# IJEGE-11_BS-Gartner-et-alii

*Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza*

*DOI: 10.4408/IJEGE.2011-03.B-093*

**IMPLEMENTATION OF POST-FIRE DEBRIS-FLOW HAZARD**

**ASSESSMENTS ALONG DRAINAGE NETWORKS,**

**SOUTHERN CALIFORNIA, U.S.A.**

*et alii,*2008;

*et alii*, 2010). These multi-variate models

ing combinations of predictive variables that describe

the extent and severity of fire within a drainage basin,

the drainage basin morphology and soil characteris-

tics, and storm rainfall characteristics. These models

are specific to particular geographic regions and fire

regimes. Some models can be used to estimate debris-

flow susceptibility within the first few years follow-

ing a fire (e.g. G

*et alii*, 2008; C

*et alii,*

factors to quantify the diminishing effect of fire on de-

bris-flow susceptibility, allowing the model to be ap-

plied over a range of timescales following a fire (e.g.,

G

*et alii*, 2000; G

*et alii*, 2009).

mation system (GIS) by identifying specific drainage

basin outlets, and then extracting the measures of

the model input variables for the drainage basin ar-

eas upstream from the drainage basin outlets. These

measures, along with specified design storm rainfall

conditions, are then used to estimate the probability

and volume of debris flow for each identified drainage

basin outlet (Fig. 1). Although this approach can be

used to identify debris-flow susceptibility for specific

locations, it provides only a single estimate for each

drainage basin, and thus does not reflect the range of

debris-flow hazards that may exist upstream of the

**ABSTRACT**

Rapid assessments of potential debris-flow hazards

following a fire are necessary to provide timely infor-

mation to the public, land managers, and emergency-

response agencies about locations most prone to debris-

flow impact. Here we present a method to implement

a set of existing debris-flow susceptibility models

along a drainage network using input variables that are

quantified for the contributing drainage basin areas to

each grid cell along a drainage network. This method

accounts for the spatially variable properties within

contributing drainage basin areas as debris flows travel

through the drainage network. Applying the models

along drainage networks, rather than to an entire drain-

age basin, provides hazard assessments that identify the

potential impacts within the primary channels of a wa-

tershed, where destructive debris flows may both erode

and deposit large volumes of material.

**K**

**ey**

**words**

**:**debris-flow susceptibility, post-fire erosion, drai-*nage networks, continuous variables*

**INTRODUCTION**

are currently used to assess hazards from recently

burned drainage basins in southern California (e.g.

C

*et alii,*2009; C

*et alii*, 2010), and the

*J.E. GARTNER, S.H. CANNON & P.M. SANTI*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

models to generate estimates of debris-flow probabil-

ity and volume for each grid cell along the drainage

network. Ranked output from the debris-flow volume

and probability models are added together to generate

a combined relative debris-flow hazard ranking.

specific assessment of potential debris-flow suscepti-

bilities within a burned area. Maps that identify haz-

ardous locations within the drainage network may be

used to help guide post-fire debris flow mitigation

plans and plan emergency evacuation routes. Fur-

ther, such an application provides a means to estimate

how debris-flow volumes change as they travel down

drainage networks.

by a discussion of the process used to generate the

continuous variable grids used as data input to the

models. We then present results of an assessment for

a hypothetical drainage basin. Within this basin, we

identify several locations within the drainage network

where estimates of debris-flow probability, debris-

flow volume, and combined relative debris-flow haz-

ard ranking could be beneficial. This example dem-

onstrates how the continuous variable approach for

applying debris-flow susceptibility models provides

spatially specific information on debris-flow suscep-

tibilities within a burned drainage basin.

drainage basin will be greatest in the channels through

which a debris flow travels, eroding and depositing

material, and on the fan below the drainage basin

outlet where material is deposited. In addition, if as-

sessments of debris-flow probability and volume are

needed for multiple locations along a channel, then

the process of identifying each drainage basin outlet,

delineating drainage basins, and obtaining measures

for the input variables used in the models is labor in-

tensive and time-consuming. Last, this approach iden-

tifies debris-flow hazards only in flow-accumulating

terrain, so that hazards in inter-basin areas are not as-

sessed, as in Fig. 1.

