Unsaturated Hydraulic Conductivity Estimation of a ...

Forest, Range & Wildland Soils

Unsaturated Hydraulic Conductivity Estimation of a Forest Soil Assuming a Stochastic-Convective Process Marián Homolák Viliam Pichler* Department of Natural Environment Faculty of Forestry Technical University in Zvolen T.G. Masaryka 24 960 53 Zvolen, the Slovak Republic

William A. Jury Department of Soil and Environmental Sciences University of California Riverside, CA

Jozef Capuliak Institute of Terrestrial Ecosystems ETH Zürich Zürich, Switzerland

JoAnn O’Linger Spitzer Science Center California Institute of Technology Pasadena, CA 91125

Juraj Gregor Department of Natural Environment Faculty of Forestry Technical Univ. in Zvolen T.G. Masaryka 24 960 53 Zvolen, the Slovak Republic

Measurement of soil hydraulic conductivity requires considerable time and effort, which makes it difficult to characterize this important parameter across larger areas, especially remote forest regions. Forest soils are frequently texturally coarser than those in agricultural areas, making them more probable candidates for applications building on the stochastic-convective hypothesis. We developed a method for measuring unsaturated soil hydraulic conductivity based on the analysis of a dye tracer resident concentration profile. In the experiment, partially saturated, steady-state water flow was established in a forest allophanic soil by a sprinkler operating at 50 mm h−1, after which the water application was switched to a 10 mg L−1 Brilliant Blue FCF solution. The tracer was applied continuously until its cumulative infiltration reached 125 mm, after which the stained soil profile was exposed and photographed. The picture was subjected to an image analysis procedure designed to obtain the resident concentration profile of the tracer. The concentration was fitted to the solution of the convective lognormal transfer function, whose parameters were used in further calculations using functional relationships derived from the stochastic-convective framework. The resulting hydraulic conductivity as a function of soil water content agreed within an order of magnitude with the relationship obtained by the instantaneous profile method. While the Mualem–van Genuchten model better reproduced the shape of that relationship, it strongly underestimated the hydraulic conductivity across the soil water content interval of interest (0.1–0.4). Finally, ways to improve the predictive capacity of the stochastic-convective approach in terms of the general trends of the functional relationship were proposed. Abbreviations: cdf, cumulative density function; CLT, convective-lognormal transport; IPM, instantaneous profile method; MVG, Mualem–van Genuchten; pdf, probability density function; SC, stochasticconvective; SWC, soil water content; SWRC, soil water retention curve; TDR, time domain reflectometry.

A

lthough it seemed unlikely in the 1980s that the future would hold any heightened interest in the management of water relations in forests (Miller, 1990), the present situation often requires active forestry measures, such as forest density reduction, to improve extractable water availability and water yield from forests (Tryon, 1972; Stednick, 1996). In fact, the assessment of water fluxes in various types of landscapes and forests has been an important part of major recent ecological and ecohydrologic studies, e.g., Valentini (2003) and Lichner (2007), which required knowledge of soil hydraulic properties. To this end, information on the hydrophysical and hydraulic properties of some soil classes, e.g., andic soils, are rather limited (Bartoli et al., 2007). There are a number of direct laboratory methods for measuring soil hydraulic conductivity, such as steady-state head or flux control methods or non-steady-state Boltzmann transform and sorptivity methods. The choice of method depends on factors such as the nature of the soils, the soil water suction range to be covered, or the purpose for which the measurement is being made (Klute and Dirksen, 1986). In recent decades, laboratory methods have usually aimed to predict the soil hydraulic conductivity from the soil water retention curve (SWRC). Although each drainage or recharge event may show a unique soil water content–matric potential relationship (Philip, 1964; Mualem, 1973), SWRC-based methods have come into widespread use, using the Mualem–van Genuchten (MVG) parametric representation (Hunt, 2004; Schaap and van Genuchten, 2006), which is (Kutílek and Nielsen, 1994) Soil Sci. Soc. Am. J. 74:292–300 Published online doi:10.2136/sssaj2009.0200 Received 22 May 2009. *Corresponding author ([email protected]). © Soil Science Society of America, 677 S. Segoe Rd., Madison WI 53711 USA All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.

