Numerical modeling of debris flows. Application to Rebaixader (Pyrenees) and Mocoa (Colombia)

Numerical modeling of debris flows. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) Final Thesis developed by: Laura Isabel Molano Correa Directed by: Marcel Hürlimann Vicente Medina Master in: Geotechnical Engineering with Specialization in Geotechnics Barcelona, June 2023 Department of Civil & Environmental Engineering MASTER FINAL THESIS Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 1 Table of Contents Abstract ................................................................................................................................ 2 Resumen ............................................................................................................................... 3 1. Introduction ....................................................................................................................... 4 1.1 Debris-flows Modeling ..............................................................................................................6 1.1.1 Review of Existing Numerical Models ........................................................................................................... 6 1.1.2 Flow Resistance Laws.................................................................................................................................... 9 1.2 Research Objectives ................................................................................................................ 11 2. Study Areas and Events Description ................................................................................. 12 2.1 Mocoa Site .............................................................................................................................. 12 2.1.1 General Characteristics of Mocoa .............................................................................................................. 12 2.1.2 Previous Studies and Data Collection ......................................................................................................... 16 2.2 Rebaixader Site ....................................................................................................................... 19 2.2.1 Monitoring System ..................................................................................................................................... 20 2.2.2 Description of Monitoring Data .................................................................................................................. 22 3. Methodology ................................................................................................................... 24 3.1 Description of FLATModel ....................................................................................................... 24 3.1.1 Initial Conditions and Parameters .............................................................................................................. 25 3.1.2 Calibration and validation model with historical events ............................................................................ 27 3.2 Analytical methodology of boulders transport applied to Rebaixader ....................................... 30 3.2.1 Single Rigid Block Model on an Inclined Plane ........................................................................................... 30 3.2.2 Impact by Hydrodynamic Force .................................................................................................................. 31 4. Results and Discussion ..................................................................................................... 33 4.1 Back-analysis of the 2017 Debris Flow in Mocoa ...................................................................... 33 4.2 Back-analysis of the 2020 Debris Flow in Rebaixader ................................................................ 38 4.3 Analytical Application of Impact and Transport of Boulders ..................................................... 44 4.3.1 General Aspects .......................................................................................................................................... 44 4.3.2 Application to Rebaixader Site.................................................................................................................... 45 5. Conclusions ...................................................................................................................... 50 References........................................................................................................................... 52 Annexes .............................................................................................................................. 55 Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 2 Abstract Debris flows are one of the most hazardous geomorphological processes in mountain areas with complex behavior due to the high flow velocity, long run-out, and destructive power. The present assessment is based on numerical modeling to reproduce historical events and to predict the characteristics of a future one. Two debris flows events have been evaluated, one occurred in the Northern Andes Mountain range (Colombia), while the other event occurred in the Central Pyrenees (Spain). The back-analysis was applied to calibrate and validate simulation results for each debris flow caused by a set of parameters related to the mountain environment conditions. In this study, the analysis of the simulations is developed by the 2D finite volume code FLAT- Model. Although different flow resistance laws were integrated in the numerical code, we will be comparing Bingham, and Voellmy with and without entrainment. The basal entrainment from erodible beds was evaluated, the simulation runs incorporating the Voellmy with entrainment model into FLATModel. The calibration stage involves making simplifications and proper assumptions to obtain adequate results based on historical and field-measured and monitoring data of the events. The back-analysis has been completed to find the rheological parameters which can reproduce the reference results. In order to study debris flows dynamics, numerical modeling of two historical events was performed. Simulating Voellmy with entrainment offered satisfactory results regarding the flow path and total volume for both cases. Thus, the outcome of applying the basal entrainment provides the right agreement with field observations. The final volume is sensitive to the parameter φent, but the impact and transport capacity is influenced by the local terrain slope and flow velocity. The concept of the critical radius is introduced to describe the areas where the flow develops a more destructive capacity and can mobilize a larger boulder size. The present study shows that in spite of many uncertainties, debris flow modeling is a key tool for researchers to increase the understanding of flow dynamics and reduce the impacts of these natural hazards. Keywords: Debris flows; numerical modeling; basal entrainment; transport of boulders; impact force; Rebaixader; Mocoa. Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 3 Resumen Los flujos de detritos son uno de los procesos geomorfológicos más peligrosos de las zonas montañosas, con un comportamiento complejo debido a la alta velocidad del lujo, el largo recorrido y el poder destructivo. Para esta evaluación, se utiliza la modelación numérica para reproducir eventos históricos y predecir sus características en el futuro. Se han evaluado dos eventos de flujos de detritos, uno ocurrido en la Cordillera de los Andes del Norte (Colombia), mientras que el otro evento ocurrió en los Pirineos Centrales (España). Se aplica el análisis retrospectivo para calibrar y validar los resultados de la simulación de cada flujo de detritos, causado por un conjunto de parámetros relacionados con las condiciones ambientales de la montaña. El análisis de las simulaciones se desarrolla mediante el código de Volumen Finito 2D FLATModel. A pesar de que el código numérico integra diferentes leyes de resistencia al flujo, se realiza la comparación de Bingham y Voellmy con y sin arrastre. Se evalúa el arrastre basal de lechos erosionables, y las simulaciones ejecutadas incorporaron el modelo Voellmy con arrastre en FLATModel. La etapa de calibración involucra hacer simplificaciones y suposiciones apropiadas para obtener resultados adecuados de los eventos basados en datos históricos medidos y monitoreados en campo. El análisis retrospectivo se ha completado para encontrar los parámetros reológicos que pueden reproducir los resultados de referencia. Para analizar la dinámica de los flujos de detritos, se realiza el modelado numérico de dos eventos históricos. La simulación de Voellmy con arrastre ofrece resultados satisfactorios en cuanto a la trayectoria del flujo y el volumen total para ambos casos. Por lo tanto, el resultado de aplicar el arrastre basal proporciona la concordancia correcta con las observaciones de campo. El volumen final es sensible al parámetro φent, pero la capacidad de impacto y transporte está influenciada por la pendiente del terreno local y la velocidad del flujo. El concepto de radio crítico se introduce para describir las áreas donde el flujo desarrolla una capacidad más destructiva y puede movilizar un tamaño de roca más grande. El presente estudio muestra que, a pesar de existir muchas incertidumbres, la modelación de flujo de detritos es una herramienta clave para que los investigadores aumenten la comprensión de la dinámica del flujo y reduzcan los impactos de estos peligros naturales. Palabras clave: Flujos de detritos; modelación numérica; arrastre basal; transporte de cantos rodados; fuerza de impacto; rebaixader; Mocoa. Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 4 1. Introduction The study of debris flows remains a matter of research due to its complex behavior and great impact on geological risk management. These types of flows imply the transportation of granular solids and fine particles in a multiphase integrated by water and air. Debris flows are defined as rapid movements of saturated debris in a steep channel (Jakob & Hungr, 2005), a main feature of debris flows is the fact that they move different grain sizes of sediment including gravels to boulders (Jhonson & Rodine, 1984). Once it starts, it can be highly erosive entraining sediments that make its volume grow to size. We understand erosion as removing sediment from the channel bed, while entrainment is incorporating the eroded sediment into the debris flow (Frank, et al., 2017). For this, debris flow is a high-energy phenomenon that represents a potential hazard. In any case, the mountain environment conditions, the characteristics of the flow, and the event frequency due to regional weather, geology, morphology, and hydrology make it difficult to understand. Debris flows are a well-known geomorphic process in the wide world, and it is considered the most active geomorphic hazard in mountain areas (García-Ruiz, et al., 2002). Two debris flow cases in different locations have been evaluated and analyzed to deepen the study of this type of hazard. One event occurred in the Northern Andes Mountain range (Colombia), while the other event occurred in the Central Pyrenees (Spain). The first case takes place in South America, with a varied topography, where the Andes Mountains have a large extension on the continent. The Andes Mountains were formed by the subduction of the Nazca Plate under the South American Plate (Prada-Sarmiento, et al., 2019). Several fault systems such as the Mocoa-La Tebaida Fault and the Cantayaco Fault were generated in southwestern Colombia. The tectonic weakening of the local geology reflects critical conditions on basin hillslopes which are covered by erodible materials from highly weathered rocks (García- Delgado, et al., 2019). Previous events of landslides, debris flows, and mudflows were developed in the Mocoa basin triggered by the prolonged and intense rainfalls of a tropical zone. The topography of the area varies from flat to hilly to steep and the water sources have produced deep V- Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 5 shaped channels because of the high erosion rates (Prada-Sarmiento, et al., 2019). Although previous events have occurred in the Mocoa basin, the catastrophic event in 2017 has motivated the investigation of flow description and volume estimation through numerical modeling. In contrast, the second case occurs in the Pyrenees, frequently affected by flows triggered mainly by rainstorms (Portilla, et al., 2010). Identifying several episodes in this zone incentives the investigation of the susceptibility’s causes and dynamical behavior (Portilla, et al., 2010). The characteristics investigated in the Pyrenees resemble those found in the Alps (Portilla, et al., 2010), where the steepness of slopes, the high production of accumulated debris, the frequent occurrence of rainstorms, and the characteristics of some lithological outcrops stand out (García-Delgado, et al., 2019). The case under study occurred in the Rebaixader catchment in which a monitoring system detects torrential flows and collects information to compare with the models. The monitoring setup includes sensors related to in-situ measurements of initiation and flow dynamics (Hürlimann, et al., 2014). The regions with hazard phenomena such as debris flow implement mitigation measures classified as structural and non-structural (Hübl, et al., 2009). Structural measures are divided into active or passive mitigation. Where the active one intervenes directly in the process (Hübl, et al., 2009). A very common structural mitigation measure is debris flows barriers built with concrete (Hübl, et al., 2009). The design requires the estimation of the impact force of the debris flows against the obstacle. The impact models are principally based on theoretical considerations, realworld observations, and laboratory experiments (Hübl, et al., 2009). Impact signal results from current laboratory tests investigations show a typical impact process of debris flows described by a turbulent font (Cui, et al., 2015). Moreover, the grain impact loading is random, and the impact frequency of the big grains was likely to increase with the depth (Cui, et al., 2015). The tendency is that large grains are concentrated in the surface and middle parts of the flows, but the laboratory simulations are limited by the flume size to represent the effects of big boulders (Cui, et al., 2015). Several observations conclude that the large blocks are transported by debris flows, even though the flow is turbulent, the blocks stop, and the debris is carrying them (Jhonson & Rodine, 1984). Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 6 For the mitigation of this hazard, it is essential to understand the dynamics of flows by estimating rheology or entrainment to predict the debris behavior. Numerical models have been developed to forecast the run-out distance, the impact force, and the erosive process. Each debris flow corresponds to a set of parameters that accurately represent a single event and consequently, modeling is important to predict the spatial hazard of debris flows (García-Ruiz, et al., 2002). In this study, the analysis of the simulations is developed by the 2D finite volume code FLATModel. The application of FLATModel to catchments in the Pyrenees made it possible to generate hazard maps and validate the implementation of basal entrainment (Medina, et al., 2008), (Hürlimann, et al., 2008). The field-measured data were compared with the simulation results regarding the main deposit’s extension and the thickness of the final deposits (Hürlimann, et al., 2008). The evaluation of specific debris flows also provided information that described how the stop-and-go mechanism is simulated by FLATModel (Medina, et al., 2008). Considering the successful application in the Pyrenees basins, the numerical model is implemented for the first time in a catchment located in the Colombian Massif. The calibration and validation of the back-analysis for the Mocoa event have many limiting factors. The measured field data of flow depth and velocity during the event was lacking. Additionally, there is no available rheological data on the material. 1.1 Debris-flows Modeling 1.1.1 Review of Existing Numerical Models There are many numerical models for simulating single-phase or multiple-phase flows. The approach for these models is based on the fact that future debris flows will behave comparably to those that have previously occurred (Jhonson & Rodine, 1984). The simulations with single-phase models are frequently used to predict and evaluate the behavior of an event (Medina, et al., 2008). Working with two phases implies handling separately the fluid and grains. This assumption is based on the effect of the sediment grains’ interactions and in most cases, the phases remain uncoupled during all analyses (Medina, et al., 2008). Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 7 Regardless of the definition of the phases, measuring flow parameters is challenging because the material properties may change in time and space (Rickenmann, et al., 2006). Normally, the models allow more than one flow resistance law, and it can assume the density as a known parameter. Even more, it is determinant to have an accurate digital surface model because the results may improve if flow obstructions such as buildings are included (Núñez-Andrés, et al., 2019). In addition, the availability of the terrain data before and after an event can be compared to obtain the quantification of mobilized volume and erosion (Núñez-Andrés, et al., 2019). The table below makes a comparison of some numerical models. The most recent codes are trying to incorporate the use of multiple-phase flows and the simulation of entrainment. The latter process should be considered in debris flow simulations because can strongly increase the event’s volume, runout distance, and impact force (Baggio, et al., 2021). Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 8 Table 1. Summary table of some available numerical models. NAME (REFERENCES) NUMBER OF PHASES FLOW RESISTANCE LAW SIMULATION OF ENTRAINMENT NUMERICAL SCHEME COST D-CLAW (George & Iverson, 2014) Biphasic Turbulent-Coulomb Finite Volume Free DFEM (Naef, et al., 2006) Monophasic Bingham, dilatant, turbulent and Coulomb X Finite Element Free FLATModel (Medina, et al., 2008) Monophasic Manning, Coulomb, Voellmy, Bingham, Herschel-Bulkley X Finite Volume Free FLO-2D (Cesca & D’Agostino, 2008) Monophasic Turbulent-Coulomb- viscous X Finite Difference Commercial Morpho2DH (Takebayashi & Fujita, 2020) Monophasic Turbulent, Coulomb, and creep X Finite Element Free RAMMS (Frank, et al., 2015) Monophasic Voellmy X Finite Difference Commercial R. AVAFLOW (Baggio, et al., 2021) Mono-, bi- and triphasic Bingham plastic (liquid phase), viscous Coulomb or visco-plastic (coarse solid phase) X Finite Difference Free RIVERFLOW2D (Pasculli, et al., 2021) Monophasic 7 rheological models Finite Volume Commercial TRENT-2D (Stancanelli & Foti, 2015) Biphasic Voellmy X Finite Volume Free Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 15 Precipitation is a process associated with wearing a way of soil and it raises the susceptibility to landslides and infiltration (Medina, et al., 2017). The Putumayo location has a higher degree of erosion due to the seasonal rain and the proximity to the Amazonian region. In consequence, this zone presents a higher fracturing degree attributed to tectonic weakening and intensify by climate conditions (Medina, et al., 2017). Outcrops of Monzogranite are unstable and promote the formation of sedimental deposits and frequent mass movements. The Monzogranite of Mocoa has compositionally variations to granite, granodiorite, quartz monzonite, quartz diorite, and monzodiorite (Medina, et al., 2017). Figure 3 presents granodiorite outcrops heavily fractured and weathered upstream of Taruca Creek. The bed material corresponds to fractured Monzogranite, which reaches an effective friction angle of around 30° (Medina, et al., 2017). Figure 3. Outcrops of granodiorite were observed during field visits at Taruca Creek (Pontificia Universidad Javeriana, 2017). Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 16 2.1.2 Previous Studies and Data Collection Based on the historical archives of Mocoa, the fluvial-torrential events date from the years 1947 and 1960 for the Mulato River and the Taruca Creek respectively, but the deposits under the urban area are even older (Medina, et al., 2017). A large part of the Taruca and Taruquita Creeks fan is placed in the urban area. The magnitude of the damage in the 1960 debris flow event is not comparable with the 2017 event due to population growth. Besides, there have been geomorphological alterations causing elongated V-shaped basins that suggested active valleys where bedrock incisions are rewarded by several landslides (García-Delgado, et al., 2019). The dynamics of both creeks are controlled by fluvial-torrential events with entraining material and damming where the channel narrows or is obstructed by active mass movements (Medina, et al., 2017). The catastrophe that occurred on March 31, 2017, was caused by subsequent mass movements in the Mocoa basin. The debris flow events were triggered by four days of high-intensity rainstorms during the rainy season (Prada-Sarmiento, et al., 2019). The Colombian Geological Service (SGC) has developed projects to classify mass movements, record observations, and estimate