Geometric shape, water availability and under ice volume of Alberta lakes

Abstract

Water availability information can be vital to the execution of informed management decisions. Since only a small fraction of Alberta lakes have surveyed bathymetry data, accurate estimation of lake water availability is often challenging. In this study, we analyzed available bathymetry data from 77 lakes, distributed over six major river basins and five natural regions of Alberta, and developed dimensionless relationships between volume and depth. We compared these relationships with the analytical relationship between volume and depth for five idealized lake shapes, viz. as cylindrical, pseudo-parabolic, parabolic, conic, and inverse-parabolic. Our study shows that considering the volume-depth relationship, 48% of Alberta lakes fall under parabolic shape, 29% fall under conic shape, and the rest (23%) fall under either pseudo-parabolic, inverse-parabolic, or cylindrical shape. We also developed four different models to estimate maximum lake volume (a proxy of lake water availability) and 5% under ice volume (a proxy for winter allocation limit of lake water) assuming an ice thickness of 80 cm. These models have been developed in such a way that allows the user to apply the models based on data availability and can be used in absence of site-specific data (e.g., bathymetry) to estimate volume, and subsequently water availability in lakes. Finally, we propose a formulation of percent volume reduction due to small water withdrawal, which requires only maximum depth of a lake to estimate a potential volume reduction limit for a water withdrawal.