Modelling glacial lake outburst flood impacts in the Bolivian Andes

2.1 Geographical setting

This study focused on the glaciated ranges of the Cordillera Oriental, Bolivia; from north to south these are the Cordillera Apolobamba, the Cordillera Real (including Huayna Potosí, Mururata, Illimani), and the Cordillera Tres Cruces (Fig. 1). The three lakes identified by Kougkoulos et al. (2018) as having the highest risk include Laguna Arkhata, Pelechuco Lake, and Laguna Glaciar (Fig. 1). The only documented GLOF in Bolivia occurred at Keara (Fig. 1), which serves as a test case for our modelling approach. The Keara GLOF took place on 3 November 2009 at about 11:00 a.m. local time and involved the complete drainage of an ice-dammed lake (Hoffmann and Weggenmann 2013). This event flooded cultivated fields, destroyed several kilometres of a local dirt road, washed away pedestrian bridges, and killed a number of farm animals (Hoffmann and Weggenmann 2013). Fortunately, there were no human fatalities.

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2.2 Topographic data acquisition

We also acquired an ASTER GDEM V2 with a 30-m horizontal resolution because, in Agua Blanca, a community situated downstream of Pelechuco lake, our SPOT-derived 2-m DEM contains a gap due to terrain shading. For this small area the ASTER GDEM was used instead. The ASTER GDEM has been used in several GLOF modelling studies (e.g. Gichamo et al. 2012; Wang et al. 2012; Watson et al. 2015) because it is free to download, and covers most of the Earth’s landmass. In other cases, the DEM resolution has been resampled into a higher resolution in order to enable a higher level of precision in GLOF modelling, although the underlying DEM accuracy is not improved (e.g. Bajracharya et al. 2007; Allen et al. 2009; Rounce et al. 2016). In this study, we also applied a hydrological correction by filling sinks on both high (SPOT 2 m)- and low (ASTER GDEM 30 m)-resolution DEMs.

2.3 Estimating lake volume

This relationship yields an R² value of 0.83 and a P value < 0.0001 (Appendix A1).

Laguna Arkhata is bedrock-dammed, but as yet there are no depth-area relationships that exist for such lakes. Therefore, lake depth for Laguna Arkhata was calculated using Eq. 2.

We calculated the errors on the constants within each of the two linear regression models in Eqs. 1 and 2 (at a confidence level of 95%) and applied those errors to determine a range of lake depths for the three lakes under investigation (Appendix A1, Table 1). Lake volume (V) was estimated by multiplying the measured lake area (in Google Earth Pro) by the derived lake depth from Eq. 1 or 2, and the errors associated with lake volume were estimated by propagating the errors associated with lake depth.

2.4 Estimating peak discharge

All pro-glacial lake size estimations (e.g. area, depth, volume) can be found in Table 1.

2.5 Dam-breach hydrograph and modelling parameters

Numerous parameters (e.g. peak discharge, sediment load, channel roughness) can modify the flood inundation and flow behaviour of a simulated flood, leading to uncertainty in flood modelling and risk assessment (Anacona et al. 2015; Wang et al. 2015b; Kropáček et al. 2015). Table 1 presents a summary of the modelling scenarios undertaken, together with the accompanying values for each model parameter (i.e. lake volume, percentage of lake drainage, outburst duration, Manning’s value, peak discharge). We discuss each of these parameters in turn.

We followed Fujita et al. (2013) in calculating potential flood volume (PFV) as the product of lake area and either the mean depth (Dm) or the potential lowering height (Hp); Fujita et al. (2013) recommend using the lower of these two values to calculate PFV. We compared our values for Dm (Sect. 2.3; Table 1) against those calculated for Hp. Hp is the amount of lake lowering expected during a GLOF assuming that, after GLOF initiation, incision into the moraine dam will proceed until the angle between the lake and the downstream area is lowered to 10° (termed the ‘depression angle’). We created depression angle maps (Appendix A2) and mapped the steep lakefront area (SLA) 1-km downstream of each lake, following Fujita et al. (2013), in order to calculate Hp (see Appendix A2). In all cases, the value of Dm is lower than that calculated for Hp, and so Dm is used in the calculation of lake volume.

