This article was downloaded by: [University of Saskatchewan Library] On: 06 September 2013, At: 15:11 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Archives of Agronomy and Soil Science Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/gags20 Prediction of saturated hydraulic conductivity of compacted soils using empirical scaling factors Seyed Hamid Ahmadi a & Ali Reza Sepaskhah a a Irrigation Department, Faculty of Agriculture, Shiraz University, Shiraz, Islamic Republic of Iran Published online: 06 Jul 2011. To cite this article: Seyed Hamid Ahmadi & Ali Reza Sepaskhah (2012) Prediction of saturated hydraulic conductivity of compacted soils using empirical scaling factors, Archives of Agronomy and Soil Science, 58:11, 1303-1316, DOI: 10.1080/03650340.2011.579598 To link to this article: http://dx.doi.org/10.1080/03650340.2011.579598 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms- and-conditions
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This article was downloaded by: [University of Saskatchewan Library]On: 06 September 2013, At: 15:11Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Archives of Agronomy and Soil SciencePublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/gags20
Prediction of saturated hydraulicconductivity of compacted soils usingempirical scaling factorsSeyed Hamid Ahmadi a & Ali Reza Sepaskhah aa Irrigation Department, Faculty of Agriculture, Shiraz University,Shiraz, Islamic Republic of IranPublished online: 06 Jul 2011.
To cite this article: Seyed Hamid Ahmadi & Ali Reza Sepaskhah (2012) Prediction of saturatedhydraulic conductivity of compacted soils using empirical scaling factors, Archives of Agronomy andSoil Science, 58:11, 1303-1316, DOI: 10.1080/03650340.2011.579598
To link to this article: http://dx.doi.org/10.1080/03650340.2011.579598
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.
This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
Prediction of saturated hydraulic conductivity of compacted soils
using empirical scaling factors
Seyed Hamid Ahmadi* and Ali Reza Sepaskhah
Irrigation Department, Faculty of Agriculture, Shiraz University, Shiraz, IslamicRepublic of Iran
(Received 9 January 2011; final version received 1 April 2011)
A new empirical-based scaling method is introduced to predict saturatedhydraulic conductivity (Ks) of compacted soils. This method is an improvementof the former non-similar media concept (NSMC) model that is generalized fortilled and untilled conditions. In this method, geometric mean particle sizediameter (dg), geometric standard deviation (sg) and saturated soil watercontent (total porosity) are successfully incorporated in the empirical-basedscaling factor of Ks. Results showed that the scaled model overestimated Ks by*18%, whereas the NSMC model underestimated Ks by *21%. However, thescaled model based on the similar media concept (SMC) failed to predict Ks.Because of the complexity and high uncertainty in determining the shapefactor parameter in the NSMC model, it is suggested that the new scaledmodel might be used reliably in practical cases to predict Ks in the variouslayers of compacted soils irrespective of the tillage condition. Furtherassessment of the new scaling model in other areas, in which new collecteddata are available, is recommended.
Keywords: geometric mean particle diameter; geometric standard deviation;scaling; saturated hydraulic conductivity; soil compaction; tilled and untilledsoils
Introduction
Saturated hydraulic conductivity (Ks) is an important soil hydraulic parameter inlarge- and small-scale hydrologic studies that influences the efficient management ofsoil and water. In general, it is a matching factor for predicting unsaturatedhydraulic conductivity (Kus) from soil water characteristics data (van Genuchten1980) that controls water and solute movement in the soil profile. However, manyfield and laboratory studies have shown that Ks is greatly subjected to spatial andtemporal variability and, therefore, it is difficult to represent a single value for aspecific geographic site (Zhuang, Nakayama et al. 2000).
Scaling methods based on the similar media concepts (SMC) of Miller andMiller (1956) and non-similar media concepts (NSMC) of Miyazaki (1996) providepowerful tools to approximately describe field spatial and temporal variability insoil hydraulic properties. Application of scaling methods to the soil hydraulic
properties includes, but is not limited to, Ks (Ahuja and Williams 1991; Miyazaki1996; Zhuang, Nakayama et al. 2000; Nakano and Miyazki 2005), Kus (Brooks andCorey 1964; van Genuchten 1980; Poulsen et al. 1998; Zhuang et al. 2001; Basileet al. 2006), infiltration rate (Youngs and Price 1981; Ahuja et al. 1984; Rasoulzadehand Sepaskhah 2003; Machiwal et al. 2006) and soil-water retention curves (Kosugiand Hopmans 1998). In general, the scaling method relates the soil properties ofdifferent soil types or spatial locations by using simple conversion factors called thescaling factors (Ahuja and Williams 1991). Scaling factors are either physically based(dimensional analysis) and rely on existing physical similarities in the system, orempirical-based (functional normalization) and rely on the relationship between theparameters in the system (Tillotson and Nielsen 1984).