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SSSAJ: Volume 74: Number 1 • January–February 2010

K ( h) = Ks

{

⎡1+(α h )n ⎤ w ⎢⎣ ⎥⎦ mb n ⎡1+(α h ) ⎤ w ⎣⎢ ⎦⎥ n−1

1−(α hw )

−m

}

2

[1]

where K(h) is the soil hydraulic conductivity as a function of matric potential h, Ks is the saturated hydraulic conductivity, and α, n, and m are fitting parameters with allowable ranges of α > 0, n > 1, |h| ≥ 0 and 0 < m < 1. The parameter b was introduced to evaluate soil pore tortuosity effects on hydraulic conductivity and its value was suggested to be 0.5 by Mualem (1976), principally based on his analysis of repacked soils. Another step toward a more realistic unsaturated hydraulic conductivity (Kunsat) prediction was made by the introduction of bimodal retention curves (Durner, 1994), which enable a more accurate description of heterogeneous pore space. A large number of small soil samples are usually needed to account for the soil’s spatial variability, and they must remain undisturbed during extraction and transport. Generally, field methods require less replication because they can be applied to larger soil volumes without compromising the original soil structure (Green et al., 1986) and introducing artificial boundaries. Sometimes the volume of measurement may be large enough to encompass the representative elementary volume of soil required to achieve a mean value. Among the field methods, tension infiltrometers are reliable for soil hydraulic conductivity measurement near saturation (Ankeny et al., 1991). Introduction of the minidisk infiltrometer (Zhang, 1997) made repeated measurements much easier owing to the extreme portability of the device, but the subsequent calculations require an estimation of the soil type. On the other hand, double-ring infiltrometers use the ponding of water over the soil surface until steady state is achieved. One concern for the applicability of field methods in forests is the high amount of water needed to attain steady-state conditions. Hendrayanto et al. (1998) dealt with this issue by proposing a single-ring infiltrometer applicable to sloping terrain with a limited water supply. The method is based on the measurement of changes in soil water contents and capillary pressure heads during a 4-d period. Long periods of time and larger amount of water are also necessary for the application of steady-flow methods, in which flux density is changed in steps (Kutílek and Nielsen, 1994). Thus, regardless of the method, the excessive time required for Kunsat determination represents one of the main obstacles preventing routine acquisition of the data needed for the regionalization of forest soil transport properties. In recognition of this limitation, the purpose of this study was to develop an in situ steady-flux method based on the analysis of resident concentration profiles of a mobile, nonreactive tracer achieved under a single flux density, q0, at the soil surface that would substantially reduce long periods of measurement time. Our efforts benefited from new image processing methods (Kasteel et al., 2005) that allow a detailed mapping of the concentration of anionic dye tracers, such as Brilliant Blue FCF (Flury and Flühler, 1995). Its effectiveness at water tracing can be compromised by dye sorption to soil particles, as well as by a simultaneous application of other ionic tracers, such as Br−. Despite these limitations, Brilliant Blue FCF remains one of the most effective dye tracers for vadose zone hydro-


logic studies because of its high visibility and mobility, and its low toxicity (German-Heins and Flury, 2000; Morris et al., 2008).

THEORY Because forest soils in mountainous regions are often quite coarse and shallow in extent due to their origin from slope deposits (Šály, 1986; Gömöryová et al., 2008), they are likely to be good candidates for stochastic-convective (SC) flow modeling. Under the assumptions of this model, a solute added uniformly to the soil surface is transported through stream tubes that form near the surface and remain isolated thereafter (Jury and Scotter, 1994). These assumptions work best when the time required for lateral mixing exceeds the time to reach depths near the surface. Soils in which the SC model has been successfully applied include a loamy sand (Poletika and Jury, 1994) and a fine sandy loam (Ellsworth et al., 1996). Vanderborght et al. (2000) and Persson et al. (2005) postulated a SC process at higher flow rates, when preferentially longer continuous pores were activated, and after the soil water content (SWC) fell below a critical θ ~ 0.22 and part of the porosity was deactivated, respectively.

