Numerical Simulation of the Lahars Triggered by the 1877 Eruption Of

Numerical simulation of the lahars triggered by

the 1877 eruption of Cotopaxi Volcano (Ecuador)

E. Aguilera,* L. Cavarra^ M. T. Pareschi^M. Rosi' "ESPE, Campus Politecnico S. Clara, Sangolqui, Ecuador

'Dip. Sc. della Terra, via S. Maria n.53 1-56100, Pisa, Italy

Abstract

The lahars triggered by snow and ice melting during the 1877 explosive eruption of the volcano Cotopaxi have been simulated. A numerical model, based on mass and momentum balance, under the assumption of constant volume (no sedimentation, no erosion) and homogeneous flow (constant sediment concentration and no significant differences between water/grains velocity), has been used. The maximum heights reached along the northward and the southward paths of the 1877 lahars were reproduced by the simulations. Comparison with the historical chronicles allowed us to infer the total volume of 150 mil nP, for the south lahar, and a volume of 60 mil m^, for the north lahar.

1 Introduction

"Lahar" is an Indonesian word used in the volcanological literature to indicate debris flows and mudflows originated on the volcanoes' slope, directly or indirectly triggered by a volcanic eruption. There are different mechanisms in which lahars are generated. Hot pyroclastic flows and surges can melt ice and snow and evolve into debris flows, as at Mount St. Helens (Washington, USA) in 1980 (Pierson*) and Nevado del Ruiz (Colombia) in 1985 (Pierson et aP). Volcanic eruptions can also catastrophically release water stored in crater lakes and trigger voluminous lahars as at Mt. Ruapehu, New Zealand, in 1968 and 1975 (Cummans^).

Liquefaction of saturated volcanic debris avalanches saturated with water can also initiate large-scale lahars. A lahar of this type was produced in the North Fork Toutle River at Mount St. Helens, in 1980, as a result of the shaking on the debris avalanche by seismic tremor during the plinian eruption.

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Secondary lahars are produced by heavy rainfall on freshly deposited tephra or other loose material on volcano slopes. Devastating lahars of this kind have been produced by tiphoons since 1991 at the Pinatubo Volcano (Philippines) as a result of the rapid erosion of pyroclastic-flow deposits.

Among hazards associated with volcanic activity, lahars are certainly among the most dangerous and destructive. The second largest volcanic disaster of this century, after that of Mt. Pelee in 1902, was caused on November 1985 by the lahars produced during the eruption of Nevado del Ruiz which killed about

25,000 people and destroyed the town of Armero, located 60 km away from the volcano.

Figure 1: Location map of the Cotopaxi area and the valleys along which lahars flowed.

Cotopaxi, the highest active volcano on earth (5897 m asl), is worldwide known for the magnificence of its cone, topped by snow fields and glaciers

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down to an altitude of 4500-4800 m, and for its attitude to produce devastating lahars. Pyroclastic flows and surges emitted during the explosive eruptions of Cotopaxi interact with ice and snow (of the ice cup) and trigger large lahars. The examination of the historical chronicles shows that, over the last 450 years, at least 11 eruptions caused the formation of more or less voluminous lahars (Almeida^). Among these, lahars produced during the 1877 eruption represents the most important event. The three large lahars triggered during this eruption, described by Sodiro^ as "...formidables baterias hidrdulicas que en poco mas de una hora difundieron la desolacion y ruina en dilatados terrenos hasta entonces tan amenos y productivos", caused destruction up to 100 km from the source (BlongG).

In this paper we present the results of the reconstruction and numerical simulation of the two lahars which flowed in the main and most populated valleys surrounding the volcano.

2 Numerical model

The lahars of 1877 has been simulated by a model based on mass and momentum balance for channelled flow (Macedonio & Pareschi?) where the energy dissipation term is expressed by the formula:

Sf = %d-3- (1)

valid under the hypotesis of a dilatant fluid. In eqn. (1), U is the cross-section mean velocity, h is the flow depth and nj is a suitable coefficient. According to Macedonio & Pareschi? the value of the coefficient n

3 Simulation of the 1877 lahars

The lahars flowed along Rio Pita and Rio Santa Clara (northward) and along

Rio Cutuchi (southward) (Fig. 1) have been simulated because these are the most populated valleys surrounding the volcano and those for which more historical information is available. Owing to the lack of reliable information on the 1877 lahar of Cotopaxi, the

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characteristics of similar directly observed and also well studied lahars (the 1985 Nevado del Ruiz and the 1980 and 1982 Mt. St. Helens lahars) have been used to define the hydrograph shape (i.e. the graph of flow discharge vs time in a given section) and the volume of water and the solid concentration. Other information (some checking points along the lahar paths) have been obteined from historical chronicles of the eruption (Sodiro^, Wolf^). Same chronicles are in fact precise enough to indicate the height and/or the arrival time of the lahar waves. In the first section, a triangular shaped hydrograph was chosen as upstream boundary condition. When another upstream boundary condition is requested (supercritical flow in the second section), the critical condition is added. Under the reasonable assumption that the topography and, above all, the bed slope of the valleys, over which the 1877 lahars flowed, were not too different from the present one, we have usedl km spaced topographic cross-sections to reconstruct 3D shape of the channel. Some of cross-sections have been obtained from fotorestitution, the others were directily provided from field survey.

