# Prediction of the soil saturated paste extract salinity from extractable ions, cation exchange capacity, and anion exclusion.

IntroductionThe saturated paste extract is the universal standard solution for soil salinity appraisal (Rhoades et al. 1999). However, 1: 5 soil to water (w/v) extracts are used in many instances instead for the same purpose (Rayment and Lyons 2011). Furthermore, the 1: 5 extracts have also been proposed for soil dispersion assessment instead of saturated paste extracts (Rengasamy et al. 1984; Sumner et al. 1998). The saturation extract is obtained from a soil saturated paste, preparation of which is time and labour intensive. It has escaped laboratory automation, firstly because the saturation water content is, in general, difficult to predict--it depends on several soil properties, mainly texture, clay mineralogy, and organic matter content, and therefore, the saturation point has to be empirically determined; and secondly because, during water addition and mixing, the consistency of the soil paste changes from solid, to semi-solid, to plastic, which would demand laboratory machinery that is heavier than usual to stir the sticky semi-fluid mass.

The 1: 5 suspension, having a fixed soil to water ratio and a liquid consistency, is more readily prepared and extracted than the saturated paste. However, the water content in the 1:5 extract is usually 15-50 times greater than that of the field-moist soil. The saturated paste, although time and labour intensive, provides soil moisture content only 1.5-5 times field moisture levels. This makes saturated paste extract more representative of the soil solution than the 1: 5 extract.

An optimum method for soil salinity and dispersion appraisal should have the advantages of the preparation of the 1:5 suspension, and provide the information of the saturated paste extract. Such a method has been sought by several researchers (Sonmez et al. 2008; Chi and Wang 2010) through the following methodology: (i) obtain saturation and 1:5 extracts from the same set of soil samples; (ii) determine the relevant properties for salinity and dispersion assessment in both extracts, basically the electrical conductivity at 25[degrees]C ([EC.sub.25]), main ion concentrations, and sodium adsorption ratio (SAR); (iii) calibrate predictive equations usually by simple linear regression of the property of the saturated paste extract of interest on the corresponding property of the 1:5 extract; (iv) obtain and analyse 1:5 extracts from the soils to be tested; and (v) predict their saturated paste extracts properties using the regression equations.

The use of 1: 5 extracts to assess soil salinity and dispersion following this methodology can be, however, very misleading when the calibration set and the soil samples to be tested have significantly different water contents at saturation, and when there are soil samples with gypsum in the calibration and/or testing sets (Visconti et al. 2010a). To overcome these limitations, the regression equations have been improved by including other predictor variables, mainly the water content at saturation (Slavich and Petterson 1993), and/or developing different regression equations depending on gypsum presence and absence (Khorsandi and Yazdi 2011). Despite these improvements, the confidence intervals (95%) to predict the [EC.sub.25] and SAR of the saturated paste extracts using regression equations are seldom lower than [+ or -] 1 dS [m.sup.-1] and [+ or -] 1 [(mmol [L.sup.-1]).sup.1/2], respectively, which give average relative standard deviations not lower than 20 and 13%. These errors are large enough to prevent the use of regression equations in applications demanding more than an estimate.

Process-based models could be an alternative to regression equations in order to achieve lower prediction errors. For example, Rieu et al. (1998) designed a model to calculate the soil solution and exchange complex equilibrium composition at different water contents. It was specifically tested to simulate the dilution and concentration of the soil solution between saturation and the 1:5 soil to water ratio, giving promising results. Analytical data requirements to predict the saturated paste extract composition included, in addition to the main ion concentrations in the 1:5 extract, the C[O.sub.2] partial pressure, calcite and gypsum contents, cation exchange capacity (CEC), and the extractable contents of soil cations. However, whether all of these data are necessary and sufficient to make accurate enough predictions with this type of model has not been investigated.

The objective of this work was to find out the minimum set of hypotheses, and thus data, that process-based models need to make reliable enough predictions of saturated paste extract main ion composition, and therefore [EC.sub.25] from extractable ion contents, which are obtained from 1: 5 extracts for anions and ammonium acetate extracts for cations.

Materials and methods

Study area and sampling

Soil sampling was carried out in the irrigated agricultural area of the Segura River Lowland (Vega Baja del Segura-Baix Vinalopr) in SE Mediterranean Spain. The soils are cbaracterised by high calcium carbonate equivalent contents, are medium to very low in organic matter, medium- to fine-textured, base-saturated, non-sodic, slightly to moderately saline, and non-gypsiferous with some exceptions. These irrigated soils are mostly classified as Xerofluvents (Soil Survey Staff 1999) or Calcaric Fluvisols/Haplic Calcisols (FAO 1998). In total, 39 points were sampled. At each sampling location, two, three, or four samples were taken at four depths (0-10, 10-30, 30-65, and 65-95cm). The soil samples were air-dried, ground, and sieved through a 2-mm mesh sieve in the laboratory. More details about the study area, soils, and sampling can be found in Visconti (2009).

Obtainment and analysis of soil water extracts

In total, 133 soil samples were used in this study. The water used to prepare all extracts had an [EC.sub.25] [approximately equal to] 1 [micro]S [cm.sup.-1]. Soil saturated paste extracts were prepared and obtained according to the method of Rhoades (1996), with the only stipulation that no sodium hexametaphosphate was added to the extract. The gravimetric water content at saturation was determined on a paste subsample by means of oven-drying at 105[degrees]C. The 1:5 suspensions were prepared by adding 60 mL of water to 12 g of soil, and were shaken for 24 h. The extracts were obtained by centrifugation at 1400[g.sub.N] for 10 min. The solutions were then decanted and filtered.

