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Published in Vadose Zone Journal 2:618-626 (2003)
© 2003 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

SPECIAL SECTION - ADVANCES IN MEASUREMENT AND MONITORING METHODS

Field Application of a Portable Air Permeameter to Characterize Spatial Variability in Air and Water Permeability

Bo V. Iversen*,a, Per Moldrupb, Per Schjønninga and Ole H. Jacobsena

a Danish Institute of Agricultural Sciences, Dep. of Agroecology, Research Centre Foulum, P.O. Box 50, DK-8830 Tjele, Denmark
b Environmental Engineering Section, Dep. of Life Sciences, Aalborg University, Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark
* Corresponding author (bo.v.iversen{at}agrsci.dk).

Received 18 March 2003.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
The saturated hydraulic conductivity (Ks) is an essential parameter for modeling water and chemical transport in the vadose zone. Since in situ measurements of Ks are complex and time-consuming, indirect methods that are dependable, fast, and inexpensive with regard to assessing magnitude and spatial variability in Ks at the field scale are needed. In situ measurements of air permeability (ka,in situ) may fulfill these criteria. In this study, a portable insertion-type air permeameter was used to measure ka,in situ in the Ap and B horizons at five agricultural field sites in Denmark with soil types ranging from sand to sandy loam. Around 100 ka,in situ measurements were performed within 2 d at each field site. The data showed spatial correlation in ka,in situ at three out of five sites, with correlation distances between 30 and >120 m. On the basis of additional laboratory measurements on large, undisturbed soil samples (6280 cm3), a log-log linear relationship between air permeability (ka) measured at the actual soil-water content (close to field capacity) and Ks was found. The Ks–ka relation was in agreement with an earlier predictive relationship based on undisturbed 100-cm3 samples from nine other field sites. Using pedotransfer functions for Ks based only on soil texture yielded an unrealistic narrow range in predicted Ks values whereas pedotransfer functions based on ka,in situ yielded a more realistic prediction range. Measurements of ka,in situ constitute a promising indirect method for assessing spatial variability in Ks at the field scale.


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
THE QUALITY AND RELIABILITY of predictions by physical models describing vadose zone processes depend on the quality of the input data. Today, the use of spatially distributed models has dramatically increased the need for data input and knowledge of the spatial variability of the soil physical parameters. The large amount of data for soil hydraulic properties needed in these models is often considered nonattainable because direct measurements of soil hydraulic properties are labor intensive, time-consuming, and expensive. Alternatively, these properties have to be estimated from more easily available soil data by the use of pedotransfer functions (Bouma, 1989).

The saturated hydraulic conductivity (Ks) is an essential parameter in the analysis and modeling of water flow and chemical transport in the soil. Often, the parameter is used in predictive relationships for the unsaturated hydraulic conductivity based on the water retention characteristics (e.g., Campbell, 1974; Mualem, 1976; van Genuchten, 1980), where the saturated hydraulic conductivity (Ks) is used as the reference point. Field-scale variability of Ks is often large (several orders of magnitude). Also, measurements of Ks in the field (Reynolds et al., 2002) are time-consuming, and measurement efficiency and accuracy are often not proportional to the amount of time used (Minasny and McBratney, 2002). Measurements of Ks are often impossible to accomplish at more than a few points at a field site within a given budget; hence, detailed knowledge of the spatial variability in Ks cannot be obtained. Therefore, indirect methods that are dependable, fast, and inexpensive with regard to assessing magnitude and spatial variability in Ks at the field scale are needed. Determination of Ks from more easily obtainable soil properties such as soil texture, porosity, or air permeability (ka) has been proposed (e.g., Giménez et al., 1997; Mckenzie and Jacquier, 1997; Poulsen et al., 1999b; Loll et al., 1999; Timlin et al., 1999; Schaap et al., 2001).

