Erosion after an extreme storm event in an arid fluvial system of the southern Atacama Desert: an assessment of magnitude, return time, and conditioning factors of erosion caused by debris flows

We have calculated a mean erosion of 1.3 mm caused by an individual storm event in March 2015 that impacted a large mountainous area of the southernmost Atacama Desert. The calculated erosion agrees with millennial erosion rates and with return time of high sediment discharge events previously reported in the study area. Here, we quantify for the first time the contribution of an individual extreme storm event to long-term erosion rates in the Atacama Desert. This is significant because erosion rates, related to high sediment discharge events in arid fluvial systems, are hard to measure with sediment load 5 due the destruction of gauges by devastating flashfloods and thus have not been directly measured yet. During the March 2015 storm, debris flows were reported as the main sediment transport process. Erosion of gullies and channels are the main source of sediments that finally generate debris flows that reach the tributary junctions and the trunk valleys. The sediment yield to the tributary outlets strongly depends on the hydraulic capacity of catchments to store sediments in the drainage network between storms. Larger tributary catchments, high hydrological hierarchy, low topographic gradient and gentle slopes are the 10 most susceptible catchments to generate debris flows that reach alluvial fans at any storm event from large debris volumes stored in the drainage network. Our findings better assess debris flow susceptibility of arid catchments, which is significant for the southernmost Atacama Desert valleys because human settlements and industries are mostly established in alluvial fans.

Immediately after the March 2015 storm we performed a field survey in El Huasco river valley. We observed (1)  Width (w) and thickness (t) of fan toes were measured in the field with a measuring tape for 16 alluvial fans, whereas their axial length (l) was measured on the available satellite imagery. Width and length for the rest of the fans (33) was measured from RapidEye images. In these cases, we estimated 1 meter of debris flow thickness on average for each fan based on mean field observations. The volumes have been corrected with a bulking factor which considers a porosity value of 30% (Nicoletti and Sorriso-Valvo, 1991). 20 We have characterized the erosion possesses within catchments from both fieldwork observations and the analysis of optical satellite imagery retrieved from Planet Team (2017). The available images of 3m/pixel for Planet Scope imagery and 6.5m/pixel for RapidEye imagery does not assist in the identification of rills and small gullies. Thus, field observations are crucial to identify these erosion processes.
Topographic attributes of catchments were selected in order to analyze their influence on debris flow generation and erosion 25 processes after the March 2015 storm. In order to characterize the tributary catchments, the topographic attributes were selected based on their influence on different process such as peak flow generation and debris storage (Strahler, 1958;Melton, 1965;Howard and Kerby, 1983;Wilford et al., 2004): Area, Length (straight-line between tributary outlets and its more distant point), Maximum elevation, Gradient, Average Slope, Gravelius index (Shape), Hypsometry, Melton ratio (index of roughness that normalizes relief by area; Melton (1957)), Drainage density, maximum Strahler order, concavity, and steepness index of 30 the main thalweg.
A statistical analysis was calculated in order to find outliers or anomalies in the topographic attributes that might control debris flow generation in tributary catchments. The significance of each attribute in debris flows generation is determined by an Analysis of variance (ANOVA). The ANOVA determines if the mean values are similar between the catchment classes that generated debris flows against catchments that did not generate debris flows. The proposed tests consisted in splitting the total data variance into several components (between groups and within groups) and in comparing these components with a Fisher mean test with a critical value of 0.05 (Box et al., 1978;Davis, 2002  with different sediment to water ratios. Debris flows were followed by a strong incision that facilitated sediment transport 30 from alluviated channels downsystem. When these debris flows lost confinement at the outlet of the tributary catchments their deposition occurred (Fig. 2fg). Hillslopes or gravitational landslides and rockslides are the main sediment sources that characteristically fill these channels within storm periods and after storm events. The large volume of sediments is enhanced by the low-frequency of extreme storm events that usually impact the area. Hence, the time return of extreme storm events in this arid zone ranges from 1 event/ 200 years to 1 event/ 40 years (Ortega et al. (2019) and references therein) facilitates the storage of sediments in inter-storm periods and thus prepare these channels to yield sediment downsystem at any extreme storm event that impacts the area. This geomorphological 'behaviour' is known in literature as transport-limited catchments (Bovis and Jakob, 1999) and is characteristic of arid landscapes.
Size Factor and Relief Factor show an inverse correlation for catchments that generated debris flows and for catchments where clean water flows flushed downsystem (without debris flows generation) (Fig. 5a). The inverse correlation is also ob- served in the percentage of catchments that generated debris flows because the percentage increases with Size Factor while decreases with the increase of Relief Factor (Fig. 6ab). In fact, debris flows were present only in 18% of very small and low hierarchical catchments (low values of Size Factor, smaller than 0.25). In contrast, debris flows were present in 57% of large and high hierarchical catchments (high values of Size Factor, greater than 0.75). Debris flows occurred only in 14% of the catchments with high mean slope values and high topographic gradient (high-Relief Factor, greater than 1.75) whilst in 51% 5 of the catchments with low slope values and low topographic gradients, debris flow occurred (low-Relief Factor, minor than 1.25). These results suggest that debris flows were generated from larger and high hierarchized catchments with low topographic gradients and low mean slopes, whereas from smaller and stepper catchments debris flow were sparsely generated (Table 1).
The six topographic attributes (Area, Length, Strahler Order, Slope, Gradient, and Melton ratio) considered in the two 10 conditioning-factors are reclassified to 0, 1 and 2 depending on the percentage of catchments favorable to debris flow generation. Finally, the weighting factor calculated by the PCA resulted in a normalized catchments-clustering is added (Fig.   7).
Size Factor and Relief Factor also shows a positive correlation with volumes of debris flow deposits (Fig. 8ab). Volume of sediment smaller than 6,000 m 3 were supplied from small and low-hierarchical catchments (low values of Size Factor, 15 minor than 0.25), whereas from large and high hierarchical catchments (high values of Size Factor, greater than 0.75) volumes were higher than 6,000 m 3 . On the other hand, sediment supply was smaller in catchments with high mean slopes values and high topographic gradients (high-Relief Factor, greater than 1.75) rather than in catchments with low slopes values and low topographic gradients (low-Relief Factor, minor than 1.25). Therefore, topographic attributes involved in the two conditioningfactor are also significative in debris flow deposit volumes.
MeanSHn and IQRSHn present a weak correlation in both catchments' types (catchments that generated debris flows and which not) (Fig. 5b). Additionally, no correlation was reported between MeanSHn-IQRSHn and Size-Relief Factors ( Fig.   5c-f). The percentage of catchments generating debris flows does not vary significantly in relation to the range of MeanSHn and IQRSHn (Fig. 6cd). The latter suggests that unaltered-rock strength represented by MeanSHn and weathering degree been reported in agreement with previous reports in arid zone hillslopes response to rainfall that have quantified the great contribution from gullies from 50 to 80% of the overall sediment yield ([Poesen et al., 2003).

