# High Spatio-Temporal Resolution CYGNSS Soil Moisture Estimates Using Artificial Neural Networks
## 2 Theoretical Background
### Challenges  
Despite the potential usability of the CYGNSS data products in the reflectivity calculations through (4) or (5), the uncertainties in the determination of these data products in the present Level 1 data version (v2.1) would introduce errors in the estimations. Uncertainties in the current CYGNSS data include estimation of the receiver gain as well as the GPS transmitted power and gain. Furthermore, the transmitter and the receiver ranges to the specular point (SP) might involve errors since the current SP calculation of the CYGNSS mission uses an ellipsoidal model of the Earth, ignoring topography over land ([PERSON] et al., 2017; [PERSON] et al., 2018). Since the equations from (4) to (11) can only provide the optimal solution with the computation of an absolute reflectivity, such errors would require subsequent corrections for accurate SM retrieval. Additionally, varying land covers (especially, mixtures of heavy vegetation canopies such as forests) and topographic relief over land can introduce an ambiguity about where and under what conditions the coherent reflection regime is dominant. When the incoherent component of the bistatic received power superimposes or dominates the coherent reflections, the use of (4) and (5) would lead to inaccuracies. In addition to the aforementioned challenges so far, the SM retrieval process itself contains high complexity and nonlinearity. This is because Equations (4) through (11) imply that the retrieval problem is dependent not only on the reflectivity and SM but also on the vegetation, surface roughness, topography, and soil texture through a combination of linear and nonlinear relations. Moreover, these land geophysical parameters have distinct variability ranges. In addition, the CYGNSS DDM instrument (DDMI) has diverse sensitivities to these parameters [43]. As a result, CYGNSS observations exhibit nonlinear relations with the dynamic land parameters. This leads to parameter ambiguity, where varying combinations of multiple land geophysical parameters might result in the same or close sensor measurements. Parameter ambiguity makes the SM retrieval an ill-posed problem. Additionally, to obtain accurate retrieval results, the impact of the measurement geometry (incidence angle) as well as the internal and external noise need to be properly accounted for. Previous airborne GNSS-R experiments and modeling studies reported supporting observations and simulated results for these effects, where a dynamic range of roughly 15 dB is determined jointly by the several dynamic geophysical parameters throughout crop seasons [34; 44]. The CYGNSS constellation has sub-daily, quasi-random observations with fine spatial resolutions. Despite the advantage due to high spatio-temporal resolution, this complicates the use of ancillary data for accurate representation of the land geophysical parameters. In other words, finding sufficiently accurate input parameters at the high spatio-temporal resolutions of the CYGNSS observations to correct the vegetation and surface roughness effects as well as solving the Fresnel reflection equations are a concern. It is evident from Equations (4)-(11) that knowledge of the various parameters from vegetation and surface roughness to soil texture is needed at CYGNSS's resolution for accurate retrieval using the given physical model for the coherent reflection assumption. In fact, simplified LUTs (such as land cover-based or globally constant values) or average values per coarse grids were used to approximate these parameters in the coarse spatial resolution SM retrieval missions such as SMOS [45] and SMAP [38]. The reduced sensitivity of the radiometers to the roughness and vegetation makes this possible for the relatively coarse observations of these missions.