Journal of Earth Science, Vol. 23, No. 5, p. 768–774, October 2012 Printed in China DOI: 10.1007/s12583-012-0283-0

ISSN 1674-487X

Define the Energy Cone Threshold and Extent of Tianchi Volcano Yuan Wan (万园), Jiandong Xu* (许建东), Bo Pan (潘波) Key Laboratory of Active Tectonics and Volcano, Institute of Geology, China Earthquake Administration, Beijing 100029, China ABSTRACT: Energy cone is a unique but characteristic slope that describes the extent of deposits left around a volcano by various flowage phenomena, usually regarded as the boundary of pyroclastic and the source region of lahar. The energy cone value is determined as 0.07 by the energy-line model combined with the parameters of plume height and gradient, and the energy cone spread extent is defined by the numerical simulation method LAHARZ to simulate with this value based on the 1 : 50 000 digital elevation model of Tianchi (天池) Volcano, and the source region profiles in the north and south slope can prove the correctness of this threshold. This energy cone threshold and extent can be used as the reference of pyroclastic flow and lahar simulation. KEY WORDS: energy cone, energy-line, pyroclastic, lahar, LAHARZ.

INTRODUCTION Tianchi Volcano is located on the Changbai Mountain block of the Heilongjiang subplate. Its terrain feature is centering around Tianchi Volcano and decreasing peripheral and height is from 1 700 to 2 749 m a.s.l.. The cone of Tianchi Volcano is composite layered and composed of Pleistocene trachyte, pantellerite, and multiperiod pumiceous pyroclastic deposit and passed by early stage of shield-forming basalts period (Pliocene to Early Pleistocene), middle stage of trachyte cone-composing period (Pleistocene), and late stage of sheet-making volcanic pyroclastic This study was supported by the Natural Science Foundation of China (No. 40972209) and the Special Projects of the Fundamental Scientific Research of the Institute of Geology, China Earthquake Administration (No. IGCEA1103). *Corresponding author: [email protected] © China University of Geosciences and Springer-Verlag Berlin Heidelberg 2012 Manuscript received October 25, 2011. Manuscript accepted January 18, 2012.

period (Holocene epoch). Tianchi Volcano erupted in Holocene epoch, the pumiceous fallout deposit and pumice flow deposit sheet-liked covered the cone, and the shield basalt was formed in the eruptions that happened before 2 ka BP and in the year 1215 AD (Yang and Bo, 2007; Yang et al., 2006, 2003; Xu, 2006; Liu, 2005; Wei et al., 2004). The energy cone is a unique but characteristic slope that describes the extent of deposits left around a volcano by various flowage phenomena (Yang et al., 1999). Volcanologists have used such energy cones to describe the distance run-out by debris avalanches that originate on volcano flank or summits and by pyroclastic flows (Lee, 1984). These cones often referred to as energy, mobility, or H/L cones have an apex that usually coincides with a volcano summit and has a slope determined by a characteristic ratio of vertical drop (H) to horizontal run-out distance (L) for different volcano processes. Values of H/L ratios that define boundaries of “near volcano” or “proximal” hazard zones typically range from ~0.01 to 0.3 depending on the size and type of the proximal event (Walker et al., 1995). In general, the extent of the energy cone is

Define the Energy Cone Threshold and Extent of Tianchi Volcano

known as the accumulation extent of pyroclastic, and in LAHARZ, a lahar simulation software, the energy cone indicates the origination of lahar, confirming that the extent of the energy cone is important for limiting the extent and simulating pyroclastic and lahars. The energy cone is determined by the topography of volcano, and different volcanoes have different energy cone values; for example, the energy cone value of St. Helens is 0.235 and the value of Orizaba Volcano in Mexico is 0.18. At present, the main mathematical models for calculating the energy cone are energy-line model and Bingham model, and both of them are based on measured rheological properties (Alfred and Michael, 1989). The energy-line model is based on the Bernoulli equation, where the gravitational force is balanced by the inertial force of the flow plus frictional resistance, and it is often used in simulating lahars, for example, simulation software LAHARZ uses this mathematical model. The Bingham model is generally used for calculating the nonuniform flow movements such as pyroclastic, and it is determined from initial conditions, gravitational accelerations, and resistance to motion. The Bingham model can simulate the hydrodynamics characteristic in detail, the energy-line model matches the digital elevation model (DEM) better, and energy-line model is used to define the energy cone threshold and the extent of Tianchi Volcano in this paper. Mass movements such as pyroclastic and lahars descending from volcanoes, directly or indirectly related to eruptive activity, are among the most serious and far-reaching volcanic hazards. Many volcanoes with potential lahar hazards endanger human’s settlements and infrastructures. Modeling the pyroclastic and the lahars become crucial for hazards assessment, and the most important and principal thing is to define the energy cone value, because it is the basis of the imitation. However, it is still a gap in domestic energy cone research, and this paper is trying to define the energy cone value for Tianchi Volcano to be the imitation basis of pyroclastic and lahars. THEORY In order to define the extent of energy cone, the effects and the extent of pyroclastic surge eruptions should be ascertained first. Eruptions produce suspensions of pyroclastic particles in a turbulent gaseous matrix that behaves like gravity-driven flows of cohe-