The [EC.sub.25], pH, and alkalinity of all the extracts were determined within 2 h of collection. The [EC.sub.25] was measured with a Crison microCM 2201 conductivity meter (Crison Instruments SA, Barcelona, Spain) with a temperature probe and standard conductivity cell constant of 1.1 [cm.sup.-1], which was checked every day with a traceable KCl standard solution of 1413 [micro]S [cm.sup.-1]. The pH was measured with a Crison GLP22 pH meter (Crison Instruments SA) that was previously calibrated every day with traceable standard solutions of pH 7.02 and 9.21. The alkalinity was determined by potentiometric titration with location of the equivalence point according to the Gran (1952) methodology. Both the saturated paste and 1:5 extracts were analysed for sodium ([Na.sup.+]), potassium ([K.sup.+]), magnesium ([Mg.sup.2+]), calcium ([Ca.sup.2+]), ammonium (N[H.sub.4.sup.+]), sulfate (S[O.sub.4.sup.2-]), chloride ([Cl.sup.-]), nitrite (N[O.sub.2.sup.-]), and nitrate (N[O.sub.3.sup.-]) within 4 days of extract collection. Both anions and cations were detected and measured by ion chromatography in a Dionex DX-120 ion chromatograph (Dionex Corp., Palo Alto, CA, USA) with conductivity cell detector. More details about the obtainment and analyses of soil water extracts can be found elsewhere (Visconti 2009; Visconti et al. 2010b). The complete dataset used in this study can be found in Visconti (2009).

Determination of cation exchange capacity and soil cations

The CEC was analysed by the 'displacement after washing' method of Chapman (1965), which uses: (i) sodium acetate 1 M at pH 8.2 to saturate the exchange complex, (ii) ethanol to wash of excess saturating solution, (iii) ammonium acetate 1 M at pH 7 to displace sodium, and (iv) determination by atomic absorption spectrometry (AAS). Extractable [Na.sup.+], [K.sup.+], and [Mg.sup.2+] contents soil were obtained by five sequential ammonium acetate 1 M extractions, followed by AAS determination (Visconti 2009).

The exchangeable contents of [Na.sup.+], [K.sup.+], and [Mg.sup.2+] at water saturation ([m.sub.EXCi]([[theta].sub.sat])) were determined by subtracting the saturated paste extract cation contents ([m.sub.SSi]([[theta].sub.sat])) from extractable contents ([m.sub.Ti]). This calculation was carried out with Eqn 1 where [[theta].sub.sat] is used to indicate that the properties were determined at the saturation water content.

[m.sub.EXCi]([[theta].sub.sat]) = [m.sub.Ti] - [m.sub.SSi]([[theta].sub.sat]) (1)

Since the soils are calcareous and some contain also significant amounts of gypsum, the soil exchangeable [Ca.sup.2+] content was determined by subtracting the sum of exchangeable cations [Na.sup.+], [K.sup.+], and [Mg.sup.2+] from the CEC.

Reporting of results

All mean values in this study have been reported as the 95% confidence interval for the mean (mean [+ or -] standard error x [t.sub.0.05]).

Assessment of prediction errors

The standardised difference (S[D.sub.i]) between the observed value ([O.sub.i]) for a property in the replicate i of the system being simulated, that is the soil samples, and the corresponding model prediction ([P.sub.i]) was calculated with Eqn 2:

S[D.sub.i] = ([O.sub.i]- [P.sub.i])/([O.sub.i] + [P.sub.i]) (2)

The properties of the SD are listed elsewhere (Visconti 2009). The most important are that it is dimensionless, is bounded within the interval [-1, 1], and is normally distributed more frequently than the residual difference [O.sub.i] - [P.sub.i]. The SD was used in this investigation to compare observations and model predictions. The Student's t-test for the mean SD of each property was used as criterion for model validation. Other classical validation parameters (Loague and Green 1991) such as maximum error and root mean square error are also reported in this study.

Criterion for statistical significance The high number of replicates of the system under study (n = 133) gave rise to t-tests with high statistical power. This was calculated to be equal to 0.997 if balanced Type I and Type II error risks were chosen ([alpha] = [beta]). If this was the case, then [alpha] = [beta] = 0.003, and therefore a P-value <0.003 was regarded as providing a statistically significant evidence of departure from the null hypothesis, i.e. that the mean SD was significantly different from zero.

First approach: preliminary model of dilution factor

The most simple approach for assessing the ion concentrations in the saturated paste extract ([c.sub.SEi]) from the 1:5 extract ([c.sub.1:5i]) was based on just the principle of matter conservation as given by Eqn 3. This approach is called 'preliminary model of dilution factor'. In Eqn 3, [[theta].sub.gsat] and [[theta].sub.g1:5] are, respectively, the gravimetric soil water content at saturation and of the 1:5 suspension from which the 1:5 extract is obtained, both in g [g.sup.-1].

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

The expected pH of the saturated paste ([pH.sub.SP]) and electrical conductivity at 25[degrees]C of the saturated paste extract ([EC.sub.SE]) were simulated with the chemical speciation program SALSOLCHEMIS (Visconti et al. 2010c), using as inputs the ion concentrations predicted with Eqn 3 ([c.sub.SEi]), the C[O.sub.2] partial pressure in the saturated paste (pC[O.sub.2SP]), and ion pair formation constants collected in Lindsay (1979) except for the formation of the ion pairs CaC[O.sub.3.sup.o] and CaHC[O.sub.3.sup.+]. It was assumed that these ion pairs do not form (Visconti et al. 2010c). As the pC[O.sub.2SP] depends on the soil organic matter content and the soil depth, the following values ofpCO2sP were used: [10.sup.-0.744], [10.sup.-0.954], and [10.sup.-1.144] kPa for the 0-10, 10-35, and 35-95 cm soil layers, respectively. These pC[O.sub.2SP] are mean values for each soil depth, which were estimated calculating the chemical speciation of the solution in the saturated pastes, again by means of the chemical speciation software SALSOLCHEMIS (Visconti et al. 2010c). The inputs to SALSOLCHEMIS were, in addition to the chemical equilibrium constants, the ion composition of the saturation extracts and the [pH.sub.SP]. The EC was calculated from the main ion contents according to Visconti et al. (2010b).

Second approach: equilibrium with calcite, gypsum, and C[O.sub.2]

In heavily calcareous and more or less gypsiferous soils, calcite and gypsum weathering and precipitation exert a remarkable effect on their soil solution main ion contents, and thus salinity (Suarez 2005). The main ion concentration in equilibrium with these two minerals and C[O.sub.2] can be calculated with chemical equilibrium models such as SALSOLCHEM, which is part of the SALTIRSOIL model (Visconti et al. 2011). The concentrations of main ions in the saturated paste extract previously predicted (Eqn 3), in addition to the C[O.sub.2] in the saturated paste (pC[O.sub.2SP]) previously calculated, were used as input data to SALSOLCHEM. Also, the same ion pair formation constants that were used in the first approach were used here. Additionally, the values 4.62 and 8.29 were, respectively, taken as the solubility products (i.e. pKs) of gypsum and calcite (Visconti et al. 2010c).