the volumes contributed to drainage. Based on the study carried out by Medina, et al., (2017), a total of 629 mass movements were cartographically identified. The use of the photointerpretation technique allowed identify 179 mass movements in the Taruca, and Taruquita creeks of which 84 of them provided eroded material to the flow (Medina, et al., 2017). These 84 mass movements correspond to debris flows because its deposit matrix consists of boulders and angular monzogranite blocks (Medina, et al., 2017). In addition, Medina et al. (2017) estimated that subsequent debris flows events added to the drainage around 187831 m3 to reach an approximate total volume of 2.25x106 m3 in the fan. Subsequently, the volume in the fan was updated to 3x106 m3 and the eroded material represents 13% of the total debris volume (Medina, et al., 2017). The flow height was described in the study of Medina, et al., (2017) (see Figure 25), where it is observed that the highest flow depth was about 13 m in the channel of Taruca and Taruquita creeks. It should be noted that these zones are related to the points of the greatest slopes change of the torrent (Medina, et al., 2017). In the Medina, et al., (2017) report was concluded that the Taruca and Taruquita mass movements gain volume rapidly, at first removing the organic Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 17 material and then the water and sediment volume increased, which led to a rise in the erosion capability and obstructions were overcome. Regarding the dynamics of the flow and the material accumulation, the transport of boulders may hinder free movement and causes damming. The obstructions represent energy accumulation which results in higher velocities when the material is released. One year later Ruiz, et al., (2018) with the SGC developed a project for hydraulic calibration, the geomorphometric of the micro-basins, and mass movement hazard mapping. In contrast to the previous study Ruiz, et al., (2018) used FLO2D to simulate the 2017 event and they compared their flow velocities outcomes with the empirical ones described in Medina, et al., (2017). The numerical modeling discharge results for the basin established by the San Antonio, Taruca, and Taruquita creeks were in a range of 55 m3/s to 220 m3/s (Ruiz, et al., 2018). Likewise, the velocities fluctuate between 2.78 m/s and 17.22 m/s with a range flow depth of 1.3m to 11.7m (Ruiz, et al., 2018). The simulate mobilized volume was 2123583 m3 with a solids concentration of 45% (Ruiz, et al., 2018). Nevertheless, the study stands out that the uncertainties of the section results (see Table 5) are significant because of the complex geological-structural conditions (Ruiz, et al., 2018). Even more, the lack of instrumentation in the micro-basin does not allow us to know with certainty the behavior of the flow. In consequence, they suggest the comparison of the results focuses on the affected urban areas (Ruiz, et al., 2018). Other authors (Pontificia Universidad Javeriana, 2017), (Prada-Sarmiento, et al., 2019), (García-Delgado, et al., 2019) relied on the SGC projects to describe and increase the understanding of the triggering factors, of transport, and deposit of mass movements. Additionally, the early warning system (EWS) was designed by Pontificia Universidad Javeriana after the event in 2017 and was developed through field technician visits supported by the National Unit for Disaster Risk Management (UNGRD). The EWS had a period of research and numerical modeling through software, where the academy and the UNGRD generated a baseline to make public decisions. Monitoring equipment to measure hydraulic and meteorological conditions were implemented. Moreover, an alert communication system was incorporated which is Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 18 integrated by sirens, local communication equipment, and data storage providing management real-time data. (Pontificia Universidad Javeriana, 2017) During the field visits, they observed that the deposits in the upper part of the Taruca basin are thin with the Monzogranite outcrops, while the accumulation increased in the lower part of the Taruca and Taruquita creeks (Pontificia Universidad Javeriana, 2017). The thickness of the accumulation can reach up to 4-5m and they identified different mass movements which stand out: the Monzogranite rockfall and translational landslides (Pontificia Universidad Javeriana, 2017). The change in rock composition from igneous domain to sedimentary added to the slope change, enables material to deposit as shown in Figure 4. In contrast, Figure 5 presents the lower level where the matrix consisted of size grains of medium sand to coarse sand with angular shapes (Pontificia Universidad Javeriana, 2017). Also, they noted fragments of diameters from 0.2m to 3m of granodiorite and granite with a maximum percentage of clay of 20% (Pontificia Universidad Javeriana, 2017). Figure 4. Deposit caused by torrential flow at Taruca Creek (Pontificia Universidad Javeriana, 2017). Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 19 Figure 5. Deposit distribution downstream of the Taruca and Taruquita confluence (Pontificia Universidad Javeriana, 2017). 2.2 Rebaixader Site The Rebaixader site is a small catchment located in the Central Pyrenees, which has been affected by many debris flow events due to high mountain morphology. The drainage basin covers a total area of 0.5 km2, where the bedrock is composed of Paleozoic metamorphic rocks, and the material that covers the bedrock is colluvium and granular glacial deposits (Núñez-Andrés, et al., 2019). The basin is divided into four zones of analysis as shown in Figure 6: scarp, funnel, channel, and fan. The scarp includes the entire initiation area where there is unlimited sediment availability with the highest slopes, in a range of 30° to 60°. Then downstream, the funnel is located, and it presents a large amount of accumulated sediment due to the channeling of the flow. This zone has a mean slope angle of about 30° before arriving at the channel, and it remains around 30° across to channel. The last zone is the fan with the lowest slopes between 15° and 20°, where the material is deposited or sometimes the debris drains into the Noguera Ribagorçana River. Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 20 Figure 6. The Rebaixader site a) Slope angle map based on the ICGC data with dashed polygons to indicate the different morphologic domains (contour lines: 50m; raster resolution: 1x1m). b) Location of the Rebaixader site. c) Satellite image with the four morphologic domains. 