HYDROLOGICAL PROCESSESHydrol. Process. 17, 2567–2580 (2003)Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/hyp.1273

Subsurface topography to enhance the prediction of thespatial distribution of soil wetness

V. Chaplot1* and C. Walter2

1 IRD-UR049, Ambassade de France, BP 06, Vientiane, Laos2 UMR Sol, Agronomie, Spatialisation, ENSA-INRA, 65, rue Saint Brieuc 35042, Rennes Cedex, France

Abstract:

The estimation of the spatial distribution of soil wetness within a catchment is one of the most important issues inhydrological and erosion modelling. So far, such models have been based on soil surface topographic informationonly. However, soil hydrology is also controlled by subsurface flow pathways that may not be explained only bysurface terrain features. This study examined how the topography of the lower limit of the soil cover could improvequantitative modelling for the spatial prediction of soil wetness. The study was conducted in an agricultural catchmentof the Armorican Massif (western France) characterized by impermeable granitic saprolites. Two digital elevationmodels (DEMs) with a 10-m grid mesh and with a 0Ð3 m vertical resolution were generated from field investigationsthroughout the catchment. One DEM was a numerical representation of the soil surface and the other describedthe topography of the boundary between the soil cover and the underlying impermeable saprolite. Soil wetness (�)was surveyed systematically from 1996 to 1997 along a hillslope. The sampling scheme consisted of 149 nodesof a 10-m grid where � at 0–10 cm was estimated using time-domain reflectometry. The value of � at depths of20–30, 50–60 and 110–120 cm was estimated for a subset of 112 data points using a gravimetric method. Forboth surface and subsurface DEMs, soil wetness at all depths significantly correlated with the topographic attributes,namely the distance to the stream bank, the elevation above the stream bank (E), the downslope gradient, the revisedcompound topographic index (CTI), and the specific monodirectional and multidirectional catchment areas. The bestcorrelations were observed between �10 of winter 1996 and the physically based attributes E and CTI estimatedby using the subsurface DEM (r D 0Ð83 and 0Ð86, respectively). Two multiple non-linear regression models for �10

spatial prediction were generated using non-autocorrelated topographic attributes estimated from both surface andsubsurface topography. Model validation using a new set of 41 data points showed root mean square errors (RMSE)lower than 10% of the �10 range. The model based on subsurface topography decreased RMSE by 43%. Predictionerrors were not spatially distributed. Finally, theses results are discussed in respect of processes involved in hillslopehydrology. Copyright 2003 John Wiley & Sons, Ltd.

KEY WORDS soil water content; DEM; modelling; hydrology; landscape

INTRODUCTION

Soil wetness determines the production of surface runoff, which is the driving mechanism for nutrient andsediment transport in landscapes. For this reason, a better representation of the spatial and temporal variationsof soil wetness is needed. Since the studies of Beven and Kirkby (1979) it is well accepted that the prevailingwetness state at a point is related to the ratio of the area drained per unit contour length (A), possibly varyingover time (Barling et al., 1994; Beven and Freer, 2001), divided by the local slope gradient (S).

Modelling approaches for predicting soil wetness based upon physical concepts have more recently takenadvantage of topographic attributes other than A and S. Among these attributes, several were shown to berelated to zones of water accumulation in soils: the elevation above the stream bank (E, Crave and Gascuel,1996); the downslope gradient (DG, Merot et al., 1995), which is the ratio between E and the shortest

* Correspondence to: V. Chaplot, IRD—UR 049, Ambassade de France, BP 06 Vientiane, RPD Laos. E-mail: chaplotird@laopdr.com

Received 25 February 2002Copyright 2003 John Wiley & Sons, Ltd. Accepted 8 January 2003

2568 V. CHAPLOT AND C. WALTER

distance to the stream (D); the compound topographic index (CTI, Moore et al. 1993) and revised CTI(CTI D ln(AMU/DG), Merot et al., 1995), where AMU is the upslope contributing and multidirectional area(Quinn et al., 1991); and the terrain curvature (Burt and Butcher, 1986; Thompson et al., 2001).

Furthermore, the increased accuracy of digital elevation models (DEMs), a widely available data sourcerepresenting the continuously varying topographic surface of landscapes (Moore et al., 1991), can also improvespatial estimations of soil wetness. The use of DEMs of low horizontal resolution overestimate the extensionof soils saturated by water through a systematic overestimation of upslope contributing areas (Quinn et al.,1991; Zhang and Montgomery, 1994; Farajalla and Vieux, 1995; Brasington and Richards, 1998) or downslopegradient (Chaplot et al., 2000a) and an underestimation of slope angles (Zhang and Montgomery, 1994;Thompson et al., 2001).

