University of Nevada, Reno

Quantifying environmental controls on the magnitude of glacial lake outburst floods and the resulting impacts to hydrology and geomorphology: Lago Cachet Dos, Patagonia, Chile

A thesis submitted in partial fulfilment of the requirements for the degree of Master of Science in Hydrology

by

Jonathan D. Jacquet

Dr. Scott McCoy/Thesis Advisor

December, 2016

THE GRADUATE SCHOOL

We recommend that the thesis prepared under our supervision by

JONATHAN DANIEL JACQUET

Entitled

Quantifying Environmental Controls On The Magnitude Of Glacial Lake Outburst Floods And The Resulting Impacts To Hydrology And Geomorphology: Lago Cachet Dos, Patagonia, Chile

be accepted in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

Scott Mccoy, Ph.D., Advisor

Daniel Mcgrath, Ph.D., Committee Member

Adrian Harpold, Ph.D., Graduate School Representative

David W. Zeh, Ph.D., Dean, Graduate School

December, 2016

i

Abstract

The sudden release of water from an ice-dammed lake poses substantial hazard to the

downstream environment, but the degree to which peak discharge depends on environmental

variables that change with climate remains unclear. We combine in situ measurements of

environmental variables with high-resolution discharge measurements from a glacier-

dammed lake, Lago Cachet Dos (LC2), to evaluate environmental conditions that influence

the peak discharge of observed glacial lake outburst floods (GLOFs). Since April 2008, 20

GLOFs have initiated out of LC2, located on the eastern edge of the Northern Patagonia

Icefield, Chile and flooded areas along the Rio Colonia- Rio Baker system. GLOF frequency

has averaged 1-3 events annually and calculated peak discharges exiting LC2 have ranged

widely from 2,000 to >15,000 m3/s. We show that, consistent with physics-based theory, increasing water volume released, lake temperature, and the rate of meltwater input into the glacially dammed lake all increase the peak discharge of observed GLOFs. Additionally, we quantify the hydrologic and geomorphic response to episodic GLOFs using multi-temporal satellite imagery and field observations. Peak discharge exiting the source lake exceeded

15,000 m3/s, but became progressively muted downstream. At ~40 km downstream, peak

discharges were generally < 2000 m3/s, but still > 15 times the median discharge. The GLOFs

resulted in > 40 m of downcutting and erosion of ~25 x106 m3 of sediment from the source

lake basin and a non-steady channel configuration downstream. Our results suggest that more

accurate predictions of GLOF magnitude from ice dammed lakes can be made by

incorporating additional measurements of environmental conditions and that quantifying

GLOF water and sediment fluxes in the Colonia system may provide insight into potential

changes that similar fluvial systems could experience after the onset of large floods. ii

Table of Contents Chapter 1: Introduction ...... 1 What is a glacial lake outburst flood? ...... 1 Examples of Paleo-GLOFs ...... 3 Where do GLOFs occur and why should we care? ...... 3 Chapter Summaries ...... 5 Chapter 2: Environmental controls on the variability of peak discharge of glacial lake outburst floods: Lago Cachet Dos, Chile ...... 6 Abstract ...... 7 1 Introduction ...... 8 2 Study Area: Lago Cachet Dos, Patagonia, Chile ...... 9 3 Theoretical Background for Drainage of Ice-Dammed Lakes ...... 12 4 Data and Methods ...... 14 4.1 Calculating GLOF Discharge from Glacially Dammed LC2 ...... 14 4.2 Estimating Total Volume of Water Drained from LC2 during GLOFs ...... 16 4.3 Measurements of Water and Air Temperature ...... 17 4.4 Rate of inflow ...... 17 5 Results ...... 18 5.1 Peak Discharge and Volume of LC2 GLOFs ...... 18 5.2 Correlation of Environmental Variables to Peak Discharge ...... 20 6 Discussion ...... 22 6.1 Accuracy of Empirical Equations Used to Predict Peak Discharge ...... 22 6.2 Importance of Lake Temperature in Predicting Peak Discharge ...... 24 6.3 Significance of Inflow Rate and Implications under a Changing Climate ...... 24 7 Conclusions ...... 25 Supporting Information ...... 27 Chapter 3: Hydrologic and geomorphic changes resulting from episodic glacial lake outburst floods: Rio Colonia, Patagonia, Chile ...... 32 Abstract ...... 33 1 Introduction ...... 33 2 Study Area: Cachet-Colonia-Baker Valley, Patagonia, Chile ...... 35 2.1 Thinning and Retreat of the Colonia Glacier ...... 35 2.2 History of GLOFs in Cachet and Colonia Valleys...... 35 iii

3 Methods ...... 38 3.1 Measuring Changes in Hydrologic Regime: Rio Colonia and Rio Baker...... 38 3.2 Measuring Sediment Transport from Glacially Dammed LC2 Lake Basin ...... 38 3.3 Estimating GLOF Discharge from Glacially Dammed LC2 ...... 40 3.4 Quantifying Changing Planform Channel Morphology: Rio Colonia ...... 41 4 Results and Discussion ...... 42 4.1 GLOF Characteristics and Changes in Hydrologic Regime ...... 42 4.2 Sediment Transport in the Glacially Dammed LC2 Lake Basin ...... 44 4.3 Quantifying Changing Channel Morphology on the Rio Colonia ...... 47 5 Conclusions ...... 50 Supporting Information ...... 52 Chapter 4: Conclusions ...... 65 Environmental Controls on Peak Discharge from GLOFs ...... 65 Effects on Hydrology and Geomorphology from Episodic GLOFs ...... 66 Future Research ...... 67 References ...... 68

iv

List of Tables

Chapter 2 Table S1. GLOF peak discharges and volumes...... 31

Chapter 3 Table S1. GLOF peak discharges and volumes...... 64 Table S2. Areal, volumetric, and vertical metrics calculated for each DEM of difference ...... 64

v

List of Figures

Chapter 2 Figure 1. Map of the region surrounding the Colonia Valle ...... 11 Figure 2. GLOF discharge hydrographs for the outlet of the source lake, LC2 ...... 19 Figure 3. Correlation plot of peak discharge versus volume drained, lake and air temperature, and inflow rate ...... 22 Figure S1. Hydrographs of GLOFs from the Rio Baker en Colonia gauge...... 27 Figure S2. Plot of lake temperature, hourly air temperature, and daily air temperature...... 28 Figure S3. Lake temperature recorded during six GLOFs...... 28 Figure S4. Plot of daily inflow rate into LC2...... 29 Figure S5. Plot of residuals from the water temperature versus peak discharge linear regression model...... 29 Figure S6. Multiple linear regression model using predictor variables lake temperature, volume drained and inflow rate...... 30 Figure S7. Global compilation of peak discharge and volume...... 30

Chapter 3 Figure 1. Map of the region surrounding the Colonia Valley...... 36 Figure 2. DEM of Difference (DoD) maps ...... 45 Figure 3. Persistence of channels along the Rio Colonia...... 49 Figure S1. Hydrographs of GLOFs measured along the Rio Baker...... 52 Figure S2. Hydrographs of GLOFs from the Rio Baker en Colonia gauge...... 53 Figure S3. The six largest meteorological floods for the period of record (2001–2016) ...... 54 Figure S4. GLOF hydrographs for the outlet of the source lake, LC2...... 55 Figure S5. A collection of images showing cutbank erosion on the Rio Cachet ...... 56 Figure S6. A collection of images showing incision through a tributary delta ...... 57 Figure S7. A collection of images showing erosion along the Rio Cachet ...... 58 Figure S8. Field photos from January 2016...... 59 Figure S9. Landsat image showing changes in lake-full extent of LC2...... 60 Figure S10. Map and plots presenting the measurements of grain size from LC2...... 61 Figure S11. Field photos Rio Cachet from January 2016...... 62 Figure S12. Histogram and plot showing the temporal distribution of Landsat images...... 63 1

Chapter 1: Introduction

What is a glacial lake outburst flood?

Glacial lake outburst floods (GLOFs) are the catastrophic drainage of an ice-

dammed or moraine-dammed lake (Tweed and Russell, 1999; Carrivick and Tweed,

2016). Failure of moraine-dammed lakes account for 30% of observed GLOFs globally

(Carrivick and Tweed, 2016). The most common drainage mechanism is overtopping,

which is followed by progressive incision and breeching of the dam (Iribarren Anacona et

al., 2015). Overtopping of the moraine dam can be triggered by a number of different processes, but two of the most common are: an influx of water from heavy precipitation events or waves generated by ice avalanches or rockfalls (Clague and Evans, 2000). The advance of glaciers during the Little Ice Age, and subsequent retreat has formed numerous moraine-dammed lakes globally, which are now susceptible to catastrophic

drainage (Clague and Evans, 1994; Richardson and Reynolds, 2000; McKillop and

Clague, 2007; Iribarren Anacona et al., 2015).

GLOFs resulting from the failure of an ice-dammed lake are often referred to as jökulhlaups, which is an Icelandic term derived from the words jökul (meaning glacier) and hlaup (meaning sprint or burst) (Roberts, 2005). Ice-dammed lakes are found in

three distinct glacial environments: supraglacial, subglacial, and ice-marginal. Subglacial

and ice-marginal lakes are the most common and generally store a greater volume of

water (Tweed and Russell, 1999). Triggering mechanisms for the drainage of ice- dammed lakes are difficult to assess, but the most widely invoked mechanism is ice-dam

flotation (Tweed and Russell, 1999). Thorarinsson (1939) described the process of ice

dam flotation in detail, showing that failure occurs when the hydrostatic pressure of the 2 ice-dammed lake exceeds the overburden pressure of the ice dam. As glacial ice generally has a density of 900 kg/m3 compared to freshwater’s density of 1,000 kg/m3, drainage is predicted to occur when the lake level reaches 90% of the height of the ice dam (Tweed and Russell, 1999). Alternative triggering mechanisms such as syphoning or ‘tapping’ of the lake by the glacier’s internal drainage system are plausible but more difficult to test.

