The Percolation Phase Transition in Sea Ice

Abstract

Sea ice exhibits a marked transition in its fluid transport properties at a critical brine volume fraction p c of about 5 percent, or temperature T c of about -5°C for salinity of 5 parts per thousand. For temperatures warmer than T c , brine carrying heat and nutrients can move through the ice, whereas for colder temperatures the ice is impermeable. This transition plays a key role in the geophysics, biology, and remote sensing of sea ice. Percolation theory can be used to understand this critical behavior of transport in sea ice. The similarity of sea ice microstructure to compressed powders is used to theoretically predict p c of about 5 percent.Sea ice is a complex, composite material consisting of pure ice with brine and air inclusions, whose size and geometry depend on the ice crystal structure, as well as the temperature and bulk salinity. It is distinguished from many other porous composites, such as sandstones or bone, in that its microstructure and bulk material properties vary dramatically over a small temperature range. For brine volume fractions p below a critical value p c Ϸ 5%, columnar sea ice is effectively impermeable to fluid transport, whereas for p above p c (Ͼ5%), brine or sea water can move through the ice. The relation of brine volume to temperature T and salinity S (1) implies p c corresponds to a critical temperature T c Ϸ -5°C for S ϭ 5 ppt; we refer to this critical behavior as the "law of fives." Perhaps the most direct observations of this are that the time rate of change of sea ice salinity dS/dt due to gravity drainage vanishes for brine volumes below 5% (2, 3) and that the permeability of thin sea ice decreases by more than two orders of magnitude as the surface temperature is lowered, in a small critical region around -5°C (4).Brine transport is fundamental to such processes as sea ice production through freezing of flooded ice surfaces, sea ice heat fluxes, and nutrient replenishment for sea ice algal communities, as well as being an important factor for remote sensing. However, the basic transition controlling brine transport has received little attention. Percolation theory (5, 6) has been developed to analyze the properties of materials where connectedness of a given component determines the bulk behavior. We show that it provides a natural framework to understand the critical behavior of sea ice. In particular, we apply a compressed powder percolation model to sea ice microstructure that explains the law of fives, the observed behavior (4) of the fluid permeability in the critical temperature regime, as well as data on surface flooding collected recently on sea ice in the Weddell Sea and East Antarctic regions. It was observed in the Arctic (7) that a snow storm and its resultant loading on a sea ice layer can induce a complete upward flushing of the brine network. In the Antarctic, it was observed that the freezing of a surface slush layer, with resultant brine drainage, induced convection within the ice, whereby rejected dense brine is replaced by nutrient-rich sea water ...

Hydrocarbon biodegradation by Arctic sea-ice and sub-ice microbial communities during microcosm experiments, Northwest Passage (Nunavut, Canada)

“…The "law of five" states that sea ice that has a brine volume fraction of 5% and the typical salinity of 5 ppt will be impermeable at temperatures below -5°C (Golden et al 1998). Conversely, at temperatures warmer than -5 °C, the sea ice will be permeable because brine inclusions become connected, allowing heat, brine, nutrients and seawater to move through ice (Golden et al 1998).…”

“…Conversely, at temperatures warmer than -5 °C, the sea ice will be permeable because brine inclusions become connected, allowing heat, brine, nutrients and seawater to move through ice (Golden et al 1998). …”

Effect of melting Antarctic sea ice on the fate of microbial communities studied in microcosms

“…Ice temperatures in the visited area were above -5°C and showed clear signs of warm ''springsummer'' regime (Table 2). Brine volume fractions indicate that the ice cover was highly permeable upon arrival on site, with values greater than the 5 % permeability threshold along the entire profile (Golden et al 1998; Table 2). The beginning of the sampling period was characterized by intense gravitydriven brine drainage.…”

Halocarbons associated with Arctic sea ice

“…Brine volume (the ratio of brine volume to that of the sea water from which it came) in the ice ranged from 11 to 51%, well above the 5% threshold for brine network connectivity [Golden et al, 1998]. Chl a concentrations ranged from 0.006 to 0.09 µg l -1 in the ice, 0.013 to 1.1 µg l -1 in the water underneath, and up to 3.4 µg l -1 at the DCM in waters in which the phytoplankton bloom was well underway.…”