 2 4 5 5 0 ¼ f s β jβ j 0 þ f d 4 α  T 33 02 0 03 0 1 0 0 fv 4 þ 0 1 05 3 0 0 1

α 1 0

3 0 05 0 ð5Þ

3.2. Soil moisture retrieval from model-based polarimetric decompositions In this study, soil moisture was retrieved from the three incoherent polarimetric decomposition methods applied to the time series of UAVSAR data acquired over SMAPVEX12 agricultural fields. The results obtained under several vegetation cover conditions were compared, validated, and discussed according to the advantage and limitations of each method. The rationale here is that, the shape and spatial orientation of different crop types vary with the phenological development stages. Thus, the performance of the decomposition methods for soil moisture retrieval also may vary with the crop types and the growth seasons. Fig. 4 shows the schematic diagram of the retrieval methods using the above described three polarimetric decompositions. 3.2.1. Volume scattering removal from the coherency matrix [T] First, the volume scattering contribution in the full coherency matrix [T] was computed (dashed part in Fig. 4) using the three different decomposition methods. It was then removed from [T] to obtain the ground scattering component which is composed of surface and dihedral scattering. For Freeman-Durden decomposition, the unique random volume coherency matrix in Eq. (1) was subtracted from [T]. For Hajnsek decomposition, the orientation of the crop (horizontal, vertical and random) was determined according to the value of the scattering ratio Pr (Yamaguchi et al., 2005), then the corresponding volume coherency matrix in Eq. (3) was selected to account for the volume scattering contribution. Finally, for An decomposition, the original [T] matrix was rotated around the LOS with an angle ϕ which minimizes the power

of T33 element of the Eq. (5). Then a pure random volume coherency matrix was considered for the vegetation layer. In addition to the volume scattering contribution, the volume scattering intensity fv was also computed for the three different decompositions by solving the system of Eqs. (1), (2) and (5) respectively. After removing the volume scattering from [T], the soil moisture was retrieved from the dominant scattering mechanism in the remaining ground matrix. It was determined using a criteria on Re (ShhSvv⁎). In case of dominant surface scattering mechanism, the Bragg scattering (β) was extracted for the three decompositions. For dominant dihedral scattering mechanism, the Fresnel scattering α and the dihedral intensity fd were extracted, and both α and fd were jointly used to decouple the soil moisture and vegetation water content. The soil moisture retrieval from dominant surface and dihedral components are complementary to each other. 3.2.2. Normalization of the polarimetric parameters β, α, and fd The sensitivity of the polarimetric SAR signal to geophysical parameters is highly dependent on incidence angle. For instance, as the incidence angle increases, the β parameter becomes more sensitive to soil moisture (Fig. 5), but the number of valid β values decreases (detail in Subsection 4.3). Thus, the normalization of β from low to high incidence angle allowed to enhance the signal sensitivity to soil moisture, and maintain the original number of valid β values at the same time. The normalization of polarimetric parameters allowed us to compare the information originally sensed under different incidence angles. In this study, the 40° incidence angle corresponding to the mid-swath was selected as a constant reference incidence angle. Indeed, according to Mladenova et al. (2013) and Wagner et al. (1999), the mid-swath incidence angle is the best reference for normalization in order to minimize the overall systematic errors in the data. In this research, the extracted surface parameter (β) and dihedral parameters (α, fd) were normalized using the histogram method (Mladenova et al., 2013) in order to reduce the incidence angle effect on the estimated soil moisture. The histogram method preserves the variability of the original signature in contrast to the method of cumulative frequencies. According to the performance of this method on the backscattering coefficients, Mladenova et al. (2013)

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Fig. 4. Schematic diagram of soil moisture retrieval over agricultural fields using three polarimetric decomposition methods. The dashed box represents the different processes for volume scattering mechanism. The normalization process is detailed in the right dotted box.

obtained a bias of 0 dB when comparing the normalized values to observations made at 40° incidence angle from other flight lines. In this study, for a given pixel with a land cover type vc, observed at an original incidence angle θ, the normalized βnorm,vc value at 40° is calculated from the original βθ,vc as follows (Mladenova et al., 2013): ^ o β norm;vc ¼ β40o ;vc þ β 40 ;vc