Another promising direction for the improvement of soil wetness prediction models could be to betterconsider soil properties (O’Loughlin, 1986; Moore et al., 1988; Gerla, 1999; Gomez and Plaza, 2001). Soilcover affects water movements in hillslopes through the soil’s natural tendency to become less permeablewith increasing depth. Finally, lateral fluxes occur along slopes thus increasing soil wetness in the downslopedirection. Local soil saturation occurs in hillslopes when the accumulated water flux, the product of theupslope catchment A and the area drainage flux q, passing across an element of contour of length b, exceedsthe product of the local soil transmissivity T and the local surface gradient S (Equation 1, O’Loughlin, 1986):

Aq/b ½ TS �1�

So far, modelling approaches for the prediction of soil wetness assume both lateral surface and subsurfaceflows to be defined by surface topography. However, subsurface flow pathways may be even more affected inlandscapes by continuously varying subsurface topographic features such as horizons, saprolites or bedrockupper limits. Until now, little work has been done at the watershed level to evaluate how soil wetness modelscould be improved by taking into account such features. In the Armorican Massif, soils have developed intoa loamy material of 1 to 3 m depth overlying impermeable granitic or schistic saprolites. Recent soil wetnessprediction models showed high prediction errors that have to be addressed (Crave and Gascuel-Odoux, 1996;Chaplot et al., 2000b). In an agricultural watershed of 4Ð5 ha, a systematic survey over 1996–1997 allowedsoil water content at several depths (0–10, 20–30, 50–60 and 110–120) to be compared with terrain attributesestimated from DEMs of, in the first case the soil surface topography and, in the second case, the topographyof the boundary between the soil cover and the underlying impermeable saprolite.

MATERIALS AND METHODS

Site description

The study area is located in the eastern part of the Armorican Massif (western France), a complex basementof Proterozoic and Palaeozoic bedrock. It is a granitic catchment of about 4Ð5 ha located in the upper part ofthe ‘La Roche’ stream catchment (7Ð8 km2), a first-order stream with a mean flow discharge over 1995–1997of 59 L s�1 (Grimaldi and Chaplot, 2000). This 4Ð5 ha catchment is characterized by hillslopes 150 to 250 mlong with a mean elevation range of 10 m. Hillslope topography is relatively smooth with slope angles varyingfrom 0 to 2% close to the stream bank and on summits, to 6% on the backslope.

In the Armorican Massif, granites and schists are the two dominant substrata, comprising 80% of theregion’s surface. Other substrates include mica schists, orthogneisses and sedimentary rocks. Deep mechanicalweathering of the bedrock occurred during the Variscan orogeny, where mylonitization and strong fracturingoccurred. This weathering produced deep saprolites (>30 m), rich in kaolin and mainly impermeable (Wyns,1991). During the late Miocene and early Quaternary, saprolites were subjected to erosion, owing to strongcyclic climatic regime changes from periglacial to temperate and to a succession of tectonic movements (VanVliet-Lanoe et al., 1998). Finally, saprolites have been overlain by aeolian deposits during the past 300 kyr

Copyright 2003 John Wiley & Sons, Ltd. Hydrol. Process. 17, 2567–2580 (2003)

PREDICTION OF SOIL WETNESS 2569

from west to east of the Armorican Massif. Subsequent to their deposition the aeolian sediments were locallyreworked on slopes by solifluction, water erosion and local alluviation (Le Calvez, 1979). Owing to thepresence of subsurface impermeable layers, water drainage tends to accumulate in favourable locations suchas hillslope hollows and footslopes, where waterlogged soils are observed (Chaplot et al., 2000a). Well drainedsoils characterize upper parts of hillslopes.

At the study site, the soil cover has developed into a loamy material overlying a typical impermeablegranitic saprolite (Curmi et al., 1998). The depth of the soil cover varies from 0Ð8 to 3 m. Variations in soildepth do not seem to be linked directly to the topography of the soil surface. Soils are variably distributedalong slopes, from loamy Hapludalfs (Soil Survey Staff, 1999) upslope, Aqualfs and Glossaqualfs backslopeand downslope and Fluvaquentic Sphagnofibrists and/or Dystrochrepts near the stream bank.

Fluvaquentic Sphagnofibrists, which occur along the stream banks, are characterized by a high organicmatter accumulation (mean of 350 kg C m�2; Chaplot et al., 2001). Previous studies have also shown thatloamy horizons of Hapludalfs, Aqualfs and Glossaqualfs are marked by low hydraulic permeability, i.e.average values of 0Ð007 m day�1 (Curmi et al., 1998), whereas underlying saprolites exhibit much lowerpermeability (<0Ð005 m day�1; Grimaldi and Chaplot, 2000).

Climate is oceanic with a yearly mean precipitation and temperature for the past 20 years of 898 mm and10Ð1 °C, respectively.

The study watershed is situated in a part of the Armorican Massif with relatively moderate agricultureintensification. From 1995 to 1997, almost 65% of its total surface area was under pasture, the remainingsurface being under corn. One particular aspect of land-use distribution in landscapes is that the near-streambank zones were exclusively under pasture.

