Dubois-B is the model selected for generating SAR synthetic data. The Dubois model, introduced by Dubois and Van Zyl (1994) was developed using scatterometer data and later tested on airborne datasets. Being a semi-empirical approach, it combines theoretical modeling with coefficients derived through experimental data fitting (Dubois et al., 1995). The Dubois model is a widely used approach to characterize the backscattering coefficient, by establishing its relationship with radar parameters, such as incidence angle, wavelength, and frequency, as well as surface properties like roughness and dielectric constant. Using the VV and the HH polarizations, the model solves for two unknown variables: dielectric constant and surface roughness, enabling the retrieval of soil moisture and surface roughness. The Dubois model algorithm has shown significant success in bare soil areas, as noted by several studies as that of Sikdar and Cumming (2004) and Neusch and Sties (1999).

However, some studies have highlighted the limitations of the Dubois model (Baghdadi et al., 2016; Merzouki et al., 2010; Choker et al., 2017). Notably, Choker et al. (2017) evaluated Dubois model using a wide dataset of SAR data (at L-, C- and X-bands) and soil measurements acquired over numerous agricultural sites (in France, Italy, Germany, Belgium, Luxembourg, Canada and Tunisia), reporting overestimations of the measured σ⁰ mainly in HH polarization, when soil moisture is below 20 vol.%, or k Hrms above 2.5 (k is the wavenumber), or θ higher than 30° (Choker et al., 2017). Furthermore, Dubois is limited to the two co-polarization (VV and HH) which is restrictive when using cross polarization SAR data. In order to overcome this limitation, Baghdadi et al. (2016) developed the Dubois-B, a recalibrated version of the Dubois model. The Dubois-B incorporates HV as well as HH and VV polarizations and was validated on an extensive dataset, encompassing a wide range of incidence angles (18°–57°), in various climatic zones (humid, semi-arid, and arid sites) and for radar wavelengths (L, C, and X). Dubois-B was not calibrated for the S-band because remotely sensed SAR S-band data is not yet available. In this study, Dubois-B is assumed to be valid for the Sband since its wavelength (∼9 cm), lies in between the wavelengths of C and L frequency bands.

Dubois-B demonstrated a superior performance across different radar wavelengths, incidence angles, for both HH and VV polarizations with decreased Biases and RMSE when compared to Dubois (Baghdadi et al., 2016). The expression for HV, VV and HH in the Dubois-B model are the following (Equations 1–3, respectively) σ H V 0 = 10 − 2 , 325 × cos ⁡ θ − 0.01 × 10 0 , 011 × cot θ × SSM ×   k .   H r m s 0.44 × sin θ (1) σ V V 0 = 10 − 1 , 138 × cos ⁡ θ 1 , 528 × 10 0 , 008 × cot θ × SSM × k .   H r m s 0.71 × sin θ (2) σ H H 0 = 10 − 1 , 287 × cos ⁡ θ 1 , 227 × 10 0 , 009 × cot θ × SSM × k .   H r m s 0.86 × sin θ (3) Where SSM is the volumetric soil moisture measured in volumetric percent (vol.%), k is the wavenumber equal to 2π/λ (λ is the wavelength), Hrms is the root mean surface height (surface λ roughness) in cm, and θ is the incidence angle in radian. The Dubois-B model was used to generate a synthetic dataset of backscattering coefficient (σ⁰) for L- and S-bands (wavelength equal to 23.84 and 9.37 cm, respectively) in the VV, HH, and HV polarizations. The inputs required by the Dubois-B model for σ⁰ generation are: SSM, Hrms, and θ. The maximum SSM value used in the simulations (40 vol.%) was set as such because e radar signal increases with soil moisture up to a threshold of about 35–40 vol.% (Holah et al., 2005). Beyond this threshold, the radar signal begins to decrease, making the estimation of moisture less reliable, since the same backscattering coefficient value could correspond to two different moisture values (after saturation). The range of θ chosen, from 30° to 50° corresponds to approximately the range of θ for NISAR (NISAR, 2025).

Table 1, shows the ranges of input parameters used for the Dubois-B simulations, as well as the total number of elements generated for each frequency band (defined by one wavelength) and polarization.