When ice-dammed lakes drain, water is typically routed through a subglacial tunnel towards the glacier terminus, although other forms of drainage have been observed such as overtopping of the glacier or flow along the glacier margins (Tweed and Russell,

1999). GLOFs that drain through a subglacial tunnel produce a very distinct discharge hydrograph compared to meteorologically induced floods (Nye, 1976; Spring and Hutter,

1981; Clarke, 1982; Tweed and Russell, 1999; Clarke, 2003). A GLOF hydrograph is characterized by discharge that increases exponentially, representative of the progressive enlargement of the drainage tunnel. Upon reaching the peak, discharge abruptly crashes attributable to a decrease in water supply and the collapse of the drainage tunnel due to the overburden cryostatic pressure (Nye, 1976; Spring and Hutter, 1981; Clarke, 1982;

Tweed and Russell, 1999; Clarke, 2003). GLOFs can last from days to weeks depending on the geometry of the system and other environmental variables such as lake volume and lake temperature, where larger volumes and colder temperatures can prolong an event

(Tweed and Russell, 1999; Clarke, 2003). Once a glacial system has entered a GLOF cycle or the repeated filling and draining of an ice-dammed lake, outburst floods are likely to continue until a stable drainage pathway is established usually as the result of glacial retreat (Tweed and Russell, 1999). 3

Examples of Paleo-GLOFs

During the last deglaciation, GLOFs produced some of the largest freshwater

floods on Earth (>106 m3/s), as a result of the drainage of enormous proglacial lakes both

fed and dammed by retreating continental scale ice sheets (Baker and Bunker, 1985;

O’Connor and Baker, 1992). Ice-dammed glacial Lake Missoula, impounded up to 2500 km3 of water, and experienced several drainage events between 13—17 ka with peak

discharges up to 17 x 106 m3/s that incised channel networks on a continental scale

(Baker and Bunker, 1985; O’Connor and Baker, 1992). Lake Agassiz was another

proglacial lake dammed by the Laurentide Ice Sheet, with a staggering maximum volume

of ~150,000 km3 (Clarke et al., 2004; Teller et al., 2002). It has been proposed that

several GLOFs partially draining this massive lake into the North Atlantic altered ocean circulation patterns and prompted major Northern Hemisphere climatic changes including the Younger Dryas and the 8.2 ka cold event (Clarke et al., 2004; Teller et al., 2002).

Paleofloods have also been documented in Patagonia, Chile where there is geomorphic evidence of the punctuated drainage of an ice-dammed lake on the eastern side of the

Northern Patagonia Icefield (Turner et al., 2005; Bell, 2008). These pulses of meltwater had volumes up to 2,000 km3 and similar to the North American examples, are thought to

have impacted the regional climate of southern South America and Antarctica (Glasser et

al., 2016).

Where do GLOFs occur and why should we care?

Modern GLOFs occur in glaciated regions across the globe, and while they do not have the volumes and peak discharges of some of the largest paleo-floods, they still have 4

significant impacts on landscapes, infrastructure, and human populations (Tweed and

Russell, 1999). GLOFs initiate from proglacial and ice-marginal lakes, which are

ubiquitous features of glaciated regions. Under the current trend of global deglaciation,

the number and volume of glacial lakes is increasing (Chen et al., 2007; Loriaux and

Casassa, 2013; Iribarren Anacona et al., 2015). Congruently, the number of observed

GLOFs has exponentially increased since early reports in the 16th and 17th centuries,

partly attributable to better detecting techniques, but also, the result of deglaciation

following the Little Ice Age (Iribarren Anacona et al., 2015; Carrivick and Tweed, 2016).

Worldwide GLOFs have been directly responsible for at least 10,000 deaths and have

caused considerable damage to farmlands, homes, roads, bridges, and other infrastructure

(Carrivick and Tweed, 2016). The largest modern GLOFs have peak discharges of up to

~ 50 x 104 m3/s (Magilligan et al., 2002). While this is about an order of magnitude

smaller than meteorological floods from the largest global rivers, GLOFs are generally

triggered in the headwaters of watersheds, which are accustomed to much smaller flows

and hence these floods result in a larger relative increase in discharge than the largest

meteorological floods (Cenderelli and Wohl, 2001; Magilligan et al., 2002).

Consequently, GLOFs can have peak discharges 60 times greater than normal

meteorological floods, which can significantly impact the geomorphology along these

upper reaches (Cenderelli and Wohl, 2003). Since the mid-1990s there has been an apparent decline in the number of recorded GLOFs, which is conspicuous as the number and size of glacial lakes has increased globally and as remote observations have greatly increased our capability to monitor inaccessible glacier regions (Carrivick and Tweed,

2016). Despite suggestions of recent declines in GLOF frequency, outburst floods still 5

pose a significant hazard, particularly in an evolving climate system and in glaciated

regions that have seen an increase in human activity.

Chapter Summaries

Chapter 1 of this thesis evaluates how environmental variables, specifically lake temperature, inflow rate, and volume, control peak discharge of GLOFs using one of the most comprehensive datasets from an ice-dammed lake, Lago Cachet Dos (LC2),

Patagonia, Chile. Additionally, I address how these non-stationary environmental

variables may impact future GLOF discharge from LC2 under a changing climate.

Chapter 2 of this thesis quantifies how episodic GLOFs that began in 2008 have

changed the hydrologic regime, and then documents the geomorphic response of the

fluvial system from the source lake to the end of the braid plain on the Cachet-Colonia-

Baker system on the eastern edge of the Northern Patagonia Icefield (NPI). By quantifying GLOF water and sediment fluxes, I provide insight into the potential changes that similar fluvial systems could experience after the onset of large floods.

6

Chapter 2: Environmental controls on the variability of peak discharge of glacial lake outburst floods: Lago Cachet Dos, Chile

J. Jacquet1, S. W. McCoy1, D. McGrath 2,3, D. A. Nimick4, J. Okuinghttons5, , and J. Leidich6

1Department of Geological Sciences and Engineering, Global Water Center, University of Nevada, Reno, Nevada, USA, 2Geosciences Department, Colorado State University, Fort Collins, Colorado, USA, 3U.S. Geological Survey, Anchorage, Alaska, USA, 4U.S. Geological Survey, Helena, Montana, USA, 5Ministry of Public Works. Chile, 6Patagonia Adventure Expeditions, Cochrane, XI Region, Chile.

Will be submitted to Geophysical Research Letters – Cryosphere

7

Abstract

The sudden release of water from an ice-dammed lake, referred to as a glacial

lake outburst flood (GLOF), poses a substantial hazard to downstream environments. The

degree to which peak discharge of a GLOF depends on environmental variables that

change with climate remains unclear, which in turn makes predictions of the magnitude

of such events uncertain in areas with rapidly changing climate. We combine in situ

measurements of environmental variables during GLOFs (total volume drained, lake

temperature, and inflow rate) with hourly discharge measurements from a glacier- dammed lake, Lago Cachet Dos (LC2), to evaluate environmental conditions that influence the peak discharge of observed GLOFs. Since April 2008, 20 GLOFs have initiated out of LC2, located on the eastern edge of the Northern Patagonia Icefield, Chile and flooded areas along the Rio Colonia- Rio Baker system. GLOF frequency has varied from 1–3 events annually and calculated peak discharge exiting LC2 have ranged widely

from 2,000 to >15,000 m3/s. We show that, consistent with physics-based theory, increasing total lake volume drained, lake temperature, and the rate of meltwater inflow into the glacially dammed lake all increase peak discharge of observed GLOFs.

Consequently, evolving climatic conditions of a region can greatly influence future

GLOF hazards as historic observations of peak discharge might be poor predictors of future flood magnitude. Our results suggest that more accurate predictions of GLOF magnitude from ice dammed lakes can be made by incorporating additional measurements of environmental conditions. 8

1 Introduction

Glacier mass loss is a significant contributor to global sea level rise and modifies

the timing and volume of runoff delivered to the downstream environment (Jacob et al.,

2012; Gardner et al., 2013). This reduction in ice mass has also contributed to increasing

the number and volume of periglacial lakes (Chen et al., 2007; Loriaux and Casassa,

2013; Iribarren Anacona et al., 2015). The catastrophic drainage of glacial lakes due to dam failure produces glacial lake outburst floods (GLOFs) or jökulhlaups (Tweed and

Russell, 1999; Carrivick and Tweed, 2013). Of all recorded GLOFs, 70% have initiated from ice-dammed lakes as opposed to moraine-dammed lakes (Carrivick and Tweed,

2016). GLOFs present a significant hazard to downstream human populations and infrastructure in glaciated and periglacial regions (Shaun D Richardson and Reynolds,

2000; Huggel et al., 2004; Kargel et al., 2012; Carrivick and Tweed, 2016) and South

America has been identified as the continent most at risk (Carrivick and Tweed, 2016).

Understanding the time evolution of an outburst flood, and ultimately predicting peak discharge is crucial to mitigating GLOF impacts.

The Clague-Mathews relation is one of the most widely used equations to predict peak discharge of GLOFs through a simple power-law relationship between peak discharge and volume of the ice-dammed lake,

= (1) 𝑏𝑏 𝑄𝑄𝑚𝑚𝑚𝑚𝑚𝑚 𝐾𝐾 ∙ 𝑉𝑉𝑚𝑚𝑚𝑚𝑚𝑚 where K=75 and b=0.67 (Clague and Mathews, 1973). The Clague-Mathews relation

describes the general trend of increasing peak discharge with increasing lake volume, but

deviations from this relationship, particularly from regions with multiple recorded events, 9 are striking and call into question the general predictive ability of such simple empirical equations that solely rely on total lake volume (Ng and Björnsson, 2003).