Field study

Soil samples were taken from a limited area of the 4Ð5 ha catchment, a hillslope 160 m long with a 10-maltitude range. Volumetric soil wetness at depth ranges 0–10 cm (�10), 20–30 cm (�30), 50–60 cm (�60) and110–120 cm (�120) was measured from January 1996 to August 1997. Time-domain reflectometry (TDR)was used for topsoil wetness, whereas �30, �60 and �120 were evaluated using a gravimetric method. Thesampling set for �10 was composed of 149 nodes of a 10-m grid. In addition, from this main sampling set,112 data points were randomly selected for �30, �60 and �120 estimation. In order to calculate the gravimetrichumidity, the samples (150–300 g) were weighed before and after drying at 105 °C for 72 h. The volumetricsoil wetness was then calculated using the bulk density of each undisturbed horizon using 250-ml volumecylinders (Chaplot et al., 2001).

Sixteen sampling surveys were performed over the study period with a sampling frequency varyingthroughout the year to focus on rainy and dry periods. Thus, the time between two sampling surveys wasincreased in winter and in summer. Each survey was taken not less than 24 h after the last rainfall event.In order to lessen the working time in the field, only one transect of the study hillslope was investigatedeach time. When significant differences with the previous survey were observed, i.e., either wetter or drierconditions in soils, the whole hillslope was investigated.

The coordinates (longitude and latitude) of each of the 149 sampling points were derived from a singlegeoreferenced point using a theodolite. In order to perform measurements at identical locations, permanentsticks were positioned over the hillslope from the first survey. At the end of 1997 the depth to the uppersurface of the saprolite was estimated from morphological description using augered holes at each of the 149locations. The contact between loamy soil cover and compact sandy clayed saprolite was distinct. In addition,saprolite determination was facilitated by a clear rusty or grey matrix depending on the duration of conditionsof saturation by water.

The wettest and driest situations on 11 December 1996 and 9 April 1997, respectively, will be presentedhere.

Copyright 2003 John Wiley & Sons, Ltd. Hydrol. Process. 17, 2567–2580 (2003)

2570 V. CHAPLOT AND C. WALTER

Topographic analysis

Two DEMs with a 10-m resolution and a 0Ð3-m vertical precision have been generated over the studycatchment from a detailed topographic survey using a theodolite. The first DEM is a numerical representationof the soil surface topography. Four-hundred and ninety-four additional points over the 4Ð5 ha catchmentwere added to the initial data set of 149 data point inside the selected hillslope along the central depressionof the catchment. The second DEM, of the upper boundary of saprolites, was generated over the catchmentusing (i) the set of 149 data points for which the depth to saprolite upper boundary was determined by augerhole; (ii) the set of 494 data points for which, owing to the difficulty of field investigation, we considered atheoretical depth to the saprolite upper boundary equal to 1Ð5 m, corresponding to the mean depth observedat the study site.

For DEM construction we used the GRID tool of Arc Info 7Ð1 (ESRI, 1997). The fitting procedure(‘TOPOGRID’ function of Arc/Info 7Ð1 Geographic Information System, Hutchinson, 1989) ensures thesmoothest fit to point and contoured elevation data taking into account specified break-lines such as riversor ravines. The actual stream bank position was used in the drainage enforcement algorithm of TOPOGRID,which attempted to modify the DEM to yield continuous drainage surfaces.

Several topographic attributes or indexes were derived from this DEM. Previous studies in the ArmoricanMassif have shown a strong relationship between the soil wetness and/or the duration of saturation by waterin soils and the elevation above the stream bank considering the shortest flow path from each cell to thestream (E) (Crave and Gascuel, 1996); the downslope gradient (DG) (Merot et al., 1995), which is the ratiobetween E and the shortest distance to the stream (D); the upslope contributing and multidirectional area(AMU) expressed in metres per unit width perpendicular to the flow direction, as defined by (Quinn et al.,1991); and the revised compound topographic index [CTI D ln(AMU/DG)]. The CTI approach differs fromthose most commonly adopted (e.g. McKenzie and Ryan, 1999) because the downslope gradient (DG) replacesthe local slope gradient (S). Other topographic attributes include the altitude of data points (A); the specificmonodirectional catchment area (AMO, Moore and Grayson, 1991); the stream power index (SPI, Bell et al.,1994; SPI D AMU ð S); and the profile, plan and tangential curvatures (Curvpr, Curvpl, Curvta, Zevenbergenand Thorne, 1987). Variables D, A and E have been estimated from theodolite measurements. VariablesS, AMO and the curvatures were derived using the GRID function of Arc-Info (ESRI, 1994). Finally, weestimated AMU using software developed at ENSA Rennes (Squividant, 1994) based on the algorithm ofQuinn et al. (1991).

