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The influence of cross-sectional channel geometry on rheology and flux estimates for active lava flows

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A Correction to this article was published on 04 February 2020

Abstract

Lava rheology and effusion rate are critical factors in determining the evolution of lava flows. However, direct and accurate field measurements are difficult to carry out, and estimates are usually based on measurements of the flow’s surface velocity and assumptions of sub-surface geometry. Using numerical flow models, we show that the potential for error due to geometry uncertainty is minimized if a semi-elliptical cross-sectional channel shape is assumed. Flow is simulated for isothermal Newtonian, temperature-dependent Newtonian, and isothermal power-law rheology lavas. For isothermal Newtonian lava, we find that the error in channel shape alone can make apparent viscosity estimates ∼3.5 times too large (e.g., for inappropriate use of the Jeffreys equation on a narrow semi-elliptical channel). For a temperature-dependent rheology, using an analytical approximation for Newtonian flow in a semi-elliptical geometry yields apparent viscosity and flux values that are more accurate than estimates which assume a rectangular geometry, for all channel shapes considered, including rectangular channels. Viscosity calculations for real channels on Mauna Loa and Mount Etna show that for a Newtonian rheology, a semi-elliptical analytical solution gives an approximation three times closer to the actual viscosity than a rectangle with the same depth while, if the lava is shear-thinning (power law exponent m = 0.6), a rectangular approximation is 15 % more accurate. Our results can be used to bracket possible viscosity and flux estimates when channel topography is poorly constrained.

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Acknowledgments

EL was supported during this work by the NSF grant EAR-1118943. Hannah Dietterich is thanked for processing the Mauna Loa lidar data. We thank the two reviewers of this paper, Jesse Robertson and Oryaelle Chevrel, and editor Matt Patrick, for their thorough and thoughtful reviews, which helped to improve this manuscript.

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Authors and Affiliations

  1. Lamont-Doherty Earth Observatory, Columbia University, New York, NY, USA

    Einat Lev

  2. Lancaster Environment Centre, Lancaster University, Lancaster, UK

    Mike R. James

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  1. Einat Lev
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Correspondence to Einat Lev.

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Editorial responsibility: M. R. Patrick

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Lev, E., James, M.R. The influence of cross-sectional channel geometry on rheology and flux estimates for active lava flows. Bull Volcanol 76, 829 (2014). https://doi.org/10.1007/s00445-014-0829-3

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