*OBJECTIVES AND APPROACH*

es potential hazards within recently burned areas than

the present drainage-basin wide approach. With this

new method, termed the continuous variable method,

we generate sets of continuous variable grids to im-

plement the debris-flow susceptibility models along

the drainage network. The continuous variable grids

provide measures of the model input variables for

each grid cell along a drainage network based on the

upstream conditions (Fig. 2). These continuous vari-

*Fig. 1 - Map showing results from a drainage-basin wide*

*approach for implementing a model for estimating*

*post-fire debris-flow volumes. This map shows es-*

*timated debris-flow volumes expected at drainage*

*basin outlets (open circles) as a function of model*

*input variables obtained for each drainage basin.*

*Debris-flow volumes at additional locations (solid*

*circles), for example, at road crossings within the*

*drainage basin, are not identified. The gray area*

*represents the inter-basin area for which hazard*

*information is also not obtained*

*Fig. 2 - Schematic illustration of the continuous variable*

*method, where grids of continuous variables are*

*defined for each contributing area to each grid cell*

*along the drainage network. The size of each con-*

*tributing area increases with distance downstream*

**IMPLEMENTATION OF POST-FIRE DEBRIS-FLOW HAZARD ASSESSMENTS ALONG DRAINAGE NETWORKS, SOUTHERN CALIFORNIA,**

*Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza*

tween 300 and 1,000,000 m

*et alii,*2008;

*et alii*, 2010). Independent variables associat-

age basin relief, the length of the longest flow path

within the drainage basin, the drainage basin area with

gradients greater than or equal to 30 percent, several

measures of soil physical properties, the basin area

burned at high, moderate, and low severity, total trig-

gering storm rainfall, storm duration, and measures of

peak rainfall intensity at different durations. The data

used to define the independent variables include 10-m

resolution DEMs and burn severity grids, 1:250,000

scale soil maps, and tipping bucket rain gage data col-

lected in the field

volume to a set of predictor variables with the form;

*α*are coefficients and

*x*are variables, and i is

the number of variables used in the model (H

multiple linear regression statistics (adjusted r

debris-flow volume from an independent test dataset

(G

*et alii*, 2008). In general, each model in-

fects of drainage basin morphology, soil properties,

burn severity, and storm rainfall on debris-flow vol-

ume. The volume model presented in C

*et alii*

of debris flow volumes from a test dataset to within

an order of magnitude.

*MODELS FOR ESTIMATING DEBRIS-FLOw*

PROBABILITY

PROBABILITY

gistic multiple regression analyses of databases that

link observations of debris-flow presence or absence

with independent variables similar to those described

above (R

*et alii*, 2008; C

*et alii,*2010).

updated. As a result, the predictive variables in the mod-

els, and their coefficients, may change. In this paper we

provide a framework to implement a generic set of de-

bris-flow susceptibility models along drainage networks

using continuous variable grids so that the approach will

be applicable to both existing and future models.

**BACKGROUND**

tabases consisting of measures of debris-flow volumes

and observations of debris-flow occurrence as the de-

pendent variables, and independent variables that char-

acterize drainage basin morphology, soil conditions,

the extent and severity of the fire, and storm rainfall

conditions (e.g., G

*et alii*, 2008; R

*et alii*,

*et alii,*2009; C

*et alii*, 2010).

debris flow is associated with both a single drainage ba-

sin for which the independent variables are defined and

a single storm rainfall event.

from drainage basins with areas between 0.01 km

*et alii*, 2005; G

*et alii*, 2008;

*et alii,*2008; G

*et alii*, 2009; C

*et*

*alii*, 2010). Measurements of debris-flow volume and

observations of debris-flow occurrence were made

along drainage networks at channel confluences or

road crossings, at the mouth of the drainage basin, or

at locations along first order channels where single de-

bris-flow paths were identified (G

*et alii*, 2008;

*et alii*, 2008). Because these measurements and

age networks with drainage basin areas between 0.01

and 30 km

range of basin areas. Increased erosion due to wildfire

is most pronounced within the first two to three years

following a fire and so these models are temporally

applicable to this time period (C

*et alii,*2010).

