Risk from Lahars in the Northern Valleys of Cotopaxi ...geo1.espe.edu.ec/wp-content/uploads/2013/04/V-CotopaxiAguilera04.pdf · Risk from Lahars in the Northern Valleys of Cotopaxi

Natural Hazards 33: 161–189, 2004.© 2004 Kluwer Academic Publishers. Printed in the Netherlands.

161

Risk from Lahars in the Northern Valleys ofCotopaxi Volcano (Ecuador)

E. AGUILERA1, M. T. PARESCHI2�, M. ROSI3 and G. ZANCHETTA3

1ESPE, Campus Politecnico Santa Clara, Sangolquì, Ecuador; 2CNR-Istituto Geoscienze eGeorisorse, via S. Maria 53, I-56126 Pisa, Italy; 3Dipartimento di Scienze della Terra, Universityof 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 isassessed through numerical simulation of a maximum expected event. Considerations of past activitysuggest that an event like that of the 1877 eruption is the maximum expected lahar event. Reviewof the historical records reveals that northerly flowing lahars initially followed the Rio Pita and RioSalto; at “La Caldera”, owing to a sharp bend in the channel, the lahar partly overflowed into RioSanta 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 reachedby the 1877 lahar along the northern valley. The volume of lahar triggered by an eruption similar tothat of 1877 is estimated to have a volume about 2/3 of that of 1877. This hypothesized reductionof volume is attributed to shrinkage of the summit glacier over the past century. However, dramaticpopulation growth along valleys exposed to lahar hazard over the past 100 years makes the presentrisk from lahars higher than in the past. The sharp bend of “La Caldera” represents a crucial sitecontrolling lahar propagation: should a lahar overflow into the Santa Clara valley the risk increasesconsiderably due to the much higher concentration of human settlements along the valley. Results ofa lahar simulation in which the entire flow is artificially forced into Rio Pita suggest that constructionof 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 wellas distal areas from the volcano (Blong, 1984). The ability to affect areas situated atgreat distance from the source was shown dramatically at Nevado del Ruiz volcano(Colombia), where lahars generated by the melting of the summit glacier traveledmore than 70 km before devastating the town of Armero and claiming more than22,000 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 historicaland stratigraphic data (Scott, 1988; Scott et al., 1995; Vallance and Scott, 1997).However, precise delineation of the areas effected by the passage of past laharsis often difficult to reconstruct in detail from the stratigraphic record. Starting inthe 1980’s various authors have attempted to numerically model lahars to assesstheir hazard (Laenen and Hansen, 1988; Vignaux and Weir, 1990; McArthur etal., 1990; Takahashi, 1991; Macedonio and Pareschi, 1992; Barberi et al., 1992;Caruso and Pareschi, 1993; Costa, 1997; Iverson et al., 1998). An advantage ofmodelling resides in the ability to derive parameters such as mass discharge, flowdepth, flow width and flow velocity, once initial characteristics of a simulated eventare defined. Knowledge of such parameters is of critical importance for the organ-ization of the evacuation plans. In addition, assessment of lahar hazard throughhydraulic numerical modelling can be of great utility in the study and design ofpermanent structures (dams or dykes) aimed at reducing or eliminating the risk ofpopulated areas or infrastructures. Although these models employ hydraulic the-ory simplifications they provide sophisticated tools for practical forecast of laharrunout and inundation limits.

In this paper we address the problem of lahar hazard assessment in the valleynorth 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 eruptionof 1877 along the northern drainage system of the volcano up to 50 km from thecrater, 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, thevolume of a lahar potentially generated under present conditions is probably lessthan that of the 1877 lahar. Nevertheless the overall lahar risk from an eruptionat Cotopaxi has increased dramatically because of the growth of population in theLos 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 mostactive volcanoes of Ecuador, lies about 50 km SE of Quito in the Northern VolcanicZone (Thorpe et al., 1982). The volcanic edifice rises about 2,900 m above thehighlands of the Interandean Depression, a tens of km-wide graben-like structurerunning 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 summitcrater whose floor is occupied by a small pyroclastic cone. The summit of thevolcano is topped by a 21 km2 permanent glacier that extends down to an altitudeof 4,500–4,800 m, reaching the lowest elevations on the eastern side as result of aprecipitation gradient across the mountain (Jordan, 1983).

Cotopaxi acts as an important watershed divide, draining water respectively tothe 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 RioTamboto the east (Figure 1a). Various settlements occur along the river valleys.The towns of Latacunga and Salcedo are, respectively, 43 and 55 km from thevolcano 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 RioPita/Rio Santa Clara/Rio San Pedro valleys. The residential areas of Sangolqui and


Figure 1b. Close-up on the northern catchment of the Cotopaxi volcano. The numbers insquare brackets refer to localities where historical information on 1877 lahar available (seealso Table I).