Nye (1976) was the first to develop a physics-based theory describing the time evolution of the flow of water through an ice-walled in a glacier. In simple terms, Nye’s theory describes the process of englacial conduit evolution as a competition between thermally induced growth of conduit cross-sectional area and viscous flow of ice causing conduit collapse. Subsequent refinement of the model by Spring and Hutter (1981) and

Clarke (1982, 2003) reduced the number of simplifying assumptions and highlighted the importance of environmental variables, particularly lake temperature, in controlling the discharge hydrograph. Validating these theoretical predictions concerning the importance of environmental variables has been difficult due to incomplete observations from ice dammed lakes (Clarke, 1982; Clarke and Waldron, 1984; Sturm and Benson, 1985;

Desloges et al., 1989; Björnsson, 1992; Clarke, 2003). In this paper we test how environmental variables (lake temperature, inflow rate, and volume) control peak discharge of GLOFs using one of the most comprehensive datasets from an ice-dammed lake, Lago Cachet Dos (LC2), Patagonia, Chile. Additionally, we address how these non- stationary environmental variables may impact future GLOF discharge from LC2 under a changing climate.

2 Study Area: Lago Cachet Dos, Patagonia, Chile

LC2 is an ice-marginal lake on the eastern margin of the Northern Patagonia

Icefield (NPI) that is dammed, at its southern boundary, by the Colonia Glacier. Since

~1800, LC2 drained via bedrock spillways, the first at an elevation of 460 m (1850– 10

1960), and the second at an elevation of 418 m (1960–2008) (Nimick et al., 2016).

Beginning in April 2008, LC2 entered a GLOF cycle, where 1 – 3 events occur annually.

Drainage occurs via a subglacial tunnel in the Colonia Glacier, with flood water eventually being routed into the Rio Baker, Chile’s largest river by volume (Figure 1)

(Friesen et al., 2015a). Between April 2008 and November 2016, there have been a total of 20 GLOFs. In this paper we only evaluate 19 of the 20 GLOFs, as the October 2010

GLOF was an outlier as it exhibited an unusually long drainage time and small peak

discharge. 11

Figure 1. Map of the region surrounding the Colonia Valley. (a) Landsat 8 true-color image from January 18, 2014 showing the GLOF source lake, Lago Cachet Dos (LC2), flood path along the Colonia Valley, and Rio Baker with gauge locations. Inset: Map of South America with extent of satellite image shown by red box. Letters A and B denote locations of stream gauges on the Rio Baker including the Rio Baker en Colonia, and the Rio Baker bajo Nadis, respectfully. (b) Profile through LC2 and the Colonia Glacier following the predicted flood path. (c) Hypsometry of LC2 that relates lake elevation to area.

GLOFs from LC2 have coincided with an acceleration in retreat and thinning of

the Colonia Glacier, the NPI’s largest glacier on the eastern side (Willis et al., 2012). 12

Outlet glaciers of the NPI have been retreating since the end of the Little Ice Age (~1870

A.D.) (Rignot et al., 2003; Rivera et al., 2007; Barcaza et al., 2009; Glasser et al., 2011;

Davies and Glasser, 2012; Willis et al., 2012; Loriaux and Casassa, 2013). Between the

Little Ice Age maximum and 1996 longitudinal retreat of the Colonia Glacier terminus

was ~1.5 km (Winchester and Harrison, 2000) and since 1996 up until 2016 the glacier

retreated an additional 1.5 km (Figure 1). The Colonia Glacier thinned in the ablation

zone at an average rate of −1±1 m/yr between 1975 and 2001 (Rivera et al., 2007) and

subsequently accelerated to −2±1 m/yr between 2001 and 2011 (Willis et al., 2012).

The physical geometry of LC2 and the Colonia Glacier is well constrained.

Jacquet et al. (In review) generated 1.5 m resolution DEMs of the entire LC2 lake basin

shortly after LC2 drainage events in October 2013, February 2014, and December 2015

and calculated hypsometric functions for LC2 to relate elevation to lake area (Figure 1b

and Figure 1c). Additionally, an airborne geophysical survey of the Colonia Glacier using ground penetrating radar revealed the bedrock topography below the ice (Blindow

et al., 2012).

3 Theoretical Background for Drainage of Ice-Dammed Lakes

The theoretical relationship describing discharge from an ice-dammed lake was

first presented in a landmark paper by Nye (1976). Nye’s model used differential

equations for non-steady water flow through a single circular conduit to describe the

exponential rise in maximum discharge that was observed during GLOF events. The

theory states that discharge is a function of the runaway increase in flow capacity brought

about by melt-widening of the englacial conduit due to viscous heat generated by 13

turbulent fluid flow. Flow stops rapidly when the conduit pressure decreases and plastic

deformation of ice closes the conduit. Spring and Hutter (1981) expanded on the Nye theory by removing many of the simplifying assumptions and developed a complete model that describes the temporal evolution of water velocity, discharge, temperature, and cross-sectional area over the full length of the conduit. Unfortunately, the numerical solutions they developed required long computation times, so simplifying assumptions were reintroduced in order to obtain results. Clarke (1982) improved the Nye theory to include the effects of reservoir water temperature and reservoir geometry, but still

utilized the idealization of a “seal” point located sufficiently close to the reservoir that

served as a single point where flow was restricted thus controlling discharge for the entire

outburst flood. Fowler and Ng (1996) modified the original Nye theory by introducing a

sediment laden conduit bottom and found that sediment transport could play an important

role in the evolution of the conduit size and shape. Clarke (2003) slightly modified the

Spring-Hutter (1981) formulation, which consisted of four conservation equations for

water mass, ice mass, linear momentum, and energy.

In Clarke’s model, the time evolution of discharge is described in terms of water

pressure, cross-section area of the conduit, water velocity, and water temperature. As the

reservoir begins to drain, the initial discharge is controlled by the gradient in hydraulic

head along the conduit. Water flowing through the conduit causes melting of the walls

due to a combination of viscous heat dissipation set by water velocity and thermal heat

transfer set by the temperature of the source lake. If the rate of ice creep closure is

insufficient to balance the melting rate of the conduit walls, the conduit cross-sectional area expands and discharge increases. This positive feedback mechanism generally 14

results in the catastrophic drainage of ice-dammed lakes and the characteristic

exponentially rising discharge curve.

Clarke’s model establishes three environmental variables as key boundary conditions in predicting peak discharge from an ice-dammed lake including lake temperature, lake volume, and inflow rate. Lake temperature sets the boundary condition for water temperature at the inlet for the entire period of drainage and can be thought of

as a metric of total thermal energy stored in the lake. Lake volume and inflow set the rate

of decrease in lake surface elevation through time, which is used in calculating water

pressure (Clarke, 2003).

4 Data and Methods

4.1 Calculating GLOF Discharge from Glacially Dammed LC2

The Chilean Dirección General de Aguas (DGA) initiated hourly stage

observations at LC2 in May 2009. Initial measurements captured the upper ~20 m (45%

of total lake volume) of the lake under full conditions. A second sensor added in February

2012 measured the upper ~40 m of LC2 (68% of total lake volume). Neither time-series

is complete because of damage suffered during GLOFs and the inaccessibility of the site.

The LC2 stage and hypsometric function were combined to calculate discharge Q using

the following equation:

(6) ( ) = ( ) 𝑑𝑑ℎ𝑤𝑤 𝑄𝑄 𝑡𝑡 −𝐴𝐴 ℎ𝑤𝑤 where A(hw) is the hypsometric function from the𝑑𝑑𝑑𝑑 DEM closest in time to the GLOF

event and dhw/dt is the change in stage per unit time. We measured the discharge exiting

the lake during 9 of the possible 19 GLOF events using this method (Figure 2a). We 15 observed approximately exponentially rising hydrographs and did not measure a decrease in discharge for all but one GLOF, suggesting that peak discharge was not measured due to the limited vertical extent of the stage observations.

To estimate peak discharge of the GLOFs (which occurred below observed stage levels), we modeled each individual GLOF event using an exponential function fit to the observed discharge data (Figure 2a). By setting the integral of the analytical solution equal to the volume drained for the GLOF event, we solved for the duration of the GLOF in hours (t).

= (3) 𝑡𝑡 �𝑡𝑡∗ 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 We assumed that the discharge𝑉𝑉 curves crash𝑆𝑆 ∙ 𝑒𝑒to zero immediately after reaching peak discharge (i.e. there is no falling limb to the discharge curve).

For the remaining 10 GLOFs that were not directly measured from LC2, we estimated peak discharge at LC2 by using a linear correlation between discharge measured at LC2 and discharge measured at downstream gauging locations on the Rio

Baker (Figure 2b). The DGA operates two stream gauges (accessed at http://dgasatel.mop.cl/) along the Rio Baker downstream of the Rio Colonia-Baker confluence. To quantify the peak GLOF discharge measured at the Rio Baker gauges, we subtracted the Rio Baker base flow from the hydrograph (Figure S1). Because GLOFs measured on the Baker stream gauges rise to a maximum in approximately 15 hours

(Jacquet et al., In Review), we estimated base flow on the Rio Baker (i.e., the discharge not associated with a GLOF event) as the discharge measured 24 hours before the peak discharge was attained during a GLOF event. We then developed a linear regression equation for both downstream gauges to relate peak discharges from LC2 to those 16

measured along the Rio Baker (Figure 2b). The gauge at Baker en Colonia was damaged

during the highest discharges, as a result we use the regression equation for the Baker

bajo de Nadis to estimate the peak discharge for the 10 GLOFs that were not recorded at

the LC2 stage gauge.

4.2 Estimating Total Volume of Water Drained from LC2 during GLOFs

We estimated the total volume of each GLOF event using stage and hypsometry data from LC2. Because the stage gauge only recorded the upper 20 to 40 m of the lake stage we could only calculate minimum and maximum values for total volume drained.

