E3S Web of Conferences 415, 01018 (2023)
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https://doi.org/10.1051/e3sconf/202341501018

Debris flow susceptibility mapping in Colorado Front Range,
USA: a comparison of physics-based and data-driven
approaches
Te Pei1, and Tong Qiu1*
1Department of Civil and Environmental Engineering, The Pennsylvania State University, University Park, PA 16802, USAAbstract. This study used an inventory of debris flow triggered by a storm event in Colorado Front Range
as an example to compare the capability of data-driven and physics-based approaches for regional-scaledebris flow susceptibility mapping (LSM). Nine debris flow contributing factors were collected for thepresent study based on the availability of geophysical data in the study area. These contributing factors
represent hillslope geometries, surface hydrology, and soil conditions. For the physics-based approach, theinfinite slope model was used to directly determine the debris flow susceptibility for the study area by
calculating the factor of safety (FS) based on parameters derived from geophysical data. For the data-driven
approach, an artificial neural network (ANN) was developed to predict debris flow susceptibility for thestudy area by learning relationships from the contributing factors using the debris flow inventory. The results
showed that both physics-based and data-driven models predicted debris flow susceptibility in the study areawith relatively high accuracy; the data-driven approach outperformed the physics-based approach as it could
extract complex features which the physics-based approach did not consider.

1 Introduction
Debris flows are common natural disasters around theglobe. Understanding where these landslide hazards arelikely to occur is essential for hazard mitigation andprovides situational awareness for the public.
Landslide susceptibility mapping (LSM) measures
the spatial distribution of landslide risk given a
combination of contributing factors [1]. Methods for
LSM can be broadly classified into physics-based anddata-driven methods. The physics-based methods relyon the physics understanding of slope failure in soil
mechanics. For example, the infinite slope model has
been widely used to evaluate landslide risk for rainfallinduced shallow landslides on natural terrain (e.g., [24]). However, accurate input parameters for physicsbased approaches, such as soil strength and hydrologicalparameters, are relatively difficult to obtain on aregional scale. In addition, the performance of physicsbased approaches may be limited due to simplified
physical assumptions. On the other hand, data-driven
approaches establish functional relationships between
landslide risk and contributing factors based on
observations of landslide occurrence (e.g., [5-8]). The
research community has been currently focusing on
data-driven methods due to the recent advances inremote sensing and machine learning (ML) techniques[9].
In the present study, LSM was conducted for adebris flow-affected region in Colorado Front Range

using both physics-based and data-driven approaches.
The debris flow inventory and study area are firstdescribed in the following sections, followed bydescriptions of the debris flow contributing factors andmethodologies. Last, the performance of developed
LSM models using the two approaches was evaluatedand compared, and debris flow susceptibility maps forthe study area were produced.

2 Study area and debris flow inventoryThe Colorado Front Range is a mountain range of theSouthern Rocky Mountains of North America located in
the central portion of the State of Colorado. It is formedby orogenic uplift related to regional compression
during the Laramide orogeny in the Late Cretaceous toearly Tertiary [10]. The Colorado Front Range has abroad elevation variation ranging between 1,500 m and
4,300 m; it spans four major topographic elements andfive ecosystem zones [11, 12]. The vegetation density,
soil development, and regolith production are dependent
on the slope aspect [13]. Boulder County in theColorado Front Range area was selected as the studyarea, where 60% of the mapped debris flows werelocated in this County.
The present study used a well-documented debris
flow inventory to develop and evaluate the performanceof LSM models. A storm event in September 2013
triggered more than one thousand debrie flows acrossthe Colorado Front Range. Detailed information for* Corresponding author: tuq1@psu.edu© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0(https://creativecommons.org/licenses/by/4.0/).

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global estimation of surface soil properties based on soil
profiles and remote sensing data with a spatial resolutionof 250 m. Fig. 2 shows a contour plot of thesecontributing factors in the study area.

these debris flows was recorded based on areconnaissance through field survey and high-resolution
orthorectified satellite imagery following the storm
event. Specifically, 1,138 debris flows and 212 slides
were identified and mapped [12]. Fig. 1 presents thelocation of Boulder County and the distribution of
mapped debris flow locations.

4 Methodologies
The development of LSM models for the present study
involves several key steps, including dataset
preparation, LSM model development and evaluation,and generation of final landslide susceptibility map. Fig.
3 illustrates the workflow for the present study.

Fig. 1. Location of Boulder County and distribution of debris
flow events triggered by the 2013 storm event.

3 Collection of geophysical data
In the present study, nine debris flow contributing
factors were chosen based on the data availability andtypes of debris flow that occurred in the study area,
including elevation, slope, aspect, topographic wetnessindex (TWI), normalized difference vegetation index(NDVI), sand content, clay content, bulk density, andfield capacity. These contributing factors reflect theeffects of hillslope geometries, hydrologic conditions,and soil properties. Fig. 2 shows a contour plot of thesecontributing factors in the study area.

Fig. 3. Workflow for the present study.