*MODELS FOR ESTIMATING DEBRIS-FLOw*

VOLUMES

VOLUMES

within a drainage basin, or as the amount of material

*J.E. GARTNER, S.H. CANNON & P.M. SANTI*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

large estimated volume of material. The least hazard-

ous basins are characterized by both low probabilities

and the smallest volumes. In between these extremes

are basins that are characterized by a combination of

either relatively low probabilities and larger volume

estimates or high probabilities and smaller volume

estimates. Due to the different combinations of low

to high debris-flow volumes and probabilities, C

*et alii*(2010) suggested that, for a given basin, the

together to generate a “combined relative debris flow

hazard ranking”, with the lowest values representing

the least hazardous basins, and the highest values rep-

resenting the most hazardous basins. These two sug-

gestions are followed in this paper to provide a single

hazard assessment in addition to the individual debris-

flow volume and probability estimates.

**METHODS**

grids are generated that provide measures of each of

the necessary independent variables for each grid cell

in a DEM. Independent variables used in the debris-

flow susceptibility models can be divided into four

categories: 1) measures of the drainage basin area that

meet a particular criteria (e.g., drainage basin area

with gradients greater than or equal to 30 percent), 2)

measures of the percentage of the drainage basin area

that meet a particular criteria (e.g., the percentage of

the drainage basin area burned at moderate and high

severity), 3) measures of average values of the drain-

age basin area (e.g., average gradient of the drainage

basin area), and 4) measures of the drainage basin

morphology (e.g., drainage basin relief, ruggedness,

and length of the longest flow path within the drain-

age basin). Each of these different types of variables

can be determined for each grid cell located along the

drainage network using DEMs, binary grids, integer

grids (e.g., a gradient or burn severity grid) and hy-

drology algorithms available in a GIS.

on the greatest elevation change between adjacent grid

cells. This grid is used to generate a flow-accumula-

*β*are logistic regression coefficients,

*x*are values for the predictor variables, and

*i*is the

number of variables in the model (H

logistic regression statistics (R

*et alii,*2008;

*et alii*, 2010). As above, each model in-

fects of drainage basin morphology, soil properties,

burn severity, and storm rainfall conditions on the

probability of debris-flow generation.

ing from 0.2 to 0.4. Additionally, model sensitivity

can be evaluated based on the percent of debris flow

occurrences correctly identified with a probability

greater than 50 percent. The probability model de-

veloped by C

*et alii*(2010) has a m

*COMBINED RELATIVE DEBRIS-FLOw HA-*

ZARD RANkING

ZARD RANkING

*et alii*(2010) recommended that, rather than present-

ing estimates with several significant figures, each

estimated debris-flow volume and probability be as-

signed to a class rank between 1 and 4. Estimated

debris-flow volumes less than 1000 m

m

than 25 percent are assigned to class 1, probabilities

between 26 and 50 percent are assigned to class 2,

probabilities between 51 and 75 percent are assigned

to class three, and probabilities between 76 to 100

percent are assigned to class four.

volume, with the most hazardous basins being charac-

*3*

**IMPLEMENTATION OF POST-FIRE DEBRIS-FLOW HAZARD ASSESSMENTS ALONG DRAINAGE NETWORKS, SOUTHERN CALIFORNIA,**

*Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza*

with an integer grid (e.g., a gradient grid) and then

dividing the output by a drainage basin area grid. This

action divides the sum of the upstream values of the

integer grid by the contributing drainage basin area.

*GRIDS wITH MEASURES OF THE DRAINAGE*

BASIN MORPHOLOGY

BASIN MORPHOLOGY

ruggedness, drainage basin relief, and the length of

the longest flow path within a drainage basin) require

specific hydrology algorithms. The flow-length hy-

drology tool in the spatial analyst of ArcGIS (ESRI,

2008), with the upstream option, can be used to create

a grid that represents the distance of the longest flow

path within a drainage basin. A grid that represents

the upstream relief can be determined using the Riv-

ertools program (R

the relief grid by the square root of a drainage basin

area grid (m

the outputs should mimic the grids generated here to

avoid introducing error into the model results.

*CALCULATING DEBRIS-FLOw PROBABILI-*

TIES AND VOLUMES USING MAP ALGEBRA

TIES AND VOLUMES USING MAP ALGEBRA

ity models have been generated, map algebra (ESRI,

2008) is used to calculate debris-flow volumes and

probabilities along the drainage network. Each con-

tinuous variable grid is used as the input variables in

the map algebra expression, and the outputs are grids

with cell values equal to the predicted debris-flow

volume and probability, and combined relative debris-

flow hazard ranking. These outputs are multiplied by

a binary grid representing the applicable drainage

network (between 0.01 and 30 km

estimated only along the drainage network.

