Probability and Volume of Potential Postwildfire Debris 

Flows in the 2011 Monument Burn Area, Southeastern 

Arizona

By Barbara C. Ruddy and Kristine L. Verdin

Open-File Report 2011–1181

U.S. Department of the Interior

U.S. Geological Survey
ii

U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2011

For product and ordering information:

World Wide Web: http://www.usgs.gov/pubprod

Telephone: 1-888-ASK-USGS

For more information on the USGS—the Federal source for science about the Earth,

its natural and living resources, natural hazards, and the environment:

World Wide Web: http://www.usgs.gov

Telephone: 1-888-ASK-USGS

Suggested citation:

Ruddy, B.C. and Verdin, K.L., 2011, Probability and volume of potential postwildfire 

debris flows in the 2011 Monument burn area, southeastern Arizona: U.S. Geological Survey 

Open-File Report 2011–1181, 9 p.

Any use of trade, product, or firm names is for descriptive purposes only and does not imply 

endorsement by the U.S. Government.

Although this report is in the public domain, permission must be secured from the individual 

copyright owners to reproduce any copyrighted material contained within this report.
iii

Contents

Abstract ......................................................................................................................................................................... 1

Introduction.................................................................................................................................................................... 1

Estimated Debris Flow Probabilities and Volumes......................................................................................................... 7

Use and Limitations of the Assessment......................................................................................................................... 8

References Cited........................................................................................................................................................... 9

Figures

1. Location of drainage basins of interest and soil burn severity map of the 2011 Monument burn area,

southeastern Arizona..................................................................................................................................................... 2

2. Estimated probability of potential postwildfire debris flows in the 2011 Monument burn area,

southeastern Arizona, in response to a 5-year-recurrence, 30-minute-duration rainfall................................................. 3

3. Estimated volumes of potential postwildfire debris flow in the 2011 Monument burn area,

southeastern Arizona, in response to a 5-year-recurrence, 30-minute-duration rainfall................................................. 4

Table

1. Estimated probabilities and debris-flow volumes for the Monument burn area, southeastern Arizona................... 5
iv

Conversion Factors

SI to Inch/Pound

Multiply By To obtain

Length

millimeter (mm) 0.03937 inch (in.)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

meter (m) 1.094 yard (yd) 

Area

square meter (m2) 10.76 square foot (ft2) 

square kilometer (km2) 0.3861 square mile (mi2)

Volume

cubic meter (m3) 35.31 cubic foot (ft3)

cubic meter (m3) 1.308 cubic yard (yd3) 

cubic meter (m3) 0.0008107 acre-foot (acre-ft) 

Flow rate

millimeter per year (mm/hr) 0.03937 inch per year (in/hr) 

Vertical coordinate information is referenced to the “North American Vertical Datum of 1988 (NAVD 88)”

Horizontal coordinate information is referenced to the “North American Datum of 1983 (NAD 83)”
1

Probability and Volume of Potential Postwildfire Debris 

Flows in the 2011 Monument Burn Area, Southeastern 

Arizona

By Barbara C. Ruddy and Kristine L. Verdin

Abstract

This report presents a preliminary emergency assessment of the debris-flow hazards from 

drainage basins burned by the Monument wildfire in southeastern Arizona, in 2011. Empirical models 

derived from statistical evaluation of data collected from recently burned drainage basins throughout the 

intermountain Western United States were used to estimate the probability of debris-flow occurrence and 

volumes of debris flows for selected drainage basins. Input for the models include measures of burn 

severity, topographic characteristics, soil properties, and rainfall total and intensity for a (1) 2-yearrecurrence, 30-minute-duration rainfall, (2) 5-year-recurrence, 30-minute-duration rainfall, and (3) 10-

year-recurrence, 30-minute-duration rainfall. 

Estimated debris-flow probabilities in the drainage basins of interest ranged from a low of 26 

percent in response to the 2-year-recurrence, 30-minute-duration rainfall to 100 percent in response to 

the 10-year-recurrence, 30-minute-duration rainfall. The high probabilities in all modeled drainage 

basins are likely due to the abundance of steep hillslopes and the extensive areas burned at moderately 

to high severities. The estimated volumes ranged from a low of about 2,000 cubic meters to a high of 

greater than 200,000 cubic meters. 