The output of the Dubois-B model (simulated SAR data, σ⁰) is calculated from input parameters without any added noise. However, in real world use cases, SAR σ⁰ includes a certain amount of noise, depending on the radiometric accuracy of the instrument (Shimada et al., 2009; Motohka et al., 2018; Schmidt et al., 2020; Schwerdt et al., 2017). This radiometric error must be accounted for when employing simulated SAR data. For Sentinel-1, This error is approximately 0.70 dB (σ⁰) for co-polarizations (VV and HH) and 1.0 dB for cross polarization (HV) (Schwerdt et al., 2017). For ALOS281 2, this error is less than 0.8 dB, as shown by Motohka et al. (2018). The operational radiometric accuracy of NISAR is not yet known as the satellite data is not produced yet. For this reason, we will assume that NISAR will have a radiometric accuracy similar to other currently available SAR satellite mission (Sentinel-1 and ALOS-2). Therefore, a zero-mean Gaussian random noise with standard deviations of 0.7 dB (for VV and HH) and 1.0 dB (for HV) was introduced to synthetic σ⁰ for each element in our dataset (corresponding to a given θ, SSM, and Hrms). A hundred noise samples were randomly drawn for each element. These noise values (dB) were then added to the Dubois-B-simulated 288 σ⁰, generating 100 variations for each original element in our synthetic dataset. As a result, the noisy synthetic datasets were created for L- and S-bands, and in VV, HH, and HV polarizations, each containing 5,756,400 elements. This noisy synthetic data are supposed to approximate real NISAR data, assuming that real NISAR data will have similar radiometric accuracy to that of the noisy simulated datasets. Each point of the noisy synthetic dataset operationally represents the mean of backscattering coefficient over a spatially homogeneous unit (a plot or a mesh-cell) measuring a few hundred meters square. This will strongly reduce the effect of speckle excepted on real NISAR data because we are using the mean of pixels inside of a given spatial unit the influence of speckle noise will be reduced. For example, for a plot that is around 200 m × 200 m, the effect of speckle will be reduced by a factor of 20.

In this study, a NN approach was employed to estimate soil parameters from SAR data. The NNs were trained using the Levenberg–Marquardt algorithm (Marquardt, 1963) and structured with two hidden layers, each containing 20 neurons (Baghdadi et al., 2012) with Mean squared error (MSE) used as the loss function. This method was used because previous studies have shown that a network with two hidden layers and 20 neurons per layer provided accurate SSM estimates while maintaining reasonable computational efficiency (El Hajj et al., 2017). Both hidden layers employed a ReLU activation function (Schmidt-Hieber, 2020; Lin and Shen, 2018). Three SAR configurations were considered based on the polarimetric modes available for NISAR (Brancato and Fattahi, 2021), all three configurations utilized the L and S frequencies simultaneously:

• SP configuration: corresponds to the configuration where we use acquisitions from L- and S-bands in Single Polarization configuration. Noisy radar signal at HH polarization, and noisy radar signal at VV polarization were tested.

NNs were trained using only θ and the noisy synthetic training backscattering coefficients generated from Dubois-B. Consequently, neither reference-SSM nor reference-Hrms were used as inputs for the estimation of soil parameters (SSM and Hrms) as these two are not known at the time of estimation. Furthermore, since NISAR operates the L- and S-bands in tandem, θ is the same for the two wavelengths employed (Rosen et al., 2017; Villano et al., 2018; Kellogg et al., 2020; NISAR, 2025). SSM and Hrms were estimated simultaneously using all three configurations.

Additionally, a priori information on natural soil moisture conditions was incorporated during NN training. Previous studies demonstrated that prior knowledge of soil moisture conditions significantly enhances estimation accuracy of SSM (Baghdadi et al., 2012; Hamze et al., 2021; El Hajj et al., 2017). Weather data, including precipitation and temperature from ERA5 reanalysis, in situ sensors, and remote sensing products like the Tropical Rainfall Measuring Mission (TRMM), can help indicate whether the soil is dry to slightly wet (after a prolonged dry period before SAR acquisition) or very wet (following heavy rainfall). By integrating this a priori information on SSM, the range of possible soil moisture estimates is constrained, improving both accuracy and mapping reliability in neural network models. For this reason, in addition to the NN built using the whole range of SSM (without a priori information on SSM), separate NNs are created for each of the two soil moisture state, one encompassing dry to slightly wet soil moisture conditions and one for very wet soil moisture conditions (with a priori information on SSM).