Statistical analysis and modelling

The relationship between topographic attributes estimated using (i) soil surface topography and (ii) thetopography of the upper boundary of saprolite was investigated. In addition, correlation coefficients between�10 on 11 December 1996 and 9 April 1997 and the two sets of topographic attributes are presented. Finally,the relationship between �10 on 11 December 1996 and topographical attributes estimated using the surfaceand the subsurface topography has been investigated by using non-linear regression analysis for 119 randomlychosen data points of the model construction set. The multiple regression method was used because it is apractical tool that furnishes direct quantitative results and allows us to use easily accessible variables suchas terrain attributes to predict soil wetness, a variable difficult to access. This relationship may be used todirectly predict soil wetness over large areas. Regression analyses (Neter et al., 1989) were performed withthe Statistica package for use on a personal computer (Statsoft, 1996). The estimation method used was theQuasi-Newton, with the maximum likelihood function as the loss function. Only parameters with statisticalsignificance at the 0Ð001 level were considered for computing predictive equations and reporting results

��10�Ł D constant C e�topographic attributes� �1�

The estimation of topsoil wetness ���Ł at a given point was determined by the regression model (Equation 1)considering topographic attributes. Two situations were considered for �10 estimation: (i) the use of surface

Copyright 2003 John Wiley & Sons, Ltd. Hydrol. Process. 17, 2567–2580 (2003)

PREDICTION OF SOIL WETNESS 2571

topography; (ii) the use of subsurface topography, i.e. the topography of the saprolite upper boundary. Thevalidation of these regression models was performed using the remaining set of 30 data points. Statisticalparameters were computed: the mean error, ME, and the root mean standard error, RMSE, between estimatedtopsoil water content (��Ł and observed values. The ME and RMSE values were computed as follow:

ME D 1

n

n∑iD1

[���Ł � �] �2�

RMSE D{

1

n

n∑iD1

[���Ł � �]2

}0Ð5�3�

The values for ME and RMSE decrease with increasing regression model accuracy.

RESULTS AND DISCUSSIONS

The climatic context of the study period

The years 1996 and 1997 showed mean precipitation of 709 and 741 mm, respectively. These values areslightly lower than the 30-year mean of 898 mm. The year 1996 was characterised by a dry autumn and anexceptionally wet winter with a rainfall of 160 mm in December compared with 98 mm, the 30-year mean.In 1997, rainfall was distributed uniformly over the year, except in March and April, which were dry. The9 April 1997 followed 45 days with a total rainfall of less than 15 mm against 100 mm for the mean valueof the past 30 years. Temperatures over 1996 were close to normal (mean of 10Ð2 °C against 10Ð1 °C). Thecoldest temperatures occurred in November and February (mean temperatures of 3 and 4 °C respectively) andthe warmest in July and August (17 and 18 °C respectively). The year 1997, with a mean of 11Ð7 °C, waswarmer. In 1997, January was the coldest month with a mean of 2 °C and August with a mean of 20 °C thewarmest one.

The relationship between topographical attributes estimated using surface and subsurface DEMs

Grid representations of surface and subsurface topography of the study hillslope are shown in Figure 1.Soil surface topography is relatively smooth. Altitudes vary from 193Ð1 to 200Ð2 m. Lower slope anglesare observed in the valley bottom and on the summit. A depression orientated downslope–upslope could beobserved in the middle of the study hillslope. This depression is less pronounced in the mid-slope position. Thetopography of the saprolite upper boundary showed similar trends with, however, a deeper central depressionstretching out from the stream bank to the hillslope summit. In addition, smaller depressions occur in thesoutheastern and northern part of the hillslope.

Estimations using subsurface topography differ greatly to those using surface topography. This apparentdiscordance between surface and subsurface topography is confirmed by the matrix of linear correlationpresented in Table I. The matrix diagonal shows for each attribute the correlation coefficient betweenestimations using both DEMs. Correlation coefficients were very low for DG (r D 0Ð17), Curvpr (r D 0Ð01) andCurvpl (r D 0Ð22). In contrast, correlation coefficients were high for A (r D 0Ð99), E (r D 0Ð98), S (r D 0Ð99),AMO (r D 0Ð80), AMU (r D 0Ð98) and SPI (r D 0Ð83), revealing that few differences exist between DEMs.Intermediary correlation coefficients characterize CTI (r D 0Ð64) and Curvta (r D 0Ð74).

In addition, the upper and lower parts of the matrix of linear correlation coefficients present the level ofautocorrelation between topographic attributes estimated from surface and subsurface topography, respectively.For both DEMs, correlation coefficients higher than 0Ð97 were observed between D and A or E. This isexplained by a natural tendency along hillslopes for there to be an increase in elevation with increase indistance to the stream bank. Significant coefficients were also observed between the physical index CTI andE, DG and AMU. Finally, whatever the topography considered, S and the three curvatures were only slightly

Copyright 2003 John Wiley & Sons, Ltd. Hydrol. Process. 17, 2567–2580 (2003)

2572 V. CHAPLOT AND C. WALTER

192

343.