Third approach: additional equilibrium with the exchange Complex

In medium- to fine-textured soils, the equilibrium with the exchange complex exerts another profound influence, not so much in the salinity, but in the specific contents of the soil solution ions, mainly cations. The hypothesis of equilibrium with the exchange complex was introduced in SALSOLCHEM, giving a new model called SALSOLCHEMEC (Visconti 2011). The composition of the soil solution and the exchange complex freely allowed to equilibrate with each other, and also with calcite, gypsum, and C[O.sub.2] in the saturated paste, was simulated.

The inputs to SALSOLCHEMEC include the contents of soil extractable ions referred to a dry soil basis ([m.sub.Ti]) plus the CEC, all expressed in units of [mmol.sub.C] [kg.sup.-1], and the gravimetric water content at saturation ([[theta].sub.gsat]). The extractable contents of soil anions [Cl.sup.-], N[O.sub.3.sup.-], and S[O.sub.4.sup.2-] and also alkalinity were calculated from their concentrations in the 1: 5 extract ([c.sub.1:51]) and the water content of the 1:5 suspension ([[theta].sub.g1:5]) using Eqn 4, where [z.sub.i] stands for the charge of the anion i in units of [mol.sub.c] [mol.sup.-1] and [[rho].sub.w] for the water density in kg [L.sup.-1]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

The extractable contents of ==[Na.sup.+], [K.sup.+], and [Mg.sup.2+] ([m.sub.Ti]) were determined as described above in the subsection Determination of cation exchange capacity and soil cations. The extractable contents of [Ca.sup.2+] ([m.sub.TCa]) were obtained following two different methods. On the one hand, for the 122 soils not at equilibrium with gypsum in the 1:5 extract, the exchangeable [Ca.sup.2+] content in the 1:5 suspension ([m.sub.EXCCa]([[theta].sub.1:5])) was added to the [Ca.sup.2+] content in the 1:5 extract ([m.sub.SSCa]([[theta].sub.1:5])), through Eqn 5 (see Appendix 1):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

On the other hand, for the 11 soils at equilibrium with gypsum in the 1:5 extract, the equivalent charge of extractable cations was subtracted from the equivalent charge of extractable anions plus CEC through Eqn 6:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

The same hypotheses regarding the thermodynamic equilibrium constants for the formation of ion pairs and the solubility products of calcite and gypsum, and also the values of pC[O.sub.2SP], which were previously used, were used in the SALSOLCHEMEC simulations.

The cation exchange was simulated with SALSOLCHEMEC, including the exchange equilibria of [Ca.sup.2+] by [Na.sup.+] (Ca [right arrow] Na), by [K.sup.+] (Ca [right arrow] K), and by [Mg.sup.2+] (Ca [right arrow] Mg) through the respective Kerr selectivity coefficients in activities (Table 1). The use of the Kerr, Vanselow, or Gaines-Thomas equations and the three binary cation combinations involving calcium resulted in the most effective way of modelling the exchange equilibria of [Na.sup.+], [K.sup.+], [Ca.sup.2+], and [Mg.sup.2+] in calcareous illitic soils (V1sconti et al. 2012). The values of the selectivity coefficients were -0.85 [+ or -] 0.03, 0.47 [+ or -] 0.03, and 0.26 [+ or -] 0.04 for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], respectively (Visconti et al. 2012). To calculate the selectivity coefficients and saturation status regarding gypsum, the activities of the cations in the extracts had been calculated previously with the chemical speciation program SALSOLCHEMIS (Visconti et al. 2010c).

Fourth approach: salt retention in the diffuse double layer (DDL)

In slightly to moderately saline calcareous illitic soils, the differential distribution of anions and cations from the colloid surfaces into the bulk soil solution (BSS) gives rise to the existence of salt retention in the diffuse double layer (DDL). These salts within the DDL could be extracted with high-pressure techniques such as centrifugation, but not with low-pressure techniques.

Ion contents in the DDL and effective cation exchange capacity

The hypothesis of salts retained within the DDL was introduced in this approach. Accordingly, the anion contents within the DDL ([m.sub.DDLi]) were calculated by subtraction using Eqn 7. In this equation, [m.sub.Ti] is the soil extractable content of the anion i calculated with Eqn 4, and [m.sub.BSSi] is the content of the soil anion i in the saturated paste extract (Eqn 8), which was taken as representative of the BSS, i.e. the soil solution outside the DDL:

[m.sub.DDLi] = [m.sub.Ti] - [m.sub.BSSi] (7)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

In this fourth simulation, an effective CEC ([CEC.sub.ef]) was assessed by adding the sum of anion contents inside the DDL [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] to the CEC analytically determined. In the soils at equilibrium with gypsum in the saturated paste extract, the S[O.sub.4.sup.2-] content could not be calculated using the methodology just described. This is because in these soils the difference between the soil extractable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] as calculated with Eqn 4 and the S[O.sub.4.sup.2-] content in the BSS [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] as given by Eqn 8 is equal to the sum of S[O.sub.4.sup.2-] in the DDL plus the S[O.sub.4.sup.2-] precipitated as gypsum in the saturated paste extract but not in the 1:5 extract. For the [CEC.sub.ef] calculation, the S[O.sub.4.sup.2-] content in the DDL of these soils was taken equal to the mean S[O.sub.4.sup.2-] content in the DDL of the soils not at equilibrium with gypsum in the saturated paste extract, which was 5.2 [mmol.sub.C] [kg.sup.-1].

The contents of [Na.sup.+], [K.sup.+], and [Mg.sup.2+] in the DDL were taken equal to the exchangeable contents which were determined as described above in the subsection Determination of cation exchange capacity and soil cations. The [Ca.sup.2+] content in the DDL was calculated by subtraction of the [Na.sup.+], [K.sup.+], and [Mg.sup.2+] contents in the DDL from the [CEC.sub.ef].