The impact of a priori information was assessed accordingly, NNs were trained with and without prior information on soil moisture. When splitting the noisy synthetic data to create a dataset for dry to slightly wet soils and another for the very wet soils, an overlap of 10 vol.% has been kept between the two training sub-datasets of the NNs. Here are the three developed cases (using both S- and L-bands):

• Case 1: No a priori information is used for the soil moisture state. In this case, the NN is trained using SSM between 2 and 40 vol.%.

When it comes to validation datasets, in the case without a priori information (case 1), the three NN configurations (SP, DP, and QP) were validated using the entire noisy validation dataset, with SSM values ranging from 2 to 40 vol.%. For the two cases with a priori information on SSM (cases 2 and 3), the NNs were validated using a dataset having SSM values ranging between 2 and 25 vol.% when the soil is assumed to be dry to slightly wet (case 2), and using a dataset having SSM values between 26 and 40 vol.%. in the case of very wet soil (case 3). Nine neural networks were developed for surface soil moisture and roughness estimation. Table 2 summarizes each developed neural network.

The performance analysis of each neural network was conducted on the noisy validation dataset that corresponds to each case (see Table 2). The estimated SSM and Hrms values from the neural networks are compared to the reference values (those used to simulate the SAR synthetic validation dataset), and the errors are quantified using Root Mean Square Error (RMSE) and bias (Estimated–Reference). Additionally, the RMSE and bias of SSM estimates are analyzed as a function of Hrms and θ values; while bias and RMSE of Hrms estimates were analyzed based on SSM and θ values.

The results of SSM estimation were analyzed first, by comparing estimated SSM to reference (input) SSM for each of the NNs (Figure 1).

Analysis of the results will be presented for each of the three cases: case 1: no a priori information, case 2: a priori dry to slightly wet, and case 3: a priori very wet. For single polarization NNs, the presented results correspond to HH polarization, as HH and VV exhibited similar performance. Results for VV are provided in the appendix (Supplementary Figures A7a, d, g). Likewise, results for DP configuration NNs using VV and VH instead of HH and HV can be found in the appendix (Supplementary Figures A7b, e, h). The similar soil moisture retrieval accuracy for HH and VV polarizations (difference of 0.2 vol.% without a priori soil moisture infomration) may be due to the fact that the sensitivity of the radar signal to soil moisture is not very dependent on polarization (e.g. (Sokol et al., 2004; Baghdadi et al., 2008)). A second possible explanation is that although some authors have shown a stronger sensitivity of the radar signal in HH (e.g. (Beaudoin et al., 1990)), this difference is not clearly visible in the simulated data.

Considering case 1, where we do not use a priori information, the NN developed using the single-polarization (SP) configuration (NN1) resulted in an RMSE of 8.2 vol.% (Figure 1a) compared to 5.1 vol.% for NN2 (Figure 1b), which uses dual-polarization (DP) configuration. Meanwhile, NN3 which utilizes quad-polarization (QP) configuration performed the best with an RMSE of 4.2 vol.% (Figure 1c). Furthermore, NN1 showed large over estimation of SSM for very low SSM values, and significant underestimation for high SSM values. Bias values were around 0 vol.% for all three NNs.

In case 2, where soil moisture conditions were assumed to be dry to slightly wet, the NN constructed using the SP configuration (NN4) showed an RMSE of 6.1 vol.% (Figure 1d), compared to 4.5 vol.% (Figure 1e) for NN5 (DP configuration); while NN6 (QP configuration) resulted in an RMSE of 3.9 vol.% (Figure 1f) which was the best out of the three. Similarly to case 1, the SP configuration (NN4) showed an important overestimation for low reference SSM and underestimation for high reference SSM. Bias was positive and varied from 1.5 vol.% for the SP configuration to 0.8 vol.% for the QP configuration.

Case 3 tells a similar story, NN9 (QP configuration) performed the best, with an RMSE of 3.2 vol.% (Figure 1g), followed by NN8 (DP configuration) with 3.8 vol.% (Figure 1h), and finally NN6 (SP configuration), with an RMSE of 4.6 vol.% (Figure 1i). There was no important overestimation at low SSM values, although we still have underestimation for high reference SSM values. Bias was negative ranging from −1.8 vol.% for the NN7, which uses SP configuration, to −0.5 vol.% for the NN using QP configuration.

