Introduction
Soil organic matter, soil structure and the porous system are key attributes of the regulation of water flow, nutrient supply, contaminants adsorption and desorption, and leaching losses as well as gas emissions (^{Bronick and Lal, 2005}; ^{Clothier et al., 2008}; ^{Dexter, 2004a)}. Soil structure conditions influence the pore size distribution that can be described by means of the soil water retention curve (WRC). Pores draining up to the inflection point of the WRC are structural pores whereas the remainder correspond to textural pores, which are conditioned by soil microstructure (^{Dexter, 2004a}). This author suggested using the S index to quantify soil structural quality and demonstrated that it can be used when assessing soil management practices, as it identifies areas of degradation or improvement in the soil physical conditions (^{Dexter, 2004a},^{b},^{c}; ^{Dexter and Czyz, 2007}).
Other indicators have been suggested by ^{Reynolds et al. (2009)} to express either directly or indirectly the state and/or function of porous space: macroporosity, porosity in the matrix domain, air capacity, air capacity in the soil matrix, plant available water capacity, and pore fraction with a diameter, identified either as less or more than 30 µm. By using these indicators they determined an “optimal” pore size distribution, allowing them to study various combinations of soil management practices. Additionally, they characterized pore distribution curves by mode, mean, median, skewness, dispersion and kurtosis. The authors concluded these indicators, together with the S index, are very useful for quantifying the physical properties of rigid or moderately expansive agricultural soils.
In the Mollisols of Santa Fe, one of the main productive regions in the humid Pampas in Argentina, neither were the above mentioned indicators studied nor a WRC of reference determined, both of which could have been used to distinguish which management techniques promote the improvement or degradation of soil. Due to the importance of establishing these indicators, the aims of this study were: (i) to determine indicators of the state and function of the porous system, (ii) to use them to derive a global index to characterize the soil physical quality, and (iii) to establish a reference poresize distribution curve for Argiudolls and Hapludolls of the province of Santa Fe, (Argentina).
Materials and Methods
For this study, Argiudolls and Hapludolls representative (^{INTA, 2014}) of those found in the province of Santa Fe (Argentina), with wide variations in texture, organic matter content (OM) and bulk density (ρ_{b}), were selected (Figure 1, Table 1). For each soil, different soil management conditions were studied so that considerable variability in soil physical properties would be obtained. In each case, disturbed soil samples were collected and used to determine organic carbon by Walkley and Black’s method (^{Jackson, 1982}) which were converted to OM by multiplying by 1.724. Particle size and particle density (ρ_{p}) analyses were carried out by the Bouyoucos hydrometer and pycnometer methods according to ^{Gee and Bauder (1986)} and ^{Blake and Hartge (1986a)}, respectively.
OM  Sand  Silt  Clay  ρ_{b}  


g kg^{−1} 

Mg m^{−3}  
A horizons  Mean  26 (27.0)  120 (123.6)  577 (21.3)  236 (23.6)  1.33 (4.7)  
Maximum  40  725  766  340  1.46  
Minimum  10  34  156  119  1.09  
B horizons  Mean  13 (48.0)  109 (99.0)  509 (13.8)  337 (25.8)  1.41 (2.4)  
Maximum  31  372  634  538  1.49  
Minimum  5  26  389  224  1.35 
Values between parentheses are the respective coefficients of variation in percentage. Classification of soil particles according to the United States Department of Agriculture (USDA).
Undisturbed soil samples with stainless steel 100 cm^{3} cylinders (diameter 5 cm and height 5 cm) were collected at each sampling site to determine the WRCs of A (n = 30) and B (n = 30) horizons. These samples (n = 780) were submitted to the following water potentials: 10, 20, 30, 40, 50, 60, 80, 100 cm of water column in a tension table, and 600, 1,000, 3,000, 6,000 and 15,000 cm of water column in a Richards’ pressure chamber (^{Klute, 1986}). Then, the samples were ovendried and used to determine the ρ_{b}(^{Blake and Hartge, 1986b}). WRCs that cover at least a range of tension from 10 to 15,000 cm of water column can be used to analyze structural and textural porosity, and consequently the structural condition of the soils (^{Dexter et al., 2008}). This approach was adopted in this study.