Soil compaction induced by extensive farm machinery traffic accelerates thespatial and temporal variations of Ks (Cassel 1983). Soil compaction decreases Ks byincreasing soil bulk density (Assouline et al. 1997; Nakano and Miyazaki 2005) andreducing total soil porosity, which adversely affects the soil water status on crop rootgrowth. However, application of scaling methods in investigating spatial andtemporal variations of Ks in compacted soils is rather new (Miyazaki 1996; Zhuang,Nakayama et al. 2000; Nakano and Miyazaki 2005; Assouline 2006). These studiesfollow Schafer et al. (1992) who stated that a ‘significant knowledge gaps exist in thedescription and modeling of soil compaction behavior, in relating soil compactionbehavior to agronomic responses (biological and physical) and to conservation ofsoil and water resources’.
In former studies of scaling Ks (Miyazaki 1996; Zhuang, Nakayama et al. 2000;Nakano, Nakayama and Miyazaki 2005; Assouline 2006; Rahimi-Adregani et al.forthcoming 2011), the scaling factors were based on two parameters, soil bulkdensity (rb) and shape factor, because the latter is related to soil structure andtexture. Zhuang, Nakayama et al. (2000) reported that determining the shapefactor is rather complex, which restricts the applicability of the NSMC andproposed an analytical approach to solve this complexity. Rahimi-Adregani et al.(Forthcoming 2011) tested various existing scaled NSMC models on the measuredKs of different compacted soils and reported that the tested models were highlysensitive to soil texture. Rahimi-Adregani et al. (forthcoming) also realized that theincorporated shape factors in the NSMC models were correlated with thegeometric statistical properties of soil particle size distribution, and presented anempirical formula for calculating the shape factors based on geometric statisticalproperties. Accordingly, Shirazi and Boersma (1984) reported that although soiltexture is expressed using statistical geometry (geometric mean particle sizediameter, dg, and geometric standard deviation, sg), it may be better correlatedwith soil hydraulic properties than soil texture data itself.
Therefore, it seems that there is a lack in the category of Ks scaling models suchthat none of the models includes both soil structure (bulk density and total porosity)and soil texture (particle size distribution) parameters. This study aims to introducenew scaling factors that incorporate easily measureable soil physical parameters,while simultaneously outperforming the existing scaling models to handle spatialand temporal variability of Ks in the field. This study suggests for the first time a newempirical-based scaling method (Tillotson and Nielsen 1984) that predicts Ks incompacted soils under tilled and untilled conditions for which, as an advantage, thescaling factor integrates statistical geometry properties of soil particle sizedistribution.
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Materials and methods
Study area and soil characteristics
This study was conducted in two different sites where the soils were tilled anduntilled. The first site is located in the Nekuabad area of Esfahan (central Iran),328380N 518390E, where the soil had been disturbed by an extra deep tillage using abackhoe to an operating depth of 1.0 m. The second site is located in Shiraz(southern Iran), 298370N 528320E, where one of its soil types was tilled to the depth of0.3 m, and the other soil type was kept untilled for eight years from 2000 to 2008.Soil textures at Esfahan and Shiraz sites were loam and silty clay loam, respectively.Soil texture was classified according to the particle size classification of United StatesDepartment of Agriculture (USDA), that is, clay fraction 52 mm, silt fraction 2–50mm, and sand fraction 50–2000 mm. The physical properties of the soils are given inRahimi-Adregani et al. (Forthcoming 2011).
Six replicated undisturbed soil samples, 0.105 m in diameter and 0.1 m long weretaken successively in 0.1 m increments from the soil surface down to 0.5 m in thetilled soils of Esfahan and untilled soils of Shiraz, respectively. Ten replicated coresamples were taken successively in 0.1 m increments from the soil surface down to0.3 m in the tilled soil in Shiraz. Therefore, 30 soil samples were collected from eachof the three sites with different soil texture and structure. The bulk densities of thesesamples at a depth of 0–0.3 m were in a narrow range and varied between 1.169 and1.43 Mg m73. To achieve a broader range of bulk density in this location, some ofthese samples were compacted manually using a wooden cylindrical stick to increasethe bulk density to 1.63 Mg m73. The observed difference in sampling depth (0.3 vs.0.5 m) in the tilled soils was due to the difference in tillage depth. Some statisticalproperties of the soil samples from each site are given in Table 1.