**EXAMPLE OF A CONTINUOUS VARIA-**

**BLE BASED HAZARD ASSESSMENT**

implementation in a continuous variable framework.

grid cells that flow into each grid cell. The flow ac-

cumulation grid can be weighted with another grid to

create a grid where the value of each grid cell equals

the upstream sum of values from the weight grid.

contains a measure of the contributing drainage basin

area. The drainage network for a given area (Fig. 2)

is then defined by converting the drainage basin area

grid to a binary grid; values of one are assigned to

those grid cells with drainage basin areas between

0.01 km

hydrology algorithms may be used to implement the

susceptibility models, however, this may potentially

introduce error into the results.

*GRIDS FOR MEASURES OF THE DRAINAGE*

BASIN AREA THAT MEET A PARTICULAR CRI-

TERIA

BASIN AREA THAT MEET A PARTICULAR CRI-

TERIA

with gradients greater than or equal to 30 percent),

the flow-accumulation command is weighted with a

binary grid with cell values equal to one for locations

that meet the specific criteria and then multiplied by

the grid cell area.

*GRIDS wITH MEASURES OF THE PERCEN-*

TAGE OF THE DRAINAGE BASIN AREA THAT

MEET A PARTICULAR CRITERIA

TAGE OF THE DRAINAGE BASIN AREA THAT

MEET A PARTICULAR CRITERIA

generated using a flow-accumulation command

weighted with a binary grid that represents the unique

criteria with values of one, dividing the output grid

by a drainage basin area grid, and then multiplying

this output grid by 100 to calculate a percentage value.

*GRIDS FOR MEASURES OF THE AVERAGE*

*VALUES OF THE DRAINAGE BASIN AREA*

*J.E. GARTNER, S.H. CANNON & P.M. SANTI*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

mation on expected debris-flow hazards could be ben-

eficial, including roads that cross the main channels.

Debris-flow probabilities, volumes, and combined rel-

ative debris-flow hazard rankings are calculated along

the drainage network, including the locations where

the roads intersect the drainages. This example dem-

onstrates how a land manager might use the debris-

flow susceptibility models to identify locations where

debris-flows impacts will be greatest. This informa-

tion could be used for many applications; to identify

the type of equipment needed to remove the material,

to size culverts and debris-retention structures, and to

determine if portions of the road are safe for travel

during evacuations.

*DEBRIS-FLOw VOLUME MODEL*

drainage network as a function of the drainage basin

area burned at all severities, the length of the longest

flow path within a drainage basin, the drainage basin

relief, and the peak 60-minute storm rainfall inten-

sity The drainage basin area burned at all severities

is generated as described previously by weighting a

flow-accumulation command with a grid that repre-

sents burned grid cells with values of one, and zero

for unburned. This grid is multiplied by the area of

each grid cell (1×10

length of the longest flow path within a drainage ba-

sin is determined using the flow-length command in

ArcGIS spatial analysis, hydrology toolbox with the

upstream option chosen (ESRI, 2008). The input for

this command is a flow-direction grid, and the output

is divided by 1000 to convert to units of kilometers.

The drainage basin relief is determined using the re-

lief command in Rivertools (R

bra. A value of 10 mm/hr was chosen for a peak

60-minute rainfall intensity based on values used in

a recent hazard assessment in southern California

(C

*et alii*, 2009). The resulting grid from the

volume for each grid cell within the burned drainage

network (Fig. 3).

*DEBRIS-FLOw PROBABILITY MODEL*

area with gradients greater than or equal to 30 percent,

drainage basin ruggedness, the percentage of drainage

basin area burned at moderate and high severity, the

average clay content and liquid limit of soils within

the drainage basin, and average storm rainfall intensity

dients greater than or equal to 30 percent is generated

using the flow-accumulation command, weighted with

a binary grid consisting of values of one for gradients

greater than 30 percent and values of zero for gradients

less than 30 percent. The output of this command is

then divided by a non-weighted, flow-accumulation

grid and multiplied by 100 to determine the percent-

age of the drainage basin area with gradients greater

than or equal to 30 percent. The grid with measures

for drainage basin ruggedness is determined by divid-

ing the relief grid, generated using Rivertools (R

The grids representing the average clay content and

liquid limit of soils within the drainage basin are gen-

erated using flow-accumulation commands weighted

with grids representing clay content and liquid limit

derived from the USSOILS database (s

100 to calculate percent values. A value of 10 mm/hr

is chosen for an average storm rainfall intensity based

*Fig. 3 - Potential debris-flow volumes calculated along a*

*hypothetical burned drainage network in response*

*to a 10 mm of rain in 1 hour. Debris-flow volumes*

*increase with distance downstream and increasing*

*drainage basin area*

**IMPLEMENTATION OF POST-FIRE DEBRIS-FLOW HAZARD ASSESSMENTS ALONG DRAINAGE NETWORKS, SOUTHERN CALIFORNIA,**

output that identifies the locations most susceptible to

debris-flow impacts.