San Rafael have undergone rapid growth over the past decades, becoming satellitequarters of the capital Quito.

Over the past four centuries the activity of Cotopaxi has been characterizedby the emission of lava flows and by moderate to strong explosive episodes. Lowmagnitude explosive events have emplaced deposits of lapilli and ash fall and pyro-clastic flows (scoria and pumice flows and surges), having a cumulative volumelower than 1 km3. The plinian phases are characterized by peak mass discharge upto 4×108 kg/s (Barberi et al., 1992, 1995). Syn-eruptive lahars occurred frequentlyduring the explosive activity of Cotopaxi volcano and the larger were triggered bythe 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 probablythe most effective at melting large amounts of snow and ice, which can result inquasi-instantaneous release of large masses of water and volcanic debris (Pierson,1995). Virtually all historical eruptions of Cotopaxi have produced lahars throughmelting of the summit glacier (Barberi et al., 1992, 1995). Major lahars result-ing in fatalities, substantial damage to infrastructure and building, and extensivedevastation of rural areas occurred in 1534, 1742–44, 1766, 1768 and 1877. Thevillage of Latacunga, the most populated town in the past centuries, suffered majordevastations in 1742, 1768 and 1877 (Sodiro, 1877; Wolf, 1878, 1904; Almeida,1995).

Historical information, tephrostratigraphic study, and 14C datings of deposits ofthe past 2000 years have shown that Cotopaxi has erupted regularly and followeda common pattern of activity. Nineteen major explosive eruptions (identified bylapilli-fall beds), separated by repose periods ranging from 15 to 187 years (averagerepose interval ∼120 years) were identified by Barberi et al. (1995). Because eachexplosive episode produced pyroclastic flows, surges, and lahars the recurrenceinterval of large-volume lahars can be considered equal to that of major tephraproducing explosive eruptions. On this basis, Barberi et al. (1992, 1995) concludedthat the probability of having a large 1877-like lahar is 0.57 and 0.82 in the next 100and 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 superblydescribed in the chronicles of Wolf (1878) and Sodiro (1877). The eruption beganat 10 a.m. on June 26th with a series of strong detonations that produced a plume ofgas and ash above the volcano. Shortly after the onset of the eruption, eyewitnessesreport that the summit of the crater appeared as a “potful of boiling rice whichbegin to pour out” (Wolf, 1878). In connection with this phenomenon (boilingover activity), stream of eruptive material (pyroclastic flows and lahar) descendedradially at high speed along the flanks of the volcano.


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. Theyare 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 instantaneousmelting of a portion of the glacier thickness, producing a huge mass of watersimilarly 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, mixedwith pyroclastic and ice blocks, caused intense erosion and gullying along the mainravines 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 RioTambo eastward) were all affected by large lahars. Along the Rio Cutuchi a laharreached the town of Latacunga in less than one hour. The time duration of the flowin the same town was estimated to be about one hour. Upstream of Latacunga, thelahar activity created a temporary lake, 25 km long. The lahar destroyed farms,bridges and other buildings near Latacunga. Towards the north, the lahar initiallyflowed along small channels that gradually coalesced into Rio Pita and Rio Saltorivers (Figure 1b). Because the Rio Salto drains a much narrower sector of theCotopaxi north-facing glacier than does the Rio Pita, a much less voluminous lahartraveled along the Rio Salto. Wolf, who climbed up the top of the volcano threemonths after the eruption, reported that he was not able to visit the western sideof the mountain because of the total devastation of the ice cap. However, he didvisit the northern sector of the summit area, which was only slightly affected byice melting and lahars. Whymper (1880), on his journey toward Sincholagua, inFebruary 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 betweenRio Salto and Rio Pita might have been produced by the uneven distribution ofscoria flow over the summit glacier. Indeed, the height of the Cotopaxi’s craterrim impeded northward flow and instead channeled the scoria flow eastwards andwestwards from the summit.

About 22 km from Cotopaxi, the Rio Pita and the Rio Salto join together; a fewkilometers downstream this confluence, near La Caldera, the Rio Pita turns sharplyto 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 alongthe Rio Santa Clara, up to the Los Chillos valley, before it rejoined the Rio Pitalahar in the Rio San Pedro.

We reviewed historical data sources and interviewed elderly inhabitants of theLos Chillos valley to accurately reconstruct the lahar path and to determine localflow depth and/or the arrival time of the lahars along the Rio Pita and Rio SantaClara. Although the northern valleys were only sparsely populated in the late1800’s, eyewitness chronicles provide valuable information regarding lahar pas-


Tabl

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1877

(aft

erS

odir

o,18

77;W

olf,

1878

)

Map

ref.

n.L

ocat

ion

1877

laha

rim

pact

inth

eno

rthe

rnca

tchm

ent

Rec

onst

ruct

edflo

w(F

igur

e1b

)(f

rom

Sodi

ro,1

877,

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toth

erw

ise

spec

ified

)ch

arac

teri

stic

s

1Pe

dreg

al“.

