Natural Hazards 33: 161–189, 2004. 161 © 2004 Kluwer Academic Publishers. Printed in the Netherlands.
Risk from Lahars in the Northern Valleys of Cotopaxi Volcano (Ecuador)
E. AGUILERA1, M. T. PARESCHI2 ,M.ROSI3 and G. ZANCHETTA3 1ESPE, Campus Politecnico Santa Clara, Sangolquì, Ecuador; 2CNR-Istituto Geoscienze e Georisorse, via S. Maria 53, I-56126 Pisa, Italy; 3Dipartimento di Scienze della Terra, University of Pisa, via S. Maria 53, I-56126 Pisa, Italy
(Received: 10 July 2002; in final form: 29 September 2003) Abstract. Cotopaxi volcano (Ecuador) is famous for production of large-scale lahars through melt- ing of ice and snow on its summit glacier. The lahar hazard in the northern valleys of the volcano is assessed through numerical simulation of a maximum expected event. Considerations of past activity suggest that an event like that of the 1877 eruption is the maximum expected lahar event. Review of the historical records reveals that northerly flowing lahars initially followed the Rio Pita and Rio Salto; at “La Caldera”, owing to a sharp bend in the channel, the lahar partly overflowed into Rio Santa Clara. The lahars along Rio Pita and Rio Santa Clara were conveyed to the Los Chillos valley. The simulation, using an initial flow volume of 60×106 m3 reproduces the maximum heights reached by the 1877 lahar along the northern valley. The volume of lahar triggered by an eruption similar to that of 1877 is estimated to have a volume about 2/3 of that of 1877. This hypothesized reduction of volume is attributed to shrinkage of the summit glacier over the past century. However, dramatic population growth along valleys exposed to lahar hazard over the past 100 years makes the present risk from lahars higher than in the past. The sharp bend of “La Caldera” represents a crucial site controlling lahar propagation: should a lahar overflow into the Santa Clara valley the risk increases considerably due to the much higher concentration of human settlements along the valley. Results of a lahar simulation in which the entire flow is artificially forced into Rio Pita suggest that construction of a dyke at “La Caldera” to prevent overflow would substantially reduce the general risk in the area.
Key words: Cotopaxi volcano, Ecuador, Lahar, simulation, risk.
1. Introduction Lahars are among the most hazardous volcanic phenomena, having claimed sig- nificant numbers of victims in several eruptions (Yokoyama et al., 1984; Tilling, 1989). Lahars are particularly hazardous because they can affect proximal as well as distal areas from the volcano (Blong, 1984). The ability to affect areas situated at great distance from the source was shown dramatically at Nevado del Ruiz volcano (Colombia), where lahars generated by the melting of the summit glacier traveled more than 70 km before devastating the town of Armero and claiming more than 22,000 victims (Lowe et al., 1986; Naranjo et al., 1986; Pierson et al., 1990).
Author for correspondence. E-mail: [email protected] 162 E. AGUILERA ET AL.
The classical approach to lahar hazard assessment consists in the identifica- tion of the origin, size and time-recurrence of phenomena, starting from historical and stratigraphic data (Scott, 1988; Scott et al., 1995; Vallance and Scott, 1997). However, precise delineation of the areas effected by the passage of past lahars is often difficult to reconstruct in detail from the stratigraphic record. Starting in the 1980’s various authors have attempted to numerically model lahars to assess their hazard (Laenen and Hansen, 1988; Vignaux and Weir, 1990; McArthur et al., 1990; Takahashi, 1991; Macedonio and Pareschi, 1992; Barberi et al., 1992; Caruso and Pareschi, 1993; Costa, 1997; Iverson et al., 1998). An advantage of modelling resides in the ability to derive parameters such as mass discharge, flow depth, flow width and flow velocity, once initial characteristics of a simulated event are defined. Knowledge of such parameters is of critical importance for the organ- ization of the evacuation plans. In addition, assessment of lahar hazard through hydraulic numerical modelling can be of great utility in the study and design of permanent structures (dams or dykes) aimed at reducing or eliminating the risk of populated areas or infrastructures. Although these models employ hydraulic the- ory simplifications they provide sophisticated tools for practical forecast of lahar runout and inundation limits. In this paper we address the problem of lahar hazard assessment in the valley north of Cotopaxi (Ecuador), using numerical simulation. We begin with a numer- ical simulation of lahars triggered by the melting of ice and snow by the eruption of 1877 along the northern drainage system of the volcano up to 50 km from the crater, and then we extrapolate this simulation to evaluate the present lahar hazard. Due to approximately the 1/3 shrinkage of the glacier coverage of Cotopaxi, the volume of a lahar potentially generated under present conditions is probably less than that of the 1877 lahar. Nevertheless the overall lahar risk from an eruption at Cotopaxi has increased dramatically because of the growth of population in the Los Chillos Valley.
