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WATERRESOURCES ESEARCH, OL. 30, NO. 4, PAGES 019-1028,PRIL 1994
Digital levationmodelgrid size, andscapeepresentation,
andhydrologicsimulations
WeihuaZhang and David R. Montgomery
Departmentf Geologicalciences,niversity f Washington,eattle
Abstract. High-resolution digital elevation data from two small catchments n the
western nited Statesare used o examine he effectof digitalelevationmodel DEM)
grid izeon the portrayal f the landsurface ndhydrologicimulations.levation
dataweregriddedat 2-, 4-, 10-, 30-, and 90-m scales o generate seriesof simulated
landscapes.requency istributions f slope tanB), drainage reaper unit contour
lengtha), and the topographicndex (a/tan B) were calculatedor eachgrid size
model. requency istributions f a/tanB were henused n O'Loughlin's1986)
criterionor predicting onesof surfacesaturation nd in TOPMODEL (Bevenand
Kirkby,1979) or simulating ydrographs. or both catchments, EM grid size
significantlyffectscomputed opographic arameters nd hydrographs.While channel
routing ominates ydrograph haracteristicsor largecatchments, rid size effects
influencehysicallybasedmodelsof runoffgeneration nd surface rocesses. 10-m
gridsize providesa substantial mprovementover 30- and 90-m data, but 2- or 4-m data
provide nly marginaladditional mprovementor the moderately o steepgradient
topographyf our studyareas. Our analyses uggesthat for many andscapes, 10-m
gridsize presentsa rational compromisebetween ncreasing esolutionand data
volume or simulatinggeomorphicand hydrologicalprocesses.
Introduction
Predicting patial patterns and rates of runoff generation
andmany geomorphic processes equires both a hydrologic
model nd characterizationof the land surface. Most phys-
icallybasedmodelsof hydrologicand geomorphicprocesses
rely on either spatially distributed or lumped characteriza-
tionsof local slope and the drainage area per unit contour
length e.g., Beven and Kirkby, 1979; O'Loughlin, 1986;
Vertessy t al., 1990; Dietrich et al., 1993], and digital
hydrologic esponseusing opographically driven models. In
this paper, we assess how grid size affects topographic
representation,derived topographic attributes, and hydro-
logical simulations for two small catchments using high-
resolution digital elevation data. In contrast to previous
studies, we grid the same elevation data at several different
scales o isolate the effect of grid size on landscape repre-
sentation. Issues associated with vertical sampling resolu-
tion are not addressed in this work.
elevationodelsDEMs)ommonlyreusedorsuch.tudy reas
characterizationn a wide variety of scientific,engineering,
andplanning pplications.Although he increasing vailabil-
ity of DEMs allowsrapid analysisof topographic ttributes
overeven large drainagebasins, the degree o which DEM
gridsizeaffects he representationf the land surface nd
hydrological odelinghas not been examinedsystemati-
cally.
Digitalelevation data are stored in one of the following
formats:s point elevationdata on eithera regulargridor
triangularntegratednetwork, or as vectorizedcontours
storedn a digital ine graph. Each of these ormatsoffers
advantagesor certainapplications,ut the grid format s
usedmostwidely.Several ecentstudies xploredhe effect
ofDEM gridsizeon andscapeepresentationHutchinson
andDowling, 1991;Jenson, 1991;Panuskaet al., 1991;
Quinn t al., 1991].Thesestudies howedhat distributions
of topographicttributes erived rom a DEM depend o
some egreeon grid size. None of thesestudies,however,
systematicallynalyzed he effect of grid size on either he
statisticalharacterization f the land surface,or simulated
Copyright994 y heAmericaneophysicalnion.
Paper umber3WR03553.
0043.1397/94/93WR-03553505.00
The study catchments are located at Mettman Ridge near
Coos Bay, Oregon, and Tennessee Valley in Marin County,
California (Figure 1). Previous field investigations deter-
mined the nature and distribution of geomorphic and hydro-
logic processes n each catchment. High-resolution digital
elevation data were generated for testing DEM-based pro-
cess models in these catchments. Field mapping in each
catchment reveals that the high-resolution data provide a
reasonablyaccurate portrayal of the land surface.
Mettman Ridge
The MettmanRidgecatchment ccupies.3 km2 of an
area in which previous ield mapping documented he extent
of the channel network [Montgomery, 1991]. Channel head
locations in this area are controlled primarily by shallow
debris flows from small unchanneled valleys [Montgomery
and Dietrich, 1988]. The catchment is highly dissected with
hillslope engthson the order of 30-50 m [Montgomery and
Foufoula-Georgiou, 1993]. Slopes of 30o-40 are common,
and there are a substantial number of slopes that locally
exceed 45 .