Introduction 

The objective of this report is to present a preliminary emergency assessment of the debris-flow 

hazards from drainage basins burned by the Monument wildfire in southeastern Arizona, in 2011 (figs. 

1, 2, and 3, table 1). Debris flows, fast-moving slurries of sediment and water, have been documented 

after many wildfires in the western United States (Cannon and others, 2010) and can threaten lives, 

property, infrastructure, aquatic habitats, and water supplies. Wildfires can denude hillslopes of 

vegetation and can change soil properties that affect watershed hydrology and sediment-transport 

processes. Even small postwildfire rainstorms can increase overland runoff that erodes soil, rock, ash, 

and vegetative debris from hillslopes (Cannon and others, 2008). This increased runoff concentrates in 

stream channels and entrains additional sediment that can lead to the generation of destructive debris 

flows. Debris flow hazards are most significant 1 to 3 years following wildfires (Susan Cannon, U.S. 

Geological Survey, written commun., 2010). 

Debris flows have been documented in parts of the burned area where wildfires have occurred in 

the past (1977 in the Miller Creek drainage and 1988 in Ash Canyon) (Wohl and Pearthree, 1991). In 

addition, on July 10, 2011, a postwildfire debris flow occurred in the Miller Creek drainage (Ann 

Youberg, Arizona Geological Survey, written commun., 2011). 
2

Figure 1. Location of drainage basins of interest and soil burn severity map of the 2011 Monument burn area, 

southeastern Arizona.
3

Figure 2. Estimated probability of potential postwildfire debris flows in the 2011 Monument burn area, 

southeastern Arizona, in response to a 5-year-recurrence, 30-minute-duration rainfall.
4

Figure 3. Estimated volumes of potential postwildfire debris flow in the 2011 Monument burn area, southeastern 

Arizona, in response to a 5-year-recurrence, 30-minute-duration rainfall.

110°16'

110°18'

110°14'

110°18'

31°24'

31°22' 31°22'

110°18'

31°26'

9

8

7

6

5 4

3

2

1

18

17

16

15

14

13

12

11

10

0 0.5 1 Kilometer

0 0.5 1 Mile

Explanation

Volume at drainage-basin pour point

1 to 100

101 to 1,000

1,101 to 10,000

10,001 to 100,000

greater than 100,001

Drainage-basin boundaries

Debris-flow volume along the drainage

1 to 100

101 to 1,000

1,001 to 10,000

10,001 to 100,000

greater than 100,001 

Estimated volume of a debris flow

(cubic meters) in response to a 

5-year, 30-minute rainfall

Base from 10-meter National Elevation 

Dataset NAD 1983 UTM zone 12N

network

Numbers at pour points refer to U. S.

Geological Survey drainage-basin 

numbers in table 1.
5
6

This report presents an emergency debris-flow hazards assessment, done by the U. S. Geological 

Survey in collaboration with the State of Arizona, U. S. Department of Agriculture Forest Service, and 

the Federal Emergency Management Agency Region IX. Estimates are provided of the predicted 

probability of occurrence and volume of debris that could flow from 18 drainage-basin outlets in 

response to three design (or reference) storms: (1) 2-year-recurrence, 30-minute-duration rainfall

(25–35 mm, a 50 percent chance in any given year), (2) 5-year-recurrence, 30-minute-duration rainfall

(33–45 mm, a 20 percent chance in any given year), and (3) 10-year-recurrence, 30-minute-duration 

rainfall (38–52 mm, a 10 percent chance in any given year). The procedures used for this report are 

based on the work by Cannon and others (2007; 2010) and Ruddy and others (2010).