2. The Cotopaxi Volcano and Its Lahars Cotopaxi, the highest active volcano on Earth (5,897 m a.s.l.) and one of the most active volcanoes of Ecuador, lies about 50 km SE of Quito in the Northern Volcanic Zone (Thorpe et al., 1982). The volcanic edifice rises about 2,900 m above the highlands of the Interandean Depression, a tens of km-wide graben-like structure running N-S between the western and eastern Cordilleras of the Andes (Figure 1a). The superbly regular cone is truncated by an 800 m diameter, 334 m deep summit crater whose floor is occupied by a small pyroclastic cone. The summit of the volcano is topped by a 21 km2 permanent glacier that extends down to an altitude of 4,500–4,800 m, reaching the lowest elevations on the eastern side as result of a precipitation gradient across the mountain (Jordan, 1983). Cotopaxi acts as an important watershed divide, draining water respectively to the Pacific Ocean to the west and to the Amazonia basin to the east. The main RISK BY LAHARS AT COTOPAXI 163
Figure 1a. Map of the area of Cotopaxi.
catchments are those of Rio Pita to the north, Rio Cutuchi to the south and Rio Tamboto the east (Figure 1a). Various settlements occur along the river valleys. The towns of Latacunga and Salcedo are, respectively, 43 and 55 km from the volcano along the Rio Cutuchi/Patate/Pastaza valley. The villages of Sangolqui, San Rafael and Tumbaco are 40, 42 and 55 km from the volcano along the Rio Pita/Rio Santa Clara/Rio San Pedro valleys. The residential areas of Sangolqui and 164 E. AGUILERA ET AL.
Figure 1b. Close-up on the northern catchment of the Cotopaxi volcano. The numbers in square brackets refer to localities where historical information on 1877 lahar available (see also Table I). RISK BY LAHARS AT COTOPAXI 165
San Rafael have undergone rapid growth over the past decades, becoming satellite quarters of the capital Quito. Over the past four centuries the activity of Cotopaxi has been characterized by the emission of lava flows and by moderate to strong explosive episodes. Low magnitude explosive events have emplaced deposits of lapilli and ash fall and pyro- clastic flows (scoria and pumice flows and surges), having a cumulative volume lower than 1 km3. The plinian phases are characterized by peak mass discharge up to 4×108 kg/s (Barberi et al., 1992, 1995). Syn-eruptive lahars occurred frequently during the explosive activity of Cotopaxi volcano and the larger were triggered by the rapid melting of large snow and ice volumes during eruptions (Barberi et al., 1992). Pyroclastic surges and flows that swept over the glacier ice cap are probably the most effective at melting large amounts of snow and ice, which can result in quasi-instantaneous release of large masses of water and volcanic debris (Pierson, 1995). Virtually all historical eruptions of Cotopaxi have produced lahars through melting of the summit glacier (Barberi et al., 1992, 1995). Major lahars result- ing in fatalities, substantial damage to infrastructure and building, and extensive devastation of rural areas occurred in 1534, 1742–44, 1766, 1768 and 1877. The village of Latacunga, the most populated town in the past centuries, suffered major devastations in 1742, 1768 and 1877 (Sodiro, 1877; Wolf, 1878, 1904; Almeida, 1995). Historical information, tephrostratigraphic study, and 14C datings of deposits of the past 2000 years have shown that Cotopaxi has erupted regularly and followed a common pattern of activity. Nineteen major explosive eruptions (identified by lapilli-fall beds), separated by repose periods ranging from 15 to 187 years (average repose interval ∼120 years) were identified by Barberi et al. (1995). Because each explosive episode produced pyroclastic flows, surges, and lahars the recurrence interval of large-volume lahars can be considered equal to that of major tephra producing explosive eruptions. On this basis, Barberi et al. (1992, 1995) concluded that the probability of having a large 1877-like lahar is 0.57 and 0.82 in the next 100 and 200 years, respectively. Smaller-volume lahars that might be produced during “repose” periods with different triggering mechanisms are not here considered.
3. The 1877 Eruption
The 1877 eruption of Cotopaxi, the most recent of this volcano, has been superbly described in the chronicles of Wolf (1878) and Sodiro (1877). The eruption began at 10 a.m. on June 26th with a series of strong detonations that produced a plume of gas and ash above the volcano. Shortly after the onset of the eruption, eyewitnesses report that the summit of the crater appeared as a “potful of boiling rice which begin to pour out” (Wolf, 1878). In connection with this phenomenon (boiling over activity), stream of eruptive material (pyroclastic flows and lahar) descended radially at high speed along the flanks of the volcano. 166 E. AGUILERA ET AL.