The soil core samples were placed in water for 12 h for saturation. Ks was thenmeasured using the traditional constant head method (Klute and Dirksen 1986). Drybulk densities were then determined by oven-drying the samples at 1058C for 24 hwith little shrinkage.
Data
In addition to the measured data already mentioned (Rahimi-Adregani et al.,forthcoming 2011), which comprosed Ks values in two soil textures subjected todifferent degrees of compaction under tilled and untilled conditions, we collected Ks
and bulk density data reported in the literature (Miyazaki 1996; Nakano andMiyazaki 2005; Assouline 2006). These data reported the impact of different degreesof compaction on bulk density and Ks of different soil textures. Each of these datasources include a series of pairs (rb, Ks) ranging from high to low compaction overthe entire soil depth. The data covers a wide range of soil textures from light to heavysoils and their basic information and characteristics are given in Table 1.
The whole dataset is divided into two groups for calibration and validationpurposes. The calibration data were used to obtain a scaled curve based on theproposed empirical scaling factors, and the validation data were used to checkthe validity of the empirical scaled curve and the empirical scaling factors. Thecalibration and validation datasets were chosen so that each group included a widerange of soil textures and bulk densities (Table 1). Moreover, we split our measureddata (Rahimi-Adregani et al., forthcoming 2011) such that every other measured
data in each soil texture and tillage condition was used in the calibration and theremaining data were used in the validation. Therefore, the whole range of bulkdensities was included in both calibration and validation. In the validation step, thenew empirical-based scaling model was further compared with the SMC model(Campbell, 1985) and the NSMC model (Zhuang, Nakayama et al. 2000).
Scaling theory
The general mathematical expressions of the statistical geometry of particle sizedistribution are given as (Shirazi and Boersma 1984):
dg ¼ exp ðaÞ ð1Þ
sg ¼ exp ðbÞ ð2Þ
where
a ¼Xni¼1
fi lnðMiÞ ð3Þ
b2 ¼Xni¼1
filn2ðMiÞ � a2 ð4Þ
In these equations, dg is the geometric mean particle size diameter (mm), sg is thegeometric standard deviation, fi is the mass fraction of particle size class i (sand, silt,clay), and Mi is the arithmetic mean of particle diameter in particle size class i(0.001 mm for clay, 0.026 mm for silt, and 1.025 mm for sand).
The sole objective of scaling is to coalesce a set of functional relationships into asingle function using the scaling factors that describe the set as a whole (Rasoulzadehand Sepaskhah 2003; Machiwal et al. 2006). In Equations (5) and (6), the empiricalscaling factors are the mathematical terms in the right hand that convert Ks and rb toK�s and r�b, respectively, at the left hand (Tillotson and Nielsen 1984). These scalingfactors and scaling models are applicable for different soil textures and soil depths.According to the empirical-based scaling concept (Tillotson and Nielsen, 1984) thefollowing scaled models (Equations (5) and (6)) coalesce the measured pairs of data(rb, Ks) of different depths into a single function or a scaled curve:
Ks� ¼ Ks
0:5 � ys4
1� ysð Þ0:5� Z
sg3 � dg0:1 � d
ð5Þ
rb� ¼ rb
rbmax
ð6Þ
where Ks� and r�b are the scaled saturated hydraulic conductivity and soil bulk
density, respectively, Ks and rb are the measured saturated hydraulic conductivity(LT71) and soil bulk density (ML73), rbmax is the highest soil bulk density aftermaximum compaction (LT71) in a soil texture, ys is the saturated soil moisturecontent or total porosity (fraction), Z is the constant water viscosity (ML71 T71),
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and d is the constant surface tension of soil water (MLT72). L, T and M stand forlength, time and mass, respectively.
For calibration purposes (Table 1), pairs of (rb, Ks) associated with different depthsof a specific soil were applied in Equations (5) and (6) to obtain the scaled values of K�sand r�b of that specific depth. It is noteworthy that due to compaction, the values of Ks
and rb vary with soil depth and by using Equations (5) and (6) these spatial variationsshould disappear or diminish. The scaled values of Ks
� and rb� calculated in calibration
were used to find the scaled model. Having found the scaled model, the remianing data(validation soils, Table 1) were used to validate the scaled curve.