Therefore, the quad-polarization configuration achieved the best SSM estimation, with errors consistently lower than the two other configurations tested (single-polarization and dual-polarization configurations). Furthermore, NNs constructed using a priori knowledge of soil moisture conditions performed better than NNs constructed without knowledge of soil moisture conditions, with improvements of RMSE. Estimated compared to reference Hrms.

Estimated Hrms were compared reference Hrms in Figure 2. When examining case 1 (without a priori knowledge of soil conditions), NN1 (Figure 2 using SP configuration) resulted in an RMSE of 0.7 cm (Figure 2a), while NN2 (using DP configuration) performs slightly better with an RMSE of 0.6 cm (Figure 2b), and NN3 (using QP configuration) performs the best estimations with an RMSE of 0.3 cm (Figure 2c). Bias was similar across the board at around 0.01 cm. For case 2 (a priori dry to slightly wet), NN4, which uses SP configuration, showed an RMSE of 0.6 cm (Figure 2d), while NN5 (Figure 2e, DP configuration) had an RMSE of 0.5 cm, and NN6, which uses the quad polarization, resulted in an RMSE of 0.3 (Figure 2f). NN4 and NN5 exhibited positive bias, with values of 0.15 and 0.06 cm, respectively, while NN6 showed no bias. For case 3 (a very wet) NN7, using the SP configuration, resulted in an RMSE of 0.5 cm (Figure 2g), RMSE was similar for NN8 (using DP configurations, Figure 2h), while NN9 (QP configuration) had an RMSE of 0.3 cm (Figure 2i). Bias was negative for the tested NNs, being highest for NN7 at −0.13 cm, followed by −0.07 cm for NN8 and −0.04 cm for NN9.

Similar to SSM estimation, quad-polarization configuration performed the best Hrms estimation, with errors around half of the two other configurations (SP and DP configurations). Furthermore, the neural networks in our article output both soil moisture (SSM) and surface roughness (Hrms), and since the radar signal is related to both soil moisture and roughness, an improved estimation of SSM in the case of a priori information on SSM (thanks to the optimized estimation of soil moisture within a reduced range of SSM values) can lead to an improvement in Hrms estimation. This improvement is negligible for the QD configuration, which performs well in all three cases; however, we saw improvements between 0.1 and 0.2 cm for the SP and DP configurations (Figure 2).

In this section, SSM estimation errors were analyzed using RMSE and bias metrics as a function of Hrms and θ values for each configuration in our study (SP, SP, and QP) and for each case (no a priori knowledge, a priori dry to slightly wet, a priori very wet). As in Section 3.1, for SP configuration, the NN tested utilized the HH polarization; results for VV are provided in the appendix (Supplementary Figures A8 and A9). Likewise, results for VV and VH instead of HH and HV can also be found in the appendix (Supplementary Figures A8 and A9).

Figure 3 shows the RMSE on SSM estimation as a function of θ and Hrms for the various NNs. For NNs constructed without a priori knowledge of soil moisture conditions, NN1 (SP configuration) had RMSE values ranging from around 6.0 vol.% for low θ values (30°), to around 9.5 vol.% for high θ values (50°). RMSE ranged from ∼3.5 to ∼6.0 vol.% for NN2 (DP configuration), and from ∼3.0 to ∼5.0 vol.% for NN3 (QP configuration). Figure 3b shows the effect of θ on RMSE when using a priori knowledge of dry to slightly wet soil conditions. RMSE ranged from ∼5.0 to ∼6.0 vol.% for NN4 (SP configuration), from ∼3.5 to ∼5.0 vol.% for NN5 (DP configuration), and from 2.8 to around 4 vol.% for NN6 (QP configuration). Figure 3c shows that RMSE ranged from ∼4.0 to ∼4.5 vol.%, for NN7 (SP configuration), from ∼3.0 to ∼4.0 vol.% for NN8 (DP configuration), and from ∼2.5 to ∼3.5 vol.% for NN9 (QP configuration). Therefore, RMSE increased as θ increased. Furthermore, incorporating a priori knowledge of soil moisture conditions, and using QP polarization reduced RMSE and narrowed its range as marked by the difference between the maximum and minimum RMSE (ΔRMSE) that was approximately 3.5 vol.% for NN1 and around 1.0 vol.% for NN9.

