# Incorporating Aleatoric Uncertainties in Lake Ice Mapping Using RADARSAT-2 SAR Images and CNNs
## 2 Background  
CNN applications via remote sensing imagery have shown promise in recent studies, having been successfully applied to optical imagery and SAR observations for classification, object detection, and data fusion tasks. These studies have implemented CNN as either the core of their deep learning system or a significant part of them. [PERSON] and [PERSON] [24] have demonstrated how CNN can be used for target detection using hyperspectral images, and [PERSON] et al. [25] and [PERSON] et al. [26] have applied Gabor-Deep and contextual region-based CNN on SAR images, respectively, to detect objects. To improve CNNs' performance in fully retrieving the spatial information, new architectures and expansions have been proposed [27]. As an example, capsule networks (CapsNets) as new neural network structures with the capability of recognizing the spatial information of the image space are being merged with CNNs to classify complex image scenes [27].  
Few studies, however, have been conducted on the application of CNNs to the problem of lake and sea ice mapping. [PERSON] et al. [23] mapped ice concentration in the Gulf of Saint Lawrence using RADARSAT-2 images. They compared ice concentration using different methods of multi-layer perceptron (MLP40), CNNs, and an ice concentration product derived from passive microwave data using an algorithm developed based upon ARTIST project (Arctic Radiation and Turbulence Interaction STudy) known as ARTIST Sea Ice (ASI) [28]. [PERSON] et al. [29] used CNNs to classify sea ice types using 2018 and 2020 Sentinel-1 SAR images and gained an average classification accuracy of 91%. CNNs for lake/sea ice classification can be used in a baseline structure such as in the work reported by [PERSON] et al. [21] and [PERSON] et al. [23], or they can be utilized in complex architectures that have shown better performance in specific tasks such as work by [PERSON] et al. [22] that uses a semantic segmentation network proposed by [PERSON] and [PERSON] [30] for classifying ice/snow-covered and open water areas in alpine lakes of Switzerland.  
In the research of [PERSON] et al. [21], which builds on [PERSON] et al. [23], CNNs are used, and quality control measures are provided based on the uncertainty of the CNN output with the goal of creating reliable sources for incorporating lake ice information in operational data assimilation. In these studies, CNNs have been shown to have powerful feature learning capabilities; learning the features that map the image data to a set of training labels that come from sea ice and lake ice charts. Such training labels introduce potential error and uncertainty into the CNN model predictions, which is due to inherent errors in both spatial representativeness and image interpretation of ice experts using SAR imagery and other auxiliary data.  
In this paper, image analysis charts are used to train a CNN to predict ice and water in Lake Erie and Lake Ontario (Canada/United States of America). Given the uncertainty in the ice chart labels, a previously proposed framework [31; 32] is adopted to both quantify the uncertainty and obtain improved model predictions by taking this uncertainty into account. The important aspect to consider here is that aleatoric uncertainty cannot be reduced by inputting more data or training a deeper network. Aleatoric uncertainty arises from the nature of data; in other words, it is a measure used to identify the noise inherent in data. This uncertainty quantification can provide in-depth insight into errors inherent in the observations and help us refine where more confidence is expected in classification results. Aleatoric uncertainty is in theory different from uncertainties that are associated with model parameters, called epistemic uncertainty, although there is some ambiguity in trying to separate the two [33].