E3S Web of Conferences 415, 05004 (2023)
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https://doi.org/10.1051/e3sconf/202341505004

Constraining post-fire debris-flow volumes in the southwestern
United States
Alexander Gorr1*, Luke McGuire1, and Ann Youberg2
1Department of Geosciences, The University of Arizona, 1040 East Fourth Street, Tucson, AZ 85721, USA
2Arizona Geological Survey, The University of Arizona, 1955 E Sixth Street, Tucson, AZ 85721, USA

Abstract. Debris flows pose a serious threat to human life and infrastructure in downstream areas
following wildfire. This underscores the necessity for having a hazard assessment framework in place thatcan be used to estimate the impacts of post-wildfiredebris flows. Current hazard assessments in the western
United States (USA) use empirical models to assess the volume of potential post-wildfire debris flows.
Volume models provide information regarding the magnitude and potential downstream impacts of debris
flows. In this study, we gathered post-wildfire debris-flow volume data from 54 watersheds across the statesof Arizona (AZ) and New Mexico (NM), USA, and compared these data to the output of a widely used
empirical post-wildfire debris-flow volume model. Results show that the volume model, which wasdeveloped using data from the Transverse Ranges of southern California (CA), tends to overestimate
observed volumes from AZ and NM, sometimes by several orders of magnitude. This disparity may be
explained by regional differences between southern CA and AZ and NM, including differences in sedimentsupply. However, we found a power- law relationship between debris-flow volume and watershed area thatcan be used to put first-order constraints on debris-flow volumein AZ and NM.

1 Introduction
Debris flows are fast-moving mixtures of sediment andwater that occur in mountainous regions across the world.
They are especially common, however, on steep slopes
recently burned by wildfire. Wildfires reduce vegetation
cover [1,2] and alter soil hydraulic properties [3-5],
making burned slopes particularly susceptible to runoff
generated debris flows [6]. Post-wildfire debris flowsposea significant threat to human life [7,8] and downstream
infrastructure, including roads, bridges, and houses [8,9].
These threats have been accentuated in recent years byincreases in population along the wildland-urban interface(WUI) [10] and increases in wildfire size, frequency, andseverity [11].
The threat posed by post-wildfire debris flows
underscores the necessity for having a well-establishedhazard assessment framework that can be used to estimate
the potential impacts of debris flows. Current hazard
assessment frameworks in the western United States(USA) often consider post-wildfire debris-flow likelihood[12,13] and volume [14,15]. Likelihood models can help
identify which burned watersheds are the most susceptible
to debris flows, but they provide little information
regarding the downstream impacts of these events.
Volume models strengthen hazard assessments byproviding an estimate of debris-flow magnitude. They
also provide insight into the potential for downstream
effects, as debris-flow discharge and runout tend toincrease with volume [16,17]. Furthermore, volume is an

important input for inundation models that can be used to
identify and delineate downstream areas that are mostsusceptible to debris flow impacts [18,19].
Accurate post-wildfire debris-flow volume models are
therefore a critical element of hazard assessments.
Currently, the most widely used post-wildfire debris-flow
volume model in the western USA is the Emergency
Assessment empirical model developed by [15]. The
model was developed using data from the Transverse
Ranges of southern California (CA). Given theimportance of debris-flow volume when assessing
downstream impacts, it is critical to collect additional dataon post-fire debris-flow volume from a wider range of
geologic and climatic settings. It is challenging, in
general, to collect data to develop and test post-wildfire
debris-flow volume models because debris flows often
occur in combination with floods that erode and rework
deposits. In this study, we gathered post-wildfire debrisflow volume data from 54 watersheds across the states of
Arizona (AZ) and New Mexico (NM), USA. We compare
these data with the Emergency Assessment model [15]and provide hypotheses for apparent differences. We also
determine a power law relationship between debris-flow
volume and watershed area for our study sites in AZ andNM, similar to those calculated for other regions acrossthe world [20].

1 Corresponding author: agorr@email.arizona.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/).

E3S Web of Conferences 415, 05004 (2023)
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2 Study Sites

3 Methods

We gathered data for this study from 14 burn scars acrossthe states of AZ and NM in the southwestern USA (Fig.
1). This region is characterized by having a warm yearround climate and low annual precipitation. It is also
known for the North American monsoon, a phenomenon
that produces nearly 50% of the region’s total annual
precipitation between the months of July-September.
Monsoonal storms are often short in duration but can
produce high intensity rainfall [21]. Due to the highinterannual and decadal variability in monsoonal rainfall,droughts are not uncommon in this region. Since 2000, thesouthwestern USA has been mired in its worst
megadrought since at least the year 800 CE [22].