βθ;vc −βθ;vc ^ β

Following Hajnsek et al. (2009) and Jagdhuber et al. (2013), the retrieval method was based on the minimization of the difference between β, α and fd simulated values (βsimu, αsimu and fdsimu) and their corresponding normalized values extracted from UAVSAR data (βdata, αdata and fddata). For the dominant surface scattering case, β was simulated at 40° incidence angle by varying the soil dielectric constant εs from a minimum

ð6Þ

θ;vc

^ o are the mean value and the standard deviation where β40o ;vc and β 40 ;vc of the parameter β at 40° incidence angle for a land cover vc, βθ;vc and ^ β θ;vc are the mean value and the standard deviation of β at the original incidence angle θ for the same land cover vc. They were computed in advance for every 1° incidence angle step within the whole incidence angle range and for every land cover vc. The normalization diagram presented in Fig. 4 clearly shows that the parameters considered in Eq. (6) are different from one vegetation type to another one. However, the pixels with β = 0 must be discarded in the normalization. In addition, the same histogram method (Mladenova et al., 2013) was used to normalize the dihedral scattering parameters (α and fd) at 40° incidence angle. 3.2.3. Soil moisture retrieval process Depending on the dominant scattering mechanism in the remaining ground scattering component, the soil moisture was retrieved from the normalized β values (for dominant surface scattering case) or from the normalized α and fd values (for the dominant dihedral scattering case).

Fig. 5. Effect of incidence angle on the sensitivity of surface scattering parameter β to soil moisture.

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value of 2 to a maximum of 50, with a step of 0.5, using the following expression: βsimu

R −Rv ¼ h Rh þ Rv

ð7Þ

where the Bragg coefficients Rh and Rv are given as: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cosθ− εs −sin2 θ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rh ¼ cosθ þ εs −sin2 θ    ðεs −1Þ sin2 θ−εs 1 þ sin2 θ Rv ¼   qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 : ε s cosθ þ ε s −sin2 θ

They depend on the soil dielectric constant (εs) and the signal incidence angle (θ). The optimal soil dielectric constant εs was obtained by minimizing a cost function C s ¼ jβdata −βsimu j. For dominant dihedral scattering, which depends on both the soil and vegetation parameters, α and fd were simulated at 40° incidence angle using the following equations: Rsh Rth −Rsv Rtv eiφ Rsh Rth þ Rsv Rtv eiφ  2 ¼ 0:5Rsh Rth þ Rsv Rtv eiφ 

α simu ¼ fdsimu

ð8Þ

where φ is the phase difference between horizontal and vertical polarizations, and the Fresnel coefficients are given by: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cosθi − εi −sin2 θi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rih ¼ cosθi þ εi −sin2 θi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi εi cosθi − εi −sin2 θi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Riv ¼ 2 εi cosθi þ ε i −sin θi The subscript i denotes soil (s) and vegetation (t), with θt = π/2 − θs. For the simulations the soil dielectric constant εs was varied from 2 to 50, and the vegetation dielectric constant εt was varied from 2 to 40. A step of 0.5 was used in all cases. The optimal soil dielectric constant εs was obtained by minimizing a cost function C d ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 jα data −α simu j2 þ jfddata −fdsimu j . Indeed, via the two-dimensional optimization of Cd, both the soil and vegetation dielectric constants can be estimated from the dihedral scattering component, but only the εs for soil was considered and validated in this study. The estimated optimal soil dielectric constant εs was then converted into soil moisture using a polynomial function (Topp, 1980). The retrieved results were then validated using ground measurements of soil moisture. The advantages and limitations of each polarimetric decomposition were analyzed and discussed. 4. Results and discussion This section compares the results obtained by applying the three polarimetric decompositions to the time series of UAVSAR data acquired during SMAPVEX12. The scattering mechanisms are first analyzed, then followed by the results of ground scattering components normalized at 40° from which the soil moisture was retrieved. A comparison conducted between the soil moisture obtained from the three polarimetric decompositions, and the ground measurements of soil moisture were used to validate the performance of each method for soil moisture retrieval.