The SMC model of Campbell (1985) reads as:
Ks
Ksref¼
rbrefrb
� �1:3b
ð7Þ
b ¼Xni¼1
fi ln ðMiÞ2 �Xni¼1
fi lnðMiÞ !2
24
350:5
ð8Þ
where parameter b is calculated based on the standard soil bulk density of1.3 Mg m73 (Miyazaki, 1996).
The NSMC model of Zhuang, Nakayama et al. (2000) is:
Ks
Ksref¼
�trsrb
�1=3� 1
�trsrbref
�1=3� 1
2666664
3777775
2
ð9Þ
t ¼rbrefrb
� �e1þ rs
yrrs þ rb� 1
� �� exp dg � dg 1� yr �
rbrs
� ��rb� �� ��1ð10Þ
e ¼ rs � rbrs � rbref
" #0:5ð11Þ
yr ¼ 0:015þ 0:005Cþ 0:014rb ð12Þ
where rs is the soil particle density (ML73), rbref is the reference soil bulk density(ML73), Ksref is the reference saturated hydraulic conductivity (LT71), yr residualwater content (L3 L73), and C is the content of clay particles (%). rbref is consideredas the highest observed soil bulk density with saturated hydraulic conductivity ofKsref for each soil texture (Zhuang et al. 2001; Nakano and Miyazaki 2005).
Root mean square error (RMSE) was used to assess the accuracy of the differentscaled models in predicting Ks:
where Ksmeasured and Kspredicted are the measured and predicted Ks, respectively; and nis the number of observations.
Results and discussion
Calibration of the scaled model
Figure 1 shows the scatter plot of the non-scaled calibration dataset, and Figure 2shows this data after being scaled using Equations (5) and (6). The best-fitted scaledmodel is well represented by a two-parameter exponential curve as:
K�s ¼ 0:00000798� exp ð�11:373rb�ÞR2 ¼ 0:78 ð14Þ
Figure 1. Scatter plot of measured saturated hydraulic conductivity (Ks) against bulk density(rb) collected from different sources and used in the calibration.
Figure 2. Scaled data based on the proposed scaling factors Ks* and rb* (Eqns 5 and 6) andthe best-fitted two-parameter exponentially scaled model (Equation (14)).
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where Ks� and rb
� are the scaled saturated hydraulic conductivity and soil bulkdensity, respectively.
Equation (14) clearly shows that the scaled curve reasonably coalesces the non-scaled and scattered data of different soil textures into a single curve based on thescaling factors introduced in Equations (5) and (6). However, this shows that theintroduced scaling factors and models (Equations (5) and (6)) do well in the scalingprocess, and diminish the spatial and non-uniformity between the variables. Thescaling factors are generally developed to remove the heterogeneous nature ofdifferent datasets and create a homogenous dataset that can reasonably represent thetotal variations among the different datasets. Although there was a different numberof measurements in each soil type (Figure 1), the scaled curve was not obviouslyinfluenced by the soils having more measurement data, and it is an advantage of thescaling process that has also been approved in previous studies (Youngs and Price1981; Jabro 1992; Kosugi and Hopmans 1998; Zhuang, Nakayama et al. 2000;Zhuang et al. 2001; Nakano and Miyazaki 2005).
Similar scaling approaches have been adapted previously by Youngs and Price(1981) and Rasoulzadeh and Sepaskhah (2003) for soil hydraulic parameters.However, unlike the SMC (Miller and Miller, 1956) in which a scaling factor ispooled over the entire soil depth, in the proposed scaling method, the scaling factorsvary with soil depth and soil texture, which consider the spatial variability moreaccurately. This method is in line with the NSMC concept of Miyazaki (1996) inwhich the scaling factor is calculated for any point (measurement) along the soilprofile. Ahuja et al. (1984) found that the scaling factor varies for different soil layersin a given site and criticized using a single average scaling factor for the entire soildepth. This argument is also relevant to our data where the bulk density increasesdue to compaction. Zhuang, Nakayama et al. (2000), Nakano and Miyazaki (2005),and Rahimi-Adregani et al. (Forthcoming 2011) also successfully applied the scalingfactor for each depth and reported that it performs better than the scaling method ofCampbell (1985) which uses an average scaling factor for the entire soil depth.