Minimum drainage volumes were calculated by assuming the GLOF stopped once lake level dropped below the bottom of the stage gauge and maximum volumes were calculated by assuming complete lake drainage (Table S1). To further constrain GLOF volumes, we integrated the hydrographs along the Rio Baker during the GLOF flood wave after removing Rio Baker base flow. It was assumed that the lake drained completely if the flood volume measured along one of the Rio Baker gauges was within

5% of the maximum volume capable of draining from LC2. Otherwise a partial drainage event was assumed and the volume measured at the Rio Baker gauges was established as the flood volume. If LC2 lacked stage observations for a particular GLOF event, the Rio

Baker gauges were used as the sole source for determining GLOF volume. Once volume was determined for each GLOF event, we developed a linear regression model to determine the correlation between peak discharge and volume drained for LC2 (Figure

3a). 17

4.3 Measurements of Water and Air Temperature

In addition to the hourly stage measurements made by the DGA, water temperature was recorded at the location of the pressure transducer used to measure lake stage. Recorded lake temperature fluctuated minimally during a filling cycle, but following a GLOF the water temperature sensor was exposed to air, and fluctuated widely while recording the ambient air temperature (Figure S2). This provides an additional method to confirm the timing of a GLOF event. For the analysis conducted here, water temperature during a GLOF was recorded for six of the LC2 drainage events

(Figure S3).

Hourly air temperature measurements were made from a DGA operated weather station located at the southwestern end of LC2 approximately 50 m above the maximum lake level. We calculated daily mean temperature from the hourly temperature measurements to avoid a diurnal temperature bias in future analyses (Figure S2). Using air temperature and lake temperature, we developed a linear regression model to determine the correlation between these environmental variables and peak discharge

(Figure 3b).

4.4 Rate of inflow

We calculated the discharge into LC2 using the same method used to calculate discharge out of LC2 during a GLOF, but prior to any lake level lowering due to drainage. Hourly inflow tended to fluctuate on the order of tens of cubic meters per second, possibly due to wave action on the lake, therefore daily-averaged inflow is reported here (Figure S4). We developed a linear regression model to determine the correlation between peak discharge and rate of inflow (Figure 3c). 18

5 Results

5.1 Peak Discharge and Volume of LC2 GLOFs

Observed peak discharge from LC2 for the nine recorded GLOFs ranged from

~2700 m3/s to 11,300 m3/s. These are minimum values because the stage gauge only

captured the upper 20−40 m of the total lake depth (Figure 2a and Table S1). The

modeled peak discharges, constrained by observed hydrograph shape and the total GLOF

volume, ranged between 2700 m3/s and 16,400 m3/s (Figure 2a and Table S1). The

equation resulting from the linear regression of peak discharge from LC2 to peak

discharge observed on the Rio Baker was , = 10.25( , ) 1.37 10 −4 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝐿𝐿𝐿𝐿2 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 (R2=0.75, p=0.026) (Figure 2b). The total volume𝑄𝑄 drained during𝑄𝑄 GLOFs ranged− from𝑥𝑥 90

million m3 to 215 million m3 or 30%–100% of total lake volume and averaged 160 million m3 over the 19 events (Figure 3b and Table S1). Variability in the volume drained can be explained by differences in maximum lake level and complete or partial

drainage of the lake. 19

Figure 2. (a) GLOF discharge hydrographs for the outlet of the source lake, LC2. Squares represent the observed discharge calculated using stage observation and hypsometry. Solid line represents the modeled discharge for the sensor that sampled the upper ~40 m of LC2, or 68% of the total lake volume. Dashed line represents the modeled discharge calculated using the sensor that sampled the upper ~20 m of LC2, or 45% of the total lake volume. Discharge is plotted for the recorded duration of the GLOF defined as the period following the initiation of stage lowering. (b) Correlation plots for peak discharge from LC2 and peak discharge from both Rio Baker gauges. Baker- Colonia gauge malfunctioned during the largest GLOF on February 1, 2014.

20

5.2 Correlation of Environmental Variables to Peak Discharge

We found that key environmental variables of total lake volume drained, lake

water temperature, and inflow rate into the lake, shown to control GLOF discharge in the

modified Spring-Hutter theory for drainage of ice-dammed lakes were positively

correlated with peak discharge of GLOFs from LC2. Linear regression of total volume

drained and peak discharge resulted in an R2 of 0.61 and p-value of 0.001 (Figure 3a),

while the best fit power law in the form of Clague and Mathews relation resulted in a

K=1.04x10-15 and a b=2.29 with R2 of 0.67. Lake water temperature averaged over a

GLOF event explained 62% of the variance observed in peak discharge with a p-value of

0.062, while air temperature only explained 21% with a p-value of 0.251 (Figure 3b).

Linear regression of inflow rate into LC2 and peak discharge showed a clear increasing trend, but two large outliers resulted in an R2 of 0.30 and p-value of 0.124 (Figure 3c). 21

22

Figure 3. Correlation plot of peak discharge versus volume drained (a), lake and air temperature (b), and inflow rate (c). Inflow rate shows a tight correlation to peak discharge, but two outliers reduce the calculated r-squared value.

From the linear regression models, we concluded that lake temperature was the most important environmental variable in predicting peak discharge. To help explain some of the variability observed in the lake temperature linear regression model, we plotted the residuals against volume and inflow rate (Figure S5). We show that as lake volume increased the observed residuals increased, and as inflow rate increased the observed residuals increased. Both lake volume and inflow rate affect variability observed in the lake temperature linear regression model, and, consequently, all three variables are important in predicting peak discharge of GLOFs from LC2. As such, we performed a multiple linear regression model using all three environmental variables, which resulted in an R2 of 0.86 (Figure S6).

6 Discussion

6.1 Accuracy of Empirical Equations Used to Predict Peak Discharge

The addition of 19 well-documented GLOFS to the global dataset of Clague and

Mathews (1973) and Walder and Costa (1996) presents an excellent opportunity to test the accuracy of commonly used empirical relationships for predicting peak discharge

(Figure S7). Both the Clague-Mathews relation and the updated equation from Walder and Costa resulted in a power law with a power (b) of approximately 2/3 (Clague and

Mathews, 1973; Walder and Costa, 1996), but as others have noted this relationship performs poorly when predicting peak discharge from the volume drained from a single ice-dammed lake experiencing multiple GLOFs (Ng and Björnsson, 2003). The range of 23

volume drained for LC2 GLOFs varies by nearly a factor of 2, but peak discharge varies

by almost an order of magnitude (Figure S7), which results in a best fit b value of 2.29.

This b value is significantly larger than that of Clague and Mathews and larger than the b

value from the Grimsvotn jokulhlaups (b=1.84) (Ng and Björnsson, 2003), which is a

comparable data set in terms of number of recorded GLOFs from a single lake. As a

result of the much stronger dependence of peak discharge on volume at LC2, using the

standard Clague-Mathews relation would underestimate the largest LC2 GLOF by 13,675

3 m /s or 83%.

For global compilations, both the location and methods used to measure peak

discharge can vary significantly, likely introducing a large uncertainty to these empirical

relationships. The LC2 dataset is unique in that we were able to obtain independent peak

discharge measurements at multiple locations along the flood path; at the source lake,

LC2 and on the Rio Baker (~40 km downstream). Comparing measurements at both

locations, peak discharge downstream is dampened by up to a factor of 6. By

standardizing measurement locations and methods downstream of the source lake, the

accuracy of empirical relationships may improve. However, categorizing the 79 sub- glacially draining GLOFs from the Walder and Costa (1996) dataset by measurement

location, does not appear to decrease the scatter around the general trend between peak

discharge versus volume drained even among measurements from the source lakes

(Figure S7). Comparing peak discharge to volume drained measurements from the well

documented LC2 GLOFs only results in an R2 of 0.67. Hence, the necessity to understand the remaining environmental factors that control peak discharge for the drainage of an ice-dammed lake: lake temperature and inflow rate. 24

6.2 Importance of Lake Temperature in Predicting Peak Discharge

Lake temperature proved to be the best environmental variable for predicting peak discharge from LC2 with an R2 of 0.62. Clarke (1982) went through the process to non- dimensionalize the relationship of peak discharge to lake temperature in his 1982 discharge model and revealed the following equation:

5 = 4 (8) 3 �5 𝛽𝛽 𝑄𝑄 ⋆𝑀𝑀𝑀𝑀𝑀𝑀 � � where β is a lake temperature parameter that characterizes the relative importance of lake temperature in controlling the rate of tunnel enlargement. The plot of lake temperature and peak discharge from LC2 is consistent with Clarke’s non-dimensionalization effort, as it generally conforms to the approximate linear relationship. Lake temperature has obvious ties to the climate, but without a complete lake model capable of simulating the temporal evolution of the thermal structure, it’s difficult to predict how this will change in the future. Under regional atmospheric warming (Rosenblüth et al., 1997), it seems reasonable to assume that lake temperature of LC2 will increase, but variability in inflow rate, precipitation, seasonal timing of GLOFs, etc. could all affect lake temperature during a GLOF.

6.3 Significance of Inflow Rate and Implications under a Changing Climate

There was limited scatter between peak discharge and inflow rate, but with two large outliers the R2 was only 0.30. Inflows into the lake slow the rate at which the lake level and pressure drop during a GLOF. This has the effect of extending the duration of the GLOF, but also increasing peak discharge by supplementing flow through the glacier and preventing tunnel collapse. Our plot of inflow versus peak discharge confirms this 25

positive correlation consistent with the physics-based theory. Inflow into LC2 is directly

influenced by the climatic conditions of the NPI. Reconstruction of the Rio Baker

summer-fall streamflow over the period of 1765 to 2004 using tree rings, showed that the

most significant temporal trend during the last 239 years was a decline in discharge since

the 1980s (Lara et al., 2015). This trend corresponds with an approximately 30%

decrease in precipitation over the period of 1900-1999 associated with deviation of the

Southern Annual Mode and southward shift of the storm track (Lara et al., 2015).

Decreases in observed streamflow on the Rio Baker have occurred despite a regional

atmospheric temperature increase by between 0.4 and 1.4 °C and an increase in the loss of glacier mass from the NPI during the twentieth century (Glasser et al., 2011). While this gives us an idea of the trend in regional runoff, predicting hourly or even daily inflow into LC2 based on climatic trends is unrealistic. The only reasonable prediction resulting from a decreased inflow rate is that the annual frequency of floods may decrease given longer refilling times.