Figures 3d–f, show RMSE as a function of reference Hrms. For NNs constructed without a priori knowledge of SSM (Figure 3d), NN1 (SP configuration) had the highest RMSE for very high and very low Hrms values (∼13.0 vol.% at Hrms = 0.5 cm, and ∼9.0 vol.% at Hrms = 4.0 cm). NN2 (DP configuration) and NN3 (QP configuration) exhibited their highest RMSE values at ∼6.5 and ∼4.5 vol.%, respectively, for very low Hrms (0.5 cm). For NNs constructed for dry to slightly wet conditions (Figure 3e), RMSE for NN4 (SP) is highest for very low and very high Hrms values (∼7.0 vol.% for Hrms of 0.5 and 5.0 cm). For NN5 (DP) and NN6 (QP), RMSE values were around 4.5 and 4.0 vol.%, respectively across the range of Hrms. For NNs developed for very wet conditions, NN7 (SP configuration) and NN8 (DP configuration) had their highest RMSE values for very low Hrms (∼6.5 and ∼5.0 vol.% for Hrms = 0.5 cm) while NN9 (QP configuration) resulted in an RMSE of around 3.5 vol.% across the range of Hrms values.

RMSE was highest at both the lowest and highest Hrms values in our study, particularly when using the SP configuration. However, using the QP configuration and a priori knowledge of soil moisture conditions significantly reduced RMSE and minimized the impact of Hrms on SSM estimation.

Figure 4 presents the bias on SSM estimation as a function of θ and Hrms for the various NNs. Figure 4a shows that without a priori knowledge of soil moisture conditions, Bias is around 0 vol.% for NN1, NN2, and NN3 (no bias). In the case of a priori dry to slightly wet conditions, bias was positive, NN4 (SP configuration) had a bias ranging from 1.0 for low θ (30°) to 2.0 for high θ (50°). For NN5 (DP configuration), bias ranged between 0.5 and 2.0 vol.%, and NN6 (QP configuration) ranged between 0.5 and 1.0 vol.% (Figure 4b). When working in very wet soil moisture conditions (Figure 4c), bias that more negative greater when θ increases, ranging from −1.0 to −2.0 vol.%, for NN7 (SP configuration), from ∼−0.5 to ∼−1.5 vol.% for NN8 (DP configuration), and from ∼0 to ∼−1 vol.% for NN9 (QP configuration).

Figures 4d–f show estimation bias as a function of reference Hrms. When a priori soil condition knowledge was not used, bias values ranged from −10.0 to 7.0 vol.%, when Hrms increased from 0.5 to 4.0 cm, for NN1 (SP configuration), from −5.0 to 3.5 vol.% for NN2 (DP configuration) and from −2.0 to 3.0 vol.% for NN3 (SP configuration) (Figure 4d). NNs constructed for a priori dry to slightly wet conditions resulted in smaller ranges of bias values, with NN4 resulting in bias values varying between −5.0 to 6.5 vol.%, as Hrms increased from 0.5 to 4.0 cm NN5 resulted in bias values ranging from −3.0 to 4.0 vol.%, while bias values for NN6 ranged from −1.0 to 3.0 vol.%. For NNs constructed with a priori knowledge of very wet soil moisture conditions, bias values ranged from −6.0 to 2.0 vol.% and from −4.0 to 2.0 vol.%, respectively for NN7 (SP configuration) and NN8 (DP configuration) when Hrms increases from 0.5 to 4.0 cm NN9 (QP configuration) shows a mostly constant bias at around −1.0 vol.% for Hrms values between 0.5 and 3.0 cm, outside that range, bias increases, reaching 2.0 vol.% for Hrms of 4.0 cm.

Bias was generally more negative for lower Hrms values and more positive for higher Hrms values. However, the effect of Hrms on bias was reduced when using QP configuration and a priori knowledge of soil moisture conditions, as shown by the improvement in the range of bias between NN1 and NN9, as Δbias was ∼17.0 vol.% for NN1 and ∼2.0 vol.% for NN9.

