Diverting lava flows in the lab - Nature Research · Lava flow physics has not been used to design past diversion attempts or assess their potential consequences. In part, this reflects

Supplementary Information for “Diverting lava flows in the lab”

Hannah R. Dietterich*

Department of Geological Sciences, University of Oregon, 1272 University of Oregon, Eugene,

OR 97403 USA

and

Volcano Science Center, U.S. Geological Survey, 345 Middlefield Road, Menlo Park, CA 94025

USA

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 10964 USA

*Corresponding author: [email protected]

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 advance1,2, as well as the paucity of

analysis of flow interaction with barriers1,3-6, especially for low Reynolds number fluids7. For

Diverting lava flows in the lab

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NGEO2470

NATURE GEOSCIENCE | www.nature.com/naturegeoscience 1

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http://dx.doi.org/10.1038/ngeo2470

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 sciences8. 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 30–180°. 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


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 Project9,10.

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.% SiO2) 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 (7.1–13.25°) 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

(60–180°) 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


buried thermocouple. Planform measurements, such as advance rate and surface velocities, were

calculated from the overhead video using Matlab®, Tracker, and differential optical flow9.

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 array11,12 (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 overtopping13. The molten basalt experiments have lower Péclet

numbers than natural flows9, 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


advance of the fluid, which follows the ideal behavior of unconfined viscous flow14. 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 time15.

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.


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, Post-

emplacement photo of the same experiment showing the bow wave.

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.

0 10 20 30 40 50 60 701

1.5

2

2.5

3

3.5

4

Obstacle length (cm)

Flow

heig

ht ra

tio (H

*)

0.75 mL/s, 10°1.0 mL/s, 15°


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.

Slope

FluxObstacle

CaliperPump

Videocamera

Furnace Camera array

Visibleand IR cameras

Obstacle

Slope 1.5 m

Flux

b

a

3 m

1 m

0.8 m


Supplementary Tables

Table 1. Summary of historical diversion attempts

Year Location Style Effect 1669 Mount Etna, Italy Levee breach by excavation Incomplete attempt16

1935 Mauna Loa, USA Aerial bombing of lava tube Minor breakouts, eruption ceased soon after17

1942 Mauna Loa, USA Aerial bombing of levees Created a temporary branch that rejoined the main flow after a short distance17,18

1955 Kīlauea, USA Earthen barriers Partly successful at deflection19

1960 Kīlauea, USA Earthen barriers Barriers overtopped or undermined20

1973 Heimaey, Iceland Water-cooling Flow front stalled and thickened, harbor saved21

1983 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 overflows16,22,23

1991-1993 Mount Etna, Italy Earthen barriers, levee breach by explosives

Barriers delayed flow advance but were overtopped, levee breach was successful16,24,25

2001 Mount Etna, Italy Earthen barriers Numerous barriers delayed advance and diverted the flows, many were overtopped16,25

2002 Mount Etna, Italy Earthen barriers Oblique barriers protected property5


Table 2. Summary of experimental and natural lava parameters

Parameter Syrup Molten basalt Pu‘u ‘Ō‘ō flows26,27

Density (kg/m3) 1443 2700 2700

Viscosity (Pa s) 102 102 102

Flux (m3/s) 10-6 10-4 102–103

Slope 3–25° 7.1–13.25° 1–30°

Thickness (m) 10-3 10-2 100

Velocity (m/s) 10-3 10-2 10-3–10-1

Reynolds Number 10-5–10-4 10-3–10-1 10-1–101

Péclet Number9 N/A ~105 ~108

Obstacle internal angle 0–180° 0–180° N/A

Obstacle side length (m) 0.04–0.52 0.15–0.38 N/A

Distance from vent to obstacle (m) 0.25 0.50 N/A


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)

Along-obstacle velocity (cm/s)

Post-obstacle velocity (cm/s)

Syrup 1 15 - - - 78.1 0.71±0.02 0.086±0.002 - - 1 15 60 - 4 68.0 0.89±0.02 0.085±0.001 - - 1 15 90 - 4 96.0 1.05±0.04 0.078±0.003 - - 1 15 120 - 4 94.3 1.20±0.02 0.079±0.002 - - 1 15 180 - 4 52.0 1.52±0.01 0.118±0.001 - -