A 1:4800 scale topographic basemap derived from low-
altitude aerial photographsaken prior to timber clearingwas
1019
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1020 ZHANG AND MONTGOMERY: DIGITAL ELEVATION MODEL GRID SIZE
ME' -I'MA
RIDGE
TENNESSEE
VALLEY
Figure 1. Location map of the study catchments.
usedas the sourceof digitalelevation ata. The basemap
was scannedand vectorized usingan automated outine to
reproduceontoursdenticalo thoseon the originalopo-
graphicmap. Althoughseveraldiscrepancies ere noted
between his map and the groundsurface,herewe assume
that this data providesan accurateportrayalof the land
surface Figure 2a).
Tennessee alley
The Tennessee alley catchment ccupies .2 km2 in
whichprevious ield mapping lsodocumentedhe extentof
the channelnetwork [Montgomery nd Dietrich, 1989].
Shallowandslidingominatesedimentransportn steep
hollows nd sideslopes, iffusiveransport ominatesn
divergent noses, and saturation overland flow and channel
processes ominatesediment ransport n lower-gradient
valleys.The catchments rhythmically issected, ith hill-
slopeengthsn heorder f 30-50m [Montgomerynd
Foufoula-Georgiou,993].he opographyf he ennessee
Valley atchments less teephan hatof theMettman
Ridgeatchment;lopesf200-30arecommonnd lopes
in excess of 40 are rare.
Digital levationatawereobtainedrom ow-altitude
aerial hotographssing stereo igitizerta densitybout
every 0m [Dietricht al., 1993]. hespot levationsere
griddedo generate 5-m contourntervalmapof the
catchmentFigureb).Field nspectionevealshat hedata
providean excellentportrayal of the land surface.
Methods
Spot levationata or the wocatchmentsere ridded
at scales f 2, 4, 10, 30, and90 m using hegridmodulef
Arc/Info,with gridded levationsecordedo the nearest
centimeter. umulativerequency istributionsf threeo-
pographicttributes,ocalslopetanB), drainagerea er
unitcontourengtha), and opographicndex a/tan
werecalculatedor eachDEM of the two study atchments
using he modelof Jensonand Domingue 1988].Their
modeldefines he downslope low direction or eachcell
correspondingo the orientation f the neighboringellof
lowest elevation. The tan B for the cell is then calculated
basedon the elevationdifference etweencells.Definitionf
the spatial distribution of flow directions allows determina.
tion of the total numberof the cells that direct flow to each
cell, and husdrainage reas.Here, a is the drainagerea
dividedby the grid cell dimension alculated or the center f
the cell. Although he assignmentf all flow to a single
downsloperid cell distorts low paths n both divergent
topography nd for slopesorientedat anglesother han he
eightcardinal irectionsQuinnet al., 1991], he algorithm
has been widely used in many topographicmodels e.g.,
Marks et al., 1984; Band, 1986; Jenson, 1991]. Several
workers e.g., Quinnet al., 1991;CabralandBurges, 992;
Lea, 1992] ecentlyproposed lgorithmsncorporatingul-
250
300 200
150
3 180 ,
Contour=
a. b.
Figure . Contour apof he a)Mettman idge nd b)Tennesseealley atchments.
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ZHANG AND MONTGOMERY:DIGITAL ELEVATION MODEL GRID SIZE 1021
tiple ownslope-flowirectionshataremore uitableor
representinglowondivergentillslopes. hileweareeager
to explore hese newer algorithms, his study does not
examineheir nfluenceon topographicepresentation.
Hydrologicimulationsmployed he steady tatemodel
TOPOG O'Loughlin, 1986] o examinepatternsof surface
saturationnd TOPMODEL [Beven and Kirkby, 1979] o
predictunoffproductiono short-durationtorms. oil
hydraulicarameters ere estimatedrom field measure-
mentsMontgomery, 1991].Model simulations xplored he
effect f DEM grid size on simulated ydrologic esponse.
Landscape epresentation
Cumulative frequency distributions of tan B, a, and
a/tanB determined or each grid size modelreflectchanges
in both mean and local values. Comparisonof the distribu-
tionsof these topographic attributes allows direct assess-
mentof the influenceof grid size on landscape epresenta-
tion.