58

343.

60

343.

62

343.

72343.

66

2413

2413

.08

196

194

343.

64

343.

70

343.

68

2413

.04

200

m

199

m

198

m

197

m

196

m

195

m

194

m

199

m

198

m19

7 m

196

m19

5 m

194

m

193

m Latit

ude

(Km

)Longitude (Km)

B. Saprolite topography

A. Surface topography

Alti

tude

(m

)

Figure 1. Numerical representation of the soil surface topography (A) and the topography of the saprolite upper boundary (B) of the studyhillslope using 10-m DEMs (‘La Roche’ site, western France). For both DEMs, contour lines with a 0Ð5 m interval are shown in dark lines

correlated to the other topographic attributes. Finally, the depth to saprolite upper boundary (SD) was notsignificantly correlated with surface or subsurface terrain attributes.

Predicting volumetric soil wetness using topographical attributes

Correlation coefficients between the volumetric topsoil wetness (�10) on 11 December 1996 and 9 April1997 and selected topographical factors are presented in Table II. Correlation coefficients ranged between0Ð02 on 9 April 1997 for Curvpl estimated using surface topography, to 0Ð86 on 11 December 1996 for Eand CTI from subsurface topography. Higher correlation coefficients were observed on 11 December thanon 9 April 1997. For instance, the correlation coefficient between �10 and E decreased from 0Ð86 to 0Ð63 forsurface topography and from 0Ð85 to 0Ð64 for subsurface topography. Such a decrease is also observed for D,A, DG, CTI and AMU. On 11 December 1996, neither soil surface nor saprolite upper boundary topographiessignificantly affected the correlation coefficient for D, SD, A and AMU. However, for DG and CTI, r wasmuch higher when using subsurface topography than the soil surface topography. This is also the case on 9April 1997 for DG and CTI, where r increased from 0Ð28 to 0Ð57 and from 0Ð19 to 0Ð47, respectively.

On 11 December 1996, soil wetness at the different depths (0–10, 20–30, 50–60 and 110–120 cm) ispresented as a function of the elevation above the stream (ES) (Figure 2). Values for �10 ranged from 22 to

Copyright 2003 John Wiley & Sons, Ltd. Hydrol. Process. 17, 2567–2580 (2003)

PREDICTION OF SOIL WETNESS 2573

Tabl

eI.

Cor

rela

tion

mat

rixe

sfo

r(i

)so

ilan

dto

pogr

aphi

cat

trib

utes

esti

mat

edus

ing

the

10-m

DE

Mof

the

uppe

rbo

unda

ryof

sapr

olit

e(i

nit

alic

)an

d(i

i)to

pogr

aphi

cfa

ctor

ses

tim

ated

usin

gth

e10

-mD

EM

ofth

eso

ilsu

rfac

e(n

orm

alfo

nt).

The

foll

owin

gat

trib

utes

are

cons

ider

ed:

dist

ance

toth

est

ream

bank

(D);

soil

dept

h(S

D);

alti

tude

(A);

elev

atio

ndi

ffer

ence

toth

est

ream

bank

(E);

the

‘dow

nslo

pegr

adie

nt’

(DG

),w

hich

repr

esen

tsth

era

tio

betw

een

Ean

dth

edi

stan

ceto

the

stre

amba

nk;

the

revi

sed

com

poun

dto

pogr

aphi

cin

dex

(CT

I);

the

slop

egr

adie

nt(S

),i.e

.th

esp

ecifi

cm

onod

irec

tiona

lca

tchm

ent

area

(AM

O);

the

spec

ific

mul

tidi

rect

iona

lca

tchm

ent

area

(AM

U);

the

stre

ampo

wer

inde

x(S

PI)

(Bel

let

al.,

1994

,SP

ID

AM

Uð

S);

