distribution characteristics of hydraulic properties on a mountainous hillslope

Geosciences JournalDOI 10.1007/s12303-013-0022-2ⓒ The Association of Korean Geoscience Societies and Springer 2013

Distribution characteristics of hydraulic properties on a mountainous hillslope

ABSTRACT: Understanding the heterogeneity of infiltration hasbeen a challenging issue in improving knowledge of hillslopehydrology. Spatial distributions of the hydraulic properties on ahillslope were measured using tension infiltrometers over four dif-ferent time periods. The hillslope examined has a permanent chan-nel initiation point located in the Bongsunsa watershed, which is aheadwater for the Han River basin, South Korea. Surface hydrau-lic conductivity is affected by both pore development structure andsoil texture. In order to explore the impact of the relationship betweenspatial topographical features and the surface hydraulic proper-ties, several terrain analyses and flow evaluations were performed.The importance of flow through a larger pore size was confirmedin both the scale and variation of the spatial and seasonal perspec-tives, respectively. Although there is a substantial heterogeneity offield measurements in both spatial and temporal contexts, the thresh-old for characterizing the spatial variation of hydraulic propertiescan be obtained through several statistical tests, using two distinctdata subsets delineated from an analysis of the terrain attributesand hydraulic properties. Results reveal that threshold behaviorappears to be restricted for hydraulic properties associated withthe generation of the flow through macropores.

Key words: surface hydraulic properties, macropore, terrain analysis,infiltration

1. INTRODUCTION

Hydraulic properties under natural conditions in physicallybased hydrologic models are important factors in under-standing the hydrological processes on a hillslope scale(Grah et al., 1983; Beven, 2002; Harden and Scruggs, 2003;van Schaik, 2009; Holden, 2009). Water flux under field soilconditions is composed of both matrix flow and preferentialflows (Lawes et al., 1882). Preferential flow refers to the rela-tively rapid and spatially concentrated flux, and matrix flowrefers to slow and relatively uniform flux both water and sol-ute transport (Kung et al., 2000; Nimmo, 2011). However,there is a difficulty in predicting hydrological processes, whichoriginate mainly from the heterogeneity of the field soil layer(Allaire et al., 2009). Activity of earthworms, soil cracks, flowover distinct soil layers and hydrophobicity are all respon-sible for the uncertainty of flow in a natural system, and severalmechanisms such as crack flow, burrow flow, erosion flow,finger flow, lateral flow and macropore flow, exist for thegeneration of a flux faster than the matrix flow in a soil layer

(Beven and Germann, 1982; Noguchi et al., 1997; Zehe andFlüher, 2001; Weiler and McDonnell, 2007). Althrough manystudies have investigated the origin of macropore develop-ment, the prediction of the spatial distribution of macroporesis difficult, mainly due to uncertainty under field conditions(Beven and German, 1982; Watson and Luxmoore, 1986;Noguchi et al., 1997; Bodhinayake and Si, 2004b). For theseuncertainties, the existences of a threshold behavior inhydrological systems has lately begun to be recognized andunderstood (Zehe and Sivapalan, 2009).

The spatial distribution of hydrologic mechanisms, suchas infiltration, the development of preferential flow and thegeneration of surface runoff, have been investigated in thefield using field measurements, such as the tension infil-trometer test, surface runoff measurement and tracer testswith image analysis. The spatial development of the infil-tration characteristics depends on factors such as the topo-graphical features of the hillside, the existence and locationof any streams, the soil texture, biological activity and geo-morphological processes such as erosion and deposition offine sediment along the hillslope (Buttle and House, 1997;Zehe and Flüsher, 2001; Öhrström et al., 2002; Harden andScruggs, 2003; Holden, 2009; Wang et al., 2008; van Schaik,2009). The application of geo-statistical methods such assemivariance analysis, to various environmental componentshad provided controversial results for certain driving factors,i.e., soil texture and initial soil moisture (Zehe and Flüsher,2001); soil structure, initial soil moisture and slope (Ohr-storm et al., 2002); topography, vegetation and soil texture(van Schaik, 2009); and even no spatial dependency inhydraulic conductivity (Wilson and Luxmoore, 1988; Sobi-eraj et al., 2002). However, the study areas used in these stud-ies were either hillslopes with gentle slopes (a mean slopeof less than 10%) or hillslopes with a substantially clay-basedsoil texture.