Unlike former scaling methods in which Ks was scaled using either soil-waterretention properties (Brooks and Corey 1964; Mualem 1976; van Genuchten 1980;Libardi et al. 1980; Campbell 1985; Poulsen et al. 1998) or microscopic lengthcharacteristics (Youngs and Price 1981; Tillotson and Nielsen 1984), in the proposedscaling method, geometric statistics of the soil texture, dg and sg, are explicitlyincorporated in the scaling factors. This is in agreement with Zhuang, Nakayamaet al. (2000) and Zhuang et al. (2001) who recommended that new theories orconcepts should be formulated such that soil particle information is incorporated inthe modeling of soil hydraulic properties. Former studies implicitly identified thatusing dg in the scaling process can result in better estimation of Ks (Campbell 1985;Zhuang, Nakayama et al. 2000). This was, however, in agreement with Shirazi andBoersma (1984) who realized that dg and sg are more representative of the soil-waterbehavior rather than the soil texture itself. Zhuang et al. (2001) highlighted that theadvantage of the NSMC model over other scaling models lies on the incorporationof dg and soil bulk density into the model. In agreement with these findings,calculation of Ks using the scaled models of Cosby et al. (1984) and Brakensiek et al.(1984) was not as successful as calculations using the scaled model of Zhuang, Yuet al. (2000).
It is obvious that in the scaling factor of Equation (5), dg and sg do not haveidentical exponents meaning that sg has higher impact on the Ks than dg. This implies
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that Ks is more sensitive to variations in sg than dg; however, the d0:1g should be kept
in the scaling factor and its removal fails the model. Shirazi and Boersma (1984) alsohighlighted the importance of sg and its physical interpretation in soil physicalstudies. It is noteworthy that in Equation (5) the exponent of total porosity is 4,which means high importance for soil structure in the scaling process. Therefore, it isconcluded that those parameters (sg and ys) that are more linked to soil structurecarry more weight in the scaling method.
A sensitivity analysis was performed to determine the contribution of sg and dg toKs. Both sg and dg varied by +10% and +20% relative to original values. Figure 3shows the results of these analyses. It is worth mentioning that r�b changes between*0.7 and 1, and therefore the scaled curve could be used in future for r�b values inthis range. However, this range may cover the majority cases of relative soil bulkdensity and compactions conditions and in very rare situations (very highcompactions), lower values of r�b might be achieved.
Two regions could be distinguished in Figure 3. The first corresponds to r�b values40.88. In this area, variations in sg and dg do not distort the new lines from thescaled curve and this implies that Ks
� might be more dominated by soil structure(total porosity) as represented in the scaling factor (Equation (5)) than soil texture.According to Equation (6), it is clear that r�b values closer to 1 translate into highersoil compaction and in such conditions hydraulic conductivity could be highlydominated by total porosity and pore structure (Rahimi-Adregani et al. forthcoming2011). Nakano and Miyazki (2005) also reported that soil hydraulic conductivity isintrinsically related to soil structure and micropores in the soil.
In the second region, representing lower soil compactions, the lines diverge fromthe scaled curve. This may suggest that in this region both soil texture and soilstructure are governing Ks
� and the scaled curve is sensitive to both. In this region,the line corresponding to þ10% shows closer agreement with the scaled curve, andmore scaled data are bounded between this line and the scaled curve compared to theother lines. Generally, higher values of clay particles increase sg and it suggests that
Figure 3. Curves obtained from sensitivity analysis of the scaled curve (Equation (14)) basedon +10% and +20% variation in geometric statistical properties of soil particles sg and bulkdensity of the soils rb relative to the original values. The values of sg and rb have changedsimultaneously.
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at lower soil compaction rates, soil texture and specially clay fraction play animportant role on Ks
� (Nakano and Miyazaki, 2005). Zhuang, Nakayama et al.(2000) has also reported the complicated task of modeling clayey soils and arguedthat this could be the result of neglecting the soil structure in modeling.