the

profi

le(C

urv p

r�,

plan

(Cur

v pl�

and

tang

entia

l(C

urv t

a�cu

rvat

ures

.Dat

ase

tof

149

poin

ts.C

orre

latio

nco

effic

ient

sbe

twee

nto

pogr

aphi

cat

trib

utes

estim

ated

usin

gsu

rfac

ean

dsa

prol

iteup

per

boun

dary

topo

grap

hies

are

unde

rlin

ed

Var

iabl

eV

aria

ble

DSD

AE

DG

CT

IS

AM

OA

MU

SPI

Cur

v pr

Cur

v pl

Cur

v ta

D1Ð0

00Ð3

0Ł0Ð9

9Ł0Ð9

9Ł0Ð0

5�0

Ð54Ł

�0Ð08

�0Ð28

Ł�0

Ð64Ł

�0Ð13

0Ð27Ł

0Ð14

�0Ð19

Ł

SD0Ð3

0Ł1Ð0

00Ð2

8Ł0Ð3

1Ł0Ð1

2�0

Ð27Ł

�0Ð14

�0Ð20

Ł�0

Ð26Ł

�0Ð18

Ł0Ð2

0Ł0Ð1

6Ł�0

Ð18Ł

A0Ð9

8Ł0Ð1

30Ð9

9Ł0Ð9

9Ł0Ð0

8�0

Ð56Ł

�0Ð09

�0Ð28

Ł�0

Ð65Ł

�0Ð14

0Ð28Ł

0Ð14

�0Ð21

Ł

E0Ð9

7Ł0Ð1

5Ł0Ð9

8Ł0Ð9

8Ł0Ð1

4Ł�0

Ð61Ł

�0Ð09

�0Ð30

Ł�0

Ð67Ł

�0Ð14

0Ð29Ł

0Ð16Ł

�0Ð21

Ł

DG

0Ð73Ł

0Ð06

0Ð75Ł

0Ð81Ł

0Ð17Ł

�0Ð62

Ł�0

Ð120Ð0

6�0

Ð08�0

Ð120Ð2

2Ł0Ð2

0Ł�0

Ð13C

TI

�0Ð62

Ł�0

Ð22Ł

�0Ð61

Ł�0

Ð63Ł

�0Ð88

Ł0Ð6

4Ł�0

Ð20Ł

0Ð39Ł

0Ð80Ł

0Ð01

�0Ð37

Ł�0

Ð28Ł

0Ð20Ł

S�0

Ð06�0

Ð13�0

Ð05�0

Ð040Ð2

2Ł�0

Ð31Ł

0Ð99Ł

�0Ð26

Ł�0

Ð37Ł

0Ð76Ł

�0Ð01

�0Ð06

0Ð08

AM

O�0

Ð30�0

Ð32Ł

�0Ð26

Ł�0

Ð28Ł

�0Ð36

Ł0Ð4

9Ł�0

Ð130Ð8

0Ł0Ð5

6Ł0Ð3

0Ł�0

Ð42Ł

�0Ð42

0Ð29Ł

AM

U�0

Ð64Ł

�0Ð27

Ł�0

Ð62Ł

�0Ð65

Ł�0

Ð73Ł

0Ð82Ł

�0Ð38

Ł0Ð5

5Ł0Ð9

8Ł�0

Ð12�0

Ð31Ł

�0Ð20

Ł0Ð1

4SP

I�0

Ð16Ł

�0Ð29

Ł�0

Ð14�0

Ð150Ð0

5�0

Ð090Ð7

4Ł0Ð4

4Ł�0

Ð080Ð8

3Ł�0

Ð32Ł

�0Ð36

Ł0Ð2

8Ł

Cur

v pr

�0Ð01

�0Ð35

Ł0Ð0

80Ð0

70Ð1

8Ł�0

Ð070Ð0

20Ð0

10Ð0

30Ð0

90Ð0

10Ð8

0Ł�0

Ð83Ł

Cur

v pl

0Ð18Ł

�0Ð14

0Ð24Ł

0Ð23Ł

0Ð27Ł

�0Ð16

Ł0Ð0

5�0

Ð22Ł

�0Ð14

�0Ð10

0Ð75Ł

0Ð22Ł

�0Ð49

Ł

Cur

v ta

0Ð15

�0Ð05

0Ð19Ł

0Ð20Ł

0Ð18Ł

�0Ð1

�0Ð04

�0Ð45

Ł�0

Ð13�0

Ð37Ł

0Ð56Ł

0Ð83Ł

0Ð74Ł

Cor

rela

tions

sign

ifica

ntat

p<

0Ð5

Copyright 2003 John Wiley & Sons, Ltd. Hydrol. Process. 17, 2567–2580 (2003)

2574 V. CHAPLOT AND C. WALTER

Tabl

eII

.C

orre

lati

onco

effic

ient

sbe

twee

nth

evo

lum

etri

cso

ilw

etne

ssof

the

tops

oil

(0–

10cm

)on

11D

ecem

ber

1996

and

9A

pril

1997

and

soil

and

topo

grap

hica

lfa

ctor

ses

timat

edus

ing

the

10-m

digi

tal

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atio

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odel

(DE

M)

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surf

ace.