2.2.1 Monitoring System In the summer of 2009, a monitoring system was installed in Rebaixader, and over the years it has been developed and improved. The benefit of implementing a monitoring system in a site where there are no countermeasures is to allow the study of torrential activity. Currently, the system consists of four different stations to record information in the initiation zone and the channel. Two infiltration stations are located in the scarp to identify the initiation of the movement (Hürlimann, et al., 2014). Another station is the meteorological station. Finally, the flow behavior is monitored by the devices placed along about 175 m in the active channel. There are three types of monitoring devices: the geophones that measure vibrations, the ultrasonic and radar sensors to Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 21 record the flow height, and the video camera to confirm the facts (Figure 7). The devices mentioned above are wired sensor networks, although other types of sensors with wireless communication have recently been installed. In 2009 were installed the geophones and the ultrasonic device (US) which are connected by electrical wires with a Campbell Scientific CR1000 datalogger (Hürlimann, et al., 2014). Installing geophones along the channel was a success because the devices record information from a place separated from the torrent without risk of damage. Previous antecedents showed that most events were triggered by short high-intensity rainstorms during the summer, but also during spring due to the melting of snow (Hürlimann, et al., 2014). The interpretation of the data is supported with ultrasonic and radar measures and using a camera to clarify details. The sensors switch to “event” mode if the defined threshold is exceeded, for instance, the geophones threshold is defined by 20 IMP/s during three consecutive seconds (Hürlimann, et al., 2014). At this moment, the geophones record the impulse per second (IMP/s) in the datalogger internal memory. In addition, the radar and the US are measuring every second the flow depth. The distance along the channel of each sensor is listed in Table 2. Moreover, the study area is monitored with the geomatic technique of digital photography from UAV (Unmanned Aerial Vehicle) to capture the morphologic changes. In our case, the scarp has large blocks and steep slopes that increased difficulties to generate an accurate point cloud (Núñez-Andrés, et al., 2019). Table 2. Terrain distance of the devices. See Figure 7 for location. SENSOR IDENTIFIER TERRAIN DISTANCE (m) Geophone 2 - Radar 77 Geophone 2 - US 65.9 Geophone 2 - Geophone 4 139.2 Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 22 Figure 7. Instrumentation devices used in this study and installed at the channel zone for the monitoring system: two geophones, the camera, the radar, and the ultrasonic device (US). 2.2.2 Description of Monitoring Data We select the July 2020 debris flow as a recent event due to significant data availability. The debris flow was triggered by a rainstorm, where the critical hourly rainfall was about 14.6 mm/h. This threshold fits with previous correlations made in the Rebaixader torrent, where it is suggested a value of around 15 mm/h for the summer season (Hürlimann, et al., 2014). The back-analyses of this debris flow are based on the monitored information, particularly with the sensors in the channel to describe accurately the flow dynamics. Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 23 Figure 8. Monitoring data recorded for the debris flow event. Figure 8 presents the information recorded by the monitoring system in the channel during the 2020 event. Geophones 2 and 4 measured the ground vibrations signal that was transformed and recorded by impulse per second (IS). These two devices registered the information for an analysis of the seismic data of a debris flow. The most typical feature in this type of recording is the steep front because the maximum vibration is associated with the impacts of large boulders (Hürlimann, et al., 2014). Then, the recorded data tends to a gradual decrease after the front with some additional peaks due to surges (Hürlimann, et al., 2014). This behavior is observed in Figure 8 in the IS time series registered of geophones 2 and geophones 4. The difference between the series of geophones can be because of their placement along the channel. On the other hand, Figure 8 contains the hydrograph by the measured data with the ultrasonic device (US) and the radar. The event starts at noon around 12:00:00h where the first minutes of the recording showed a minimum flow depth below 10 m. The US data appears to have intervals with small variations that are related to a sensor malfunction. However, the peak of maximum increase of flow height seems to fit at the same time of the event based on US data and radar measurements. At the channel, the volume estimate of debris flows that were mobilized is around 10000 m3. This estimation was developed 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 12:00:00 12:03:00 12:06:01 12:09:01 12:12:02 12:15:02 12:18:03 12:21:03 Flow depth (cm) Ground vibration (IS) Geophone 2 Geophone 4 US Radar Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 24 with the monitored data considering a maximum flow depth of 1.6 m, an average front velocity of 4.1 m/s in the section of the flow-depth sensor, and the simplified approach described in Hürlimann, et al., (2014). 3. Methodology 3.1 Description of FLATModel The simulations of this study have been realized through the numerical model of FLATModel, which is a two-dimensional model based on the finite volume method (FVM) with the Godunov Scheme (Medina, et al., 2008). This computational scheme has the advantage of handling discontinuities and large function gradients. The governing equations are based on a depth integration using the shallow water hypothesis and integrating the Navier-Stokes equations for thin 1D flows over smooth terrain (Medina, et al., 2008). The numerical approach includes the first and second derivatives of the terrain surface to become a correct description of a continuous surface (Medina, et al., 2008). There are two ways that the model can simulate the entrainment, a static and dynamic approach. In both approaches, the entrainment occurs if the bed forces are greater than the resistance ones. The static equilibrium considers that the resultant velocity reduces because of entrainment, while with the dynamic method, the newly incorporated material is accelerated to the mean velocity of the flow (Medina, et al., 2008). FLATModel considers that flow depth is normal to the bed, so after solving the integration with the consideration of the direction and corrections about slope and curvature, the equation can be expressed by (Medina, et al., 2008): 𝜕 𝜕𝑡(ℎ ℎ𝑢 ℎ𝑣)+𝜕 𝜕𝑥(ℎ𝑢 ℎ𝑢2+𝑔𝑝ℎ2 2 ℎ𝑢𝑣 )+𝜕 𝜕𝑥(ℎ𝑣 ℎ𝑢𝑣 ℎ𝑢2+𝑔𝑝ℎ2 2)=( 0 ℎ(𝑔𝑝tan𝛼𝑥−𝑆𝑓𝑥) ℎ(𝑔𝑝tan𝛼𝑦−𝑆𝑓𝑦)) (4) Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 31 𝐹𝑟=𝜇𝑁=𝜇𝑊 cos (𝜃) (5) 𝐹𝑟=tan(𝜑)𝜌𝑠𝑜𝑙𝑖𝑑𝑉𝑔cos (𝜃) (6) Figure 10. Rigid frictional block on an inclined plane. 3.2.2 Impact by Hydrodynamic Force Debris flows are constituted by a mixture of wide-range size sediment. The influence of grain sizes is an essential factor in hydraulic properties. The grain-size distribution modifies the response of flow properties in terms of frictional shear resistance and pore-fluid pressure (Wang, et al., 2018). Fine grains content governs the rheology, while the coarse grains are responsible for macroscopic appearances such as the suspension of boulders on the flow surface, and the configurations of the surge front (Yong, L., et al., 2013). To estimate the impact force of debris flows, we used the models proposed for structural mitigation that are divided into hydraulic and solid collision. The hydraulic model (Fi) is classified as hydro-static and hydro-dynamic as described in equation 7. The analytical analysis is focused on the contribution of the first component of equation 7 that corresponds to hydrodynamic impact force. 