Pyroclastic fall deposits of the 1877 eruption consist of lapilli up to 20 cm thick, dispersed westward. Pyroclastic flows consist mostly of scoria-flow deposits. They are only locally preserved, having been mostly remobilized and/or buried by syn- eruptive lahars (Barberi et al., 1995). It is likely that the scoria flow over the snow and ice caused the instantaneous melting of a portion of the glacier thickness, producing a huge mass of water similarly to other well known cases like Nevado del Ruiz and Mount St. Helens (Pierson et al., 1990; Pierson, 1985, 1995). Beyond the glacier the water, mixed with pyroclastic and ice blocks, caused intense erosion and gullying along the main ravines of the volcano and rapidly evolved into sediment-water slurries. According to Sodiro (1877) and Wolf (1878) the three main valleys originat- ing on Cotopaxi (the Rio Cutuchi southward, the Rio Pita northward and the Rio Tambo eastward) were all affected by large lahars. Along the Rio Cutuchi a lahar reached the town of Latacunga in less than one hour. The time duration of the flow in the same town was estimated to be about one hour. Upstream of Latacunga, the lahar activity created a temporary lake, 25 km long. The lahar destroyed farms, bridges and other buildings near Latacunga. Towards the north, the lahar initially flowed along small channels that gradually coalesced into Rio Pita and Rio Salto rivers (Figure 1b). Because the Rio Salto drains a much narrower sector of the Cotopaxi north-facing glacier than does the Rio Pita, a much less voluminous lahar traveled along the Rio Salto. Wolf, who climbed up the top of the volcano three months after the eruption, reported that he was not able to visit the western side of the mountain because of the total devastation of the ice cap. However, he did visit the northern sector of the summit area, which was only slightly affected by ice melting and lahars. Whymper (1880), on his journey toward Sincholagua, in February 1880, crossed “el pequeño rio Pedragal”, the old name of Rio Salto, confirming that it had been only marginally affected by the lahars. Wolf (1878) suggested that the prominent difference of devastation between Rio Salto and Rio Pita might have been produced by the uneven distribution of scoria flow over the summit glacier. Indeed, the height of the Cotopaxi’s crater rim impeded northward flow and instead channeled the scoria flow eastwards and westwards from the summit. About 22 km from Cotopaxi, the Rio Pita and the Rio Salto join together; a few kilometers downstream this confluence, near La Caldera, the Rio Pita turns sharply to the right. At this point the 1877 lahar partly overflowed into the Rio Santa Clara (Sodiro, 1877; Wolf, 1878). A portion of the 1877 lahar flowed about 20 km along the Rio Santa Clara, up to the Los Chillos valley, before it rejoined the Rio Pita lahar in the Rio San Pedro. We reviewed historical data sources and interviewed elderly inhabitants of the Los Chillos valley to accurately reconstruct the lahar path and to determine local flow depth and/or the arrival time of the lahars along the Rio Pita and Rio Santa Clara. Although the northern valleys were only sparsely populated in the late 1800’s, eyewitness chronicles provide valuable information regarding lahar pas- RISK BY LAHARS AT COTOPAXI 167 initial hydr. 10 m 54.5 m 12 m 8m. 1h 8m 10.5 m 30 min 7m 10.5 m > Max. flow depth > Max. flow depth > > Arrival time < Max. flow Depth ∼ > ∼ Max. flow Depth 10–12 m ∼ Max. flow depth characteristics < t so that the 1 ound floor of ı, Guangopolo, ` ı...” ` tile machines and of the maintenance 1 ...Thewaterenteredintothegr the trunk of a big avocado when the lahar passed ı, several tools and iron objects, removed by the ` d us to locate the exact point of his father house, which, ita partially overflowed into the Rio Cunugyacu, ...; . . . overflowed into the road toward Sangolqu 1 house, Rio Pita flooded the yard and the manger. ı, along Rio Cunugyacu”. ` rwise specified) ...” e northern catchment Reconstructed flow iting a thickness of mud of more 50 cm, while the sign left by the water on the flooded the garden and the ground floor of the house, . . . 8–11 m 1 thefloodinvadedtheCashapambaplain...” Max.flowdepth 2 ...depos ı and Conocoto ` house near the machines was also damaged. eaching the place called La Caldera, where the river forms a sharp bend, owing to the rush shop”. (Wolf, 1878) height. house did not suffer major damages Sangolqu according to his father tale, was marginally lapped by the flood. According to some old inhabitants of Sangolqu “Towards the North, in less than an hour the flood reached the plain among Alangas Rio Cunugyacu ...while,ontheothersideofthe the house, lahar from the Aguirre’s factory, werehere. driven into walls is more than 1 m high”. of the mud-flow, the lahartowards partially Pillocoto jumped and over Sangolqu the left levee, rather low at that point, and flowed Historical information on Rio Pita-Rio Santa Clara lahar of 1877 (after Sodiro, 1877; Wolf, 1878) ı ` Table I. sect. SC 22 sect. AG 1sect.AG2 The lahar reached a “...The stone wall, whose remains are today covered by mud up to about 50 cm of sect. PT 49 sect. PT 49 “Reaching the San Rafael farm, Rio P sect. SC 23 In the mean-time, Rio Cunugyacu sect. SC 17 sect. AG 3 The little church near the Aguirre’s factory was also reached, but it did not suffer major damages. 7.5–9 m 3 Aguirre’sfactory “...Themaindamage...consistsinthedestructionoftwotex 5 Sez. SC17 Map ref. n.(Figure 1b)1 Location 1877 lahar Pedregal impact in th (from Sodiro, 1877, if not othe “. . . the peasants of Pedregal say that the mud-flow lasted only half an hour”. 78 La Colina San Rafael farm A man, today seventy-five years old, helpe 2 LaCaldera “...r 6 Sangolqu 4 Cashapamba “From there Rio Cunugyacu is the oldFrom name the used Aguirre’s for factory. Rio Santa Clara. 1 2 168 E. AGUILERA ET AL. sage (Table I and Figure 1b). Major damage occurred along the distal reaches of Rio Pita and Rio Santa Clara.