The soil air permeability (ka) is rapid and easy to measure and has proven useful in the characterization of soil pores (e.g., Ball, 1981; Groenevelt et al., 1984) and soil structure (e.g., Kirkham et al., 1958; Blackwell et al., 1990; Schjønning et al., 1999; Moldrup et al., 2001, 2003). Knowledge of ka and its variation with soil water content is necessary for modeling convective air and gas transport in soil, for example in relation to analyzing and optimizing soil vapor extraction systems for cleanup of soils contaminated with volatile organic compounds (Poulsen et al., 1999b). Recent studies suggest that it may also be preferable to use ka at the expense of Ks to evaluate spatial variability in water and chemical transport (Loll et al., 1999; Iversen et al., 2001a, 2003), since measurements of ka are more rapid, less destructive to soil structure, and pose fewer practical problems than measurements of Ks (Kirkham, 1947). To our knowledge, spatial correlation of ka at the field scale has only been studied by Poulsen et al. (2001) and Iversen et al. (2003).

To further understand the reason behind proposing Ks–ka pedotransfer functions, the links between air and water permeability need to be considered. The relation between Ks and saturated water permeability (kws) is

[1]
where {rho} is density, g is the gravitational acceleration, {eta} is the dynamic viscosity, and subscript "w" denotes properties relating to water. Ideally, water and air permeabilities should be the same at the same fluid (water or air) phase contents. Thus, ka in a completely dry soil (void of water) should equal the saturated water permeability (kws). In reality, the measurement of ka under totally dry conditions would cause shrinkage of the soil, leading to breakdown of soil structure, making the ka and kws measurements noncomparable (Bear, 1972). Furthermore, measurements of ka and kws may differ because water as a polar fluid tends to interact with the amount of electrolyte in the water and the exchangeable cations in the soil, causing a disruption of soil structure (Quirk, 1986). Inconsistency between the two types of measurements also exists because air at atmospheric pressure does not act as a true fluid continuum in the soil and the fluid velocity is therefore not zero at solid boundaries (the Klinkenberg effect), which is opposite the case with liquids (Bear, 1972).

Despite these problems in comparing ka and kws, the basic physical relationships between ka, kws, and Ks render it probable that measurements of ka at a carefully chosen soil water matric potential can be used as an indirect method to predict kws, and thus Ks. The value of Ks is likely to be dominated by the water flow in the large soil pores since the flow rate of a fluid in fluid-filled continuous pores depends on the fourth power of the effective pore radius according to Pouseuille's Law (Hillel, 1998). When the soil is drained to or near field capacity, the flow of air will predominantly take place in the large spectrum of soil pores. On the basis of this, it seems likely that ka measured at or near field capacity will be a good prediction of the permeability of the large-pore system and thus a good prediction of Ks.

Only a few studies have presented or used predictive Ks–ka relationships (Schjønning, 1986; Riley and Ekeberg, 1989; Blackwell et al., 1990; Rasmussen et al., 1993; Riley and Eltun, 1994; Loll et al., 1999; Iversen et al., 2001a, 2003). Loll et al. (1999) suggested that ka measured at -10 kPa on undisturbed soil cores could be used to infer spatial variability in water flow and pesticide leaching at the field scale. Most recently, Iversen et al. (2003) used in situ measurements of air permeability (ka,in situ) to characterize the spatial variability of Ks in two small hydrological catchments and applied this in a distributed surface runoff model. More studies are needed to evaluate the potential for using indirect methods that combine rapid in situ measurements of soil air parameters with pedotransfer functions to evaluate spatial variability in hydraulic conductivity and in water and chemical transport.

Our objectives were (i) to quantify the spatial correlation structure of ka measured in situ at five agricultural fields by using a portable air permeameter, (ii) to reveal a predictive relationship between Ks and ka measured on large soil samples (6280 cm3), (iii) to compare the Ks–ka relationship with previously presented relationships, and (iv) to discuss the applicability of different types of pedotransfer functions for predicting Ks, according to the spatial variability in Ks.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Air Permeameter
The design of the air permeameter is based on earlier instruments used by Steinbrenner (1959), van Groenewoud (1968), Green and Fordham (1975), and Fish and Koppi (1994). The device is divided into the following components (Fig. 1):