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epe

asan

tsof

Pedr

egal

say

that

the

mud

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last

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lyha

lfan

hour

”.�

tin

itial

hydr

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0m

in2

La

Cal

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“...

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hing

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Cal

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here

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arp

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the

mud

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sage (Table I and Figure 1b). Major damage occurred along the distal reaches ofRio 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 thatof 1877, has been simulated using one-dimensional numerical model for channeledflows. The model is based on the mass and momentum balance equations for abulk mixture. The model assumes: (a) constant lahar volume, (b) negligible velo-city differences between the solid and liquid fractions, and (c) constant sedimentconcentration, that is, the flow is considered homogenous (Macedonio and Pares-chi, 1992; Caruso and Pareschi, 1993). The equations of the model are analogousto 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 quitedifferent in water flow and in lahars (Pierson, 1995; Costa, 1997; Iverson 1997).

Regarding the approximation of homogeneity, experiments performed onsamples of natural debris flow sediments (Major and Pierson, 1990, 1992) indicatethat the sediment concentration at which a mixture behaves as a homogeneousslurry 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). Inabsence of direct measurement of deposits of the Cotopaxi’s lahars, we assumeda 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). Inthis regard it is important to note that most of debris flows triggered by eruptionsand involving unaltered pyroclastic rock debris form noncohesive sediment-watermixture (Scott et al., 1995; Vallance and Scott, 1997) as confirmed by grain-sizeanalyses of lahars triggered by the snow melting during eruptions (Pierson, 1995).A linear dependence (viscous behavior) of the shear stress on the shear rate wasobserved for fine-grained natural debris flows at moderate shear rate (Major andPierson, 1990, 1992). However, at very low rates of shear (< 5 s−1) or for coarserslurry mixture dilatant or complex models are more appropriate (O’Brien and Ju-lien, 1988; Phillips and Davies, 1991; Major and Pierson, 1992). Therefore, thelahar has been assumed to have dilatant behavior, with quadratic dependence of theshear stress on the shear rate. Bagnold’s number (Takahashi, 1991), which dependson the ratio between the inertial and viscous stress, has been estimated to be a fewhundreds, suggesting such behavior. High boundary shear rates were for instancesuggested for the Nevado del Ruiz lahars characterized by steep gradients of thechannel bends and deep gorges (Pierson et al., 1990). According to Takahashi(1991), Caruso and Pareschi (1993) and Macedonio and Pareschi (1992) the mean


energy dissipation term (Sf ) introduced in the momentum balance equation, takinginto account the dilatant behavior, is:

Sf = n2dU

2/h3, (1)

where nd is a proportional empirical coefficient whose value ranges between 0.1and 0.8 m1/2 s, depending on mixture density, inter-particle fluid viscosity, sand tofines ratio, etc. (Chen, 1987; Macedonio and Pareschi, 1992); U is the flow velocityand h the flow depth. The simple rheological law (1) expresses energy dissipationin a homogenous flow and is a drastic simplification of real behavior. Recent workshave 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 stillmaintain their importance for their simplicity and flexibility, and they are stillimportant in preliminary hazard zonation (Costa, 1997; O’Brien et al., 1993).Our model only attempts to describe the gross behavior of the lahar, and mustbe interpreted accordingly.

At each time step and for each section along the valley, the model providesinformation on depth-averaged velocity, maximum flow depth, wet area, and peakdischarge. The model assumes no erosion and no sedimentation. For the 1980 Mt.St. Helens lahars, volume variation due to the incorporation of solid material duringflow was estimated to be 15% for the North Fork Tourtle River lahar over ∼10km reach of channel (Scott, 1988) and negligible for the Pine-Muddy River laharalong 10 km of flow path and by downstream-progressive increases in nonvolcanicclast within the lahars (Pierson, 1985). In contrast, large volume increase of the1985 Nevado del Ruiz lahars was inferred on the basis of extensive scouring, inmany places to bedrock, observed in steep and deeply incised channels (Pierson etal., 1990). The validity of the assumption of minor erosion for Cotopaxi laharsis discussed in the following section. In any case, it is important to rememberthat the model has severe limitation to predict the flow behavior during the firststage of lahar formation in the steep areas on the volcano flanks. In these proximalareas erosion is important. However, all our simulations start about 12 km from thevolcano crater, where the flow becomes channelized and, likely, abundant incor-poration of debris has already led the flow to evolve into lahar and bulking wouldbe significantly decreased downstream from the chosen starting point. Moreover,the assumption of no sedimentation is a big limitation mostly in the late stage ofthe flow.

