Diverting lava flows in the lab

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1 Hannah R. Dietterich* Department of Geological Sciences, University of Oregon, 1272 University of Oregon, Eugene, OR USA and Volcano Science Center, U.S. Geological Survey, 345 Middlefield Road, Menlo Park, CA USA SUPPLEMENTARY INFORMATION DOI: /NGEO2470 Diverting lava flows in the lab Katharine V. Cashman Alison C. Rust School of Earth Sciences, University of Bristol, Wills Memorial Building, Queens Road, Bristol, BS8 1RJ, UK Einat Lev Lamont-Doherty Earth Observatory, 61 Rte. 9w, Palisades, NY USA *Corresponding author: Supplementary Methods Lava flow physics has not been used to design past diversion attempts or assess their potential consequences. In part, this reflects the absence, until recently, of quantitative assessment of the effects of flow splitting on lava flow advance 1,2, as well as the paucity of analysis of flow interaction with barriers 1,3-6, especially for low Reynolds number fluids 7. For NATURE GEOSCIENCE 1

2 this reason, we performed experiments to investigate the design and influence of both splitting and confining barriers. The experimental approach allows us to collect data on the morphology and behavior of flows around obstacles in a controlled, measureable way that would be impossible in the field. We use both sugar syrup and molten basalt as experimental fluids. Sugar syrup is a simple viscous, Newtonian fluid that has frequently been used as an analogue for magma and lava in the earth sciences 8. Syrup experiments allow precise control of experimental conditions and are used to test the effects of a broad range of experimental parameters. Experiments with molten basalt allow us to extend our analysis to incorporate the effects of cooling (from an initial ~1,050 C), and thus mimic conditions of natural lava flows. However, these experiments are more difficult to perform and therefore cover a narrower range of conditions. Obstacles are placed in the path of an unconfined flow moving down a slope with a given flux and viscosity; both flux and slope are varied, as are obstacle shape, size, and orientation (Supplementary Table 3). Control experiments at the same conditions record the flow behavior without an obstacle and are used as reference. The syrup experiments were performed at the University of Bristol. The setup produces an unconfined flow with a steady extrusion of golden syrup (Tate and Lyle) through a hole in the center of an inclined plane (Supplementary Fig. 3a). A piston-style pump that supplies syrup with a variable rate provided steady fluxes of 0.5 to 1.5 ml/s. The reinforced plastic experimental surface is leveled and set at the appropriate slope (10-15 ). The obstacles used in these experiments are 3 cm thick plastic isosceles triangles with side lengths of 4 or 30 cm and vertex angles ranging from The 52 cm side, opposite the 120 vertex angle of an isosceles triangle with two 30 cm sides provided the long, oblique obstacle. The obstacle is placed in the center of the slope so that the syrup reaches it 25 cm downslope of the point of

3 extrusion. The inclined plane is marked with a 5 cm grid that is used to locate the obstacle and provide scale in photographs and videos. Planform measurements are made from an HD camcorder mounted above the experiment with the Tracker video analysis software. Vertical measurements of flow thickness are made using a caliper mounted above and just upslope of the obstacle. Molten basalt experiments were performed at the Syracuse University Lava Project 9,10. The setup consists of a furnace that can tilt to pour molten basalt at a nearly constant rate onto an inclined plane (Supplementary Fig. 3b). The gas-fired furnace is loaded with basaltic aggregate from the Chengwatana flows in Wisconsin (48 wt.% SiO 2 ) and is run at 1300 C to melt and homogenize the material, removing all volatiles. We pour the molten basalt from the furnace at a volumetric flux ranging from 100 to 300 ml/s onto a metal chute, which delivers a steady, centered stream of lava onto an inclined plane of sloped ( ) dry sand. The flow hits an obstacle after traveling approximately 50 cm from the chute. The obstacle is embedded in the sand to prevent any motion. The obstacles are made of plate steel, welded at the required angle ( ) and length (15 cm side length for splitting obstacles, 37.5 cm total length for oblique walls). Measurements are made from overhead with visible (JAI B401) and infrared (FLIR SC325) video cameras and an array of time-lapse cameras (ten Canon Powershot A3300 cameras with custom trigger system) mounted around the experiment; temperatures are monitored using a thermocouple (type K by Omega) buried in the sand upslope of the obstacle. A steel bar with 10 cm demarcations provided a scale for all experiments, and in most experiments we also surveyed fixed ceramic targets with a Nikon Nivo 5.M total station for precise ground control. Temperature measurements were recorded by the overhead calibrated FLIR camera and the

