Probability and Volume of Potential Postwildfire Debris 

Flows in the 2011 Wallow Burn Area, Eastern Arizona

By Barbara C. Ruddy

Open-File Report 2011–1214

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

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Suggested citation:

Ruddy, B.C., 2011, Probability and volume of potential postwildfire debris flows in the 2011 Wallow burn area, 

eastern Arizona: U.S. Geological Survey Open-File Report 2011–1214, 11 p.

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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 ........................................................................................................ 9

Use and Limitations of the Assessment........................................................................................................................10

References Cited..........................................................................................................................................................11

Figures

1. Location of drainage basins of interest and BARC burn severity map of the 2011 Wallow burn area, eastern

Arizona (BARC, Burned Area Reflectance Classification) ............................................................................................. 2

2. Estimated probability of potential postwildfire debris flows in the 2011 Wallow burn area, eastern Arizona in 

response to a 10-year-recurrence, 1-hour-duration rainfall............................................................................................ 3

3. Estimated volumes of potential postwildfire debris flows in the 2011 Wallow burn area, eastern Arizona in 

response to a 10-year-recurrence, 1-hour-duration rainfall............................................................................................ 4 

4. Estimated probability of potential postwildfire debris flows along the drainage network in drainage basins 62 

through 65 in the 2011 Wallow burn area, eastern Arizona, in response to a 10-year-recurrence, 1-hour-duration 

rainfall............................................................................................................................................................................ 5 

Table

1. Estimated debris-flow probabilities and volumes for the 2011 Wallow burn area, eastern Arizona ........................ 6
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 Wallow Burn Area, Eastern Arizona

By Barbara C. Ruddy

Abstract

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

drainage basins burned in 2011 by the Wallow wildfire in eastern Arizona. 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 

debris-flow volumes 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) 10-yearrecurrence, 1-hour-duration rainfall and (2) 25-year-recurrence, 1-hour-duration rainfall. 

Estimated debris-flow probabilities in the drainage basins of interest ranged from less than 1 

percent in response to both the 10-year-recurrence, 1-hour-duration rainfall and the 25-year-recurrence, 

1-hour-duration rainfall to a high of 41 percent in response to the 25-year-recurrence, 1-hour-duration 

rainfall. The low probabilities in all modeled drainage basins are likely due to extensive low-gradient 

hillslopes, burned at low severities, and large drainage-basin areas (greater than 25 square kilometers). 

Estimated debris-flow volumes ranged from a low of 24 cubic meters to a high of greater than 100,000 

cubic meters, indicating a considerable hazard should debris flows occur. 

Introduction

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 

rainstorms after a fire can increase overland runoff that erodes soil, rock, ash, and vegetative debris 

from hillslopes (Cannon and others, 2008). This increased runoff concentrates in drainage networks and 

entrains additional sediment that may 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 not been documented from the area burned by Wallow fire

in the past, yet potential debris flows in such a large burned area remain a concern for emergency 

managers. 

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

drainage basins burned in 2011 by the Wallow wildfire in eastern Arizona (figs. 1, 2, 3, and 4, table 1). 

This assessment was done by the U. S. Geological Survey (USGS) 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 debris-flow occurrence and 

volume of debris that could flow from 42 drainage-basin outlets in response to two design storms: (1) 

10-year-recurrence, 1-hour-duration rainfall of 39–49 millimeters (mm) (a 10 percent chance of 

occurrence in any given year) and (2) 25-year-recurrence, 1-hour-duration rainfall 47–58 mm (a 4 

percent chance of occurrence in any given year). The methods used for this assessment are based on the 

work by Cannon and others (2007; 2010) and Ruddy and others (2010). 
2

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

eastern Arizona (BARC, Burned Area Reflectance Classification). 
3

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

Arizona, in response to a 10-year-recurrence, 1-hour-duration rainfall. 
4

Figure 3. Estimated volumes of potential postwildfire debris flows in the 2011 Wallow burn area, easternArizona, 

in response to a 10-year-recurrence, 1-hour-duration rainfall.
5

Figure 4. Estimated probability of potential postwildfire debris flows along the drainage network in drainage 

basins 62 through 65 in the 2011 Wallow burn area, eastern Arizona, in response to a 10-year-recurrence, 

1-hour-duration rainfall.
6

Table 1. Estimated debris-flow probabilities and volumes for the Wallow burn area, eastern Arizona.