7 Conclusions

We have shown, using an extensive dataset of in situ observations, the importance

of environmental variables on controlling peak discharge during GLOFs. Each of these

variables (volume, lake temperature, and inflow rate) is non-stationary considering future

climate scenarios. Continued warming is likely to increase lake temperature which would

increase peak discharge of future GLOFs. Continued warming will also contribute to

continued mass losses from the NPI and thinning of the Colonia Glacier, which could lower the height of the ice dam and ultimately decrease the volume of water that can 26 possibly be stored in LC2. However, erosion of sediments stored in the LC2 basin, which have resulted in an increase in lake area and volume, may counter this trend. Inflows into

LC2 are likely to continue decreasing coinciding with a decreasing precipitation trend and despite an increase of runoff from glacial mass loss; still, predicting the instantaneous inflow rate on the day of a GLOF is impossible. An anomalously high inflow rate from an intense precipitation event coinciding with a GLOF could result in an extreme peak discharge. In the short-term, if lake temperature increases faster than the lake volume decreases, we can expect peak discharges to increase from LC2. Obviously, pinpointing the location of the Colonia system in the complex relationship between lake volume, lake temperature, and inflow is difficult, but we have at a minimum confirmed what variables to monitor in other glaciated systems entering a GLOF cycle.

Acknowledgments

Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. 27

Supporting Information

Figure S1. Hydrographs of GLOFs from the Rio Baker en Colonia gauge. (a) Hydrograph from each recorded GLOF with baseflow removed to allow estimation of GLOF peak discharge upon entering the Rio Baker approximately 40 km downstream from the source lake. (b) Hydrograph of all GLOFs with the GLOF discharge normalized by the peak discharge as a way to visualize the characteristic shape of GLOF hydrographs along the Rio Baker.

28

Figure S2. Plot of lake temperature, hourly air temperature, and daily air temperature. Note the large fluctuations in lake temperature immediately following a GLOF, which indicates the sensors exposure to the ambient air.

Figure S3. Lake temperature recorded during six GLOFs. Four of the six records of lake temperature show temperature increasing right at the end of the GLOF, possibly representing warm surface water moving by the sensor during drawdown. 29

Figure S4. Plot of daily inflow rate into LC2. Black dashed line represents the average inflow rate over the period of record (~9 m3/s).

Figure S5. Plot of residuals from the water temperature versus peak discharge linear regression model. Volume and inflow rate can both help to explain variability in water temperature residuals. 30

Figure S6. Multiple linear regression model using predictor variables lake temperature (units of °C), volume drained (units of m3) and inflow rate (units of m3/s).

Figure S7. Global compilation of peak discharge and volume compiled by Walder and Costa (1996) with LC2 GLOFs plotted as black squares. Note the steepness of the LC2 dataset (slope = 2.29), compared to the global dataset (slope ~ 0.67).

31

Table S1. GLOF peak discharges and volumes recorded at three stations along the GLOF flow path. We calculated peak discharge from LC2 using the observed stage and the hypsometric function for the lake. The minimum flood volume from LC2 represents the volume of water that exited LC2 as recorded by the stage gauge. Maximum flood volume represents the volume of water if the lake completely drained. We estimated the flood volume at downstream gauges by integrating the hydrographs with base flow removed.

32

Chapter 3: Hydrologic and geomorphic changes resulting from episodic glacial lake outburst floods: Rio Colonia, Patagonia, Chile

J. Jacquet1, S. W. McCoy1, D. McGrath 2,3, D. A. Nimick4, M. Fahey5, J. Okuinghttons6, B. A. Friesen7, and J. Leidich8

1Department of Geological Sciences and Engineering, Global Water Center, University of Nevada, Reno, Nevada, USA, 2Geosciences Department, Colorado State University, Fort Collins, Colorado, USA, 3U.S. Geological Survey, Anchorage, Alaska, USA, 4U.S. Geological Survey, Helena, Montana, USA, 5U.S. Geological Survey, Lakewood, Colorado, USA, 6Ministry of Public Works. Chile, 7Unaffiliated, 8Patagonia Adventure Expeditions, Cochrane, XI Region, Chile.

Accepted pending minor revisions at Geophysical Research Letters – Earth Surface

33

Abstract

Predicting changes in river flow and sediment transport is critical for hydropower,

agriculture, and hazard mitigation projects, particularly in periglacial areas where

temperature increases and ice-mass changes can shift river discharges beyond historical variability. Here, we quantify the hydrologic and geomorphic response to 20 episodic glacial lake outburst floods (GLOFs) that began in April 2008 using multi-temporal satellite imagery and field observations. Peak discharge exiting the source lake exceeded

10,000 m3/s, but become progressively muted downstream. At ~40 km downstream, peak

discharges were generally < 2000 m3/s, but still > 15 times the median discharge. The

GLOFs resulted in > 40 m of downcutting and erosion of ~25 x106 m3 of sediment from

the source lake basin and a non-steady channel configuration downstream. Quantifying

GLOF water and sediment fluxes in this system provides insight into potential change

that similar fluvial systems could experience after the onset of large floods.

1 Introduction

Proglacial and ice-marginal lakes are ubiquitous periglacial features. Recent

observations suggest they are increasing in number and volume (Loriaux and Casassa,

2013; Iribarren Anacona et al., 2015), coinciding with the retreat and thinning of many

glaciers worldwide (Gardner et al., 2013). The catastrophic drainage of these lakes due to

dam failure produces glacial lake outburst floods (GLOFs) or jökulhlaups (Tweed and

Russell, 1999; Carrivick and Tweed, 2016). Modern GLOF discharge rates, commonly

on the order of 102–104 m3/s, can exceed annual flood peaks by at least an order of magnitude (Cenderelli and Wohl, 2001, 2003), but during the waning stage of the Last 34

Glacial Maximum, GLOFs produced some of the largest freshwater floods on Earth (>

106 m3/s) and incised channel networks on continental scales (Baker and Bunker, 1985;

O’Connor and Baker, 1992). The sudden drainage of glacial lakes presents a significant

hazard to human populations and infrastructure, and the potential for GLOFs exists at a

global scale (Shaun D Richardson and Reynolds, 2000; Huggel et al., 2004; Kargel et al.,

2012; Carrivick and Tweed, 2016). Understanding how the onset and persistence of

GLOFs affect the hydrology and geomorphology of these systems is critical for making accurate predictions of impacts to areas currently, or projected to be, exposed to GLOF hazards.

Although a growing number of quantitative measurements document the geomorphic effects of GLOFs (Desloges and Church, 1992; Gomez et al., 2000;

Cenderelli and Wohl, 2001; Magilligan et al., 2002; Cenderelli and Wohl, 2003; Kershaw et al., 2005; Smith et al., 2006; Duller et al., 2014; Staines and Carrivick, 2015), the study of modern GLOFs has been limited by the unpredictability of such events, the difficulty of making in situ observations in harsh and dangerous environments, and the lack of adequate resolution pre-GLOF topography to assess geomorphic changes. The recent adoption of dam removal as a stream restoration practice has resulted in numerous studies evaluating the rapid sequence of fluvial responses on formerly impounded reservoir sediments (Pearson et al., 2011; Major et al., 2012; Wilcox et al., 2014; Randle et al.,

2015) and has provided an anthropogenic analogue for understanding sediment transport from the source lake basin during GLOFs. Here, we quantify how episodic GLOFs that began in 2008 have changed the hydrologic regime and document the geomorphic response of the fluvial system from the source lake to the end of the braid plain on the 35

Cachet-Colonia-Baker system on the eastern edge of the Northern Patagonia Icefield

(NPI).

2 Study Area: Cachet-Colonia-Baker Valley, Patagonia, Chile

2.1 Thinning and Retreat of the Colonia Glacier

The outlet glaciers of the NPI, of which the Colonia Glacier is the largest on the

eastern side, have generally been retreating and thinning since the end of the Little Ice

Age (LIA) (Rignot et al., 2003; Rivera et al., 2007; Barcaza et al., 2009; Glasser et al.,

2011; Davies and Glasser, 2012; Willis et al., 2012; Loriaux and Casassa, 2013).

Longitudinal retreat of the Colonia Glacier terminus was ~1.5 km between the LIA maximum and 1996 (Winchester and Harrison, 2000) with an additional 1.5 km of retreat

between 1996 and 2014 (Figure 1). The Colonia Glacier thinned at an average rate of

−1±1 m a-1 between 1975 and 2001 (Rivera et al., 2007) and subsequently accelerated to

−2±1 m a-1 between 2001 and 2011 (Willis et al., 2012).

2.2 History of GLOFs in Cachet and Colonia Valleys

Currently, GLOFs in the Colonia Valley result from drainage of Lago Cachet Dos

(LC2), an ice-marginal lake dammed at its southern boundary by the Colonia Glacier

(Figure 1). When GLOFs occur, lake water is routed through and possibly under the

Colonia Glacier, into a small proglacial lake, into Lago Colonia, down the Rio Colonia,

and finally into the Rio Baker, Chile’s most voluminous river (Figure 1) (Friesen et al.,

2015a). Between April 2008 and August 2016, there have been 20 GLOFs. 36

Figure 1. Map of the region surrounding the Colonia Valley showing the locations and hydrographs from active gauging stations. (a) Landsat 8 true-color image from January 37

18, 2014 showing the GLOF source lake, Lago Cachet Dos (LC2), flood path along the Colonia Valley, and Rio Baker with gauge locations. Inset: Map of South America with extent of satellite image shown by red box. Letters B, C, D and E denote locations of stream gauges on the Rio Baker including (b) Rio Baker en Chacabuco, (c) Rio Colonia estimated, (d) Rio Baker en Colonia, and (e) Rio Baker bajo Nadis. Gray shading on hydrograph records indicates period with GLOFs, while red stars indicate dates of GLOFs. Q* is the discharge normalized by the median discharge of record shown.