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sionless grains (Yang et al., 1999). In this type of eruption, the particulate material rapidly decelerates as it is explosively shot upward from the vent; for example, zero vertical velocity reaches to the height from 500 to 1 500 m (Wei et al., 2004). Gravity then causes the dense suspension to fall downward. During fallback, potential energy is converted into kinetic energy; then, a type of Bernoulli equation of motion can be applied to the system. Heim firstly applied this method of analysis to mass flowage of landslides. He considered the line connecting the top of the landslide mass before moving to the toe of the deposit as an “energy line”. A coefficient μ, equal to the tangent of the slope of this line relative to the horizontal, in conjunction with the topographic surface constrains the dynamic properties of the mode. Heim pointed out that the slope of the energy line is dependent on the volume of the fallen mass decided by the plume height; the larger the landslide, the smaller the slope of the line. Sheridan used this approach to estimate the energy-line slope for pyroclastic flows; as a first approximation, a cone with a central depression angle equals to the assumed slope of the energy line. The cone’s apex height is set equal to the height to which material is thrust above the vent. The flowage potential is strongly controlled by the elevation difference between the “energy cone” and the ground surface; when the two are equal, flow should cease. Because such gravity flows are strongly influenced by topographic gradient, the surge cloud would not reach its maximum extent in every direction. Rather, the mass flux would be greatest in area of steepest negative gradient. Values for the energy-line range from 11° to 4°, and 7° is typical. In addition, the energy cone consists of the boundary of the energy line, and defining the plume height and the average gradient can determine the value of H/L. The elevation and slope of the energy cone relative to the elevation and slope of the topography give the acceleration or deceleration, velocity, and run-out time of the surge. The main parameters for motion parallel to ground surface are calculated from three equations (Michael and Michael, 1982). (1) a(i)=g(sinβ-ucosβ) where a(i) is the surge acceleration, g is the acceleration due to gravity, β is the slope of the land surface, and μ is the Heim coefficient (tangent of the energyline slope).

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v2(i)=v02+2a(i)s(i) (2) where v(i ) is the velocity, v 0 is the initial velocity, and s (i ) is the slope distance. (3) t(i)=2s(i)/[v0+v(i)] where t (i ) is the run-out time. Sheridan has used the results of this simple approach to the Mount St. Helens blast, as shown in Fig. 1. These values are consistent with observation.

The difference between the elevation of the energy surface and the ground topography, Δh(i), directly yields the potential component velocity provided the surge is truly ground-hugging. (4) v(i)=[2gΔh(i)]1/2 Taking boundary conditions into consideration, the total flow field vectors and streamlines and mass deposition per unit area can also be computed.

Figure 1. Generalized energy-line data for the 18 May, 1980. ENERGY CONE CALCULATION OF TIANCHI VOLCANO The energy cone threshold is calculated by the apex location, apex height, and slope, which define the initial velocity and the distribute extent; then, LAHARZ is used to simulate the energy cone extent on the basis of 1 : 50 000 DEM of Tianchi Volcano to ascertain the real boundary on the topographic map, and the reliability of the boundary is verified with 18 profiles in lahar source region. Combining the formula calculation, numerical simulation, and the profile confirmation, we can demarcate the energy cone in Tianchi Volcano. PLUME HEIGHT CALCULATION The cone’s apex height is set equal to which material is thrust above the vent. The flowage potential is strongly controlled by the elevation difference between the “energy cone” and the ground surface: flow should cease where the two are equal, and the plume height decides the initial velocity. Morton’s plume model 1956 is appropriate for calculating the plume

