U.S. DEPARTMENT OF THE INTERIOR 

U.S. GEQLOGtCBL SURVEY *

Geographic inforrifetion systeni^IS^ procedure fo 

preliminjary delineation of debris^fioV hazard areas 

from a digite! terraiMnodel, Madison

Ru

By 

tipbell1 and Pete Chirico

Documentation for and preliminary evaluation of the diital terrain data and GIS proced

applied to make the potential debris rflow hazards map > 

avestigations Series Ma;vi-262j&B (Morgan and others,

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. Qpologic;

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l Survey MiscelfaneouV

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en-File Report 99-336

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i report is preliminary and liui i^ot been reviewed for conformity with- ~\ \0>'. Geological Survey 

editorial standard^ or the North Anu-riean Strati uraphic Code. Ai|y use of t ade, product, or firm

aames is fofcjjcscripti^purposes or

[f.S. Geological Survey^

Department of Earth Scierifc^ i 

JJniversity fiff California, Riversiiic 

Overside, CA^2521

i not imply endorsement by the I .S. Go>

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CONTENTS

Page

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

Procedure and model .............................................. 2

Data input to model................................................ 3

Model concepts ................................................... 4

ARC/INFO .ami program ........................................... 6

Discussion .................................................... 8

Acknowledgments ................................................ 10

References ................................................... 11

ILLUSTRATIONS

Page 

Examples of input data and grid manipulations to produce a preliminary

debris-flow hazards map ......................... 12

Reference on Page Page

Figure 1. Digital line graph topography and shaded terrain model . . 2 13

Figure 2. Slope map .................................... 2 14

Figure 3. Stream order .................................. 2 15

Figure 4. Stream (thalweg) elevations ....................... 2 16

Figure 5 a. 10 meter euclidian allocation of stream elevations ...... 2 17

Figure 5b. 30 meter euclidian allocation of stream elevations ...... 2 18

Figure 5c. 50 meter euclidian allocation of stream elevations ...... 2 19

Figure 6a. Flow depths for 10 meter euclidian allocation ......... 3 20

Figure 6b. Flow depths for 30 meter euclidian allocation ......... 3 21

Figure 6c. Flow depths for 50 meter euclidian allocation ......... 3 22

Figure 7. 50 meter euclidian allocation of stream orders ......... 3 23

Figure 8. Combined flow-depth grids constrained by slope and order 3 24

Figure 9. Completed hazard map ........................... 3 25

TABLE

Page

Table 1. Comparisons of model-predicted and inventoried hazards ............ 9
GEOGRAPHIC INFORMATION SYSTEM (GIS) PROCEDURE FOR

PRELIMINARY DELINEATION OF DEBRIS-FLOW HAZARD AREAS

FROM A DIGITAL TERRAIN MODEL, MADISON COUNTY, VIRGINIA

by Russell H. Campbell and Pete Chirico

INTRODUCTION

Studies of debris-flow and flood effects of a severe storm in Madison County, Virginia, on 

June 27, 1995, have identified dynamic (rainfall and average depth of debris-flow surges) and 

static (slope, channel position and relative elevation) terrain factors that contribute to vulnerability 

to debris-flow hazards (Morgan and others, 1997; Morgan and others, in press). The spatial 

distribution of vulnerable areas, as defined by this combination of factors, has been delineated on 

a map using a geographic information system (GIS) to manipulate terrain models made from U.S. 

Geological Survey digital line graph (DLG) data for 7.5 min. (l:24,000-scale) quadrangle maps. 

The procedure yields a map that shows the areas in and adjacent to stream channels that would be 

affected by a debris-flow surge of user-specified depth, as approximated from a digital terrah 

modeL It differs from other procedures for mapping potential debris-flow runout, which require 

user inputs that specify initial volumes (e.g., Iverson and others, 1998; Ellen and others, 1993).

The procedure is carried out as a single ARC/INFO1 .ami (ARC macro language) 

program. The preliminary hazard map prepared by this procedure for the Madison County s*udy 

area identifies most of the areas that were affected by debris flows during the June 27, 1995, 

storm. Most of the disparities between model-predicted hazard areas and the inventoried effects 

of that storm can be attributed to inaccuracies in the digital terrain model, particularly where 

slopes and stream gradients are flatter than about 14 degrees. In addition, some computational 

problems arise where stream flow is other than north-to-south because of the sequence with 

which calculations are carried out in ARC/INFO GRID.

