Taking a "coarser" look, Part 2

Note: Below are my updated thoughts. If you're especially curious, you can check out my Part 1 for the original interpretation of some initial data.

Introduction

I'm currently working on a project that explores what insights can be found by analyzing the planview geometry of a lava flow's margin (that is, it's outline on a map) at "coarse" scales, by which I mean 10s and 100s of meters). Why coarse scales? There are a few reasons, but in a nutshell:

1. Coarse scales are more commonly supported in satellite images of the surfaces of other planets.
2. My co-workers and I recently showed that margin geometry at finer scales (say, 1-10 m) is difficult to interpret. (Preprint here.)
3. In the results of that same paper, there are also hints (but only hints) that finer and coarser scales may represent distinctly different regimes (behaviors). Hence, to put it casually, finer and coarser scales may have different stories to tell.

A series of studies led by Barbara Bruno made a strong case that there was some relationship between a flow's morphologic type (traditionally defined by submeter surface textures) and its margin geometry. However, these studies effectively looked at all scales simultaneously, so the newly discovered hints of different regimes (my point #3 above) was intriguing. Moreover, even if morphologic type could conceivably dictate the fine-scale geometry of a flow margin, it seems less likely that these types would dictate the geometry at 10s and 100s of meters.

Therefore I formed a hypothesis: Although there is a correlation between morphologic type and margin geometry across a wide range of scales (as demonstrated by Barbara Bruno and her co-workers), that correlation at coarse scales is secondary. Instead, coarse-scale margin geometry is primarily determined by the dynamics of the flow.

This hypothesis is plausible because the dynamics of the flow, especially velocity shear (or, more approximately, how fast the lava is flowing), do correlate with morphologic type. Indeed, if the hypothesis proves accurate, it wouldn't be the first time that a correlation with morphologic flow type was only later realized to be related more directly to the dynamics of a flow.

Methods and Study Site

To test this hypothesis, I focused on the Holuhraun flow field in Iceland. Because this flow field was emplaced recently, during late 2014 and early 2015, it was very well documented, both on the ground and remotely by satellite.

I am using a time series of Sentinel 1 radar images (usually ~10 m/pixel) to capture the flow field's growth at a mean temporal resolution of ~5 days. Radar is particularly useful here as it is not obscured by the long polar night, frequently cloudy weather, or plume vented by the eruption. I carefully aligned these images using a custom program (an early version of which is described here). Now I am mapping the progressive margin as captured by each image and analyzing its geometry.

In addition, this mapping provides constraints on the dynamics of the flow locally. For example, if a flow lobe grows by 5000 square meters between images A and B, and A and B are separated by 5 days, we can say that the average areal growth is 1000 square meters per day. If we further assume that the typical thickness of the flow does not vary greatly (which is supported by observations made on the ground during the eruption; see Bonny et al. (2018)), this areal growth rate corresponds to a volumetric discharge rate. Similarly, we can estimate the flux (which is the discharge per unit width and is related to the velocity of the flow) by dividing that local discharge rate by some measure of the margin width.

Results and Discussion

Our first round of analyses use the same fractal method to analyze margin geometries that we developed in our fine-scale paper (which, in turn, was inspired by the work of Barbara Bruno). To use this method, a margin must be continuous, have a minimum length, and satisfy some other criteria. Consequently, not all of the progressive margins can be analyzed with this method, and we plan to consider other methods that would be more broadly applicable in the future. Those margins that can be analyzed by the fractal method are marked with yellow dots in part (a) of the the figure below.

These fractal analyses revealed distinctly different fractal dimension D values (which measure geometric "roughness"; (b) in figure above) for the various margins. Because all four analyzed margins come from portions of the flow with the same morphologic type (spiny pāhoehoe), these differences cannot be explained by morphologic type. However, based on our areal mapping, the time-averaged dynamics experienced by these regions are distinctly different and could plausibly be the source of the variation in D. (See table below.)

With only four margins analyzed so far, it is challenging to confidently identify what aspect of the flow's dynamics are most likely to determine the coarse-scale margin D. However, there are hints that D may negatively correlate with the local volumetric discharge or flux. Either interpretation would be consistent with the earlier coarse-scale results of Barbara Bruno and her co-workers, which only considered morphologic type. However, neither of these correlations fit the current data perfectly. For example, the negative correlation between D and local volumetric flux would require treating lobe-shaped margins differently from much broader fronts. Further analysis, probably including non-fractal methods, will likely shed more light on the governing conditions.

In addition to these coarse-scale analyses, we also reused the fine-scale geometries that we measured in the field in 2015. By subsetting these geometries to approximate the coarse-scale Dec29a and Dec24b (crudely) with ICE-01f and ICE-01g, respectively, we can test whether fine and coarse scales represent different regimes in this case. Indeed, although these fine-scale data correspond almost exactly at scales up to 4 m, they progressively diverge at coarser scales and reasonably approximate the respective D values of their coarse-scale counterparts at 80 m. (See (b) in figure above.) This behavior is exactly what we would expect if margin geometry is controlled by morphologic type at fine scales (again, spiny pāhoehoe in both cases) but by some other conditions, such as emplacement dynamics, at coarse scales.