4.2. THE INPUT DATA

The adopted model requires information on the bed slope and on the shape ofthe valley. No detailed information is available on the morphology of the valleyaffected by the lahars of 1877. Although rivers affected by recurrent lahar passage


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 sincethe passage of the 1877 lahars.

The river beds of Rio Pita, Rio Salto and Rio Santa Clara drop more than 1,200m in elevation in few tens of kilometers. Proximal reaches have mean slopes ofabout 4% with maximum gradient as large as 10%. Two cascades are present alongthe Rio Pita, 23 and 28 km from the volcano. Approximately 35 km from Cotopaxiboth the Rio Pita and the Rio Santa Clara enter the Los Chillos valley; here meanslopes 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 fromaereophotogrammetric restitution or from field surveys. Finer cross-sections, withan average spacing of about 200 m, better resolve some crucial zones, such as LaCaldera where lahar can overflow in response to a narrow valley bend. A total of105 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 thebranches of the drainage network (the cascades are considered discontinuities). Thereach include the upper Rio Pita and Rio Salto (I and II); the lower Rio Pita reachbelow the confluence (III); Rio Pita from La Caldera to the 2nd cascade (IV), thelower Rio Pita (V) and the Rio Santa Clara (VI) up to Los Chillos valley and theconfluence with Rio San Pedro (VI).

Ordinary discharges and flow depths in the Rio Pita are very low, on the order of1–3 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 fromhistorical accounts of the 1877 lahar. Hence, we simulated a lahar passing along adry 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 atthe first (last) section of each reach, according to supercritical or subcritical flow. Inthe simulations the upstream boundary conditions of each reach are obtained fromoutput of the previous reach. At the last section of each reach, if supercritical flowoccurs, no boundary conditions are needed; if flow is subcritical and one conditionis 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 isforced at the first section of reaches III and V, downstream of the two cascades. Atthe 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 producinga 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 initialhydrograph was deduced from the duration Tmax and from the total lahar volume.


Figure 2. (a) Bed slopes (a) and valley half widths (b, c, d) at 10 m (continuous line) and 30m (dotted line) for Rio Salto (b), Rio Pita (c) and Rio Santa Clara (d).


Figure 3. Main reaches in the northern catchment of Cotopaxi volcano considered in thesimulation.


In the simulation, Tmax was assumed equal to 1/2 hour, in agreement with historicalinformation available at Pedregal (Ref. 1 in Table I), a little agricultural center afew kilometers down-valley from the initial sections.

Lahar volume estimation was deduced from geological and geomorphologicaldata and from comparison of the Rio Pita-Rio Salto drainage basins with that ofRio Cutuchi. The volume of the 1877 lahar along Rio Cutuchi was estimated to be150× 106 m3 in a previous work (Barberi et al., 1992). Since the surface of theglacier of the Rio Cutuchi basin is more than twice that of the Rio Pita-Rio Saltoand 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 alongthe northern crater rim, a smaller portion of the upper Rio Salto drainage basin wasaffected 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 isclear 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 therange 35–80 × 106 m3 and nd in the range 0.2–0.6 m1/2 s. Simulated peak flowdepths are reported in Table II and compared with historical information. In thesame Table, arrival times at Sangolquì along Rio Santa Clara are also reported.

Twelve runs have been performed with a constant coefficient nd ; nine with twodifferent values, the higher one applied along the upper reaches, and the other onealong the lower course, where the lahars enter the meandering, less channeled LosChillos valley. Unfortunately, almost every historical value (peak flow depths) islocated on the downstream-most reaches of Rio Santa Clara and Rio Pita, and noadditional information on arrival times, peak discharge or flow depths are availableupstream.

Run n. 7, using an initial volume of 60 × 106 m3, shows the best fit of simulatedpeak flow depths with those provided by historical documents and was thus chosenas 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 toohigh or too small; nd values greater than 0.5 (lower than 0.3) m1/2 s produce flowdepths that are too small (too large). Arrival times at Sangolquì are around half-hour, hence in agreement with the historical information, which reports an arrivaltime to Sangolquì of less than an hour (Table I). It is interesting to compare thecomputed arrival times with arrival times estimated using the method of Pierson(1998) for flows having peak discharge > 10.000 m3/s. According the empiricalrelations proposed by Pierson an arrival time of less than 1 h is expected fordistance downstream from the source less then 50 km, which is not in contrastwith our simulation.


