# Incorporating Aleatoric Uncertainties in Lake Ice Mapping Using RADARSAT-2 SAR Images and CNNs
## 6 Discussion  
In this paper, the incorporation of aleatoric uncertainty in a CNN was elaborated and results presented. The model was designed to produce two outputs to estimate the probability of ice and water, and the variance of this estimate. Adapting the model by using the custom loss function provides uncertainty estimates of the predicted probability that are found highly effective in retrievals, specifically in sections of the lakes that exhibit more complex textures such as along lakeshores and ice edges. To gain deeper insight into how uncertainty informs predictions, one possible method would be to examine how misclassification correlates with higher levels of uncertainty. This will frame an approach to improving predictions either by creating a better training set or by fusing the predictions in focused areas with other observations/model predictions. Due to limited access to an independent source of observations with equivalent/higher spatial resolution for the same acquisition dates, such experiment could not be performed in our research. One potential candidate for running the experiment was Landsat images, but images covering the study area were obscured by clouds, making them an inconsistent and thus unsuitable source of information for this study. There are other potential data sources that are discussed hereafter.  
Despite the high spatial resolution and imaging capabilities of SAR under cloudy conditions, interpretation of SAR imagery is challenging and requires expert knowledge. Therefore, the preparation of training labels for supervised learning algorithms is costly, as is the case for lake ice classification. For this research, we used available ice analysis charts to provide our training labels. These charts are created at CIS by experts with decades of experience interpreting SAR imagery. Visual interpretations and simultaneous mapping are done by looking at the SAR images as well as historical ice patterns and meteorological conditions. These labels do not contain small-scale features in the ice cover, and the richness of visual cues across ice concentration levels is less than that of sea ice concentration datasets. This finding, in combination with the fact that a deeper CNN was not useful (not shown), leads us to hypothesize that the information content of image analysis charts for lake ice is lower than that for sea ice. We envision creating an enhanced training set using other data sources, such as optical imagery with a high revisit time that increases the chances of obtaining cloud free images that can also be incorporated in the classification framework (uncertainty characterization). A practical example of such a potential data source is the Daily Lake Ice product generated by the Climate Change Initiative (CCI+) Lakes project of the European Space Agency through processing of MODIS Terra/Aqua top-of-atmosphere reflectance data (MOD/MYD02). However, the prospective research is certain to face challenges, such as lower spatial resolution than SAR and cloud obstruction. By understanding the spatio-temporal variability of ice cover, we can confine the use of the lower resolution observations to regions with less variability. On the other hand, more frequent observations from MODIS will allow us to trace pixels of ice/water and fill the gaps caused by cloud cover. However, we would have to quantify any uncertainties introduced by a composite product.