Variation of salinity with water level in shallow lakes is complex and rich in information

Global trends of lake salinization and desiccation from climate change, land use change and water abstraction are impairing ecosystem services and freshwater biodiversity. In semi-arid lakes salinity tends to vary inversely with water levels: fresh when fuller and more saline at lower water levels. This long-recognized covariation is sometimes used to inform salt budgets from lake bathymetry and paleoclimate from salinity proxies, but limnologists have no understanding why they differ from lake to lake or a theoretical underpinning for how salinity scales with water level. Here, for the first time, theory for this scaling is developed alongside a systematic analysis of data from 152 shallow lakes showing, contrary to common assumptions, salinity varies with water level as a piecewise power-law with up to four segments. The segments evident in data sequentially describe dominance by salt precipitation, vertical water fluxes, lateral outflows, and equilibration with inflows as water levels increase. The exponents are shown theoretically and empirically to depend upon power-law scaling of bathymetry and lake outflow. Understanding these physical controls provides a means to better predict changes to salinity in semi-arid lakes facing projections of warming, drying, and ongoing land use change, as well as the effects of some adaptive management responses.