In this section, Hrms estimation were assessed using RMSE and bias values as a function of reference SSM and θ values for each configuration in our study (SP, SP, and QP). RMSE has been calculated without a priori knowledge of soil moisture conditions because the results of Section 3.2 showed that using a priori knowledge did not significantly enhance Hrms estimation. Figure 5a shows the RMSE on Hrms estimation as a function of reference θ. For NN1 (SP configuration), RMSE values decreased from ∼0.9 to ∼0.6 cm when θ increases from 30° to 50°. For NN2 (DP configuration), RMSE went from ∼0.7 down to ∼0.5 cm when θ increases, while for NN3 (QP configuration), RMSE values decreased from ∼0.4 to ∼0.3 cm when θ decreased. ΔRMSE, calculated as the difference between maxRMSE and minRMSE, was ∼0.3 cm for NN1, compared to ∼0.2 cm for NN2, and ∼0.1 cm for NN3, which had the lowest RMSE values overall. Figure 5b shows RMSE as a function of reference SSM. NN1 had its highest RMSE at around 1.0 cm for very low and very high SSM reference SSM values (2 vol.%, and 40 vol.%, respectively). The lowest RMSE achieved by NN1 was around 0.6 cm for an SSM value of around 20 vol.%, NN2 showed RMSE varying between ∼0.5 and ∼0.6 cm, while NN3 had the lowest overall RMSE varying between ∼0.3 and ∼0.4 cm.

Therefore, RMSE decreased when θ increases. Moreover, RMSE was highest for very low and very high SSM values. However, for the QP configuration (NN3), these effects were not as strong when compared to the other polarization-configurations.

Figure 6a presents the bias values as a function of reference θ. Bias was around 0 cm for the three NNs tested with NN3 having slight positive bias of around 0.1 cm for really high and really low θ values (30° and 50°, respectively). The bias was also examined as a function of reference SSM (Figure 6b). For NN1 (SP configuration), there was a negative bias for low SSM values (lower than 20 vol.%), reaching −0.8 cm at an SSM of 2.0 vol.%. Conversely, for high SSM values (>20 vol.%), the bias was positive, reaching 0.8 cm at an SSM of 40 vol.%. Similarly, for NN2 (DP configuration) and NN3 (QP configuration), the bias followed the same trend: negative for low SSM values and positive for high SSM values. For NN2, the bias reached −0.4 cm at an SSM of 2.0 vol.% and 0.4 cm at 40 vol.%. For NN3, the bias was the smallest, reaching −0.2 cm at 2.0 vol.% and 0.2 cm at 40 vol.%.

Errors in SSM estimates from neural networks were shown to be influenced by SAR incidence angle (θ) and by soil surface roughness (Hrms). Regarding the effect of incidence angle, RMSE on SSM was highest when θ was highest for all NNs tested, however QP configuration proved to be less affected by θ when compared to other configurations. This degradation in SSM estimation with increasing radar incidence is well documented in the literature, as the sensitivity of the radar signal to soil moisture decreases with increasing incidence angle due to noise caused by soil roughness (Aubert et al., 2011; Baghdadi et al., 2008).

Additionally, for NNs constructed with a priori knowledge of dry to slightly wet soil moisture conditions, there was a slight overestimation (positive estimation bias) that gently increased when θ increases. Inversely, for NNS constructed with a priori very wet soil moisture conditions, a slight underestimation (negative estimation bias) was observed, slightly increasing when θ increases. This underestimation of SSM for high moisture values (30–40 vol.%) is due to saturation of the radar signal for this range of SSM (30–40 vol.%) (Baghdadi et al., 2016).