4. Numerical Simulation of 1877 Lahars Along Rio Pita and Rio Santa Clara
4.1. THE MODEL The propagation of a lahar along the northern valleys, similar in magnitude to that of 1877, has been simulated using one-dimensional numerical model for channeled flows. The model is based on the mass and momentum balance equations for a bulk mixture. The model assumes: (a) constant lahar volume, (b) negligible velo- city differences between the solid and liquid fractions, and (c) constant sediment concentration, that is, the flow is considered homogenous (Macedonio and Pares- chi, 1992; Caruso and Pareschi, 1993). The equations of the model are analogous to those for clear-water flow, but they differ in the energy-dissipation coefficient (Sf ), which accounts of lahar rheology (Chen, 1987; Costa, 1997), which is quite different in water flow and in lahars (Pierson, 1995; Costa, 1997; Iverson 1997). Regarding the approximation of homogeneity, experiments performed on samples of natural debris flow sediments (Major and Pierson, 1990, 1992) indicate that the sediment concentration at which a mixture behaves as a homogeneous slurry is strongly related to the sand concentration. If the sand concentration in- creases, the total solid fraction must increase to maintain the integrity of the slurry. For water/sediment mixtures in which the ratio of fines to sand is 1:5, for example, sediment concentration was as great as 0.66 (Major and Pierson, 1990, 1992). In absence of direct measurement of deposits of the Cotopaxi’s lahars, we assumed a grain size distribution similar to that of the Nevada del Ruiz lahar deposits (5% fines = silt + clay and 95% coarser particles = sand + gravel, Pierson, 1995). In this regard it is important to note that most of debris flows triggered by eruptions and involving unaltered pyroclastic rock debris form noncohesive sediment-water mixture (Scott et al., 1995; Vallance and Scott, 1997) as confirmed by grain-size analyses of lahars triggered by the snow melting during eruptions (Pierson, 1995). A linear dependence (viscous behavior) of the shear stress on the shear rate was observed for fine-grained natural debris flows at moderate shear rate (Major and Pierson, 1990, 1992). However, at very low rates of shear (< 5s−1) or for coarser slurry mixture dilatant or complex models are more appropriate (O’Brien and Ju- lien, 1988; Phillips and Davies, 1991; Major and Pierson, 1992). Therefore, the lahar has been assumed to have dilatant behavior, with quadratic dependence of the shear stress on the shear rate. Bagnold’s number (Takahashi, 1991), which depends on the ratio between the inertial and viscous stress, has been estimated to be a few hundreds, suggesting such behavior. High boundary shear rates were for instance suggested for the Nevado del Ruiz lahars characterized by steep gradients of the channel bends and deep gorges (Pierson et al., 1990). According to Takahashi (1991), Caruso and Pareschi (1993) and Macedonio and Pareschi (1992) the mean RISK BY LAHARS AT COTOPAXI 169 energy dissipation term (Sf ) introduced in the momentum balance equation, taking into account the dilatant behavior, is: = 2 2 3 Sf nd U /h , (1) where nd is a proportional empirical coefficient whose value ranges between 0.1 and 0.8 m1/2 s, depending on mixture density, inter-particle fluid viscosity, sand to fines ratio, etc. (Chen, 1987; Macedonio and Pareschi, 1992); U is the flow velocity and h the flow depth. The simple rheological law (1) expresses energy dissipation in a homogenous flow and is a drastic simplification of real behavior. Recent works have shown solid-fluid interactions, grain-friction and grain-interaction (Iverson, 1997) can play an important role in the physics of sediment-laden flow and rig- orous, physically based, predictive dynamic models have been recently developed (Iverson, 1997). However, hydraulic one-dimensional fully dynamic models still maintain their importance for their simplicity and flexibility, and they are still important in preliminary hazard zonation (Costa, 1997; O’Brien et al., 1993). Our model only attempts to describe the gross behavior of the lahar, and must be interpreted accordingly. At each time step and for each section along the valley, the model provides information on depth-averaged velocity, maximum flow depth, wet area, and peak discharge. The model assumes no erosion and no sedimentation. For the 1980 Mt. St. Helens lahars, volume variation due to the incorporation of solid material during flow was estimated to be 15% for the North Fork Tourtle River lahar over ∼10 km reach of channel (Scott, 1988) and negligible for the Pine-Muddy River lahar along 10 km of flow path and by downstream-progressive increases in nonvolcanic clast within the lahars (Pierson, 1985). In contrast, large volume increase of the 1985 Nevado del Ruiz lahars was inferred on the basis of extensive scouring, in many places to bedrock, observed in steep and deeply incised channels (Pierson et al., 1990). The validity of the assumption of minor erosion for Cotopaxi lahars is discussed in the following section. In any case, it is important to remember that the model has severe limitation to predict the flow behavior during the first stage of lahar formation in the steep areas on the volcano flanks. In these proximal areas erosion is important. However, all our simulations start about 12 km from the volcano crater, where the flow becomes channelized and, likely, abundant incor- poration of debris has already led the flow to evolve into lahar and bulking would be significantly decreased downstream from the chosen starting point. Moreover, the assumption of no sedimentation is a big limitation mostly in the late stage of the flow.