Slope
Cumulativeslope distributionsare more sensitive o DEM
gridsize or the steeperMettman Ridge catchment han or
the moderategradient TennesseeValley catchment Figure
3). For both study areas, the percent of the catchment
steeperhan a given slope systematicallydecreases s the
DEM grid size increases, and the largest effect is for the
steepest ortions of the catchments. In the case of the
Mettman Ridge catchmerit, the mean slope declines from
0.65 or the 2-m grid size model to 0.41 for the 90-m grid size
model Figure 3a). This result is consistent with, but more
pronouncedhan those of previous studies [Jenson, 1991;
Panuska t al., 1991]. Grid size influence on slope distribu-
tionss lesspronounced or the TennesseeVaLleycatchment
(Figure3b), where the mean slope is 0.34 for the 2-m grid
modeland 0.29 for the 90-m grid size model. The distribu-
tions or both catchmentssuggesthat grid sizessmaller han
l0 m yield only marginal mprovement n slope representa-
tion. Since he slope of a grid cell represents n average
slope or the area coveredby the cell, increasingDEM grid
sizeshould esult n decreasing bility to resolve he slope
characteristicsf steeperand more dissectedopography.
The cumulativeslopedistribution or the Mettman Ridge
catchment, specially or the 10-m and 30-m grid size mod-
els,arestepped,while distributionsor both argeandsmall
gridsizesare smoother.We suspect hat this reflects he
smallnumberof grid cells n large grid size modelsof this
catchment.ewer grid cells or the smallerMettmanRidge
catchment should result in a more discontinuous cumulative
distributionhan or the Tennessee alley catchment.
Drainage reaper Unit Contour ength
Cumulative istributions f a alsoare sensitive o grid size
(Figure). Largergridsizes ias n favorof larger ontrib-
uting reas, ithcomparableffectsn both atchments.or
theMettman idge atchment,hemean alueof a increases
from 0m for a 2-mgridsize o 102m for a 90-mgridsize.
In theTennesseealleycatchment,he mean alueof a
increasesrom19m for a 2-mgridsize o 120m for a 90-m
grid size.
For eachgrid size, a singlepixel defineshe smallest
possiblealueof a and huswhere the cumulativerequency
distributionsf a reach 100% of the catchment rea. The
1.0
0.0
0.0
", l. ---- 30m
, t... ' .... 90m
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
tanB
1.0
0.4
o.2
0.0
0.0
-. x_ .... 30m
..... 90m
0.2 0.4 0.6 0.8 1.0
tanB
Figure 3. Cumulative requency distributionsof slopede-
rived for different DEM grid sizes. (a) Mettman Ridge. (b)
TennesseeValley.
algorithm used to compute a determines this minimum
value. While it is intuitive that larger grid size limits the
resolutionof fine-scale opographic features, the effect on
both the mean and local a is significant or topographically
driven hydrologic and surface process models.
Topographic ndex
The topographic ndex (a/tan B) is an important compo-
nent of many physically based geomorphic and hydrologic
models,as t reflects he spatial distribution of soil moisture,
surface saturation, and runoff generation processes [e.g.,
Beven and Kirkby, 1979; O'Loughlin, 1986; Moore et al.,
1986].Derivation of frequency distributionsof a/tan B is the
first step for hydrologicalsimulations n most topographi-
cally driven hydrologic models.
Grid size significantly affects the cumulative frequency
distributionsof a/tan B (Figure 5). Decreasinggrid size shifts
the cumulative distribution toward lower values of a/tan B,
with the greatesteffect on smaller values. Again, computed
frequencydistributions ystematicallyconverge oward that
of the finestgrid size. For the Mettman Ridge catchment, he
mean In (a/tan B) increases rom 3.4 for a 2-m grid size to 5.6
for a 90-m grid size. In the TennesseeValley catchment, he
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1022 ZHANG AND MONTGOMERY: DIGITAL ELEVATION MODEL GRID SIZE
1.0
0.8
0.6
0.4
0.2
0.0
0.0
2111
----- lorn
.... 30rn
N'N?
' 410 6.0 8.0 10.0
In(a)
21o
12.0
1.0
0.8
0.6
0.4
0.2
0.0
0.0
I' '', ', ; '
I \, \ \ - lorn
[ \', : ', " .... 30
I \, , ',, .....
L ,x ",
I ',,",
\ ',
\'\ , ",,
I
l '%'...
2.0 4.0 6.0 8.0 10.0
ln(a)
12.0
Figure 4. Cumulative requency distributionsof the drain-
agearea per unit contour ength or differentDEM grid sizes.
(a) Mettman Ridge. (b) TennesseeValley.
mean n (a/tan B) increases rom 4.0 for a 2-m grid size o 6.2
for a 90-m grid size. The influenceof grid size on both mean
and local valuesof a/tan B demonstrateshe potential or
affecting opographically asedhydrologicmodels asedon
this parameter.
The effectof grid size on spatialpatternsof a/tanB is even
more striking Figure 6). Detailed eatures hat appearon
finer-gridDEMs are obscured n coarser-grid EMs, with a
progressiveossof resolutionor both he drainage etwork
definedby the higher values of a/tan and hillslopes
associated ith the lower valuesof a/tan . Degradation f
these geomorphic eatures affects the simulationof runoff
production nd geomorphic rocessesn topographically
driven models.
