Under-ice convective regimes driven by sunlight and sediment temperature control water–ice heat flux

Seasonal and perennial lake ice covers are declining, yet the mechanisms driving these changes remain insufficiently constrained. While atmospheric forcing is comparatively well understood, under-ice thermal dynamics-driven by sediment heat and solar radiation-are less certain. These energy inputs vary widely across lakes and seasons, and their contributions to ice melt are poorly quantified. We develop a minimal conceptual model that captures three essential elements of under-ice dynamics: the nonmonotonic equation of state, sediment-water heat exchange, and solar heating. Combining theory with direct numerical simulations informed by field observations, we map the under-ice dynamics, revealing five distinct regimes-one conductive and four convective-including three previously unrecognized. For each regime, we derive scaling laws linking governing parameters to the upward heat flux transferred to the ice. This framework provides a predictive foundation for quantifying under-ice heat transfer and parameterizing climate models, with implications for climate projections, biogeochemical cycling, and ecosystem dynamics in cryospheric waters.