4.2. THE INPUT DATA The adopted model requires information on the bed slope and on the shape of the valley. No detailed information is available on the morphology of the valley affected by the lahars of 1877. Although rivers affected by recurrent lahar passage 170 E. AGUILERA ET AL. and deposition should undergo significant changes in their general morphology (Rodolfo and Arguden, 1991; Montgomery et al., 1999), as a first, broad approx- imation we assume no major variation in cross-valley profiles or in bed slope since the passage of the 1877 lahars. The river beds of Rio Pita, Rio Salto and Rio Santa Clara drop more than 1,200 m in elevation in few tens of kilometers. Proximal reaches have mean slopes of about 4% with maximum gradient as large as 10%. Two cascades are present along the Rio Pita, 23 and 28 km from the volcano. Approximately 35 km from Cotopaxi both the Rio Pita and the Rio Santa Clara enter the Los Chillos valley; here mean slopes decrease to about 1.5% and the riverbeds become wider and meandering (Figures 2a–d). The shape of the channel assumed in the simulation was reconstructed by lin- early interpolating between cross-sections spaced 1 km apart, obtained either from aereophotogrammetric restitution or from field surveys. Finer cross-sections, with an average spacing of about 200 m, better resolve some crucial zones, such as La Caldera where lahar can overflow in response to a narrow valley bend. A total of 105 sections were used: 61 sections for Rio Pita (along ∼40 km), 13 for Rio Salto (∼10 km) and 31 for Rio Santa Clara (∼20 km). Each simulation was subdivided into 6 reaches (Figure 3), corresponding to the branches of the drainage network (the cascades are considered discontinuities). The reach include the upper Rio Pita and Rio Salto (I and II); the lower Rio Pita reach below the confluence (III); Rio Pita from La Caldera to the 2nd cascade (IV), the lower Rio Pita (V) and the Rio Santa Clara (VI) up to Los Chillos valley and the confluence with Rio San Pedro (VI). Ordinary discharges and flow depths in the Rio Pita are very low, on the order of 1–3 m3/s and 1–2 m (EMAP-Quito, 1996 oral com.). These values are, respectively, <0.005% and <5% than the peak discharge and peak flow depth estimated from historical accounts of the 1877 lahar. Hence, we simulated a lahar passing along a dry channel in all sections (initial conditions: discharge rate and flow depth = 0). In general two or one (zero or one) boundary conditions have to be assigned at the first (last) section of each reach, according to supercritical or subcritical flow. In the simulations the upstream boundary conditions of each reach are obtained from output of the previous reach. At the last section of each reach, if supercritical flow occurs, no boundary conditions are needed; if flow is subcritical and one condition is needed, since no field data are available, it forces the condition of critical flow: celerity (related to depth) equal to flow velocity. The condition of critical flow is forced at the first section of reaches III and V, downstream of the two cascades. At the first section of reaches I and II the input data are triangular shaped hydrographs. This is a convenient and plausible choice when data are too scarce for producing a detailed hydrograph of past lahar events (Iverson et al., 1998; Iverson, 1997) and it has been used in previously studied lahars having similar triggering mech- anisms (e.g. 1980 Mt. St. Helen; Pierson, 1985). The peak discharge of the initial hydrograph was deduced from the duration Tmax and from the total lahar volume. RISK BY LAHARS AT COTOPAXI 171
Figure 2. (a) Bed slopes (a) and valley half widths (b, c, d) at 10 m (continuous line) and 30 m (dotted line) for Rio Salto (b), Rio Pita (c) and Rio Santa Clara (d). 172 E. AGUILERA ET AL.
Figure 3. Main reaches in the northern catchment of Cotopaxi volcano considered in the simulation. RISK BY LAHARS AT COTOPAXI 173
In the simulation, Tmax was assumed equal to 1/2 hour, in agreement with historical information available at Pedregal (Ref. 1 in Table I), a little agricultural center a few kilometers down-valley from the initial sections. Lahar volume estimation was deduced from geological and geomorphological data and from comparison of the Rio Pita-Rio Salto drainage basins with that of Rio Cutuchi. The volume of the 1877 lahar along Rio Cutuchi was estimated to be 150× 106 m3 in a previous work (Barberi et al., 1992). Since the surface of the glacier of the Rio Cutuchi basin is more than twice that of the Rio Pita-Rio Salto and assuming uniform ice erosion, a maximum volume of about 60–70 × 106 m3 may be inferred for the lahar. Due to the presence of a topographic barrier along the northern crater rim, a smaller portion of the upper Rio Salto drainage basin was affected by pyroclastic flows than that of Rio Pita, about a 1:5 ratio, which, in turn, could translate in a similar ratio between the Rio Salto and Rio Pita lahars volumes. On the basis of the limitation imposed by the model and the input data, it is clear that the produced results are conservative when estimating peak discharge, flow depth, velocity and travel time.
4.3. RESULTS Twenty-one different simulations were performed with initial total volumes in the 6 3 1/2 range 35–80 × 10 m and nd in the range 0.2–0.6 m s. Simulated peak flow depths are reported in Table II and compared with historical information. In the same Table, arrival times at Sangolquì along Rio Santa Clara are also reported. Twelve runs have been performed with a constant coefficient nd ; nine with two different values, the higher one applied along the upper reaches, and the other one along the lower course, where the lahars enter the meandering, less channeled Los Chillos valley. Unfortunately, almost every historical value (peak flow depths) is located on the downstream-most reaches of Rio Santa Clara and Rio Pita, and no additional information on arrival times, peak discharge or flow depths are available upstream. Run n. 7, using an initial volume of 60 × 106 m3, shows the best fit of simulated peak flow depths with those provided by historical documents and was thus chosen as a reference simulation for the 1877 lahar. Lahar volumes larger than 70 × 106 m3 and lower than 50 × 106 m3 yielded calculated flow depths respectively too 1/2 high or too small; nd values greater than 0.5 (lower than 0.3) m s produce flow depths that are too small (too large). Arrival times at Sangolquì are around half- hour, hence in agreement with the historical information, which reports an arrival time to Sangolquì of less than an hour (Table I). It is interesting to compare the computed arrival times with arrival times estimated using the method of Pierson (1998) for flows having peak discharge > 10.000 m3/s. According the empirical relations proposed by Pierson an arrival time of less than 1 h is expected for distance downstream from the source less then 50 km, which is not in contrast with our simulation. 174 E. AGUILERA ET AL. 5 5 5 5 overflowed < < < < ı 60 min) into R.S.Cl t< SC 17 5m) ( . 10 h> Sect. SC23 (min) at Sangolqu` 11 m) (