In this study, we selected a steep hillslope with a channelinitiation point to characterize the spatial distribution ofhydraulic properties in conjunction with the topography(see Fig. 1). Topography is the main driver of water trans-port and the subsequent distributor of the soil water contentalong a hillslope under humid and temperate climate con-ditions (Anderson and Kneale, 1980). Comparisons betweensoil moisture and terrain surrogates have been investigated

Yongseok GwakSanghyun Kim* } Department of Environmental Engineering, Pusan National University, Busan 609-735, Republic of Korea

*Corresponding author: [email protected]

Yongseok Gwak and Sanghyun Kim

assuming a steady state saturation tendency (Beven and Kirkby,1979; Western et al., 1999; Baggaley et al., 2009; Kim, 2009a).

In this study, a tension infiltrometer (Ankeny et al., 1988)was used to measure the spatial distribution of saturated andunsaturated hydraulic properties at several transects on ahillslope. Based on these field measurements as well as lab-oratory analyses including soil properties and terrain anal-ysis of the study area, this paper explores two issues, whichare as follows; firstly, what is the relationship between themeasured hydraulic properties and the terrain features for ahillslope with a permanent channel? This issue also includedan exploration of the distribution of preferential flows fordifferent pore in conjunction with topographic attributes.The second issue explored was whether there is a thresholdfor the terrain factors in characterizing the spatial distribu-tion of the hydraulic properties in the study area. The dominantfactor in explaining the variance in hydraulic conductivitieswas identified through rigorous statistical tests.

2. MATERIALS AND METHODS

2.1. Study Area

The study area selected was a hillside at a headwater ofthe Bongsunsa Watershed in the northern part of SouthKorea, as shown in Figure 1a (latitude 37°45'25.37''N and

longitude 127°9'11.62''E). The mean annual rainfall andtemperature are 1,332 mm and 11.5 °C, respectively. The areaof hillslope is approximately 3,200 m2, with a mean slopeof 22.5°, as shown in Figure 1b. The hillslope has a per-manent channel initiation point, and stream flow generationhad been observed during all periods except for the winterseason. The primary vegetation is a mixture of Carpinus sp.and shrubby Quercus sp. The soil is composed of a mixtureof sand (53.2%), silt (39.2%) and clay (7.6%), and from soilparticle analysis is classified as sandy loam based on theUSDA soil texture triangle (Dingman, 2002). The soil depthranges between 15 cm and 100 cm, with soil layers com-posed of: layer O (between 2 cm and 4 cm and with litterto a depth of 2 cm), layer A, (between 5 cm and 11 cm), layerB (between 30 cm and 42 cm) and layer C (between 20 cmand 25 cm). A developed root zone and an abundance ofmacropore were confirmed via visual inspection, as shown inFigure 1c.

2.2. Terrain Analysis and Experimental Planning

In this study, the spatial distribution of the infiltrationmeasurement points was carefully designed to consider theflow converging and diverging flow patterns along the hill-slope. The surface topography was delineated through anintensive manual survey using Transit (DT-208P, TOPCON),

Fig. 1. The location of the Bongsunsa watershed with hillslope studied (a); Surface and subsurface elevations with measurement points(b); macropores and root zone development at the depth of 10 cm (c).


and measuring tapes and poles. The soil depth was measuredvia the manual insertion of iron poles (for 1280 points),which was used to obtain the subsurface Digital ElevationModel (DEM). The DEMs for the surface and bedrock ter-rains were constructed with a pixel size of 0.5 m by 0.5 m,as shown in Figure 1b. The spatial distribution of the sat-uration tendency could then be estimated by applying var-ious flow determination schemes, such as D8, MD8, D∞and MD∞ algorithms (O’Callanghan and Mark, 1984; Quinnet al., 1995; Tarborton, 1997; Seibert and McGlynn, 2007),with the spatial distributions of the upslope contributingarea (CA) and topographic wetness index (TI). Simplertopographic attributes, such as the local slope (LS) and thedistance to stream pixel (DS) were also considered in plan-ning the experimental practice. Based on preliminary fieldevaluations of soil moisture and topographic attributes, eval-uations of CA and TI with an MD8 algorithm wereselected for this study (Kim, 2009a). The spatial distribu-tions of the CA, TI, LS and the soil depth provided thelocations for field measurements along 5 transects on thehilltop and downslope as presented in Figures 1b and 2.