Hydrologic Simulations
We used the models TOPOG [O'Loughlin, 986] and
TOPMoDEL [Beven nd Kirkby, 1979] o investigatehe
effect of grid size on hydrologicsimulations.We examined
both representation of saturated areas within a catchment
using OPOGand he influence n hydrographsalculated
using OPMODEL or a rangeof rainfall ntensitiesnd
baseflows or the study catchments.
Surface Saturation
Many hydrological,eomorphological,nd ecological
phenomenarecloselyelated o thebehavior f thevariable
saturationreawithin catchmerit.y assumingsteady
statedrainage ondition,O'Loughlin 1986]expressedhe
conditionor surface aturation t any location n a catch-
merit as
a/tanB > At/Qo (l)
where s hemean oil ransmissivityf hecatchment,
is the total catchmerit rea, and Q 0 is the runoff ate rom he
catchmerit. he term on the right-hand ideof the equations
defined s the averagewetness tateof a catchmentW).
The total saturatedarea for a given catchmentwetnesss
simply the sum of all the local areas which have values f
a/tan B > W.
The effect of DEM grid size on the computedsaturation
area can be directly examinedusing (1) and the cumulative
distribution f a/tan B. For a given wetnesscondition,
predicted saturation areas for both catchments ncreasewith
1.0
0.4
0.2
0.0
0.0
, ' ' .... 30m
.kk ' ..... m
',,
x "-...
_ --...
2.0 4.0 6.0 8.0 10.0 12.0
1.0
0.8
0.2
0.0
Figure 5. Cumulative requencydistributions f the topo-
graphicndex, n (a/tanB), for different EM gridsizes.a)
Mettman Ridge. (b) TennesseeValley.
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ZHANG AND MONTGOMERY: DIGITAL ELEVATION MODEL GRID SIZE 1023
IIi
...
.. .. ..
, I
ii
Figurea. Maps fMettmanidgehowinghe patialistributionf he opographicndexn a/tan )
for ourdifferentEM gridsizes:, 10,30.and 0m. Darker hadesepresentargern (a/tanB).
increasingrid size. n the MettmanRidgecatchment,or
example,W = 180 m predictsa saturated rea equal o
about13%of the total catchmeritarea for a 2-m grid spacing,
32% or a 30-m grid spacing, nd 50% for a 90-m grid
spacing.he Tennessee alley catchment xhibits similar,
althoughesspronounced,elationbetween rid size and
saturated rea for a given wetnesscondition.
Catchmentesponse uringa StormEvent
We usedTOPMoDEL to explore he effectof DEM grid
size n hesimulated ydrologicesponse f eachcatchment
to a simple hort-durationainfall event.The modelpredicts
thedistributionof soil moisture and the runoff on the basisof
urface opography nd soil properties.A criticalassump-
tion of the model is that locations with similar topography
and oilpropertiesesponddenticallyo the same ainfall.
Byassumingspatially niform echargeate anda quasi-
steady ubsurfaceesponse, evenand Kirkby 1979]de-
rived a functionrelating ocal soil moisturestorage o the
topographicndex of a catchment:
S = + m{X - In (a/tan B) - m(8 - In (T)} (2)
where S is the local soil moisturedeficit, is the mean soil
moisture deficit of the basin, m is a parameter that charac-
terizes he decrease n soil conductivity with soil depth, and
A and 8 are the mean values of In (a/tan B) and In (T) for the
catchment. For locations where S > 0, the soil moisture
store is not filled and there is no surface saturation. For
locationswith S -< 0, the soil moisture store is full, and
surface saturation occurs.
The modelcomputes oth the relativeamountof subsur-
face and saturation overland runoff, as well as the spatial
distribution f these unoff processes.During a modelsim-
ulation, he meansoilmoisturedeficitof a catchment t time
t, t, is calculated y
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1024 ZHANG AND MONTGOMERY:DIGITAL ELEVATION MODEL GRID SIZE
.'.- "':f"??'":."'"." '.-..-. ..it
-.,"' ,'.=..., .. , ... .--. .......
,.,...... ..-.... . ....':,: .. ......,..".'."
....... . : .,.. '.).,.......
? , . --. . .,. ,
- ,: . . -..., '
;, .. .. .
. ,.., ' , ,
' .. .. ..
.. .-,... ....... ,.......
.. '-.
- .. , . . '., .
..
Figure 6b. Same as Figure 6a except for Tennessee Valley.
', = .t-] + (q,-]- r)At (3)
where q is the total catchment runoff at time t - 1 divided
by the catchment area, r is the net recharge rate into the soil
column, and At is the computation time step. The updated S
at all points in the catchment are then computed using (2).