Saturated paste extract and exchange complex Composition

The same equilibrium constants and C[O.sub.2] partial pressure used in the previous approaches were used in this one, with the exception of the selectivity coefficients for cation exchange. These were recalculated according to the methodology described in the third approach, using this time the cation contents in the DDL to give -0.89 [+ or -] 0.03, 0.44 [+ or -] 0.03, and 0.20 [+ or -] 0.03 for [logK.sub.CaNa], [logK.sub.CaK], and [logK.sub.CaMg], respectively. The contents of [Cl.sup.-], N[O.sub.2.sup.-], and N[O.sub.3.sup.-] in the bulk soil solution calculated with Eqn 8 ([m.sub.BSSi]) were used instead of their extractable soil contents calculated with Eqn 4 ([m.sub.Ti]). The contents of sulfate in the BSS were calculated in the same way with the exception of the soils at equilibrium with gypsum in the saturated paste extract. In this case, the contents of S[O.sub.4.sup.2-] in the BSS were obtained by subtracting the value of 5.2 [mmol.sub.C] [kg.sup.-1] from the extractable sulfate S[O.sub.4.sup.2-] contents (mvso,).

Results

First approach: preliminary model of dilution factor

The mean SD between observations and predictions for all the properties presented a negative value (Table 2), which was significantly different from zero except for N[O.sub.2.sup.-] (Table 2). This reflects the overestimation of all properties, as can be observed in the scatter plots of predictions against observations (Fig. 1). For many soil samples, the alkalinity, [Ca.sup.2+], and S[O.sub.4.sup.2-] Concentrations showed great differences between calculated and observed values, with maximum errors of 55.9 [mmol.sub.c] [L.sup.-1] (+2100%) for alkalinity, 248 mmol [L.sup.-1] (+1400%) for [Ca.sup.2+], and 281 mmol [L.sup.-1] (+1500%) for S[O.sub.4.sup.2-]. In the scatter plots of [Ca.sup.2+] and S[O.sub.4.sub.2-] observations against predictions, two areas can be distinguished, which have been separated by a dotted line in Fig. 1d and i. Under the dotted line, the observations and predictions were strongly associated, with correlation coefficients of 0.90 ([Ca.sup.2+]) and 0.94 (S[O.sub.4.sup.2-]). Over the dotted line, the correlation coefficients were siguificanfly lower, with values of 0.54 ([Ca.sup.2+]) and 0.12 (S[O.sub.4.sup.2-]). The uncorrelated points in both graphs correspond to the same soil samples. From these 20 samples, 11 are at equilibrium with gypsum both in the saturated paste extract and in the 1:5 soil to water extract, i.e. the p value of the ionic activity product (plAP) is between 4.62 and 4.72 in both extracts. As a consequence of the overestimation of all ions, the [EC.sub.SE] was also overestimated.

Statistical studies of residual errors ([O.sub.i] - [P.sub.i]) have been used with the aim of finding the origin of prediction errors in environmental pollution models (Kirchner et al. 1996; Knightes and Cyterski 2005). Instead of the residual errors, in the present work the standardised differences (S[D.sub.i]) were used with the same purpose. The matrix of product-moment correlation coefficients between the SDs of predictions and observations of the 12 properties was calculated (Table 3).

The SD of the [EC.sub.SE] was strongly correlated (r >0.77) with the SDs of [Ca.sup.2+], [Mg.sup.2+], and S[O.sub.4.sup.2-] in that order. The SDs of [Mg.sup.2+] and [Ca.sup.2+] (r=0.92), [Ca.sup.2+] and S[O.sub.4.sup.2-] (r=0.80), and to a lesser extent pH and alkalinity (r = 0.59), were also strongly correlated.

Second approach: equilibrium with calcite, gypsum, and C[O.sub.2]

The maximum errors for alkalinity, [Ca.sup.2+] and S[O.sub.4.sup.2-] remarkably decreased from 56 to 27 [mmol.sub.C] [L.sup.-1], from 248 to 7.6 [mmol.sub.C] [L.sup.-1], and from 281 to 48 [mmol.sub.C] [L.sup.-1], respectively (Tables 2 and 4). The areas of low correlation between predictions and observations of [Ca.sup.2+] and S[O.sub.4.sup.2-] in the preliminary approach (Fig. 1d and i) disappeared. The mean SD of alkalinity and pH became closer to zero. The mean SD of S[O.sub.4.sup.2-] also became closer to zero, but less so than for alkalinity and [pH.sub.SP]. The mean SD of [Ca.sup.2+] changed from -39 [+ or -] 3% to 39 [+ or -] 6%. Although it did not significantly change (in absolute value), the [Ca.sup.2+] concentration became the only property underestimated until then. This is shown in Fig. 2a, where most of the points in the [Ca.sup.2+] scatter plot are under the diagonal line (compare with Fig. ld).

The other soil solution properties ([Na.sup.+], [Cl.sup.-], etc.) logically presented the same concentrations in this second approach as in the first. As a consequence of the decrements in the concentrations predicted for [Ca.sup.2+], S[O.sub.4.sup.2-], and alkalinity, the predicted mean [EC.sub.SE] value also became closer to zero, with a mean SD decrement from -28 [+ or -] 2% to -17 [+ or -] 1%. However, despite the greater closeness between observations and predictions that were attained introducing the hypothesis of equilibrium with calcite and gypsum, the mean SDs of alkalinity, [Ca.sup.2+], S[O.sub.4.sup.2-], [EC.sub.SE], and [pH.sub.SP] were still significantly different from zero (Table 4).

The product-moment correlation coefficients among the SDs of the 12 properties (Table 5) were calculated again. The highest correlation coefficients in absolute value were between the SDs of [Ca.sup.2+], alkalinity, and pH ([absolute value of r] > 0.85). Therefore, the association between the predictive errors of alkalinity and pH increased regarding the preliminary model, and furthermore the [Ca.sup.2+] was added to this association. The correlation coefficient between the SDs of [EC.sub.SE] and [Mg.sup.2+] was very similar to these latter (r = 0.86). Another interesting high correlation coefficient was between the SDs of [EC.sub.SE] and S[O.sub.4.sup.2-] (r = 0.61). Therefore, the predictive error of the [EC.sub.SE] was still associated with [Mg.sup.2+], and S[O.sub.4.sup.2-], but this latter less than previously, which was 0.77. On the other hand, the correlation coefficient of the SDs of [EC.sub.SE] and [Ca.sup.2+], which was the highest with the preliminary model, decreased from 0.94 to 0.06. Another interesting observation was the decrease in the correlation coefficient between the SDs of [Ca.sup.2+] and S[O.sub.4.sup.2-], which changed from 0.81 with the preliminary model to 0.52 in this second approach.

