Taking a "coarser" look, Part 1

Note: Below are my original thoughts, but further results forced me to reconsider these initial interpretations. (The scientific method at work!) See my Part 2 post for an updated discussion.

Today I can share some initial results from my most recent research project. Before I get there, however, it's essential to provide just a little context. In a paper that I submitted a few months ago, I describe some discoveries I made about the plan-form shapes of lava flow margins. In a nutshell, the conclusions were these: the relationship between margin shape and the surface morphology of lava flows is much more complicated than we thought at scales of meters to a few tens of meters, and this shape can be significantly influenced by topography and post-emplacement sedimentation.

Those discoveries naturally led me to consider the situation at coarser scales, namely, scales of hundreds to thousands of meters. Those scales should be less sensitive to topography and sedimentation, and they are well represented in planetary datasets. Moreover, in my data from the earlier project, there were hints that margin shapes may be less variable at these scales, or more precisely, the fractality might be approximately scale-independent over these scales. I also reanalyzed the results of laboratory experiments by Blake and Bruno (2000), who used molten wax to simulate compound lava flows. In that reanalysis, I showed that there was a statistically significant correlation between the fractal dimension D of the margin, which measures geometric complexity, and the quantity V/Q², where V is the flow velocity and Q is the volumetric discharge.

I'm starting to explore these scales by looking at the 2014-2015 Holuhraun flow field in Iceland. This flow field is very large (covering ~84 km² with a volume of ~1.44 km³, as reported Pedersen et al. (2017)) and was well documented during emplacement. I also have high-resolution margin data for the flow field from both 2015 and 2019. I am currently quantifying development of the flow field in Sentinel 1 radar data to more closely relate the evolution of the margin geometry to other parameters of the flow, including flow velocity, volumetric flux, surface morphology, and flow direction.

To complement those efforts, I'm taking a second look at those high-resolution margin data that I collected in 2015. By dividing the margin geometry into intervals that were emplaced at specific times, I can begin to explore the relationship between the fractal dimension and other parameters. In the initial analysis, I compare 4 partially overlapping intervals and find that they roughly fall into three groups. Crucially, ICE-01c and ICE-01e come from different phases of the Holuhraun eruption: ICE-01c was emplaced as the beginning of the eruption, when discharge was ~350 m³/s, whereas ICE-01e was emplaced near the end of the eruption, when velocities were generally at their lowest values, <70 m³/s (Pedersen et al., 2017, and references therein). Nonetheless, their fractal scale-spectra (plots that measure how geometric complexity varies with scale) are relatively similar, with low D (fractal dimension) values at ~100 m. Conversely, ICE-01f has much higher D values at similar scales and was, like ICE-01e, emplaced late in the eruption. ICE-01a overlaps ICE-01c, ICE-01e, and ICE-01f and represents a continuous interval of ~19 km that was emplaced late in the eruption and is dominated, at the margin, by the same morphologic flow type, spiny pāhoehoe.

Taken together, what do these results suggest? The answer is not completely clear at the moment, but my working hypothesis is that the local flow direction is the largest distinguishing factor. Both of the scale-spectra that have low D values at ~100 m, ICE-01c and ICE-01e, are approximately parallel to the local major flow direction, whereas for ICE-01f, which has high D values at ~100 m, the margin is approximately perpendicular to the local flow direction. ICE-01a is therefore a convolution of both scenarios. Another preliminary result is that margin fractality does indeed appear to diverge across scales of tens of meters, splitting behaviors roughly into two regimes: meter scales and scales of 100 m or more, with decameter-scales being transitional.

Of course, all of these results are still in their infancy. Once I've prepared the Sentinel 1 radar data, mapped the margins and evolution of the flow, and analyzed the geometry, it's conceivable that factors in addition to flow direction, such as local discharges, could be significant. Another important question is: when comparing two margin intervals with similar local flow orientations, what factor is most influential in distinguishing their geometries, and can the respective fractalities of such margins provide constraints on that factor? Note that this is analogous to the laboratory simulations of Blake and Bruno (2000), as they measured fractality roughly perpendicular to the local flow direction. Naturally, I don't know the answers to these questions just yet, but I intend to find out!