Water content data on mass and volume bases were adjusted to equation (1) (van ^{Genuchten, 1980}) by using the RETC program Version 6.0 (van ^{Genuchten et al., 2007}).
where: θ_{gs} is the gravimetric saturation water content (kg kg^{−1}); θ_{gr} is the gravimetric residual water content (kg kg^{−1}); α is inversely related to the bubbling pressure, (cm^{−1}), n and m = (11/n) are adjustment parameters and h is the absolute value of the matric potential. Then, subscript “v” will be used to indicate volumetric water content and differentiate it from subscript “g” which stands for gravimetric water content.
WRCs, both in their gravimetric and volumetric form, were normalized, by using equation (2).
Θ being the normalized water content, also called the effective saturation.
From these curve indicators suggested by ^{Reynolds et al. (2002)}, Dexter (2004a) and ^{Reynolds et al. (2009)} namely: pore size distribution curve, S index (S_{gi}), macroporosity (POR_{p}), porosity of the soil matrix domain (POR_{m}), air capacity (AC_{t}), air capacity of the soil matrix (AC_{m}), plantavailable water capacity (PAWC), diameter pore fraction less (FC/POR_{t}) or more (AC_{t} /POR_{t}) than 30 µm were determined.
Pore volume distribution curve
The porevolume distribution curve for each soil was calculated from the first derivative of equation (1) using the volumetric water content, θ_{v} (m^{3} m^{−3}), versus ln(h), and plotted against the equivalent pore diameter (d_{e}), on a log_{10} scale (Equation 3). The effective pore diameter was described by the equation of capillarity (^{Libardi, 2005}), as shown in equation (4), and was used to describe the pore volume distribution function
where: S_{v}(h) is the slope of the soil WRC as a function of tension (h); γ = 72.8 gm s^{−2} the surface tension of water, ω≈0 the waterpore contact angle, ρ_{w}= 0.998 g cm^{−3} the water density and g = 980 cm s^{−2}the gravitational acceleration.
To make the curves comparable, the normalized pore distribution S*(h) was obtained by dividing S_{v}(h) by S_{vi}:
where: S_{vi} is the slope of the tangent at its inflection point which was calculated in the soil WRC, S_{vi}(h), using equation (6):
Poresize frequency curves were compared by using measurements of the central tendency and the spread of the curves (^{Reynolds et al., 2009}). Measurements of the central tendency of each evaluated pore frequency distribution curve were the median (d_{median}) and the mode (d_{mode}) calculated as:
Also the geometric mean (d_{mean}), standard deviation (SD), skewness and kurtosis of the pore frequency distribution curves were studied as presented in equations 9, 10, 11 and 12.
Dexter's Sgiindex
By using soil WRCs adjusted to the gravimetric water content the S_{gi} index was calculated as suggested by ^{Dexter (2004a)}. For that purpose equation 6 was used and the soil water potential at the point of inflection of each curve (h_{gi}) was determined as:
Macroporosity and Porosity of the Soil Matrix Domain
Macroporosity (POR_{p}, m^{3} m^{−3}), corresponding to pores more than 300 µm in diameter (^{Dexter and Czyz, 2007}; ^{Dexter et al., 2008}), was calculated as:
where: POR_{t}= (1ρ_{b}/ρ_{p}) is the total soil porosity calculated (m^{3} m^{−3}) and θ_{10} the volumetric water content corresponding to the tension of a 10 cm water column (m^{3} m^{−3}). Porosity in the domain of the soil matrix (POR_{m}, m^{3} m^{−3}), corresponding to soil water content with pores less than 300 µm in diameter was estimated by using soil WRCs:
Although there is no agreement in the literature about the best value for distinguishing macropores from matrix pores (^{Perret et al., 1999}; ^{Chen et al., 1993}), we used the selected pore diameters due to the water and air storage characteristics which are very different. Thus, these pore sizes can be used for distinguishing different soil quality conditions (^{Reynolds et al., 2002}).
Air Capacity and Air Capacity of Soil Matrix
Air capacity (AC_{t}, m^{3} m^{−3}) was estimated from the total porosity calculated from θ_{100;}the volumetric water content corresponding to the tension of a 100 cm water column.
Soil matrix air capacity was calculated by the equation:
AC_{m} is the porosity corresponding to pores more than 30 µm and less than 300 µm in diameter.