[FIGURE 1 OMITTED]

Third approach: further equilibrium with the exchange Complex

Saturated paste extract composition

The mean SD became closer to zero for [K.sup.+], alkalinity, [Ca.sup.2+], [Na.sup.+], [Mg.sup.2+], and S[O.sub.4.sup.2-]. According to all these decrements, the mean SD for the [EC.sub.SE] prediction also became closer to zero, going from -16.5 [+ or -] 1.0 to -7.3 [+ or -] 0.7% (Table 6). Furthermore, the mean SD of prise also became closer to zero, going from -2.0 [+ or -] 0.3% to 0.22 [+ or -] 0.11%. The predictions of [K.sup.+], alkalinity, [Ca.sup.2+], [Na.sup.+], [Mg.sup.2+], S[O.sub.4.sup.2-], [EC.sub.SE], and pH improved regarding the previous approach (Fig. 3). Despite the remarkable improvement, the mean SD of all the properties of the saturated paste extract, except [K.sup.+], was still significantly overestimated.

[FIGURE 2 OMITTED]

Exchange complex composition

The exchange complex composition could also be calculated in this simulation. The following mean SDs ordered from the lowest to the highest: 0.1 [+ or -] 0.2% ([K.sub.EXC]), 0.7 [+ or -] 0.8% ([Mg.sub.EXC]), 1.7 [+ or -] 1.7% ([Na.sub.EXC]), and -3.1 [+ or -] 1.0% ([Ca.sub.EXC]) were calculated respectively (Table 6). The mean SD could be regarded as non-significantly different from zero for [K.sup.+], [Mg.sup.2+], and [Na.sup.+] in this order, but certainly not for [Ca.sup.2+]. Therefore, contrary to what occurred with the saturated paste extract composition, the exchangeable complex composition was satisfactorily predicted, with the exception of [Ca.sup.2+].

Fourth approach: salt retention within the diffuse double Layer

Ion contents in the DDL and effective cation exchange capacity

The anion contents in the DDL at water saturation were calculated using Eqn 8. The N[O.sub.2.sup.-] and N[O.sub.3.sup.-] contents in the DDL were jointly reported as N[O.sub.X] because of the low concentration found in the 1:5 and saturated paste extracts overall for N[O.sub.2.sup.-]. The mean [Cl.sup.-] and N[O.sub.X] contents in the DDL were 1.1 [+ or -] 0.2 [mmol.sub.C] [kg.sup.-1], and 0.6 [+ or -] 0.1 [mmol.sub.C] [kg.sup.-1], respectively. The mean S[O.sub.4.sup.2-] contents in the DDL of the soils not at equilibrium with gypsum in the saturated paste extract were 5.2 [+ or -] 0.8 [mmol.sub.C] [kg.sup.-1]. For these soils, the percentage of anions in the DDL regarding the content of anions in the soil solution, i.e. DDL + BSS, was between 13 and 61%, with a mean of 27 [+ or -] 2%.

The sum of anion contents in the DDL [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] of soils not at equilibrium with gypsum in the saturated paste extract gave rise to an extra negative charge between 0.8 and 22.3 [mmol.sub.C] [kg.sup.-1], with a mean of 6.6 [+ or -] 0.9 [mmol.sub.C] [kg.sup.-1], i.e. 6% of the analytically-determined CEC. The extra negative charge provided by the sum on anions in the DDL adds to the CEC to give an [CEC.sub.ef] between 46 and 261 [mmol.sub.C] [kg.sup.-1], with a mean of 126 [+ or -] 8 [mmol.sub.C] [kg.sup.-1]. The [Ca.sup.2+] content in the DDL was recalculated to be 54 [+ or -]4 [mmol.sub.C] [kg.sup.-1] instead of 47 [+ or -] 4 [mmol.sub.C] [kg.sup.-1] considering [CEC.sub.ef] instead of CEC.

[FIGURE 3 OMITTED]

Saturated paste extract composition

The mean SDs of all properties became closer to zero regarding the previous simulation, except for exchangeable [Na.sup.+], [K.sup.+], and [Mg.sup.2+]. Regarding the properties of the soil solution, the mean SDs of [Cl.sup.-] and N[O.sub.X] were zero because in this simulation their extractable soil contents were assessed from their concentrations in the saturated extract itself, not from the 1:5 extract, i.e. Eqn 8 was used instead of Eqn 4. Apart from these ions, the mean SDs of S[O.sub.4.sup.2-], [Ca.sup.2+], [Mg.sup.2+], [Na.sup.+], and [K.sup.+] significantly decreased (in absolute value) from the previous simulation (Table 7). The mean SD could be regarded as non-significantly different from zero for most of the soluble ions: [Na.sup.+], [K.sup.+], [Cl.sup.-], N[O.sub.X], and S[O.sub.4.sup.2-] (Table 7). Despite the closeness of observations and predictions (Fig. 4), the mean SD was still significantly different from zero for [Mg.sup.2+] and [Ca.sup.2+].

In the soils not at equilibrium with gypsum in the saturated paste extract, the SDs of S[O.sub.4.sup.2-] were equal to zero, i.e. they lay on the 1:1 line (Fig. 4), because as occurred with [Cl.sup.-] and N[O.sub.X] its content in the bulk soil solution at saturation was determined from the saturated paste extract itself with Eqn 8. On the other hand, in the soils at equilibrium with gypsum in the saturated paste extract, the SDs were between -14 and 16.5% with a mean of -3 [+ or -] 2%, i.e. significantly different from zero. According to this result, the mean S[O.sub.4.sup.2-] content in the BSS was overestimated, i.e. the S[O.sub.4.sup.2-] content in the DDL of soils at equilibrium with gypsum in the saturated paste extract is higher than in soils not at equilibrium with gypsum, which was 5.2 [mmol.sub.C] [kg.sup.-1].

The mean SD of the [EC.sub.SE] became closer to zero because of the lower mean SDs presented by all the ions in solution. It changed from -7.4 [+ or -] 0.7 to 1.5 [+ or -] 0.5% regarding the previous simulation. Despite this improvement, which is further demonstrated by the closeness between the mean predicted and observed [EC.sub.SE], 4.34 and 4.40 dS [m.sup.-1], respectively, the mean SD of the [EC.sub.SE] was still significantly different from zero.