A set of empirical equations (models) developed by Cannon and others (2010) and derived from 

statistical evaluation of data collected from recently burned drainage basins throughout the 

intermountain western United States were used to estimate the probability of debris-flow occurrence and 

volumes of debris flows for selected drainage basins. The regression equation (eq. 1) of debris-flow 

probability is based on empirical data described by Cannon and others (2010, model A). The model for 

debris-flow probability is as follows:

P = e x /(1 + e x

), (1)

 where P is the probability of debris-flow occurrence in fractional form; and

x = –0.7 + 0.03(%SG30) – 1.6(R) + 0.06(%AB) + 0.07(I) + 0.2(%C) – 0.4(LL),

where,

%SG30 is the percentage of the drainage basin area with slope equal to or greater than 30

percent; 

R is drainage basin ruggedness, the change in drainage basin elevation (meters) divided by the 

square root of the drainage basin area (square meters) (Melton, 1965); 

%AB is the percentage of drainage-basin area burned at moderate and high severity (data for this 

investigation from Dave Young, U.S. Department of Agriculture Forest Service, written commun., 

2011); 

I is average storm intensity (calculated by dividing total storm rainfall [Mike McLane, National 

Weather Service, written commun., 2011] by the storm duration, in millimeters per hour); 

%C is clay content of the soil (in percent) (U.S. Department of Agriculture, National Resources 

Conservation Service, 1991, and Schwarz and Alexander, 1995), and 

LL is the liquid limit of the soil (percentage of soil moisture by weight) (U.S. Department of 

Agriculture, National Resources Conservation Service, 1991, and Schwarz and Alexander, 1995). 

Cannon and others (2010) also developed an empirical model that can be used to estimate the 

volume of debris flow that would likely be produced from recently burned drainage basins: 

 ln V = 7.2 + 0.6(ln SG30) + 0.7(AB)

0.5 + 0.2(T)0.5 + 0.3, (2) 

where,

V is the debris-flow volume, including water, sediment, and debris (cubic meters); 

SG30 is the area of the drainage basin with slopes equal to or greater than 30 percent (square 

kilometers); 

AB is the drainage-basin area burned at moderate to high severity (square kilometers); 
7

T is the total storm rainfall depth (millimeters); and 0.3 is a bias correction factor that changes 

the predicted estimate from a median to a mean value (Helsel and Hirsch, 2002).

Each of the 18 drainage basins to be evaluated was identified by a single outlet (pour point) 

located at the drainage-basin mouth, but some basins are included within larger basins (table 1). 

Conditions within the drainage-basin area upstream from that pour point were used to estimate debrisflow probability and volume for a specific design storm (Cannon and others, 2010). Locations drainagebasin pour points were identified by the Burned Area Emergency Response (BAER) team for the 

Monument fire (indicated by USGS drainage-basin numbers in figures 1, 2, and 3 and table 1). 

A preliminary map was created using a continuous parameterization technique. With this 

technique estimates of debris-flow probability and volume (Cannon and others, 2010) were obtained 

continuously along the drainage network (or flow-direction matrix) (Verdin and Greenlee, 2003; Verdin 

and Worstell, 2008). This technique was developed as an alternative to traditional basin characterization 

approaches, which requires “a priori” definition of drainage-basin outlets (pour points) and their 

corresponding basins.

Using the 1/3-arc-second National Elevation Dataset (Gesch and others, 2002) (10-meter 

nominal resolution) for the study area and the flow structure inherent in the digital elevation model 

(DEM), the independent variables driving the probability and volume equations were evaluated for 

every 10-meter grid cell within the extent of the DEM. Rainfall total and rainfall intensity were 

calculated from 800-meter precipitation grids provided by the National Weather Service (Mike 

McLane, National Weather Service, written commun., 2011). Values for all of the independent variables 

driving the predictive equations were obtained using the continuous parameterization approach in a 

geographic information system (GIS), although “ruggedness” required a separate ArcGIS program 

(ESRI, 2009) to evaluate this variable for each grid cell in the study area. Once the surfaces of the

independent variables were evaluated for every grid cell within the study area, the probability and 

volume equations were solved by using map algebra for each location. Identification of the probability 

or volume of a debris flow at any location within the study area is possible by querying the derived 

surfaces. For this assessment, a raster sampling technique was used to identify the values of debris-flow 

probability and volume at selected locations along the drainage network derived from a digital elevation 

model.

