A type of polarimetric parameter for evaluating the reliability of model-based decomposition result and its application

ABSTRACT The reliability of the model-based decomposition result, which is seldom investigated, is a key factor in determining whether decomposition parameters can be effectively applied to polarimetric synthetic aperture radar (PolSAR) applications. In this paper, a type of polarimetric parameter for evaluating the reliability of model-based decomposition result is proposed. It originates from the degree of correlation between the scattering models. The main idea is whether the measured power can be assigned to the corresponding scattering model. The more the measured power that can be allocated to the corresponding scattering model, the more reliable the decomposition result. The C-band Radarsat-2, L-band UAVSAR, X-band TerraSAR-X, and L-band E-SAR PolSAR data are selected for experiments. The results show that the type of polarimetric parameter can effectively represent the reliability of the decomposition result. The reliabilities of surface and double-bounce scattering are high in the ocean and orthogonal buildings, respectively. For oriented buildings, the reliability of the decomposition result is lower owing to the overestimation of volume scattering. For forested areas, reliability is generally higher if volume scattering is not overestimated. Furthermore, the results show that the reliability of soil moisture retrieval is positively correlated with surface scattering reliability.


Introduction
Model-based decomposition has been successfully applied to the interpretation of polarimetric synthetic aperture radar (PolSAR) images (Freeman and Durden 1998;Yamaguchi et al. 2005).The rationale beyond model-based decomposition is to fit physically based scattering models to the Pol-SAR observations (Lee and Pottier 2009;Cloude 2009).Each scattering model relates the physical properties of the scatterers to the polarimetric radar response, and this is done by accounting for shape, orientation, dielectric constants, etc.For the shape, the popular elementary scatterers are plane, dihedral, and dipole (Freeman and Durden 1998).The frequently used distribution functions are cosine (Hajnsek et al. 2009;Sato et al. 2012;Xiang, Ban, and Su 2015), von Mises (Neumann, Ferro-Famil, and Reigber 2010;Zhang et al. 2022), nth cosine (Arii, Van Zyl, and Kim 2010;Arii, Van Zyl, and Kim 2011;Huang, Wang, and Shang 2016), and uniform distribution functions (Freeman and Durden 1998;Hong and Wdowinski 2014;Hajnsek, Pottier, and Cloude 2003).
The dielectric constant of the scatterer is integrated into the scattering model to adjust the anisotropy degree (He et al. 2016).These factors enable scattering models to have clear physical meaning and can be applied to different PolSAR applications (Chen, Li et al. 2014).
Two incoherent decomposition schemes are available: model-based decomposition (Freeman and Durden 1998) and eigenvector-based decomposition (Cloude and Pottier 1997).Eigenvector-based decomposition has a clearer mathematical background and eigenvalues are orthogonal to each other.However, model-based decomposition pursues the physical meaning of scattering models and the possibility of existence in actual scenarios, but ignores the orthogonality between scattering models.In such a case, scattering models are difficult to be orthogonal to each other, which leads to correlations between the scattering models (Fan et al. 2019;Li, Zhang, andLiang 2020. Singh andMalik 2019;Zhang et al. 2011).For example, the combination of the surface and cross scattering models has a form similar to that of the volume scattering model (Han et al. 2022).These three scattering models have a higher correlation with each other.However, the pioneering Freeman-Durden decomposition, and its extended decompositions, seldom consider this correlation.When related scattering models are assumed to be independent for investigating the scattering characteristics of ground targets, the correlation between the scattering models should supplement the interpretation of PolSAR images.Furthermore, what does the correlation between scattering models mean for the decomposition result?When the correlation is greater, the measured power cannot be assigned to its corresponding scattering model, but to multiple similar scattering models.In such a case, the decomposition result of this scattering mechanism is unreliable.
For soil moisture retrieval, the X-Bragg model based on the Bragg scattering model is proposed to account for the depolarization effect of the ground surface (Freeman and Durden 1998;Hajnsek, Pottier, and Cloude 2003;Hajnsek et al. 2009).In addition, the depolarization effect is also introduced into the double-bounce scattering model (Jagdhuber 2016).The introduction of depolarization effects into ground scattering models contributes to their adaptation to surfaces with different roughness values.Considering that completely random dipoles cannot accurately characterize the anisotropic crop canopy, an adaptive volume scattering model is used to improve the accuracy of soil moisture inversion (He et al. 2016).One of the goals of these models is to reliably extract the surface scattering component.The reason is that when the surface scattering power cannot be reliably extracted, the surface scattering contribution may be overestimated or absorbed by other scattering models.The soil moisture result will be unreliable.In addition, for biomass and forest height inversion (Tomar, Kumar, and Tolpekin 2019), a more reliable volume scattering contribution is expected to be extracted.This parameter for evaluating the reliability of the decomposition parameters is meaningful for PolSAR applications.Thus, a type of polarimetric parameter, which is seldom investigated and originates from the correlation between the scattering models, is proposed.The main idea of this study is to use the proposed type of parameter to measure whether the decomposition result is reliable when related scattering models are adopted to interpret PolSAR images.
The remainder of this paper is organized as follows.In Section 2, using the Freeman-Durden three-component decomposition as an example, this type of polarimetric parameter derived from the correlation between scattering models is proposed.Section 3 describes the experiments using the C-band Radarsat-2 data over San Francisco, USA, L-band UAVSAR data over Sacramento Valley, California, and X-band TerraSAR-X data over Mumbai, India.The results validate the reasonableness of the type of polarimetric parameter for evaluating the reliability of the modelbased decomposition result.Furthermore, this section shows that the proposed parameter is complementary to related scattering models for interpreting PolSAR images.In Section 4, the experimental results of E-SAR data over Western Pomerania, Germany, validate that this type of polarimetric parameter can roughly predict the reliability of the soil moisture retrieval results.Finally, the conclusions are presented in Section 5.

