Journal of Volcanology and Geothermal Research 139 (2005) 89–102 www.elsevier.com/locate/jvolgeores Evaluating Titan2D mass-flow model using the 1963 Little Tahoma Peak avalanches, Mount Rainier, Washington M.F. Sheridana,*, A.J. Stintona, A. Patrab, E.B. Pitmanc, A. Bauerb, C.C. Nichitac aDepartment of Geology, 876 Natural Science Complex, University at Buffalo, Buffalo NY, 14260, USA bDepartment of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo NY, 14260, USA cDepartment of Mathematics, University at Buffalo, Buffalo NY, 14260, USA Accepted 29 June 2004 Abstract The Titan2D geophysical mass-flow model is evaluated by comparing its simulation results and those obtained from another flow model, FLOW3D, with published data on the 1963 Little Tahoma Peak avalanches on Mount Rainier, Washington. The avalanches, totaling approximately 10Â106 m3 of broken lava blocks and other debris, traveled 6.8 km horizontally and fell 1.8 km vertically (H/L=0.246). Velocities calculated from runup range from 24 to 42 m/s and may have been as high as 130 m/s while the avalanches passed over Emmons Glacier. Titan2D is a code for an incompressible Coulomb continuum; it is a depth-averaged, dshallow-waterT, granular-flow model. The conservation equations for mass and momentum are solved with a Coulomb-type friction term at the basal interface. The governing equations are solved on multiple processors using a parallel, adaptive mesh, Godunov scheme. Adaptive gridding dynamically concentrates computing power in regions of special interest; mesh refinement and coarsening key on the perimeter of the moving avalanche. The model flow initiates as a pile defined as an ellipsoid by a height (z) and an elliptical base defined by radii in the x and y planes. Flow parameters are the internal friction angle and bed friction angle. Results from the model are similar in terms of velocity history, lateral spreading, location of runup areas, and final distribution of the Little Tahoma Peak deposit. The avalanches passed over the Emmons Glacier along their upper flow paths, but lower in the valley they traversed stream gravels and glacial outwash deposits. This presents difficulty in assigning an appropriate bed friction angle for the entire deposit. Incorporation of variable bed friction angles into the model using GIS will help to resolve this issue. D 2004 Elsevier B.V. All rights reserved. Keywords: GIS; TIN; mass-flow model; Mount Rainier; avalanche; adaptive gridding 1. Introduction * Corresponding author. Tel.: +1 716 645 6800x3984; fax: +1 Debris avalanches and flows are frequently asso- 716 645 3999. ciated with volcanic activity or collapse of over- E-mail address: [email protected] (M.F. Sheridan). steepened slopes due to water saturation or prolonged 0377-0273/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jvolgeores.2004.06.011 90 M.F. Sheridan et al. / Journal of Volcanology and Geothermal Research 139 (2005) 89–102 periods of erosion. They pose a significant threat to majority of the deposit fills an area of 1.3 km2 that the population living on and around volcanoes. lies between the terminal moraine and the terminus Between 1900 and 1985, approximately 76,000 of Emmons Glacier, where the deposit has a people have been killed by debris avalanches, debris maximum thickness of 30 m. The thickness variation flow and pyroclastic flows related to volcanic activity within the deposit was determined using several (Tilling, 1989). This number includes the estimated cross-sections from fig. 10 in Crandell and Fahne- 29,000 killed by pyroclastic flows at St. Pierre on stock (1965). These sections were originally sur- Martinique in 1902 and the 23,000 killed by lahars veyed for a study of the White River geomorphology from the eruption of Nevado del Ruiz, Columbia in by Fahnestock (1963) just prior to the occurrence of 1985 (Tanguy et al., 1998). the avalanches. As global population grows, pressure increases to Crandell and Fahnestock (1965) identified seven develop available land. This has resulted in an different avalanche units based on surface features, increase in the numbers living on or close to active textural and color variations seen in field mapping, volcanoes. For this very reason, it is necessary to and aerial photographs. This avalanche deposit is develop accurate and usable prediction models, so that similar in appearance to deposits at other volcanoes the impact of a potential hazardous event can be such as Mount St. Helens, though on a much smaller correctly determined and appropriate actions taken. A scale. Large blocks up to 18Â40Â50 m rest on and variety of models exist for simulating various types of are partially buried by a matrix of grayish-red sand- geophysical mass flows at volcanoes, such as sized material of the same