Validation of the scaled model
Figure 4 shows the results of predictions of Ks based on the new scaled model(Equation (14)) on the validation dataset (Table 1). It shows that the scaled modelmay reasonably predict Ks in different soil textures. Overall, the validation showsthat the scaled model overestimates the Ks by*18%. This amount of overestimationis acceptable while it is highly believed that spatial variations of Ks are considerableover a studied area (Sepaskhah and Ataee 2004). Therefore, to increase the accuracyof the scaling factors for prediction of Ks, it is suggested that the empirical scalingfactors should incorporate spatial-sensitive parameters, and this would result inpredictions of Ks closer to the measured values (Ahuja et al. 1984) and large spatialvariations are diminished. Zhuang et al. (2001) found overestimation of 10–100 timesthe measured value which clearly shows that Ks modeling is not a straightforwardprocess and there might be other soil physical and chemical factors that influence it.
In order to have a reasonable representative value(s) of Ks over large areas, alarge number of Ks measurements over the area are required to reduce the impact ofspatial variability. However, measurement of Ks is costly and time-consuming,whereas measurement of rb is easy and quick. Therefore, the proposed scalingmethod is useful and applicable in areas where primary and accurate knowledge ofsurface and subsurface Ks is required for practical purposes, for example designingtile drainage spacing in extensively tilled areas, or designing surface or sprinklerirrigation systems based on the final infiltration rate (ffiKs). Nevertheless, if there isno measured data for Ks and the scaled models are used for such practical matters, itis wiser to adapt some degrees of confidence in order to prevent any economic loss.Therefore, using the new scaled model automatically includes confidence due to itsoverestimation.
Figure 4. Validation of the new scaling model on different datasets and its comparison withthe NSMC and SMC models.
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Comparison of the new empirical-based scaled model with the SMC and NSMC models
The empirical-based scaled model (new model) is compared with the SMC andNSMC models over the pooled validation dataset (Figure 4). The new scaled modeloverestimates Ks by *18% and the NSMC model underestimates Ks by *21%. TheRMSE values for both models are almost identical (Table 2). It appears that in termsof errors in predictions (RMSE), the empirical-based model and NSMC model aregenerally similar. However, it should be kept in mind that their practical use mightbe different. Ks values are frequently used in designing irrigation and drainageprojects and using inappropriate values may impose extra costs. For example, if theoverestimated values of Ks (new model) are used, the spacing between the drainsincreases which decreases the installation costs but may ultimately cause water-logging conditions that harm the crops. By contrast, using the underestimated valuesof Ks (NSMC model) will increase the installation costs of drains. Therefore, it isrecommended to use the new or NSMC model in appropriate circumstances.
It is also clear that the SMC model is a very poor predictor of Ks and fails topredict it. Failure of the SMC model (Campbell 1985) in predicting Ks comparedwith the other models has also been reported previously (Miyazaki 1996; Zhuang,Nakayama et al. 2000; Nakano and Miyazaki 2005; Rahimi-Adregani et al.forthcoming 2011). In the SMC approach, soils in a field or different fields areassumed to be similar (Miyazaki 1996), whereas in the real world the non-similarityof the actual soils limits the applicability of the SMC analysis.
Miyazaki (1996) mentioned that the reliability and applicability of the NSMCmodel depend on the correct determination of the shape factor. The advantage of thenew scaled model over the NSMC model is that none of its components carries anyuncertainties and all are physically determined. It should be kept in mind that thenew scaled model is actually a type of NSMC model, although the shape factor isreplaced by the easily measurable geometric statistical properties (i.e, dg and sg).However, it is suggested that the new scaled model might be improved by includingother important factors such as organic matter and soil architecture (Zhuang,Nakayama et al. 2000).
Zhuang, Nakayama et al. (2000), Nakano and Miyazaki (2005), and Rahimi-Adregani et al. (Forthcoming 2011) compared different scaling models in predictingKs for compacted soils under tilled and un-tilled conditions. They suggested that theNSMC models were most reliable in predicting Ks compared with the SMC models.
Table 2. The RMSE values for comparison between the newly proposed scaled, non-similarmedia concept (NSMC), and similar media concept (SMC) models in the validation step.
Source Soil texture Scaled NSMC SMC
Nakano and Miyazaki (2005) Clay loam (untilled) 0.002 0.002 0.017Miyazaki (1996) Light clay (treated as tilled) 0.005 0.004 0.072Miyazaki (1996) Loamy sand (treated as tilled) 0.000 0.000 0.001Rahimi-Adregani et al.(Forthcoming 2011)
Silty clay loam (tilled) 0.001 0.001 0.016
Rahimi-Adregani et al.(Forthcoming 2011)
Silty clay loam (untilled) 0.002 0.002 0.015
Rahimi-Adregani et al.(Forthcoming 2011)
Loam (tilled) 0.006 0.004 0.074
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However, these studies reported various results about the applicability of the NSMCmodel on different soil textures. While Zhuang and colleagues (Zhuang, Nakayamaet al. 2000; Zhuang et al. 2001) reported that the NSMC model held true for sandand loam soils, Miyazaki (1996) reported that NSMC was successful for all range ofsoil textures, both aggregated and dispersed. Another contrasting report is that ofNakano and Miyazki (2005) who found that NSMC models are poor in predictingKs in the tilled topsoil, but Rahimi-Adregani et al. (Forthcoming 2011) found acontrasting result and attributed these inconsistencies to the different soil types,calcium ion concentration, and clay minerals composition of the soils.