Applicability of the ConvectiveLognormal Hypothesis The SC hypothesis for solute transport in the soil of interest can be stated that the probability of reaching depth z in time t is the same as the probability of reaching depth l in time tl/z (Jury and Roth, 1990). This statement may be expressed mathematically as

f

f

l

⎛ tl ⎞

( z , t )= f f ⎜⎜⎝ l , ⎠⎟⎟⎟ z z

[2]

where f f(z,t) is the normalized travel-time probability density function (pdf ) recorded at depth z and f f(l,tl/z) is the normalized travel-time pdf recorded at depth l. The match between the measured and predicted travel-time pdfs at depth l can be tested using a goodness-of-fit test. Another important relation is

f

r

t z

( z , t )= f f ( t , z )

[3]

where f r(z,t) is the travel-distance resident concentration pdf recorded at time t, enabling the conversion between the travel time and travel distance pdfs of the SC process (Jury and Scotter, 1994).

Derivation of Soil Water Content–Hydraulic Conductivity Relationship and Transfer Function Parameters The approach presented here was inspired by Scotter and Ross (1994), who analyzed the upper limit of solute dispersion, and a similar derivation by O’Linger et al. (1997), who analyzed soil hydraulic properties based on solute flux concentrations. In contrast, our objective was to establish a functional relationship between Kunsat as a function of SWC (θ), and the travel distance pdf of a nonreactive solute at some reference time t. Our model framework requires the following assumptions: (i) steady-state water flow (Jw) and constant SWC within the transport volume; (ii) gravity flow (valid near the soil surface, at a high flux rate, and for a deep water table):

293

J w ~ K (Θ)

[4]

where Θ represents the maximum SWC during the experiment and the upper SWC boundary, for which K(θ) is calculated; and (iii) minimum lateral mixing (i.e., SC flow). Let us consider a saturated system with Darcy velocity Jw and the surface input of a nonreactive tracer at a constant concentration C0, where the total resident concentration in the soil Ctr [M3 L−3] is recorded at a certain depth z and a time t. Then a dimensionless resident fluid concentration Cfr = Ctr/Θ [M3 L−3] can be normalized as Cfr/C0. These resident fluid concentrations Cfr, when assembled throughout a depth interval from zero to z, establish a profile that corresponds with a survival distribution function S(x). Generally, it gives the probability that a variate X takes on a value greater than x (Evans et al. 2000), i.e., that S(x) = P(X > x). The survival function S(x) and the corresponding distribution function D(x) are related by S(x) = 1 − D(x). In our case, S(z) gives the probability that the travel distance of the tracer molecules is larger than z, or, in other words, that the “survival” or the travel distance of our tracer particles exceeds z. Then, the travel distance cumulative density function (cdf ) D(z) can be compiled directly for each profile from the respective relative concentration Cfr/C0 values. The normalized concentration cdf is equal to the fraction of the pore space that contains solute molecules that have reached the distance ζ equal to or smaller than z at an instant t. By the gravity flow assumption, the flux density through the pores with travel distances shorter than z is equal to the hydraulic conductivity of the system with the fastest (ζ > z) pore groups subtracted, or, in other words, equivalent to K(θ) at θ < Θ, where the faster pore groups comprising the transport volume between θ and Θ drained and no longer contribute to the flux. Therefore

C K (θ) =1− C0 Jw r f

[5]

and

C K (θ) =1− C0 K (Θ) r f

[6]

The derivative of D(z) according to depth z is the travel distance pdf or ffr(z,t). Thus,

d ⎜⎛ C fr ⎞⎟ 1 dK (θ) ⎜ ⎟=− ⎟ d z ⎜⎝ C 0 ⎠⎟ K (Θ) d z

[7]

Following Scotter and Ross (1994) and Steenhuis et al. (1990), for the most highly conductive pore groups, the pore water velocity v (cm s−1) may be approximated by ΔK/Δθ and so

v ( θ )= lim

Δθ→0

ΔK ( θ ) dK ( θ ) = Δθ dθ

[8]

which implies

1 dK (θ) dθ K (Θ) d θ d z v dθ =− K (Θ) d z z dθ =− K (Θ) t d z

f f r ( z )=−

294

[9]

Equations [6] and [9] allow the hydraulic conductivity and water content of the soil to be expressed in terms of the travel distance pdf of the solute fr(z,t): z

K ( z )= K (Θ) ∫ f 0

r

( ζ, t ) d ζ

[10]

and θ( z )= K (Θ)t ∫

z

z→0

f

r

( ζ, t ) d ζ ζ

[11]