Figures 4, 5 and 6 show peak flow depths and discharges of Run n. 7, along the Rio Pita, Rio Salto, and Rio Santa Clara valleys. In the same figures peak values of two simulation performed with a greater (70 × 106 m3) and a smaller (40 × 106 m3) volume are also reported for comparison. It is interesting to note that when the upper Rio Pita lahar reaches the conflu- ence with Rio Salto, the peak discharge increases again because of the tributary lahar input (Figure 4a). However, at La Caldera, peak discharge sharply decreases because of the overflow of part of the lahar into the Rio Santa Clara. Then, for about 15–20 km, peak discharge along Rio Pita remains substantially unchanged due to the steep gradients; near Sangolquì the peak discharge decreases as result of the valley enlargement and reduction of bed slope gradient. Along the whole Rio Pita, peak flow width ranges from 800 m in the upper reach, before the confluence with Rio Salto, to less than 100 m, in the deep gorge characterizing the lower I, III, IV and upper V reaches (Figure 4c); the average computed peak flow depth is around 20 m, with maximum values of 30-40 m in the narrow ravines (Figure 4b). Along almost every reach peak flow is supercritical with Froude numbers (∼2) similar to those estimated for Nevado del Ruiz lahars (Pierson et al., 1990). The volume fractions of lahar that overflows into Rio Santa Clara at La Caldera is given in Table II for different starting volumes and values of coefficient nd . Overflow occurs only when initial starting volumes are greater than ∼ 45 × 106 m3; the amount of overflow ranges from 5% to 25% of the total starting volume. Overflow at La Caldera occurs because of the free-surface tilting of the flow, which is due to the centrifugal forces generated when the lahar turns sharply to the right. From model calculation overbend occurs when the free-surface inclination α of the flows is greater than ∼ 35◦ (see the section profile at La Caldera, Figure 7). The values of tan α is computed according to the simple, idealized formula:
2 tan α = U /(rcg), (2) where U is provided by the model and the curvature radius (rc) of the reach is ∼ 180 m. The behavior of real debris flows around a curved paths are very complex since streamlines of the flow are not only curvilinear but also interwoven, resulting in spiral currents and cross waves. Experiment performed by Chen (1987) show that the bed slope, the curvature radius of the bend, the velocity and the rheolo- gical properties of the flow increase superelevation. As a consequence, tan α can have higher values relative to the idealized case of Equation (2). This implies that the overflowing at La Caldera could occur at lower velocities, or that the volume overflowed into Rio Santa Clara could be larger than that estimated from Equation (2). According to the flume experiment carried out by Iverson et al. (1994) flow superelevation on bends produces error in the correct estimation of velocity in the order of 30%. This may be assumed the potential error within our calculations. It is interesting to observe that the overflow at La Caldera acts as a “flux regulator” for the lahar of the Rio Pita. Whenever initial flow volumes exceeded ∼ 40×106 m3, peak discharge and flow depths along the low Rita Pita are buffered, 176 E. AGUILERA ET AL.
Figure 4. (a) Peak discharge, (b) peak flow depth, (c) peak flow width and (d) arrival time along Rio Pita for a lahar having a volume of 40, 60 and 70 × 106 m3. RISK BY LAHARS AT COTOPAXI 177
Figure 5. (a) Peak disharge, (b) peak flow depth, (c) peak flow width and (d) arrival time along Rio Salto for a volume of 40, 60 and 70 × 106 m3. 178 E. AGUILERA ET AL.
Figure 6. (a) Peak discharge, (b) peak flow depth, (c) peak flow width and (d) arrival time along Rio Santa Clara for a volume of 60 and 70 × 106 m3. RISK BY LAHARS AT COTOPAXI 179
Figure 7. Section profile at La Caldera, where an overflow could occur.
∗ Figure 8. Bulking (m3/m) vs tan θ h for Nevado del Ruiz lahars (field data from Pierson et al., 1990). Regression line is plotted. because the “surplus volume” spills into the Santa Clara valley. Along this valley, peak discharge is about 50% less than along the Rio Pita and peak flow depths are around 10 m (Figure 6a, b). Peak-flow widths are commonly between 100–200 m (Figure 6c). We have investigated the role of erosion along all valleys to test the reliability of our assumption of a constant total volume. In Figure 8, Sx∗h (where Sx = tan θ and θ is the bed slope and h the peak flow depth) is plotted as a function of bulking B (m3/m) for Nevado del Ruiz lahars (Laguillas, Molinos-Neireides and Guali (Pierson et al., 1990)). The linear trend observable can be explained by the 180 E. AGUILERA ET AL.
2 3 equation of uniform dilatant flow tan θ = nd U /h , and assuming the bulking B proportional to the square shear rate (dU/dz ∼ U/h)2. This square dependence is based on the assumption that bulking rate is proportional to the power dissipated by the fluid (Finnie, 1972). Using the regression line of Figure 8, total bulking along reaches I–VI can be obtained. For a total volume of 60 × 106 m3, eroded volumes are smaller than 5% (which could be considered roughly the uncertainty on arrival times, velocities, discharges, etc., by assuming a constant volume), with the exception of the first 10 km of reach VI (upper Rio Santa Clara), where erosion exceeds 30%. Computation done with a volume 30% higher along Rio Santa Clara shows, downvalley, along the final reach of Rio Santa Clara, near Sangolquì and San Rafael, variations in arrival times and peak flow-depths less than 10%.
