# Incorporating Aleatoric Uncertainties in Lake Ice Mapping Using RADARSAT-2 SAR Images and CNNs
## 1 Introduction  
Lake ice cover is an essential variable for monitoring climate change [1]. Indeed, dates associated with lake ice freeze-up and break-up processes are highly sensitive to changes and variability in air temperature [2]. Lake ice coverage (or ice concentration) also affects weather events and regional climate due to its significant impact on heat and moisture transfer between lake surfaces and the atmosphere [3, 4]. Therefore, lake ice coverage products with an accuracy of 10% or better is a requirement identified by the climate community for improving numerical weather prediction and atmospheric reanalysis products [5, 6], and for climate monitoring as determined by the Global Climate Observing System (GCOS) [1]. Another operational use needing accurate lake ice cover products is navigation and operations in ice-covered waters. There are many suitable sources of observations available for mapping and monitoring lake ice coverage such as optical satellite data (e.g., Moderate Resolution Imaging Spectroradiometer (MODIS) and Visible InfraredImaging Radiometer Suite (VIIRS)); however, synthetic aperture radar (SAR) data remain an important source for lake ice mapping at national ice services since they are largely unaffected by the presence of cloud cover and can be acquired regardless of daylight.Using imaging synthetic aperture radar (SAR) for near real-time operational applications, such as sea ice and lake ice mapping, is becoming increasingly possible due to the launch of satellite constellation missions such as Sentinel-1A/B and the RADARSAT Constellation Mission (RCM) in recent years. These missions provide observations at higher temporal resolutions ( daily to weekly coverage depending on latitude) than previously available. Automated mapping of Great Lakes ice coverage using SAR has been the focus of several studies, beginning with [PERSON] and [PERSON] [7]. For the different ice types, the researchers created a library of the co-polarized backscatter signatures at C-band. Knowing the ice conditions and variability in the Great Lakes is of great importance due to their strong impact on the regional climate, ecology, hydropower industry, and navigation [8; 9]. In addition to the benefits that SAR observations bring to lake ice mapping, they also fulfill the requirements of relatively high spatial resolution (\(\leq\)100 m) and large areal coverage (i.e., in ScanSAR mode with nominal swath widths of 250-500 km) of the Great Lakes. Manual production of Great Lakes ice charts by the Canadian Ice Service (CIS) and U.S. National Ice Center (NIC) is operational. This approach is mainly based on visual interpretation of SAR images complemented by auxiliary datasets such as optical satellite imagery and visual observations from ship and aircraft to get insight on historical ice patterns and meteorological conditions [10]. To reduce human biases associated with visual interpretation and to accelerate analysis, several automated/semi-automated ice/water mapping methods have been proposed using SAR. It should be noted that most of these studies have focused on sea ice mapping, which differs subtly from freshwater lake ice mapping. Of all the studies on sea and lake ice mapping from SAR, only a few suggest unsupervised classification, including those by [PERSON] and [PERSON] [11] and [PERSON] and [PERSON] [12], and [PERSON] et al. [13]. There are also studies that use an unsupervised classification followed by a supervised labeling of ice and water such as those by [PERSON] et al. [14] and [PERSON] et al. [15].The abovementioned studies have found that the main drawback of only relying on supervised learning is the bias introduced to training sets. This complexity of the scene and emerged variations are caused by the high inter-class and intra-class variability of backscatter [16]. The main advantages of unsupervised learning are noted as not needing the prior analysis/feature extraction of training samples which leads to an easier implementation [12]. [PERSON] et al.