4.1. Spatiotemporal variability of scattering mechanisms In Figs. 6–7, the RGB color composite of the surface, dihedral and volume scattering powers derived using the different decompositions are compared for the beginning (2012-06-17) and the end (2012-07-17) of SMAPVEX12 campaign. A land classification map (https:// smapvex12. espaceweb.usherbrooke.ca/) with overall accuracy of 82% is also provided to link the scattering characteristics to vegetation types. With the crop growth during the campaign, the overall surface scattering power decreased while the volume scattering power increased. Thus, all the three methods seem to monitor the variation of scattering mechanisms induced by the crop growth. For a single UAVSAR acquisition, the scattering mechanisms in Freeman-Durden and Hajnsek decompositions have similar spatial distribution patterns. However, for An decomposition, the volume scattering power is lower and the surface scattering power is higher than those obtained with the other methods. This is mainly a consequence of the pure random matrix used as volume model in An decomposition. Although the deorientation is to reduce the cross polarization power (An et al., 2010), its decreasing effect on the volume power of agricultural crops is less pronounced than that of the pure random volume matrix. In addition, the incidence angle effect on the scattering mechanisms is pronounced: the surface scattering power at low incidence angle (near range) is stronger than at high incidence angle (far range). For agricultural areas (after masking out the forest and urban regions), the histograms of the scattering powers shown in Figs. 6 and 7 are compared in Fig. 8. For both dates (2012-06-17 and 2012-07-17), they confirm the higher surface and lower volume scattering powers for An decomposition. However, the dihedral scattering power is similar (20% of the total signal) for the three methods. To understand the behavior of the scattering powers during the crops growth, Fig. 9 presents the temporal evolution of the volume, dihedral and surface powers along with the measured crop height for the investigated crop types (canola, corn, soybean and wheat). For each scattering power, it can be seen that the temporal patterns are similar for the three decompositions so as the magnitude of the dihedral power. Except for canola, the volume and surface powers obtained from Freeman-Durden and Hajnsek are almost superimposed for other crops. This mainly stems from the difference in crop orientation (horizontal, vertical and random). Indeed, according to Wang et al. (2016b), during the SAMPVEX12 campaign, the dominant orientation is vertical over canola fields, while it is random over corn, soybean and wheat fields. Thus, if the crop orientation is determined as random by Hajnsek decomposition, the results become similar to those of Freeman-Durden decomposition, as the same volume matrix (Eqs. (1), (3)) is used for the random structure by both models. It can be seen from the results that the volume scattering power in Freeman-Durden and Hajnsek decompositions seems too high. Indeed, in addition to the vegetation, the depolarization by the surface roughness and the randomly distributed orientation angles (due to the surface tilt in azimuth direction (Lee et al., 2000; Lee et al., 2002)) also contribute to the cross-polarization power. But, these effects are not taken into account in Freeman-Durden method according to Eq. (1), thus leading to the overestimation of volume power. Although Hajnsek method in Eq. (2) includes the effect of depolarization from surface roughness, the volume scattering power remains high as a result of the dominant random vegetation orientation (Wang et al., 2016b). The temporal variations of the scattering mechanisms are influenced by several factors, including the crop height, biomass and vegetation water content (Wang et al., 2016c). These parameters showed different temporal behaviors from one crop to another in the study area. While for the soybean, height and water content increased during the growing period, for wheat the water content was almost stable during the whole development stage (Wang et al., 2016c). The combined effects of these factors may explain the differences observed in the temporal behaviors

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Fig. 6. RGB color composite of three scattering mechanisms (R: dihedral; G: volume; B: surface) obtained using the polarimetric decompositions of (a) Freeman; (b) Hajnsek and (c) An on 2012-06-17. (d) Classified image of the study area.

of the scattering mechanisms. For some crop types, such as the canola in this study, when the growth is close to the mature stage, the volume scattering decreases, while the surface scattering increases. This results from the crops' drying out, which improves the microwave signal penetration (Hajnsek et al., 2009; Wang et al., 2016c).