  1. Compressed-gas cylinder with pressure regulator for approximate control of pressure
  2. Precision pressure regulator
  3. A bank of three precision flow meters covering different flow ranges (0.2–2.3, 1.7–10.3, and 5.7–60 dm3 min-1), each of which is connected to a stopcock, allowing the air to flow exclusively through each of the flow meters
  4. A simple water manometer
  5. A metal cylinder, confining the soil, attached to an adaptor with air inlet tubing (20-cm diam.)
  6. An adaptor and diffuser for creating a leak-free application of air to the cylinder, consisting of an annular rubber tube inflated by a simple hand pump to seal the adaptor in the metal cylinder
  7. Plastic tubing linking the flow meter bank, the adaptor, and the manometer



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  		Fig. 1. Portable permeameter used for measurements of ka,in situ (after Iversen et al., 2001b).

 
The air permeameter has several advantages compared with other permeameters. It is easily portable in the field, inexpensive, and simple to repair and operate. Consult Iversen et al. (2001b) and Ball and Schjønning (2002) for further details.

Field Measurements
Some general physical data of the studied soils are shown in Table 1. Measurements were performed in the spring and autumn of 2001. At the time of measurement, all fields displayed winter wheat (Triticum aestivum L.) stubble and had been left undisturbed since the harvest of the wheat crop the previous autumn. The five different agricultural sandy soils originated from glaciofluvial deposits (Stubkær, Kølvrå, and Simmelkær) or till deposits (Astrup and Sjørup).


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  		Table 1. Summary of sampling sites and physical properties of the studied soils. Values are arithmetic means with ±1 SD.

 
In the field, one soil profile was excavated at each site, and the soil was described and classified according to Soil Survey Staff (1999). Soil samples from each described soil horizon were brought to the laboratory to be analyzed for soil textural distribution and amount of organic matter. The soil at Kølvrå and Simmelkær was classified as a Typic Haplorthod, at Astrup as an Oxyaquic Haplorthod, at Sjørup as an Entic Fragiortod, and at Stubkær as a Spodic Udisamment. In connection to the excavated soil profiles, five 6280-cm3 (20-cm diam.) and five 100-cm3 (6.1-cm diam.) undisturbed soil cores were sampled in the Ap and B horizon, respectively. For sampling the 6280-cm3 cores, steel columns were forced into the soil with a hydraulic press mounted on a tractor. For the 100-cm3 cores, steel rings were forced into the soil by means of a hammer and a special flange. The samples were protected from evaporation and physical disruption and brought to the laboratory, where they were stored at 2 to 5°C until analysis.

A total of approximately 50 points were used for the grid measurement at each of the five sites. Approximately 34 grid points were spaced at intervals of 20 to 30 m over the entire field. Symmetrically around four of the 34 grid points, in a radius of 5 m, four extra points were established to examine the short distance variability. The excavated profile was placed within the same area as the area of the grid points. In each grid point, the in situ air permeability (ka,in situ) was measured in the Ap horizon for a depth of 5 to 15 cm and in the B horizon for a depth of approximately 50 to 60 cm using the air permeameter. At the time of measurement all five soils had a water content close to field capacity (i.e., for all soils close to -10 kPa of matric water potential), which meant that the soils were sufficiently drained to enable the flow of air predominantly to take place in the large spectrum of soil pores (Fig. 2). Before each measurement the soil surface was carefully trimmed with a shovel and the metal cylinder was inserted 10 cm vertically into the soil with a hammer and a wood guide to enable vertical insertion of the cylinder. To dampen the hammer blows, a wood board was placed on top of the cylinder. The wood guides consisted of two horizontal parallel plates, spaced 10 cm apart, with drilled holes of the same diameter as the metal cylinder. After the insertion of the metal cylinder, the soil along the inner side of the metal cylinder was carefully kneaded along the steel–soil interface to minimize air leakage. The adaptor was then carefully inserted into the upper part of the metal cylinder, and the annular rubber tube was inflated by the foot pump to create an air-tight seal. The ka,in situ was then measured by opening the precision pressure regulator to allow air to flow through the confined soil core. The flux was read from the best suitable flow meter after the pressure was regulated to a predefined value. Preferably the pressure was set to a value between 0.5 and 1 kPa. In addition to the measurements of ka,in situ, five 6280-cm3 undisturbed soil cores at each site (except the Sjørup site) were sampled in the Ap horizon at five randomly chosen grid points within the same grid as used for the measurements of ka,in situ. Also here steel columns were forced into the soil with a hydraulic press mounted on a tractor, and the samples were protected from evaporation and physical disruption and brought to the laboratory, where they were stored at 2 to 5°C until analysis. Finally, soil samples from the Ap and B horizon were taken from every grid point at the five sites and brought to the laboratory to be analyzed for soil textural distribution and amount of organic matter.