Post-storm measurements of elevation, slope, aspect, curvature, colluvial thickness, and 

amount of rainfall were made in the Madison County area, especially at source areas and along 

debris-flow paths (Morgan and others, 1997; Morgan and others, in press). The measurements 

included the depth of flows that moved through channels (vertical distances between thalwegs and 

mudlines flanking the channels). Measured depths ranged from less than 1 meter to nearly 14 

meters, but most were about 3 meters. Moreover, in many channels the surge depths were 

approximately constant for long reaches of first-, second-, and perhaps higher-order drainage 

lines. This observation implies (a) slurry volume was increased as surges moved downstream, and 

(b) the heights of surge fronts were limited by some mechanism that prevented added volume 

from "piling-up" indefinitely.

The amount and the spatial distribution of rainfall of the June 27, 1995, storm was th^ 

principal dynamic control for the spatial distribution of debris flows. The absence of debris flows 

in adjacent parts of the Blue Ridge having nearly identical static properties (elevation, slope,

1The use of the brand name of the commercial software program does not constitute endorsement by 

the U.S. Geological Survey.
aspect, curvature, colluvial thickness and lithologic character) is a consequence of lower rair%ll 

rates and amounts in those areas (Wieczorek and others, in preparation). The model for assessing 

potential debris-flow hazards, therefore, assumes that the entire study area will be subjected to 

rainfall intensity and duration similar to that received by terrain within the 650 mm isohyet fc * the 

storm of June 27, 1995. This simple model also ignores variations in thickness and shear 

resistance of colluvium, as well as aspect and curvature, which are factors that are known or 

inferred to affect the susceptibility of hillslopes to rainfall-caused initiation of debris flows.

PROCEDURE AND MODEL

The GIS model was developed chiefly as a raster procedure using ARC/INFO GRID 

functions developed for use in modeling terrain and hydrologic flow (ESRI, 1991; ESRI, 1992). 

From U.S.G.S. contour and stream digital line graphs (DLG's) raster grids of the study area were 

prepared so that elevation, degree of slope steepness, and aspect were calculated for each 1C 

meter by 10 meter cell (Figure 1, Figure 2). From the elevation grid, derivative grids were made 

for flow direction, flow accumulation, stream net (shown as a sequence of contiguous cells en a 

background of NODATA cells), and (Strahler model) stream order (Figure 3). For gridded 

elevations derived from available contour digital line graphs, we found (after several trials) that a 

flow accumulation of 50 cells is suitable for approximating the upper ends of the inventoried 

debris-flow channels. The 50-cell flow accumulation also identifies a usable approximation of 

first-order drainage lines as picked by inspection from the contour map at 1:24,000-scale, 

although the upstream end cells of first-order drainage lines identified in this way are commcTly 

somewhat down channel from the upper ends as picked by visual inspection of the contours. The 

50-cell number was not selected to represent cells in which debris flows were initiated by the June 

27, 1995, storm, but to approximate upper ends of drainage lines in which channelized slurry flow 

may have accumulated sufficient volume (and flow depth) so that cells adjacent to the thalweg 

cells may be inundated. Because the post-storm inventories showed that virtually all debris flows 

originated from cells having slopes of 26 degrees or steeper, and that deposition commonly lxa!gan 

as surges reached channel gradients of about 14 degrees, the .ami includes an (somewhat 

ineffective) attempt to incorporate this information into model constraints that include slope: 

however, the product of the .ami still includes areas adjacent to some stream lines that head in 

basins where all slopes are gentler than 26 degrees ~ in effect, erroneously showing a greate~ 

potential for hazard than is actually expected. Consequently, a final step was to edit the hazard 

map manually to remove drainages from watersheds that lack slopes of 26 degrees or greater.