Initial investigations of the GLOFs originating from LC2 used stream gauges on

the Rio Baker and found peak discharges of ~ 2,000–2,800 m3/s (Casassa et al., 2009;

Dussaillant et al., 2010). Erosion following the onset of GLOFs increased the areal

extent of LC2 from 2.98 km2 in 1979 to 4.41 km2 in 2014 (Friesen et al., 2015b). Recent

work has revealed the Neoglacial history of the LC2 lake basin, including alternating

periods of fluvial and lacustrine systems, likely tied to the extent and thickness of the

Colonia Glacier (Figure 1) (Nimick et al., 2016). These systems resulted in a thick

package of valley fill sediment between the Colonia Glacier and Lago Cachet Uno. Here,

we refer to these predominantly fine-grained sediments, that likely accumulated in the

past ~250 years (Nimick et al., 2016), as LC2 lake basin sediments. Between the LIA maximum and 1960, LC2 drained via a bedrock channel at ~500 masl at the southeastern edge of the lake (Nimick et al., 2016). By 1960, thinning of the Colonia Glacier opened an outlet channel at 420 masl. Lake level remained stable at 420 masl until GLOFs began in April 2008.

The series of GLOFs that began in 2008 from LC2 are not the first to have occurred in the Colonia Valley (Tanaka, 1980). Around 1881, a large GLOF initiated

from Lago Arco, which at the time was dammed by the Colonia Glacier. GLOFs 38 continued from Lago Arco until a stable drainage path was established in the 1960s

(Harrison and Winchester, 2000).

3 Methods

3.1 Measuring Changes in Hydrologic Regime: Rio Colonia and Rio Baker

We documented flood hydrographs and changes in hydrologic regime due to

GLOFs using stream-gauging records from the Rio Baker. The Chilean Dirección

General de Aguas (DGA) operates several stream gauges (accessed at http://dgasatel.mop.cl/) along the Rio Baker including one upstream of the Rio Colonia-

Baker confluence and two downstream (Figure 1). We estimated the hydrograph for the ungauged Rio Colonia by differencing discharge records from the gauges upstream and downstream of the Rio Baker-Colonia confluence. We normalized each discharge record by the median discharge over the 2001 to 2016 interval to quantify relative changes in discharge after the onset of GLOFs.

We estimated base flow on the Rio Baker (i.e., the discharge not associated with a

GLOF event) as the discharge measured 24 hours before the peak discharge was attained during a GLOF event. To quantify the peak discharge due to GLOF events measured at the Rio Baker gauges, we then subtracted the Rio Baker base flow from the hydrograph

(Figures S1 and S2). We integrated the hydrographs with base flow removed to estimate the total volume of water drained from LC2 (Table S1).

3.2 Measuring Sediment Transport from Glacially Dammed LC2 Lake Basin

To quantify sediment transport in the LC2 lake basin due to GLOFs from LC2, we differenced multi-temporal digital elevation models (DEMs) to create DEMs of 39

difference (DoDs) (Figure 2 and Figures S5-S9). We acquired WorldView stereo satellite

images of the LC2 lake basin shortly after LC2 drainage events in November 2012,

October 2013, February 2014, and December 2015, which we post-processed using

SOCET SET photogrammetry software to produce 1.5 m resolution DEMs. As a pre-

2008 elevation baseline for DoDs, we used measurements from the Shuttle Radar

Topography Mission (SRTM), which collected topographic data at ~26 m resolution in

February 2000 (Farr et al., 2007). Based on Landsat images showing limited meter-scale

change to the subaerial LC2 lake basin sediments between 2000 and 2008, we attributed

the observed geomorphic change over the time interval between SRTM acquisition in

February 2000 and our first satellite stereo pair in November 2012 to GLOFs after April

2008. Further, as bathymetric data for LC2 does not exist pre-2012, our initial DoD

(Figure 2b) only includes subaerial portions of the LC2 lake basin.

We co-registered the DEMs to ensure proper horizontal and vertical alignment prior to differencing. We shifted all DEMs horizontally and vertically to align with the

October 2013 DEM based on areas of stable ground contained within each DEM, primarily ice-free bedrock landforms. We determined the optimal three-dimensional shift as the shift that produced a minimum root-mean squared error amongst the stable-ground elevation points. We used the average root-mean-squared error from the co-registration process as an estimate for the vertical error in each DEM. We then summed the errors for the two DEMs being differenced in quadrature to determine the minimum vertical change we could observe (~0.5 m). All DoD cells with differences less than ±0.5 m were treated as unchanging. In addition to performing co-registration, we adjusted DEMs to ensure their concurrency (i.e., cell resolution, grid center points, and geographic extents were all 40

the same). We performed the differencing of DEMs using the Geomorphic Change

Detection Software plugin for ArcMap (Wheaton et al., 2010).

We calculated the average rate of sediment removal from LC2 for each DoD by

dividing the net volume change by the duration over which LC2 was freely draining

during the time interval between DEM acquisitions (Figure 2e). Duration of free drainage

included the GLOF event as well as time after the event during which Rio Cachet, the

river flowing through the LC2 basin, was free-flowing and transporting sediment. We quantified the number of free-draining days by visually checking for the presence or absence of LC2 forming near the ice dam using both Landsat and commercial satellite images. We assumed drainage stopped at the midpoint in the interval between images that switched state from lake absent to lake present. From the uncertainty in the number of free-draining days and the uncertainty net volume change, we calculated the error associated with the rate of sediment removal (Figure 2e).

3.3 Estimating GLOF Discharge from Glacially Dammed LC2

The DGA initiated hourly stage observations at LC2 in May 2009. Initial

measurements captured the upper ~20 m (45% of total lake volume) of the lake under full

conditions. A second sensor added in February 2012 measured the upper ~40 m of LC2

(68% of total lake volume). Neither time-series is complete because site inaccessibility and damage suffered during GLOFs. For each DEM, we calculated a hypsometric function for LC2 to relate elevation to lake area. The LC2 stage and hypsometric function were combined to calculate discharge Q using

(1) ( ) = ( ) 𝑑𝑑ℎ𝑤𝑤 𝑄𝑄 𝑡𝑡 −𝐴𝐴 ℎ𝑤𝑤 𝑑𝑑𝑑𝑑 41

where A(hw) is the hypsometric function from the DEM closest in time to the GLOF

event and dhw/dt is the change in stage per unit time. This method determined discharge exiting the lake during GLOFs (Figure S4) as opposed to the discharge at the mouth of

Rio Colonia ~40 km downstream. We observed approximately exponentially rising hydrographs and did not measure a decrease in discharge, suggesting maximum discharge was not measured due to the limited vertical extent of the stage observations. Hence, peak discharges presented here are minimum estimates. We calculated minimum drainage volumes by assuming the GLOF stopped once lake level dropped below the bottom of the gauge and maximum volumes by assuming complete lake drainage (Table S1).

3.4 Quantifying Changing Planform Channel Morphology: Rio Colonia

We used Landsat 5 TM, 7 ETM+, and 8 imagery over the time interval 1984 to

2016 to evaluate changes in Rio Colonia planform channel morphology prior to and after the onset of episodic GLOFs in 2008 (Figure 3). To do so, we calculated the Normalized

Difference Water Index (NDWI) as,

(2) = . + 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 − 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 We applied a threshold to the NDWI for each image to produce a binary river

mask. To evaluate the planform stability before and after the onset of episodic GLOFs in

2008, we calculated a normalized channel persistence metric, defined as the ratio of the

total time for which a pixel had water divided by the length of record, for both pre- and

post-GLOFs intervals. 42

Discharge can dramatically change channel configuration in braided fluvial

systems despite relatively stable channel locations (Smith et al., 1995). For example, the

Rio Colonia at lower discharges may activate only 1–2 main channels, yet at higher

discharges this may increase to 3–4. In an attempt to avoid a discharge bias on the

ungauged Rio Colonia, we calculated persistence using a similar seasonal distribution of

Landsat images for both the pre- and post-GLOF intervals (Figure S12).

4 Results and Discussion

4.1 GLOF Characteristics and Changes in Hydrologic Regime

Stream gauges along the Rio Baker documented a dramatic shift in the hydrologic

regime following the onset of episodic GLOFs in April 2008 (Figure 1). Prior to GLOF

onset, the Rio Baker hydrograph was characterized by seasonal discharge variability with

peak discharges observed primarily during warm summer months (Figure 1a). After the

onset of GLOFs and only downstream of the Colonia-Baker confluence, the hydrograph has been dominated by large, short-duration (~24–48 hrs) discharge peaks associated with GLOFs (Figure 1).

Between April 2008 and August 2016, 20 GLOFs originated from LC2 and flooded the Colonia and Baker Valleys. During these GLOFs, discharge at the Rio

Colonia-Baker confluence was elevated above base flow for ~48 hours, with peak discharges generally in the range of 2500–3500 m3/s including Rio Baker base flow or

1500–2500 m3/s without (Table S1 and Figures S1 and S2). Integrating the hydrograph during GLOFs suggests a total volume of 120–215 million m3 of water passed through

the Baker system (full lake volume ~215 million m3), indicating both complete and 43 partial drainage of LC2 is possible (Table S1). GLOF discharges estimated for Rio

Colonia upon entering the Rio Baker ~40 km from the source lake, were generally > 15 times the median discharge of the observational period (Figure 1b). The Rio Colonia

GLOFs produced discharges on the Rio Baker 3–4 times greater than the median discharge and approximately two times greater than peak seasonal discharges (Figure 1c).

These results demonstrate that GLOFs can increase the magnitude and frequency of floods, even on very large rivers like the Rio Baker.

GLOF hydrographs measured at the Baker en Colonia gauge, ~40 km downstream from the source lake LC2, had a characteristic shape with a rapid rise to peak discharge in approximately 15 hours and much gentler fall (Figure S1 and S2), similar to many precipitation-induced floods (Nash, 1957; Rodríguez-Iturbe and Valdés, 1979). Although the GLOF hydrographs had a similar shape to typical meteorological floods when measured far from the GLOF source, the timescales for rising to and falling from the peak discharge were distinct (Figure S3). The GLOF hydrographs rose and fell more rapidly than similar meteorological flood events on the Rio Baker, suggesting that identification of GLOFs using only stream gauging data is possible.

