zhang and mont 2004 digital elevation model grid size landscape representation_etc

8/10/2019 Zhang and Mont 2004 DigitaL Elevation Model Grid Size Landscape Representation_etc

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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


4/10


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


6/10

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


7/10


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


8/10


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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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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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.

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D. R. Montgomerynd W. Zhang,Department f Geological

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(Received ctober 5, 1993; evisedDecember , 1993;

acceptedDecember 20, 1993.)

zhang and mont 2004 digital elevation model grid size landscape representation_etc

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