Tabl

eII

.P

eak

flow

dept

hsat

som

elo

cati

ons

and

arri

val

tim

eto

the

regi

onof

San

golq

uı̀(a

long

Rio

San

taC

lara

,w

hen

over

flow

occu

rs)

for

diff

eren

tV

olum

esan

dva

lues

ofnd

.His

tori

cali

nfor

mat

ion

are

also

repo

rted

inB

rack

etin

the

seco

ndro

w

Com

pute

dpe

akfl

owC

ompu

ted

peak

flow

dept

h(m

)–

Rio

San

taC

lara

Arr

ival

tim

e

dept

h(m

)-

Rio

Pit

a(m

in)

atS

ango

lquı̀

RU

NV

olum

end

La

San

Raf

aelf

arm

Agu

irre

’sfa

ctor

yC

asha

-se

ct.S

C17

′S

anR

afae

lfar

mse

ct.

Vol

ume

(%)

(106

m3

)(m

1/2

s)C

olin

aS

ect.

PT

49S

ect.

PT

49′

Sec

t.A

G1

Sec

t.A

G2

Sec

t.A

G3

pam

ba(1

0<

h<

12m

)S

ect.

SC

22′

Sec

t.S

C23

′S

C17

′ov

erfl

owed

(h∼

8m

)(h

>10

m)

(h<

10.5

m)

(h>

12m

)(h

∼7

m)

(7.5

<h

<9

m)

(h>

8m

)(8

<h

<11

m)

(h>

10.5

m)

(t<

60m

in)

into

R.S

.Cl

180

0.4–

0.3∗

8.9

11.9

10.6

17.1

10.4

12.3

13.6

12.9

12.5

16.5

2425

270

0.4–

0.3∗

8.9

11.9

10.6

14.9

8.8

10.8

11.0

11.0

10.7

13.6

2715

370

0.6–

0.3∗

9.2

12.3

11.1

12.5

7.5

9.2

8.6

8.8

8.9

11.3

3210

460

0.2

7.2

9.8

8.9

15.2

8.7

10.1

11.2

11.5

11.3

15.1

2125

560

0.3

8.6

11.5

10.2

14.8

8.8

10.7

11.2

11.1

10.8

13.8

2620

660

0.4

9.8

12.8

11.2

13.5

8.2

10.7

8.9

9.4

9.2

11.5

3210

760

0.4–

0.3∗

8.8

11.8

10.5

13.2

7.8

9.6

9.0

9.2

9.1

11.5

3310

860

0.5–

0.3∗

9.1

12.1

10.8

11.1

7.0

8.6

7.2

7.3

8.0

10.1

345

960

0.6–

0.3∗

9.2

12.1

10.9

6.3

5.5

6.8

4.1

3.8

––

53<

5

1048

0.2

7.2

9.8

8.9

13.3

7.6

8.7

9.5

9.8

10.0

12.9

2420

1148

0.3

8.6

11.4

10.1

11.9

7.3

8.9

7.9

8.1

8.5

10.7

3110

1248

0.4

9.6

12.2

10.7

6.9

6.0

7.1

4.4

4.1

––

58<

5

1348

0.4–

0.3∗

8.8

11.5

10.3

6.6

5.6

7.1

4.3

4.2

––

50<

5

14∗∗

480.

6–0.

3∗8.

410

.99.

7–

––

––

––

––

1540

0.2

7.2

9.7

8.9

11.0

6.6

7.7

7.8

7.6

8.5

10.8

2610

1640

0.3

8.5

11.1

10.0

5.3

5.1

6.1

3.5

3.1

––

58<

5

17∗∗

400.

48.

410

.99.

7–

––

––

––

––

18∗∗

400.

4–0.

3∗8.

410

.99.

7–

––

––

––

––

1936

0.2

7.1

9.7

8.8

8.3

5.8

6.8

5.8

5.5

6.3

7.7

315

20∗∗

360.

38.

210

.69.

4–

––

––

––

––

21∗∗

360.

48.

510

.49.

2–

––

––

––

––

∗ The

low

erco

effi

cien

tnd

isus

edin

the

larg

erse

ctio

nsof

Los

Chi

llos

Val

ley.

∗∗T

hela

har

does

noto

verfl

owin

toth

eR

ioS

.Cla

ra.