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  		Fig. 2. Soil water characteristic curves for the (a) Ap and (b) B horizons in the excavated profiles (n = 5). Error bars show ±1 SD. Also plotted is the water content of the soil at the time of measurement (shown by a circle and the drop lines).

 
Laboratory Measurements
Air permeability (ka,lab) was measured in the laboratory on the 6280-cm3 soil columns at the actual water content using a modification of the air permeability device used in the field (Iversen et al., 2001b). Then the soil columns were saturated with water from beneath for at least 24 h, and Ks was measured by using the constant head method of Klute and Dirksen (1986).

The 100-cm3 soil cores were weighed and placed on top of a sandbox and saturated with water from beneath. The soil water characteristic was determined by draining the soil sample successively to matric water potentials of -1, -1.6, -5, -10, -16, -50, -100, and -1600 kPa, using a sandbox for matric potentials from -1 to -10 and a ceramic plate for matric water potentials from -16 to -1600 kPa. Water content at -1600 kPa was determined after the soil had been ground and sieved through a 2-mm sieve. After determining the soil water characteristic the soil samples were oven dried at 105°C for 24 h and weighed to determine the bulk density and water content.

Calculations
At low pressure gradients, the flow of air through porous media is comparable to water flow. Fluid independent permeability (k) of the soil is estimated via Darcy's Law from measurement of air or water flow, according to

[2]
where q is flux density, p is pressure, and x is distance in flow direction. Air permeability measured in the laboratory (ka,lab) is calculated using an integration of Eq. [2] (Kirkham, 1947):

[3]
where Q is the volumetric flow rate, as is the cross-sectional area, and Ls is the length of the sample.

When measuring ka,in situ, the air pressure at the lower end of the sample is not known because the air still has to flow through an (unknown) volume of soil before it reaches the soil surface (Fig. 1). The consequence of the lack of boundary conditions means that a "shape factor" (A) has been introduced into the calculation of ka,in situ, taking into account the geometry of the flow lines when the air leaves the lower part of the measuring cylinder in the soil (Grover, 1955; Kirkham et al., 1958; Boedicker, 1972; Liang et al., 1995). As a result, Eq. [3] is reorganized by replacing as and Ls by the shape factor (A) (Grover, 1955):

[4]

The shape factor A may be regarded as an estimate of the as/Ls quotient in Eq. [3] in a measuring condition where neither as nor Ls involved in the flow is well defined. Earlier studies (e.g., Grover, 1955) produced nomograms for estimating the shape factor for different sample diameters and insertion depths. In our study, A was determined using the finite element model (ANSYS F) developed by Liang et al. (1995).

The shape factor equation of ANSYS F is

[5]
where D is the inside diameter of the soil core.