Freeman-Durden decomposition
The landmark Freeman-Durden decomposition is a frequently used method for PolSAR image interpretation.In this paper, it is used as an example to derive this type of parameter.The Freeman-Durden decomposition decomposes the measured data T 3 into surface, double-bounce, and volume scattering matrices (Freeman and Durden 1998) where P s , P d , and P v are scattering powers.b is a model parameter that is expressed as follows where f 1 represents the local incidence angle on the horizontal surface. 1 g is the dielectric constant of the horizontal surface.a is the model parameter expressed by where f 2 represents the incidence angle on the vertical surface. 1 t is the dielectric constant of the vertical surface.A popular method of deriving the volume scattering model is to consider the orientation of particles and integrate all possible orientation angles (Antropov, Rauste, and Hame 2011).For Freeman-Durden decomposition, the particles are assumed to be dipoles with a uniform distribution.The scattering models shown in Equation (1) are used to describe three structures with specific dielectric constants.They have a clear physical meaning.However, orthogonality is not considered in the establishment of the scattering model.Note that because volume scattering is a high-entropy scattering process, making the volume scattering model completely orthogonal to the surface and double-bounce scattering models is difficult (Han et al. 2022).Hence, for model-based decomposition schemes, it is unreasonable to assume that the scattering models are independent of each other.The related degree of scattering models is a complementary characteristic of the nonorthogonal scattering decomposition scheme for the interpretation of PolSAR images.