4.2. Dominant scattering cases in the ground scattering component The ground scattering component is composed of surface and dihedral scatterings which are complementary to each other for soil moisture retrieval. In case that the condition Re (ShhSvv⁎) N 0 is satisfied, the

Fig. 7. RGB color composite of three scattering mechanisms (R: dihedral; G: volume; B: surface) obtained using the polarimetric decompositions of (a) Freeman; (b) Hajnsek and (c) An on 2012-07-17. (d) Classified image of the study area.

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Fig. 8. Histograms of scattering powers on (a) 2012-06-17 (Fig. 6) and (b) 2012-07-17 (Fig. 7).

ground component is dominated by surface scattering from which the soil moisture is retrieved. Otherwise, the dominant dihedral scattering is used to retrieve the soil moisture. Fig. 10 compares the temporal evolution of the percentage of dominant surface scattering cases obtained from the three polarimetric methods for different crop types. The quasi-identical (0.1% difference) percentage of dominant surface scattering mechanism is obtained between the decompositions of Freeman-Durden (Fig. 10(a)) and Hajnsek (Fig. 10(b)). In particular, for canola fields, although more volume power is removed from the full coherency matrix using FreemanDurden decomposition than Hajnsek method (Fig. 9), the dominant scattering condition applied to the ground component leads to very similar results. In contrast, the dominant surface scattering results obtained from An decomposition (Fig. 10(c)) is higher than those provided by the other two methods. With An decomposition, surface scattering is always found to be the dominant component (N50%) for the four crop types. This is expected, mainly since the pure random volume model used in this decomposition method changes the relative power of the three scattering mechanisms. Due to the complementarity between the dominant surface scattering and the dihedral scattering in the ground component, Fig. 10 also indicates important dihedral scattering with Freeman-Durden and Hajnsek decompositions over the canola, corn and wheat fields before DOY185 and at the end of the field campaign for soybean and corn fields. Indeed, at the early crop development, Hajnsek et al. (2009) also reported a dominant dihedral scattering component which diminished at the later crop development. The increase in the percentage of dominant dihedral scattering observed at the end of SMAPVEX12 campaign is explained by the fact that the crops were almost at the mature stage, with perishing foliage, favoring the geometric configuration of dihedral scattering mechanism. 4.3. Normalized dominant ground scattering component at a reference incidence angle The scattering mechanisms are influenced by incidence angle. Thus, in order to reduce this effect, a normalization process was conducted on the polarimetric parameters (β, α and fd) which are used to retrieve the soil moisture. 4.3.1. Dominant surface scattering cases For dominant surface scattering conditions in the remaining ground coherency matrix, soil moisture retrieval relies on the sensitivity of the surface scattering parameter β to the dielectric constant, which is directly related to the soil moisture (Topp, 1980). As shown in Fig. 5, β is dependent on the incidence angle, and its sensitivity to soil moisture is significantly enhanced at higher incidence angles. Therefore, for a soil

moisture retrieval from β, the effect of incidence angle must be accounted for or reduced. Fig. 11 displayed the normalization results of β parameter computed from two polarimetric decomposition methods (the β images of Freeman-Durden are similar to those of Hajnsek decomposition and are not shown). In Fig. 11(a), the original β image was extracted from Hajnsek decomposition applied to UAVSAR data acquired on 2012-0617 with incidence angles between 25° to 65°. The available values of β are more distributed in the near range than in the far range, and are particularly not observed over the forested area (Figs. 6–7). Furthermore, in agreement with Fig. 5, the β values at near range (low incidence angle) are higher than those at far range (high incidence angle). When normalized at a reference angle of 40° using Eq. (6), the spatial distribution of β from Hajnsek decomposition shows almost no dependence with the incidence angle variation (Fig. 11(a), right). In contrast to Hajnsek method, the original β image in Fig. 11(b) from An decomposition shows better spatial distribution of β values, even over the forest area. This mainly resulted from the pure random volume model, which increases the surface scattering power and decreases the volume scattering power (Fig. 9). The normalization process removes the incidence angle effect from β image (Fig. 11(b), right). Overall, the errors associated to the process are 19%, 18%, and 14%, respectively for FreemanDurden, Hajnsek and An decompositions.