Equation [5] was evaluated by Iversen et al. (2001b), who obtained reasonable results when carrying out measurements of ka,in situ at four different sites at two soil depths (Ap and B horizon). After the ka,in situ measurement, they exhumed the soil column from the soil and ka was measured again with well-defined boundary conditions on 3140-cm3 large soil cores. The in situ measurements were performed using the same size of steel cylinder and the same insertion depth (10 cm) as the present study.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
To provide an overall view of the field data, Fig. 3 shows the measurements of ka,in situ at all grid points in the Ap and B horizon at the five sites as a function of coarse sand content. The approximately 100 measurements of ka,in situ at each field site were accomplished without problems within two normal working days, illustrating the potential of the portable air permeameter to obtain many data rapidly and with ease. Figure 3 implies some degree of correlation between coarse sand content and ka,in situ [log(ka,in situ)] (m2) = 0.0127 Coarse sand (%) - 11.6, r2 = 0.25). This is likely attributable to a higher coarse sand content typically indicating a higher content of larger pores, again leading to a higher air permeability. Since these sandy soils in general are weakly structured, measurements would be expected to reflect permeability in the soil matrix and would not be dominated by effects of continuous, structural macropores. However, the large fluctuations in ka,in situ for the Astrup soils may be related to influence of structural macropores at some measurement locations on the field. Also other factors such as the content of organic matter and degree of soil pedogenesis might have an influence on the ka,in situ values.



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  		Fig. 3. Measurements of ka,in situ at all grid points in the Ap and B horizon at the five sites as a function of coarse sand content.

 
Table 2 shows the results of measured air and water permeabilities. Results are shown both for measurements of ka,in situ in the field and measurements of ka,lab and kws in the laboratory on the large columns (6280 cm3). The comparison between ka,in situ and ka,lab could be considered a test of the reliability of the shape factor, A, in Eq. [4]. A relatively good agreement between the two types of measurements was found even though the measurements were not related to exactly the same soil volume as in the work of Iversen et al. (2001b). Measurements of ka,in situ were related to the grid measurements (n {approx} 50) whereas measurements of ka,lab were related to the five grid points (Ap horizon, n = 5) and the excavated soil profiles (Ap and B horizon, n = 5). Therefore, measurements of ka,in situ covered a larger area with a higher number of measurements compared with measurements of ka,lab.


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  		Table 2. Soil permeability (air or water) measured at the five studied sites. Values are arithmetic means on the log-transformed values with ±1 SD.

 
For the sandy glaciofluvial soils, the lowest values of k (ka,in situ, ka,lab, and kws) were found in the A horizon compared with the B horizon. This is probably related to the high amount of organic matter in the Ap horizon (Table 1) having a large effect on the soil structure. For the more loamy, structured till soils (Astrup and Sjørup) differences in k between the Ap and B horizon are probably to a larger extent explained by differences in the amount of macropores within the soil profile.

Except for the Stubkær site, values of ka,in situ in the nontilled B horizon showed a higher variation compared with the Ap horizon. The variation of k in the Ap horizon is restrained because of the redistribution of soil in connection with tillage and the high content of organic matter in this horizon.

Values of ka,lab are higher than values of kws (Table 2). If k was fluid independent, it would logically be expected that the two permeability estimates (ka,lab or kws) would be equal or that kws would be larger. Higher values of kws would be excepted because permeability measurements using water as the fluid include the whole pore system, in contrast to measurements of ka,lab where the flow of air could be reduced by the small amount of water in the soil. However, differences between ka,lab and kws are explained rather by differences in the pore continuity characteristics in the soil when measuring with air or water as the fluid. When measuring ka,lab, the smooth water surfaces along the pore walls are favorable for the transport of air, whereas when measuring kws, the pore walls are less smooth and less favorable for the transport of water. The deviation between the two types of measurements could also be related to the Klinkenberg effect. The same difference between the two types of measurements was also found by Schjønning (1986), Blackwell et al. (1990), and Iversen et al. (2001a).

Spatial Variability of Air Permeability
Despite the relatively low amount of grid points to construct the experimental variograms, spatial dependency between data points were found for both horizons of two of the sandy sites (Kølvrå and Simmelkær) and for the B horizon only of one of the loamy sands (Astrup) (Table 3). For the other sites no clear dependency was found between data points. The largest range (120 m or more) was found for the sandy soils whereas a low range (30 m) was found for the loamy soil. The differences in ranges is probably related to the depositional processes of the two types of sediments (fluvial and till). Examples of experimental and fitted variograms from the Kølvrå and Simmelkær sites are shown in Fig. 4. The high {gamma} value of the sill for the B horizon reflects a more heterogeneous soil compared with the more homogeneous Ap horizon.


