E3S Web of Conferences 415, 04002 (2023)
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https://doi.org/10.1051/e3sconf/202341504002

Forecasting the inundation of postfire debris flows
Katherine R. Barnhart1*, Ryan P. Jones1, David L. George2, Francis K. Rengers1, and Jason W. Kean1
1
2

U.S. Geological Survey, Box 25046 DFC MS 966; Denver, CO 80225, USA
U.S. Geological Survey, 1300 SE Cardinal Court, Vancouver, WA 98683, USA

Abstract. In the semi-arid regions of the western United States, postfire debris flows are typically runoff
generated. The U.S. Geological Survey has been studying the mechanisms of postfire debris-flow initiation
for multiple decades to generate operational models for forecasting the timing, location, and magnitude of
postfire debris flows. Here we discuss challenges and progress for extending operational capabilities toinclude modeling postfire debris-flow inundation extent. Analysis of volume and impacted area scaling
relationships indicated that postfire debris flows do not conform to assumptions of geometric self-similarity.
We documented sensitivity of impacted areas to rainfall intensity using a candidate methodology for
generating inundation hazard assessments. Our results emphasize the importance of direct measurements ofdebris-flow volume, inundated area, and high temporal resolution rainfall intensity.

1 Introduction and history
Wildfire exacerbates debris-flow hazards byincreasing surface-water runoff generation, erosion, andmobilization of sediment, and consequently, debris-flow
sediment volumes. The role of fire in debris-flow
initiation has been recognized in southern California,
USA, for nearly a century [e.g., 1]. In contrast withdebris flows generated from shallow landslides [2],postfire debris flows in the semi-arid western UnitedStates are typically initiated by overland flow scour,rainsplash, and rilling [3–5]. However, these initiation
mechanisms are not unique to burned watersheds, andsimilar mechanisms can generate debris flows inunburned watersheds [6]. Burned watersheds may also
be susceptible to shallow landslides [e.g., at times ofpartial hydrologic recovery, 7,8].
The U.S. Geological Survey (USGS) and the
National Weather Service (NWS) have collaborated on
postfire debris-flow early warning since 2005 [9].
Extensive monitoring of debris-flow-susceptible
watersheds with high-temporal resolution rain gages andflow stage sensors [e.g., 10, and additional observational
datasets cited in 11] yielded an understanding of what
rainfall characteristics triggered postfire debris flows
and an empirical model used to forecast the likelihoodof a debris flow given a rainfall intensity [11,12]. The
inputs to this empirical model include burn severity, 15minute rainfall intensity (I15), soil erodibility, andwatershed topography. For calendar year 2021, 66
assessments totaling over 18,000 square kilometers
were produced by the USGS. In addition to the empirical
likelihood model, an empirical volume model was used
for hazard assessments. The volume model assumes

uniform rainfall over a watershed and was based on
observations of debris-flow size, I15, burn severity, andtopographic characteristics [13]. The likelihood andvolume models provided situational awareness about thetiming and location of postfire debris flows, and the sizeof these flows (magnitude).
Existing capabilities do not provide information
about the extent of debris-flow inundation, maps ofwhich might provide situational awareness for land andemergency management professionals. Extending
postfire debris-flow hazard assessments to include
forecasts of runout requires the information used incurrent hazard assessments, and additional informationsuch as identification of a suitable runout model, theability to parameterize mobility characteristics, and the
propagation of uncertainty in input constraints into
uncertainty in impacted areas.

2 ScopeThis study focuses on two questions central towidespread application of runout models. The two
considered questions are not directly related; however,
we considered them both because they highlight thechallenges associated with two major aspects offorecasting
postfiredebris-flowrunout:(1)
understanding the relationship between mobility
characteristics and parameterization of reduced
complexity models, and (2) characterizing thesensitivity of inundation to rainfall intensity.
First, are the mobility characteristics of debris flows
sourced in burned watersheds different from thoseoriginating from unburned watersheds? We took asimple approach to addressing this question and* Corresponding author:

krbarnhart@usgs.gov
Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.
Elizabeth Singh-Search digitized runout from reference [1]. Comments from Marina Pirulli, Mark Reid, Dennis Staley, Rex Baum,
Brian Shiro and Janet Carter improved the content and clarity of the manuscript.