4.3.2. Dominant dihedral scattering cases The normalization of the dihedral scattering parameters α and fd was conducted with the same method (Eq. (6)) previously used for β parameter. As shown in Fig. 12, the incidence angle effect on α is not significant as on the surface scattering component. Furthermore, less α values are available at near range than far range, due to dominant surface scattering cases which covered around 95% of the near range area. Compared to the results of Hajnsek (Fig. 12(a)), less α values are obtained from An decomposition (Fig. 12(b)) due to the enhanced dominant surface scattering which in turn reduced the dominant dihedral scattering cases. The overall error of normalized α parameter is 20%, 21%, and 29%, respectively for Freeman-Durden, Hajnsek and An decompositions. In contrast to α, the spatial distribution of original fd is influenced by the incidence angle variability (figures not shown here), and the maximum fd values appears around 45° incidence angle. The overall normalization errors for fd are all around 15% for the three decomposition methods, as the number of available pixels used for the normalization is close to each other. In order to be consistent with the surface scattering component, the normalized dihedral component (α, fd) at 40° reference angle were jointly used for soil moisture retrieval when the dihedral scattering is dominant.

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Fig. 9. Temporal variations of the scattering mechanisms with respect to crop height.

Fig. 10. Percentage of dominant surface scattering cases in the ground scattering component using the decomposition of (a) Freeman-Durden; (b) Hajnsek and (c) An.

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Fig. 11. Normalization results of the surface component from (a) Hajnsek decomposition; (b) An decomposition applied to UAVSAR data acquired on 2012-06-17. Original β covered incidence angle ranging from 25° to 65° while normalized β is at a reference incidence angle of 40°. White color represents the non-dominant surface scattering case (or dominant dihedral scattering) and the physically non-valid values of β.

Fig. 12. Normalization results of the dihedral component from (a) Hajnsek decomposition; (b) An decomposition applied to UAVSAR data acquired on 2012-06-17. Original α covered incidence angle ranging from 25° to 65° while normalized α is at a reference incidence angle of 40°. White color represents the non-dominant dihedral scattering case (or dominant surface scattering) and the physically non-valid values of α.

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4.4. Spatiotemporal distribution of the retrieved soil moisture Figs. 13 and 14 show the soil moisture spatial distribution maps derived from the three polarimetric decomposition methods for the beginning (2012-06-17) and the end (2012-07-17) of SMAPVEX12 campaign. In order to increase the retrieval rate, these results include the complementary soil moisture estimates from both the dominant surface and dihedral scattering components. In these figures, the white color represents the non-invertible pixels and the cases for which the dominant surface or the dihedral scattering mechanisms correspond to non-physical conditions: β b −1, or α beyond the range of 0–2 and fd b 0. The values of the retrieved soil moisture show high variability (0.1 to 0.5 m3/m3) within a given field and from one field to another due to the spatial heterogeneity in soil texture, surface roughness and crop growth status. The percentage of invertible pixels significantly decreased from the beginning to the end of the campaign (Figs. 13–14). This is due to well-developed crops which increased the volume scattering, as well as its modeling complexity and thus made difficult the access to the ground scattering component for soil moisture retrieval. Over forested area, physically valid values of β are only derived from An decomposition (Fig. 11(b)). This suggests the potential of this decomposition method for soil moisture retrieval over such high vegetation condition at both the beginning and the end of the campaign (Figs. 13–14), in contrast to Freeman-Durden and Hajnsek decompositions, from which the values of β are not available due to the dominant dihedral scattering. Indeed, although valid values of a (Fig. 12(a)) and fd are obtained over the forested area from Freeman-Durden and Hajnsek decompositions, the soil moisture retrieval fails. This is due to high coupling of soil and vegetation moisture at 40° incidence angle, and