Figures 4, 5 and 6 show peak flow depths and discharges of Run n. 7, along theRio Pita, Rio Salto, and Rio Santa Clara valleys. In the same figures peak valuesof 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 tributarylahar input (Figure 4a). However, at La Caldera, peak discharge sharply decreasesbecause of the overflow of part of the lahar into the Rio Santa Clara. Then, forabout 15–20 km, peak discharge along Rio Pita remains substantially unchangeddue to the steep gradients; near Sangolquì the peak discharge decreases as result ofthe valley enlargement and reduction of bed slope gradient. Along the whole RioPita, peak flow width ranges from 800 m in the upper reach, before the confluencewith 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 isaround 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 Calderais 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, whichis 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 theflows is greater than ∼ 35◦ (see the section profile at La Caldera, Figure 7). Thevalues of tan α is computed according to the simple, idealized formula:

tan α = U 2/(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 complexsince streamlines of the flow are not only curvilinear but also interwoven, resultingin spiral currents and cross waves. Experiment performed by Chen (1987) showthat 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 canhave higher values relative to the idealized case of Equation (2). This implies thatthe overflowing at La Caldera could occur at lower velocities, or that the volumeoverflowed 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) flowsuperelevation on bends produces error in the correct estimation of velocity in theorder 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 “fluxregulator” 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,


Figure 4. (a) Peak discharge, (b) peak flow depth, (c) peak flow width and (d) arrival timealong Rio Pita for a lahar having a volume of 40, 60 and 70 × 106 m3.


Figure 5. (a) Peak disharge, (b) peak flow depth, (c) peak flow width and (d) arrival time alongRio Salto for a volume of 40, 60 and 70 × 106 m3.


Figure 6. (a) Peak discharge, (b) peak flow depth, (c) peak flow width and (d) arrival timealong Rio Santa Clara for a volume of 60 and 70 × 106 m3.


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 etal., 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 arearound 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 reliabilityof 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 ofbulking B (m3/m) for Nevado del Ruiz lahars (Laguillas, Molinos-Neireides andGuali (Pierson et al., 1990)). The linear trend observable can be explained by the


equation of uniform dilatant flow tan θ = ndU2/h3, and assuming the bulking B

proportional to the square shear rate (dU /dz ∼ U/h)2. This square dependence isbased on the assumption that bulking rate is proportional to the power dissipatedby the fluid (Finnie, 1972). Using the regression line of Figure 8, total bulkingalong reaches I–VI can be obtained. For a total volume of 60 × 106 m3, erodedvolumes are smaller than 5% (which could be considered roughly the uncertaintyon arrival times, velocities, discharges, etc., by assuming a constant volume), withthe exception of the first 10 km of reach VI (upper Rio Santa Clara), where erosionexceeds 30%. Computation done with a volume 30% higher along Rio Santa Clarashows, downvalley, along the final reach of Rio Santa Clara, near Sangolquì andSan 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 volcanicphenomena will include both thepra fallout and pyroclastic flow/surge. The latterphenomenon is here believed to be the primary cause of lahars. Over the pastcenturies, two major changes have occurred, which, in the case of eruption like1877, can have respectively reduced the level of lahar hazard and yet increased thelevel of risk in the valley draining the north side of Cotopaxi.

A major factor that may lead to a significant reduction of the maximum expectedlahar is the 1/3 shrinkage of area of the summit glacier during the past 100 years. Byassuming that future lahars will be generated by pyroclastic flows and that laharswill result from a uniform melting of the glacier surface, the contraction of theglacier may result in a consequent reduction of lahar volume. Other generativeprocesses such as the release of water stored in the ice mass by seismic shaking arebelieved to play a minor role compared to processes acting at the surface of the icecap (Pierson et al., 1990). The result of such reasoning is that maximum expectedlahar volume may be in the range of 40–60 × 106 m3. However, these speculationare valid only in the case the pyroclastic density currents affect the whole extensionof the ice cap. In this case the extension of the ice cap play a role in defining thefinal 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 hasaccompanied drastic change in land-use from mainly agricultural to predominantlyresidential. In 1996 the total population living in valleys north of Cotopaxi reachedabout 100,000 people, mostly concentrated in the towns of Sangolquì, San Rafaeland 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 hasoccurred along Rio Santa Clara. Table III and IV summarize the information onthe 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.


Tabl

eII

I.B

uild

ings

and

infr

astr

uctu

res

invo

lved

alon

gR

ioP

ita

for

avo

lum

ere

spec

tivel

yof

60an

d40

×10

6m

3

Lah

arvo

lum

e=

40×

106

m3

Lah

arvo

lum

e=

60×

106

m3

Bui

ldin

gM

ean

Nea

rest

Des

crip

tion

Peak

Arr

ival

Ext

ento

fPe

akA

rriv

alE

xten

tof

and

heig

htse

ctio

nhe

ight

time

dam

age

heig

httim

eda

mag

e

infr

astr

uctu

res

(ma.

s.l.)

(ma.

s.l.)

(min

.)(m

a.s.

l.)(m

in.)