© 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, 04002 (2023)
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compared the volume-inundated area scaling for debris
flows from burned and unburned watersheds. Second,
how does uncertainty in rainfall intensity used as input
to the volume model [13] propagate into uncertainty ininundated area forecast by a runout model? We
considered this question by testing an approach forgenerating a retrospective hazard assessment for the 9January 2018 Montecito, California, USA, debris-flow
event (hereafter “Montecito event”) [14]. In this event,intense rain (I15=84–99 mm/h) fell on the steep slopes of
the Santa Ynez Mountains previously burned by theThomas Fire, mobilizing sediment from hillslopes andchannels [15,16] into multiple boulder-laden slurries
that ran out onto a ~4 km-wide coalesced alluvial fan(Fig. 1) [14].

the four mass flow types, we fit two linear statisticalmodels relating log10V and log10𝜀. The first model, M1,
states that log%& 𝜀 can be described as a constant, a:log%& 𝜀 = 𝑎, and the second model, M2, includes adependence on the independent variable, log%& 𝑉, using
the coefficient b: log%& 𝜀 = 𝑎 + 𝑏 log%& 𝑉.
After fitting M1 and M2 with observations fromeach mass flow type, we compared the model fits using
a standard Analysis of Variance (ANOVA) procedure,summarized by an F-statistic. The ANOVA tests the null
hypothesis that none of the variation in the dependent
variable, log10𝜀, is explained by the independent
variable, log10V. A large value of the F-statistic indicatesrejection of the null hypothesis that 𝜀 is not a constant.
We do not attempt to formally relate 𝜀 to debrisflow geotechnical properties or runout model mobility
parameters. However, because 𝜀 relates mean depth andinundated area, it reflects flow mobility. An increase in
𝜀 at a given volume indicates a less mobile flow (asmaller extent or deeper deposit depth).
3.2 Uncertainty due to rainfall intensity
Prior work found that three different runout models weresimilarly successful at simulating the Montecito event[24], and simulation performance was more sensitive todebris-flow volume than debris-flow mobility. We built
on this work and tested a simple candidate approach forgenerating a hazard assessment. For southern California,
the link between rainfall and debris-flow volume isexpressed with an empirical model developed by
Gartner [13]. We coupled this empirical volume modelwith the D-Claw runout model [25,26] and considered
four I15 value scenarios: 25, 50, 75, and 100 mm/h. For
each watershed burned by the Thomas Fire and each I15
value, we calculated the sediment volume from the
Gartner model and the water volume based on
multiplying the watershed area with depth of rainassociated with a 15-minute storm. Debris-flow material
with sediment concentrations implied by the calculated
water and sediment volumes was initialized using a
triangular hydrograph following [27] at the watershed
outlets delineated as part of the current likelihood andvolume hazard assessment methodology. Following
prior work [24], we used an initial permeability of k0 =1·10-11 m2, a critical state solid volume fraction of mcrit =
0.64, and a threshold of 0.3 m for minimum flow depth
to depict debris-flow extent.

Fig. 1. Map of observed inundated area and potential source
watersheds from the Montecito event.

3 Methods
3.1 Volume-area scaling
We evaluated the relationship between debris-flow
volume, V, and inundated planimetric area, B for
different mass flow types. We evaluated thisrelationship as a proxy for mobility characteristics.
Previously, a relation between V and B was derived forlahars by postulating that lahars of diverse sizes weregeometrically similar, implying a constant relationshipbetween mean depth, ℎ", and B [17]: 𝜀 = ℎ"/√𝐵 =𝑉/𝐵!/# . These authors postulated that 𝜀 was a small
constant. Conservation of mass results in 𝐵 =𝑐 𝑉 #/! with 𝑐 = 𝜀 $#/! . Application of volume-areascaling relationships for estimation of inundation hazard
zones requires that 𝜀 remains constant for different
flows, an assumption confirmed for lahars, rockavalanches, and debris-flows [17,18].
We tested this assumption for runoff-generated
debris flows from burned and unburned watersheds andcompared the results with landslide-sourced debris
flows and lahars. We compiled existing values of B and
V for landslide-sourced debris flows and lahars [18,19],
runoff-generated debris flows from burned watersheds[1,20–22], and debris flow events from the Italian Alpsthat were likely primarily runoff-generated but
originated from unburned watersheds [23]. For each of

4 Results
4.1 Scaling analysis
We found that 𝜀 is not constant with volume for debris
flows from burned watersheds (Fig. 2). Instead, 𝜀 has
higher values for low volumes and decreases withincreasing volume. This contrasts with lahars, whichhave a constant value of 𝜀 across the range of volume
considered. The F-statistic for burned, runoff-generated
debris flows was 37 (Table 1), consistent with rejecting
the hypothesis that 𝜀 is constant. On the other hand, the2

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Table 1. Summary of linear model fits.
Debris flows
Burned, runoff generated(n=62)

Unburned, landslidesourced (n=50)

Unburned, runoffgenerated (n=27)

Lahar (n=28)

Model

M1

M2

M1

M2

M1

M2

M1

M2

Estimate a-1.7***

0.12-1.9***-1.5***-2.3***-1.26**-3.3***-0.069***Standard error a

0.11

0.32

0.073

0.21

0.099

0.52

0.087

0.070

Estimate bNA-0.49***

NA-0.097*NA-0.24*

NA-2.8

Standard error b

NA

0.08

NA

0.051

NA

0.12

NA

0.51

0.86

0.69

0.49

0.48

0.48

0.45

0.46

0.46

45

28

10

9.3

5.3

4.5

5.7

5.5

NA

37

NA

3.6

NA

3.9

NA

0.95

NA

9.8·10-8***NA

0.062*

NA

0.061*

NA

0.34

Residual standard
error
Residual sum ofsquares
F-statistic(comparison to M1)
Probability(>F)
Retain or reject null
hypothesis that 𝜀 isconstant