0.75 10 - - - 83.7 0.74±0.01 0.050±0.000 - - 0.75 10 30 - 4 82.0 0.84±0.01 0.049±0.003 - - 0.75 10 60 - 4 82.0 0.86±0.04 0.049±0.001 - - 0.75 10 90 - 4 79.0 0.96±0.01 0.053±0.003 - - 0.75 10 120 - 4 79.0 1.03±0.02 0.052±0.001 - - 0.75 10 180 - 4 45.0 1.44±0.01 0.063±0.002 - - 1.5 15 30 - 30 88.2 1.18±0.11 0.098±0.001 0.090±0.000 - 1.5 15 60 - 30 74.9 1.22±0.22 0.100±0.003 0.100±0.005 - 1.5 15 120 - 30 101.5 1.72±0.14 0.098±0.004 0.110±0.004 - 1.5 15 150 - 30 78.2 2.14±0.17 0.108±0.004 0.086±0.004 - 0.75 15 60 - 30 22.4 0.86±0.26 0.083±0.002 0.086±0.003 - 0.75 15 120 - 30 88.2 1.40±0.07 0.067±0.000 0.068±0.002 - 0.75 10 30 - 30 101.5 1.01±0.07 0.045±0.001 0.042±0.001 - 0.75 10 90 - 30 58.3 1.02±0.32 0.056±0.001 0.067±0.001 -

1 15 - 20 52 45.0 1.18±0.03 0.125±0.006 0.161±0.003 - 1 15 - 35 52 45.0 1.32±0.01 0.110±0.006 0.161±0.001 - 1 15 - 45 52 55.0 1.59±0.05 0.128±0.006 0.165±0.001 - 1 15 - 65 52 44.0 1.82±0.02 0.121±0.005 0.142±0.000 - 1 15 - 65 52 51.0 1.81±0.03 0.120±0.006 0.156±0.000 - 1 15 - 75 52 52.0 2.28±0.10 0.128±0.006 0.098±0.005 -


1 15 - 88.3 52 31.0 2.38±0.03 0.130±0.006 0.095±0.000 - 1 15 - 90 52 46.3 2.52±0.09 0.137±0.006 0.078±0.001 -

0.75 10 - 90 5.7 79.0 1.17±0.18 0.051±0.003 - - 0.75 10 - 90 42.4 94.8 2.44±0.10 0.048±0.001 0.031±0.001 - 0.75 10 - 90 60 52.0 2.31±0.01 0.063±0.002 - -

1 15 - 90 5.7 68.0 1.39±0.36 0.089±0.002 - -

Molten basalt 290 10 90 - 15 150.0 4.8±0.1 3.47±0.17 - 1.89±0.05 198 10 120 - 15 150.0 6.2±0.1 3.01±0.17 - 0.96±0.06 277 7.1 - - - 150.0 2.2±0.1 1.41±0.02 - 0.71±0.01 294 7.1 60 - 15 150.0 4.6±0.1 2.12±0.01 - 1.59±0.02 211 13.25 60 - 15 150.0 5.4±0.1 2.80±0.02 - 0.96±0.02 220 13.25 - - - 150.0 2.1±0.1 2.45±0.03 - 1.39±0.05 207 13.25 180 90 15 150.0 9.0±0.1 1.31±0.03 1.76±0.08 0.57±0.00 182 13.25 120 - 15 150.0 6.5±0.1 1.61±0.02 - 1.54±0.04 233 13.25 60 - 30 150.0 5.0±0.1 3.18±0.03 - 1.93±0.04 258 13.25 180 30 37.5 150.0 5.5±0.1 3.31±0.05 1.91±0.04 2.37±0.06 268 13.25 180 60 37.5 150.0 5.3±0.1 5.64±0.10 7.58±0.30 4.37±0.10 263 13.25 120 - 30 150.0 7.2±0.1 2.03±0.04 - 1.88±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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Diverting lava flows in the lab - Nature Research · Lava flow physics has not been used to design past diversion attempts or assess their potential consequences. In part, this reflects