faDebrisFOAM validation using field data surveyed in Crucecita (Chile) alluvial fan for the event of 13 th May 2017

. The openFOAM solver faDebrisFOAM was recently developed to simulate debris flows with the finite area method. This new solver includes, among other capabilities, a variable density for the solid-liquid mixture, erosion and deposition processes, and a terrain modification algorithm. To test the performance of this new solver, we simulate the debris flow event that occurred in the Crucecita alluvial fan on the 13th May 2017 in the Atacama Desert, Chile. Thanks to pre-and post-event topographies, we have an accurate measure of the morphological changes that took place. Comparing the field data and our numerical model results shows that faDebrisFOAM can reproduce the main flooded, eroded, and deposited areas. Once the model is calibrated, we study the behavior of the terrain modification algorithm. Finally, we discuss the advantages of using this model to reproduce erosion and deposition processes together with changing rheologies for a debris flow event.


Introduction
Due to climate change, increases in temperatures, droughts, and extreme precipitation events, an increment of debris flow triggering has taken place. A significant part of the Chilean territory is exposed to debris flows due to the presence of the Andes Cordillera that runs along all of Chile. In 2015, a catastrophic debris flow event impacted the Atacama Desert in northern Chile. In the following years, smaller events occurred in more specific parts of Atacama.
Garces et al. [1] characterized the behavior of Crucecita creek for the debris flow event that occurred in 2015 using the FLO-2D commercial software. The authors concluded that, despite the correct representation of the event in general terms, this numerical model should improve how it resolves the erosion and deposition processes and changes in rheology, to achieve better representations of the sediment transport processes in alluvial fans.
This work presents the use of a recently developed model called faDebrisFOAM [2]. This solver is validated by employing accurate field measurements of the topographic changes observed in Crucecita for the 13th May 2017 event. Furthermore, a comparison of the field data and our numerical model results is presented here. Finally, it is concluded about the advantages that this solver has in representing erosion and deposition processes, added to the fact that it can consider changes in the rheology simultaneously. * Corresponding author: agarces@uchile.cl

Study site
Crucecita basin has an area of 13 km 2 , being a lateral tributary to the El Carmen River in the southern limit of the Atacama Desert. This creek has been previously studied due to the debris flows that occurred in 2015 [1,3]. As a result of the previous studies, high-resolution topography was surveyed in the confluence zone with the river, including Crucecita's alluvial fan.

2017
In May 2017, another precipitation event occurred at Crucecita creek. While El Carmen Basin receives 60 mm per year on average, this rainfall event accumulated 188 mm, with maximum intensities of ~6.7 mm/h. As a result of the 2015 event, a gully incision developed in the Crucecita alluvial fan. In 2017, this incision, which connects the apex with the river, conveyed flows from the creek to the main river. After the 2017 event, a new high-resolution topography was surveyed to characterize the main topographic changes that occurred in the creek. Figure 1 shows satellite images of the pre-and postevent conditions. The incision that connects the apex and the river widened during the 2017 event. As a result of the sediment coming from the creek, a deposit was generated in the river confluence, blocking the original river path. Consequently, the river was forced to find a new course around this lobe (avulsion).