𝐹𝑖=𝑎𝜌𝑑𝑒𝑏𝑟𝑖𝑠𝑣2ℎ0𝑤+0.5𝑘𝑔ℎ02𝑤 (7) Where a is the pressure coefficient, ρ is the density of the debris flow in kg/m3, and v is debris velocity at impact in m/s. The second term is the hydrostatic force which has the static impact coefficient k, and gravity g. Both terms have in common the variables of debris thickness h0, and debris width w, in meters. However, this force can be understood as a force per unit area, Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 32 transforming the force equation into a minimum value of pressure (pi) with a factor of ½ as shown in equation 8, or a maximum pressure, pmax (equation 9). 𝑝𝑖≈12𝜌𝑑𝑒𝑏𝑟𝑖𝑠𝑣2 (8) 𝑝𝑚𝑎𝑥≈𝑎𝜌𝑑𝑒𝑏𝑟𝑖𝑠𝑣2 (9) The empirical factor (a) depends on the flow type, where values about 2.0 are recommended for laminar flow and fine-grained, but for coarse-grained materials, the value must be higher than 4.0 (Hübl, et al., 2009). Rebaixader site has a high concentration of sediments with a wide granulometry, so 2.5 will be considered for the increase factor in equation 9 (pmax). According to the previous equation, the variation of the impact pressure as a function of mean velocity is plotted. Figure 11 shows the behavior of impact pressure pi and pmax as a function of mean velocity with a constant terrain slope of 30°. The mean velocity of the plot is based on the outcomes from Voellmy with entrainment simulation along the flow trajectory. It is observed that the pressure has exponential behavior, considering the hydro-dynamics model with a factor of increase grows much faster. Figure 11. Impact pressure pi and pmax behavior as a function of mean velocity. 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 Impact pressure (kPa) Mean velocity (m/s) Impact pressure (pi) Hydrodinamic pressure (pmax) Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 33 4. Results and Discussion 4.1 Back-analysis of the 2017 Debris Flow in Mocoa The back-calculation technique was applied to calibrate and validate the parameters of the Voellmy model with entrainment in FLATModel. Because the only reference information to perform the simulations is the shape of the inundated area, initially we focus on the propagation and deposition path. Several simulations were developed to carry out a sensitivity analysis of the rheological parameters. The back-analysis covers the flow behavior along the Taruca and Taruquita creek assuming an initial volume of 1163 m3 and omitting the subsequent events. The neglect of the temporal dimension added difficulty to define a time of departure for each creek. This is because the numerical modeling starts the movement with the entire initial volume at time zero. The open sources of the geographic information system of the Colombian Geological Service (SGC) have DEMs of different resolutions. The selection criteria are to consider the terrain elevations before the event and the more detailed DEMs available (spatial resolution of 2m and 5m). A preliminary evaluation was performed using the DEM with 2m resolution to find the configuration of the rheological parameters. The drawback is that the model takes more than a day to run one simulation and the calibration requires an iterative process of simulations. That is why we selected the DEM with a cell size of 5m which was used to perform the back-analysis of the 2017 Mocoa event. The sensitivity analysis of the three main rheological parameters of Voellmy with entrainment was developed comparing the simulated path with field observation and satellite images. The best-fit simulation was obtained by μ=0.07, Cz=10.3 m½/s and φent=28.4°. Figure 12 and Figure 13 illustrate the maximum flow depth and maximum velocity respectively along the torrent where the inundation area is compared for a computational time of 1000s and 1300s. In the first perception, the simulated flow adjusts to the area registered in the field, but it seems to overflow the established polygon boundaries. Additionally, the computational time of 1000s is not enough for the flow to reach the fan, while increasing the time results in a longer path. Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 34 Figure 12. Maximum flow depth modeled for Voellmy with entrainment flow resistance law: a) Computational time t= 1000s, b) Computational time t=1300s. Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 35 Figure 13. Maximum velocity modeled for Voellmy with entrainment flow resistance law: a) Computational time t= 1000s, b) Computational time t=1300s. Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 36 Remarkably, the shape of the resulting deposit does not match the reported deposit width since the simulated flow still has a narrow width and appears channelized. This behavior ignores what happened due to the flow running into the urban infrastructure and making its way between the streets. To represent the effect of urban infrastructure the model needs to be equipped with the arrangement of obstacles that restricted the flow such as buildings, trees, or light posts. FLAT- Model by the file of domain enables to set up of the path through which flow is allowed. This aspect was not considered but it is suitable for improving the outcomes in the fan regarding future reviews. The idea for future review would be to introduce all the elements of the fan that disturb the flow (for example the buildings as seen in Figure 14) to complement the domain file with pass restrict the rule to evaluate the urban infrastructure interaction. Now, the best scenario is achieved by running t=1300s as the flow can reach the fan and give time to build up sedimentary material. In addition, this simulation provides a good agreement between the simulated total volume of 2.8x106 m3 with 3x106 m3 reported by the SGC. Figure 14. Urban infrastructure data in the Mocoa fan. Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 37 In the absence of monitoring devices along the basin, the validation of the numerical simulation outcomes was carried out by using the field reports after the event. Moreover, the optimal results are accompanied by a literature review and assessment of assumptions. Thus, it should be kept in mind that the DEM provided by SGC has inconsistent elevations reported in Pontificia Universidad Javeriana, 2017. They also concluded that despite the drawback, the available DEM is in better agreement with the observed drainage and satellite images (Pontificia Universidad Javeriana, 2017). The least consistent elevations are outlined in the fan and before the convergence point of the creeks (Pontificia Universidad Javeriana, 2017). The modified DEM was not published, and its changes were about ±1.5m according to their field observations. Consequently, we generated Figure 15 where is shown a mapping of the maximum flow depth ranging from 1m to 13m to enhance the path match. Figure 15. Maximum flow depth modeled for Voellmy with entrainment zoom in at the fan zone. The magnitude of the debris flow event under study resulting in major damages to the population and infrastructure, not only because of the large volume mobilized but also because of the size of the blocks. The transported boulders were of such a size that explosives were needed to remove them (Pontificia Universidad Javeriana, 2017). For this reason, the design of protection measures in Mocoa involves 20m high dams, and some of them are along Taruca creeks and Sangoyaco River already operating (Pontificia Universidad Javeriana, 2017). Therefore, the implementation of entrainment in the simulation suggests a success because much of the transported material was due to erosion and not only from landslides. Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 38 4.2 Back-analysis of the 2020 Debris Flow in Rebaixader Modeled results and monitored data were compared by types of outcomes. On one side the hydrographs measured by the radar sensor and the ones simulated by FLATModel at the position of this sensor were evaluated. On the other side, the observed erosion depths, which were obtained by the DEM of Difference (DoD) from the UAV surveys, were compared with the ones calculated by the entrainment modeled with FLATModel. FLATModel simulated the event at Rebaixader with three flow resistances law. Many different simulation runs were executed to calibrate the corresponding parameters of each model until getting the parameters in Table 3. The most important location in the simulation domain was at the end of the channel, where the flow-depth sensor is installed. Therefore, at this point, the flow characteristics are known, and the volume estimation is 10000 m3. Figure 16 illustrates the simulated maximum flow depth, and Figure 17 presents the maximum velocity, both for the three flow resistance laws. The maximum flow depth values can reach more than 3 m, while the range of the maximum velocity is more sensitive to the variation of the resistance law. The first approach was applying Voellmy fluid that gave a good fit of the flow characteristics with the parameter combinations of Cz=9.8 m1/2/s and µ=tanφ=0.11. The simulation improves by contemplating the effect of entrainment and therefore, the final best-fit values of the input properties are Cz=11.2 m1/2/s, µ=tanφ=0.15, φent=36.2°; and the minimum flow depth (H_min) and velocity (v_min) are established at 0.10 m and 0.50 m/s respectively. In contrast, the best-fit Bingham parameters were 0.66 kPa for the threshold basal shear stress (τ0), μm=0.1 kPa s, and ρ=2000 kg/m3. The simulations applying Bingham rheology do not give very reliable results because the behavior does not describe correctly the one observed. After adjusting the rheological parameters for each flow resistance law, the outcomes were compared (see Figure 16 and Figure 17). One of the reasons for this is attributed to the fact that the Voellmy expression of the basal shear stress requires determining a value of the terrain slope to start moving (Medina, et al., 2008). Besides, viscous Bingham parameters were calibrated, and laminar behavior was ruled out because the flow was turbulent. Nevertheless, the outcome from the calibration was not satisfactory, despite the optimization, so this restates that this rheology is inappropriate to reproduce the event. Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 39 Figure 16. Maximum flow depth modeled for the three different flow resistance laws: a) Bingham, and b) Voellmy without entrainment. c) Voellmy with entrainment. Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 40 Figure 17. Maximum velocity modeled changing the flow resistance law: a) Bingham, b) Voellmy without entrainment. c) Voellmy with entrainment. Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 47 Based on the available Digital Elevation Model (DEM) of 2019 with a cell size of 1x1m, we extracted a longitudinal profile of terrain slope angles. Besides it is considered to take a standard value of internal friction angle for mixtures of gravel-sand with few fines of 35° and debris density of 2000 kg/m3. Also reviewing the study of the granulometric properties, we found the density of the solids in the Rebaixader basin is 2590 kg/ m3. The incorporation of the above information in equation 10 allows us to generate a distribution of critical radius. Once the distribution of the critical radius is obtained, Figure 23 is developed where it is observed the correlation between the critical radius and the mean velocity using the minimum and maximum impact pressure formulation. Additionally, it can be observed in Figure 20 that the missing blocks when the orthophoto in 2019 and 2020 were compared. Through the simulation with Voellmy with entrainment it is possible to know the velocity when the maximum flow depth impacts each identified block at the channel. Also, the radius of each boulder was set up with the visual estimation of the orthophoto. The boulders are included in Figure 23 distinguishing two types of marks (stable and mobilized) and considering an uncertainty of 20% because of the upstream block surface covered by sediment. All the mobilized blocks are above the curve of velocity associated with minimum impact pressure (pi). One of them required a higher velocity as well as a hydrodynamic impact. Regarding the stable ones, it is observed two blocks are above the curve related to minimum impact pressure. This means the debris flow would have needed more velocity at the moment of impacting these blocks. Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 48 Figure 23. The critical radius as a function of mean velocity for a terrain slope of 30° identifies the critical radius for stable and mobilized blocks during the event with an associated error of 20%. A practical application of all previous results may be indicating the spatial distribution of the critical radius as shown in Figure 24. The investigated case study can be mapped by critical radio (Figure 24) to predict the zone where eroded material is added more easily. The intensely red areas in Figure 24 are mostly contained in the upper part of the scarp and in the channel where the critical radius is an order of magnitude above the meter. This agrees with the fact that the terrain slope in the scarp is the highest and the volume grows rapidly. In this investigation, we focus on the erosion of the channel because of the availability of information. Thus, it is possible to post-process the erosion depth modeled after the identification of the big boulders and the bedrock. 