Finally the mean SDs (in absolute value) of alkalinity and pH decreased. They changed from 3 [+ or -] 2% to -2 [+ or -] 2% and from 0.22 [+ or -] 0.11% to -0.11 [+ or -] 0.12%, respectively, and therefore, they could be regarded as non-significantly different from zero.

Exchange complex composition

Regarding the cations in the DDL, the SDs of [Ca.sup.2+] became closer to zero. Contrary to this, the mean SD (in absolute value) of the exchangeable [Na.sup.+], [K.sup.+], and [Mg.sup.2+] slightly increased. In any case, the mean SD could be regarded as non-significantly different from zero for all the exchangeable cations.

Discussion

First approach: preliminary model of dilution factor

The preliminary model is based on the hypothesis that all ions behave as conservative solutes; however, the overestimation of all ions suggests that solutes are not conserved in the solution when it concentrates. In this model, the error in the prediction of [Ca.sup.2+] is associated with the error in the prediction of S[O.sub.4.sup.2-], and both errors, together with the error in the prediction of [Mg.sup.2+], are strongly associated with the error in the prediction of [EC.sub.SE].

The non-conservative behaviour observed for [Ca.sup.2+], S[O.sub.4.sup.2-], and alkalinity can be explained because of precipitation reactions. As the soil solution concentrates from the 1:5 suspension to the saturated paste, the soil solution achieves saturation or increases its saturation state regarding gypsum and/or calcite. As saturation is attained or increased, the ions [Ca.sup.2+], S[O.sub.4.sup.2-], and alkalinity precipitate from the soil solution as minerals calcite and/or gypsum. Regarding [Mg.sup.2+], for which prediction error is associated with the errors of [Ca.sup.2+] and S[O.sub.4.sup.2-], it may also be removed from the soil solution due to its co-precipitation with [Ca.sup.2+] to produce magnesian calcite, or its precipitation with carbonate or silicate to produce, respectively, hydromagnesite and nesquehonite or sepiolite (Suarez 2005). The errors in the prediction of [Ca.sup.2+], S[O.sub.4.sup.2-], and alkalinity, become enormous when dealing with gypsiferous soil samples.

Second approach: equilibrium with calcite, gypsum, and C[O.sub.2]

The association between the prediction errors of [Ca.sup.2+], alkalinity, pH, and to a lesser extent S[O.sub.4.sup.2-] in this second approach was further studied, defining a new concept, i.e. the S[O.sub.4.sup.2-] and alkalinity in excess over calcium (SAEC) according to Eqn 9:

SAEC = Alk + 2[S[O.sub.4.sup.2-]] - 2[[Ca.sup.2+]] (9)

The mean SAEC of the 1:5 extracts was 3.7 [+ or -] 0.6 [mmol.sub.C] [L.sup.-1], which led to a predicted SAEC of 42 [+ or -] 5 [mmol.sub.C] [L.sup.-1] for the saturated paste extracts when the preliminary model was applied. When the second model was applied, the predicted SAEC presented the same value (42 [+ or -] 5 [mmol.sub.C] [L.sup.-1]). In SALSOLCHEM, for each [Ca.sup.2+] equivalent removed from the soil solution as calcite or gypsum, one equivalent of either alkalinity or S[O.sub.4.sup.2-] is also removed. Accordingly, very low [Ca.sup.2+] concentrations were predicted coinciding with high concentrations of alkalinity and [Ca.sup.2+]. Moreover, high alkalinity concentrations gave rise to high pH values, which led to the high and negative correlation between the SDs of pH and [Ca.sup.2+].

[FIGURE 4 OMITTED]

Contrary to this, the observed SAEC in the saturated paste extracts presented a mean of 12 [+ or -] 3 [mmol.sub.C] [L.sup.-1], less than a third of the SAEC predicted with both the preliminary model and second models. As the overall concentration of the soil solution increases from the 1:5 suspension to the saturated paste, the SAEC decreases, and the relative concentration of [Ca.sup.2+] with regard to alkalinity and S[O.sub.4.sup.2-] increases. Therefore, as the soil solution concentrates, some [Ca.sup.2+] is provided by another soil source, which is not calcite or gypsum. This [Ca.sup.2+] supply replaces some of the [Ca.sup.2+] removed from the soil solution as the minerals precipitate, thus decreasing the SAEC value. This [Ca.sup.2+] could be supplied from the soil exchange complex.

Third approach: further equilibrium with the exchange complex

According to the known 'valence dilution effect' (Bohn et al. 2001) as the soil solution concentrates, the ratio of exchangeable divalent to monovalent cations decreases, and therefore the ratio of divalent to monovalent cations in the soil solution increases. This effect explains the underestimation of the [Ca.sup.2+] concentration, and also the overestimation of [Na.sup.+] and [K.sup.+], which with a mean SD of -56 [+ or -] 2% was the most overestimated ion in the second approach (Table 4). The introduction of the hypothesis of equilibrium with the exchange complex improved the prediction of all the properties of the saturated paste extract. However, with mean SDs of -5.6 [+ or -] 0.7, -9 [+ or -] 6, and 19 [+ or -] 5%, the anions [Cl.sup.-] , N[O.sub.2.sup.-], and N[O.sub.3.sup.-], which were among the best predicted properties of the saturated paste extract with the preliminary model, still presented mean SDs significantly lower than zero (Table 6); that is, they were significantly overestimated. The same [Cl.sup.-], N[O.sub.2.sup.-], and N[O.sub.3.sup.-] predictions were obtained with the first and second approaches, producing together with the excess errors of S[O.sub.4.sup.2-], [Ca.sup.2+], and [Mg.sup.2+], the overestimation that the [EC.sub.SE] still presented in the third approach. The overestimation of N[O.sub.3.sup.-] and N[O.sub.2.sup.-] may be explained by the likely denitrification in the saturated paste, which does not occur in the 1:5 suspension due to the continuous shaking. However, the overestimation of [Cl.sup.-] could not be explained with the same argument because the [Cl.sup.-] ion cannot be reduced any more. Furthermore, with the third approach, not only N[O.sub.3.sup.-], N[O.sub.2.sup.-] , and [Cl.sup.-] were significantly overestimated, but also S[O.sub.4.sup.2-] , [Ca.sup.2+], and [Mg.sup.2+] were still so. Therefore, the question about where in the saturated paste extract is the excess [Cl.sup.-], and also S[O.sub.4.sup.2-], N[O.sub.3.sup.-], and N[O.sub.2.sup.-] that afterwards appear in the 1:5 extract, was raised.

