# High Spatio-Temporal Resolution CYGNSS Soil Moisture Estimates Using Artificial Neural Networks
## 3 Soil Moisture Retrieval Methodology  
We have developed a new, CYGNSS-based SM retrieval methodology that exploits a non-parametric, nonlinear machine learning (ML) technique, namely ANN. The decision to use this method is motivated by its following properties and correspondences to the aforementioned requirements as well as challenges of the SM retrieval from CYGNSS observations:  
* Nonlinear ML algorithms are known for their solid power to solve regression problems where a mix of linear and nonlinear dependences exists between parameters [47]. * Such techniques, ANNs in particular, are capable of approximating/learning complex mappings within multi-dimensional parameter spaces with the help of advanced learning algorithms. * ANNs can, in principle, be trained to approximate any measurable function to any desired degree of accuracy to represent arbitrary input-output relations [48]. It should not turn out that the methodology in this study relies on such arbitrary relations. On the contrary, the CYGNSS observables and ancillary data that are major inputs to the regression process are used in order to fulfill the linear/nonlinear relations as well as calibration/correction requirements shown in Section 2. The property of ANNs makes the use of proxy input features possible for the purpose of fine-tuning the overall model performance. * ANNs are non-parametric models, meaning that the number of parameters that can be input to the retrieval process is flexible, in contrast to the requirement for fixed number of parameters in the parametric models (such as traditional regression models, physical and/or empirical models). This can help advance the CYGNSS-based SM retrieval approaches by introducing the use of additional parameters into the retrieval process. For instance, the CYGNSS trailing-edge slope (TES) can be input into the SM retrieval as a coherency/incoherency indicator in addition to reflectivity, as previously practiced for a study of inundation detection by using another non-parametric learning method [35], instead of dealing with the explicit determination of the coherency. * The non-parametric nature of ANNs make these models applicable to learn many different kinds of data regardless of their statistical properties. In other words, the retrieval process can integrate data coming from different sources with even poorly-defined (or unknown) probability distributions and relate them well to the parameter of interest [47]. To illustrate, LUT-based SMAP  
Figure 1: Multiple CYGNSS observations (uncalibrated DDM SNR) that are averaged into the SMAP grids. Data are from 14–18 September 2018 over North Carolina, USA (The landfall of the Hurricane Florence was on 14 September 2018). data such as h-parameter (roughness parameter) and _stem factor_[39] can be incorporated into the CYGNSS SM estimates, combining with in situ data such as land cover and NDVI. * Consequently, such models have to make fewer assumptions about the data distribution, compared to the parametric models. This should not, in turn, mean that the parameters of the CYGNSS-based SM retrieval process have poorly-defined probability distributions. In contrast, it will be demonstrated throughout this section that most of the input parameters coming from CYGNSS observations and ancillary data exhibit well-defined distributions. However, it is a powerful flexibility for ancillary data usage that there is no need to make any assumption about the data distributions. * The use of such learning algorithms eliminates the need for development of a parametric model that is aimed at explicitly solving the electromagnetic relations and/or relating the in situ observations to sensor measurements. This could be beneficial for the SM retrieval from CYGNSS observations to overcome the aforementioned limitations of ancillary data and possibility of too simplistic assumptions. * ANNs are generally said to be a good balance between accuracy, stability, and computational speed [9].