Regarding the effect of Hrms on SSM estimation, when no a priori information on SSM was used, very low or very high Hrms led to an increase in RMSE for SP configuration. For DP configuration, RMSE on SSM decreased when Hrms decreased; while QP configuration was not significantly affected by Hrms. For a priori dry to slightly wet condition, RMSE on SSM for SP configuration was highest for very low or very high Hrms, while Hrms did not affect RMSE on SSM for the DP and QP configurations in this soil moisture condition. Regarding a priori very wet conditions, RMSE on SSM for the SP and DP configurations increased when Hrms decreases, while Hrms did not significantly affect RMSE of the QP configuration. Regarding bias, lower Hrms values led to more negative SSM estimation bias while higher Hrms values led to more positive SSM estimation bias for all cases, with QP configuration performing the best being affected less than SP and DP configurations by Hrms. These over- and under-estimation of the SSM estimates depending on the range of Hrms were observed by El Hajj et al. (2017), who note that a smooth surface (Hrms < 1 cm) results in decreased backscattering and underestimated SSM with high RMSE on SSM. On the other hand, a rough surface (Hrms > 3.0 cm) augments radar backscatter, leading to SSM overestimation. However, NNs using the Quad polarization configuration were able to mitigate this limitation of smooth or rough surfaces.

Regarding Hrms estimation errors, RMSE on Hrms was shown to be affected by θ for both SP and DP configurations, as RMSE decreases when θ increases. This better estimation of ground roughness for high values of θ is due to a better sensitivity of the radar signal to roughness for high values of θ compared to low incidence angles values because the dependence of the radar signal on surface roughness in agricultural areas is mainly significant at high incidence angles (Baghdadi et al., 2008). Hrms estimated from QP configuration was not shown to be affected by θ. SSM affected Hrms estimation errors for very high and for very low SSM, when using SP configuration, however there was no significant effect for neither the DP or QP configurations. On the other hand, SSM affected bias for Hrms estimation with negative bias for low SSM value and positive bias for high SSM values with QP configuration being affected less than the SP and QP configuration.

In this study, three cases were examined 1) no a priori knowledge of soil moisture conditions, 2) soil conditions were considered known as dry to slightly wet, 3) soil conditions were considered known as very wet. Incorporating a priori information that can be easily obtained from in situ precipitation stations or from other sources (remote sensing data or/and model-based simulation) enhances the precision of SSM estimates. However, in the cases where soil moisture conditions is known, the range of SSM values in the training phase are smaller (case 2: 2 vol.% ≤ SSM ≤ 30 vol.%; case 3: 20 vol.% ≤ SSM ≤ 40 vol.%) compared to the range of SSM values when no a priori soil moisture knowledge were used (case 1: 2 vol.% ≤ SSM ≤ 40 vol.%), reducing the over- and underestimations of SSM. Therefore, in order to correctly assess the improvement in SSM estimation in the cases of a priori information on SSM, the same range of SSM has be considered when calculating RMSE on SSM estimates. Table 3 shows RMSE and Bia values on SSM estimation when using the same range of SSM values for NN constructed without and with a priori information of soil moisture conditions. When comparing NNs for without a priori knowledge of soil moisture condition (case1: NN1, NN4, and NN7) to NNs constructed with a priori knowledge of dry to slightly wet conditions (case 2: NN2, NN5, and NN8), RMSE was calculated using only SSM values ranging between 2 and 25, which is the range used for a priori dry to slightly wet NNs. Similarly, when comparing non a priori NNs to NNs constructed with a priori knowledge of very wet conditions (case 3: NN3, NN6, and NN9), RMSE was calculated using only SSM values ranging between 26 and 40, which is the range used for a priory very wet NNs. Table 3 shows that the improvement in RMSE on SSM for a priori dry to slightly wet NNs in “non a priori” NNs was 1.2 vol.% for SP configuration, 0.5 vol.% for DP configuration, and 0.3 for QP configuration. For “a priori very wet” NNs, the improvement in RMSE was 3.6 vol.% for SP configuration, 1.4 vol.% for DP configuration, and 1.0 vol.% for QP configuration. Therefore, using a priori knowledge of soil moisture conditions slightly improved the SSM estimation results when working in dry to slightly wet soil conditions, and greatly improved soil moisture estimation when working in very wet soil condition for all NISAR configurations.

NISAR will provide both of S and L frequency bands simultaneously, enabling dual-frequency radar observations during a single pass (NISAR, 2025; Kellogg et al., 2020). This is a significant feature of NISAR, not currently available in other SAR constellations. For this reason, our work used L and Sbands in tandem; however, it is important to assess the use of two frequency bands by comparing it to results we get using a single frequency band.