Rio

Pita

Pita

-Tam

bo33

41PT

13Su

pplie

sso

uth

dist

rict

ofQ

uito

3357

16Su

bmer

ged

3360

14Su

bmer

ged

aque

duct

conn

ectio

n

Bri

dge

onro

ad25

33PT

44B

ridg

egi

ving

acce

ssto

stat

e25

3924

Subm

erge

d25

3922

Subm

erge

d

toPi

ntag

high

way

La

Col

ina

2495

PT47

′ –PT

47R

esid

entia

ldi

stri

ctof

Sang

olqu

ı̀25

04–2

507

28Pa

rtia

llyflo

oded

2505

–250

725

Part

ially

flood

ed

(∼3,

000

inha

bita

nts)

Play

aC

hica

2485

PT49

Res

iden

tial

dist

rict

ofSa

nR

afae

l24

8532

Part

ially

flood

ed24

8630

Part

ially

flood

ed

(∼3,

000

inha

bita

nts)

“Isa

bela

”br

idge

2468

PT49

′ –PT

50B

ridg

egi

ving

acce

ssto

resi

dent

ial

2476

–247

135

Subm

erge

d24

77–2

472

31Su

bmer

ged

dist

rict

sof

Sang

olqu

ı̀and

S.R

afae

l

“ElT

ingo

”br

idge

2457

PT50

–PT

51A

cces

sto

road

goin

gth

roug

hto

wns

2471

–244

941

Subm

erge

d24

72–2

450

32Su

bmer

ged

alon

gri

ghtb

ank

ofR

ioPi

ta

Rio

Salto

Sifo

ne“E

lSal

to”

3278

ST15

–ST

16Pi

ta-T

ambo

wat

erpi

pelin

e33

08–3

288

17Su

bmer

ged

3309

–329

114

Subm

erge

d

Bri

dge

onR

ioSa

lto32

75ST

15–S

T16

Bri

dge

givi

ngac

cess

toth

ero

ad33

08–3

288

17Su

bmer

ged

3309

–329

115

Subm

erge

d

ofaq

uedu

ct

Bri

dge

onR

ioSa

lto32

73ST

16–S

T17

On

the

road

toPe

dreg

al32

88–3

272

17Su

bmer

ged

3291

–327

415

Subm

erge

d


Tabl

eIV

.B

uild

ings

and

infr

astr

uctu

res

invo

lved

alon

gR

ioS

anta

Cla

rafo

ra

volu

me

resp

ectiv

ely

of60

and

40×

106

m3

Lah

arvo

lum

e=

40×

106

m3

Lah

arvo

lum

e=

60×

106

m3

Bui

ldin

gM

ean

Nea

rest

Des

crip

tion

Peak

Arr

ival

Ext

ento

fPe

akA

rriv

alE

xten

tof

and

heig

htse

ctio

nhe

ight

time

dam

age

heig

httim

eda

mag

ein

fras

truc

ture

s(m

a.s.

l.)(m

a.s.

l.)(m

in.)

(ma.

s.l.)

(min

.)

Rio

S.C

lara

Tani

pam

ba30

95C

DN

1To

wn

ofab

out2

00in

habi

tant

s–

–N

oda

mag

e30

9716

Part

ially

flood

ed“S

anFe

rnan

do”

2678

SC7

Bri

dge

conn

ectin

gdi

stri

ctof

El

––

No

dam

age

2661

23N

oda

mag

eB

ridg

ePr

ado

(site

ofA

ndin

a-E

SPE

Agr

onom

yIn

stitu

te)

“San

taR

osa”

2640

SC7

The

stat

ion

supp

lies

part

ofth

e–

–N

oda

mag

e26

6123

Subm

erge

del

ectr

ical

stat

ion

Sang

olqu

ı̀vill

age

“Lor

eto”

brid

ge25

90SC

10B

ridg

egi

ving

acce

ssto

dens

ely

––

No

dam

age

2599

24Su

bmer

ged

popu

late

dag

ricu

ltura

lar

ea“C

hillo

”Fa

rm25

32A

G2–

AG

3O

nly

farm

hous

ere

mai

nsan

dan

––

No

dam

age

2535

–253

625

Floo

ded

hist

oric

alm

onum

ent

Selv

aA

legr

e25

32SC

12To

wn

ofab

out5

,000

inha

bita

nts

––

No

dam

age

2540

25Pa

rtia

llyflo

oded

“Jua

nSa

linas

”25

07SC

15M

osti

mpo

rtan

tHig

her

Edu

catio

n–

–N

oda

mag

e25

1228

Floo

ded

Col

lege

Inst

itute

inth

ear

ea“E

lCho

clo”

