Bayesian estimates of ice optical properties for lake ice modeling

Ice and snow cover on frozen lakes is a natural barrier to solar radiation, seasonally reducing energy penetration that controls under-ice thermal dynamics and biological productivity. However, direct measurements of under-ice irradiance remain scarce due to logistical constraints. We compiled data from 46 freshwater lakes across the Northern Hemisphere, including 722 daily irradiance observations and corresponding ice and snow thickness records. Ice quality data (black ice, white ice, snow cover) were available for 15 lakes (626 measurements). Using this dataset and a Bayesian implementation of the Beer-Lambert law, we estimated statistical distributions of albedo and attenuation coefficients. Median albedo values were 0.55 for black ice, 0.60 for white ice, 0.56 for total ice, and 0.94 for snow, with corresponding attenuation coefficients of 0.78, 4.34, 1.75, and 8.96~m⁻¹, respectively. These refined optical properties address critical data gaps, improving under-ice irradiance predictions and enhancing understanding of lake processes under changing ice conditions.