We assume that the solute travel distance z at a certain time t, or ffr(z,t), is lognormally distributed between stream tubes according to the convective-lognormal transport (CLT) model ( Jury and Roth, 1990). Depending on its shape, the survival function could be represented by various distributions, including γ and lognormal distributions (Baricz, 2008). Because our method rests on the CLT model embedded in the SC theory, the transport process is represented by the logarithmic mean μ and σ2 as the corresponding variance of the travel distances, which can be fitted from a lognormal depth function:

⎧⎪ [ ln ( z )−μ ]2 ⎫⎪ 1 z ⎪⎬ f ( z,t )= exp ⎪⎨− ⎪⎪ ⎪⎪ 2σ2z 2πσ z z ⎩⎪ ⎭⎪ r

[12]

Consequently, the expressions for K(z) and θ(z) become

⎡ μ−ln ( z ) ⎤ 1 ⎥ K ( z )= J w erfc ⎢ ⎢⎣ 2 2σ ⎥⎦

[13]

and

⎧⎪ ⎫ ⎛ ⎡ −μ+σ2 + ln ( z ) ⎤ ⎪ 1 σ2 ⎞ ⎥⎪ θ ( z )= exp ⎜⎜⎜−μ+ ⎟⎟⎟ J w t ⎪⎨1+erf ⎢ ⎬ [14] ⎢⎣ ⎥⎦ ⎪ ⎝ ⎪⎩⎪ 2 2⎠ 2σ ⎪ ⎭ where Jw is input or drainage flux density. Thus, as the travel distance measured implicitly in the solute experiment scrolls from 0 to zmax, the K(θ) function is defined across the range from 0 to Θ. The actual pdf form, i.e., ffr(z,t), must be determined by solute transport experiments in the medium of interest.

MATERIALS AND METHODS Field Tracer Experiment The experimental area was located in the Javorie Mountains (48°26'27" N, 19°16'18" E) within the West Carpathian volcanic range in the central part of Slovakia. It extended to the top of the Mt. Javorie massif, at an elevation of 920 to 960 m above sea level, within a 90-yr-old montane temperate beech (Fagus sylvatica L.) forest. Local annual temperature is 4.0°C and yearly precipitation averages 850 mm. The experiment was conducted in September 2007 on an Andic Dystrudept (Soil Survey Staff, 2003; IUSS Working Group Reference Base, 1998) that developed from andesite and tuff slope deposits. It falls into the silty loam textural class and its hydrophysical properties are given in Table 1. The groundwater table and capillary fringe were found at depths of 2.5 and 2.0 m, respectively, by means of electric resistivity tomography and groundwater monitoring in a nearby soil pit. The experimental plot was a square 1 by 1 m, cleared of tree litter and surface humus. A trench was opened along one side of the square, and


Table 1. Hydrophysical properties of the Andic Dystrudept experimental soil. Soil Specific Bulk Stony Porosity Sand depth density density fraction cm 0–10 10–20 20–30 30–40 40–50 50–60 60–70 70–80 Average

— Mg m−3 — 2.59 1.39 2.64 1.37 2.66 1.23 2.68 1.39 2.67 1.29 2.69 1.36 2.71 1.31 2.71 1.53 2.66 1.35

— % (v/v) — 16.22 62.54 15.53 63.48 13.16 66.80 14.18 62.13 12.36 64.00 13.01 62.27 12.18 63.65 13.28 56.82 13.74 62.71

Silt

during the next 2 h. In addition, soil salinity changes effected by the KBr were measured using the TDR every 10 min during the first experiment.