Fourth approach: salt retention in the diffuse double layer

Centrifugation of soils yields solutions that are more saline than other soil extracts. This effect has been well documented for both variable charge (Geibe et al. 2006), and non-variable charge soils (He et al. 2012). Specifically, the latter authors found that shaking plus centrifuging of soil-water 1:5 suspensions yields extracts of higher salinity than any other laboratory method. In the centrifugal displacement of soil solutions, an increasingly significant part of the DDL is sampled, mixed with the BSS, and jointly extracted as the pressure exerted by centrifugation increases (Wolt 1994). In our work the extraction of the soil solution from the 1:5 soil-water suspension was carried out by centrifugation at ~1400 [g.sub.N], which was estimated to produce a pressure of 800 kPa on the soil. This is 9-10 times higher than the pressure gradient exerted on the saturated paste during extraction (85~0kPa). This high pressure applied on the soil during the centrifugation process could extract part of the soil solution of the DDL, whereas this did not occur when the saturated paste extract was obtained.

The negative surface charge of colloidal soil particles produces a differential distribution of anions and cations in its surroundings when the soil is wet (Fig. 5). As counter ions, cations are attracted to the negative particle surfaces, whereas anions are excluded. However, diffusion counteracts this process of ion segregation. Electrostatic attraction and diffusion balance each other, and thus cation and anion concentrations form a continuous distribution from the particle surface until the BSS. Cation concentrations decrease as a function of the distance from the particle surface until they eventually reach their concentration in the BSS ([C.sub.0]). Anion concentrations, in turn, increase from zero at the surface of the charged particle to the concentration they have in the bulk soil solution, which is also [C.sub.0] (Fig. 5). The limit between the DDL and the BSS is located at the point where the equivalent concentration of cations equals the equivalent concentration of anions, i.e. [C.sub.0].

[FIGURE 5 OMITTED]

According to their distribution under low pressure conditions (Fig. 5), part of the soil anions are kept within the DDL of the soil colloids together with some extra amount of cations so as to neutralise them. The situation depicted in Fig. 5 has been simplified in Fig. 6a, where only the areas under the curves of cation and anion concentrations have been represented. Therefore, the three different areas in Fig. 6 are interpreted as amounts of charge in equivalents. The anions in the DDL together with the extra amount of cations constitute true retained salts by the soil colloids under low pressure conditions (Fig. 6a). The difference between the cation and anion equivalents in the DDL is equal to the soil CEC in equivalents. As the pressure on the soil increases, the DDL is compressed and part of the anions, and also water, which were within the DDL are released into the BSS together with an equivalent part of cations. This salt release from the DDL increases the amount of salts of the BSS (Fig. 6b). Finally, if the pressure on the soil continues growing, it could bring the soil colloids so tightly to each other as to make the cations form almost a one-cation-thick layer on the charged particles, i.e. a Helmholtz double layer (Fig. 6c). At that pressure, all the retained salts in the DDL, and also water, would be released to the BSS.

In the non-gypsiferous soils analysed in this work, the sum of extractable contents of soil anions plus the CEC equals the sum of extractable cations as determined by the extractable cation extraction method. Thus, the pressure attained when centrifuging the 1:5 suspensions in this work seems to have sufficed to extract practically all the salts retained in the DDL, i.e. to have reached almost the situation depicted in Fig. 6c. This is interesting because for soils at field moisture, pressures up to 800kPa exerted by centrifugal displacement were estimated to extract only 25% of the soil solution in the DDL (Wolt 1994).

[FIGURE 6 OMITTED]

The salt retention in soils where negative charged particles are present has been traditionally analysed in terms of the 'anion exclusion' effect. The anion exclusion as the difference between the soil solution contents and the extractable contents of anions on a dry-soil basis (Bolt et al. 1978) is given by the opposite of Eqn 7. The anion exclusion tends to zero as the soil is increasingly compressed by quicker centrifugations. As pressure increases on the soil, on the one hand, the anion concentration in the BSS decreases, and on the other hand, the amount of salts in the BSS increases. Both facts are compatible because the compression of the DDL not only extracts anions to the BSS, but also the water within.

The prediction of the properties of the saturated paste extract improved with the quantification of the salt retention in the DDL, or in other words, the quantification of the anion exclusion. On the other hand, the prediction of the properties of the exchange complex also remarkably improved for [Ca.sup.2+] or slightly worsened for the rest of cations. In this latter approach, [Mg.sup.2+] and [Ca.sup.2+] in the saturated paste extract could be regarded as slightly underestimated. The slight underestimation of [Mg.sup.2+] suggests that the precipitation of magnesian calcite, hydromagnesite, nesquehonite, or sepiolite is almost negligible in the soils under study. This is also supported by the fact that the extractable [Mg.sup.2+] content does not significantly increase with the number of ammonium acetate 1 M extractions (Visconti 2009). However, the slight underestimation of these cations drove the slight underestimation of the [EC.sub.SE].

Conclusions

The composition of the saturated paste extract of calcareous and gypsiferous soils can be reliably predicted from the anion contents of the 1:5 extract, the ammonium acetate extractable cation contents, the CEC, and an estimation of the anion contents within the diffuse double layer of the soil colloids, i.e. the anion exclusion. This conclusion was attained introducing the following four hypotheses in a process-based predictive model: (i) the principle of matter conservation in the soil solution as it concentrates from the 1:5 to the saturated paste extract; (ii) free equilibration of the soil solution with minerals calcite and gypsum under the C[O.sub.2] partial pressure of the saturated paste; (iii) further equilibration of the soil solution with the soil exchange complex; and (iv) salt retention in the DDL of the soil colloids. Starting from the simplest hypothesis each time the model could not be validated on the basis of the t-test for the SD, the next hypothesis was included. The hypothesis of salt retention in the DDL was necessary because centrifugation has a profound effect in the anion exclusion, and the 1:5 extracts, as well as on the soil cation extracts, were separated from their suspensions through centrifugation.