Any area with a soil moisture deficit larger than the incre-
mental precipitation in a unit time step will only produce
subsurface runoff, while those areas with either a soil
moisture deficit smaller than the incremental precipitation n
a unit time step, or that were saturated during the previous
time step will produce both subsurfaceand saturation excess
runoff. The subsurface low rate q/, of the catchment s
calculated by
qt,= e-('-)e-g/m (4)
The saturationxcess unoffqo is the sumof excess oil
moisturenddirectprecipitationhat allson the saturated
areas. This is expressed as
qoZ +r dA
where .,. s heareaof thecatchmentithsurfaceaturation
(i.e.,S -< 0). Total unoff at any imesteps thesum f
subsurfacend surface unoff.While the equationor sub-
surfacelow s only elated o the meanvalueof a/tanB, A,
theequationor saturationxcesslow s also elatedo he
distribution orm. Thus the influenceof DEM grid sizeon
predicted response differs for (4) and (5).
We first examine he simulated ubsurface ydrologic
responsesing 4) withoutconsideringithersurfacelo, or
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ZHANG AND MONTGOMERY:DIGITAL ELEVATION MODEL GRID SIZE 1025
0.80
0.60
0.40
0.20
120,0 ....... , .......
?'- lOO.O
" '"
".,., -----4m
-. ----- lorn
"-.. .... 3o,,-, 80.0-
""' '90m
60.0
..
........ --.... 40.0
..................... '--
20.0
I ...... i ' 0.0
10.0 20.0 30.0 40.0 50,0 0.0
time (hr)
--,2rn
---- lorn
.... 30m
..... OOm
0.00
0.0 I 0.0 20.0 30.0 40.0
time (hr)
50.0
0.80 100.0 -- 2m
' ----4m
., 80.0
0.40
0.20
20.0
0.00 0.0
0.0 10.0 20.0 30.0 40.0 50.0 0.0 10.0 20.0 30.0 40.0 50.0
time () time ()
Figure 7. Runoffhydrographsor differentDEM grid sizesunderdifferent ainfall and initial base low
conditions. a) Mettman Ridge catchmentunder 5 mm/h rainfall and 3.5 mm/day initial base flow. (b)
Mettman Ridge catchmentunder 100mm/hrainfalland 3.5 mm/day nitial base low. (c) TennesseeValley
catchment under 5 mm/h rainfall and 3.5 mm/day nitial base flow. (d) TennesseeValley catchment under
100 mm/h rainfall and 3.5 mm/day initial base flow.
interactionsetweensurfaceand subsurfacelow paths.This
example pproximatesconditions of small initial base flow
and ainfall n steep catchments.For this case, it is shown
that yadjustinghe nitialvalues f the mean oildeficit ,
themodelwill produce he same unoffhydrographs,nde-
pendentof the form of a/tan B distribution.
Given ny wo meanvaluesof In (a/tanB), A, andX2,we
have he ollowing ase low equations:
qbl= e-X'-S)e-'/m (6)
qb2 e ( : - )e S:/m (7)
Thenecessaryonditionor qbl = qb2 s
(S2- S) = m(,X - x )
(8)
Once nitial values of the mean soil moisturedeficit are set
accordingo this functional elation, the relation will hold or
all imesteps uring storm, eadingo an dentical ydro-
graph.n other words, DEM grid size doesnot affect he
computedydrographs singonly the subsurfacelow equa-
tion.
We alsoexaminedhe effectof DEM grid sizeon simu-
lated hydrologic esponseconsideringboth subsurface nd
saturation excess flow. We assumed that soil parameters
were spatiallyuniform in our simulation o isolate the effect
of topographicepresentation.We usedvaluesof 70 mm and
360 mm/h for the parameter m and surface hydraulic con-
ductivity, respectively. For simplicity, we only calculated
runoff production and ignored flow routing in channels.
Simulations were conducted with four rainfall intensities (5,
10, 50, and 100 mm/h) sustained for 4 hours and five initial
base flow conditions (1, 2.5, 3.5, 4.5, and 9.5 mm/day). The
lowest simulated rainfall intensity (5 mm/h) occurs fre-
quently in these areas, and the highest simulated rainfall
intensity (100 mm/h) represents an extreme event. At most
times, the antecedent base flow rates for the study areas are
less than 4 mm/day.
The effect of grid size on computed hydrographsdepends
on both rainfall intensity and initial base flow (Figure 7). To
quantitativelyexamine these results, we normalized peak
discharges omputedwith different grid size modelsby the
corresponding eak dischargescomputed from the 90-m
DEM.
A plot of normalized eak discharge ersusgrid size or a
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1026 ZHANG AND MONTGOMERY: DIGITAL ELEVATION MODEL GRID SIZE
1.0
0.4
O.2
2 .o 4o.o 60.0 so.o
grid size (m)
0.0
0.0
1 oo.o
1.o
0.8
. ,,,
0.4
. .,,
0 0.2
0'00.0 20.0
..,.. ..//
.. ..,'/ /
....'