The GLOF hydrographs calculated at the source lake LC2 differed in shape and discharge magnitude compared to those measured ~40 km downstream at the Baker en

Colonia gauge (Table S1 and Figure S4). At LC2, the initial rise in discharge was gentle and approximately exponential, which is characteristic of GLOFs initiated from expansion of ice conduits through an ice dam (Nye, 1976; Spring and Hutter, 1981;

Clarke, 1982). Calculated GLOF peak discharge originating from LC2, despite being minimum values, had a median of ~4300 m3/s and a maximum that exceeded 10,000 44

m3/s, but the extensive travel path between the source lake and the downstream gauges dampened peak discharge by up to a factor of 4 (Table S1). Peak discharge for LC2

GLOFs was strongly dependent on distance downstream and thus comparison of LC2

GLOFs with GLOFs elsewhere needs to be done judiciously. By standardizing

measurement locations downstream of the source lake, the accuracy of empirical

relationships determined from global compilations of GLOF peak discharge (e.g., Clague

and Mathews, 1973; Björnsson, 1991; Walder and Costa, 1996; Ng and Björnsson, 2003)

could potentially be increased.

4.2 Sediment Transport in the Glacially Dammed LC2 Lake Basin

The primary response in the LC2 lake basin to episodic GLOFs was the rapid

erosion of sediments stored within the lake basin (Figure 2 and Figures S5-S9). In less than a year after GLOFs initiated, sediment removal expanded the length of LC2 by ~2 km (Figure S9). From 2008 to 2015, ~25 million m³ of sediment was removed from the

LC2 lake basin, lowering the valley floor by more than 40 m in certain locations (Figure

2 and Table S2). 45

Figure 2. DEM of Difference (DoD) maps showing patterns and magnitude of sediment transport in Lago Cachet Dos following the onset of GLOFs in April 2008. (a-c) DoDs showing elevation changes between acquired DEMs. (d) Longitudinal profiles along the thalweg of Rio Cachet during times when LC2 was empty showing the amount of sediment removed from the LC2 lake basin through time. (e) Measured expansion rate and estimated erosion rate for each DoD period with associated error shown as gray boxes. Exponential fits are shown as dashed lines.

The evolution of the longitudinal profile of Rio Cachet highlights that most of the sediment erosion occurred in the package of sediment upstream of LC2 during 2008–

2012 and from the mid-section of the LC2 lake basin during 2012–2015 (Figure 2d). The package of sediment stored in the LC2 lake basin is predominantly sand sized (Figure

S10), but the grain size in the active channel is much larger, ranging from gravel, cobbles, to even boulders in some rapids (Figure S11a-d). The upstream and downstream 46

ends of the longitudinal profile are composed of meter-scale glacially deposited boulders and bedrock, respectively, thus limiting erosion at these locations (Figure S11e-f). The

upstream boulder deposits make it unlikely that Rio Cachet will incise through the

moraine/delta complex that impounds Lago Cachet Uno to connect the two lakes.

The average sediment erosion rate measured over each DoD interval and the rate

of longitudinal expansion of LC2 (Figure 2e and S9 and Table S2) show that sediment

erosion rates were highest during the initial post-GLOF period and then generally

decreased through time. The mean sediment erosion rate decreased ~fivefold from the initial post-GLOF period to last period of observation in 2014–2015, while rates of longitudinal expansion of LC2 decreased by over an order of magnitude during this time.

Initial sediment erosion rates during the first few GLOFs were likely much higher then we document by averaging over the initially widely spaced DEMs. These decreasing rates of sediment erosion are consistent with observations from well-documented

anthropogenic dam removal studies showing that sediment erosion rates are greatest

immediately following dam breaching, as fine-grained and unconsolidated sediments are

exposed to flow, and then decrease in the proceeding months to years as the river

reencounters the pre-dam base level (Pearson et al., 2011; Major et al., 2012; Wilcox et

al., 2014). During the catastrophic removal of the 15-m tall Marmot Dam on the Sandy

River, Oregon, 15% of the impounded sediment was evacuated within the first 60 hours

and 50% within 7 months (Major et al., 2012). The catastrophic breaching of the 38–m

tall Condit Dam on the White Salmon River, Washington also followed the trend, where

an estimated 10% of the impounded sediment was removed within the first 2 hours and

20% was removed within 24 hours (Wilcox et al., 2014). 47

The LC2 DEMs reveal a flight of terraces that step down to the 2015 river level, which are landforms characteristic of pulsed fluvial incision (Hancock et al., 1999;

Randle et al., 2015). The post-2012 DoDs show that areas with large amounts of erosion occur at sites where lateral migration of active channels resulted in cutbank erosion and removal of terraces (Figure 2c and Figures S5-S9). Field observations in January 2016 during lake-empty conditions confirm that active channel migration and cutbank erosion were rapidly removing terraces. These observations indicate that fluvial processes likely perform the majority of sediment erosion when stored sediments are exposed to a free- flowing Rio Cachet. As such, the duration that LC2 is empty and the Rio Cachet is freely flowing through the LC2 lake basin is an important factor controlling the quantity of sediment removed from the lake basin.

4.3 Quantifying Changing Channel Morphology on the Rio Colonia

The observed GLOFs resulted in the establishment of new primary channels and significant rearrangement of pre-existing channels on the Rio Colonia braid plain (Figure

3). Prior to the onset of GLOFs, Rio Colonia was characterized by 1 to 2 persistent and near stationary primary channels with smaller side channels that became active only during high flow (Figure 3a). Following the onset of GLOFs, plan form channel mobility, channel rearrangement, and sediment deposition at the Rio Colonia-Rio Baker confluence markedly increased (Figure 3b and c) supporting observations reported by Bastianon et al. (2012). New primary channels were established in locations previously occupied by small channels, while other channel courses were abandoned. These rearrangements resulted in across-valley channel shifts of over a kilometer in some locations (Figure 3c).

In other locations, primary channels migrated 10 to 300 m since the onset of GLOFs in 48

2008 and side channels increased in size and quantity. At the Rio Colonia-Rio Baker confluence, increased sediment deposition prograded a delta into the Rio Baker by over

200 m, which locally decreased the width of the Rio Baker to ~60 m compared to its

~300-m width upstream and ~200-m width downstream (Figure 3c).

49

Figure 3. Persistence of channels along Rio Colonia for pre-2008 interval (a) and post- 2008 GLOF interval (b). (c) The difference in channel persistence from pre-2008 to post- 2008. New channels are indicated by magenta colors. Abandoned channels and other areas that were once water and are now land (e.g., progradation of delta) are indicated by light blue colors. Continuously active channels are indicated by dark blue colors. Background is Landsat 8 panchromatic image January 21, 2015.

While a significant amount of geomorphic change has occurred along the Rio

Colonia, a few conditions unique to this system are worth considering before applying

these results to help anticipate the response of other similar systems to the onset of

GLOFs. First, observed geomorphic changes may be limited because the Rio Colonia

may still be recovering from the passage of a much larger prehistoric GLOF (Dussaillant

et al. (2010) reports estimated discharges of ~16,000 m3/s) and historic GLOFs

originating from Lago Arco during the late 1800s and mid 1900s (Tanaka, 1980; Harrison

and Winchester, 2000). Second, GLOFs sourced from LC2 transit two lakes (the 2 km

long proglacial lake and the 8 km long Lago Colonia) before flowing down the Rio

Colonia and thus lose their coarse-grained sediment load. Floodwaters entering the Rio

Colonia braid plain only carry sediment in suspension, and thus more erosion and less

aggradation is likely in comparison to the effects of a GLOF entering the braid plain

transporting sediment at capacity.

Despite the somewhat unique features of the Colonia Valley, our results are

comparable to the limited observations from other braided rivers subjected to GLOFs.

The 1996 GLOF on the Skeiðarársandur in Iceland, while significantly larger than any

Colonia GLOF with a peak discharge of 5.3x104 m3/s, transited a proglacial depression

that captured a significant portion of the coarse-grained sediment load prior to the

floodwaters entering the downstream braid plain (Magilligan et al., 2002). This Icelandic 50

GLOF resulted in significant rearrangement of downstream channels, although recovery

to a pre-GLOF state was estimated as ~4 years (Smith et al., 2006). In contrast, Desloges

and Church (1992) concluded that two GLOFs along the Noeick River in British

Columbia represented a catastrophic shift in flow regime that resulted in significant

change along the braid plain and that recovery to equilibrium conditions would take on

the order of decades to a century.

5 Conclusions

The Rio Colonia and the Rio Baker experienced a dramatic change in discharge

regime with the onset of GLOFs from ice-dammed LC2. GLOFs occurred 1–3 times per

year during 2008–2016 and exceeded the median discharge on the Rio Colonia by a

factor of 15 and the median discharge on the much larger Rio Baker by a factor of 4. The

peak discharges calculated at the source lake ranged from 2,000 m3/s to 11,300 m3/s but

due to the long and complicated flood path, discharge was muted to ~1500–2500 m3/s by

~40 km downstream. Travel along the flood path also altered the hydrograph shape from

gently but exponentially rising at the source lake to sharply rising downstream, with

implications for testing the fidelity of GLOF initiation models using measurements

collected at a distance downstream.

Rapid draining of the source lake and subsequent periods of fluvial activity resulted in massive erosion of stored sediment within the source lake basin with > 40 vertical meters of incision at some locations and a total eroded volume of ~25 x 106 m³.

The rate of sediment erosion decreased through time implying that initial sediment

concentrations leaving the source lake were likely high and similar to conditions 51 observed in catastrophic anthropogenic dam removals. Further downstream on the Rio

Colonia braid plain, the onset of GLOFs increased the rate of channel migration, the frequency of channel rearrangement, and the extent of sediment deposition into the Rio

Baker. In total, our observations highlight the impacts that the onset of large, frequent flood events can have on the hydrology and geomorphology of an ice-marginal fluvial system. Given the observed and projected rates of change in these areas, more quantitative observations of the type presented here could help clarify future responses of fluvial systems to a changing climate.

