# High Spatio-Temporal Resolution CYGNSS Soil Moisture Estimates Using Artificial Neural Networks
## 5 Discussion  
The proposed learning-based SM retrieval methodology generates promising overall performances with comparable accuracy to the reference SM data, demonstrating that it could be generalized for the global SM estimation. For this purpose, the current trained model can be used over global terrains with close statistical distributions of the bio-geophysical parameters (vegetation cover, topography, and surface roughness) in the present analysis. Alternatively, the model can be further trained over a much larger and globally-representative data set with additional CYGNSS observations, terrain characteristics, land cover classifications, as well as possible new input features. As more data samples are added to the training, the learning performance is expected to improve. In any case, a future work will be conducted for comparison of the proposed method to global SM sources (such as SMAP). A potential limitation in a global comparison scenario is the lack of reference SM data at high spatio-temporal resolutions. This was the main motivation of this study to employ ISMN sites with a 9-km grid of SM representativeness. Assuming constant SM over such a grid is another source of limitation in this study, which is inevitable for the current state-of-the-science. The reference SM data, either ISMN sites in this study or SMAP-like global observatory data, are not the ground truth and have their own internal errors. Moreover, ISMN measurements have a quite different resolution (point-scale) than CYGNSS observations (distributed scattering). In addition to extending the use of the current method, a future work could be conducted to investigate several non-parametric, nonlinear machine learning algorithms as well as the optimization of the current ANN model to obtain its full potential. Despite a number of actions to get the best performance out of the learning model (such as preprocessing of the data with the quality controls, assessment of the input feature contributions, and use of derived proxy parameters), the scope of this study is not an in-depth analysis of the learning methods. The present method has many sources of constraints and uncertainties, some of which have been addressed and dealt with to a degree in this study, and all could be investigated further in future work. These can be explained as follows:  
CYGNSS observations and data products involve a number of uncertainties that might have affected the results of this study. During this study, multiple reflectivity approximations from CYGNSS data products were used as model inputs. The learning performance of the model varied greatly with these different reflectivity approximations. This indicates a changing level of uncertainty throughout the CYGNSS dataset. CYGNSS parameter uncertainties can be described as follows: (i) SP calculation with the geoid assumption was originally developed and works well for ocean [42]; however, it can generate large offsets for SP locations over land as the elevation and topographic relief get higher. Since this problem is said to be resolved with the CYGNSS Level 1 Science Data, Version 3.0 in a near future, we applied a number of strategies that did not involve explicitly solving the actual SP location: With the help of the coherency assumption, we used the peak _brcs_ value to calculate \(\Gamma_{brcs}\), which should reflect the actual coherent reflections; we filtered out _brcs_ DDM peak delay rows that fall outside a range of \([7,10]\); we also incorporated CYGNSS-derived TES, elevation, and slope as proxy coherency parameters to the ANN model. In addition, analyzing terrains with relatively low topographic relief (slopes up to 2) and elevations no more than roughly 1300 m in this study limits the effects of this uncertainty; however, these parameters would get higher values in a global application.