The stream channels are depicted as contiguous strings of single cells (a 1-cell-wide 

thalweg) on a background of NODATA cells. Elevations for each thalweg cell are determined from 

the grid of elevations (Figure 4). Stream gradient can be measured as the slope of each thalveg 

cell. Three new grids are formed by allocating the thalweg elevations to adjacent cells for three 

selected distances. (The distances are selected on the basis of the densities of drainage lines of 

different orders to minimize overlap of the expansion of one drainage into adjacent drainage 

basins or sub-basins. In the Madison County terrain, we used 50 m, 30 m, and 10m, 

respectively.) A surge depth of 3 meters was then added to the allocated thalweg elevations in 

each of the three grids. The result is 3 grids of contiguous cells, expanded from the thalweg grid, 

with elevations of the assigned surge depth, on a background of NODATA cells (Figures 5a, 5b and 

5c). Subtracting the terrain elevations from the allocated surge elevations, constrained to
differences greater than 0, yields three grids showing surge depths on a background 

cells (Figures 6a, 6b and 6c). The surge-depth grids can be constrained by stream order by using 

still another grid, created to allocate stream order designations to cells for the maximum of the 

previously selected distances (50 m in Madison County; Figure 7). Channel width commonly 

increases, and stream density commonly decreases, with increasing stream order and decreasing 

stream gradient. Therefore, it seems appropriate to use wider limits for the allocations of higherorder drainage lines (Figure 8). At their down-channel extremes, most of the debris flows entered 

flooding streams that rose to cover the distal ends of fans. Consequently, the flood hazard ir 

mapped as overriding the debris-flow hazard in areas below the upper limits of mapped flood 

inundation in 1995 (Figure 9).

DATA INPUT TO MODEL 

Five grids provide the information input to the .ami that generated the hazard map:

<elevation-grid>, a grid of elevations in meters at a 10-m spacing. U.S.G.S. contour DLG's for 

the 6 quadrangles that cover the study area were used to prepare line covers for the 

contours of each quadrangle. After converting the contour DLG's to ARC covers, the 

covers for the six adjoining 7.5' quadrangles that make up the entire study area were 

joined using the ARC append command, and edited along the individual quadrangle 

boundaries to insure against generating boundary artifacts in subsequent manipulations of 

the data. Next, the ARC command, createtin, was used to create a TIN surface from the 

attributed contour lines cover; the TIN was clipped to the study area boundaries; the ARC 

command, tinarc, was applied to convert the TEN into a polygon coverage with attributes 

for elevation, aspect azimuth, and slope; and the ARC command, polygrid, was usec* to 

prepare elevation, slope, and aspect grids at 10-meter spacing from the polygon cove*-. 

(Note: An initial attempt to use tin lattice to create the grids directly from the TIN failed 

to provide grids that registered exactly to the other coverages of the same map area 

possibly a result of operator error in defining the TIN boundary). The grid, <elevationgrid>, is the result of the first iteration of the GRID function, fill, on the initial elevation 

grid derived from the polygon cover (fill is a subroutine used to remove spurious sinks 

and peaks from elevation grids). (Examination of current <elevation-grid> for the 

Madison County study area indicates that it requires further editing to become truly 

depressionless.) The example, Figure 1, displays the elevation, aspect, and slope 

combined as a shaded relief map.

<slope-grid>, is an integer grid created from the floating point grid initially derived from the 

polygon cover of the TIN, which was categorized using the GRID function slice for the 

more rapid calculation of the ami. <slope-grid> cells are attributed in five slope 

categories: 0-14 degrees, 14-26 degrees, 26-34 degrees, 34-45 degrees, and greater than 

45 degrees. The example, Figure 2, displays the selected intervals of slope.

<stream-order-grid>, a grid showing stream lines, attributed with the Strahler stream order of 

each link, was prepared from the elevation grid using the flowdirection and 

flow accumulation GRID functions to create grids of flow direction and, subsequently, 

flow accumulation. A stream net was then delineated using a threshold of 50 cells for 

flow accumulation in stream order. That is, all cells that receive flow from fewer than 50
cells are assigned the value NODATA. (50 10-m cells = 5000 square meters in area, crone-half a hectare.) The 50-cell threshold was selected, after trials, to represent a fctorder drainage that appears appropriate for the 1:24,000-scale contour maps in the study 

area. Stream orders were determined using the GRID function streamorder to operate 

on the stream net and flow accumulation grids. The example, Figure 3, illustrates the 

result of the streamorder function. Notice that it does not everywhere reproduce th^ 

assignment of order that would be made by inspection of the contours.

<thalweg-elevation-grid>, a grid in which the stream net cells are attributed with their elevations 

using the GRID con function. As shown in the example, Figure 4, stream lines form 

strings of adjacent cells, each attributed with its elevation, on a field of cells having the 

value NODATA. Where gradients are steep each 10-meter cell is a different color, 

indicating elevation changes of at least one meter between adjacent cells; where grad: °*its 

are gentle, two or more adjacent cells may show a single color, indicating elevation 

differences of less than one meter.