Retain at 90% confidence,
reject at 95% confidence

RejectRetainNA=not applicable. Stars denote confidence level *p<0.1; **p<0.05; ***p<0.01

Fig. 3. Simulated inundation areas using different values of
I15. White boxes indicate locations discussed in the text.

hypothesis that 𝜀 is constant implies that delineation of
hazard zones using V-B scaling relationships cannot use
a constant value for 𝜀.

Fig. 2. Relation between deposit volume and 𝜀 for fourmass flow types. Solid lines and gray region indicate M2model fit and standard error, respectively.

F-statistic for the lahar category was 0.34, consistent
with retaining the null hypothesis that 𝜀 is constant.
Debris flows sourced from shallow landslides andrunoff generation in unburned watersheds showed aweak negative relation between 𝜀 and V (Fig. 2). The Fstatistics for these two mass flow types were 3.6 and 3.9,
respectively (Table 1), which resulted in retaining thenull hypothesis that 𝜀 is constant at the 90% (p=0.1)
confidence level or rejecting it at the 95% (p=0.05)
confidence level.
The decrease in 𝜀 with increasing volume for debris
flows from burned watersheds is consistent with aconstant value of ℎ" across the more than four orders ofmagnitude for V in our compilation of observed events.
For low values of V, 𝜀 for burned watersheds is larger
than all other mass flow types. At high values of V, 𝜀 iscomparable in magnitude to lahars. Rejection of the

4.2 Example forecast varying rainfall intensity
Simulations using different rainfall intensities resulted
in substantially different inundation areas (Fig. 3). At I15
values of 25, 50, 75, and 100 mm/h, simulated
inundation extents were 1.3, 2.6, 4.2, and 5.6 km2,
respectively. The I15 of 50 mm/h inundated a comparable
total area as the observed event. The scenario with I15 of
100 mm/h inundated most but not all the area affectedby the event and overpredicted inundation in some areas(square #1).
At the lowest I15 value, simulated debris-flow runout
roughly followed the 5–20-m wide active channels thatare most deeply entrenched within the coalesced alluvial
fan. Most simulated flow paths were wider than thischannel, reaching the lateral extent of the next mostentrenched distributary channel. As the I15 increased, the3

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References

extent of inundation increased, and included areas
unconfined by a channel at any scale. The areas with thelargest mismatch between model and observation were
those where topography does not confine the flow(square #2)

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5 Discussion
Our results indicate that geometric self-similarity does
not hold for debris flows generated by burnedwatersheds. This finding implies that reduced
complexity models that rely on volume-area scaling
relationships to determine the distal extent of affectedareas based on volume cannot adequately represent
postfire hazard assessment using a single value of 𝜀. We
considered that this result may have occurred because
most postfire debris flows are runoff-generated rather
than sourced from discrete slope failures. For example,
runoff-generated debris flows may have a lower solid
volume fraction than slope failure-sourced debris flows.
However, this explanation is not consistent with theanalysis of data from the Italian Alps [23], where debris
flows originate from runoff process, indicating a
constant value of 𝜀 (at the 90% confidence level). The
contrast may indicate a process difference in theinundation dynamics of runoff generated debris flows
from burned and unburned watersheds.
The example forecast at Montecito, California, (Fig.
3) demonstrates the strong sensitivity that I15 has on
affected area. Specifically, because inundated area
increased with increasing rainfall intensity, accurate
forecasting benefits from input of a range of plausible
intensities. This sensitivity originates from theimportance of I15 in the empirical volume model [13].
Development of postfire debris-flow inundation hazard
assessments for areas outside of southern California
would warrant either validation of the southern
California volume model or the establishment of new,location-specific volume models. An alternative is thegeneration of physical process-based volume models.
Creation of empirical volume models involves direct
observation of mobilized volume and candidate
independent variables, specifically high-temporalresolution rainfall.

6 Outlook and conclusions
Forecasting postfire debris-flow runout is feasible
because of extensive work documenting themechanisms, timing, susceptibility, and magnitude ofthis this type of debris flow. Generation of a reliable
methodology for runout hazard assessments would
benefit from more detailed case studies that document
initiation mechanisms, high temporal-resolution
rainfall, total mobilized volume, deposit extent, andgeotechnical properties of hillslope materials anddebris-flow slurries. Two potential research areas are (1)generating new or validating existing capabilities forevent volumes outside of southern California; and (2)linking field observations, laboratory geotechnicalmeasurements, and model parameters describing debrisflow mobility.

4