5. Present Risk
Volcanic history of Cotopaxi suggests that in the case of reactivation, the volcanic phenomena will include both thepra fallout and pyroclastic flow/surge. The latter phenomenon is here believed to be the primary cause of lahars. Over the past centuries, two major changes have occurred, which, in the case of eruption like 1877, can have respectively reduced the level of lahar hazard and yet increased the level of risk in the valley draining the north side of Cotopaxi. A major factor that may lead to a significant reduction of the maximum expected lahar is the 1/3 shrinkage of area of the summit glacier during the past 100 years. By assuming that future lahars will be generated by pyroclastic flows and that lahars will result from a uniform melting of the glacier surface, the contraction of the glacier may result in a consequent reduction of lahar volume. Other generative processes such as the release of water stored in the ice mass by seismic shaking are believed to play a minor role compared to processes acting at the surface of the ice cap (Pierson et al., 1990). The result of such reasoning is that maximum expected lahar volume may be in the range of 40–60 × 106 m3. However, these speculation are valid only in the case the pyroclastic density currents affect the whole extension of the ice cap. In this case the extension of the ice cap play a role in defining the final volume of the lahar. A dramatic growth of population along the valleys, in particular in the Los Chil- los area, has occurred since the ruinous lahar of 1877. This increased settlement has accompanied drastic change in land-use from mainly agricultural to predominantly residential. In 1996 the total population living in valleys north of Cotopaxi reached about 100,000 people, mostly concentrated in the towns of Sangolquì, San Rafael and Rumimpamba. The present average rate of population growth is still very high, approximately 4.5% per year. Of particular note is that much of the growth has occurred along Rio Santa Clara. Table III and IV summarize the information on the settlements and the main structures along the Rio Pita and Santa Clara valleys. Table V and VI summarizes the population living in the two valleys. RISK BY LAHARS AT COTOPAXI 181 3 m 6 10 × 60 3 m = 6 10 × Lahar volume 3 m 6 10 × 40 rrival Extent of Peak Arrival Extent of = Lahar volume ı 2504–2507 28 Partially flooded 2505–2507 25 Partially flooded ` fael 2485 32 Partially flooded 2486 30 Partially flooded f Quito 3357 16 Submerged 3360 14 Submerged ı and S. Rafael ` s to the road 3308–3288 17 Submerged 3309–3291 15 Submerged r pipeline 3308–3288 17 Submerged 3309–3291 14 Submerged Pedregal 3288–3272 17 Submerged 3291–3274 15 Submerged 3,000 inhabitants) 3,000 inhabitants) ∼ ∼ of aqueduct districts of Sangolqu along right bank of Rio Pita ( ( –PT 47 Residential district of Sangolqu –PT 50 Bridge giving access to residential 2476–2471 35 Submerged 2477–2472 31 Submerged Buildings and infrastructures involved along Rio Pita for a volume respectively of 60 and 40 Table III. Bridge on Rio Salto 3273 ST 16–ST 17 On the road to Bridge on Rio Salto 3275 ST 15–ST 16 Bridge giving acces “El Tingo” bridge 2457Rio Salto Sifone “El PT Salto” 50–PT 51 Access to road 3278 going through towns 2471–2449 41 ST 15–ST 16 Pita-Tambo wate Submerged 2472–2450 32 Submerged “Isabela” bridge 2468 PT 49 Playa Chica 2485 PT 49 Residential district of San Ra andinfrastructures (m a.s.l.) height section (m a.s.l.) height (min.) time damage height (m a.s.l.) (min.) time damage BuildingRio Pita MeanPita-Tambo Nearestaqueduct connection Bridge on roadto 3341 Description PintagLa Colina 2533 PT 13 PT 44 Supplies 2495 south district o Bridge giving PT access 47 to state Peak 2539 A highway 24 Submerged 2539 22 Submerged 182 E. AGUILERA ET AL. 3 m 6 3 10 m 6 × 10 60 × = Lahar volume 3 m 6 10 × No damage 2510–2495 30 Partially flooded 40 = rrival Extent of Peak Arrival Extent of Lahar volume s – – No damage 2482 35 Partially flooded ı – – No damage 2483 31 Partially flooded ` ı – – No damage 2495 31 Submerged ` bitants – – No damage 2540 25 Partially flooded itants – – No damage 3097 16 Partially flooded trict of El – – No damage 2661 23 No damage mportant roads – – No damage 2512-2510 30 Flooded gher Education – – No damage 2512 28 Flooded ı village ` An avenue along which thereschools are 7 (7,500 students), an hospital, – a police barrack andhouses many – Ammunitions factoryResidential district of Sangolqu – – No damage 2483 31 No damage Agronomy Institute) populated agricultural area historical monument –SC 22 An historical–SP 1 building Town with about 20,000 inhabitant – – No damage 2482–2477 35 Flooded –SC 18 Bridge on the road to Sangolqu Buildings and infrastructures involved along Rio Santa Clara for a volume respectively of 60 and 40 Table IV. San Rafael 2474 SC 21 Old bridge on Rio 2489Cittadella Yaguachi Sc 17 ESPE 2485War Academy SC 20 2476 2486 SC 21 SC 21 University with 3,000 students – – No damage 2484 35 Partially flooded College“El Choclo”“Avenida Mercado” 2500 2507 SC 16–SC 17 SC 15-SC 16 Crossroads of three i Institute in the area BuildingandinfrastructuresRio S. Clara Mean (mTanipamba a.s.l.)“San Nearest Fernando”Bridge height 2678 3095 section Description“Santa Rosa” SCelectrical 7 CD station N1“Loreto” bridge 2640“Chillo” Town 2590 Farm of about Bridge 200 SC connecting inhab 7 dis Selva SC Alegre 10 2532“Juan Salinas” Peak The AG station 2–AG 3 supplies part 2532 of Bridge the giving 2507 access A to Only densely farm house remains SC and 12 Prado an (site Sangolqu SC of 15 – Andina-ESPE – – (m a.s.l.) (min.) height Town of about – Most 5,000 important inha – Hi time – damage No damage No damage No damage 2661 2599 height 2535–2536 (m a.s.l.) 25 23 (min.) 24 time Flooded damage Submerged Submerged Santa Clara” “S. Barbara” factory 2490 SC 20 RISK BY LAHARS AT COTOPAXI 183
Table V. Inhabitants along the Rio Pita valley and the fraction involved for a lahar of 40–60 × 106 m3.Due to the minor changes in peak flow depths along the last reach, no significant differences occur between the two cases
Urban centers Total population Percent of population at risk
Pedregal 350 0 Rumipamba 600 0 La Colina 3,000 30 Playa Chica 3,000 40
Table VI. Inhabitants along Rio Santa Clara valley and the fraction involved for a lahar of 60 × 106 m3
Urban centers Total population Percent of population at risk
Tanipamba 200 50 Selva Alegre 5,000 30 Sangolqu`ı 5,000 20 Cittadela Yagugachi 3,000 40 San Rafael 20,000 5
Table VII. Public structures potentially in- volved by a lahar along Rio Santa Clara
Schools Number of users
ESPE 3,000 College Juan Salinas 2,250 IASA 600
Other buildings Number of users
Cantonal Hospital 130 S. Barbara farm 200 Electrical station S. Rosa 30,000 184 E. AGUILERA ET AL.