[BAER, burned area emergency response; HUC, U.S. Geological Survey hydrologic unit code;>, greater than; <, less than]

Drainage-basin 

number for pour 

point (fig.1–4)

BAER Description or HUC 12 number and name Longitude Debris flow in response to a 

10-year, 1-hour rainfall

Debris flow in response to a 

25-year, 1-hour rainfall

degrees, 

minutes, 

seconds

Probability 

(percent)

Volume

(cubic 

meters)

Probability 

(percent)

Volume

(cubic 

meters)

1a 150200010105 Riggs Creek-Nutrioso Creek 109°11'56" 2 > 100,000 3 > 100,000

2b 150200010104 Rudd Creek 109°11'56" 1 > 100,000 1 > 100,000

3c 150200010206 Water Canyon Creek 109°18'47" < 1 80,500 < 1 90,500

4 150200010204 South Fork Little Colorado River 109°24'58" < 1 > 100,000 1 > 100,000

5 150200010201 West Fork Little Colorado River 109°27'25" 1 95,600 1 > 100,000

6 150200010202 East Fork Little Colorado River 109°27'25" 1 > 100,000 1 > 100,000

7d 150200010102 Colter Creek 109°12'25" 1 > 100,000 2 > 100,000

8e 150200010103 Paddy Creek-Nutrioso Creek 109°12'25" 7 > 100,000 12 > 100,000

9f 150200010101 Auger Creek 109°12'58" 4 > 100,000 6 > 100,000

10g 150400040301 San Fracisco River-Luna Lake 109°04'55" 1 > 100,000 2 > 100,000

11 150400040501 Coleman Creek 109°09'36" 2 > 100,000 3 > 100,000

12h 150400040503 Campbell Blue Creek 109°02'42" 2 > 100,000 3 > 100,000

45 Gary Hart 109°14'24" < 1 781 < 1 878

46 Home by Colter Cr. 109°15'18" 1 > 100,000 2 > 100,000

47 Home with Headcut 109°14'24" 16 2,890 25 3,250

48 Lena Hamblin Home 109°13'08" 1 96 1 107

49 Milligan B. Olsen Property 109°17'42" 1 6,400 2 7,220

50 Sec. 21 Pourpt. (Mulching Anaysis) 109°10'19" 9 6,890 14 7,740

51 Sec. 22 Pourpt. (Mulching Analysis) 109°10'01" 14 10,300 21 11,600

52 Sec. 24 House 109°07'52" 4 1,940 7 2,170

53 RobertODell 109°08'38" 12 20,000 18 22,400

54 Aspen Lodge 109°09'36" 11 1,390 18 1,560

55 S. Mountain Home #14 109°09'04" < 1 407 < 1 456

56 Eager Wash A Drainage 109°19'26" < 1 10,300 < 1 11,500
7

57 Coon Spr. 109°22'12" 15 7,560 23 8,520

58 W. Fork Dry Rd 261H2 109°19'41" 1 1,930 2 2,170

59 Grapevine Residence 109°20'24" < 1 39,800 < 1 44,800

60 Water Cyn. Admin. 109°17'38" < 1 73,000 < 1 82,100

61 E. Fork Davis Culvert 109°06'54" 19 15,600 28 17,500

62 W. Fork Davis Culvert 109°07'37" 26 23,000 37 25,900

63 Woods Cr. Culvert 109°08'46" < 1 48 < 1 54

64 Watts Cr. 109°10'23" 29 100,000 41 > 100,000

65 Alpaca Residence 109°10'55" 17 15,400 26 17,300

66 Hulsey Cr. 109°11'10" 7 31,500 11 35,400

67 Milk Cr. Terry Ranch 109°11'20" < 1 25 1 29

68 Slade Res. 1320 109°17'31" < 1 24 < 1 26

69 Slade Res. 2 109°17'35" < 1 83,400 < 1 93,700

70 John May Res. 109°09'29" 1 47,000 2 52,800

71 Casita Escondia 109°11'10" 11 > 100,000 17 > 100,000

72 Luce Ranch 109°09'58" 2 > 100,000 4 > 100,000

73 Sprucedale 109°19'37" < 1 38,400 1 43,200

74 Paddy Cr. Res. 109°09'58" 15 > 100,000 23 > 100,000

a includes drainage-basin numbers 61, 62, 63, 64, 65, and 70 b includes drainage-basin number 49 c includes drainage-basin numbers 58, 60, 68, and 69 d includes drainage-basin number 46 e includes drainage-basin numbers 50, 51, 66, 67, 71, and 74 f includes drainage-basin numbers 45, 47, and 48 g includes drainage-basin numbers 52, 53, 54, and 55 h includes drainage-basin number 72
8

A set of empirical equations (models) was used to estimate the probability of debris-flow 

occurrence and volumes of debris flows for selected drainage basins. These models were developed by 

Cannon and others (2010) and were derived from statistical evaluation of data collected from recently 

burned drainage basins throughout the intermountain western United States. 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 e is the mathematical 

constant (approximately 2.718...); 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 

assessment provided by Nancy Loving, 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 at which the soil changes from plastic to liquid behavior 

(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); 

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 42 evaluated drainage basins was identified by a single outlet (pour point) located at 

the drainage-basin mouth, however, some subbasins are included within larger basins (table 1 and 

figure 1). Conditions within the drainage-basin area upstream from the identified pour point were used 

to estimate debris-flow probability and volume for a specific design storm (Cannon and others, 2010). 
9

Locations of drainage-basin pour points were identified by the Burned Area Emergency Response 

(BAER) team for the Wallow fire (indicated by drainage-basin numbers in figures 1, 2, and 3 and 

table 1). 