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  		Table 3. Fitted variograms (linear with sill) of the log-transformed measurements of ka,in situ in the grid points at the five studied sites.

 


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  		Fig. 4. Experimental and fitted variograms of log-transformed measurements of ka,in situ at two depths at the Kølvrå and Simmelkær sites.

 
Predicting Ks from ka
In this work we assumed that a linear correlation exists between log(Ks) and log(ka); that is,

[6]

Figure 5a shows the general log-log linear prediction relationship between Ks and ka,lab found in the present study:

[7]



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  		Fig. 5. (a) Log-log relationship between Ks and ka,lab measured in the laboratory on the 6280-cm3 soil columns sampled in the grid and from the soil profiles. The 95% prediction interval and r2 are given (values of n, {alpha}, and ß are found in Table 4). Also plotted is the log-log relationship found by Loll et al. (1999). (b) Log-log relationship between ka,lab and Ks from the present study in combination with the log-log relationship on 6280-cm3 soil columns found by Iversen et al. (2001a). Also plotted is the log-log relationship and 95% prediction interval found by Loll et al. (1999).

 

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  		Table 4. Log-log relationships [log (Ks) = {alpha}log(ka) + ß] in relation to different studies.

 
The relationship has a prediction accuracy around ±0.7 orders of magnitude.

Loll et al. (1999) explored the existence of a general prediction relationship between ka (measured at a matric water potential at -10 kPa) and Ks. The data used were measurements of ka and Ks on 100-cm3 soil samples from nine soils (Schjønning, 1986; Riley and Ekeberg, 1989). The general log-log linear prediction relationship of Loll et al. (1999) combining the nine data sets (n = 1614) had a prediction accuracy of ±0.7 orders of magnitude:

[8]

As shown in Fig. 5a, the found relationship of the present study compares well with Eq. [8] (Loll et al., 1999). In Fig. 5b measurements of the present study are combined with earlier data of Iversen et al. (2001a). Also plotted is the relationship and the 95% prediction interval of Loll et al. (1999). In the study of Iversen et al. (2001a), Ks and ka were measured on three different soils ranging from sand to sandy clay loam. In that study measurements also were performed on 6280-cm3 soil samples, but before the ka measurement, the soil samples were drained to soil water potential of -5 kPa, in contrast to the measurements in the present study where ka,lab was measured at the actual water content being close to field capacity (Fig. 2). Despite the likely differences in soil water potential, there seems to be a good relation between the two data sets. The results therefore confirm those of Iversen et al. (2001a) that it is the large pores of the soil that almost exclusively are active for the value of ka in accordance with Pouseuille's Law. As long as the larger pores are drained of water, deviations in the soil water potential have only a minor effect. Other studies have evaluated the log-log relation between ka and Ks, both on different sample sizes or different soil water potentials when measuring ka (Table 4). According to Table 4, neither size of soil sample nor different soil water potential has a larger effect on the prediction relationship. Only the study of Iversen et al. (2001a), which used measurements on 6280-cm3 soil samples where the samples were drained to -5 kPa before the measurements of ka, had a log-log relationship deviating clearly from the relationship of Loll et al. (1999). Therefore, when comparing the other four relationships in Table 4, it seems realistic that a general prediction relationship such as Eq. [8] (Loll et al., 1999) can be used on most soils as long as the soil is drained to a matric potential close to or dryer than field capacity.

Comparison with Other Pedotransfer Functions
Pedotransfer functions can be used to estimate various soil hydraulic parameters. The choice of pedotransfer function will depend on the choice of available data. Also, some basic soil physical characteristics will likely show better correlation with the soil hydraulic properties compared with other data. The success of the predictions by the pedotransfer functions will therefore highly depend on the accessibility and the use of the best suitable data.