3.1 The southward path

The southward path of the lahar has been simulated as far as 140 km away the volcano. A total of 135 sections were obtained to reconstruct the topography of the valleys. Three different total volume (45, 90 and 150 mil m^) have been considered for the simulations, which corresponds, assuming a solid volume concentration of 70%, to respectively 1 m, 2m and 4m average thickness of melted ice from the 1877 glacier. The lahar flowed initially along three main path: Rio Saquimala, Rio Alaquez and the upper part of Rio Cutuchi (Fig. 1). The drainage basins of the three initial valleys have comparable surface, then each contributes for 1/3 of the total volume. In the first sections (situated at about 12 km from the volcano, where the lahar becames channelled) a triangular shape for the hydrograph and peak discharge in the range 30,000^-50,000 rn^/s have been chosen. In tables 1 values of maximum flow depth in section 8 (upper Rio Cutuchi), that corresponds to the first of the checking points (the San Agustin del Callo farm), obtained for different values of lahar volume, nj coefficient and peak discharge of the initial hydrograph are presented. Simulations with a volume of 50 mil m^, peak discharge of 50,000 nP/s and friction coefficient nj=0.4 m^s match the historical datum at San Agustin del Callo farm (observed hmax=9±l m) and the arrival time at Latacunga (

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Table 1: Maximum flow depths in section 8 computed for different input data. Volume Peak nW Maximum height (m) (10& m^) discharge (ml/2s) in section 8 (m^/s) 15 30000 0.1 5.0 15 30000 0.15 5.6 15 50000 0.1 5.0 15 50000 0.15 5.9 15 30000 0.8 6.7 15 50000 0.8 6.3 30 30000 0.1 6.5 30 30000 0.15 6.2 30 30000 0.25 7.4 30 50000 0.1 6.0 30 50000 0.35 7.9 30 50000 0.45 7.6 30 30000 0.8 9.2 30 50000 0.8 9.8 50 30000 0.15 5.5 50 30000 0.3 7.6 50 30000 0.45 8.3 50 50000 0.1 7.0 50 50000 0.4 10.4 50 50000 0.5 10.0 50 30000 0.8 11.1 50 50000 0.8 11.7

Figure 2 shows computed maximum flow depth and peak discharge for each section of the final segment (lower stretch of Rio Cutuchi and Rio Patate-

Pastaza). As n«j varies, variations in maximum flow depth are generally below 15%, while peak discharges display variations greater than 40%. The input hydrograph used in the simulations was the sum of that obtained as output in the simulations of the previous segments. Table 2 reports the computed maximum flow depths compared with the historical information at the check points.

Table 2: Comparison of computed flow heights of 1877 lahar of the Rio Cutuchi and Rio Patate-Pastaza valleys with historical information. Locality Maximum flow Distance from the Maximum flow height height (m) starting point of the (m) (historical data) simulation (km) (computed) Ilitio farm 12 + 33 0 26 Rumipamba farm = 20 3 19 Saquimalag farm > 15 12.8 19 San Gabriel factory > 10 32.5 13 San Gabriel bridge Destroyed 33.6 17 Bolivar bridge Destroyed 51.5 16 San Martin bridge Destroyed 114.7 63 Banos bridge Destroyed 116.4 14

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It shows that the simulations with a volume of 150,000 mil m^ and nj=0.15 ml/2s give results that fit rather well the available information on the 1877 lahar in the Rio Cutuchi and Rio Patate-Pastaza valley.

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Figure 2: Computed maximum flow depths (a) and peak discharges (b) with different values of na for the lower course of Rio Cutuchi and Rio Patate-Pastaza

3.2 The northward path

Toward north lahar has been simulated as far as the Los Chillos valley, placed at about 50 km from Cotopaxi. Two lahars flowed along two initial paths: Rio Salto and the upper Rio Pita. Few kilometres past the confluence of the two

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valleys, in the narrow bend called "La Caldera", part of the resulting lahar overflowed into the Rio S. Clara's valley. From that point the two lahars proceed separately till Los Chillos valley along Rio Pita and Rio Santa Clara (Fig. 1). The morphology of the three valleys has been reconstructed using a total of 113 cross-sections, some of which spaced about 200 m each other to better reconstruct the morphology of the valley in the vicinity of some relevant checking points. Simulations with different total volumes, starting from the volume of 60 mil m3, and values of the coefficient n^ in the range 0.2+0.6 m^s were performed.

As a result of the crater rim irregularity, the sector of the glacier that actively fed the lahar into the Rio Salto is considered to have a volume 1/5 of that of Rio Pita lahar. The hydrograph at the first section is triangular with a duration of 1/2 hour, according to the historical chronicles.