<inventory-grid> shows the flooded areas and the debris-flow tracks inventoried by fieldwork 

and air photo interpretation following the June 27, 1995, storm. The ARC command, 

poly grid, was used to create <inventory-grid> from the ARC polygon cover of inventory 

mapping,>. An item, SEL, in the polygon attribute table was assigned integers 1, 

<inventory-cover 2, 3, and 4, to designate nocolor, debris flows, stream floods, and 

background color, respectively, (1, <4nocolor", identifies border zones outside the stuty 

area; and 4, "background color", identifies zones within the study area that lack debrisflow or flood features). These integers became the attributes in the .VAT of <inventorygrid>. Figures 8 and 9 include <inventory-cover> as an overlay, illustrating the 

distribution of inventoried debris-flows and flooding.

MODEL CONCEPTS

The procedures in the ami can be described as four steps:

STEP 1. Create euclidian allocation grids, based on the elevations of the cells marking the 

stream lines, for threshold distances of 50m, 30m, and 10m. The eucallocation GRID 

function operates on the grid <thalweg-elevation-grid> to extend the area attributed with 

the elevation of the single-cell-width stream line to distances of 50, 30, and 10 meter?, 

respectively. The resulting grids display the stream lines as bands of cells, 11,7, and 3 

cells wide on a background of NODATA cells. Figures 5a, 5b and 5c show an example 

using a small part of the Madison County study area.

The eucallocation function results in only an approximation of the ideal extension 

of attributes. Ideally, we would like to extend the elevation of the thalweg cell to adjacent 

cells in a direction perpendicular to the stream lines for the respective distances, forming a 

band of cells in which a cross-sectional area of the drainages can be calculated for a jriven 

depth. The eucallocation function extends a thalweg cell elevation radially, in all 

directions; but the succession of partial overwrites as grid algebra calculations proceed 

systematically along rows from the upper left corner of the grid to the lower right comer 

results in bands of cells that lie across, and approximately perpendicular to, the drainage 

lines, as shown in Figures 5a, 5b and 5c. (The 10, 30, and 50-meter"expansion distances
are necessary limits to calculations that would otherwise result in spreading the highest 

elevation over the entire area.) Unfortunately, the systematic sequence of cell-based 

calculations yields different sequences of partial overwrites for northerly-flowing and 

southerly-flowing streams. For southerly-flowing streams, expansion of downstream cells 

having lower elevations partially overwrites the expansion of higher elevation cells 

upstream. For northerly-flowing streams, expansion of upstream cells having higher 

elevations partially overwrites the expansion of lower elevation cells downstream. 

The depth of the debris-flow surge (user selected, in this case 3 meters), as 

measured from the thalweg to the surface, is then added to every cell that has a value not 

equal to NODATA. Subtracting the elevation of the terrain (<elevation-grid>) from the 

elevation of the debris-flow surface yields grids with values representing the depth of the 

surge. Examples of the results are shown in Figures 6a, 6b and 6c. Because of the 

upstream-downstream reversal in the sequence of partial overwrites the calculated depths 

along northerly and southerly flowing streams are not strictly comparable. The potential 

error from this effect has not yet been folly evaluated, but the reclassification in STEP 1 

helps to avoid an inappropriate comparison of depths.

STEP 2. To constrain by stream gradient (slope of thalweg cells) and stream order, be^in by 

creating a euclidian allocation of stream order using a 50-meter distance, the maximum 

used in Step 1 , as illustrated in Figure 7. Then combine the depth grids of Step 1 , 

constrained by slope category and stream order such that where slope is equal or lesr than 

14 degrees and the stream order is greater than 1 , the result calls for the surge depth from 

the 50-meter look; where slope is between 14 and 26 degrees and the stream order k 

greater than 1 , use the surge depth from the 30-meter look; and where the slope is eaual 

to or greater than 26 degrees and stream order is equal to or greater than 1 , use the rurge 

depth from the 10-meter look. The result is illustrated by Figure 8.

STEP 3 To remove inventoried areas inundated by the 1995 flood from the gridded hazard 

area, use the value 3 (for stream floods) from <inventory-grid> to assign the value 

NODATA to areas where debris-flow potential overlaps the mapped flooded area. The 

result is illustrated in Figure 9. To constrain results to the inventoried study area, use the 

value 1 from the <inventory-grid> to identity areas of NODATA cells in the <hazardSTEP 4. For ease in plotting and map display, reclassify the result of step 3, above, to show 

all debris-flow surge depths as one color and convert the grid to a polygon cover, so that 

it will respond to the ARCPLOT mapangle command. The gridpoty function results in a 

cover having a .PAT item named GRID-CODE in which the value for areas affected by 

the surge is 6, and unaffected areas are 0.

