## 5 Discussion and Future Directions
Although the random roughness scales in the IGOT model can vary spatially, in this work, we fixed the value due to a lack of spatial information on these roughness scales. Another possible reason for the discrepancies is the presence of fading effects due to this random roughness that our incoherent model failed to capture [33]. The cutoff wavenumber between the short-scale and the long-scale component of the IGOT model needs to be such that the assumptions made in Section 2.1 are valid. Specifically, the long-scale component is smooth relative to the wavenumber and the short-scale component has a narrow correlation function. In ocean application, this cutoff was selected between \(k/6\) and \(k/3\)[22], depending on the wind speed. In [34], the cutoff was selected to be \(3k(\sigma_{X}\sigma_{Y})^{1/2}\), where \(\sigma_{X}\) and \(\sigma_{Y}\) are the standard deviations of the long-scale component in the \(x\) and \(y\) directions, respectively. The model in [34] was developed for both ocean and land applications, and the cutoff wavenumber was selected to ensure a smooth transition between the two scales and the constraints of each component. In validating the IGOT model, both \(\sigma_{L}\) and \(\sigma_{S}\) were fixed to a single value for each area. However, these parameters can vary spatially. Varying \(\sigma_{L}\) was explored in [31] by estimating the parameter from lidar measurements with 30 cm spatial resolution. The results showed that estimating \(\sigma_{L}\) from lidar can improve the matching with CYGNSS observations. In theory, \(\sigma_{S}\) can also be estimated from lidar for some surfaces. For surfaces with known spectral shapes, the spectra of the surface can be estimated from the lidar measurements. Then, \(\sigma_{S}\) can be estimated from the area of the spectra within the small-scale roughness region. The JER DDM presented in Figure 12 resembles a land DDM from flat regions. Thus, the WAF projection of the SP has an almost convex shape, as shown in Figure 12c. These DDM properties are the result of the special characteristics of this area. The JER sites are located in a relatively flat region with minimal vegetation and almost homogeneous soil moisture. Thus, the IGOT model can potentially assist in validating the CYGNSS calibration over land and other systems in the future. However, a lidar DEM needs to be used instead of the SRTM DEM to reduce the DEM noise. It should be noted that the validation should be restricted to the DDMs located in the flat area and not the full extent of the analyzed JER tracks. This model can be used in a physics-based soil moisture retrieval method to estimate the surface soil moisture value from CYGNSS observation(s). Such a method was presented in [35], which used a global optimizer and a forward model to estimate soil moisture from CYGNSS DDMs. However, unlike the IGOT model, the forward model in [35] can be applied to flat terrains only. Thus, by replacing the model in [35] with the IGOT model, the retrieval method can be extended to retrieve soil moisture value from areas with topography. Studying the sensitivity of the IGOT model to noise and errors in its input parameters and their implications on soil moisture retrievals is essential for estimating the performance of using the IGOT model for retrievals.