To appropriately account for the centrifuge effect at the "La Caldera" bend, the superelevation (Ah) between the inside and the outside of the bend has been computed according to the formula (Chow 10):

AU U^b Ah = - (2)

where U is the computed velocity, g the gravitational acceleration, r^ the radius of curvature of the bend and b the channel width. Then the lahar volume has been proportionally divided between the final stretch of Rio Pita and Rio Santa Clara. In table 3 the maximum flow depths resulting from the simulations are compared with the values inferred by the historical chronicles for the checking points. Simulations with a volume of about 60 mil m^ and friction coefficient nj-0.4 ml/2s give results in good agreement with the historical information for the northward path of the 1877 Cotopaxi lahar. Figure 3 shows the maximum flow depths and peak discharges for the lower course of Rio Pita and Rio Santa Clara. It is important to observe that for lahars with volumes larger than 35 mil irA the maximum flow depth in the sections along Rio Pita remains unchanged for the same value of nj, while it increases with increasing volumes along Rio Santa

Clara. On the contrary, for volumes less than 35 mil m^ lahars do not overflow into the Rio Santa Clara.

4 Conclusions

In spite of the simplistic assumptions (homogeneous flow with constant volume), the model used to simulate the 1877 Cotopaxi eruption lahars provides results in good agreement with the available information on the actual 1877 lahars, both for the northward and for the southward paths.

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Z 3000 28 30 32 34 36 38 40 42 44 46 48 50 52 29 31 33 35 Distance from volcano (km) Figure 3: Maximum flow depths and peack discharges along the lower course of Rio Pita and Rio Santa Clara, computed for a total volume of 60 mil m^ and nd=0.4.

The same numerical model can therefore be used to assess lahar hazard for future eruptions at Cotopaxi, by using appropriate input data, in order to predict a range of possible values of discharge and flow depth along the most populated valleys surrounding the volcano. Under the reasonable assumption that the next eruption of Cotopaxi probably will be a 1877-like eruption (Barbed et al^), the main change respect to 1877 is that the glacier area is about 2/3 of that of 1877. Expected lahars could have therefore reduced volumes, in the order of 40 mil m3, for the north lahar, and a volume of about 90 mil m^ for the south lahar. Although the present hazard appears to be lower than in 1877, with maximum flow depths in the range 5+15 m for Rio Cutuchi, 10-30 m for Rio Pita and 5-2-20 m for Rio Santa Clara, the total value (human lives, buildings, roads, bridges, ecc.) has drastically increased in the last decades. Just to mention some data, the populations of Latacunga and Sangolqui increased with a rate of 5% per annum between 1982 and 1990. Performed calculations suggest maximum hazard expected and its spatial zonation. Another important results is about the peak arrival time in inhabited areas, which could be used in the design of alert systems.

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References

1. Pierson, T.C. Initiation and flow behavior of the 1980 Pine Creek and

Muddy River lahars, Mount St. Helens, Washington, Geol Soc Am Bull , 1985, 96, 1056-1069.

2. Pierson, T.C., Janda, R.J., Thouret, J.C., Borrero, C.A. Perturbation and melting of snow and ice by the 13 November 1985 eruption of Nevado del Ruiz, Colombia, and consequent mobilization, flow and deposition of lahars, J. Volcanol Geotherm. Res., 1990, 41: 17-66.

3. Cummans, J. Chronology of mudflows on the South Fork and North Fork Toutle River following the May 18 eruption. In: Lipmann PW, Mullineaux DR (eds) The 1980 Eruptions of Mount St. Helens, Washington, US Geol Surv Prof Pap 1250, Washington DC, 1981, 479-486.

4. Almeida, E. Flujos de lodo del volcan Cotopaxi, Revista Geografica Instituto Geografico Militar Quito , 1995, 34, 153-161.

5. Sodiro, L. Relacion sobre la erupcion del Cotopaxi acaecida ed dia 26 de junio de 1877, Imprenta Nacional, Quito, Ecuador, 1877.

6. Blong R.J. Volcanic hazard. A source book on the effects of eruptions,

Academic Press, Orlando, 1984.

7. Macedonio, G., Pareschi, M.T. Numerical simulation of some lahars from Mt. St. Helens, / Volcanol Geotherm Res , 1992, 54, 65-80.

8. Major, J.J., Pierson, T.C. Debris flow rheology: experimental analysis of fine-grained slurries, Water Resour Res, 1992, 28-3, 841-857.

9. Wolf, T. Memoria sobre el Cotopaxi y su ultima erupcion acaecida el 26 de junio de 1877, Imprenta del Comercio, Guayaquil, Ecuador, 1878.

10. Chow, V.T. Open-channel hydraulics., McGraw-Hill, New York, 1959.

11. Barberi, F., Coltelli, M., Frullani, A., Rosi, M., Almeida, E. Chronology and dispersal characteristic of recentli (last 5000 years) erupted tephra of Cotopaxi (Ecuador): implications for long-term eruptive forecastings, J Volcanol Geotherm Res , 1995, 69, 217-239.