The volume of water drained from the lake is highly uncertain principally because this will be determined by the triggering mechanism, which could vary in nature and severity, and the resilience and integrity of the impounding dam. Hence, three different drainage volumes were modelled, which represent optimistic, intermediate, and pessimistic scenarios. Different values for the extent of lake drainage were defined, ranging from 20% of the lake volume for the optimistic scenario, 50% for intermediate, and 100% for the pessimistic scenario. These scenarios are guided by previous work on GLOF drainage volumes. For example, Anacona et al. (2014) studied 14 Patagonian moraine-dammed lakes before and after GLOF events and found that two lakes emptied entirely (100% drainage), four emptied by more than 50%, two by around 50%, and six lakes generated smaller outbursts with less than 20% drainage. In another study, Kropáček et al. (2015) modelled 125% lake drainage for their worst-case (pessimistic) scenario, with the additional 25% drainage accounting for possible future lake expansion in response to continued glacier recession. However, all lakes in our study are already at or very close to their maximum filling capacity, and so it is not necessary to model larger lakes. The lake drainage value for Keara was set to 100% since the observational evidence indicates that the lake drained completely (Hoffmann and Weggenmann 2013). For the other three lakes, we suggest that it is unlikely that they would drain completely, but we use the 100% drainage scenario as the worst possible case.

Previous studies have recommended a flood duration between 1000 and 2000s based on empirical data from the Swiss Alps (Haeberli 1983; Huggel et al. 2002). Therefore, we used 1000 s and 2000 s as outburst duration for the pessimistic and optimistic scenarios, respectively, and 1500 s for the intermediate scenario. As Worni et al. (2012) and Westoby et al. (2014a) suggest, if there are no data on lake outflow duration and lake discharge, the outflow hydrograph can only be validated indirectly (e.g. with the Keara event as a validation point in this case). Although simulations of drainage duration can be tuned to fit an observed hydrograph, hydrograph forecasting is difficult because nonlinear flood physics make drainage duration sensitive to the initial conditions (Ng and Björnsson 2003), which are usually uncertain. All three of our potentially dangerous glacial lakes are either bedrock- or moraine-dammed, so we made the assumption that flood discharge would increase linearly to a peak, after which it decreases linearly to 0 m³/s over a time span equal to that of the rising limb; in other words, hydrographs were assumed to be triangular in shape as has been applied in previous GLOF modelling studies (Anacona et al. 2015; Kropáček et al. 2015; Somos-Valenzuela et al. 2015; Wang et al. 2015b) (Fig. 2). Some previous studies have considered that the higher the peak discharge, the longer the flood duration (Anacona et al. 2015; Wang et al. 2015b), whereas others assume a shorter flood duration for a higher peak discharge (Somos-Valenzuela et al. 2015). We chose to use the latter option such that our worst-case pessimistic scenario has the highest peak discharge and shortest flood duration, and the optimistic scenario has the lowest peak discharge and longest flood duration. Ice-dammed lake failures usually generate flood hydrographs with a relatively slow, exponentially rising limb, and a rapidly falling limb (Kingslake 2013). Nevertheless, we chose to use a triangular-shaped hydrograph for the Keara ice-dam breach because no detailed data were available concerning the event, and we can compare more readily with results from the three lakes that are yet to generate GLOFs.

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In-channel and floodplain Manning’s values for each scenario were set to represent mountain streams without vegetation (Table 1), although we could only verify the type of terrain by performing an inspection on Google Earth and from our own fieldwork observations at Pelechuco, in the Cordillera Apolobamba.

2.6 Hydrodynamic modelling of GLOFs

Modelling of GLOF hazard and risk has been undertaken in several regions around the world, using a variety of different approaches. Some studies have used simple geometric models such as the modified single flow (MSF) (Huggel et al. 2002; Allen et al. 2009; Prakash and Nagarajan 2017), the random walk process (Mergili and Schneider 2011), or the Monte Carlo Least Cost Path (MC-LCP) (Watson et al. 2015; Rounce et al. 2016, 2017) to make a rapid assessment of potential flood inundation. Such models require very little input data and can be applied to many lakes, but serve as a first-order assessment that cannot go as far as to produce realistic flood maps. Other studies have focused on more detailed modelling approaches using HEC-RAS 1D (Bajracharya et al. 2007; Dortch et al. 2011; Klimeš et al. 2014; Watson et al. 2015), HEC-RAS 2D (Anacona et al. 2015; Wang et al. 2015a, b), FLO 2D (Petrakov et al. 2012; Somos-Valenzuela et al. 2015), and BASEMENT (Worni et al. 2012, 2013; Somos-Valenzuela et al. 2016), all of which require further data such as channel bed roughness, and the volume of water that could drain from the lake. These techniques are capable of generating inundation maps (area affected, runout distance, and depth of flow) that can be used to inform risk management and mitigation strategies.