A type of polarimetric parameter for evaluating the reliability of decomposition results
To derive the type of polarimetric parameter, Equation (1) can be re-expressed using rank-1 scattering vectors Note that the rank of the volume scattering models is three.It is impossible to vectorize the volume scattering model directly.Therefore, it is vectorized by an eigenvalue decomposition.For the measured data, the power of a scattering vector can be expressed as (Cloude 2009) (Note that, in this paper, it is called the measured power to distinguish it from the surface, double-bounce, and volume scattering powers) where MP v denotes the measured power.† represents conjugate transpose.v is the scattering vector v = cos a cos 2t sin a cos 2ue ic − i cos a sin 2u sin 2t sin a sin 2ue ic + i cos a cos 2u sin 2t where a, t, u, c are polarimetric parameters associated with the geometric and physical properties of targets (Touzi 2007).The measured powers corresponding to different scattering mechanisms can be obtained when these four parameters have different values.For example, when a = 0, t = 0, u = 0, c = 0, there is measured power corresponding to ideal surface scattering.
Combined with Equations ( 4)-( 6), the measured powers corresponding to the surface, doublebounce, and volume scattering models are Note that the modulus of the projected scattering vector is normalized to one.It is expected that the reliability parameter is related to the scattering mechanism represented by the projection vector and measurement data, but is independent of the modulus of the projection vector.For Freeman-Durden decomposition, the scattering models are assumed to be unrelated.If this assumption holds, the measured powers corresponding to the surface, double-bounce, and volume scattering should be equal to the Freeman-Durden decomposition result MP s = P s MP d = P d when scattering models are unrelated However, in practice, scattering models are generally related.In such a case, Equation ( 8) does not hold.When the scattering powers are divided by the measured powers, a type of polarimetric parameter that measures the correlations of the three scattering models can be derived R s , R d , and R v measure the correlations among the surface, double-bounce, and volume scattering models.
Furthermore, what does the correlation between scattering models mean for the decomposition result?When the measured power is basically assigned to the corresponding scattering model, it is conceivable that the decomposition result is reliable because the characterization of the scattering model is a clear ground target.In this case, R i (R s , or R d , or R v ) could reach the maximum value of one.However, when the measured power is not primarily assigned to the corresponding scattering model, but to multiple similar scattering models, the decomposition result is unreliable because the scattering model describes an ambiguous ground target.In this case, R i could reach the minimum value of zero.Therefore, this type of parameter, which originates from the correlation between the scattering models, can be used to evaluate the reliability of the decomposition result.For Equation ( 9), it describes the reliabilities of different scattering mechanisms.Based on Equation ( 9), another parameter describing the overall reliability of the decomposition result can be derived as follows: where SPAN denotes the total measured power.Similar to Equation ( 9), the value of R o generally ranges from zero to one.The larger the value of R o , the more reliable the decomposition result is.Furthermore, for the volume scattering, the reliability is fixed at zero for the four situations shown in Equation ( 11).This is because the contributions of other scattering mechanisms may be less than zero.These scenarios occasionally occur because of overestimation of the volume scattering contribution (Cloude et al. 1999) Furthermore, for surface and double-bounce scattering, the reliability is fixed at zero for the four situations shown in Equation ( 12), since it is contrast to the ground truth For the proposed parameter, a comparison between model-based and eigenvalue-based decompositions is worth discussing.The advantage of model-based decomposition is that scattering models have a physical meaning, which is more suitable for natural targets.In contrast, the advantage of eigenvalue-based decomposition is orthogonality, which ensures that the scattering mechanisms can be distinguished entirely (Cloude et al. 1999).If a decomposition scheme combines these two advantages, it can contribute to the development of target decomposition.Therefore, for model-based decomposition, we attempt to evaluate the orthogonality.The correlation between scattering models should be as low as possible.In contrast, for eigenvalue-based decomposition, the parameter associated with the physical meaning should be used for evaluation.We believe that the decomposition scheme should pursue a balance between orthogonality and the preservation of physical meaning.
Note that the proposed parameter is different from the similarity parameter (Yang, Peng, and Lin 2001;An et al. 2009).The reliability parameter is related not only to the correlation between the scattering models, but also to the geometric and physical properties of the ground targets.For the same decomposition scheme, the reliability varies with the ground targets.The proposed parameter can be regarded as a dynamic parameter, whereas the similarity parameter is a static parameter.Furthermore, the similarity parameter describes the relationship between two scattering models, whereas the proposed parameter measures the relationship between multiple models.Note that this paper considers only the Freeman-Durden decomposition as an example.This type of parameter can also be applied to other model-based decomposition schemes, such as Chen general four-component decomposition (Chen, Wang, Xiao, et al. 2014).The core aspect is whether the measured power is assigned to a corresponding scattering model.