3.1 Volume Measurements
We measured the volume of sediment deposited by 55
post-wildfire debris-flows from 54 debris flow-producing
watersheds. For all of the debris flows that occurred
between 2019-2021 (33 of the 55 debris flows), we
measured the volume of the deposits in the field. We usedeither a measuring tape or laser range finder to measure
the length of every edge of each deposit. We used thesemeasurements, in conjunction with the azimuth of eachmeasurement, to calculate the area of the deposits. We
collected depth measurements at locations where we
could easily distinguish the debris-flow deposits from thepre-event surface, such as the edge of the deposit or where
subsequent flood flow incised through the debris-flow
deposits. We averaged theses values to calculate the depthof the deposit. Then, we multiplied the average depth by
the area of the deposit to calculate the debris-flow volume.
For the 22 debris flows that occurred before 2019, we
used a variety of methods to calculate the volume of theflow. For 4 of the debris flows, we made pre-event andpost-event channel cross-section measurements andcalculated the amount of material that was removed fromthe channel. For the remaining debris flows, we identified
deposits on the ground and took GPS points as well as
depth estimates. We then used aerial photographs at ascale of 1:12000 to estimate the extent of deposits and to
calculate the area. We calculated volumes using theinformation regarding deposit area and depth [24].

Fig. 1. We studied 54 debris flow-producing watersheds across
14 burn scars in Arizona (AZ) and New Mexico (NM), USA.

Over that same time period, the region has seen an
increase in large and high severity wildfires [23]. Our
study spans the burn scars of 14 wildfires that burned in
the southwestern USA between 2010 and 2021. Thesefires burned through a range of vegetation communities,
from the Sonoran Desert at low elevations, to chapparaland scrubland communities at moderate elevations, andponderosa pine and mixed conifer forests at higher
elevations.
For this study, we gathered volume data for 54 debrisflow producing watersheds across the 14 burn scars.
These watersheds varied in area from 0.01 km2 to 5.69
km2, and in average slope from 11.9° to 48.4°. They also
varied in burn severity as eight watersheds burned at 0%
moderate or high severity, while others burned at over
80% moderate or high severity. Most of the watersheds
we studied were located entirely on public land and were
undeveloped. Subsequently, the debris flows they
produced had little/no impact on infrastructure and human
life. However, several debris flows, including those at the
Woodbury Fire (Fig. 1) severely damaged roads resulting
in multi-year closures. One debris flow, which occurred at
the Flag Fire (Fig. 1) damaged a private house.

3.2 Comparison with Established Methods
After we collected the post-wildfire debris-flow volumedata from AZ and NM, we assessed how the Emergency
Assessment model [15] performed when compared to theobserved volumes. This model predicts the volume of
sediment produced by debris flows within two years of a
wildfire using the equation:
𝐿𝑛(𝑉) = 4.22 + 0.39√𝑖𝑖15 + 0.36ln𝐵𝑚ℎ + 0.13√𝑅 (1)where V is the volume of sediment (m3), i15 is the peak
rainfall intensity over a 15-minute period (mm/h), Bmh is
the watershed area burned at moderate and high severity(km2), and R is the watershed relief (m) [15].
In order to calculate the predicted volume for each of
the 54 watersheds that we studied, we first calculated thevalues of each of the three input parameters required by
the Emergency Assessment model [15]: i15, Bmh, and R.
We collected rainfall data using rain gauges that were
installed within 3 km of the outlet of each watershed. We
used this rainfall data to calculate i15. We used soil burnseverity data from the Burned Area Emergency Response(BAER) program to calculate the Bmh within eachwatershed. Finally, we used 10m resolution digital
elevation models (DEM) to calculate R for eachwatershed. We then used the Emergency Assessment
model [15] to calculate a debris-flow volume for each of
the 54 watersheds for which we had observed volumes.
We also studied the relationship between post-wildfire
debris-flow volume and watershed area. Previous studies
determined power law relationships for debris-flow
volume as a function of watershed area using data fromCA and the Intermountain West [20]. We compared the2

E3S Web of Conferences 415, 05004 (2023)
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the largest observed debris flows also had the largest
modeled volumes (Fig. 2). The correlation coefficient
between the observed debris-flow volumes and themodeled volumes was 0.64.
When calculating the correlation coefficient between
observed and modeled debris-flow volumes, we excluded
the eight watersheds that the Emergency Assessment
model underestimated. All eight of those watersheds
burned exclusively at low severity. The model requires thenatural log of watershed area burned at moderate or highseverity (Bmh) (Eq 1), so when Bmh equals zero, it isundefined and results in a predicted volume of 0 m3. Thismeans that the Emergency Assessment model will always
predict a volume of 0 m3 if a watershed is not burned atmoderate or high severity, even though watersheds burned
at low severity may still be at an elevated risk for postwildfire debris flows [25].
While the Emergency Assessment volume model [15]generally performs well in the area for which it wasdeveloped (the Transverse Ranges of southern CA),regional differences between southern CA and AZ andNM, such as those in vegetation, climatic setting, andrainfall characteristics, may contribute to reduced model
accuracy for post-wildfire debris flows in AZ and NM.
For example, dry ravel commonly loads channels withrelatively fine hillslope sediment immediately following
fire in the Transverse Ranges [26,27], providing anabundant source of sediment for debris flows in that
region. However, evidence of dry ravel was not observed
at our study areas in AZ and NM. These differences
resulted in the model overestimating most of the observed
volumes by several orders of magnitude (Fig. 2), which
could then lead to overestimates of debris-flow runout andinundation extent [18,19].

best fit power law for our data to the best fit power for two
datasets from [20]: the WUS <1 and WUS 1-3 datasets.
The WUS <1 dataset contains debris flows from burnedbasins in the western USA that occurred within one year
following wildfire, and the WUS 1-3 dataset contains
debris flows from burned basins in the western USA that
occurred between one and three years after wildfire. We
compared our data to these two datasets because all of ourdebris flows occurred within the first three yearsfollowing
wildfire.