...' ..,"'/." /*
...' ..
" .' / , initialbaseflow
..-' .,,,,"/ ./'/
.... ..- .,." ",f .o,
, o,-' ,,-' / /' / -- -- 2.5 am/day
..... ,.-' ..../ /"/ ----- 3.5mm/dy
. ..." " /' .... 4.5am/day
, r , , ,
40.0 60,0 6.0 %0.0
grid size m)
Figure 8. Computed peak dischargeversus DEM grid size
for a rainfall intensity of I0 mm/h and different initial base
flows. Peak dischargesare normalized to those of the 90-m
grid size. (a) Mettman Ridge. (b) Tennessee Valley.
10 mm/h rainfall at various antecedent base flow rates is
shown n Figure 8. In general, the computedpeak discharge
increases with increasing grid size. However, as the initial
base low increases, he effect of grid size on the computed
discharge decreases. There are also some deviations from
the positive correlation between the computeddischargeand
the grid size, especially for the Mettman Ridge catchment.
Further examination reveals that the deviations n Figure 8a
reflect variations in the back-calculated mean initial soil
moisture deficit. For a given initial base flow, the mean soil
moisture deficit generally decreases as the grid size in-
creases,but there s a deviation rom this trend at a 30-m grid
size, where the initial mean soil moisturedeficit s larger than
that of 10-m grid size. With a larger moisture deficit and
thereforea smallersaturatedarea, the runoff production ate
will be smaller. For the TennesseeValley catchment,both
the computed nitial mean soil moisture deficit and peak
dischargevary more systematicallywith grid size.
The effect of rainfall intensity on the relation between
computed discharge and the grid size is more complex
(Figure 9). Within a rainfall intensity range of 5- to 10 mm/h
for the Mettman Ridge catchment and 5- to 50-mm/h for the
Tennessee alley catchment, he difference etweenhe
peakdischargerom grid sizessmaller han 90 m and hat
from a 90-mgrid ncreases ith the rainfall ntensity. s
rainfall ntensity urther increases,however, thesediffer-
ences ecrease.his esultsexpectedonsideringhatpeak
discharge ouldbe the same or all grid size models or he
extreme ases f (1) no surface aturation ndera verysmall
rainfall ntensityand (2) completesurfacesaturation nder
very large rainfall intensity.
Within a rangeof reasonableainfall ntensitiese.g., ess
than 50 mm/h), peak dischargedifferencesare less than
for gridsizessmallerhan30 m for the Tennesseealley
catchment,and less han 8% for grid sizes smaller han 10m
for the Mettman Ridge catchment.This suggestshat theres
a DEM grid size beyond which computedhydrologice-
sponse s less sensitive o grid size, and that this grid size s
approximately10m for TennesseeValley catchment nd4 m
for the Mettman Ridge catchment.
Discussion
The analysespresentedabove are based on the single-
direction flow-partitioning algorithm. This algorithm does
not resolve hillslope divergence, introducing artifacts hat
influence cumulative frequency distributions of a and tanB.
Quinn et al. [1991] showed that for the same grid size he
single-directionalgorithm yields higher tan B values, and
therefore ower a/tan B, than a multiple-direction lgorithm.
They also illustrated that DEM grid size influences he
distributionof a/tan B for multiple-directionalgorithms,with
the percentof area having arger a/tan B increasingwithgrid
size. Thus the flow-partitioningalgorithm also affects opo-
graphic representation, n addition to the grid size depen-
dence documented n this paper.
The effect of DEM size on the distribution of derived
slopeshas mportant mplications or geomorphicand hydro-
logic modeling and land management decisions basedon
such models. While a coarse-grid DEM may be most prac-
tical for modeling large-scale geomorphic processes, he
coefficients ncorporated in process models and transport
laws at suchscalesare not analogous o thosemeasuredn
field studies.
The effect of DEM size on the derived a/tan B will affect
prediction f the spatial istribution f runoffprocesses,nd
the associated aterial ransportprocesses ver a land
surface.Runoffprocesses re governedby neither he inest,
nor the coarsest scale topography within a landscape.
Rather, they are governedby processes ctingover interme-
diate scales. f the DEM grid size is too large, then many
topographiceaturessuchas hollows, ow-orderchannels,
andhillslopeswill not be resolved.We suggesthat themost
appropriateEM gridsize or topographicallyriven ydro-
logic models s somewhat iner than the hillslope cale
identifiable in the field.