In addition to the hazard assessments for the discrete drainage basins identified by pour points, a 

continuous parameterization technique was used to map potential debris-flow hazards along the 

drainage network of each basin. With this technique estimates of debris-flow probability and volume 

(Cannon and others, 2010) were obtained continuously along the drainage network (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 (m)

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-m grid cell within the extent of the DEM. Rainfall totals and rainfall intensities were 

calculated from 800-m 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). 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 

(Verdin and Greenlee, 2003; Verdin and Worstell, 2008) was used to identify the values of debris-flow 

probability and volume at selected locations along the drainage network derived from a DEM. 

The continuous parameterization technique allows for faster parameter characterization, and the 

ability to characterize debris-flow hazard upstream from any location, not just at predefined basin 

outlets. The continuous parameterization technique provides a synoptic view of the entire study area, 

which aids in the identification of smaller basins with high probabilities of debris flows 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 potential for debris flow. These can be easily identified with the continuous 

parameterization 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 generally were low. 

Conditions in all of the basins resulted in debris-flow probabilities less than 30 percent in response to 

the 10-year-recurrence, 1-hour-duration rainfall. Conditions in all of the basins except basin 64 

(estimated probability was 41 percent) resulted in debris-flow probabilities less than 40 percent in 

response to the 25-year-recurrence, 1-hour-duration rainfall. These low probabilities are likely due to a 

combination of gentle gradient hillslopes and little drainage-basin area burned at moderate and high 

burn severities. The larger basins, especially those greater than 25 square kilometers (km2

), had the 

lowest estimated probabilities and the largest estimated volumes. It is possible for a larger drainage 

basin to have a low probability of a debris flow at the pour point and for debris flows to be produced 

from the subbasins within the larger drainage basin. Cannon and others (2010) found that debris flows 

were not observed at the outlets of drainage basins greater than about 30 km2 (12 square miles) in area. 
10

Although the estimated probabilities for the designated basins are mostly low, there still is the potential 

for debris-flow impacts to any buildings, roads, bridges, culverts, or reservoirs located both within these 

drainages and immediately downstream from the burned area. It is important to recognize that even 

small debris flows at the basin outlets could cause considerable damage to infrastructure. 

Estimated debris-flow volumes ranged from 24 m3 for drainage basin 68 in response to a 

10-year, 1-hour rainfall to greater than 100,000 m3 at several drainage basins in response to the two 

design rainfalls. The model predicts volumes greater than 100,000 m3, however, there is high 

uncertainty at volumes greater than 100,000 m3

 (Susan Cannon, U.S. Geological Survey, written 

commun., 2011). Drainage basins with the largest areas had the largest estimated debris-flow volumes. 

Although the estimated probabilities for the designated basins are low, the volume of debris flow 

that might be produced could be considerable for some drainage basins. Thus, one could expect debrisflow impacts to any buildings, roads, bridges, culverts or reservoirs located both within these drainages 

and immediately downstream from the burned area. Estimated debris-flow probabilities in the drainage 

basins of interest ranged from less than 1 percent in response to both the 10-year-recurrence, 1-hourduration rainfall and the 25-year-recurrence, 1-hour-duration rainfall to a high of 41 percent in response 

to the 25-year-recurrence, 1-hour-duration rainfall. 

Hazardous areas within drainage basins 62 through 65 are identified by the continuous 

parameterization approach and are shown on figure 4. The red channel reaches upstream from the pour 

point indicate debris flow probabilities as high as 81–100 percent. Although the probabilities of a debris 

flow occurring in response to the 10-year-recurrence, 1-hour duration rainfall at the pour points of these 

drainage basins are between 17 and 29 percent (table 1), the continuous parameterization techniques 

indicate locations along specific channel reaches where the probabilities are much higher.

Use and Limitations of the Assessment

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

basins and along their channels (or drainage networks) in the area burned by the 2011 Wallow wildfire. 

Estimates were made in response to two design storms: (1) a 10-year-recurrence, 1-hour-duration 

rainfall (a 10 percent chance of occurrence in any given year) and (2) a 25-year-recurrence, 1-hourduration rainfall (a 4 percent chance of occurrence in any given year). Some areas within the selected 

drainage basins may have higher debris-flow probabilities than those shown at the drainage-basin outlet, 

or pour point, shown in figure 2, and debris flows may not be produced from all basins during a 10- or 

25-year recurrence rainfall. The estimates are likely 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 wildfire, but are beyond the scope of this assessment. 

This assessment is preliminary and is subject to revision. It is being provided due 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. 
11

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. 

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: U.S. Geological Survey 

Techniques of Water Resources Investigations, book 4, chap. A3, 522 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.