4 Results and Discussion
The debris flows we observed ranged in volume from 25
m3 to 14,000 m3. Most of the debris flows (39 of 55 or71%) had volumes between 100 m3 and 10,000 m3.
Twelve of the debris flows (22%) were less than 100 m3
in volume, while only 4 debris flows (7%) had a volume
greater than 10,000 m3. The mean debris-flow volume inour dataset was 2105 m3. The maximum and mean
volumes for our AZ and NM dataset are much lower thanthose of the 92 debris-flow volumes used to develop theEmergency Assessment model [15], which were 864,308
m3 and 46,198 m3, respectively.

Fig. 2. Over 85% of the volumes predicted by the Emergency
Assessment Model [15] were overestimated compared to what
was observed. Those that were overestimated (orunderestimated) by more than an order of magnitude are shownin red. The thing dashed lines indicate an order of magnitude.

The Emergency Assessment model [15] tended tooverestimate debris-flow volumes in our AZ and NM
dataset. The model overestimated volume for 47 of the 55(85%) debris flows. Furthermore, only 11 of the 55 (20%)
debris-flow volumes were predicted within an order ofmagnitude (Fig. 2). While the model tended tooverestimate debris-flow volumes, there was a pattern
between the modeled and observed volume whenexcluding eight outliers described in more detail below. In
other words, the debris flows with smaller observed
volumes generally had smaller modeled volumes, while

Fig. 3. The power law relationship between debris-flow volume
and watershed area in AZ and NM indicates that debris flows inthis region are smaller in size, but scale in the same way as debris
flows in CA and across the Intermountain West [20].

When viewed as a power law function of watershed
area, AZ and NM debris-flow volumes followed arelationship similar to that observed elsewhere in the3

E3S Web of Conferences 415, 05004 (2023)
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References

western USA [20] (Fig. 3). The best fit power law
equation for our dataset was:𝑉 = 2120.1𝐴0.83

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where V is the debris-flow volume (m3) and A is thewatershed area (km2). The coefficient of 2120.1 is lower
than those found for the WUS datasets in [20], indicatingthat the debris flows in our dataset are smaller than thosein the WUS datasets (Fig. 3). However, the exponent issimilar to that of the WUS <1 dataset, which indicates thatvolumes scale with watershed area in a similar way inthese two datasets (Fig. 3). Results suggest that thisrelationship can be used to place first-order constraints on
post-wildfire debris flows in AZ and NM. However, avolume model specific to AZ and NM could improvedebris-flow hazard assessments in this region.

5 Conclusions
Post-wildfire debris flows pose a serious threat to humanlife and infrastructure in many mountainous regions
around the world. This threat is exacerbated as wildfire
size and severity increase and population continues togrow. Estimates of debris-flow volume are an integral partof many hazard assessments. In this study, we compared
the Emergency Assessment model [15], which wasdeveloped using data from the Transverse Ranges ofsouthern CA, against 55 observed post-wildfire debrisflow volumes from AZ and NM, USA. Results showedthat the Emergency Assessment model [15] overestimated
85% of observed debris-flow volumes, oftentimes bymore
than an order of magnitude, and underestimated observed
volumes when watersheds burned only at low severity(Fig. 2). We also calculated a power law relationshipbetween volume and watershed area for debris flows in
AZ and NM. We found that while post- wildfire debrisflow volumes in AZ and NM are generally smaller thanthose in CA and across the Intermountain West, for agiven watershed area, they tend to scale with watershedarea in a similar way (Fig. 3). Differences in magnitude
between the models and observations could be partiallyexplained by regional differences in sediment supply,
among other factors. While the power law relationship canbe used to place first-order constraints on debris-flow
volume, results suggest that there could be benefits todeveloping an AZ and NM-specific post- wildfire debrisflow volume model and highlight the need to further
examine controls on post-fire debris-flow volume. Thiseffort will be the focus of future studies.
This work was supported by the Joint Fire Sciences Program
through grant #L20AC00029, the Arizona Department ofEmergency and Military Affairs (DEMA) through the Federal
Emergency Management Agency (FEMA) Hazards Mitigation
Grants Program, and by the Arizona Geological Survey. This
material is based upon work supported by the National Science
Foundation under Grant No. 1951274.

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