4.1 Dataset preparation
For the present study, 803 mapped debris flow locationsin the study area and their corresponded values of debris
flow contributing factors were used as positive samples.
An equal amount of non-debris flow locations wererandomly sampled within the study area, excluding
those debris flow locations. These non-debris flow
points and their corresponding values of contributing
factors were used as negative samples.
4.2 Physics-based model
The infinite slope model was selected as the physicsbased model for the present study, which is commonlyused for predicting shallow landslides such as the debris
flows in this study. The factor of safety (FS) is
calculated as the ratio between the soil shear strengthand the driving force:
FS Fig. 2. Debris flow contributing factors for the study area: (a)elevation (m); (b) slope (deg); (c) aspect (deg); (d) TWI (-); (e)NDVI (-); (f) sand content (%); (g) clay content (%); (h) bulk
density (10 kg/m3); and (i) field capacity (%).

c  ( H   w h) cos 2  tan  H sin  cos (1)where h is the height of the groundwater table; H is thesoil layer thickness;  is the soil unit weight;  w is theunit weight of water; β is the slope angle; and  and c
are the soil friction angle and cohesion, respectively. For
simplicity, submerged slopes with seepage parallel tothe slope were assumed when calculating FS (i.e.,h  H ). The input parameters for the infinite slopemodel were estimated based on the debris flow
contributing factors. For example, β is based on theslope from DEM. H is estimated based on an elevationdependent relationship as [15]:Among these contributing factors, the elevation isbased on the digital elevation model (DEM) provided by
the 3D Elevation Program (3DEP) with 10-m spatialresolution. The slope and aspect were calculated fromthe DEM, representing the slope geometries and facingdirections. The TWI was also calculated from the DEM
to represent topographic control on surface hydrology.
The NDVI was calculated based on near-infrared andred bands from Landsat-8 satellite images and was used
to represent vegetation coverage. The soil information
was obtained from SoilGrids [14], which provides a2

E3S Web of Conferences 415, 01018 (2023)
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https://doi.org/10.1051/e3sconf/202341501018

Table 1 presents the AUC scores for the infinite slope
and the ANN models based on the same five-fold crossvalidation procedure. Typically, a classification modelwith AUC scores greater than 0.9 can be considered anexcellent classifier. As shown in Table 1, both theinfinite slope model and the ANN model achieved
relatively high AUC scores, indicating that the twoapproaches can be successfully applied to predict thedebris flow susceptibility in the study area. In addition,
the ANN model yielded a higher AUC score than theinfinite slope model, which can be attributed to the factthat the ANN model was able to directly extract complex
features from data based on debris flow labels, including
those hidden features the physics-based model fails toconsider.

(2)

where H and Z are the local soil layer thickness andelevation, respectively; Hmin and Zmin are the minimum
soil layer thickness and elevation, respectively; Hmax andZmax are the maximum soil layer thickness and elevation,respectively. For the present study, H min  5 cm andH max  2 m .  is estimated using sand content and an
empirical relationship from [16]. For estimating c, thesoil itself is cohesionless [17]; however, root
reinforcement in slope stability was considered. The
values of c were obtained by applying a linear
transformation to the full spectrum values of NDVI [18]by setting the minimum cohesion of value 0.0 kPa andthe maximum at 15.0 kPa.

Table 1. Cross-validation results for LSM models
ModelsInfinite slope model
ANN model

4.3 Data-driven model
From the data science perspective, the application of
LSM can be considered a classification problem wherefeatures of debris flow contributing factors are extracted
and grouped based on their relationships andcontributions to the debris flow label. For the presentstudy, an artificial neural network (ANN) with threehidden layers was used to represent a data-driven model,
which is a commonly used model in ML.

Furthermore, the developed LSM models based on
the two approaches were subsequently used to predictdebris flow risk for the study area. Figs. 4 and 5 present
the debris flow susceptibility maps using the two
approaches, where mapped debris flow locations areshown as black triangles. By comparing Figs. 4 and 5, it
can be noted that the high debris flow risk areas
predicted by both approaches generally agreed well withthe mapped debris flow locations, and the areas withhigh susceptibility but were not mapped by thereconnaissance following the 2013 event can beconsidered debris flow-prone areas. In addition, it canbe noted that the ANN model tends to over-estimate
debris flow risks compared to the infinite slope model,
especially in the west part of the study area, which canalso attribute to the hidden features extracted by theANN model. Additional study is recommended toinvestigate the generalization capabilities of data-driven
models on LSM.

4.4 Performance evaluations
The present study used the 5-fold cross-validation
technique [19] for model performance evaluation,corresponding to an 80%/20% sample split. In crossvalidation, the dataset is divided into five folds, and themodel is trained using four folds and validated using theremaining one fold. This process repeats five times toallow each fold to be served as a validation fold, and thefinal model performance is the average model
performance for each validation fold.
The performance of classification models istypically evaluated based on the confusion matrix andreceiver operating characteristic (ROC) curve. The ROC
curve is a 2D plot of false positive rate (FPR) vs. true
positive rate (TPR) for all classification thresholds. TheFPR and TPR can be calculated as:TPTP  FNFPFPR FP  TN

TPR Avg. AUC
0.894
0.930

(3)
(4)

The area under the ROC curve (AUC) can becalculated based on the ROC curve, which is often used
as a single-value evaluation for classification models. It
measures the model’s capability to distinguish twoclasses. The AUC score was used as the performanceindicator for the present study.

Fig. 4. Debris flow susceptibility map for the study area basedon the infinite slope model.

5 Results and discussion

3

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Fig. 5. Debris flow susceptibility map for the study area basedon the ANN model.

6 Conclusion
Through a case study on debris flows triggered by astorm event in Colorado Front Range, this study
compares the capabilities of physics-based and datadriven approaches for LSM on a regional scale. Basedon the cross-validation results, both approaches can besuccessfully used to predict debris flow risks across thestudy area with appropriately selected debris flow
contributing factors, and the data-driven approach wasable to outperform the physics-based approach in termsof the AUC score. However, it should be noted that thesuccessful application of data-driven approaches
requires high-quality debris flow inventory with asufficient amount of debris flow records, which may not
be available in certain applications. On the other hand,using domain knowledge, physics-based approaches canprovide debris flow risk estimates in a label-freefashion.
This research was partially supported by Google AI Impact
Challenge Grant 1904-57775. The second author’s effort wassupported by the U.S. National Science Foundation underAward No. ICER-2022444. These supports are gratefully
acknowledged.

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