Clay

——— % (w/w) ——— 22.65 65.52 12.20 22.66 65.04 12.84 22.97 62.68 13.04 23.06 62.16 13.12 24.32 61.00 13.32 24.96 60.76 13.44 26.02 58.12 14.24 30.19 53.16 14.60 24.60 61.06 13.35

two rows of time domain reflectometry (TDR) probes (10 cm in length) were installed at 30- and 60-cm depth, 10 probes in each row. They were connected to a TDR field-operated meter that could simultaneously monitor moisture and salinity (Easy Test, Lublin, Poland). After the site preparation, a sprinkler was placed over the experimental site (Fig. 1). The sprinkler consisted of a board supporting 1600 needles with a 0.5-mm diameter, arranged in a 40 by 40 grid (Fig. 2). Each needle was individually connected to a liquid distribution tank through plastic tubing. The tank was supplied with water or solute by a piston diaphragm dosing pump (DME 150, Grundfos Alldos, Reinach, Switzerland) operating within the range of 0.1 to 140.0 L h−1 with negligible pulsation. The board supporting needles had an industrial vibrator attached to it to assure even more uniform distribution of droplets over the experimental plot. Two separate experiments were conducted so as to prevent Brilliant Blue FCF mobility decrease in the presence of Br− in the solute. Both experiments could be characterized as a variable solute mass boundary value problem (Toride and Leij, 1996) because a larger fraction of solutes was injected in the higher velocity stream tubes during the topsoil sprinkling. Depending on whether the Br− or dye solute was used, the soil surface was initially sprinkled with pure water at a rate of 60 or 50 mm h−1, respectively, for 6 h. The rate was established as the limit just short of developing locally ponded conditions. Parallel TDR readings indicated that steadystate flow conditions were eventually established. Afterward, the water input was replaced by a Br− solute input (KBr, 0.365 g L−1) or the Brilliant Blue FCF solute (10 g L−1) in the first or second experiment, respectively,

Acquisition of Tracer Resident Concentration and Fitting Model Parameters Immediately following the cessation of sprinkling, a soil profile 1 by 1 m in size was exposed by a miniexcavator in the middle of the square plot and then cleared of roots by scissors, cleaned using a soft brush, and finally photographed by a digital camera (Canon EOS 450D) mounted on a stable tripod. Before photographing, a dedicated frame with 1- by 1-m inner dimension and a ruler was attached to the profile to allow geometric and uneven illumination corrections. The photographs were recorded and stored in the raw format. To obtain the Brilliant Blue FCF dye tracer total resident concentrations (Ctr = Cfr Θ), the image analysis and calculation method developed by Forrer et al. (2000) were used. The method uses a polynomial to express the logarithm of the dye concentration within the RGB space, including the depth z as an explanatory variable. The routine was implemented within the processing framework in GNU R (R Development Core Team, 2007) and C, with the help of the ImageMagick image processing library. The method enabled us to determine the resident concentration profile with a spatial resolution of 1 mm. For calibration, 30 soil samples were taken from the stained soil profile and dried for 15 h at 80°C. From each soil sample, 0.5 g was weighed into an extraction column. The columns were put on a vacuum vessel. Ten milliliters of a 4:1 (v/v) ratio of water and acetone was added as an extraction solvent, and the vessel was evacuated with a low pressure of about −60 kPa. The Brilliant Blue FCF fraction that was extracted by the mixture of the water plus acetone was larger than that extracted by water alone. The extract was filtered through a 0.45-μm filter. The concentration of Brilliant Blue FCF was measured spectrophotometrically at a wavelength of 630 nm. Subsequently, a lognormal distribution cdf was fitted onto the respective relative concentration profile according to Eq. [12]. The FindFit routine, available within the Mathematica 7 software (Wolfram Research, Champaign, IL) and based on the Levenberg–Marquardt method (Press et al., 1989), was used for this purpose, rendering the mean (μ) and standard deviation (σ) as the lognormal distribution parameters. Both values were inserted into Eq. [13] and [14] along with the flux Jw and the time t. Corresponding SWC and Kunsat values were calculated, assembled in a list of ordered pairs, and plotted. The same procedure was applied to the travel distance pdf obtained by the conversion of the Br− tracer travel time pdf, using Eq. [3]. Finally, resulting Kunsat values were compared with the hydraulic conductivity as measured by the instantaneous profile method (IPM) on undisturbed soil samples in the laboratory, as well those predicted from SWRC using the MVG model.

Independent Estimation of Water-ContentDependent Hydraulic Conductivity

Fig. 1. The sprinkler design and arrangement of the time domain reflectometry (TDR) probes.