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tanc

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amba

nk(D

);so

ilde

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(SD

);al

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de(A

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evat

ion

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eren

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the

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);th

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grad

ient

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G),

whi

chre

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ents

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rati

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nE

and

the

dist

ance

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est

ream

bank

;th

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und

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ope

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ient

(S),

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ific

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nal

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ea(A

MO

);th

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nal

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MU

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erin

dex

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1997

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1997

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Copyright 2003 John Wiley & Sons, Ltd. Hydrol. Process. 17, 2567–2580 (2003)

PREDICTION OF SOIL WETNESS 2575

0-10 cm

Soi

l wet

ness

(%

)

20

40

60

80

100

20-30 cm

Surface topography

Saprolite topography

Elevation above the stream bank (m)

Soi

l wet

ness

(%

)

20

40

60

80

100

50-60 cm

Elevation above the stream bank (m)

110-120 cm

Surface topography

Saprolite topography

Surface topography

Saprolite topography

Surface topography

Saprolite topography

0 2 4 6 8 0 2 4 6 8

Figure 2. Soil wetness at several depths (0–10, 20–30, 50–60 and 110–120 cm) as a function of the elevation above the stream (ES)estimated from surface topography and from the topography of the saprolite upper boundary. Data for 11 December 1996 (wet period)

89%, whereas values for �30, �60 and �110 were between 10 and 90%. No significant differences were observedbetween topographies. Soil wetness at all depths studied decreased with increasing elevation above the stream.Between 0 to 4 m, values for �10 decreased sharply. Up to 4 m, values for �10 decreased only slightly. For �greater than 10 cm, a similar pattern could be observed, i.e., a decrease of soil wetness with increasing ES.However, between elevations of 0–2 m, the 50–60 and 110–120 cm samples exhibited a great degree ofscattering. Between 2 and 8 m altitude, soil wetness showed limited variations (Figure 2). On 9 April, the �10

range of values is much smaller (between 8 and 54%). The same decrease in values for �10 with increasingES is observed but with greater scattering below 4 m (Figure 3).

Figure 4 presents the soil wetness data on 11 December 1996 as function of compound topographic index(CTI). Using the topography of the saprolite upper boundary, soil wetness at all depths studied increasedwith increasing CTI, whereas using surface topography, CTI variations do not affect �. The �30, �60 and�110 values exhibited a greater range for CTI estimated using subsurface topography. On 9 April, greaterscattering characterized the samples for subsurface topography and no significant trend is observed for surfacetopography.

Non-linear exponential estimations have been considered here because topsoil wetness was relatedexponentially to elevation difference to the stream bank and the revised compound topographic indexCTI as topographical attributes. Then, exponential regression analyses (Neter et al., 1989) were performed.Multiple regressions between topsoil water content (�10� from 11 December and topographic attributesnonautocorrelated estimated using surface or saprolite upper boundary topographies have been generated

Copyright 2003 John Wiley & Sons, Ltd. Hydrol. Process. 17, 2567–2580 (2003)

2576 V. CHAPLOT AND C. WALTER

Compound topographic index (CTI)108642

Top

-soi

l wet

ness

(%

)

20

40

60

80

Elevation above the stream bank (m)

Top

-soi

l wet

ness

(%

)

20

40

60

80Surface topographySaprolite topography

Surface topographySaprolite topography

0 2 4 6 8

Figure 3. Topsoil wetness (0–10 cm) as a function of the elevation above the stream (ES) and the compound topographic index (CTI) on9 April 1997 (dry period)

as follows:

��10�surf D 19Ð96 C e[4Ð38��0Ð39ðE���0Ð05ðCTI�] r2 D 0Ð80 �4�

��10�saprolite D 123Ð60 C e[3Ð69��0Ð56ðE�C�0Ð03ðCTI�] r2 D 0Ð89 �5�

Both equations included the physically based topographic attributes of index, elevation difference above thestream bank (E) and compound topographic index (CTI). Mean error, ME, and root mean square error, RMSE,between estimations and observations on 30 data points of the validation set were lower for Equation (5) thanfor Equation (4). Mean error and RMSE were �0Ð1 and 6Ð04 for surface topography and �0Ð04 and 3Ð81for the topography of the saprolite upper boundary, respectively (Table III). The use of the topography ofthe saprolite upper boundary reduced RMSE by 43%. The topography of the saprolite upper boundary alsoseemed to better predict �10 mean and standard deviation (Table III).

An error analysis was performed by plotting RMSE of topsoil water content (�10� over the study area.The RMSE for regressions using surface and subsurface topography is presented in Figure 5. Errors were notdistributed in a spatial pattern, i.e. RMSE did not significantly vary whatever the position within the hillslope,the altitude or the distance from the stream bank.