Experiments and investigation
Experiments were performed to validate that this type of polarimetric parameter can reasonably assess the reliability of the decomposition result.The C-band Radarsat-2 data over San Francisco, USA, Lband UAVSAR data over Sacramento Valley, California, X-band TerraSAR-X data over Mumbai, India, and L-band E-SAR data over Western Pomerania, Germany, are selected for experiments.Long-wavelength SAR signals have stronger penetration performance and are more conducive to extracting ground surface scattering information.In addition, they are more sensitive to larger structures.Short-wavelength SAR signals are convenient for obtaining vegetation canopy scattering information, and contribute to obtaining the randomness of ground targets.SAR signals with different bands have unique characteristics.Therefore, PolSAR data with different bands are selected to validate the proposed type of parameter.

C-band Radarsat-2 PolSAR data
A color-coded image of the Freeman-Durden decomposition of the C-band descending Radarsat-2 PolSAR data is shown in Figure 1.This image includes different interesting areas, such as forests, oceans, and buildings with orientation angles of approximately 0°, 5°, and 30°.The resolutions in the azimuth and range directions are approximately 4.8 and 4.7 m, respectively, and the corresponding incidence angle is approximately 29°.As shown in Figure 1, surface scattering is dominant in ocean areas.The significant scattering contribution for orthogonal and lightly oriented buildings is double-bounce scattering.In addition, surface scattering caused by the roof and pavement can be observed.Forests and highly oriented building areas are both interpreted as volume scattering dominant areas.The misinterpretation of oriented buildings occurs because the volume scattering model is not suitable for these areas (Chen, Wang, Li, et al. 2014).The following describes the reliability of the Freeman-Durden decomposition result.
The reliabilities R s , R d , R v corresponding to the surface, double-bounce, and volume scattering are shown in Figure 2.For ocean areas, the reliability of surface scattering is the highest, followed by double-bounce scattering and volume scattering.This is consistent with the fact that the scattering characteristics of the ocean can be described well by surface scattering.This phenomenon reveals that the contribution of surface scattering and its model parameters can be effectively applied to PolSAR applications, whereas that of volume scattering cannot.For forest areas, the reliabilities of surface and double-bounce are not high.This is because the measured powers generated by the surface and double-bounce scatterers cannot be assigned to these two scattering models.This shows that, for forest areas, under the observation of C-band SAR signals, the decomposition results of surface and double-bounce scattering are useless.In addition, the medium volume scattering reliability in the forest area is due to the overestimation of the scattering contribution.This may result in the intensity of the polarization channel being less than zero.In this case, reliability is fixed at zero.Furthermore, in forest areas, R s and R d are lower than R v .This shows that, although the overestimation of the volume scattering contribution leads to the stability of R v decreasing to zero in some areas, R v is still the most reliable for forest areas.This observation is consistent with expectation.As expected, for orthogonal and lightly oriented buildings, the reliability of double-bounce scattering is the highest.In addition, although the intensity of the surface scattering is not high, its reliability of surface scattering is somewhat high, revealing that in orthogonal and lightly oriented buildings, the decomposition results of surface and double-bounce scattering can operate together to assist in PolSAR applications.However, most of the existing works use surface or double-bounce scattering only to invert soil moisture (Hajnsek et al. 2009;Hajnsek, Pottier, and Cloude 2003).Here, we suggest that these two scattering models can be combined to invert the soil moisture.For highly oriented building areas, the reliabilities of all three scattering mechanisms are low, indicating that all three mechanisms are unreliable in these areas.The reason for this phenomenon is that the measured power generated by the dihedral structures is allocated to the volume scattering model rather than to the double-bounce scattering model.This result is consistent with expectation, since for highly oriented building areas, dihedral structures are misinterpreted as a cloud of dipoles.This validates the reasonableness of the type of polarimetric parameter for evaluating the reliability of the decomposition result.
The overall reliability of the Freeman-Durden decomposition result of the Radarsat-2 PolSAR data is shown in Figure 3(a).Generally, the overall reliabilities of the ocean, orthogonal, and lightly oriented building areas are the highest, and that of the forest is medium, but that of highly oriented buildings is the lowest.This reveals that Freeman-Durden decomposition can be successfully applied to PolSAR applications in ocean, orthogonal, and lightly oriented building areas, but not in areas with highly oriented buildings.Interestingly, this is also consistent with the rationality of the Freeman-Durden decomposition result.This shows that the type of reliability parameter is complementary to model-based decomposition in interpreting PolSAR images.Furthermore, an interesting phenomenon observed in the black box areas is the low reliability of the decomposition result, compared with the surrounding sea areas.As shown in Figure 3, there are many obvious speckle noises in the black box areas.This indicates that the type of parameter can reveal the influence of speckle noise on the decomposition result.The greater the area affected by speckle noise, the less reliable the decomposition result.
The entropy of the Radarsat-2 data is shown in Figure 3(b).Oceans with low entropy have high reliability, and orthogonal buildings with medium entropy have medium reliability.This observation is in line with our expectations.As the ground scatterers become more complex, the response signals of different scatterers are coupled.It is often difficult to effectively distinguish between them.However, for forest areas, the low R v is due to the overestimation of the volume scattering contribution.The overall reliability of the Yamaguchi decomposition result of the Radarsat-2 PolSAR data is shown in Figure 3(c).The R o is somewhat large in forest areas although the entropy is high.This is because the Yamaguchi volume scattering model can reduce the estimation of the volume scattering contribution.If the contribution of volume scattering is not overestimated, high reliability can be obtained for forest areas with high entropy.In other words, if the scattering power generated by the plane or dihedral structures, is not allocated to the volume scattering model, R o tends toward one.
In summary, the proposed reliability parameter is used to measure whether different scattering mechanisms can be distinguished.For Freeman-Durden decomposition, in ocean and building areas, an increase in entropy reduces the degree of reliability because it increases the risk of coupling of scattering mechanisms.However, for complex scenes such as forests, the reliability is generally higher if the volume scattering is not overestimated.Its specific value depends on the coupling degree of the canopy and ground contributions, which is related to the incidence angle, and wavelength.For example, for long wavelengths, ground and canopy contributions are of equal magnitude (Van Zyl and Kim 2011).The decomposition result may be less stable because they are not easily distinguishable.However, for short wavelengths, where the volume scattering contribution is dominant (Van Zyl and Kim 2011), the stability of the decomposition is high, since there is little need to distinguish between the different scattering mechanisms.
The relationship between this type of parameter and a major problem in model-based decompositionnegative scattering poweris discussed further.Figure 4(a,b) shows the absolute values of the ratios of the negative surface and double-bounce scattering powers to the total power.For ocean, orthogonal, and lightly oriented building areas, the negative power can be ignored.However, negative power is evident for forested and highly oriented building areas.The higher the correlation between scattering models, the greater the chance that the measured power of a scattering vector is incorrectly and repeatedly assigned to multiple scattering models with high correlation.This may lead to an insufficient distribution of the measured power, and negative scattering power emerges.The negative power result is highly consistent with the reliability degree of the decomposition result, further validating that this type of parameter can effectively evaluate the reliability of the decomposition result.