Data concerns in scaling methods
In general, experimental data that relate the impact of increasing soil bulk density onsoil hydraulic properties are quite scarce (Assouline et al. 1997; Moret and Arrue2007). However, we were able to find additional data for validation purposes in therecent studies of Miyazaki (1996), Nakano and Miyazaki (2005), and Assouline(2006).
An important concern in study and similar studies is that the investigated dataoriginate from diverse literatures and, therefore, are subjected to systematic errorsresulting from different measurement methods (e.g. methods of calculating Ks,method of compaction), different soil structures having similar textures, andaccuracy of data presentation. Similarly, mineralogy of clay soils (Benson and Trast1995), initial soil moisture content (Benson and Trast 1995; Lipiec and Hakansson2000), and method of soil compaction (Benson and Trast 1995) all affect the resultsof the compaction tests. It is worth mentioning that Benson and Trast (1995)revealed that the Atterberg limits (liquid limit, plastic limit and plasticity index)correlated well with hydraulic conductivity. Therefore, it is concluded that the soilhydraulic properties models may show different responses to the datasets when claycontent constitutes a major part of the soil texture. In most Ks modeling studies suchfactors are neglected and it is recommended that they be incorporated to improve themodeling performance in future studies.
The new scaling model is applicable to predict the spatial and temporal variationsin Ks over an entire soil profile that is subjected to soil compaction; whether byextensive tillage (Assouline et al. 1997) or natural consolidation in untilled soils(Ahuja et al. 1998). Nakano and Miyazaki (2005) recommended that the study of theeffect of soil compaction on Ks should focus on soil types that have identical soilparticles, clay minerals, total nitrogen and carbon. Accordingly, a primaryassessment (data not shown) of the new scaling model on the data of UNSODA(Nemes et al. 1999) revealed that the observed pairs of (rb, Ks) should be measuredon a specific compacted soil type under tilled or untilled conditions. Zhuang et al.(2001) did not find satisfactory results in modeling Ks and Kus of diverse data inUNSODA database. This was probably because the soil structure (pore size, shape,and orientation) of similar soil textures varies greatly in different locations and suchdifferences are not yet included in the scaling factors. In a recent study, Sadeghi andGhahraman (2010) reported that for improving the scaling process of Ks, not only issimilarity in soil structure necessary, but also soil-water retention characteristicsshould be similar. Therefore, this remains a challenging issue in the prediction of Ks
that should be considered in future research studies to improve the accuracy of Ks
models (Zhuang, Nakayama et al. 2000, Zhuang et al. 2001).
1314 S.H. Ahmadi and A.R. Sepaskhah
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Conclusion
In this study, a new empirical-based scaling method is proposed for predicting Ks.The scaling factor for Ks incorporates the geometric statistical parameters of soilparticles, i.e. geometric mean particle size diameter, dg, and geometric standarddeviation, sg. The proposed scaling method is an improvement and justification ofthe former non-similar media concept (NSMC) models for predicting Ks. The newscaling method relies on different datasets including compacted soils under tilled anduntilled conditions. Results showed that the new scaling model can be used reliablyin different conditions to predict Ks in compacted tilled and untilled soils. Whereasthe new scaling model overestimated Ks by 18%, the NSMC model underestimatedKs by 21%. The advantage of the new empirical-based model compared with theNSMC is that there is no shape factor in the scaling factor, which bears some levelsof uncertainty. However, using either the empirical-based or NSMC models topredict Ks depends on the type of the study. It was also found that the SMC modelwas not satisfactory in predicting Ks compared with the new scaling model andNSMC. It is recommended that the new scaling model should be evaluated based onnew data of other locations in order to extend its validity. Our evaluation was basedon available data in the literature, which holds primary data specifications applied inthis scaling method.
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