2507

SC15

-SC

16C

ross

road

sof

thre

eim

port

antr

oads

––

No

dam

age

2512

-251

030

Floo

ded

“Ave

nida

Mer

cado

”25

00SC

16–S

C17

′A

nav

enue

alon

gw

hich

ther

ear

e7

––

No

dam

age

2510

–249

530

Part

ially

flood

edsc

hool

s(7

,500

stud

ents

),an

hosp

ital,

apo

lice

barr

ack

and

man

yho

uses

Old

brid

geon

Rio

2489

Sc17

′ –SC

18B

ridg

eon

the

road

toSa

ngol

quı̀

––

No

dam

age

2495

31Su

bmer

ged

Sant

aC

lara

”“S

.Bar

bara

”fa

ctor

y24

90SC

20′

Am

mun

ition

sfa

ctor

y–

–N

oda

mag

e24

8331

No

dam

age

Citt

adel

laY

agua

chi

2485

SC20

′R

esid

entia

ldi

stri

ctof

Sang

olqu

ı̀–

–N

oda

mag

e24

8331

Part

ially

flood

edE

SPE

2486

SC21

Uni

vers

ityw

ith3,

000

stud

ents

––

No

dam

age

2484

35Pa

rtia

llyflo

oded

War

Aca

dem

y24

76SC

21′ –

SC22

An

hist

oric

albu

ildin

g–

–N

oda

mag

e24

82–2

477

35Fl

oode

dSa

nR

afae

l24

74SC

21′ –

SP1

Tow

nw

ithab

out2

0,00

0in

habi

tant

s–

–N

oda

mag

e24

8235

Part

ially

flood

ed


Table V. Inhabitants along the Rio Pita valley and thefraction involved for a lahar of 40–60 × 106 m3. Dueto the minor changes in peak flow depths along thelast reach, no significant differences occur betweenthe 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 thefraction 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

Sangolquı̀ 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


Future occurrence of an overflow at La Caldera and consequent flow of a laharalong Rio Santa Clara valley is thus of crucial importance for the overall lahar riskassessment. For a volume of 40 × 106 m3, the expected minimum event, overflowat 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 forsuch lahar. For a lahar of 60 × 106 m3, the reference maximum event, overflowoccurs, with a major risk along Rio Santa Clara (Tables III and IV). Figure 9 showsareas of inundation for the maximum expected event in the Los Chillos valley. Anestimation of people potentially exposed to hazard in the areas flooded by laharis given in Tables V, VI and VII. Due to the presence of numerous and populatedsettlement 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 10aand 10b show, respectively, the maximum invasion and the maximum flow depthalong 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 mrespectively, indicating that the increase of devastating power would be minor. Theresults of the simulation thus suggests that the construction of a barrage dyke at LaCaldera forcing the whole lahar volume to divert into the Rio Pita would be quitesuccessful in reducing the risk in terms of the number of people to be evacuatedand potential economic losses.

6. Conclusion

The reconstruction of the 1877 lahars along the northern catchments of Cotopaxiallowed us to calibrate the maximum expected lahar and to quantify the presentrisk. 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 thesummit glacier in the last century, respectively. The most “optimistic” scenariopredicts that the lahar would flow entirely along the Rio Pita threatening a totalpopulation of around 2,500 people. A more conservative scenario predicts that atLa Caldera a fraction of a lahar would overflow into the much more populatedSanta Clara valley. Overflow implies a drastic increase of hazard to structures andalso increase of threatened population from 2,500 to 12,000 people. Modellingillustrates 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 inthe catchments due to the much higher concentration of human settlements in theSanta Clara valley. Moreover, simulations suggest that the construction of barragedike at La Caldera, able to divert the whole lahar volume into the Rio Pita wouldreduce the risk.


Figure 9. Peak invasion in the La Chillos valley in for a volume of 60 × 106 m3. The hatchedarea is that invaded by the lahars.


Figure 10. (a) Maximum flow half width and (b) maximum flow along the last reach of RioPita for a volume of 60 × 106 m3. The lahar is forced to flow entirely along Rio Pita, placingan artificial barrier at La Caldera (dotted line), or overflowed at La Caldera (continuous line).


The more than one century of the repose of Cotopaxi compared to its averageeruption rate (one eruption every 120 years) suggests that the probability of havingan eruption in the next few decades is fairly high. The next eruption will likelyproduce large volume lahars, some of which will impact the Los Chillos valley.It is therefore imperative to incorporate lahar hazard assessment in the land-useplans of the region. The simulation of a maximum expected lahar, combined withprevious studies on the frequency of eruptive activity, provide fundamental data forquantification of hazard. These simulations, although affected by approximations,like precise lahar volume, hydrograph and rheology of the lahar, can be useful forboth evacuation planning and general development planning.

Acknowledgments

This work was carried out with a financial contribution from CNR-GNDCI andGNV. The Escuela Politecnica del Ejercito del Ecuador (ESPE), is greatly ac-knowledged for having provided topographic maps, field surveyed topographiccross-sections along the considered valley and historical information.

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