L-band UAVSAR PolSAR data
Another complementary image acquired by the L-band UAVSAR system is provided in Figure 5(a).The resolution in the azimuth and range directions is approximately 2.4 m.The incidence angle of the image from left to right is approximately 25°to 65°.There are highly oriented buildings, plantations, and four crops.Crops take up most partial areas of this image.The SAR image was acquired on 20 July 2011.For the Freeman-Durden decomposition result shown in Figure 5(a), the winter wheat has just been harvested, so the dominant scattering mechanism is surface scattering.Sunflower areas are at maturity.Due to their dense canopy, the volume scattering power accounts for a higher proportion, and surface scattering is not significant.Corn is also at maturity.Since its canopy is not dense, and its branches are developed, both volume and double-bounce scattering occupy a certain proportion.Alfalfa is a perennial crop whose dominant scattering mechanism is not obvious.
The reliabilities of the L-band UAVSAR PolSAR data for different scattering mechanisms are shown in Figure 6.For the plantation areas, the reliabilities of surface and double-bounce are somewhat improved compared to the experimental results of the C-band.This is due to the stronger penetration of the L-band SAR signals.The stronger penetration results in an enhanced ground scattering contribution, ensuring that more of the measured powers corresponding to surface and double-bounce scattering are allocated to these two models.It improves the reliabilities of surface and double-bounce scattering.This observation reveals that, for the L-band decomposition result, the surface and double-bounce scattering parameters can be more effectively applied to Pol-SAR applications compared with the C-band decomposition result.In addition, the reliability of the volume scattering is also improved, which shows that the volume scattering power is not as overestimated as the C-band results.In addition, compared with the C-band, the experimental results of the L-band show that the reliabilities of the three scattering mechanisms are improved to varying  degrees for highly oriented buildings, which is due to the less random degree of scatterer under the observation of L-band SAR signals.This will generate a relatively smaller cross-scattering contribution, avoiding the absorption of the power originating from the dihedral structures by volume scattering.The reliability and reasonableness of the decomposition result are again highly consistent, further validating the type of parameter.
For the harvested winter wheat area, the reliability of surface scattering is the highest, which implies that surface scattering can be better used for ground parameter inversion, such as soil moisture.Although the volume scattering power is not high, the reliability of volume scattering is not low.This shows that although the type of polarimetric parameter is related to the scattering power, it is not the main determinant.The main factor is whether the measured power is mainly allocated to the corresponding scattering model, rather than multiple similar scattering models.For the sunflower areas, as expected, the reliability of volume scattering is very high.Note that the reliability of surface scattering fluctuates significantly even for the same field.In this case, one can select the points with higher reliability to invert the soil moisture.It is expected that this will contribute to the improvement of the accuracy of soil moisture inversion.For corn areas, the reliabilities of the three scattering components are relatively high, indicating that the correlations among the three scattering components are low.This means that these three components can be effectively distinguished from each other.This is expected because an important goal of model-based decomposition is to effectively separate different scattering components.In addition, for part of the corn areas, due to the overestimation of the volume scattering power, the reliabilities of the various scatterings are very low.Since the alfalfa area is being harvested, the reliabilities of different scattering mechanisms fluctuate.