Governing equations
González [2] implemented the faDebrisFOAM solver in openFOAM to represent the movement of shallow debris flows over slightly curved surfaces. This model was based on [4,5], uses the method of finite areas, and inherits functions from its predecessor model faSavageHutterFOAM [5]. Gonzalez [2] made important improvements such as (1) variable density, (2) terrain modification algorithm (TMA), (3) hydrograph for the inlet boundary condition, (4) incorporation of erosion, deposition, and friction equations for debris flows.
To include these improvements, González [2] developed the system of equations (1) to (5) presented below. Equations (1) and (2) correspond to the continuity equations for the solid-liquid mixture and water, respectively. Equations (3) and (4) conform to momentum equations in their tangential and normal components, respectively. Equation (5) considers the processes of erosion and deposition for the modification of the terrain.
where is the density of the solid-liquid mixture, ℎ is the height and ̅ the flow rate. Despite being a model whose equations have been vertically averaged, the velocity vector continues to be a three-dimensional vector because the flow moves along a threedimensional surface. corresponds to the volumetric concentration of water. These variables are defined at the centroid of each element and vary in time .
The area S = ∂V corresponds to the area of the control volume V, while SB corresponds to the lower boundary of this control volume. This border conforms to the terrain.
In equations (3) and (4), and correspond to the tangential and normal components of the acceleration of gravity , is the basal shear stress and the basal pressure.
corresponds to the normal vector to the surface . With , ∇ = ( − ) ⋅ ∇ and = ( ) ⋅ are defined, which correspond to differential operators tangential and normal to the surface, respectively.
faDebrisFOAM incorporates the ability to modify the terrain using the Terrain Modification Algorithm (TMA). To consider ground modifications, it is necessary to know the density of the substrate and the volumetric concentration of water in the substrate . When this algorithm is activated, the boundary SB moves with a speed , defined as positive pointing out of the control volume. This velocity is calculated from the entrainment of sediments rates into the flow and the rate of deposition , such that = − .
For the friction models, faDebrisFOAM includes the Manning, Quadratic-rheology, and Voellmy-Salm models. This solver also includes seven entrainment models and four deposition models. They can be reviewed in [2].

Field data characteristics
We characterized the morphological alterations during the May 2017 event at the confluence of the Crucecita stream with the El Carmen River. The characterization was made by high-resolution sequential topographies. Through the difference of these sequential topographies, we obtained the so-called DEM of Difference (DoD) [6]. DoDs are helpful in measuring the eroded and deposited volumes and their distribution.
The pre-event topography is a LiDAR topography with a resolution of 1m/pixel and has an associated error of σ1 = 0.07m. On the other hand, the post-event topography results from a photogrammetric UAV survey and has an associated error of σ1 = 0.16m. Consequently, the generated DoD has an associated error propagation of =0.17 m. A coregistration procedure is necessary to remove the possible offsets of our topographies prior to differentiating the DEMs [7].
We used demcoreg for the DEM coregistration. Demcoreg reduces the random error from 0.23 m to 0.15 m. This reduction in the random error highlights the importance of the coregistration procedure to keep the minimum detection threshold as small as possible. Since the error propagation and the random error are similar, the minimum detection threshold is defined as 0.2 m.

Simulation and validation of the May 2017 event
For the numerical simulation, on the other hand, we decided to use the Voellmy-Salm equation for the resistance law, the RAMMS model [8] for the sediment entrainment, and the Fagents & Baloga [9] model for the deposition rate of the sediment. These models contain calibration parameters found by trial and error, comparing the field and simulated variables such as the final flooded areas and the estimated flow heights.

Results
During the 2017 event, the Crucecita alluvial fan suffered an erosion of the channel slopes but deposition in the channel bed. In the original channel of the El Carmen River, a deposit up to 6 meters high pushed the river path towards the opposite side of the valley, generating an adjacent erosion of up to 6 meters. At the alluvial fan toe, the original channel of the El Carmen River was blocked, so the river sought a new path, which is identified in Figure 2.a as a red area due to the erosion generated.
The debris flow simulation using faDebrisFOAM is presented in Figure 2.b. Here, the volumetric sediment concentration of the river and the debris flow are shown. The debris flow coming from Crucecita creek has a CV=0.4, whereas the river starts at its inlet with CV=0. At the confluence, the mixture of these two flows is not instantaneous. Here, the debris flow remains in a welldefined lobe of high sediment concentration. Conversely, the river is forced to flow over the opposite side of the valley without increasing its sediment concentration. The mixing of both flows starts downstream from the confluence point, where the volumetric sediment concentration is around 0.1.

Conclusions
Having sound field evidence of a debris flow event is difficult, especially in areas such as the Atacama Desert, where debris flow events are not frequent. The DoD presented here gives us a unique possibility to validate numerical models and study the processes that take place in the confluence of a debris flow with a trunk river.
Since faDebrisFOAM is a recently developed model, its validation is still a work in progress. Here, erosion and deposition processes simulated by the model are compared against the field data showing a good correlation. Interestingly, the model shows an inefficient mixing process where most of the sediment remains at the alluvial fan toe, while the rest continues downstream, changing the sediment concentration of the river. This was also observed on the field but needs further investigation to validate the mixing process.