EPILOGUE. The resulting polygon cover contains a few areas showing the effect of a debrisflow surge, even though the areas that contribute to their drainage do not include slopes as 

steep as 26 degrees. Because debris flows are unlikely to originate from headwater rreas 

having gentle slopes, map units indicating postulated effects of debris flows in the 

downstream areas were removed by manually editing the polygon cover.
ARC/INFO .AML PROGRAM

The following program was written for specific grids and covers created for the Madison 

County study. The file names have been generalized to better identity file types. Paths to other 

directories have been eliminated; therefore, the .ami reads as if all source covers and grids are in 

the same directory as the .ami. Running requires substantial disk space for making a number of 

intermediate grids and covers. The study area in Madison County includes an area of 75-100 

square kilometers which, at 1:24,000-scale, required a minimum of 40-60 mb of disk capacity 

Several expressions in Steps 1 and 3 that could be nested to produce an .ami with fewer command 

lines, have been left as single expressions to assist in describing the procedure.

Following is the text of the .ami: 

/* ######### hazmake.aml ############ 

/*

/* Assemble the necessary starting grids 

/* <elevation-grid> 

/* <slope-grid> 

/* <thalweg-elevation-grid> 

/* <stream-order-grid> 

/* <inventory-grid> 

/*

/* STEP 1. Create euclidian allocation grids, extending the 

/* elevations of the ceDs marking the stream lines, 

/* <thalweg-elevation-grid>, for threshold distances 

/* of 50m, 30m, and 10m. 

/*

display 9999 1 

grid

eualloc50 = eucallocation(<thalweg-elevation-grid>, #, #, 50) 

eualloc30 = eucallocation(<thalweg-elevation-grid>, #, #, 30) 

eualloclO = eucallocation(<tharweg-elevation-grid>, #, #, 10) 

/*

/* Then add desired debris-flow surge depth to the allocation grid 

/*

eua!53 = eualloc50 + 3 

eua!33 = eualloc30 + 3 

eual!3 = eualloclO + 3 

/*

/* Next, subtract the terrain elevations from the eual* 

/* elevations, yielding three grids of surge depth over the 

/* digital terrain model. 

/*

<flow-depth-grid53> = con((eua!53 - <elevation-grid>) gt 0, (eua!53 - <elevation-grid>)) 

<flow-depth-grid33> = con((eua!33 - <elevation-grid>) gt 0, (eua!33 - <elevation-grid>)) 

<flow-depth-grid!3> = con((eual!3 - <elevation-grid>) gt 0, (eual!3 - <elevation-grid>)) 

/*
/* STEP 2. To constrain by stream gradient (slope) and stream

/* order, begin by creating a euclidian allocation of

/* stream order. Use a 50m look (the max used above).

/*

eucordSO = eucallocation(<stream-order-grid>, #, #, 50)

/*

/* and create a new grid, constrained by slope category

/* and stream order, that combines the flow-depth grids.

/*

<fjrst-hazard-grid> = con(<slope-grid> le 14 && eucord50 gt 1, ~

<flow-depth-grid53>, ~ 

con(<slope-grid> It 26 && <slope-grid> ge 14 && eucord50 gt 1,

<flow-depth-grid33>, ~ 

con(<slope-grid> ge 26 && eucord50 ge 1, ~

<flow-depth-grid!3>))) 

/*

/* STEP 3. To remove areas of inventoried floodways from the 

/* gridded hazard area and constrain map to area inventoried, 

/* remember that the <inventory-grid> has the values 

/* 1, 2, 3, and 4, = nocolor, debris flows, stream floods, 

/* and background color, respectively. 

/*

<second-hazard-grid> = setnull (<inventory-grid> = 3, <first-hazard grid>) 

/*

/* and to remove features outside the study area 

/*

<third-hazard-grid> = setnull (<inventory-grid> = 1, <second-hazard-grid>) 

/*

/* STEP 4. For ease in plotting and map display, reclassify 

/* from flood depths to show all one color 

/*

<final-hazard-grid> = con (<third-hazard-grid> gt 0, 6) 

/*

/* and convert the grid to a polygon cover, so that it 

/* will respond to the arcplot 'mapangle1 command. 