composition. The deposit FLOW3D (Kover, 1995), LaharZ (Iverson et al., surface has several curvilinear ridges and troughs 1998) and DAN (Hungr, 1995), all of which have demarking lateral and distal margins of the various their advantages and disadvantages. avalanche units. Of the seven avalanche units identi- This study compares simulations using Titan2D, a fied, Unit 3 is presumed to be the largest and the new geophysical mass-flow model developed at the furthest traveled. University at Buffalo (Pitman et al., 2003; Patra et al., During movement, at least one of the avalanches submitted for publication), with an earlier model, ran up the lower west-facing slope of Goat Island FLOW3D. The 1963 Little Tahoma Peak avalanches Mountain to a maximum height of 90 m. Ava- on Mount Rainier, Washington were selected to lanche Unit 3 also ran up the north-facing slope of validate the models on the basis of the wealth of Goat Island Mountain, opposite the terminal mor- published data available on the dynamics and features aine, to a height of 43 m. This indicates that Unit of these avalanches and their deposits. 3 was deflected by the terminal moraine through the gap between it and the valley wall incised by the White River. Unit 3 continued to flow another 2. The 1963 Little Tahoma Peak avalanches 600 m downstream past the moraine, coming to rest about 1.6 km upstream from the White River Little Tahoma Peak is located on the eastern flank Campground. of Mount Rainier volcano (Fig. 1). The steep north Velocities calculated from the runup heights give face rises some 600 m above the Emmons Glacier. values of 42 m/s at Goat Island Mountain and 24 m/s On December 6th 1963, and possibly over a period at the terminal moraine. These are assumed to be of several weeks afterwards (Norris, 1994), a series minimum velocities at the two locations. Crandell and of seven avalanches descended from the north-facing Fahnestock (1965) determined a velocity of 134 m/s slope. After impacting the Emmons Glacier at the for the units at the point they left Emmons Glacier and base of the peak, the avalanches proceeded to flow became airborne, hitting the ground some 600 m over the glacier and down the White River Valley for down valley. It is at this point that they presumed that a distance of 6.8 km while descending approximately the avalanches trapped air that enabled them to travel 1900 m. An estimated 10Â106 m3 of brecciated 2800 m beyond the glacier’s terminus. According to andesitic lava flows and other debris covers 5.1 km2 seismic records from the time, the largest avalanche of the White River Valley and Emmons Glacier. The created a signal that was recorded for approximately M.F. Sheridan et al. / Journal of Volcanology and Geothermal Research 139 (2005) 89–102 91 Fig. 1. Location of Little Tahoma Peak avalanche deposits. Red outline indicates mapped extent of area over which the 1963 avalanches passed as mapped by Crandell and Fahnestock (1965); superimposed on USGS aerial photographs acquired in 1994. Insert shows location with respect to Mount Rainier National Park. 300 s on the Longmire seismic station (LON) hazards. These include velocity, basal friction, seismograph (Norris, 1994). areal distribution and deposit thickness and the volume of material at the source region. These will be discussed in detail in the following section. 3. Avalanche dynamics Table 1 compares several parameters between the work of Crandell and Fahnestock (1965) and the There are several parameters important in results from the flow models FLOW3D and modeling debris avalanches and assessing their Titan2D. 92 M.F. Sheridan et al. / Journal of Volcanology and Geothermal Research 139 (2005) 89–102 Table 1 where h is the angle between downslope direction and Comparison of published data on the Little Tahoma Peak a normal to the curved path. Hence, magnitude of the avalanches and the results of simulations done with the FLOW3D and TITAN2D models velocity is given by: Published FLOW3D TITAN2D v2 ¼ rgsinacosh ð4Þ data Run out length (km) 6.8a 6.8 6.8 The actual path of curvature is not always Fall height (km) 1.9a 1.9 1.9 circular, being a function of the velocity and the 3 6a 6 Volume (m )10Â10 N/A 1Â10 surface slope vectors; that is, r is not constant, but (total) (single) Maximum 30a N/A 3 (single) it does have a finite value at any location in space, thickness (m) (total of 7) from which the velocity can be calculated. While Maximum 134a 82 75 this is quite a simple relationship, it is also quite velocity (m/s) rigorous in that friction is not ignored—friction a Maximum run up 90 201 60 changes velocity and hence the radius of curvature. height (m) Bed friction angle – 8.58 128 However, approximations do have to be made for Internal friction – 0.01 338 the values of r, a and h.