X-band TerraSAR-X PolSAR data
The descending TerraSAR-X PolSAR data acquired over Mumbai, India is selected for the experiments.The color-coded SAR image of Freeman-Durden decomposition is shown in Figure 7, which covers various ground targets, such as orthogonal and oriented buildings, and forests.To reduce the impact of speckle noise on the decomposition results, and make the azimuth and range resolutions comparable (10m × 10 m), the PolSAR image was processed with a multilook of 4 in the azimuth direction and 5 in the range direction.As shown in Figure 7, the volume scattering in the forest area is absolutely dominant due to the weak penetrating performance of the X-band SAR signals.As expected, the dominant scattering mechanisms for orthogonal and highly oriented building areas are double-bounce and volume scattering, respectively.The water area appears black, possibly due to specular scattering.Then, the following focuses on the reliability of the Freeman-Durden decomposition result.
The reliabilities of surface, double-bounce and volume scattering for TerraSAR-X data are shown in Figure 8.For water areas, the reliabilities of double-bounce and volume scattering are low.In addition, surface scattering is also unreliable.The possible reason for this phenomenon is that the backscattering intensity is low, resulting in a low signal-to-noise ratio and low reliability.This shows that the proposed parameter can reflect the quality of SAR signals.For oriented building areas, the surface and double-bounce scattering is less reliable compared to the L-band results.This is because the short-wavelength SAR signal is more sensitive to the orientation of the ground target, which causes the instability of surface scattering and double-bounce scattering.For orthogonal building areas, the reliability of double-bounce scattering is the same as that of the results of the C-band results.Their reliabilities are both large.However, compared with the C-band, the reliability of surface scattering is reduced.The reason for this phenomenon is that X-band SAR signals are more sensitive to the randomness of ground targets, which makes surface scattering unreliable.For forested areas, the higher reliability of volume scattering reveals that the volume scattering contribution is not seriously overestimated.Furthermore, compared to the L-band, the reliability of surface scattering is higher.The reason for this phenomenon is that large leaves cannot be regarded as dipoles, but rather appear as disks (Han et al. 2021).This makes surface scattering also occur at the top of the forest canopy, increasing the reliability of the surface scattering.