/*

<hazard-cover> = gridpory(<final-hazard-grid>) 

/*

/* which creates a cover with an item named GRID-CODE in 

/* the .PAT that has the value 6. 

/*

/* then leave grid 

/* 

quit
/* and in ARC, build the cover for lines

/*

build <hazard-cover> line

/*

/* (Apparently, 'gridpoly1 creates a .PAT, but does not

/* automatically create arc topology. So to plot the lines,

/* it is necessary to build line topology.)

&return

DISCUSSION

The hazard map (Morgan and others, 1997, plate 2) was prepared using the foregoing .ami 

For a preliminary evaluation of performance, it can be compared with the inventory of actual debrisflow hazard areas for the storm of June 27,1995, as shown in Table 1. In the Madison County study 

area, which includes 2,680,058 10-meter cells (26,801 hectares), the model delineates areas totaling 

400,253 cells as having a potential for debris-flow hazard, of which 36,066 (9.0%) were affected by 

inventoried debris-flows from the storm of June 27, 1995. Much of the over prediction can be 

attributed to the decrease in rainfall with distance away from the center of the "bullseye" fonred by 

the storm isohyets (see Morgan and others, 1997, fig 1.). As should be expected, restricting tin total 

area to progressively higher storm rainfall ~ the areas included within the 350mm, 450mm, 5f Omm, 

and 650mm isohyets, respectively ~ increases the ratio of inventoried to model-predicted (expressed 

as percent) to 11.0%, 15.8%, 21.2%, and 26.0%, respectively.

Of the 2,279,805 cells delineated as outside the zone of potential hazard, 2,253,019 cells 

(98.8%) had no inventoried hazard and 26,786 cells (1.2%) had inventoried debris-flow effects. 

Visually, the hazard map appears to discriminate satisfactorily between areas of potential debris-flow 

hazard and areas unlikely to be at hazard from debris flows.

On the disappointing side, of a total of 62,852 inventoried hazard cells, the model predicts a 

potential hazard in 36,066 cells, or about 57%, leaving 26,768 cells, approximately 43% of the 

inventoried hazard cells, in areas where the potential for hazard is not predicted by the model These 

proportions remain constant, even when areas are restricted to the limits delineated by the 350mm, 

450mm, 550mm, and 650mm isohyets for the storm rainfall Some of this error may be inherent in 

the use of a single average depth, applied to all stream channels, because volumes (and associated 

depths) may be expected to vary from one drainage to another. However, a major part of the error 

can be attributed to the inability of the digital terrain model to discriminate the correct courses of 

drainage channels across fens and other areas having slopes of 14 degrees and less. As shown on 

Figure 3, several channels delineated in the digital terrain model by GRID functions, depar4 from 

courses that human interpretation from the contours might select. These departures inf icnce 

succeeding grids, and comparison of Figure 3 with Figures 8 and 9 shows that to be a major source 

of error. It seems clear that significant reductions in error would result from comparing the streamnet grid with the contour map, and editing the grid to conform with stream lines interpreted from the 

contours prior to preparation of the <stream-order-grid> and the <thalweg-elevation-grid>.
Table 1. a. Comparing model-predicted hazard cell count (predicted frequency) with 

inventoried hazard cell count (actual frequency).

Predicted Predicted

Hazard No-hazard Total

Inventoried hazard 36,066 26,786 62,852 

Inventoried no-hazard 364.187 2.253.019 2.617.206 

Total 400,253 2,279,805 2,680,058

Table 1. b. Comparing "successful" predictions of hazard cells 

with "failed" (incorrect) model predictions.

Predicted

Hazard

36,066

364.187

400,253

Predicted

No-hazard

2,253,019

26.786

2,279,805

Total

2,289,085

390.973

2,680,058

Successes*

Failures*

Total

*("Success" = Predicted and Inventoried results the same.)

*("Failure" = Predicted and inventoried results are different.)

Yates continuity correction, on the null hypothesis that the inventoried and 

predicted distributions are not the same,

400,253 x 62,852/2,680,058 = 9,386.6; 

which is less than 36,066.

Table 1. Comparisons of model-predicted and inventoried hazards. 