The continuous parameterization technique allows for faster parameter characterization and the 

ability for characterization upstream from any location, not just predefined basin outlets. The continuous 

parameterization technique provides a synoptic view of the entire study area which aids in the 

identification of smaller, high-probability basins within a larger basin. This allows for rapid evaluation 

of potential "hot spots" within the burned area -- locations with potentially high probabilities of large 

debris flows. Although modeled probabilities and volumes at the pour point of a predefined basin 

might be relatively low, locations within the drainage basin might have substantially higher debris flow 

potential. These can be easily identified with this technique.

Estimated Debris Flow Probabilities and Volumes

The estimated debris-flow probabilities and volumes in response to the different rainfall 

scenarios are presented in table 1. Estimated probabilities of debris flows were high for most basins. 

Conditions in 13 of the 18 basins resulted in debris-flow probabilities greater than 80 percent in 

response to the 2-year-recurrence, 30-minute-duration rainfall; 16 out of 18 basins in response to the 5-

year-recurrence; 30-minute-duration rainfall; and 17 out of 18 in response to the 10-year-recurrence, 30-

minute-duration rainfall. Drainage basin 15 showed the lowest probabilities, which ranged from 26 to 69 

percent in response to the 2-year-recurrence, 30-minute-duration rainfall and the 10-year-recurrence, 30-
8

minute-duration rainfall, respectively. Debris-flow probabilities for USGS drainage basins 6, 12, and 18 

ranged from 92 to 100 percent for 2-year-recurrence, 30-minute-duration rainfall and 10-yearrecurrence, 30-minute-duration rainfall. These high probabilities are likely due to a combination of steep 

hillslopes burned at moderate and high burn severities, and indicate a potential for substantial debrisflow impacts to any buildings, roads, bridges, culverts, and reservoirs located both within these 

drainages and immediately downstream from the burned area. However, even small debris flows that 

affect structures at the basin outlets could cause considerable damage.

Estimated debris-flow volumes ranged from 2,680 m3 for USGS drainage basin 1 to 216,000 m 

3 for USGS drainage basin 6 for a 10-year-recurrence, 30-minute-duration rainfall. Estimated debris 

flow volumes for drainage basins 6, 12, and 18 were at least an order of magnitude greater than those 

estimated for the 15 other drainage basins. About 90 percent of USGS drainage basin 12 is composed of 

USGS drainage basin 18. Although larger rainstorms produced estimates of larger debris-flow volume, 

the increase in estimated volumes for most basins from a 2-year-recurrence, 30-minute-duration rainfall 

to a 10-year-recurrence, 30-minute-duration rainfall only increased by about 20 percent. A 2-yearrecurrence, 30-minute-duration rainfall (a relatively “small” rainfall amount) is likely to produce a high 

probability of a debris flow. 

An example of the additional detail provided by the continuous parameterization approach is 

shown in USGS drainage basin 15 on figure 2. While the probability of a debris flow occurring at the 

pour point of the drainage basin is 50 percent (table 1), the probabilities of a debris flow along the 

channels upstream from the pour point are much higher. The red channel reaches along the drainage 

network upstream from the pour point of basin 15 indicate higher debris flow probabilities at these 

locations with values as high as 81–100 percent.

Use and Limitations of the Assessment

This assessment presents estimates of debris-flow probability and volume for selected drainage 

basins in the area burned by the Monument wildfire. Estimates were made in response to three design 

[or reference] storms: (1) a 2-year-recurrence, 30-minute-duration rainfall (a 50 percent chance in any 

given year). (2) a 5-year-recurrence, 30-minute-duration rainfall (a 20 percent chance in any given year) 

and (3) a 10-year-recurrence, 30-minute-duration rainfall (a 10 percent chance in any given year). 

Larger, less frequent storms are more likely to produce larger debris flows; however, the analyses 

indicate that even relatively common rainfall events could result in substantial runoff and erosion 

producing debris flows. Some areas within the selected basins may have higher debris-flow probabilities 

than those shown at the drainage-basin outlet, or pour point, shown on figure 2, and debris flows may 

not be produced from all basins during a 2 or 5-year recurrence rainfall. The estimates are meant to be 

valid for up to 3 years after the wildfire (Susan Cannon, U.S. Geological Survey, written commun., 

2010). The maps may be used to prioritize areas where emergency flood warnings or erosion mitigation 

may be needed prior to rainstorms within these basins, at their outlets, or in areas downstream from 

these basins. This assessment evaluates only postwildfire debris flows (Cannon and others, 2007). 

