How nonlinearities of the equation of state of seawater generate the polar halocline and promote sea ice formation

The equation of state of seawater determines how density varies with temperature and salinity. Although it has long been known that the equation of state is nonlinear, there seems to be an overall feeling in the physical oceanography community that associated effects might be secondary in importance. This can be seen for example from the fact that most current theories of the large-scale circulation pre-assume a linear equation of state. Yet we contend here that these nonlinearities are responsible for the main transition in mixed layer properties observed in the World Ocean, the one separating so-called alpha regions (stratified by temperature) and beta regions (stratified by salinity). Beta regions are characterized by a halocline shielding surface cold waters from the influence of warmer deep waters, a condition for sea ice to form in polar region. Through numerical experiments where different equations of state are tested, we show that nonlinear effects of the equation of state: 1) strongly modulate surface buoyancy forcings, especially in mid- to high-latitudes, 2) generate the polar halocline by reducing there the influence of temperature on density, and consequently 3) enables sea ice formation in polar regions. The main nonlinear effect comes from the fact that the thermal expansion coefficient reduces to nearly zero at the freezing point, decreasing drastically the influence of surface cooling on the polar stratification. Other nonlinear effects, such as cabbeling or thermobaricity, are found of lesser importance although they have historically been the focus of intense research.