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especially the non-convergence of minimization function in the retrieval process. Therefore for the subsequent statistical results analyses (Subsections 4.5 and 4.6), the forest area will not be considered. Over agricultural fields, more retrieval results are obtained in near range than far range from the Freeman-Durden and Hajnsek methods. As for the soil moisture retrieval results from An decomposition, in agreement with the spatial distribution of β (Fig. 11(b)), there is no difference between the near and far range. Indeed, for all the methods the spatial distribution pattern of the retrieved soil moisture mainly corresponds to that of the normalized β (Fig. 11(a)), which is the principal scattering component for soil moisture retrieval. Nevertheless, over some agricultural fields dominated by the dihedral scattering in the ground component, the soil moisture retrieval from An decomposition is not possible, while it is over the forested area with dominant and valid values of β. Fig. 15 compares the soil moisture retrieval rates obtained from the three decomposition methods applied to UAVSAR time series of SMAPVEX12 campaign. An decomposition shows the highest retrieval rate. These results express the added-value of both the deorientation process applied to the coherency matrix and the use of a pure random volume model. 4.5. Comparison of the retrieved and measured soil moisture Fig. 16 presents a comparison between the ground measurements of soil moisture and those retrieved using the three decomposition methods over different fields at the beginning of the campaign. Each point represents the matching between the mean field values of the retrieved and measured soil moisture. The retrieved results from the surface and the dihedral components are displayed as points with black

Fig. 13. Spatial distribution of soil moisture retrieved on 2012-06-17 from the three decompositions (a) Freeman-Durden; (b) Hajnsek and (c) An. White color represents the noninvertible pixels.

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Fig. 14. Spatial distribution of soil moisture retrieved on 2012-07-17 from the three decompositions (a) Freeman-Durden; (b) Hajnsek and (c) An. White color represents the noninvertible pixels.

and red standard deviation lines, respectively. An overall underestimation is obtained from the three approaches, and much more for soil moisture values higher than 0.4 m3/m3. For such wet conditions, about 0.15 m3/m3 difference is observed between the measured and the retrieved soil moisture from the three decompositions. Thus, in agreement with Baghdadi et al. (2008), under wet soil conditions

(mv N 0.35 m3/m3), it is difficult to accurately retrieve soil moisture due to the saturation of SAR signal. It can be seen that Hajnsek method provided valid soil moisture estimation from the dihedral scattering component, in particular over canola and corn fields. The dihedral scattering components are significant over the canola and corn fields compared to those of soybean and wheat

Fig. 15. Temporal variation of the soil moisture retrieval rates from the three polarimetric decompositions.

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Fig. 16. Comparison of the measured and retrieved soil moisture on 2012-06-17 from the three decompositions (a) Freeman-Durden; (b) Hajnsek; (c) An. The points with black and red standard deviation lines represent the retrieved soil moisture from surface and dihedral component, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

(Section 4.2), mainly due to the differences in crop shape and structure. Indeed, for canola and corn the solid stalks were developed early at the beginning of SMAPVEX12 campaign. In contrary, the stalks of wheat can only be strong in a later phenological development stage. Thus, at the beginning of the campaign, among the three decomposition methods, that of Hajnsek, which better integrates the dihedral scattering component, presents the best performance for soil moisture retrieval with RMSE of 0.10 m3/m3 and Pearson correlation coefficient of 0.49 (Fig. 16). These results obtained at an early phenological stage are probably impacted by the surface roughness which influences the fd parameter for the three methods. However, a compensation of fd parameter in the Hajnsek method (Eq. (2)) allows a proper estimation of soil moisture from the dihedral component. In agreement with the ground measurements (Fig. 2), Fig. 17 shows drier fields at the end of the campaign than at the beginning (Fig. 16). At the end of SMAPVEX12 campaign, although the dominant dihedral scattering component increased (Fig. 10) particularly for Freeman-Durden and Hajnsek decompositions, it failed to retrieve the soil moisture due to the high complexity of crop structure at mature stage. Thus, Fig. 17 mainly includes the retrieved soil moisture from only the surface scattering component. At a late phenological stage (2012-07-17), An decomposition which tends to enhance the surface scattering, offers the best performance for soil moisture retrieval compared to the other methods. Besides, compared to Fig. 16, it appears from Fig. 17 that at the end of SMAPVEX12 the retrieval performance of each decomposition method increases over canola, corn and wheat fields, while it decreases over soybean fields. This can be explained by the difference in soil moisture conditions combined with the changes in crop shapes and structures between the two dates.