at different locations along a drainage network in a

burned area. The application of an existing model for

post-fire debris-flow volume indicates that volumes

will generally increase with distance down the drain-

age network, reflecting the addition of material from

sequentially larger drainage basin areas, and more im-

portantly, longer channel lengths (s

*et alii,*2008).

debris flows originating in lower-order portions of the

drainage network will progressively increase in vol-

ume as they travel downstream. The rate of volume

increase is a function of basin morphology, the extent

and severity of the burned area, soil physical proper-

ties, and storm rainfall.

crease and decrease along the drainage network, reflect-

ing changing conditions within drainage basin areas.

Specifically, an area that is unburned or burned at low

(C

*et alii*, 2009). These grids and average storm

which is processed using map algebra (ESRI, 2008).

The resulting grid from the map algebra represents

the debris-flow probability at each grid cell along the

burned drainage network (Fig. 4)..

*COMBINED RELATIVE DEBRIS-FLOw HA-*

ZARD RANkING

ZARD RANkING

ranked values of the estimated debris-flow volume and

probability. These values ranged between 2 and 5 (Tab.

1). In addition, combined relative debris-flow hazard

rankings were calculated for each of the locations of

interest indicated on Figure 5 (Tab. 1).

**DISCUSSION AND CONCLUSIONS**

vides additional information to basin-wide hazard

assessments. This new method estimates debris-flow

volumes and probabilities at all locations along the

drainage network, where debris-flow impacts are most

likely to be most significant. Implementation of this

approach also eliminates the need to manually iden-

tify specific drainage basin outlets of interest, thus de-

creasing the time needed to generate emergency post-

fire debris-flow hazard assessments. In addition, the

combined relative debris-flow hazard ranking identi-

*Fig. 4 - Debris-flow probabilities estimated along a*

*burned drainage network in response to 10 mm of*

*rain in one hour. Probabilities can both increase*

*and decrease along the drainage network, reflect-*

*ing changing conditions within contributing areas*

*Fig. 5 - Combined relative debris-flow hazard rankings*

*calculated along a burned drainage basin net-*

*work. Rankings can both increase and decrease*

*along a drainage network, reflecting changes in*

*probability estimates associated with changing*

*conditions within drainage basin areas*

*Tab. 1 - Debris-flow susceptibilities for locations of inter-*

*est within a burned drainage basin*

*J.E. GARTNER, S.H. CANNON & P.M. SANTI*

the upper reaches of the drainage are more suitable for

an evacuation route, as opposed to the road that passes

through locations 3 through 6.

ceptibility models and provides more spatially specific

information on potential debris-flow hazards following

wildfire. Future research on how topography affects

debris-flow processes of channel incision, transport and

deposition will better identify where debris-flow inci-

sion and transport give way to debris-flow deposition.

**ACKNOWLEDGEMENTS**

Godt, and the two anonymous reviewers of the 5

tional Review Committee for their helpful comments

on this paper.

in a channel reach where debris-flow probability esti-

mates decrease with distance downstream. The lower

probability estimates result from the mitigating effects

of unburned areas, and areas burned at low severity

within the drainage basin. Similarly, the channel above

location 3 on Figure 4 shows probabilities that increase

and then decrease with distance downstream due to the

effects of the drainage network passing through an area

of lower gradients. These changes in debris-flow prob-

abilities are also reflected in the map showing the com-

bined relative debris-flow hazard ranking.

network, guide post-fire debris-flow hazard mitiga-

tion plans, and plan emergency evacuation routes. For

example, these maps indicate that debris-flow impacts

will be greatest at locations 1, 2, and 6, and the least at

locations 7 and 4, thus providing information on where

to focus post-fire channel erosion mitigation treat-

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