Copyright 2003 John Wiley & Sons, Ltd. Hydrol. Process. 17, 2567–2580 (2003)

PREDICTION OF SOIL WETNESS 2577S

oil w

etne

ss (

%)

20

40

60

80

100

Compound topographic index (CTI)2 4 6 8 10 2 4 6 8 10

Soi

l wet

ness

(%

)

20

40

60

80

100

Compound topographic index (CTI)

0-10 cm 20-30 cm

50-60 cm 110-120 cm

Surface topographySaprolite topography

Surface topographySaprolite topography

Surface topographySaprolite topography

Surface topographySaprolite topography

Figure 4. Soil wetness at several depths (0–10; 20–30; 50–60 and 110–120 cm) as function of the compound topographic index (CTI)estimated from surface topography and from the topography of the saprolite upper boundary. Data for 11 December 1996 (wet period)

Table III. Mean of observed and estimated topsoil wetness (�10� usingsurface topography [(�10�Ł

surface] and the topography of the saprolite upperboundary [(�10�Ł

saprolite]; standard deviation (SD); mean error, ME and rootmean square error, RMSE between estimations and observations

Mean SD ME RMSE

Observed �10 38Ð8 17Ð5(�10�Ł

surface 38Ð7 16Ð3 �0Ð10 6Ð04(�10�Ł

saprolite 38Ð8 16Ð8 �0Ð04 3Ð81

CONCLUSION

In this study of an agricultural catchment, soil wetness (�) estimated over 1996–1997 at 0–10, 20–30,50–60 to 110–120 cm was significantly correlated with the topographic attributes, elevation above thestream bank (E) and compound topographic index (CTI). Crave and Gascuel (1996) also demonstrated highcorrelation between � and E under similar conditions of the Armorican Massif but with a schistose saprolite.Therefore, topography is confirmed as being one of the most important determinants of soil wetness spatialdistribution. The best correlations were observed during wet seasons. During dry seasons with a large amountof data scattering, other environmental factors such as evapo-transpiration could affect soil wetness spatialdistribution.

Copyright 2003 John Wiley & Sons, Ltd. Hydrol. Process. 17, 2567–2580 (2003)

2578 V. CHAPLOT AND C. WALTER

15

0

343.

58

343.

60

343.

62

343.

72343.

66

2413

2413

.0810

5

343.

64

343.

70

343.

68

2413

.04

Latit

ude

(Km

)

Longitude (Km)

Validation setConstruction set Using saprolite topography

Using surface topography

RM

SE

of t

opso

il w

etne

ss

(cm

3 cm

-3)

Figure 5. Root mean square error (RMSE) between topsoil wetness (�10� predicted using regression models at the 30 data points ofthe validation set from topographical attributes estimated using either surface or subsurface topography, respectively. Location of both

construction and validation sets in the study hillslope (‘La Roche’ site, Western France)

The present study revealed that topographic attributes estimated using the DEM of the saprolite upperboundary better explained the spatial distribution of � than topographic attributes estimated using the DEMof the soil surface. Using the topography of the saprolite greatly improved the soil wetness spatial prediction.The very low permeability of saprolites (<0Ð005 m day�1, Grimaldi and Chaplot, 2000) induces the lateralflux of water in soils along slopes and is responsible for increasing soil wetness in the downslope direction.This could explain the greater accuracy of � spatial distribution using subsurface topography and gives supportto the suggestion these water fluxes are mainly driven by the topography of the saprolite upper boundary.One reasonable explanation for this is that the lateral water fluxes in soils along slopes induced by the verylow permeability of the saprolite are mainly driven by the topography of the saprolite upper boundary.

The DEM gives accurate prediction of soil wetness spatial distribution. However, to obtain better accuracywe can use subsurface topography. Modelling soil wetness spatial distribution using the topography of asubsurface feature such as the saprolite upper boundary may be extended to other areas also characterized bya non-parallelism between surface and subsurface topographies. This should be the case of numerous naturalsystems. For these situations, taking into account the topography of hydrological discontinuities would alsoimprove the prediction of the trajectory of flows down hillslopes and consequently the estimation of the spatialdistribution of soil wetness.

Despite DEMs of surface topography now being widely available, numerical representations of thetopography of subsurface discontinuities are not easily accessible over large areas. Indeed, no convenientdata bases are offered for representing the continuously varying topography of subsurface discontinuities ofthe Earth. Such information may be spatially accessed using for instance geophysical techniques. Chaplotet al. (2001) on the same study site showed a high correlation between the apparent resistivity obtained usingthe radio magneto tellurique (RMT) and the depth to saprolite upper boundary (r2 D 0Ð51). Other geophysicalmethods such as GPR may also be relevant to estimate the spatial variations of subsurface features includingthe depth to the saprolite upper boundary (Dominic et al., 1995; Lapen et al., 1996; Freeland et al., 1998).However, these last techniques need a great amount of field work and data processing that could not be entirelyjustified for such a purpose. Finally, a promising possibility of accessing the depth to the saprolite upperboundary is to generate quantitative soil–landscape models. Indeed, such models that relate soil properties tomore accessible soil-forming factors, such as surface topography or geology, have shown their usefulness inestimating the soil depth over large areas (e.g. Gessler et al., 1995; Bourennane et al., 2000).

Copyright 2003 John Wiley & Sons, Ltd. Hydrol. Process. 17, 2567–2580 (2003)

PREDICTION OF SOIL WETNESS 2579

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