4 buried thermocouple. Planform measurements, such as advance rate and surface velocities, were calculated from the overhead video using Matlab, Tracker, and differential optical flow 9. Thickness measurements were made after emplacement and by 3D reconstruction of the flow using Structure-from-Motion digital elevation models (DEMs) built through time from a set of simultaneous photos taken by the camera array 11,12 (Supplementary Fig. 1). With our precise ground control, the DEMs have a horizontal resolution of 10 mm and a maximum vertical error of ± 5 mm. Fluxes were measured by dividing the total flow weight by the measured density and duration of the experiment, as well as by measuring volume change through the DEM time series. Our experiments are scaled in a way that allows their results to be applied to natural lava flows. All experiments have low Reynolds numbers (Supplementary Table 2), representing a laminar flow regime where viscous forces dominate over inertial forces that is equivalent to the natural basaltic lava flow fronts they are meant to simulate. The results may also be relevant for other slow-moving viscous flows, such as glaciers flowing into topographic features, but are a poor approximation for high effusion rate, channelized flow in lava. Geophysical flows with higher Reynolds numbers, including debris flows and rivers, will have a greater inertial response to obstacles, facilitating obstacle overtopping 13. The molten basalt experiments have lower Péclet numbers than natural flows 9, indicating that heat conduction is more important relative to advection in the experiments; nonetheless, advection dominates over conduction in both the experiments and natural lava flows. The syrup and molten basalt experiments both compare well to analytical theory for the behavior of viscous and cooling flows without obstacles. The syrup experiments are performed at conditions where the surface tension of the syrup (0.08 N/m) had a negligible impact on the

5 advance of the fluid, which follows the ideal behavior of unconfined viscous flow 14. Where the syrup intersects the obstacle, we use different obstacle materials to investigate the effects of the contact angle and find that at the measurement location of approximate 2 mm upslope of the obstacle, the bow wave height values are not affected. The molten experiment behavior follows that of a viscous flow that develops a crust and channelizes, forming a constant channel width and advance rate with time 15. The addition of the obstacle in these experiments cannot be readily described with analytical fluid dynamics theory. We use the dimensionless ratios of H* (the thickness of the flow behind the obstacle relative to the thickness of a control experiment) and V* (the advance rate of the flow along or after the obstacle relative to the advance rate immediately prior to obstacle intersection) to quantify the experimental results in a way that can be applied to natural flows under similar conditions. These results can be used to develop new theory for the viscous response of flows to collision with obstacles. Supplementary Notes In Fig. 2b, data from the Pu u Ō ō eruption includes episodes 3, 5, 7 8, 10 11, 15, 18, 29, and 40. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

6 Supplementary Figures Supplementary Figure 1. a, Lava flow thickness of a molten basalt experiment calculated by differencing digital elevation models constructed using instantaneous Structure from Motion photogrammetry11,12. The horseshoe-shaped zone of high thickness shows the bow wave. b, Postemplacement photo of the same experiment showing the bow wave ml/s, ml/s, 15 Flow height ratio (H*) Obstacle length (cm) Supplementary Figure 2. Influence of the length of the obstacle on syrup bow wave height for orthogonal barriers (φ=90 ) of different lengths. Error bars show two standard deviations.

7 0.8 m a Video camera Pump Slope Caliper Flux Obstacle 1 m b Visible and IR cameras Furnace Camera array Flux 3 m Obstacle Slope 1.5 m Supplementary Figure 3. Schematics of the experimental setups. a, Setup for analogue lava experiments at the University of Bristol. b, Setup for the molten basalt experiments at the Syracuse University Lava Project.

8 Supplementary Tables Table 1. Summary of historical diversion attempts Year Location Style Effect 1669 Mount Etna, Italy Levee breach by excavation Incomplete attempt Mauna Loa, USA Aerial bombing of lava tube Minor breakouts, eruption ceased soon after Mauna Loa, USA Aerial bombing of levees Created a temporary branch that rejoined the main flow after a short distance 17, Kīlauea, USA Earthen barriers Partly successful at deflection Kīlauea, USA Earthen barriers Barriers overtopped or undermined Heimaey, Iceland Water-cooling Flow front stalled and thickened, harbor saved Mount Etna, Italy Earthen barriers, levee breach by explosives Mount Etna, Italy Earthen barriers, levee breach by explosives Barriers diverted the flow but were overtopped, levee breach failed but debris created in the attempt did cause significant overflows 16,22,23 Barriers delayed flow advance but were overtopped, levee breach was successful 16,24, Mount Etna, Italy Earthen barriers Numerous barriers delayed advance and diverted the flows, many were overtopped 16, Mount Etna, Italy Earthen barriers Oblique barriers protected property 5

9 Table 2. Summary of experimental and natural lava parameters Parameter Syrup Molten basalt Pu u Ō ō flows 26,27 Density (kg/m 3 ) Viscosity (Pa s) Flux (m 3 /s) Slope Thickness (m) Velocity (m/s) Reynolds Number Péclet Number 9 N/A ~10 5 ~10 8 Obstacle internal angle N/A Obstacle side length (m) N/A Distance from vent to obstacle (m) N/A

10 Table 3. Table of experimental results Flux (ml/s) Slope (deg) θ (deg) Φ (deg) Obstacle side length (cm) Viscosity (Pa s) Bow wave height (cm) Pre-obstacle velocity (cm/s) Alongobstacle velocity (cm/s) Post-obstacle velocity (cm/s) Syrup ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

11 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Molten basalt ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±0.03 Bow wave height for control experiments is the flow thickness at the location where the obstacle tip would otherwise be located. Bow wave height errors are two standard deviations. Velocity errors are standard errors.

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