Plantavailable water capacity
For this purpose field capacity values (FC) were estimated, considering them as volumetric water content at a tension of 100 cm, and the permanent wilting point (PWP), was estimated as volumetric water content at a tension of 15,000 cm. Plantavailable water capacity (PAWC) was estimated as: PAWC = FCPWP (^{Veihmeyer and Hendrickson, 1949}). Finally the pore fraction with a diameter less (FC/POR_{t}) than and the pore fraction with a diameter more (AC_{t}/POR_{t}) than 30 µm were calculated as indicated by ^{Reynolds et al. (2002)}.
The tension of 100 cm was used to define the field capacity water content due to pores with diameters < 30 µm and are considered as storage pores that contain water available for plants. In addition, these pores are influenced by texture and organic C content but not by increases in soil bulk density (da ^{Silva and Kay, 1997}; ^{Kay and Angers, 2000)}.
Structural stability index
The risk of structural degradation was assessed by the “structural stability index” (SI) (^{Reynolds et al., 2009}) calculated as:
where: OM is the organic matter content (g kg^{−1}); clay and silt are granulometric fractions (g kg^{−1}).
Global Index of soil physical quality
An index with a range between 0 and 1 was assigned to each attribute (OM, ρ_{b}, S_{gi}, AC_{t}, POR_{p}, PAWC, FC/POR_{t} and SI) according to the value obtained for each horizon. A value of 1 stands for the optimal condition for the attribute and 0 for the most limiting condition. As the value decreases, the condition becomes more unfavorable. The indexes between 1 and 0 were established taking into account the reference values mentioned in the literature for each parameter (^{Reynolds et al., 2009}). Once all indexes were obtained, they were summed to produce the horizon score considering 8 as the maximum value, whereby eight attributes with an index of 1 each equals 100 %.
Five horizons with the highest score were used to draw an average WRC considered as an “average reference curve” for horizons with good structural quality. Additionally, the confidence interval for each normalized water content (Q ± s) was calculated, generating a curve with minimal values and another with maximal values. For each one of these two curves d_{mean}, d_{mode}, d_{median}, SD, skewness and kurtosis parameters were determined, establishing a reference interval used to describe the shape of the curves and the pore frequency distribution of the horizons studied.
Relationships between indicators were studied using linear regression models in which the coefficient of determination (r^{2}) and statistical significance (p< 0.05) of the correlation were evaluated. In order to verify whether granulometric fractions, ρ_{b} and OM content affected S_{gi}values, a multiple regression analysis was carried out using a “stepwise” selection procedure (SAS, Statistical Analysis System, version 5.0, 1991). Analogously the relationship between structural quality index, SI, with ρ_{b}, POR_{t}, S_{gi}, POR_{p}, POR_{m}, AC_{t}, AC_{m}, FC, PWP, PAWC, FC/POR_{t} and AC_{t}/POR_{t}was analyzed.
Results and Discussion
Soil physical quality indicators
Only 14 A horizons showed values between 30 and 50 g kg^{−1} organic matter. All others presented lower values. Despite the wide particle size variation in the soils studied, an increase in ρ_{b} was observed when OM decreased (Figure 2).
Soil bulk density in A horizons was lower than the critical density estimated according to ^{Daddow and Warrington (1983)}, even when various researches have demonstrated that small ρ_{b}increases can cause root growth reductions even if they are below the critical limit. Total porosity of the soil (POR_{t}) was between 0.432 and 0.567 m^{3} m^{−3}. When analyzing air capacity (AC_{t}) corresponding to pores with diameters more than 30µm diameter, the low values observed, especially in the B horizon, indicated evidence of the difficulties of these soils in terms of fluid flows. This indicator suggests the existence of reduced air volume to be used after heavy rainfall and confirms aeration problems found in different studies in the least limiting water range (^{Damiano and Moschini, 2011}; ^{Miretti et al., 2010}).
Macroporosity (POR_{p}) was low. The POR_{p} geometric mean of all values in A horizon was 0.032 m^{3} m^{−3} and in B horizons 0.010 m^{3} m^{−3}. Considering the optimal value of 0.07 m^{3} m^{−3}(^{Reynolds et al., 2009}), in 42 cases, values were below this index and in 31, lower than 0.04 m^{3} m^{−3}. Thus, in the soils studied the capacity to rapidly drain excess water and allow for root proliferation is not optimal due to the high content of silt or clay, the low sand content and the presence of occluded pores that are typical of the matrix in these soils (^{Taboada et al., 2008}).
