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A cellular automaton model of a descending heat probe on Europa

Presentation #315.05 in the session Icy Satellites: Surfaces, Ice Shell, and Interior (Poster)

Published onOct 23, 2023
A cellular automaton model of a descending heat probe on Europa

Introduction: A melting probe could potentially reach Europa’s subglacial ocean [1-2]. While this type of technology has been deployed on terrestrial ice sheets [3], understanding of a probe’s performance in the challenging environment of Europa’s ice shell is still limited. In particular, the time that the probe would take to descend through the ice shell and reach the ocean is uncertain. Laboratory experiments show that descent rates through ice at temperatures relevant to Europa (~100 K – 260 K) can range from ~8×10-6 m/s [4, 5] to ~2×10-4 m/s [6]. Furthermore, the thickness of Europa’s ice shell may be anywhere between ~15 km and ~100 km [7].

In this work, I address the question of the descent time of a hypothetical heat probe melting its way down through Europa’s ice shell.

Method: I use a cellular automaton to model heat conduction in a 1D vertical slab of water ice, based on a setup originally used for studying frozen soils [8]. Cellular automata (CA) are computational models where cells evolve based on predefined rules (here given by the heat conduction equation) and states of neighboring cells [9]. CA provide idealized microscopic conditions that reproduce the physics at macroscopic scales. The length of the vertical column corresponds to the current best estimate of the thickness of the upper, conductive part of Europa’s ice shell (10 km) [7]. The ice column is divided into 104 cells of equal length. The initial ice temperature profile is a power function of depth. The probe is simulated as a cell of constant temperature that conducts heat to the ice cell below it. When that ice cell reaches the melting temperature, it is replaced by the probe cell.

Results: As expected, a hotter probe traverses the conductive ice shell faster than a cooler probe. A probe temperature of 400 K leads to a travel time of 12 y, while a probe temperature of 280 K results in a travel time of ~260 y.

Future work: Future model improvements include consideration of ice porosity, salinity and obstacle avoidance in a 2D setup.

References: [1] Cassler B. et al. (2021) AcAau 189, 606. [2] Durka M. J. et al. (2022) AcAau 193, 483. [3] Aamot H. W. C. (1970) International Symposium on Antarctic Glaciological Exploration, Hanover, N. H. [4] Treffer, M. et al. (2006) Plan. Sp. Sci. 54, 621. [5] Ulamec S. et al. (2007), Rev. Environ. Sci. Biotechnol. 6, 71. [6] do Vale Pereira P. et al. (2023), PSJ 4, 81. [7] Howell S. (2021) PSJ 2, 129. [8] Nagare R. M. et al. (2015) Soil 1, 103. [9] Ilachinski A. (2001) Cellular Automata: A Discrete Universe, World Scientific.

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