Exploring Self-similarity in Hawaiian Lava Flows

Acknowledgements Work in the Hawai‘i Volcanoes National Park was conducted under National Park Service science permit # HAVO-2012-SCI-0025. This material is based in part on work supported by the National Science Foundation Graduate Research Fellowship under Grant No. 2012116373. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors(s) and do not necessarily reflect the views of the National Science Foundation. Discussion Our early results support the conclusion of [1-2] that lava flow margins are fractals, based on the high R2 (Table 1) for Richardson plots [3]. The field results are also consistent with the respective ranges of fractal dimension D that [2] gives for ‘a‘ā and pāhoehoe. (See color-coding in Table 1.) However, these results also suggest that the fractal dimension of lava flow margins cannot be as reliably measured remotely as they can be in the field, because D values for the remote data tend to be intermediate between the ‘a‘ā and pāhoehoe ranges. Although [2] do not explicitly compare the D values from field and photographic data of the same flows, the D values for both sets of data are consistent. What accounts for this difference between our results and those of [2]? There are likely at least two causes. First, we are intentionally not as careful as [2] to choose “simple” cases. Line H, which is partially mantled by aeolian deposits, is a conspicuous example of this choice, which is meant to mimic the realities of applying such fractal analysis to flows in a planetary context—for which there is no ground truth. Likewise, line L transitions from slabby pāhoehoe with lesser ‘a‘ā to completely ‘a‘ā over its course. For the remaining lines, the greatest source of discrepancy is probably due to the intimate association of ‘a‘ā and pāhoehoe from different generations at our chosen field sites. As a consequence, the flow margins mapped from orthoimagery may include both lava flow end members. Because both non-simple cases and closely associated ‘a‘ā and pāhoehoe will exist on other planets, detection and/or mitigation techniques for these conditions must be developed if the fractal analysis method is to be useful in that context. These are among our next goals, as well as the following: finetuning our fractal analysis algorithm to minimize noise, deriving a means to quantify error in the results (because R2 is insufficient), and objective division of a lava flow margin into its distinct components of different D (cf. [2]). Fig. 1: Our field sites on the island of Hawaii. From left to right: ‘a‘ā flow on pāhoehoe in the Ka’u Desert partially mantled by aeolian deposits; ‘a‘ā flow (M) and slabby pāhoehoe flow (L) with lesser ‘a‘ā that transitions to fully ‘a‘ā, both of which lie on a substrate of older pāhoehoe (N, O); Muliwai a Pele—a section of the 1974 A.D. Mauna Ulu ‘a‘ā channel levee over pāhoehoe; pāhoehoe on moderately vegetated pāhoehoe; and two adjacent pāhoehoe-on-pāhoehoe flows on the coastal plain. The beginning and end of each walked traverse is marked by the same letter, and dashed lines indicate the corresponding lines mapped from 1 m/pixel U.S.G.S. digital orthographic quadrangle (DOQ) images. In several places (e.g., A and B), the same or similar traverses were walked multiple times to determine how much the results varied and explore different spatial sampling intervals with the differential GPS rover used to acquire the field data. The color ramp is keyed to the fractal dimension D and applies to all mapped lava flow margins. The context map is true color and the traverse maps are false color DOQs. North is up in all maps. Table 1