To compare the results obtained by the proposed method with independent measurements, K(θ) was determined by means of the IPM (Watson, 1966). Soil samples were taken from the 20-cm depth using metal cylinders 5.5 cm in diameter and 5.0 cm in height, which were then fitted with three pairs of sensors for the measurement of soil moisture and water potential, i.e., TDR probes and microtensiometers, installed at heights of 1.0, 2.5, and 4.0 cm from the bottom of the column.

295

Table 2. Convective-lognormal transport model mean (μ) and standard deviation (σ) of the travel distance probability density functions at a reference time (t = 2 h) for the Br− and dye tracer experiments, as well as their corresponding resident concentration modes (zmode). Model parameter μ, log(cm)

σ, log(cm) zmode, cm

Fig. 2. Tracer application needles arranged in a 40 by 40 grid and embedded in a support panel.

The columns were initially fully saturated by capillary rise, after which the top end of the column was covered and 24 h was allowed for the column to reach thermodynamic equilibrium. After that, the column was uncovered and the values of soil moisture and water potential were measured inside the three layers of the column while the soil sample was drying by evaporation from its surface. The data were automatically measured, recorded, and stored by a computer system controlling the apparatus. The K(θ) calculations were performed according to Sławinski et al. (2004). The K(θ) was also estimated using Eq. [1] and the van Genuchten relationship (van Genuchten, 1980) fitted onto the soil water retention data.

KBr tracer experiment Dye tracer experiment 3.53 1.41 4.67

3.11 0.36 19.51

occur owing to the convex nonlinearity of the sorption isotherm (German-Heins and Flury, 2000). An additional cause for a possible decrease in the dye tracer mobility was eliminated by the separation of the two experiments. A comparison between the Br− and dye experiments in terms of model parameters, however, revealed differences between means (μ) and dispersions (σ) of the travel distance natural logarithm, both of which resulted in distinct modes of the two spatial distributions (zmode) (Table 2). While the peak of the dye tracer concentration profile moved significantly deeper into the soil than the zmode of the KBr travel distance pdf, as obtained from Eq. [3], its dispersion

Data Evaluation The two-sample Kolmogorov– Smirnov test (Sokal and Rohlf, 1995) was used to test the goodness of fit between the travel time pdf measured at or predicted for the depth of 60 cm during the first experiment.

RESULTS AND DISCUSSION The Dye Tracer Experiment The Brilliant Blue FCF dye tracer patterns were relatively well identifiable on the forest soil profile. While no isolated dye stains could be observed, the existence of distinct permeability regions, as seen in Fig. 3a, corresponds to a spatial autocorrelation of the stream tube velocities with a correlation coefficient ρ ~ 0.5, according to a Monte Carlo simulation (O’Linger, 1998). An ocular inspection of the dye-stained profile did not reveal a self-sharpening of the Brilliant Blue FCF tracer front or a strong color contrast to the soil material (Fig. 3a) that sometimes 296

Fig. 3. (a) Soil profile stained by the Brilliant Blue FCF solute; (b) planar distribution of the relative total resident concentration of the dye tracer; (c) relative fluid resident concentration profile; and (d) relative fluid resident concentration fit. SSSAJ: Volume 74: Number 1 • January–February 2010

1987). Besides, the image analysis results were affected by a presumably lesser optical detectability of the dye solute at low concentrations. To conclude, the observed transport parameters differences between the two experiments could not be qualitatively explained by the dye sorption on the soil matrix. Instead, distinct instrumentation provided a viable interpretation thereof.

Assessment of the Convective-Lognormal Transport Model Applicability The proposed method rests on still another assumption, namely the SC framework and, more specifically, the CLT hypothesis. The Kolmogorov–Smirnov two-sample test was used to assess the validity of this hypothesis using the differFig. 4. Comparison of the relative fluid concentration (Cfr/C0) of a KBr solute as ence between the flux concentrations at the 60-cm depth as measured at and predicted for the 60-cm depth. The prediction was made using measured during the first experiment and those predicted the measured relative fluid concentration at the depth of 30 cm projected by the based on the CLT transfer function model Eq. [2] and data convective-lognormal model. measured at the reference depth of 30 cm (Fig. 4). According was small. In fact, solute transport tends to be uniform in andic to the test, the maximum difference between the two travel time soils (e.g., Magesan et al., 2003; Eguchi and Hasegawa, 2008). In cumulative density functions D was 0.05 with a corresponding P contrast, the Br− pdf dispersion was comparatively large owing to a of 0.99. So, the null hypothesis was accepted and the SC hypothsmall volume sampled by the TDR and the fact that sampling variesis was considered valid for solute transport under the respective ance increases as the sample support size decreases (Zhang et al., experimental conditions, i.e., similar water contents (Fig. 5) and ap-