0 2 4 6 8 10 12 14 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Mean velocity [m/s] Critical radius [m] Hydrodinamic pressure (pmax) Impact pressure (pi) Stable Mobilised Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 49 Figure 24. Spatial distribution of critical radius along the Rebaixader basin. Determination of the entrainment is a key step in the prediction of debris flow magnitude and behavior with the difficulties of obtaining data on entrainment depth, and then correlating these data with the flow resistance law parameters (Jakob & Hungr, 2005). One challenge of the simulation of debris flow is the prediction of the volume without the entrainment of sediment. The implementation of entrainment in a runout model can improve the quality of the prediction of flow patterns due to better accuracy of the flow depth and discharge of the flow (Frank, et al., 2015). Generally, the entrainment is caused by erosion and bed destabilization as a result of drag forces acting at the base of the flow (Jakob & Hungr, 2005). Another important fact is the dependency of the entrainment on the local terrain slope. In consequence, the threshold of the terrain slope to start the erosion may change from one event to another, or between individual surges (Jakob & Hungr, 2005). The mapping of critical radio is a way to characterize vulnerability from debris-flow impact based on the destructive ability of the flow. This method is convenient and repeatable to estimate the most threatened areas within a hazardous region from debris flow. Therefore, the assessment provides useful information to support landslide risk management. More often the quantitative debris flow risk assessments form the basis of decision-making on the engineered mitigation measures (Jakob, et al., 2012). Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 50 5. Conclusions Entrainment during debris-flow events is an important aspect of hazard assessment and the calibration of rheological and entrainment parameters is a complex task. The results of this study confirm the importance of debris-flow modeling to understand and describe the flow dynamics using back-analysis. The numerical code FLATModel was applied to two real cases in Rebaixader and Mocoa. The reconstruction of the events involved available data from previous studies, field measurements, and monitoring data. The historical disaster event of 2017 in the Mocoa basin occurred because of four days of highintensity rainstorms during the rainy season (La Niña event). Other factors contributed to the scale of the damage in terms of property loss and ecological environment. One of the major factors is hillslope instability added to the erosion process along the torrent. The present work has only been performed in the Taruca and Taruquita Creeks focusing on the mass movements which correspond to debris flows. Several simulations were required to adjust the Voellmy fluid model parameters with entrainment and to obtain the best fit. The final selection of the rheological parameter was μ=0.07, Cz=10.3 m½/s and φent=28.4°. The Digital Elevation Model (DEM) of the extent before the event was necessary for the back analysis with a reasonable spatial resolution of 5m, although some uncertainties were reported. The temporal sequence of different mass releases represents a limitation to simulate what happened. Another drawback is related to the absence of exact measurements of the flow depth or flow velocity due to the lack of instrumentation. Despite these uncertainties, the simulated final volume setting Voellmy with entrainment coincides rather well with data reported by the SGC and previous studies based on field observations. Regarding the Rabaixader case, the implementation of different flow resistance laws was applied to FLATModel. The Rebaixader DEM has better resolution than Mocoa DEM due to monitoring with the geomatic technique of digital photography from UAV. The simulation results indicated the best fit is achieved by including the effect of basal erosion along the flow trajectory employing Voellmy with entrainment parameters (Cz=11.2 m1/2/s, µ=tanφ=0.15, φent=36.2°). Thus, a real benefit of monitoring systems is seen in the sense of permitting the comparison Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 51 between measured and modeled data. Another advantage is the possibility to assess the DoD technique which confirms cell-by-cell the change in elevation between pre- and post-event topography. The results of DoD are contrasted with the final topography obtained from the simulation. This admits to the conclusion that debris flows are formed by the progressive incorporation of sediment material from the erodible bed during the entrainment process. The analysis of the impact and transport of boulders established a baseline to understand the sensitivity analysis of the rheological parameter φent. The video recording of the 2020 event let us see many big boulders in the flow front and the orthophotos of 2019 and 2020 confirm that there are missing blocks along the torrent. This raises the question of the maximum boulder size that can be transported which is not uniform throughout the basin. The impact and transport capacity is mainly influenced by the terrain slope and the flow velocity. This study describes the critical radius to illustrate the susceptible areas where the flow develops a more destructive capacity and can mobilize a larger boulder size. Regarding future research lines, it is proposed the study on the stabilization of hillslopes and controlled drainage of debris flows. Part of the following works should focus on the entrainment of bed material as characteristic feature behavior of debris flows. Considering debris flows gain much of their mass and destructive power by entraining material, the evaluation of the critical radius is promoted. Because the debris flows mitigation measures are still in innovation processes, a method is needed to determine the most suitable location along the torrent to minimize damage. Moreover, the prediction of the debris flow path must be evaluated by the incorporation of an accurate representation of the topography. 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Takebayashi, H. & Fujita, M., 2020. Numerical simulation of a debris flow on the basis of a twodimensional continuum body model. Geosciences, Volume 10(2), p. 45. Wang, B., Li, Y., Liu, D. & Liu, J., 2018. Debris flow density determined by grain composition. Landslides, Volume 15, pp. 1205-1213. Yong, L.; Xiaojun, Z.; Pengcheng, S.; Yingde, K.; Jingjing, L., 2013. A scaling distribution for grain composition of debris flow. Geomorphology, Volume 192, pp. 30-42. Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 55 Annexes Figure 25. Flow depth map of 2017 debris flow event in Mocoa (Medina, et al., 2017). Molano, 2023 Numerical modeling of debris-flow behavior. Application to Rebaixader (Pyrenees) and Mocoa (Colombia) 56 Table 5. Comparison of the discharge modeled (FLO2D) and empirical results with the methods Wudu and Chezy. The sections are placed in Taruca(Tc) and Taruquita creeks (Tq), and Mulato River (Mt) (Ruiz, et al., 2018). METHOD SECTIONS SECTIONS FLO2D EMPIRICAL RESULTS TERRAIN Medina, et al., (2017) Ruiz, et al., (2018) Q Q U DISTANCE (m) (m3/s) (m3/s) (m/s) Wudu Tc1 Tc1-5 55.66 2920.7 17.4 680 Tc1b Tc1b-4 1931.3 18.5 1200 Tc2 Tc2-3 110 1238.7 10.8 1900 Tc3 Tc3-6 2425.8 11.6 2250 Tc3b Tc3b-7 1652.1 11 2750 Tc4 Tc4-8 1312.3 9.4 2990 Tc5 Tc5-9 362 913.9 9.2 3500 Tq1 Tq1-1 165 473.7 5.9 2100 Tq2 Tq2-2 222 355.6 6.1 2400 Mt1 Mt1-12 236.4 5.6 10600 Mt2 Mt2-13 700.1 5.5 11000 Chezy Tc1 Tc1-5 108 1976.4 11.8 680 Tc1b Tc1b-4 1391.7 13.3 1200 Tc2 Tc2-3 1365.9 11.9 1900 Tc3 Tc3-6 390 2986.7 14.2 2250 Tc3b Tc3b-7 2093.1 14 2750 Tc4 Tc4-8 1274.2 9.2 2990 Tc5 Tc5-9 909.5 9.1 3500 Tq1 Tq1-1 588.6 7.4 2100 Tq2 Tq2-2 416.6 7.2 2400 Mt1 Mt1-12 137 388.1 9.2 10600 Mt2 Mt2-13 217 1099.8 8.6 11000