4.6. Temporal evolution of retrieved and measured soil moisture Fig. 18 shows the temporal behaviors of the soil moisture estimated from the three polarimetric decompositions applied to UAVSAR time series, along with the measured soil moisture for different crop fields. The corresponding statistics are summarized in Table 1. The highest Pearson correlation coefficient and the lowest RMSE value are highlighted (bold characters) in the table. In agreement with rainfall events (Fig. 2) and the estimated soil moisture (Fig. 18), the following observations can be made: • For canola, the temporal evolution of soil moisture estimated by Hajnsek decomposition is the closest to the temporal variation observed in the measured soil moisture. Hajnsek decomposition also provides the best Pearson correlation coefficient and the lowest RMSE. • For corn, the temporal evolution of the retrieved soil moisture from the three decompositions follows the similar pattern as the measured soil moisture. Before DOY 185, the retrieved results from the three methods are close to each other and to the measurements. After DOY 185, they are slightly overestimated. In Table 1, all decompositions show significant correlation, but the best retrieval results are provided by Freeman-Durden decomposition. • For soybean, the estimated soil moisture values from the three methods display similar tendencies as the measurements, but they are underestimated before DOY 185. An decomposition presents the best correlation, but it has the highest RMSE value, and underestimates soil moisture during the entire period. • For wheat, the three decompositions follow the same trend, which is different from that of the measurements. Before DOY 185, a significant underestimation of around 10–15% is observed with the three

Fig. 17. Comparison of measured and retrieved soil moisture on 2012-07-17 from the three decompositions (a) Freeman-Durden; (b) Hajnsek; (c) An. The points with black and red standard deviation lines represent the retrieved soil moisture from surface and dihedral component, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 18. Temporal evolutions of the retrieved and measured soil moisture for each crop type.

methods. The underestimation is less pronounced after DOY 185. The three approaches provide almost the same RMSE values (0.14– 0.15 m3/m3), which are the highest among all crop types considered. The best correlation coefficient is obtained with Freeman-Durden decomposition.

Fig. 18 and Table 1 clearly show that the performance of the three decompositions for soil moisture retrieval depends on the crop type and on its phenological development which governs its structure (height, shape, orientation) and biomass. In this study, the vegetation scattering characteristics are only modeled using the dipoles. But, for some crop type at a specific growth stage (e.g. wheat at the early growth stage), the vegetation layer is more likely as spherical scatterers. This can partially explain the underestimated results obtained from the

Table 1 Correlation coefficient and RMSE values between measured and retrieved soil moisture using the three different polarimetric decompositions. ‘**’ denotes extreme significance p b 0.01, ‘*’ denotes significance p b 0.05. Crop types

Statistical index

Freeman

Hajnsek

An

Canola

R RMSE (m3/m3) R RMSE (m3/m3) R RMSE (m3/m3) R RMSE (m3/m3)

0.18 0.076 0.78** 0.059 0.64* 0.095 0.61 0.15

0.54 0.072 0.70* 0.083 0.45 0.071 0.12 0.14

– 0.10 0.68* 0.071 0.76** 0.11 0.38 0.15

Corn Soybean Wheat

three decomposition methods over the wheat field before DOY 185. In addition, the results obtained over corn and soybean fields show encouraging correlations with the ground measurements during the SMAPVEX12 campaign. For these crops, the assumed dipole shape is probably appropriate for modeling the vegetation volume scattering component (Hajnsek et al., 2009). Furthermore, considering the vegetation orientation, only the random case is used in the decompositions of Freeman and An. As for Hajnsek decomposition, although three different orientation cases are used, the obtained results show that threefixed orientation are also not enough to simulate the complex structure of the vegetation orientation which significantly varies during the growing season and with the crop types. 5. Conclusion This paper analyzes three model-based polarimetric decompositions (An et al., 2010; Freeman and Durden, 1998; Hajnsek et al., 2009) applied to time series of UAVSAR acquisitions during the SMAPVEX12 campaign for soil moisture retrieval over vegetated agricultural fields. In contrast to several past investigations using the scattering powers domain of polarimetric decompositions for the classification and the identification of the scattering mechanisms, this study focused on soil moisture estimation from the ground scattering component, which is obtained once the volume scattering is removed from the coherency matrix. Compared to the Freeman-Durden and Hajnsek decompositions, the volume scattering power in An decomposition is reduced and the surface scattering is in turn enhanced to the benefit of soil moisture retrieval. The characteristics of the scattering mechanisms are found to be highly dependent on crop types and the growth status. For soybean,