Figure 6a shows the log-log relation between Ks measured in the laboratory and Ks estimated from ka,lab using Eq. [8] (Loll et al., 1999). The data include measurement on the 6280-cm3 soil columns sampled in the Ap horizon in relation to the grid points and in the Ap and B horizon in relation to the excavated soil profiles at the five different sites. As seen from the figure, Eq. [8] generally underestimated the mean values of each site (excavated soil profiles only) with RMSE in log Ks of 0.37.



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  		Fig. 6. (a) Log-log relation between Ks measured in the laboratory and Ks estimated from ka using Eq. [8] (Loll et al., 1999). The data include measurement on the 6280-cm3 soil columns sampled in the Ap horizon in relation to the grid points and in the Ap and B horizon in relation to the excavated soil profiles. Root mean square error is calculated on the arithmetic means of each site from the log-transformed data (data from the excavated soil profiles only). (b) Log-log relation between Ks measured in the laboratory and Ks estimated from Rosetta (Schaap et al., 2001) and Eq. [9] (Poulsen et al., 1999a). The data include measurements on the 6280-cm3 soil columns sampled in the Ap and B horizons in relation to the excavated soil profiles. Values of Ks (measured) are arithmetic means of each site on the log-transformed data.

 
Two alternative Ks prediction methods are considered for comparison. First, the computer program Rosetta (Schaap et al., 2001) implements pedotransfer functions based on artificial neural networks to predict hydraulic properties of the soil. Input data such as soil texture (percentages of clay, silt, and sand), bulk density, and water contents at different soil water potentials are used. Second, Poulsen et al. (1999a) used soil hydraulic data from Hansen (1976) and Puckett et al. (1985) and found a log-log relationship between Ks and the soil air content at a soil water potential of -10 kPa (denoted {epsilon}10 and labeled the soil macroporosity).


[9]

The {epsilon}10 is a measure of the amount of large soil pores having tube-equivalent pore diameters >=30 µm. The relationship of Poulsen et al. (1999a) therefore supports that it is the large soil pores that almost exclusively are dominating the transport of water when the soil is fully saturated. Figure 6b shows the log-log relation between arithmetic mean values of log Ks measured in the laboratory (n = 5) and Ks estimated from Rosetta (Schaap et al., 2001) and Eq. [9] (Poulsen et al., 1999a). The data include measurements on the 6280-cm3 soil columns sampled from the excavated soil profile. To predict Ks using Eq. [9] arithmetic mean values of {epsilon}10 (n = 5) from each site estimated from the soil water characteristics were used. In relation to Rosetta, inputs of soil texture distribution (clay, silt, and sand, n = 1) and the soil bulk density (arithmetic mean values of each site, n = 5) were used to predict Ks. Also these parameters were measured in relation to the excavated profiles only and not measured directly on the 6280-cm3 soil samples. Figure 6b shows that both methods underestimated the log Ks values, as was the case of Eq. [8] (Loll et al., 1999); compare Fig. 6a. Equation [9] (Poulsen et al., 1999a) gave a better prediction of log Ks, with a RMSE of 0.37 compared with 0.53 for Rosetta (Schaap et al., 2001). The measured values of Ks in the Ap horizons were especially well predicted by Eq. [9]; also, the predicted Ks values in the B horizon were within the 95% prediction interval given by Poulsen et al. (1999a), corresponding to ±0.98 orders of magnitude.

Compared with the prediction of Rosetta (Schaap et al., 2001), the improvement in the prediction of log Ks using Eq. [8] (Loll et al., 1999) or Eq. [9] (Poulsen et al., 1999a) showed that the introduction of easily measurable and dynamic transport parameters such as ka or {epsilon}10 gives more reliable estimates of Ks. In Rosetta, more static parameters such as soil texture and bulk density gave less reliable results when predicting Ks. No clear difference was found between the prediction by Eq. [8] and [9]. In perspective, {epsilon}10 is more labor-intensive to measure than ka, and ka can be measured in situ, which decreases the workload and increases the applicability even more. This favors the measurement of ka in comparison to {epsilon}10. However, if a portable air pycnometer was developed that allowed rapid, on-site (excavated samples) or in situ measurements of {epsilon} ({epsilon}in situ) at or near field capacity, this would also seem promising for estimating field-scale variability in Ks. Further, a combined air permeameter and air pycnometer used with pedotransfer functions for estimating Ks from both ka,in situ and {epsilon}in situ would be highly interesting, although outside the scope of the present study.

