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

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 similar to 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.