height that was worked out on the basis of the raising plume in ideal even liquid environment. A Brini-type eruption column with adequate development can be divided into three parts in terms of structure: the lower air blast area, the central convection zone and the top diffusion zone, the height of the convection zone constitutes of the main part of the eruption column, and the buoyancy effect determines the ascending impetus of the eruptive material in the convective region. As a large amount of air in the edge of the eruption column inflates after being involved and heated, it makes the total density of the eruption column less than the density of the surrounding atmosphere. Although the ascending speed is not fast, but as the deceleration is much lower than that in the air blast area, this can drive the eruption column climb to a great height. HB sign as the ascending height of the eruption column driven by the buoyancy effect, above this height, affected by the hierarchical structure of the atmosphere the density of the surrounding air is less than the total density of the eruption column, and the reverse buoyancy effect tends to make the eruption decline. The

Define the Energy Cone Threshold and Extent of Tianchi Volcano

excess momentum at the top of the convection zone tends to make the eruption material ascend inertially. These combined effects make eruption column horizontal diffuse, and meanwhile ascend to the final height HT, and finally constitute the umbrella-shaped cloud in the diffusion zone at the top of eruption column. Typically, (HT–HB)/HT>0.25–0.3. The total height of the eruption column HT directly relates to the emitted heat volume. The following formula can be used to predict the height of eruption column (Wei et al., 2004) (5) HT=5.773(1+n)-3/8[σ·Q·S( θ e– θ ao)]1/4 where Q is the releasing rate of magma volume, S is the magma heat capacity, θ e is the initial temperature of the eruption, θ ao is the sea-level air temperature, σ is the magma density, and n is the ratio of the vertical gradient of the absolute temperature and the environmental decline rate. Parameters varied with different volcanic formulas. For example, Wilson et al. (1978) observed eruption columns from eight eruptions with cloud heights in the range 2–45 km and volume rates of magma production in the range from 10 to 2.3×105 m3/s and concluded the formula as HT=8.2Q0.25. As for the Tianchi Volcano, Wei et al. (personal communication), in 95-11 Project-China modern volcano monitoring and research of the China Seismological Bureau, calculated that the Brini eruption columns of Tianchi Volcano reached the height up to 25 km, and the residual momentum of inertia increased to detritus to the maximum height of 35 km in 1199 eruption. Based on this eruption column height value, the debris-flow initial velocity of 79 m/s can be defined. GRADIENT CALCULATION Pyroclastic generated in 1215 AD eruption surrounded the volcano cone; sheet distributes in cleugh, low-lying, and gentle area. To the north, crossed Erdaobai Town, 50 km away from Tianchi Volcano, various lahars’ original profiles are found in the south of Erdaobai Town 40 km away from the crater of Tianchi Volcano, and pumice-rich lahar profiles of lahar facies that had experienced multiple transporting are found on both sides of the river along the direction from the drainage area of Erdaobai River to Liangjiang River. All these sections have obvious fluvial facies features, grain-supported structures, well sorted, and

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obvious in stratification; most of which are nearly horizontal and parallel ones. Some of these sections have bedrocks exposed at its bottom and some are rich of carbonized wood. All these are proof that the Erdaobai drainage area is existing and prone to occurrence of lahars. To the south, the Yalu River gorge in the south were all formed from the original channel filled by pumice flow and deep incised by running water, the classic profile where the lahar cover on the pyroclastic is found on the south slope, the latitude-longitude is 41°50′33.10″N, 128°5′48.10″E, and this section shows unorganized distribution of pyroclastic facies on its basement and has lahar facies section showing horizontal bedding in sorting covered it. The secondary lahar and original pyroclastic after transportation are the proofs of that the Yalu River is also prone to lahar. To the east, the Pleistocene and Holocene lahars are widely distributed at Tumen River, which are usually above the third terrace (Cui et al., 2005), and lahar deposits by repeated transportation, which are poor sorted, and inconspicuous fluvial facies can be found in the riverbed and the gulch full of pyroclastic at Shuangmufeng Peak, Chongshan, Luguo, and so on and wildly distributed pyroclastic gorge such as Jingjiang gorge provide sufficient material source for lahar occurrence. To the west, there is no obvious volcanic lahar disaster that exists, but the Songjiang River is selected to calculate the average gradient because the pyroclastic disaster spread facet and center the crater after volcanic eruption, and it is prone to form lahars along the river by rainwashing. In general, six typical rivers are chosen as the lahar disaster riverway to calculate the verage gradient, which is the Erdaobai River and Sandaobai River in the north, the Yalu River in the south, the Songjiang River in the west, and the Tumen River and Erdaobai River in the east. Firstly, intrinsic sink points of the six riverways in 1 : 50 000 DEM should be filled and fixed. Some depression areas are the wrong data in the DEM forming process, but some others indicate the real terrain such as quarry or cave; these are the obstacles of riverway calculation and need to be disposed by algorithm depression filling in DEM processing to ensure the calculation accuracy of forming nondepression DEM. The depression areas are disposing by delimiting the contribution area of each depression, fixing the lowest elevation in the contribution area,