The field-scale variability in Ks seems more realistically predicted by Eq. [8] (Loll et al., 1999) than by Rosetta (Schaap et al., 2001). Using the percentages of clay, silt, and sand at the grid points at the five sites (Ap and B horizon), estimates of Ks only varied over 1.5 orders of magnitude. In contrast, estimates of Ks from the measurement of ka,in situ using Eq. [8] showed a variation of >3.7 orders of magnitude, which is much more realistic compared with the Ks measurements on the large undisturbed soil cores in Fig. 5. Considering that the prediction accuracy in Ks when using a pedotransfer function is typically no more than one order of magnitude, the use of pedotransfer functions based on soil texture such as Rosetta will not suffice to give realistic estimates of spatial variability in Ks. Inclusion of more dynamic transport parameters such as ka and/or {epsilon}10 seems a more realistic approach. Although Eq. [8] underestimated the measured Ks values to some extent in this study, pedotransfer functions using ka,in situ (and potentially also {epsilon}10) to predict Ks seem to be a promising tool to cover the spatial variability in Ks at the field or hydrological catchment scale. In relation to spatial distributed hydrological models, the knowledge of the spatial variation of the infiltration parameters is often crucial (e.g., Merz and Bardossy, 1998). Since the spatial variation of Ks is often large, cheap information and many, less precise measurements can often be more efficient than a few, more expensive and precise measurements (Minasny and McBratney, 2002). The results of this study in combination with Iversen et al. (2003) suggest that the use of ka,in situ measurements together with Ks–ka pedotransfer functions is a promising alternative to the traditional Ks measurements to get the "most value for money" in regard to characterizing field-scale spatial variability in Ks and, subsequently, in characterizing runoff, infiltration, and chemical transport.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
The method of using a portable insertion-type air permeameter to evaluate the spatial variability of air and water permeability at the field scale was investigated. Spatial correlation in air permeability (ka) at three of five field sites was observed, with correlation distances between 30 and >120 m. Around 100 in situ measurements of ka (ka,in situ) were performed at each field site within two normal working days, making the method rapid and inexpensive.

A good linear log-log relationship was found between air permeability (ka) and saturated hydraulic conductivity (Ks) measured on large soil samples. The results supported use of a general Ks–ka prediction relationship such as the one of Loll et al. (1999) on most soils when the soil is drained to a water content near field capacity. Prediction accuracy is expected to be around one order of magnitude.

The general log-log relationship of Loll et al. (1999) was tested against two other pedotransfer functions. The introduction of dynamic transport parameters such as soil macroporosity ({epsilon}10) or ka in the pedotransfer functions gave more reliable estimates of Ks. Using a pedotransfer function based only on soil texture yielded an unrealistic narrow range in predicted Ks values compared with predictions of Ks from measurements of ka,in situ using the relationship of Loll et al. (1999). Measurements of ka,in situ appear a promising indirect method for assessing spatial variability in Ks at the field scale. The portable air permeameter in combination with appropriate pedotransfer functions should offer a rapid, inexpensive, and effective tool to help evaluate field-scale spatial variability in air, water, and chemical transport properties near or at the soil surface. This will provide valuable input to spatially distributed water and chemical transport models for the vadose zone.


   ACKNOWLEDGMENTS
 
This work was supported by the Danish project: "Concept for Appointing Areas Vulnerable to Pesticides" financed by the Danish Parliament. The project aims to develop an operational concept for identifying areas where shallow aquifers are vulnerable to pesticide contamination. The focus in the first part of the project is on sandy soils. The authors wish to thank the technical staff at the Danish Institute of Agricultural Sciences (S.T. Rasmussen, M. Koppelgaard, B.B. Christensen, J.M. Nielsen, and P. Jørgensen) for their valuable work in the field and in the laboratory.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 




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