10
The selective generation of debris flows on tributary catchments has been reported previously in Andean catchments (Colombo, 2010;Lauro et al., 2017). This random activation might be explained by different coupling degrees between catchments and trunk valley (Fryirs et al., 2007;Mather and Stokes, 2017)  Susceptibility assessment to debris flow generation can be evaluated in terms of its topography attributes of each watershed, almost in the first phase of risk study inhabited areas (Wilford et al., 2004). In one sense, susceptibility of debris flow generation in the southern Atacama Desert is linked to the capacity of sediment-store in drainage network during the inter-storm  considered with caution, and rather its order of magnitude should be considered.

Conclusions
The debris-flows generation in arid valleys is controlled by the amount of available sediments stored within the catchments of the southernmost Atacama Desert. Thus, the efficiency of catchments to store sediments which depends in topographical attributes dictates whether the catchments are activated or not during extreme storm events. The sediment is stored during the 25 inter-storm periods and therefore is susceptible to be transferred by debris-flows at any extreme storm that impacts the area. The alluviated channels are the main entrainment sediment zones during extreme storms whilst debris-supply from landslides on hillslope is not necessary for the debris flow generation in these arid catchments during extreme storm events. The instantaneous increase in run-off during a storm and the entrainment sediment has been associated to a high altitude of the zero-isotherm and the heterogeneous cell storms distribution. Studies that incorporate as predictors the classification of catchment-clustering 30 proposed here could be implemented to debris flow susceptibility assessment in arid catchments of the Atacama Desert, because this assessment are scarce and usually require exhaustive field-work observations.
Recently there has been some consensus that storms such as March 2015 in Atacama Desert occur on average every 100 years for the last 5,500 years (Ortega et al., 2019). Thus, the erosion rates associated with these storms are of the order of 10-2 mm/year in El Huasco river valley if we consider the erosion measurements after March 2015 storm. The order of magnitude of erosion is the same as the erosion rates calculated over the long term in the Huasco River valley (Aguilar et al., 2014). This indicates that these storms have a relevant influence on the erosion and evolution of these arid fluvial systems of the Atacama 5 Desert. It is these storms that denude effectively the coverage of sediments in the arid catchments of the southern Atacama Desert. However, the influence of the different surface processes in the preparation of the sediment cover before storms has yet to be characterized. New direct data, including quantitative geomorphological analysis of erosion, sedimentation and soil formation are required to quantify and have a knowledge of the rates, the routes, and the magnitudes of each process in the landscape evolution of the Atacama Desert.