2.3. In Situ Measurement of Hydraulic Characteristics

A tension infiltrometer, (designed by Ankeny et al., 1988),was used for the in situ measurements of saturated andunsaturated hydraulic conductivities. Tension infiltrometershave been widely used due to their applicability in the fieldand strength in evaluating preferential flow (Logsdon andKaspar, 1995; Carey et al., 2007; Jarvis, 2007). However, ifthe local slope is greater than 20%, then the experimentalerror associated with the surface slope can be significant(Bodhinayake et al., 2004c). It is also essential that the mem-brane disk and sand layer are adequately attached to ensurethat the experimental practice retain an appropriate tensionpressure (Sullivan et al., 1996; Vandervaere et al., 2000).The order of tension was –8, –6, –3, –1 and 0 cm, since areverse order may lead to the hysteresis effect (Reynoldsand Elrick, 1991). As a preliminary experimental procedure,each designated point was cleaned to a depth of 10 cm andcovered with a 5-mm-thick layer of fine and saturated sand.Infiltration measurements were continued until steady-stateconditions were reached under each tension, which generallytook place between 10 and 30 minutes in this study. Bothunsaturated and saturated hydraulic conductivities were esti-mated using two assumptions, which are Wooding’s equation(Eq. 1, Wooding, 1968) and Gardner’s equation (Eq. 2, Gard-ner, 1958).

(1)

(2)

where Q is the water inflow rate [L3T–1]; K(h), the hydrau-

lic conductivity [LT–1]; h, the metric suction potential [L];KS, the field saturated K; r, the radius of the disk [L]; andα, Gardner’s parameter [L–1], which was determined exper-imentally (Wooding, 1968; Reynolds and Elrick, 1991).

Equations (1) and (2) imply an assumption of uniformsoil particles and an exponential profile of hydraulic con-ductivity, which have been widely used in many approaches(Messing and Jarvis, 1993; Hussen and Warrick, 1993; Baird,1997; Casanova et al., 2000; Bodhinayake and Si, 2004b).

The hydraulic conductivities for tensions at –9, –6, –3 and0 cm were reversely calculated to evaluate the contributionof flow depending on the pore size distribution. The pore sizedistribution was categorized into four classes: macropores,and mesopores I, II, and III. There are several criteria forthe classification of pore size depending on the purpose ofthe analysis (Luxmoore, 1981). In this study, a macroporewas defined as the flow for a suction potential of less than–3 cm, which corresponds to a pore diameter greater than 1mm (Luxmoore, 1981; Watson and Luxmoore, 1986; Baird,1997). Mesopores I, II and III were classified as having diam-eters of 0.5 mm, 0.33 mm, and less than 0.33 mm, respec-tively. The macropore flow ratio for several pore classes, φi,was estimated using the saturated hydraulic conductivityand the unsaturated hydraulic conductivities (Watson andLuxmoore, 1986; Baird, 1997; Holden, 2009; Hu et al., 2009),estimated as follow:

, f = 0...n (3)

where subscript i denotes the pore size classification and fis the order of tension for the hydraulic conductivity andK(0) = KS.

The effective porosity for all classes of pores indicates thepore portions available for actual transport ability in theinfiltration process within the soil layer. Based on the cap-illary and Poiseuille’s equations, Bodhinayake et al. (2004a)further refined a method to estimate the effective porosity,as follows:

(4)

where µ is the viscosity of water [ML–1T–1]; ρ, the waterdensity [ML–3]; g, the gravitational acceleration [LT–2]; andγ, the surface tension of water [MT–2]; and H(a), H(b) arethe matric suction potentials corresponding to pore radii aand b, respectively. Combing Equations (2) and (4), theeffective porosity can be calculated using flux measure-ments for various tensions. The effective porosity ratio (ξi)can be estimated via the total porosity and effective poros-ities, as follows:

(5)

Q π r2K h( ) 1 4π rα⋅-------------+⎝ ⎠

⎛ ⎞⋅=

K h( ) KS exp α h⋅( )⋅=

φi %( )K hf( ) K hf 1+( )–

KS----------------------------------- 100×=

ε a b,( ) 2µρgγ 2------------- K h( )d

hd--------------h2

H a( )

H b( )

∫ hd=

ξiε a b,( )

εtotal---------------- 100⋅=


where a and b denote the pore radii [L]. The soil moisturewas measured using Time Domain Reflectometry (TDR)with MiniTrase (SoilMoisture Equipment Corp. 2005) at adepth of 10 cm. A soil core sampler (core size, 100 cm3,Soilmoisture Equipment Corp, USA), was used to collectsoil samples from all measurement points to obtain thebulk density and porosity, which were then determining thestandard operating procedure (Black, 1965; Dane and Topp,

2002; Dingman, 2002). Using both a sieve and Laser dif-fraction particle size analyzer (LS13320, Beckman Coultercorp., USA), which defines the soil texture based on thestandard of U. S. Department of Agriculture (Dingman,2002), the distribution of particle sizes within the soil ateach measurement point was determined. In situ measure-ments of the hydraulic conductivity were performed forall points in Figure 1b over four different time periods:

Fig. 2. The topographic index (TI) by Quinn et al. (1995) (a); the local slope (LS) as tanβ‚ (b); the upslope contributing area (CA, m2)(c); and the soil depth (SD, m) (d).