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the volume power increase and the surface power decrease with the crop growth. However, for some crop types as canola, when the crops are close to the mature stage, the dying out process leads to an increased surface power and a decreased volume power. Indeed, at this stage, the microwave signal penetration depth is enhanced due to dry vegetation. After removing the volume scattering contribution from the full coherency matrix, the dominant scattering component (surface or dihedral) in the remaining ground coherency matrix was used to estimate the soil moisture. In order to reduce the incidence angle effect on the soil moisture retrieval, all the parameters governing the dominant surface scattering (Bragg scattering coefficient β) and the dominant dihedral scattering (the Fresnel coefficient α and the scattering intensity fd) were normalized to a reference incidence angle of 40° using the same histogram matching method. The soil moisture estimation results gained from the dominant surface and dihedral scattering cases are then merged to increase the inversion rate. Although the normalization process may introduce some uncertainties, the sensitivity of polarimetric parameters to soil moisture is enhanced at 40°. To our knowledge, it is the first time that the polarimetric parameters are normalized to remove the incidence angle effect on the soil moisture retrieval. At the early development stage, the surface scattering component and in some cases the dihedral scattering component contributed to retrieve the soil moisture, while at the later development stage, the surface scattering component is almost the only scattering mechanism from which the soil moisture can be estimated. Since in An decomposition the surface scattering component is always dominant (N 50%) during SMAPVEX12 campaign, it provides the best performance at the end of the campaign, when the crops are well developed. At the beginning of the campaign, Hajnsek decomposition, which better integrates the soil moisture estimates from the dihedral scattering component, presents the best performance. In addition, the results show that the performance of the three decompositions for soil moisture retrieval depends on soil moisture conditions, crop type and on crop phenological development. Very wet soil condition (higher than 0.4 m3/m3) showed poor soil moisture retrieval performance from the three decompositions, with a difference of about 0.15 m3/m3 between the measured and the retrieved soil moisture from the three decompositions. Freeman-Durden model gave the best results for corn (R = 0.78, RMSE = 0.059 m3/m3) and wheat (R = 0.61, RMSE = 0.15 m3/m3). Hajnsek decomposition performed well for canola (R = 0.54, RMSE = 0.072 m3/m3), while better results were obtained for soybean (R = 0.45, RMSE = 0.071 m3/m3) using An decomposition. Nevertheless, over the wheat fields before DOY 185, a significant underestimation of soil moisture was obtained from the three decompositions, due probably to a poor quantification of wheat volume scattering. Overall, the performance of the polarimetric decomposition for soil moisture retrieval is highly determined by the quality of the volume scattering estimation. However, in this study, fixed volume scattering models with random orientation are used in the Freeman-Durden and An decompositions. As for the Hajnsek decomposition, despite the use of different volume scattering models according to crop orientations, the predefined volume coherency matrices have probably their limits to dynamically model the variability in crop structure (shape, orientation, etc.). Thus, the development of dynamic and generalized volume scattering model should be further investigated to improve both the soil moisture retrieval accuracy and retrieval rate over vegetated agricultural fields. Acknowledgments The study was funded by the Canadian Space Agency Class Grant and Contribution Program (14SUSMAPSH) as part of the Canadian plan to spatial missions of soil moisture, and by the National Science and Engineering Research Council of Canada (283211-2011). The authors would like to thank the National Aeronautics and Space Administration (NASA) for providing the UAVSAR datasets and the SMAPVEX12

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