Physical quality degradation in these soils exacerbates these problems as evidenced in Argiudolls and Hapludolls irrigated with sodicbicarbonated waters and in Argiudolls when conventional tillage or notill systems were applied without the inclusion of adequate rotations (^{Pilatti et al., 2006}; ^{Ghiberto et al., 2007}; ^{Imhoff et al., 2010}).
Small pore predominance was exhibited when evaluating the pore fraction of pores with less (FC/POR_{t}) and more (AC_{t}/POR_{t}) than 30µm diameters. Only in 13 cases, all in the A horizon, did FC/POR_{t} show values between 0.6 and 0.7. In 43 of all 60 cases this indicator was over 0.7 evidencing aeration and nitrate production problems due to the scarce amount of more than 30µm diameter pores present (^{Reynolds et al., 2002}). The effect was noticeable in B horizons and both parameters presented a correlation with ρ_{b} as shown in Figure 3.
S_{gi} indicator variations ranged between 0.024 and 0.077 in A horizons and between 0.021 and 0.049 in B horizons (Table 2). Considering that the structural stability index SI > 9 % indicates a stable soil structure, 7 % < SI < 9 % a low degrading risk, 5 % < SI < 7 % a high degrading risk, SI < 5 % structurally degraded soils (^{Reynolds et al., 2009}) , in 52 out of the 60 cases the value was SI < 5 %. This situation is a consequence of the high silt and clay content and the low organic matter proportion in the soils studied. On the other hand, SI was 10.8 when silt and clay content were 156 and 119 g kg^{−1} respectively; this Hapludoll representing an extreme case among all soils analyzed because of its granulometry (sandy loam). Based on these considerations, the S_{gi} index was shown to be consistent with the results obtained, showing higher values with an increase in SI.
POR_{p}  AC_{t}  PAWC  FC/POR_{t}  SI  S_{gi}  


m^{3} m^{−3} 

%    
A Horiz.  Mean  0.03  0.12  0.20  0.73  3.2  0.039  
Max.  0.09  0.19  0.31  0.89  10.8  0.077  
Min.  0.00  0.05  0.14  0.63  1.1  0.024  
B Horiz.  Mean  0.01  0.06  0.18  0.83  1.5  0.030  
Max.  0.07  0.16  0.28  1.05  4.6  0.049  
Min.  0.00  0.02  0.12  0.65  0.5  0.021  
 
Reference Values ^{(†)}  > 0.07(1)  > 0.15(1)  > 0.2(1)  0.60.7(1)  > 9.0(1)  > 0.05(1)  
0.070.04(0.5)  0.150.10(0.5)  0.150.2(0.7)  7.09.0(0.7)  0.0350.05(0.7)  
< 0.04(0)  < 0.1(0)  0.10.15(0.3)  7.05.0(0.3)  0.020.035(0.3)  
< 0.1(0)  < 5.0(0)  < 0.02(0) 
POR_{p}: macroporosity; AC_{t}: air capacity; PAWC: plantavailable water capacity; FC/POR_{t}: diameter pore fraction lower than 30 µm; SI: structural stability index; S_{gi}: S index. (†): Values between parentheses indicate the score assigned to the property in each horizon.
Taking into account the global index obtained for each horizon from OM, ρ_{b}, S_{gi}, AC_{t}, POR_{p}, PAWC, FC/POR_{t} and SI attributes, horizons could be organized into four groups presenting the following general characteristics.
Group 1  With a score above 70 %, horizons show more than 15 % higher than 30 µm (AC_{t}) diameter pores and macroporosity (POR_{p}) higher than 7 %. The FC/POR_{t} index is between 0.6 and 0.7, which ensures a proper balance between air and water supply. In these cases OM content ranged from adequate to optimal and was associated with good structural stability rates (SI). S_{gi} was between 0.035 and 0.05, indicating good physical quality. In soils with a high sand content and without a good capacity for water retention values were S_{gi} > 0.05.
Group 2 Scoring between 50 and 70 %, AC_{t} continued at levels above 15 % but POR_{p} levels were lower than in the previous group, with values between 4 and 7 %. Horizons in this group appear to undergo structural degradation, a situation probably originated by the decrease in OM associated with the high silt content that is characteristic of the parent material of the Mollisols studied.
Group 3 With a score below 50 %, their AC_{t} is lower than 15 % and their POR_{p} below 4 %, evidencing serious problems of air supply and water percolation.