August 9, 2006; September 28, 2006; March 21, 2007;and June 7, 2007. In order to minimize the impact fromantecedent rainfall events, the experimental periods werecarefully selected so that negligible rainfall had fallen dur-ing the 10 days prior to each measurement practice (seeTable 1).

2.4. Statistical Analysis

In order to investigate the existence of a threshold for afew distinct hydraulic characteristics such as K(h) and α inconjunction with topographic attributes and soil texture, asequential analysis of variance was introduced using SPSSsoftware (SPSS Inc.). All hydraulic conductivities were log-transformed before performing the statistical analyses. Athreshold used to distinguish two separate datasets wasintroduced and the significance of difference was evaluated.It is possible to accomplish this using a two steps proce-dure. Firstly, it is necessary to perform a preliminary test tocheck the normality of dataset using the Shapiro-Wilk test,which uses the maximum number in 50 samples (Shapiroand Wilk, 1965; SPSS, 2003; Mohanty and Mousli, 2000).If the dataset is found to have no significant normality, aWilcoxen rank sum test can then be used. The second stepof the procedure is to test the statistical difference betweenthe two datasets and if the condition of homogeneous vari-ance is fulfilled, then the ANOVA analysis is used (Zhou etal., 2008; Hu et al., 2009; Holden 2009). If the condition ofhomogeneous variance is not fulfilled then, Welsh-Aspin testis employed (SPSS, 2003) In this study, the Welch-Aspinprocedure was used for subsets with non-homogenous vari-

ance, and the independent samples t-test is used for the othersubsets.

3. RESULT AND DISCUSSIONS

3.1. Hydrological Conditions and Hydraulic Conductivities

Laboratory analyses of the soil samples indicated thatporosities at a depth of 10 cm ranged from 50 to 65% witha mean and the coefficient of variation (CV) of 59.5 and8.6%, respectively. The average and CV of the bulk densitywere 1.08 g/cm3 and 13%, respectively. Soil textures wasclassified as being sandy loam for locations on the upslopepart and along the convex part of the study area, (points A2,A4, B1, B2, B3, C1, D1, D2, E1, E2, and E3). Points on thedownslope or on the concave region were mainly composedof loam (Fig. 1). The local slopes in the upslope and mid-slope parts were relatively higher than those in the downs-lope part. The in situ measurements occasionally sufferedfrom disturbances associated with human error and locality,such as rodent habitat or ant colony, and from soil erosioncaused by unexpected storms during the experimental period.The data obtained from transects D, E, and V on August 9,2006 and those for transects D and V on June 7, 2007 wereremoved from the results because the experimental condi-tions substantially violated the steady state assumption dur-ing the flux measurement. Table 2 summarizes the statisticsof the hydraulic conductivities, Gardner’s parameter and theantecedent soil moistures. The saturated hydraulic conduc-tivity showed high CVs for all four measurements, indicat-ing significant heterogeneity, regardless of the season, butthe spatial variance of Gardner’s parameter, α, was relativelyuniform. The seasonal difference in α is minor indicatingthat the soil structure is temporally unchanged. The hydrau-lic conductivities for relatively higher tensions showed smallerCVs than those for lower tensions. Considering the statisticsfor hydraulic conductivity, the data from –3 cm or from notension (K(–3), Ks) appeared primarily appeared to addressthe characteristics of spatial variation. The antecedent soilmoisture content for September 28, 2006, was considerablylower than for other seasons, as illustrated in Table 2.