Cell counts in the Madison County study area, approximately 

bounded by the 350 mm isohyet of the June 27, 1995 storm (see 

Wieczorek and others, in prep, fig. 2a), which also approximates 

the limits of debris-flow events associated with the storm (see 

Wieczorek and others, 1996, pi. 1).
The frequency of erroneous predictions decreases with increasing slope angles, as shown by 

the following tabulation:

Slope Erroneous predictions 

(deg) (percent) 

< 14 42-52 

14-26 30-32 

26-34 16-21 

34-45 2-5 

>45 <1

The range in erroneous predictions is affected by the severity of the storm rainfall. Over 42% of the 

erroneous predictions where slopes are 14 degrees or less, occur within the 350mm isohyet, and this 

proportion reaches 52% for the area within the 650mm isohyet for storm rainfall.

The associations of erroneous predictions with gentle slope areas indicates that improved map 

accuracy should result if the elevation grid, which forms the basis for the derivative maps of slope, 

stream lines, and stream order, were more accurate and more detailed than is presently provided by 

the contour DLG's, at least in low-slope (less than 14 degrees) areas. Perhaps supplemental digital 

elevation data for tow-slope areas could be incorporated into the elevation grid. The results of testing 

indicate that, although the combination of available terrain data and GIS procedures in this particular 

.ami produces too many errors to be a reliable cell-specific indicator of potential hazard, it nay be 

useful in providing a general guide to areas where special mitigation or emergency-response measures 

should be considered.

Improved performance can be expected from more detailed digital terrain model. Editing the 

stream-net grid to conform with visual picks of drainage lines from the contour maps, and to identify 

streams that lack steep slopes (26 degrees and greater) in their watershed areas, can be expected to 

reduce errors. Extending application to other areas will surety require adjustments in: 

Step 1. user-designated factors such as surge depth and limiting distances for euclidian allocations; 

development and incorporation of subroutines to compensate for the effect of upstream and 

downstream calculation sequences, should be investigated, 

Step 2. adjustments to slope and stream order constraints, and addition of other possible constraints,

in the way depth grids are combined, 

Step 3. map input, for example, mapped flood plains and debris-flow fans could substitute for actual

post-storm inventories,

Step 4. a routine that results in more accurate depth grids in Step 1 might permit the use of model 

depths instead of restricting the model to a "yes" °r a "no" on inundation.

ACKNOWLEDGMENTS

The concept of modeling the potential for debris-flow hazard with a user-specified surge 

height should be attributed to B. A. Morgan and G. F. Wieczorek, both of the U.S. Geological 

Survey in Reston, VA. The development of the .ami was greatly aided by discussions with John 

Jones, Susan Price, David Seller, and Patricia Packard, all of the U.S. Geological Survey in Reston, 

VA. We are also grateful to Rachael Hauser, U.S. Geological Survey and University of California, 

Riverside, and to Gerald Wieczorek, U.S. Geological Survey, Reston, VA, for helpful reviews of the 

manuscript.

10
REFERENCES 

ESRI (Environmental Systems Research Institute), 1992, Hydrologic Modeling Tools: Environmental

Systems Research Institute Inc., Redlands, California, p. 1-1 - 1-14. 

ESRI (Environmental Systems Research Institute), 1991, Cell-based modeling with GRID:

Environmental Systems Research Institute Inc., Redlands, California, 333 p. 

Ellen, S.D., Mark, R.K., Cannon, S.H., and Knifong, D.L, 1993, Map of debris-flow hazard in the

Honolulu District of Oahu, Hawaii: U.S. Geological Survey Open-File Report OF 9j -213,

25 p., plate 1:30,000. 

Iverson, R.M., Schilling, S.P., and Vallance, J.W., 1998, Objective delineation of lahar-inundation

hazard zones: Geological Society of America Bulletin, v. 10, no. 8, p. 972-984. 

Morgan, B.A., Wieczorek, G.F., and Campbell, R.H., in press, Historical and potential debrir-flow

hazard map of area affected by the June 27,1995, storm in Madison County, Virginia: U.S.

Geological Survey Miscellaneous Investigation Series Map I-2623B, 1:24,000. 

Morgan, B.A., Wieczorek, G.F., Campbell, R.H., and Gori, P.H., 1997, Debris-flow hazards ir areas

affected by the June 27, 1995, storm in Madison county, Virginia: U.S. Geological Survey

Open-File Report 97-438, 15 p., 2 tables, 2 plates 1:24,000. 

