Crocus Melting on Mars

Melting of ice is physically difficult to achieve under present-day Mars conditions [1,2,3], and the observational evidence for liquid water is ambiguous. The frost point temperature on Mars (~200 K) is far below the melting point of pure ice (273 K). Hence, water ice diffuses into the ambient atmosphere long before it reaches the melting point. Moreover, the total pressure of the atmosphere lies near the triple point pressure, so that ice near 0°C sublimates so rapidly that evaporative cooling exceeds the solar constant [1]. Here, one specific pathway for the formation of liquid water on present-day Mars is quantitatively evaluated: Melting of seasonal water frost in rough terrain [4]. In areas that are seasonally shadowed, water frost accumulates, and when the sun rises again, temperature increases rapidly. A rapid transition from cold to hot will involve little sublimation loss. A suite of quantitative models is used to investigate whether seasonal water frost can melt on present-day Mars.

When the water vapor content of the atmosphere is a non-negligible fraction of the total atmosphere pressure, as will be the case near melting, there is a strong buoyancy force that leads to free turbulent convection and strong evaporative cooling. The classical parametrization of the turbulent flux [1] has been updated based on more recent literature [4].

To obtain surface temperatures, a numerical model is used that includes direct solar irradiance, subsurface conduction, terrain shadowing, terrain irradiance, and sky irradiance. The surface energy balance is integrated over time at steps of 1/50th of a solar day (sol) for several Mars years. 

The model site is at a latitude of 30°S and assumes a thermal inertia of 400 Jm^-2K^-1s^-1/2. For a boulder, idealized as a half-sphere that sticks out from the surface, the situation is favorable. Beyond the southern (poleward) end of the boulder, water frost continuously accumulates for hundreds of sols, decimeters of CO₂ frost also accumulate [5], and, when evaporative cooling is not considered, peak temperatures are well above the melting point. The location is seasonally shadowed around the winter solstice. Once the sun rises, the CO₂ ice begins to sublimate, but the CO₂-H₂O ice composite cannot warm until all of the CO₂ ice has disappeared. The first day of spring without seasonal CO₂ frost is known as "crocus date''. After the crocus date, the surface temperature rises from 145 K to 273 K from sunrise until noon.

With evaporative cooling, the surface does not reach the melting point. On the first full sol after the crocus date, the temperature rises to 256 K and 0.1 kg/m² of frost (a 100 μm thick layer) are lost until it first reaches this temperature. The next day, the peak temperature is 260 K and at this point 0.5 kg/m² of frost have been cumulatively lost. The evaporative cooling is too strong to allow 273 K to be reached. The Viking 2 Lander observed almost continuous early frost 10-20 μm thick, and later patchy frost probably 100-200 μm thick [6]. More frost may accumulate in well-shadowed alcoves. Hence, the mass lost within a sol or two after the crocus date is within the amount that can be expected to be present.

The thermal model calculations demonstrate that sudden transitions from frost-accumulating conditions to near-melting conditions occur, but ultimately there is not enough energy available to compensate for the evaporative cooling.  An energetically favorable situation is the sun rising at the equator at perihelion. In this case, peak temperatures within about 10 K of the melting point within one or two sols of the crocus date are realistic. 

Protruding topography in the mid-latitudes creates locations that experience a rapid transition from conditions where water frost accumulates to high solar energy input.  Beyond the pole-facing side of a boulder, CO₂ and H₂O frost can accumulate seasonally, and when the CO₂ frost disappears in early spring, the water frost is heated to near melting temperature within one or two sols. The rapid temperature rise occurs on and following the crocus date. Evaporative cooling prevents temperatures from rising to 273 K even at an atmospheric pressure as high as 1000 Pa and even with a sublimation lag of several mm of dust. Overall, melting of pure seasonal water ice is not expected under present-day Mars conditions. Dark water frost (albedo 0.15) can reach peak temperatures within about 10 K of the melting point, and the loss of ice experienced during the warming phase is no larger than the amount of seasonal water frost that can be expected to be present. For bright water frost (albedo 0.4) peak temperatures within about 15 K of the melting point are  realistic.

At these temperatures, seasonal water frost can melt on a salt-rich substrate. Hence, crocus melting behind boulders can lead to the formation of brine under present-day Mars conditions. Salts are commonplace on Mars and have a range of eutectic temperatures. The temperatures produced through crocus melting behind boulders would suffice, even at atmospheric pressures below that of the triple point of pure water. The process will repeat periodically as long as the salt is not depleted. Overall, it is realistic that seasonal water frost melts on salt-rich ground. Since the seasonal H₂O frost layer is very thin, the total volume of brine produced is small.

Acknowledgments: This material is based upon work supported by NASA through the Habitable Worlds Program.

References: [1] A.P. Ingersoll (1970) Science 168, 972. [2] M.A. Kreslavsky & J.W. Head (2009) Icarus 201, 517. [3] M.H. Hecht (2002) Icarus 156, 373. [4] N. Schorghofer (2020) ApJ 890, 49. [5] K.J. Kossacki & W.J. Markiewicz (2004) Icarus 171, 272. [6] T. Svitek & B. Murray (1990) JGR 95, 1495.