Fig. 5. Soil water content during the two experiments: the Br− experiment at the (a) 30- and (b) 60 cm depths; and the Brilliant Blue FCF experiment at the (c) 30- and (d) 60-cm depths. SSSAJ: Volume 74: Number 1 • January–February 2010

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plication rates (Si, 2002). Although the SWC at the 30-cm depth was approximately 4% higher than in the 60-cm layer, the difference reflected distinct porosities at both depths (Table 1). A small SWC decrease during the experiment was caused by a slightly reduced flux rate due to a beech leaf fragment partially clogging the suction hose, as revealed by the TDR readings during the experiment. The linear regression coefficient of the decrease was statistically insignificant.

Assessment of the Unsaturated Hydraulic Conductivity Estimation In our experiment, dye tracer molecules traveling at high partial saturation of the pore space experienced substantially less tortuous paths compared with a situation when pores having diameters greater than that corresponding to the applied pressure head become filled with air. In other words, the proposed method operates with a minimum-tortuosity framework. It is the reason why our Fig. 6. Unsaturated hydraulic conductivity of a loamy forest soil as a function K(θ) values are higher than those obtained from the IPM of its water content obtained from: (a) the dye tracer or (b) Br− profile as (at lower SWCs) or SWRC-based prediction (Fig. 6). In interpreted through the convective-lognormal transport theory, (c) the Mualem– van Genuchten model, and (d) the instantaneous profile method. addition to that, recent work (Tuller and Or, 2001) has suggested that neglected liquid retention and film flow of structural and matrix pores, the fitting of two sets of hydraulic led to poor predictive capabilities of Kunsat at low saturation. The conductivity parameters may be necessary (Kutílek and Jendele, value of K(θ) as estimated in our dye tracer experiment was of the 2008). We speculate that the use of steady-state gravity flow cousame magnitude as in a Humic Ustivitrand (Basile et al., 2006) pled with the SC model may help circumvent some of these issues at 0.3 ≤ θ ≤ 0.4. With its conspicuously flat run, our K(θ) functhrough establishing high-connectivity or low-tortuosity condition was also similar to values determined for aq Typic Hapludox tions during the entire experiment and removing the need for the (Hurtado and de Jong van Lier, 2005) and Walla Walla silt loam matching of various parameters whose relationship to tortuosity (Chen and Payne, 2001) with comparable silt and clay contents. and pore connectivity has not yet been sufficiently developed. But The shape of K(θ) derived from the SC theory was probably deat the same time, a more satisfactory reproduction of the general termined by the smoothing effect of averaging the horizontally functional relationship by the SC approach will probably have to heterogeneous soil permeability. The secondary reason may have lean on using a weighted sum of two lognormal cdfs featuring physbeen due to exclusion of any hysteresis and residual water effects. ically interpretable parameters μ and σ that could provide a more The match between Kunsat as measured in the dye tracer exadequate description of bimodal resident concentration data. periment on the one hand and the established methods on the othTechnical Feasibility er hand is ambivalent. The resulting functional relationship K(θ), as derived from the dye tracer experiment, was in reasonable agreeOur method required ~400 L of water per experiment. For ment with the results obtained by the IPM, i.e., within an order of practical reasons, this amount can be reduced by approximately magnitude for 0.15 < θ < 0.40 (m3 m−3). It is in this interval that 50 to 75% in temperate mountainous areas when performing the bulk of the water and solute transport in forest soils occurs. the experiments following the natural recharge of soils during The K(θ) values calculated from the Br− experiment clearly corsnowmelt. Such timing would diminish a potential disadvantage responded with the lower zmode. of the proposed approach compared with some other field methDespite a closer agreement with the expected trend, the MVG ods using less water (e.g., Hendrayanto et al., 1998), as well as the model with b = 0.5 produced a prediction between one to two amount of time needed for the establishment of steady-state conmagnitudes lower than the CLT model and the IPM. Similar to ditions. In view of these findings, the main strength of the proChen and Payne (2001), who compared the Klaij and Vachaud posed method consists in the provision of a soil hydraulic conducmethod with the MVG model, the latter approach predicted a tivity assessment that is considerably quicker and less laborious steeper K(θ) decrease at lower SWC (θ < 0.25). This disagreement than many other methods. Irrespective of the antecedent soil wacould be partly fixed by using b, which accounts for pore tortuosity ter content, the duration of the entire experiment should remain and connectivity in Eq. [1], as a fitted parameter. Such an approach within a span of 5 to 10 h, including soil profile exposure, for shalwas suggested by Hendrayanto et al. (1999) and Schaap and Leij low and moderately deep forest soils. This short duration consid(2000) to rectify predictions based on the MVG model, which oferably improves the efficacy of field measurements and it could ten strongly underestimate the hydraulic conductivity of forest soils facilitate their routine application in forest soils. It also minimizes (Shinomiya et al., 2001). In forest soils with two different domains the effect of desiccation by tree roots, which could otherwise have 298