Table 1. Antecedent accumulated rainfalls in mm for all experimen-tal dates

Antecedent Days 5 10 15 20 30Dates

9 Aug. 2006 0 1 226.5 243 880.528 Sept. 2006 0 3 3 13.5 2021 Mar. 2007 0 0 4.2 56.7 56.77 Jun. 2007 0 2.9 4.6 61.3 152

Table 2. Statistics of measured hydraulic conductivities (K(h)), Gardner’s parameter (α) and antecedent volumetric soil water contents(θi) at a depth of 10 cm

Parameter K(–9a) K(–6a) K(–3a) KS α θi

Statistics µ CV µ CV µ CV µ CV µ CV µ CVDate|Unit cm/hr % cm/hr % cm/h % cm/h % m–1 % % %

9 Aug. 2006 0.7 41 1.9 36 5.7 61 21.3 107 32.8 49 24.6 1128 Sept. 2006 0.6 68 1.7 92 5.5 142 21.7 189 30.1 45 15.6 2121 Mar. 2007 0.4 68 1.2 100 4.1 160 16.0 231 31.7 36 25.5 137 Jun. 2007 0.3 51 1.1 60 3.8 76 14.0.5 98 36.9 28 23.1 11

aThe numbers in parenthesis such as –9 and –6 are tension in cm.The µ and CV denote the mean and the coefficient of variation, respectively.


3.2. Contributions of Flow with Distribution of Pore Size

The field infiltration process can be configured by mea-suring the flow distribution for several classes of pore sizes.The flow through different size of pores is presented in Fig-ure 3a. The seasonal difference in the flow contribution isneglected for all classes of pore sizes. The mean flow formacropores, as shown in Figure 3a, was approximately 15cm/hr, but for mesopores I, II, and III it tended to decreasewith smaller pore size, indicating that field infiltration wasprimarily generated via the larger size of pores. Since thescales of the standard deviation decreased with smaller poresizes, (such as mesopores III), even with a logarithmic scaleof flow, as shown in Figure 3a, the CVs of the flow for thesmaller pore size tended to be reduced compared to thosefor the bigger pores. In fact, the seasonal variations of theCV in the macropores was larger, (between 130 and 270%),than for mesopore III (between 40 and 60%). Soil textureappeared to control the flow for the smaller sized pores, but

the structure of the soil appeared to determine the flow inthe bigger pores, which is associated with biological activ-ities such as fine root development or worm holes (Allaireet al., 2009). Figure 3b shows the distribution of the effec-tive porosity for the classes of pore size. The mean of thesum of the effective porosities was 0.022% [m3/m3×100],which was composed of those for macropores, and meso-pores I, II and III of 0.0033%, 0.0069%, 0.0054% and 0.0062%,respectively. These results are substantially different to theporosity from the bulk density test. This implies that poresize for flow generation is very small and most soil porescan be classified into dead pores that are not completelyconnected (Noguchi et al., 1999; Bodhinayake et al., 2004a).Unlike the distribution of the contribution to flow shown inFigure 3a, the distribution of effective porosity was more orless similar. However, the distributions of the CVs for effec-tive porosity were similar to the contribution to flow in boththe pore size distribution and its impact from the seasonaldifference (CVs for macropores and mesopores III ranged

Fig. 3. The pore size classification and the distribution of flow contribution (a); and the effective porosity (b); and the ratio of flow (c);and the ratio of effective porosity (d). The upper part of bar denotes the standard deviation.


between 125 and 245%, and 45 and 65%, respectively.). Inorder to provide a viewpoint for the relative contribution ofthe various pore sizes, the ratios of the total flow and theirstandard deviations are presented in Figure 3c. The seasonaldifference in the mean also appears smaller than the differ-ence associated with the pore size. The spatial variabilityappears to be greater than the seasonal variation, which canbe explained by the heterogeneity in connectivity betweenpores. The means of macropores and mesopores I, in termsof their flow ratios, were 60% and 21%, respectively; indi-cating more than 81% of the flux was generated through thepores with a greater diameter size than 0.5 mm. Figure 3dshows the distribution of the ratios of effective porosity tothe total effective porosity for different pore sizes. The ratioof the effective porosity for a macropore was slightly morethan, or less than 10% and those for mesopores I, II and IIwere 26%, 26% and 38%, respectively. Even though theproportion of effective porosity for a bigger pore sizewas small, the majority of the flow was generated in the

macropores. Other studies also report that the macroporevolume ratio was only 0.04%, and that contributions to thetotal flow were 73% and 85% in loamy and fine loamy soils,respectively (Watson and Luxmoore, 1986; Wilson and Lux-moore, 1988), and 64% for macropores in a fen peat (Baird,1997). Similar scales of porosity and flow to those found inthis study were estimated for grassland (Bodhinayake andSi, 2004b). Case studies using dye tracers or a pressure platecombined with the tension infiltrometer have also reportedthat macropores account for only 2.8% of the total porosityin clay soil, but carried 88.7% of the flow (Lin et al., 1998),or that 0.001% of the effective porosity in macropores con-tributes to 65% of the total flow in the organic soil layer(Carey et al., 2007). Even though the definitions of poresizes in different studies are not exactly identical and the soilcomposition is different between datasets, the importance ofthe contribution of bigger pores with a relatively small pro-portion of the porosity was commonly significant in the infil-tration processes.