Group 4  B horizons have less than 10 % higher than 30 µm diameter pores and less than 4 % higher than 300 µm higher diameter pores, except for some horizons with over 15 % sand, the score being approximately 40 in these cases. For A horizons to surpass a score of 40 they should have approximately 3 % OM and lower than 1.3 Mg m^{−3}ρ_{b,} to compensate for the increased silt content in those horizons. Soils presenting B horizons with a score of about 40 (the highest one obtained in B horizons) would be the most productive ones and would be characterized by having a higher sand content and lower silt content than the rest, which seems to compensate for the lower OM content in A horizons of a similar score.
Water Retention Curves
Normalized water retention and pore distribution curves corresponding to A and B horizons of Mollisols were studied together with the reference curve (Figure 4). The reference curve of A and B horizons was fitted to α = 0.053 cm^{−1}, n = 1.1988 and m = 0.1658 parameters, and was characterized by the values of d_{mode} that occurred at 72 % of saturation and a tension of h = 84.5 cm, d_{median} that took place at 50 % saturation and h = 609 cm, and d_{mean} with h = 1,544 cm. As described by ^{Blott and Pye (2001)} this distribution is “extremely poorly sorted” (i.e. very large range in equivalent pore diameters, SD > 16), “very fine skewed” (great excess of small equivalent pore diameters relative to a lognormal distribution, Skewness < 0.3), and “mildly leptokurtic” (slightly more peaked in the center and more tailed in the extremes than a lognormal distribution, Kurtosis = 1.11–1.50).
The values of skewness and kurtosis of the curves of the four soil groups were similar to the values of the reference curve (Table 3), but as physical quality becomes poorer, the characteristic pore diameter decreases. In particular, in Groups 3 and 4, central tendency measurements are outside the reference range indicating the existence of physical quality problems in these groups’ horizons. These problems can also be inferred from Figure 4 where, especially for B horizons, in which for the same potential, soils present a higher effective saturation degree than in the reference curve. This is directly related to the higher amount of lower diameter pores and consequently, to aeration and drainage problems.
Parameter  d_{median}  d_{mode}  d_{mean}  SD  Skewness *  Kurtosis 


µm 


Group 1: Value >70  4.6  49.3  1.5  84.9  0.40  1.14 
Group 2: Value 5070  3.7  32.4  1.3  118.9  0.39  1.14 
Group 3: Value < 50  2.2  21.2  0.8  73.5  0.39  1.14 
Group 4: B Horizons  0.5  14.1  0.1  103.1  0.42  1.13 
 
Reference Range^{†}  3.4 – 6.8  31 – 39  1.2 – 3.0  68.7 – 145.4  0.40 – 0.38  1.14 – 1.15 
The values are the geometric means of the soils of each group, *arithmetic mean. ^{†}Calculated starting from the confidence interval of the reference curve(Q ± s), being the adjustment parameters for generating the minimum values α = 0.0545 cm^{−1}, n = 1.2174, m = 0.1786 and the maximum values α = 0.05143 cm^{−1}, n = 1.18175, m = 0.1538.
The reference curve can be also used to calculate effective saturation values at various matrix potentials (equation 2). Considering the average of five soils with higher scores of bulk density and particle density of 1.24 Mg m^{−3} and 2.55 Mg m^{−3} respectively, calculated POR_{t}would be 0.514 m^{3} m^{−3}. These were the values used to calculate POR_{p}. For this purpose the value of effective saturation was determined at h = 10 cm which, multiplied by total porosity, was equal to 0.035 m^{3} m^{−3}. Similarly, AC_{t} was determined, being 0.153 m^{3} m^{−3}, FC 0.361 m^{3} m^{−3}, PWP 0.136 m^{3} m^{−3} and PAWC 0.225 m^{3} m^{−3}. The pore fraction, having a pore diameters lower (FC/POR_{t}) than 30 µm, would be 0.7 and the one higher (AC_{t} /POR_{t}) than 30µm diameter would be 0.3. These values are within the range mentioned by other authors (^{Orellana and Pilatti, 2000}; ^{Pilatti et al., 2012}; ^{Reynolds et al., 2002}; ^{Reynolds et al., 2009}) and represent useful indicators for guiding sustainable soil management.
Conclusion
Porosity in the macropore domain was low. A small decrease can, in this domain, cause severe physical restrictions in soils with a high silt percentage. Then, the capacity to rapidly drain water excesses and allow for root proliferation is not optimal due to the high silt or clay content, in A and B horizons respectively, and the low sand content which are characteristic of the matrix of the soils studied.