a considerable impact (Novák 1987). Such results are in line with the scope of our research, which aimed at making a contribution to a routine acquisition of soil hydraulic conductivities in forests.

CONCLUSIONS An accurate quantification of water fluxes in soils requires parameters that cannot be easily acquired in remote forest areas due to laborious, time-consuming, and costly measurements. Therefore, the assessment of soil water fluxes has often drawn on soil textural classes and related pedotransfer functions (Gerardin and Ducruc, 1990; Espino et al., 1995). At the same time, the CLT model was shown successful in describing solute transport in several loamy soils that are widely represented among temperate forest soils. Its feasibility for our experimental soil was assessed and supported by field testing the agreement between predicted and measured travel time pdfs of a Br− tracer at two soil depths. Therefore, we used the CLT model as embedded in the SC theory to derive a pair of equations that would produce K(θ) from a dye tracer resident concentration profile, which can be obtained from a simple field experiment. The profile was obtained from a Brilliant Blue FCF dye tracer experiment and subsequent image analysis, based on a spectrophotometrical calibration performed on variably stained soil samples. The procedure led to a polynomial expressing the dye concentration logarithm within the RGB space with the depth z as an explanatory variable. In the presented case, dye solute was applied onto an Andic Dystrudept soil under steady-state flow conditions with a constant flux rate q0 = 5 cm h−1 and θ ~ 0.4. The needed functional relationship K(θ) was obtained through the insertion of lognormal distribution parameters (μ and σ) of the resident dye concentration into a pair of equations derived from the CLT transfer function model. As a result, the predicted hydraulic conductivity values agreed within an order of magnitude with the results produced by the IPM for 0.15 < θ < 0.40. This is the interval in which the bulk of the water and solute transport in this forest soil presumably occurs. The MVG model prediction would require the b parameter to be fitted to attain a similar agreement with the IPM data. A weak optical detectability of the dye at low resident concentrations led to a poor resolution, however, which in turn may have contributed to discrepancies between the trends of the SC, IPM, and MVG model data. This problem could possibly be remedied in two ways: (i) through a more accurate calibration in the interval of low resident concentrations, and (ii) a subsequent representation of the dye concentration profile by a weighted sum of two lognormal cdfs that would reflect the probable bimodal nature of the resident concentration data, which would result from water and solutes flowing through both matrix and structural domains. Furthermore, the applicability of the proposed approach across various SWC intervals and for other major forest soil types remains to be tested. In its current form, the proposed approach provides a possible alternative for a quick hydraulic conductivity assessment within a widely represented group of loamy forest soils.

ACKNOWLEDGMENTS We thank Dr. V. Novák (Institute of Hydrology, Slovak Academy of


Sciences, Bratislava) as well as Prof. C. Sławiński (Institute of Agrophysics, Polish Academy of Sciences, Lublin) for producing Mualem–van Genuchten K(θ) prediction and values obtained by the instantaneous profile method. This investigation was supported by scientific grants awarded by the Research and Development Agency APVV-0468-06 and the Scientific Grants Agency of the Ministry of Education and the Slovak Academy of Sciences no. 1/0703/08 and MVTS COST FP0601.

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