Fig. 4. The saturated hydraulic conductivities at the depth of 10 cm and the local slope as tanβ (a); and the distance to the stream (b);and contributing area (c) and the topographic index by Quinn et al., (1995) (d). *The closed circles, open circles, closed triangles, andopen triangles denote the data in August 9 2006, September 28 2006, March 21 2007, and June 7 2007, respectively.


3.3. Hydraulic Properties and Terrain Surrogates

The relationship between the local topography and thesurface hydraulic conductivities was explored to test oneunderlying hypothesis of this study, i.e., whether the spatialdistribution of the saturation tendency or drainage densityinfluences the soil structure, which can also result in thedevelopment of bigger pores. The most widely used topo-graphic attributes in hillslope hydrology are probably thelocal slope (LS), the upslope contributing area (CA), thetopographic index (TI) and the distance to the stream (DS).In this study, the spatial distribution of hydraulic properties,such as K(–9), K(–6), K(–3), Ks and α, and 7 different terrainattributes, including CAs and TIs for Single Flow Direction(SFD) and Multiple Flow Direction (MFD) algorithms (O’Cal-langhan and Mark, 1984; Quinn et al., 1995); together withLS, DS and soil depths (SD) were used to investigate theimpact of topography on the surface hydraulic characteristics.

Figure 4a presents the LS (tanβ, where β is the local angle)

and the Ks for all data. The Ks for September 28, 2006 (opencircles), shows a rather dispersed distribution to the LS, butthe other data has a tendency to show than when LS is low,Ks displays greater variation; even for the logarithmic scale,as shown in Figure 4a. The relatively low soil moisturescaptured on September 28, 2006 (see Table 2) explain thedispersed Ks (Gupta et al., 2006). The relationship betweenDS and Ks is shown in Figure 4b, but no significant rela-tionship is revealed. The relationship between soil moistureand the distance to the stream was only found to be sig-nificant in soil depth of 30 cm (Kim, 2009b). The saturatedhydraulic conductivity and the contributing area, or thetopographic index estimated by the MFD algorithm (Quinnet al., 1995), are shown in Figures 4c and d. The frequencyof high Ks was mostly found both in the higher CAs andTIs. The increasing trends in the mean and CVs of Ks wasfound both in the higher CAs and TIs, respectively. Thehigh correlations between soil moisture at a depth of 10 cmand CA or TI (Kim, 2009b) also confirmed the field mea-

Fig. 5. The Gardner’s parameter (α) estimated at the depth of 10 cm and the local slope as tanβ (a); and the distance to the stream (b);and contributing area (c) and the topographic index by Quinn et al., (1995) (d). *The notations of symbols are identical to Figure 4.


surements of Ks in this study. The other terrain attributes, suchas CA and TI by SFD algorithm and SD, did not show anynotable relationship. The trends in Figures 4a, b, c, and d, tendedto disappear with higher tensions, such as K(–6) and K(–9).

The spatial distribution of Gardner’s parameter (α), andthose for LS, DS, CA and TI are shown in Figures 5a, b, c, andd, respectively. Gardner’s parameter, the inverse of the mac-roscopic capillary length, is closely related to the macroporeflux governed by gravity, and also reflects the soil structureconnected to pore development. It is possible that the sim-ilarity between Figures 4 and 5 are associated with the gravitycontrol of both Ks and α, but the minor differences could alsooriginated from the interaction differences between the suctionpotential and the unsaturated hydraulic conductivity whichresulted from the spatial distribution of smaller sized pore.

3.4. Flow with Pore Size Distribution and Terrain Surrogates

The distribution of flow with pore size classification canbe analyzed in conjunction with terrain attributes. Figures

6a, b, c, and d show the CA and flow via macropores, andmesopores I, II and III, respectively. The macropore flowshowed a substantial increases in both magnitude and vari-ance when CA was slightly greater than 10 m. A similar behav-ior can be observed in Figure 6b for the flow via mesoporesI but is on a smaller scale than that of macropore flow. Theflow via mesopores II and III did not show any significantvariation at any points of the CA. Figure 7 shows theinverse relationship between the flow classification and LS.The maximum and variation of flows via macropores werehighest when LS was about 0.1 and tended to decrease witha higher LS, as presented in Figure 7a. As the size of thepores decreased, the trend shown in Figure 7a also decreased(see Figs. 7b and c), and finally disappeared in mesoporesIII (see Fig. 7d). Figures 8a, b, c and d show the TI and flowsvia the macropores, mesopores I, II and III, respectively.Unlike the relationship between LS and its flow classifica-tion in Figure 7a, the maximum and variance of flow viamacropores tended to increase from low to high TIs, asshown in Figure 8a. This increasing trend moderately dimin-

