Over the past decades, several numerical models have been developed to understand, simulate and predict debris flow events. Typically, these models simplify the complex interactions between water and solids using a single-phase approach and different rheological models to represent flow resistance. In this study, we perform a sensitivity analysis on the parameters of a debris flow numerical model (FLO-2D) for a suite of relevant variables (i.e., maximum flood area, maximum flow velocity, maximum height and deposit volume). Our aims are to (i) examine the degree of model overparameterization and (ii) assess the effectiveness of observational constraints to improve parameter identifiability. We use the Distributed Evaluation of Local Sensitivity Analysis (DELSA) method, which is a hybrid local–global technique. Specifically, we analyze two creeks in northern Chile (

In steep mountain environments, intense and localized storms can trigger the sudden movement of sediments, generating flash floods with solid volumetric concentrations up to 40 %–60 %

Over the last decades, numerical models have emerged as a powerful tool to understand the behavior and magnitude of debris flow events, since they allow for the quantification of key variables used by engineers and decision-makers for risk management

The use of debris flow models for practical problems typically requires the implementation of single-phase numerical models

How sensitive are debris flow model results to uncertain – and typically fixed – rheological parameters?

What are the most effective post-event measurements to constrain the parameter search towards more realistic simulations?

We choose two ephemeral creeks located nearby in the upper Huasco River basin, Acerillas and La Mesilla (Fig.

The Acerillas creek (15 km

Flow discharge data at the outlet of each creek were obtained from a distributed hydrological model, HEC-HMS (Hydrologic Engineering Center Hydrologic Modeling System) version 4.2

Calibration records for stream gauge stations

We use the two-dimensional FLO-2D debris flow model

Sensitivity analysis (SA) is a powerful tool to characterize the effects of variations in input factors on environmental-model responses

In this work, we apply the Distributed Evaluation of Local Sensitivity Analysis (DELSA) method

First-order sensitivities are obtained using local gradients that quantify the sensitivity of a modeled output

Local sensitivities can be analyzed in a disaggregated manner – through their cumulative frequency distribution across the parameter space – or aggregated by computing a specific statistical property, e.g., the median of all local sensitivity measures for a particular pair of parameter and target variables. We use both approaches to analyze SA results.

In this paper, we focus on the effects of debris flow model parameters on four response variables: maximum average runoff speed

The FLO-2D parameters considered for DELSA are those that describe the fluid rheology (Table

The detention coefficient SD is a model parameter that controls flow detention. The FLO-2D user's manual and previous studies

Debris flow concentration is assumed to vary with streamflow between a minimum concentration

Values range of the model parameters. P: poise; dyn: dyne.

We explore the effects of parameter uncertainty on simulated debris flow variables at the two case study creeks. We also examine the utility of using reference values for specific variables to constrain the search of physically plausible parameter sets. Such values are obtained from a reference simulation conducted by

Based on the reference simulation, we choose reference values of

Parameter values for reference models on

First, we seek to identify the minimum sample size

Effects of sample size

Figure

Figure

DELSA sensitivity indices (synthetized as the median from the cumulative frequency distribution) for all parameters and model responses. Results are displayed for Acerillas (red) and La Mesilla (black) creeks, and the sampling uncertainty (bootstrapping with 1000 times resampling) is indicated by boxplots. The vertical bold line in the boxplot is the median; the body of each boxplot shows the interquartile range (

As expected, the simulated deposited volume Vol

Another parameter that provides large sensitivities – especially in simulated mean flow velocity

The large sensitivities in model response to variations of

Our results show some differences with related previous work.

Figure

Effects of parametric uncertainty in normalized model responses for the original parameter sample (top panels) and alternative observational constraints – flow velocity (FVEL), flow depth (FH), flood area (FAREA) and sediment volume (FVOL) – and joint area–volume constraint (FAREAVOL). Results are displayed for Acerillas (black) and La Mesilla (red) creeks. The hatched area for

Figure

Most simulations overestimate deposited volumes and flow depth, especially at Acerillas. For flow velocity, the ensemble of parameter sets provides mixed results in both creeks, with underestimation in most cases (median values lower than the reference values); however, there are still several parameter sets that produce an overestimation of flow velocity. The results obtained for maximum area reveal differences among both creeks: in Acerillas, most parameter sets tend to overestimate the flood area, whereas most simulated values are within the expected range at La Mesilla. This could happen because Vol

Figure

The maximum flood area and deposited volume are relatively easy to measure and are probably the most used post-event measurements for calibrating debris flow models

Figure

Effects of applying a flood area–volume observational constraint (FAREAVOL) on parameter identifiability. Results are displayed for Acerillas (black) and La Mesilla (red) creeks. The vertical bold line in the boxplots is the median; the body of each boxplot shows the interquartile range (

The reference SD value is close to the upper range in La Mesilla after applying the FAREAVOL constraint, and also much larger than the resulting maximum values filtered at Acerillas. This result is somewhat expected, since SD does not provide large model sensitivities in that domain. Similarly, the reference

Figure

The main goal of this study was to characterize the sensitivity of model responses to variations in uncertain rheological parameters, using only independent information on parameter values (i.e., the situation comparable to Sobol, as proposed by

We performed a sensitivity analysis on the parameters of a widely used numerical debris flow model (FLO-2D) and assessed the effects of applying observational constraints on parameter identifiability. Our study domains are two morphologically different ravines, Acerillas and La Mesilla, located in the Atacama region (

We found that

The comparison between the original model parameter ranges (

We obtain that SD strongly affects model results at La Mesilla, having also large effects on simulated deposited volumes at Acerillas. Moreover, this study provides evidence that SD is one of the most important parameters controlling flow behavior and could possibly surrogate rheology in the model

Future investigations should aim to improve the structure of debris flow models and hence achieve better simulations of deposition and erosion processes, stopping phases, and changing rheologies. Further, the development of computationally frugal methods to improve the understanding of parameter interactions in environmental models emerges as an attractive avenue for future research.

Lidar topography and used streamflows are available at

GZ, AG, PM and SM were involved in the conceptualization. GZ, PM and SM contributed to the methodology and analysis and drafted the paper. GZ configured the model, conducted simulations, analyzed the results and made the figures. GZ, AG, PM and SM contributed to writing, review and editing.

The authors declare that they have no conflict of interest.

We thank Tomás Gómez and Miguel Lagos for contributing the streamflow data used in this study and Martin Mergili and Mary Hill for their thoughtful comments and suggestions for improving this article. We also thank the support of the Faculty of Physical and Mathematical Sciences, Universidad de Chile, through the Department of Civil Engineering and “Centro de Investigación, Desarrollo e Innovación de Estructuras y Materiales” (IDIEM). Finally, the authors thank the Chilean Ministry of Public Works (MOP-DOH) and the CONICYT/PIA (project no. AFB180004). Pablo A. Mendoza acknowledges the support of a Fondecyt postdoctoral grant (no. 3170079).

This research has been supported by the Faculty of Physical and Mathematical Sciences of the Universidad de Chile through the Advanced Mining Technology Center (AMTC).

This paper was edited by Thomas Glade and reviewed by Mary Hill and Martin Mergili.