Another mplications for flood orecastingn a drainage
basin. Our results ndicate hat with the samevalues or soil
parametersutdifferent EM gridsizes,hemagnitudef
the peak runoff rate, and therefore the runoff volume,
predictedn responseo a givenstormmaydiffersignifi-
cantly.These esults, owever,are only for runoffproduc-
tion;hydrographst thebasinmouth lso eflectoutingf
flow hroughhechanneletwork. ridsize ffectshould
be smalleror a largedrainage asinwhere unoffhydro-
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ZHANG AND MONTGOMERY:DIGITAL ELEVATION MODEL GRID SIZE 1027
1.00
0.80
.,..
" 0.60
0 0.40
0.20
1.00
0.80
2rn
-----4m
----- lorn
.... 30m
0.60
0.40
0.20
0.00
0.0
rain (rnm) ain (mm/hr)
Figure 9. Computedpeak discharge ersusDEM grid size for an initial base low of 2.5 mrn/dayand
different ainfall intensities.Peak discharges re normalized o thoseof the 90-m grid size. (a) Mettman
Ridge. (b) TennesseeValley.
00.0
graphs re dominatedby channelrouting. Even so, the
influence f DEM grid size on predicted runoff production s
an mportant onsiderationor interpreting ydrological im-
ulations singa topographicallydriven model.
A particularly ntriguing mplication s for calibrationand
validationof dynamic physically based hydrologic models.
All hydrologicalmodels make simplifyingassumt;tions nd
onlyapproximate eal hydrologicsystems. n practice,cal-
ibration s required to obtain acceptable correspondence
between field results and model simulations. Calibrated
parametersor a particular catchment are then used for
hydrologicalorecasting either for the same catchment, or
for a different catchment with similar physical properties.
However, our results show that DEM grid size, rainfall, and
initialbase flow all affect simulated hydrographscomputed
with he sameset of parametervalues.Consequently,model
calibrationsre grid size specific.
AppropriateGrid Size
The resultsof our study nvite the questionof what defines
an appropriate rid size for simulationsof geomorphicand
hydrologicrocesses sing opographically riven models.
This question s best examined n two parts; the relation
betweenand surfaceand the spot elevationdata used o
createa DEM and that between grid size and the original
spot elevation data.
The data used to create a DEM are a filtered representa-
tion of landscape ampledat some regularor irregular
intervalo builda collection f elevation ata.The spacing f
theoriginaldata used o constructa DEM effectively imits
the esolutionf the DEM. Decreasinghe grid sizebeyond
the esolution f the originalsurveydata doesnot increase
theaccuracy f the andsurfaceepresentationf the DEM
andpotentiallyntroducesnterpolation rrors.The relation
of heoriginal levation ata o the andsurfaces a crucial,
but oftenneglected, haracteristicf a DEM. This is a
problemwith many commercially vailableDEMs. While
thereare data collection trategieshat could optimize
landscapeepresentatione.g.,denseopographicampling
inareasfcomplexopographynd parseamplingnareas
withsimpleopography),he average pacingf the data
used to derive a DEM provides a guide to the grid size that
would take full advantageof the original spot elevation data,
and thusprovide he most aithful landscape epresentation.
We suggest hat the length scale of the primary landscape
featuresof interestprovides naturalguide o an appropriate
grid size. The mostbasicattribute of many landscapess the
division imo topographicallydivergem hillslopesand con-
vergentvalleys. A grid size smaller than the hillslope ength
is necessaryo adequatelysimulateprocesses ontrolledby
land form. For other processes, he most appropriate grid
size for simulation models is best scaled in reference to the
processbeing modeled.For example, a coarse e.g., 90 m)
grid size may be most appropriate for modeling orogenic
processes ver large areas and long time scales.
Our results mply that it is unreasonable o use a 30- or
90-m grid size to model hillslope or runoff generationpro-
cesses n moderately o steep gradient topographywithout
some calibrationof the process model. While a 10-m grid is
a significantmprovement ver 30 m or coarsergrid sizes,
finergrid sizesprovide elatively ittle additional esolution.
Thus a 10-m -gridsize presents a reasonablecompromise
between increasing spatial resolution and data handling
requirementsor modeling urfaceprocessesn many and-
scapes.
Conclusions
The grid size of a DEM significantly affects both the
representation f the land surface and hydrologicsimula-
tions based on this representation.As grid size decreases,
landscapeeaturesare more accurately esolved,but faithful
representationf a land surfaceby a DEM depends n both
grid size and the accuracyand distributionof the original
survey data from which the DEM was constructed.These
resultshave mportant mplicationsor simulations f hydro-
logicand geomorphic rocessesn natural andscapes. ur
ability to model surface processessoon will be limited
primarilyby dataqualityand other ssues irectly elated o
processesnderconsideration. e suggesthata gridsizeof
10 m would suffice or many DEM-based applicationsof
geomorphic nd hydrologicmodeling.