Here, GLOFs were modelled (inundation area, arrival time, depth, and velocity) using the 2D US Army Corp of Engineers model, HEC-RAS 5.0.3 (http://www.hec.usace.army.mil/). HEC-RAS was used because it is downloadable free of charge, and has been employed successfully to model GLOF inundation in a number of previous studies (e.g. Bajracharya et al. 2007; Dortch et al. 2011; Klimeš et al. 2014; Anacona et al. 2015; Wang et al. 2015a, b; Watson et al. 2015). The 2D version of this model can simulate multi-directional and multi-channel flows, which are characteristic of GLOFs (Westoby et al. 2014a, b; Wang et al. 2015b; Watson et al. 2015). The model set-up included the definition of upstream and downstream boundary conditions, the creation of a grid with elevation data, the selection of Manning’s roughness values, slope parameters, and the model spatial domain. The unsteady flow simulation was performed for all four Bolivian GLOF case studies in order to observe: (1) peak flow propagation, (2) flood inundation extent, and (3) the flood water depth.

We used our simulated dam-breach hydrographs for the upstream boundary condition of each model (see Sect. 2.5 for more details). The normal depth option was used for the downstream boundary condition. This latter option uses Manning’s equation to estimate a stage for each computed flow. To use this method, the user is required to enter a friction slope for the reach close to the boundary condition. If no detailed data exist, the slope of water surface can be used as a good estimate for the friction slope (Brunner 2010). This type of boundary condition should be placed far enough downstream of the study reach (i.e. potentially impacted communities) such that any errors it produces will not affect the results of the GLOF runout area (Brunner 2010; Watson et al. 2015). Hence, we placed the boundary 2-km downstream of the last community potentially affected by a GLOF from each lake. In addition, even though HEC-RAS has the ability to simulate debris flows, GLOFs were simulated as clear-water flows due to a lack of information about the nature of stream beds. We acknowledge that GLOFs are very likely to erode and entrain debris as they propagate downstream, and possibly evolve into debris flows, although many other studies also model GLOFs as clear-water flows due to data constraints (e.g. Anacona et al. 2015; Kropáček et al. 2015; Wang et al. 2015b; Watson et al. 2015).

Our overall approach was to test the model against field observations of the 2009 Keara event to ensure that realistic flood depths and inundation extent were achieved. The same modelling methodology was then applied to the three potentially dangerous lakes identified by Kougkoulos et al. (2018).

2.7 Population and infrastructure data

Population and infrastructure data are required to assess potential GLOF impacts. These data were acquired from the GeoBolivia portal (http://geo.gob.bo/portal/), which offers open access to the 2012 population census and infrastructure data of the Bolivian National Statistical Institute. To quantify the downstream impacts, we manually counted the number of buildings affected by the flood. For each community, we also divided the total population of the community by the number of buildings in the community to estimate the number of people per building. This enabled us to estimate the number of people impacted by the flood. However, we acknowledge that there are likely to be spatial differences in population within each community, and, because of seasonal migration within Bolivia (Oxfam 2009), there will be temporal population variations (which we have not considered further in this study).

Field observations in the Cordillera Apolobamba region in July 2015 demonstrate that building structures are usually single-storey residential dwellings made of unreinforced brick walls (Fig. 3). Roofs are mostly constructed from corrugated steel sheets. According to Reese et al. (2007), this type of structure is vulnerable to flood depths of greater than 2 m, and from observations of other types of extreme flood events, such as tsunamis, lahars, and debris flows, only the concrete floor is likely to remain intact after the passage of a ≥ 2 m flood (Reese et al. 2007). Hence, for each one of the three scenarios simulated for each lake, we estimate the impact on the downstream communities taking into account two inundation depths (1) the extent of the flood from the > 0 m flood depth and (2) the extent of the flood from the > 2 m flood depth.

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