Acknowledgments

Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

52

Supporting Information

Figure S1. Hydrographs of GLOFs measured along the Rio Baker at the Baker en Colonia gauge (black) and the Baker bajo de Nadis gauge (gray). Unlike the discharge curves measured directly from the stage gauge in LC2 (Figure S4), the GLOF hydrographs measured along the Rio Baker are characterized by a steep rising limb and a gradual falling limb. The flood stage during GLOFs approaches or exceeds the level of the gauging stations, occasionally resulting in damage and loss of the record.

53

Figure S2. Hydrographs of GLOFs from the Rio Baker en Colonia gauge. (a) Hydrograph from each recorded GLOF with baseflow removed to allow estimation of GLOF peak discharge upon entering the Rio Baker approximately 40 km downstream from the source lake. (b) Hydrograph of all GLOFs with the GLOF discharge normalized by the peak discharge as a way to visualize the characteristic shape of GLOF hydrographs along the Rio Baker.

54

Figure S3. The six largest meteorological floods for the period of record (2001–2016) at the Rio Baker en Colonia gauge (black) and the Rio Baker bajo de Nadis gauge (gray) with the GLOF that occurred June 18, 2015 (dashed), which was characteristic of the GLOFs observed, plotted for comparison. Hydrographs of meteorological floods on the Rio Baker have a much more gradual rising limb and a gentle falling limb as opposed to hydrographs of GLOFs entering the Rio Baker from Rio Colonia.

55

Figure S4. GLOF hydrographs for the outlet of the source lake, LC2. Solid line shows discharge calculated using the sensor that sampled the upper ~40 m of LC2, or 68% of the total lake volume. Dashed line shows discharge calculated using the sensor that sampled the upper ~20 m of LC2, or 45% of the total lake volume. Discharge is plotted for the recorded duration of the GLOF defined as the period following the initiation of stage lowering. Due to the approximately exponentially rising hydrographs and the lack of measurements in the lower elevations of the lake, the maximum discharge was likely not measured.

56

Figure S5. A collection of images showing large-scale cutbank erosion due to lateral migration of Rio Cachet. (a) DEM of Difference (DoD) map for the October 2013 to November 2012 period shows that greater than 14 m of lateral erosion occurred on the cutbank slope highlighted by the turquoise box. (b) Comparison between hillshades of DEMs from November 2012 (left) and October 2013 shows how the cutbank along the Lago Cachet Uno moraine/delta has expanded over the period due to growth of a meander bend. (c) Field photo of the cutbank in January 2016.

57

Figure S6. A collection of images showing incision through a tributary delta. (a) DEM of Difference (DoD) map for the December 2015 to February 2014 period shows that greater than 25 m of erosion has occurred in the area of tributary delta erosion highlighted by the turquoise box. (b) Comparison between hillshades of DEMs from February 2014 (left) and December 2015 shows how significant incision has occurred through the tributary delta. (c) Field photo of the incised tributary delta in January 2016.

58

Figure S7. A collection of images showing erosion resulting from lateral migration of Rio Cachet through a terrace at the site of a tree previously sampled for carbon-14 dating (Nimick et al., 2016). (a) DEM of Difference (DoD) map for the December 2015 to November 2012 period shows that 2-4 m of erosion has occurred at the location of the tree. (b) Comparison between hillshades of DEMs from November 2012 (left) and December 2015 shows how erosion across much of the lake bottom has occurred in this area. Location of tree marked with the green star. (c) Field photos showing erosion in the areas around the tree sampled for carbon-14. Red circles highlight the elevation of sediment in 2011. Left field photo is from October 2011. Right field photo is from January 2016. The photos verify the elevation difference calculated in the DoD (2–4 m), where field measurements show that 3.5 m of erosion has occurred at the tree. The dead, upright trees that are currently being exhumed from LC2 sediment package were part of a forest that existed from at least the mid-1200s to about 1700, when LC2 was formed; this forest represents a time when Rio Cachet drained freely (Nimick et al., 2016).

59

Figure S8. (a-c) Field photos (looking north towards Lago Cachet Uno) document the substantial erosion in the LC2 lake basin and increase in aerial extent of LC2 since the initiation of GLOFs in April 2008. (d) Map of photo location from a pre-2008 Landsat Satellite image. (e) Map of photo location from a post-2008 Landsat Satellite image.

60

Figure S9. Landsat image showing changes in lake-full extent of LC2 through time due to upstream erosion through LC2 lake basin sediments. (a) Traces of lake-full extent through time as determined from Landsat images when the lake was full. (b) Plot showing the length of LC2 measured from the glacier dam to the upstream end of LC2 through time. (c) Plot showing the rate of LC2 expansion through time. Similar to the erosion rate presented in Figure 2e in the main text, a rapid decrease in the expansion rate is observed through time.

61

Figure S10. Map and plots presenting the measurements of grain size from three different locations within the LC2 delta. (a) Map with grain size sampling locations marked with a red triangle. (b) Grain size distributions. (c) Field photos of sampled sediments.

62

Figure S11. Field photos from January 2016. (a-d) Photos showing the range of grain sizes present along the active channel of Rio Cachet when LC2 was empty. (e) Photo of the upstream end of the LC2 basin depicting meter-scale glacially deposited boulders. (f) Photo of the downstream end of the LC2 basin depicting bedrock.

63

Figure S12. (a) Histogram showing the temporal distribution of Landsat images used to calculate channel persistence before and after the onset of episodic GLOFs. (b) The figure shows that we sampled equally from each season, such that we have compared a similar distribution discharges for the periods before and after the onset of episodic GLOFs.

64

Table S1. GLOF peak discharges and volumes recorded at three stations along the GLOF flow path. We calculated peak discharge from LC2 using the observed stage and the hypsometric function for the lake. The minimum flood volume from LC2 represents the volume of water that exited LC2 as recorded by the stage gauge. Maximum flood volume represents the volume of water if the lake completely drained. We estimated the flood volume at downstream gauges by integrating the hydrographs with base flow removed.

Table S2. Areal, volumetric, and vertical metrics calculated for each DEM of difference (DoD). Errors for each DoD were calculated using the average root mean squared error (~0.5 m) from the coregistration process.

65

Chapter 4: Conclusions and Future Research

Environmental Controls on Peak Discharge from GLOFs

In Chapter 1 of this thesis, I have shown, consistent with physics-based theory, that an increase in lake volume, lake temperature, and inflow rate contributes to an increase in peak discharge of observed GLOFs. Literature assessing discharge from

GLOFs has been strongly focused on the effect of volume, but as shown here, lake temperature and inflow rate can be equally if not more important. Popular equations that describe the relationship of total lake volume to peak discharge provide a reasonable fit for the global dataset, but perform poorly when predicting peak discharge from a single ice-dammed lake experiencing multiple GLOFs. These empirical equations underestimate peak discharge from LC2 by up to 83%, resulting in a potentially dangerous prediction if this method is combined with flood routing models and used for estimates of inundation.

Theory describing the time evolution of water flow through an ice-walled conduit identified lake temperature and inflow rate as environmental variables that are capable of controlling peak discharge of GLOFs; however, a lack of in situ measurements from ice- dammed lakes have left the significance of these variables untested. Multiple measurements of lake temperature and inflow rate from LC2 provided field verification of their importance in controlling peak discharge of GLOFs. Monitoring these environmental variables amongst a changing climate is essential for future prediction of flood magnitude for LC2 and similar glaciated areas globally. 66

Effects on Hydrology and Geomorphology from Episodic GLOFs

In Chapter 2 of this thesis, I have shown the hydrologic and geomorphic response of a glacial system experiencing episodic GLOFs. GLOFs from LC2 transit two lakes and a sandur on their 40 km journey to the Rio Baker. Despite this, GLOFs still affect the hydrologic regime in terms of flood magnitude and frequency for even one of the largest periglacial rivers in South America. This is particularly important from a hazards point of view, as it shows populations and infrastructure along large main-stem rivers can be affected by GLOFs from smaller tributary rivers.

Geomorphic response in the glacially dammed lake basin was characterized by rapid erosion of stored sediments followed by a steep exponential decline in sediment removed. This rapid response is similar to observations from breach-style anthropogenic

dam removals. Erosion of sediments stored in the LC2 basin since the onset of GLOFs in

2008 has increased the lake volume capacity by approximately 10%. Given the close

relationship between volume and peak discharge, sediment removal from ice-dammed lakes can effectively increase the magnitude of GLOFs. Downstream, on the Rio

Colonia, GLOFs altered the channel morphology by rearranging pre-existing channels and establishing new primary channels. As the frequency of GLOFs persisted, channel positions remained non-stationary. At the Rio Colonia-Rio Baker confluence, increased sediment deposition prograded a delta into the Rio Baker and locally constricted the Rio

Baker to a fifth of its upstream width. This shows that GLOFs initiating from smaller tributary watersheds have the capability to affect the geomorphology of large periglacial rivers with mean discharges greater than 1000 m3/s. As temperature increases and ice-

mass changes can shift river discharges beyond historical variability, the capability to 67

predict the response of a system in terms of hydrology and geomorphology is critical for

hydropower, agriculture, and hazard mitigation projects, particularly in periglacial areas.

Future Research

Several physically based models have been developed to describe the unsteady

flow of water through a glacier. An obvious next step in this research is to evaluate the

capability of these models in predicting the discharge hydrograph from LC2. Previous

attempts at model validation used only a single GLOF event; therefore, the range in

boundary conditions provided by the LC2 dataset will truly test the predictive capabilities

of such models.

The results of the work presented here documented the tremendous amount of

stored sediment that was removed from the LC2 basin, but the effect of this sediment

laden water on the expansion of the englacial conduit is unknown. Current theory that describes flow of water through an ice-walled conduit assumes physical properties of water for a sediment-free discharge. Entrained sediment could speed up expansion of the

conduit diameter by increasing the effect of mechanical tunnel enlargement or slow down

tunnel expansion by reducing viscous dissipation of heat.

Vital to any future research of GLOFs is the closer monitoring of ice-dammed lakes especially lake temperature and full-depth stage. Observations of these two environmental variables and acquisition of lake bathymetry will provide the foundation for any prospective research. 68

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