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1028 ZHANG AND MONTGOMERY: DIGITAL ELEVATION MODEL GRID SIZE
Acknowledgments. hisresearchwassupported y NationalAero-
nauticsand SpaceAdministration rant NAGW-2652A,National
Science oundation rant RI91-17094, ndgrantsTFW FY92-010
and TFW Fy94-004 from the Sediment, Hydrology, and Mass
Wastingcommitteeof the WashingtonState Timber-Fish-Wildlife
agreement. We thank Harvey Greenberg for technical support,
Susan ensonor makingher topographicnalysismodel vailable
to us, and Bill Dietrich, Tom Dunne, and Romy Bauer or discus-
sionson subjects elated o the study.
References
Band,L. E., Topographic artitionof watershed ith digitaleleva-
tion models,WaterResour.Res., 22(1), 15-24, 1986.
Beven,K., Runoffproduction nd flood requencyn catchment f
order n: An alternative pproach, n Scale Problemsn Hydrol-
ogy, edited by V. K. Gupta et al., pp. 107-131, D. Reidel,
Norwell, Mass., 1986.
Beven,K., andM. J. Kirkby, A physically ased,variable ontrib-
utingareamodelof basinhydrology, ydrol.Sci.Bull.,24, 43-69,
1979.
Cabral, M., and S. J. Burges, DEMON: A new method or the
automated xtractionof contributing reasand drainage etworks
from ectangular EMs (abstract), osTrans.AGU, 73(43),Fall
Meeting suppl., 202-203, 1992.
Dietrich,W. E., C. J. Wilson,D. R. Montgomery,ndJ. McKean,
Analysis f erosionhresholds,hannel etworks, nd andscape
morphology singa digital errain model,J. Geol., I01(2), 259-
278, 1993.
Hutchinson, . F., andT. I. Dowling,A continentalydrological
assessmentf a new grid-based igitalelevationmodelof Austra-
lia, Hydrol. Process.,5(1), 45-58, 1991.
Jenson, . K., Applicationsfhydrologicnformationutomatically
extracted rom digital elevationmodels,Hydrol. Process., (1),
31-44, 1991.
Jenson, . K., andJ. O. Dominque, xtractingopographictruc-
ture romdigital levation ata or geographicnformationystem
analysis,Photogramm.Eng. Remote Sens.,54(11), 1593-1600,
1988.
Lea,N.J., An aspect riven inematicoutinglgorithm,n
Overlandlow nd rosionechanics,ditedyA. J.Parsons
and .D. Abrahams,p.393-407,hapmannd all, ondon,
1992.
Marks, . M., J.Dozier,nd . Frew,Automatedasinelineation
fromdigital levationata,Geo-Processing,, 299-311, 984.
Montgomery,. R., Channelnitiationnd andscapevolution,
Ph.D.dissertation,21pp., Univ. of Calif.,Berkeley, 991.
Montgomery,.R.,andW.E. Dietrich, hereo hannelsegin?,
Nature, 336,232-234, 1988.
Montgomery,. R., andW. E. Dietrich,ourcereas,rainage
density,nd hannelnitiation,WaterResour. es., 5(8), 907-
1918, 1989.
Montgomery,. R., andE. Foufoula-Georgiou,hanneletwork
sourceepresentationsing igital levationmodels,Water e.
sour. Res., 29(12), 3925-3934, 1993.
Moore,. D., S.M. Machay, .J. Wallbrink, . J. Burch, nd .M.
O'Loughlin, ydrologicharacteristicsndmodelingf a small
forestedatchmentnsoutheasternewSouth ales:relogging
condition, J. Hydrol., 83, 307-335, 1986.
O'Loughlin,. M., Predictionf surface aturationonesnnatural
catchmentsy opographicnalysis, aterResour. es., 2(5),
794-804, 1986.
Panuska,. C., I. D. Moore, ndL. A. Kramer, errain nalysis:
Integrationnto heagricultureonpointourceAGNPS) ollu-
tion model,J. Soil Water Conserr.,46(1), 59-64, 1991.
Quinn, ., K. Beven,ndO. Planchon,hepredictionfhillslope
flowpaths or distributedydrologicalodelingsing igital
terrain models,Hydrol. Process., 5(1), 59-79, 1991.
Vertessy, . A., C. J. Wilson,D. M. Silburn, . D. Connolly,nd
C. A. Ciesiolka, redictingrosion azard reas sing igital
terrainanalysis, AHS AISH Publ., 192, 298-308, 1990.
D. R. Montgomerynd W. Zhang,Department f Geological
Sciences, niversityof Washington, eattle,WA 98195.
(Received ctober 5, 1993; evisedDecember , 1993;
acceptedDecember 20, 1993.)