Schilling, S.P., 1998, LAHARZ: GIS programs for automated delineation of lahar hazard zones1 ,, U.S.

Geological Survey Open-file Report 98-638, 80 p. 

Wieczorek, G.F., Morgan, B.A., Campbell, R.H., Orndorff, R.C., Burton, W.C., Southworth, C.S.,

and Smith, J.A., 1996, Preliminary inventory of debris-flow and flooding effects of the June

27, 1995, storm in Madison County, Virginia, showing time sequence of positions of F*ormcell center: U.S. Geological Survey Open-File Report 96-13, 8 p., 1 plate 1:24,000. 

Wieczorek, G.F., Morgan, B.A., and Campbell, R.H., (in prep.), Debris-flow hazards in the Blue

Ridge of central Virginia: Environmental and Engineering Geosciences Journal, 65 ms, p.

11
Examples of input data and

grid manipulations to produce

a preliminary debris-flow

hazards map.

0 1 MILES

0 1 KILOMETERS

0 1 2^^3 THOUSAND FEET

Contour interval 40 feet

Scale and north arrow for all figures.

12
Figure 1 Contours, streams and 

roads from digital line graph data, 

on shaded relief map from digital 

terrain model. (10-m cells)

13
f\^v

*

1 V '',

s_=i^;

.f^N

^, *K^v

Figure 2. Slope map from digital 

terrain model.

Slope 

(Degrees)

>45

34-45 

26-34 

14-26 

0-14

14
Figure 3. Stream order derived from 

digital terrain model. Circled areas 

show model-defined channels that 

do not follow the courses expected 

from examination of the contours.
i i \f

\ i

( .'

% i

\ '

. " "v

'*fe

\ v » \ -» r /

' . f

.

 3 \ l 'i i. *, - -

:

'

O-' A

>)«

"V.^ x.

Figure 4. Elevations of 10-m cells 

marking stream lines derived 

from digital terrain model.

16
i / \ - ' £-.»> 

I/ \ \y*' % "^^^<>,

V ' > T* ^ ^r * ~ ^ <

v s » ;/ . \ . - 

 V -^V * 5 N** I *

\ v r/ U y ^ t\ \ * 11 v i \ " ^ \l \

%^ V * «/,. v '-A % I I*

*K» *»*}' **, * *i "^ * /"

 «**S V^ AX t\ /^-v^^ ^

V, *>O^<\V'^s\vj ~'? ^^N^JJ^k «-.^*i.

W" ^fnT7r ^ o^

/^^kc, * B^' :^; :r-iw % - * X7V v- : " % : x w.

Figure 5a. 10 meter euclidian allocation of stream elevations, with 

3 meter depth added.

*\7
^k. V- f \ ft &/: V t* \v*^ **" . \ . -^ i

V4 »v=Nx^

A^el ^1\3>^

*?£- MA > ^i&C A *«i A > «f^

^^sn^s

%k^ 5 !^ «* W.Twl^

Figure 5b. 30 meter euclidian allocation of stream elevations, with 

3 meter depth added.

18
 ^^ m ^ *ie-^/+ *»w

Figure 5c. 50 meter euclidian allocation of stream elevations, with 

3 meter depth added.

19
Depth (meters) 

3 (or more)

Figure 6a. Depths derived by subtracting terrain model (gridded 

elevations) from grid of Fig. 5a, 

subject to the constraint that 

depth cannot be negative.

20
Figure 6b. Depths derived by subtracting terrain model from grid 

of Fig. 5b, subject to the constraint that depth is not negative.

Depth (meters) 

3 (or more)

21
Depth (meters)

3 (or more)

Figure 6c. Depths derived by subtracting terrain model from grid 

of Fig. 5c, Subject to the constraint that depth is not negative.

22
Stream 

Order

1st

2nd 

3rd 

4th 

5th 

6th

[ | 7th & 

 higher

Figure 7. 50 meter euclidian allocation 

of stream orders (see Fig. 3).

23
Model 

Hazard

Mapped 

Deb. Flow

Mapped 

Flood

Figure 8. Combining grids of Figures 

6a, 6b and 6c with constraints described 

in text, showing overlay of mapped 

debris flow and flood extent from events 

associated with the storm of June 27, 

1995.

24
Model 

Hazard

Mapped 

Deb. Flow

Mapped 

Flood

Figure 9. Showing effects of removing 

mapped flooding from debris-flow 

hazard areas identified by model.

25