For this reason, single-frequency noisy datasets were built for each frequency band (L, and S-band). For each of these two, NNs were constructed and tested in the Single, Dual, and Quad-polarization configurations. Table 4 compares RMSE values for SSM estimation resulting from NN built using two frequencies and one frequency and without a priori knowledge of soil moisture condition (the entire range of SSM). L-band and S-band showed similar performance showed in the table as “L or S-band.” As seen in Table 4, NNs utilizing both L- and S-bands together consistently outperformed those relying on a single band, achieving lower RMSE values across all configurations. Specifically, in the SP configuration, RMSE increased from 8.2 vol.% (dual frequency bands) to 9.3 vol.% (single frequency band), reflecting a 1.1 vol.% performance degradation when using only one frequency. Similarly, in the DP configuration, RMSE increased from 5.1 vol.% (dual frequency band) to 6.2 vol.% (single frequency band), and in the QP configuration, it worsened from 4.2 vol.% to 5.4 vol.%, indicating a 1.2 vol.% decline. These findings underscore the benefits of dual-frequency SAR observations, which provide more accurate soil moisture estimates by integrating complementary scattering information from both frequency bands.

Table 5 compares RMSE values for Hrms estimation (cm) without a priori knowledge of soil moisture condition using both L and S bands or one of the bands only (L or S). NNs utilizing both L- and Sbands together performed better than NNs relying on a single band, achieving lower RMSE of around 0.1 cm across the different configurations.

In order to better assess the use of multiple frequencies simultaneously for soil moisture estimation, results of the dual frequency (L- and S-band) bands were compared to single frequency (L-band). When working without a priori information on SSM, using L-band alone (results not presented in the manuscript), achieved an RMSE on SSM estimation of 8.3 vol.% for SP configuration, 6.1 vol.% for the DP configuration and 5.3 vol.% for the QP configuration. Therefore, using dual frequency bands results in better SSM estimation of around 0.2 vol.% for the SP configuration, 1.0 vol.% for the DP configuration and around 1.1 vol.% for the QP configuration. NISAR Soil Moisture Science Team (2023) also investigated the benefit of using the dual frequency bands compared to L-band only, utilizing only the single polarization configuration (HH only) with results of dual-frequencies showing improvements in unbiased RMSE of 1 vol.% for corn and 0.2 vol.% for soybean over single frequency (L-band).

Concerning Sentinel-1, the S1 constellation currently provides satellite acquisitions in cross polarization configuration (VV/VH) over the majority of the Globe (P. Potin et al., 2019; Ticehurst et al., 2019). It is one of the more widely used SAR constellation for SSM and Hrms estmation (Hamze et al., 2021; Choker et al., 2017; El Hajj et al., 2017; Choker, Baghdadi, and Zribi, 2018). In recent works, (Ettalbi et al., 2023), constructed NN model trained and validated using synthetic C-band data simulated using the Integral Equation Model (IEM) model. In the validation phase using synthetic dataset, they showed that the Dual-polarization (VV and VH) lead to RMSE on SSM of around 6.0 vol.%. In addition, Choker, Baghdadi, and Zribi (2018) applied NNs, trained with synthetic data, on S1 data for SSM and Hrms estimation, with dual polarization performing better than single polarization, resulting in an SSM estimation with a RMSE of 7.5 vol.% and 5.8 vol.% when using NNs constructed without, and with a priori knowledge of soil moisture conditions, respectively. Regarding Hrms estimation, Choker et al. (2018) obtained an RMSE of 0.8 cm when working without a priori knowledge of soil moisture conditions and 0.7 cm when working with a priori knowledge of soil moisture conditions.

Compared to these findings by Ettalbi et al. (2023), and Choker et al. (2018), the NNs developed in our work performed better, resulting in lower RMSE values when using the DP and QP configurations. A few reasons are behind this improvement. Firstly, Sentinel-1 operates at a single frequency (C-band, wavelength ∼ 5 cm) whereas NISAR can rely on two bands (L and S-bands); these two independent frequency bands could provide complementary information that improve to performance of the NNS. Secondly, Sentinel-1 operates in the cross polarization mode (VV/VH), meaning that it is limited to using NNs in the DP configuration whereas NISAR can provide quadpolarization data. What is notable here is that in our work, the DP configuration was significantly outperformed by the QP configuration in terms of overall error as well as in terms of performance stability thus signaling the potential importance of NISAR for SSM and Hrms estimation.