Application of the proposed polarimetric parameter
In this section, it is verified that the proposed parameter can roughly predict the reliability of soil moisture retrieval results.L-band E-SAR data acquired on April 20, 2006, is selected for the where where k and h are the wavenumber and surface root mean square, respectively.There are two unknowns and two observations in Equation ( 13).In such a case, the surface dielectric constant can be inverted by the look-up method.Subsequently, the soil moisture is calculated by the  The black area represents the failed area for soil moisture retrieval.An interesting observation is that in areas where the reliability of surface scattering is high, the success rate of soil moisture retrieval is also high.In detail, the areas marked 843 and 160 where the reliability of surface scattering is high can basically be successfully inverted by the Oh model, whereas only part of the areas marked 230 and 250 can be inverted, resulting from the lower reliability of surface scattering.Based on the above analysis, a method for masking different areas of soil moisture inversion is proposed.Areas in which the surface scattering is unreliable can be masked.This is interesting and worthy of further investigation.
Quantitative experiments are conducted to validate that the proposed parameter can roughly predict the reliability of soil moisture retrieval results.The relationship between the bias of the soil moisture retrieval results and the reliability of surface scattering is shown in Figure 11.Note that the bias is calculated between the estimated mv estimated and the measured soil moisture mv truth : All points that are successfully inverted using the Oh model and have ground truth data are presented in Figure 11.A surprising experimental result is that, as the reliability decreases, the bias of the soil moisture retrieval results increases.An apparent trend is observed.This verifies that the proposed parameter can roughly predict the reliability of soil moisture retrieval results.This is consistent with the theoretical analysis presented in Section 3. Note that the experimental results only reveal that the reliability of soil moisture retrieval is positively correlated with surface scattering reliability.

Conclusions
A common assumption is that the related scattering models in decomposition are independent of each other.In such a case, the correlation between scattering models is a necessary supplementary polarimetric parameter for the decomposition result.We find that this type of parameter can be used to describe the reliability of the decomposition result.In addition, reliability parameter can provide references for PolSAR applications, because a higher reliability parameter tends to lead to more robust PolSAR retrieval results.Therefore, a type of polarimetric parameter for evaluating the reliability of the decomposition result is proposed based on the correlation of the scattering models.Fully polarimetric C-band Radarsat-2, L-band UAVSAR, Xband TerraSAR-X, and L-band E-SAR data are used for the experiments.The experimental results show the following (1) The proposed parameter can effectively characterize the reliability of the decomposition result.
(2) When correlated scattering models are used to interpret PolSAR images, the proposed parameter provides a new perspective for understanding the interaction process between SAR signals and ground targets.
(3) The reliability of soil moisture retrieval is positively correlated with surface scattering reliability.

Figure 1 .
Figure 1.Color-coded image of the Freeman-Durden decomposition of the C-band Radarsat-2 PolSAR data (red: double-bounce scattering contribution, green: volume scattering contribution, blue: surface scattering contribution).

Figure 3 .
Figure 3. (a) Overall reliability of Freeman-Durden decomposition.(b) The entropy.(c) The overall reliability of Yamaguchi decomposition.

Figure 4 .
Figure 4. Absolute value of the ratio of the negative scattering power to the total power for (a) surface scattering, and (b) doublebounce scattering.

Figure 9 .
Figure 9. (a) Color-coded image of X-band TerraSAR-X data (red: double-bounce scattering contribution, green: volume scattering contribution, blue: surface scattering contribution).(b) Regions in which the soil moisture was measured.

Figure 10 .
Figure 10.(a) Reliability of surface scattering.(b) Soil moisture inversion results of the Oh model.

Figure 11 .
Figure 11.Relationship between the bias of soil moisture retrieval results and reliability of surface scattering.