Fig. 6. The contributing area (CA) in m2 and the flow via macropore (a), mesopore I (b), mesopore II (c), and mesopore III (d), respec-tively. *The notations of symbols are identical to Figure 4.


ished for the flow via mesopores I, as shown in Figure 8b,and no particular trend was found between TI and flows viamesopores II and III (see Figs. 8c and d). The impact ofslope on the denominator of TI could explain Figures 8aand b. The relationships between DS and classified flowsare also presented in Figures 9a, b, c, and d. The closer thelocation to the stream, the higher and larger the magnitudeand variance of the flows via the macropores (see Fig. 9a).The flows through mesopores I, II and III did not have anynotable relationship with DS, as shown in Figures 9b, c, and d.

3.5. Statistical Tests for Thresholds in Hydraulic Properties

The relationship between terrain attributes and hydraulicconductivities, Gardner’s parameter and classified flow forpore size, was not only nonlinear, but it was extremely com-plicated to describe using a solid mathematical platform, asshown in Figures 4, 5, 6, 7, 8, and 9. We therefore char-acterized the distribution of the hydraulic properties to see

whether it was influenced by the spatial distributions of thehillslope feature. Based on illustrations between the topo-graphic factors and estimated flows, a hypothesis can beintroduced, i.e., that a threshold may exist for several fea-tures of a hillside to initiate significant changes in the statisticsof the hydraulic properties (i.e., maximum and variance).Several ANOVA tests, such as the t-test and the Wilcoxonrank sum test for two samples assuming unequal variance,were introduced to check the statistical significance of theimpact of the spatial features on the hydraulic property, thatwould be determined by the threshold. In addition to the ter-rain attributes, such as LS, CA and TI, the spatial distribu-tions of soil texture (ST), SD and DS, were used to checkthe existence of thresholds. Figures 6, 7, and 8 indicate thatthe most probable thresholds for CA, LS and TI are 16 m2,0.3 and 4, respectively. The hydraulic conductivities werelog transformed before performing the statistical analyses.ST can be divided into sandy loam and loam. Based on the6 thresholds (LS, CA, TI, ST, SD, DS), and 5 hydraulic prop-

Fig. 7. The local slope (LS) as tanβ and the flow via macropore (a), mesopore I (b), mesopore II (c), and mesopore III (d), respectively.*The notations of symbols are identical to Figure 4.


erties (Ks, K(–3), K(–6), K(–9), α), 59 subsets of data weredelineated and the normality of the data in each subset wasfirstly checked using the Shapiro-Wilk test (Shapiro andWilk, 1965). Both parametric and non-parametric tests wereused, depending on the statistical distribution of data usingthe Shapiro-Wilk test. The relationships between Ks and TI,CA and LS, and that between α and LS showed negligiblenormality, but other relationships fulfilled the normalityassumption. The abnormally high topographic surrogates(e.g., TI, CA and LS) tended to be distributed near the streaminitiation. Secondly, in order to test the homogeneity of thevariance, Levene’s test was performed and the data subsetsgenerated from K(–6) and K(–9) were found to satisfy theassumption of variance homogeneity. As shown in Figures 4to 9, data subsets for K(–6) and K(–9) showed small vari-ances which were appropriate for the ANOVA(t-test), andwhich were mainly associated with mesopores II and III.The other dataset had non-homogeneous variance features,which required use of the Welch-Aspin procedure.

Table 3 presents the statistics from the ANOVA, showingthe existence of the thresholds in the CA, LS, TI and ST.The statistics for SD and DS have not been presented dueto the absence of any notable threshold. Gardner’s param-eter had an apparent threshold for all spatial features, andstatistics for hydraulic conductivity appeared limited for thegeneration of flow via macropores such as KS and K(−3).The existence of thresholds for flow change were alsofound in the result from Or (2008). The CA showed thehighest significance levels among the terrain attributes, andST also had significant thresholds for α, KS, and K(−3). Infact, the distribution of ST appeared to be related to that ofthe CA, as shown in Figure 2c. It is likely that the upslopepart of the hillslope is composed of coarser sized soil grainsthan the downslope area. The result for the spatial distri-bution of hydraulic conductivity along the hillslope in thisstudy is similar to that of Zehe et al. (2010), which showedefficient energy dissipation in water flow due to the abun-dance of macropores in the downslope part. The analysis is