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and then defining the lowest elevation threshold. If the lowest elevation of the depression is lower than the defined elevation threshold, the FILL command can be used to fill the elevation value of vertical settlement unit in DEM. After revising the terrain noise points, and terrain feature of the six rivers is drawn in ARCGIS shown in Fig. 3, the calculation can be processed on the basis of the slope of each river, and the average gradient of Tianchi Volcano energy cone is 3.6° by each river’s gradient. Combined with the initial velocity deduced from the plume height and the average gradient, the energy cone value of Tianchi Volcano is 0.07.

the H/L grid with the elevations of the DEM at each cell location. In a temporary grid, two different arbitrary values are assigned to the cells where the H/L value is greater than the elevation or less than the elevation. A polygon is created circling around the area with one value to define the energy cone extent in Fig. 4.

Figure 2. Gradient of Erdaobai River.

Figure 4. Boundary of energy cone in Tianchi Volcano.

Figure 3. Gradient calculation. NUMERICAL SIMULATION AND THE PROFILE COMFIRMATION Entering the energy cone value to the lahar simulation software LAHARZ (Munoz et al., 2009; Vallance et al., 2001a, b; Richard et al., 1998; Iverson, 1997), the boundary of energy cone can be created combined with the DEM. After inputting the energy cone parameter value of 0.07, LAHARZ calculates a rid of H/L values where each cell’s value is determined by the difference between the elevation of the cone apex and the product of that cell’s Euclidean distance from the location of the cone apex multiplied by the constant cone slope and then compares the values of

The classic lahar source region profiles in Erdaobai River and Sandaobai River investigated by Nie et al. (2009) are listed in Table 1, and the calculated energy cone boundary traverses through these points. The maximum distance is 4.6 km and the minimum distance is 1.1 km, which indicate that the energy cone extent calculated by this model is approaching to the historical lahar source region, but the result is based on the current terrain condition, and the selected rivers’ terrain is filled or scoured by the historical lahars, then the boundary does not coincide with the historical lahars’ source points, as shown in Fig. 5. However, we conjecture that this model is more accurate in the rivers where no historical lahars occurred, such as the Songjiang River.

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Table 1 Latitude-longitude of Tianchi Volcano source region classic profile points (Nie et al., 2009) No.

Longitude

Latitude

1

128°9.429′E

42°10.896′N

3

128°7.145′E

5

128°6.343′E

7 9

No.

Longitude

Latitude

2

128°8.217′E

42°10.778′N

42°10.647′N

4

128°7.379′E

42°10.669′N

42°10.568′N

6

128°5.609′E

42°10.417′N

128°9.48′E

42°14.122′N

8

128°8.4′E

42°14.022′N

128°7.161′E

42°13.893′N

10

128°6.279′E

42°13.775′N

11

128°5.853′E

42°13.743′N

12

128°5.017′E

42°13.527′N

13

128°4.531′E

42°13.314′N

Figure 5. Classic profile points verify. CONCLUSIONS The energy cone threshold is calculated by the parameters of apex location, plume height, and the average gradient using the energy-line model. The

value is then applied in the 1 : 50 000 DEM and portrays the boundary in LAHARZ. Contrasting the boundary with the classic profiles in historical lahars source region, the extent of the energy cone is ap-

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proximate to lahars’ source points in Erdaobai River and Sandaobai River. The classic juncture point profile in the south slope where the secondary lahar covered the original pyroclastic is also approaching to the energy cone boundary. The correction of the calculating value and the extent of the energy cone can be confirmed. However, there are also some deviations in this model; for example, the average distance deviation between the boundary and the lahars’ source region profiles is 2.5 km in Erdaobai River, and the lahar source point in the south slope is 3.6 km away from the boundary. This model applies to calculate the energy cone extent in the river where historical lahars have some deviations and remains to be modified further. The result of the energy cone value and the extent can be used as the basis of numerical simulation of pyroclastic and lahars, which play guiding roles of prevention to pyroclastic and lahar disaster.

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