Substantial hazards from flash floods without debris flow may remain for many years after a fire, but are 

beyond the scope of this analysis.

This analysis is preliminary and is subject to revision. It is being provided owing to the need for 

timely best science information. The assessment is provided on the condition that neither the U.S. 

Geological Survey nor the United States Government may be held liable for any damages resulting from 

the authorized or unauthorized use of the assessment. 
9

References Cited

Cannon, S.H., Gartner, J.E., and Michael, J.A., 2007, Methods for the emergency assessment of debrisflow hazards from basins burned by the fires of 2007, southern California: U.S. Geological Survey 

Open-File Report 2007–1384, 10 p, http://pubs.usgs.gov/of/2007/1384.

Cannon, S.H., Gartner, J.E., Wilson, R.C., and Laber, J.L., 2008, Storm rainfall conditions for floods 

and debris flows from recently burned areas in southwestern Colorado and southern California: 

Geomorphology, v. 6, no. 3-4, p. 250–269 doi:10.1019/j.geomorph.2008.03.019.

Cannon, S.H., Gartner, J.E., Rupert, M.G., Michael, J.A., Rea, A.H., and Parrett, C., 2010, Predicting 

the probability and volume of postwildfire debris flows in the intermountain western United States: 

Geological Society of America Bulletin, v. 122, p. 127–144.

ESRI, 2009, ArcGIS v. 9.3: Redlands, Calif., ESRI.

Gesch, D., Oimoen, M., Greenlee, S., Nelson, C., Steuck, M., and Tyler, D., 2002, The national 

elevation dataset: Photogrammetric Engineering and Remote Sensing, v. 68, no. 1, p. 5–11. 

Helsel, D.R., and Hirsch, R.M., 2002, Statistical methods in water resources: New York, Elsevier 

Studies in Environmental Science, v. 49, 529 p.

Melton, M.A., 1965, The geomorphic and paleoclimate significance of alluvial deposits in southern 

Arizona: Journal of Geology, v. 73, p. 1–38. 

Ruddy, B.C., Stevens, M.R., Verdin, K.L., and Elliott, J.G., 2010, Probability and volume of potential 

postwildfire debris flows in the 2010 Fourmile burn area, Boulder County, Colorado: U.S. Geological 

Survey Open-File Report 2010–1244, 5 p., http://pubs.usgs.gov/of/2010/1244.

Schwarz, G.E., and Alexander, R.B., 1995, State Soil Geographic (STATSGO) data base for the 

conterminous United States: U.S. Geological Survey Open-File Report 95–449, 

http://water.usgs.gov/GIS/metadata/usgswrd/XML/ussoils.xml.

U.S. Department of Agriculture, National Resources Conservation Service, 1991, State Soil Geographic 

(STATSGO) database—Data use information: Lincoln, Nebr., U.S. Department of Agriculture, 

National Soil Survey Center, Miscellaneous Publication 1492, 110 p. [Revised July 1994]

Verdin, K.L. and Greenlee, S., 2003, Continuous parameterization using EDNA, in ESRI User’s 

Conference, San Diego, Calif., July 7–11, 2003, Proceedings: Redlands, Calif., ESRI, 9 p., accessed 

May, 2007, at http://gis.esri.com/library/userconf/proc03/p0617.pdf.

Verdin, K. L. and Worstell, B., 2008, A fully distributed implementation of mean annual streamflow 

regional regression equations: Journal of the American Water Resources Association, v. 44, no. 6, p. 

1537–1547. doi: 10.1111/j.1752-1688.2008.00258.x.

Wohl, E.E., and Pearthree, P.A., 1991, Debris flows as geomorphic agents in the Huachuca Mountains 

of southeastern Arizona: Geomorphology, v. 4, no. 3-4, p. 273–292.