Future occurrence of an overflow at La Caldera and consequent flow of a lahar along Rio Santa Clara valley is thus of crucial importance for the overall lahar risk assessment. For a volume of 40 × 106 m3, the expected minimum event, overflow at La Caldera does not occur (Table II), and the lahar flows entirely along Rio Pita. In Figures 4–6 peak discharges, flow depths, arrival times, etc. are reported for such lahar. For a lahar of 60 × 106 m3, the reference maximum event, overflow occurs, with a major risk along Rio Santa Clara (Tables III and IV). Figure 9 shows areas of inundation for the maximum expected event in the Los Chillos valley. An estimation of people potentially exposed to hazard in the areas flooded by lahar is given in Tables V, VI and VII. Due to the presence of numerous and populated settlement along Rio Santa Clara, overflow at La Caldera largely increases the risk: the number of people potentially involved increases from ∼2,500 along Rio Pita (for both the volumes) to 12,000 along Rio Santa Clara. Starting from this consideration, a simulation was also done assuming to artifi- cially force the entire volume of 60 × 106 m3 to flow into the Rio Pita. Figure 10a and 10b show, respectively, the maximum invasion and the maximum flow depth along Rio Pita, compared with the case of the 10% overflow into Rio Santa Clara. Peak flow depths and peak flow widths would increase of 1–2 m and of a few m respectively, indicating that the increase of devastating power would be minor. The results of the simulation thus suggests that the construction of a barrage dyke at La Caldera forcing the whole lahar volume to divert into the Rio Pita would be quite successful in reducing the risk in terms of the number of people to be evacuated and potential economic losses.
6. Conclusion
The reconstruction of the 1877 lahars along the northern catchments of Cotopaxi allowed us to calibrate the maximum expected lahar and to quantify the present risk. The maximum expected lahar volume ranges from 60 × 106 m3 to 40 × 106 m3, in case of 1877-like event or taking into account the volume reduction of the summit glacier in the last century, respectively. The most “optimistic” scenario predicts that the lahar would flow entirely along the Rio Pita threatening a total population of around 2,500 people. A more conservative scenario predicts that at La Caldera a fraction of a lahar would overflow into the much more populated Santa Clara valley. Overflow implies a drastic increase of hazard to structures and also increase of threatened population from 2,500 to 12,000 people. Modelling illustrates that an overflow of only 10% of the initial lahar volume of 60 × 106 m3 would be responsible for about 80% of the projected economic losses sustained in the catchments due to the much higher concentration of human settlements in the Santa Clara valley. Moreover, simulations suggest that the construction of barrage dike at La Caldera, able to divert the whole lahar volume into the Rio Pita would reduce the risk. RISK BY LAHARS AT COTOPAXI 185
Figure 9. Peak invasion in the La Chillos valley in for a volume of 60 × 106 m3. The hatched area is that invaded by the lahars. 186 E. AGUILERA ET AL.
Figure 10. (a) Maximum flow half width and (b) maximum flow along the last reach of Rio Pita for a volume of 60 × 106 m3. The lahar is forced to flow entirely along Rio Pita, placing an artificial barrier at La Caldera (dotted line), or overflowed at La Caldera (continuous line). RISK BY LAHARS AT COTOPAXI 187
The more than one century of the repose of Cotopaxi compared to its average eruption rate (one eruption every 120 years) suggests that the probability of having an eruption in the next few decades is fairly high. The next eruption will likely produce large volume lahars, some of which will impact the Los Chillos valley. It is therefore imperative to incorporate lahar hazard assessment in the land-use plans of the region. The simulation of a maximum expected lahar, combined with previous studies on the frequency of eruptive activity, provide fundamental data for quantification of hazard. These simulations, although affected by approximations, like precise lahar volume, hydrograph and rheology of the lahar, can be useful for both evacuation planning and general development planning.
Acknowledgments This work was carried out with a financial contribution from CNR-GNDCI and GNV. The Escuela Politecnica del Ejercito del Ecuador (ESPE), is greatly ac- knowledged for having provided topographic maps, field surveyed topographic cross-sections along the considered valley and historical information.
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