Fig. 8. The topographic index (TI) and the flow via macropore (a), mesopore I (b), mesopore II (c), and mesopore III (d), respectively.*The notations of symbols are identical to Figure 4.


also related to the impact of topography associated with ero-sion and deposition processes on a hillslope scale (Fernandesand Dietrich, 1997; Roering, 2008). Considering the spatialresolution between CA and ST, and its genetic process, theCA seemed to be the most apparent surrogate in character-

izing the surface hydraulic property in the context of thethreshold behavior. The increasing trend in the CA towardthe channel initiation point increases not only the probabilityof the saturation and drainage density in the downslope area,but also enlarges the range of the pore development process.

Fig. 9. The distance to stream (DS) in m and the flow via macropore (a), mesopore I (b), mesopore II (c), and mesopore III (d). The notationsof symbols are identical to Figure 4.

Table 3. Analysis of variance of measured or estimated soil hydraulic properties using tension infiltrometer, showing the existence ofthe thresholds in the contributing area (CA), the local slope (LS), the topographic index (TI) and the soil texture (ST)

Parameter CA LS TI STStatistics T or W d.f. or Z p or p T or W d.f. or Z p or p T or W d.f. or Z p or p T d.f. p

α –5.4 46.0 0.000a 508 –2.83 0.005a –4.6 55.0 0.000a –4.1 55.0 0.000a

KS 643 –3.45 0.001a 602 –1.38 0.169 526 –2.56 0.011 –3.6 53.4 0.001a

K(−3) –4.1 49.6 0.000a 1.64 56.9 0.106 –3.1 57.0 0.003a –2.3 57.0 0.023K(−6) –2.4 57.0 0.020 0.43 57.0 0.672 –1.5 57.0 0.128 –1.7 57.0 0.105K(−9) –.03 57.0 0.981 –0.99 57.0 0.328 0.36 57.0 0.717 0.24 57.0 0.809

The numbers in parenthesis are tension in cm. T, d.f., p denote the T statistic, degree of freedom, the significance level for the parametric test and W, Z, and p are Wilcoxon’s W and Zstatistics, the significance level for the nonparametric test in bold face number, respectively.aThe significance level p < 0.01.


4. CONCLUSIONS

The spatial distribution of surface hydraulic propertieswas investigated in conjunction with several topographic andsoil attributes on a hillslope scale. The evaluation of flowwith respect to pore size classification, was characterized bya variation feature along the hillslope transects, and pro-vided a better understanding of the infiltration processes onthe forested upland hillside. Both the terrain analyses andthe infiltration tests performed for this study confirmed thatthe surface hydraulic characteristics were influenced by thespatial distribution of the flow generation pattern, such asthe divergence on a convex hilltop and convergence on aconcave, or downslope part of the hillslope.

The classification of flow for the pore size distributionindicated that the scale of the seasonal variation in flow wasgreater for pores with larger sizes. The distribution of theeffective porosity also showed greater variances in both thespatial and seasonal differences for larger sized pores. Theimportance of preferential flow through macropores wasalso confirmed from both the ratios of the total flow con-tribution and the total effective porosity. Hydraulic conductivityand effective porosity showed a stronger spatial variationthan those of seasonal fluctuation.

A hypothesis, which stated that the spatial distribution ofthe saturation tendency has an impact on the developmentof larger pore sizes, was tested through comparison betweenseveral frequently used topographic attributes and the mea-sured hydraulic properties and fluxes. Even though the rela-tionships were not linear, which further implied naturalheterogeneity, they revealed the possible existence of thresholdsfor several topographic attributes. Systematic statistical testswere used to check the existence of thresholds for severalspatial features to the distribution of the hydraulic proper-ties, and these were dependent on statistical assumptions fordata subsets, such as normality and equal variance. The thresh-old behavior appeared only for Gardner’s parameter, and thehydraulic conductivities for the macropores flux. The con-tributing area was found to be the most apparent attributefor characterizing the spatial distribution of the surface hydrau-lic properties with the threshold behavior at a hillslope scale.

ACKNOWLEDGMENTS: Authors would like to express apprecia-tion to two reviewers and editor for their constructive comments andarrangement.

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Manuscript received December 16, 2012Manuscript accepted March 12, 2013

distribution characteristics of hydraulic properties on a mountainous hillslope

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