List of abbreviations: AAS, atomic adsorption spectroscopy; BSS, bulk soil solution; CEC, cation exchange capacity; [CEC.sub.ef], effective cation exchange capacity; DDL, diffuse double layer; [EC.sub.SE], electrical conductivity at 25[degrees]C ([EC.sub.25]) and at 25[degrees]C in the saturation extract; K, equilibrium constant; IAP, ionic activity product; SAR, sodium adsorption ratio; SAEC, sulfate and alkalinity in excess over calcium; SD, standardised difference; subscripts: EXC, exchangeable ion content; T, extractable ion content; SP, saturated paste; SE, saturated paste extract.

10.1071/SR12197

Appendix 1

The extractable [Ca.sup.2+] content ([m.sub.TCa]) was calculated by adding the exchangeable content of [Ca.sup.2+] as calculated from the 1:5 extract ([m.sub.EXCCa]([[theta].sub.1:5])) to the [Ca.sup.2+] content in the 1:5 extract ([m.sub.SSCa]([[theta].sub.1:5])). This is expressed by Eqn A1:

[m.sub.TCa] = ([m.sub.EXCCa]([[theta].sub.1:5])) + ([m.sub.SSCa]([[theta].sub.1:5])) (A1)

The content of [Ca.sup.2+] in the 1:5 extract was determined as such. In contrast to this, the exchangeable content of [Ca.sup.2+] could not be determined directly. The [Na.sup.+], [K.sup.+], and [Mg.sup.2+] contents in the 1 M ammonium acetate extract come from the soil solution and from the exchange complex. The [Ca.sup.2+] present in the 1 M ammonium acetate extract comes, in addition to these, also from the calcium carbonate minerals, mainly calcite. As a consequence, the exchangeable [Ca.sup.2+] has to be calculated subtracting the sum of the other three major cations ([Na.sup.+], [K.sup.+], and [Mg.sup.2+]) from the cation exchange capacity (CEC) with Eqn A2, where ([m.sub.EXCi]([[theta].sub.1:5])) stands for the exchangeable content of the cation i:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (A2)

As previously indicated the exchangeable contents ([m.sub.EXCi]([[theta].sub.1:5])) of [Na.sup.+], [K.sup.+], and [Mg.sup.2+] ([z.sub.i] > 0, [logical not]Ca) can be calculated by subtraction of their total extractable contents ([m.sub.Ti]) from their soil solution contents ([m.sub.SSi]([[theta].sub.1:5])) with Eqn A3:

[m.sub.EXCi]([[theta].sub.1:5]) = [m.sub.Ti] - [m.sub.SSi]([[theta].sub.1:5]) (A3)

Replacing [m.sub.EXCi]([[theta].sub.1:5]) in Eqn A2 by its calculation in Eqn A3, and replacing [m.sub.EXCCa]([[theta].sub.1:5]) in Eqn A1 by its value in the modified Eqn A2 gives Eqn A4, which is Eqn 5 in the text.

Acknowledgments

We thank the Conselleria d' Educacio from the Generalitat Valenciana for funding the work of F. Visconti through a postdoctoral scholarship in the framework of program VAL i+d 2010. This research has been carried out in the framework of projects CGL2009-14592-C02-01 and CGL2009-14592-C02-02 funding by the 'Ministerio de Ciencia e Innovacion'. We thank the two anonymous reviewers and the associate editor for their help to improve the article.

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Received 18 July 2012, accepted 2 October 2012, published online 13 November 2012

Fernando Visconti (A,B,C) and Jose Miguel de Paz (A)

(A) Instituto Valenciano de Investigaciones Agrarias-IVIA (GV), Centro para el Desarrollo de la Agricultura Sostenible-CDAS, Crta. Moncada-Naquera Km 4.5, 46113 Moncada, Valencia, Spain.

(B) Centro de Investigaciones sobre Desertificacion-CIDE (CSIC, UVEG, GV), Crta. Moncada-Naquera Km 4.5, 46113 Moncada, Valencia, Spain.

(C) Corresponding author. Email: fernando.visconti@uv.es

Table 1. Cation exchange equations and Kerr selectivity coefficients in activities [K.sub.Ca-Na] and [K.sub.Ca-K] in [(L [kg.sup.-1]).sup.1-2] and [K.sub.Ca-Mg] dimensionless Exchange Exchange equation Selectivity coefficient Ca [right [MATHEMATICAL EXPRESSION [MATHEMATICAL EXPRESSION arrow] Na NOT REPRODUCIBLE IN NOT REPRODUCIBLE IN ASCII] ASCII] Ca [right [MATHEMATICAL EXPRESSION [MATHEMATICAL EXPRESSION arrow] Mg NOT REPRODUCIBLE IN NOT REPRODUCIBLE IN ASCII] ASCII] Ca [right [MATHEMATICAL EXPRESSION [MATHEMATICAL EXPRESSION arrow] K NOT REPRODUCIBLE IN NOT REPRODUCIBLE IN ASCII] ASCII] Table 2. Comparison of observations and predictions for the saturated paste extract using the preliminary model of dilution factor SE, Saturated paste extract; SP, saturated paste [Na.sub.SE] [NH.sub4.SE] [K.sub.SE] No. of comparisons 133 6 133 Mean Observed 25.0 0.4 1.2 Calculated 40.7 0.7 4.1 Classical validation parameters Maximum error 55.2 0.8 15.4 Root mean square error 73.0 104.7 325.0 Standardised difference (%) Mean -26.7 -43.9 -55.6 Standard deviation 0.056 0.078 0.089 Standard errorto.os 1.0 8.2 1.5 [t.sub.calc] 54.6 13.8 72.1 P-value <0.003 <0.003 <0.003 [Mg.sub.SE] [Ca.sub.SE] [Cl.sub.SE] No. of comparisons 133 133 133 Mean Observed 6.2 8.4 22.2 Calculated 11.5 31.7 24.7 Classical validation parameters Maximum error 25.0 248.2 15.4 Root mean square error 120.1 623.9 17.5 Standardised difference (%) Mean -29.4 -39.1 -5.6 Standard deviation 0.144 0.199 0.04 Standard errorto.os 2.5 3.4 0.7 [t.sub.calc] 23.5 22.6 16.4 P-value <0.003 <0.003 <0.003 [NO.sub.2SE] [NO.sub.3SE] [SO.sub.4SE] No. of comparisons 55 129 133 Mean Observed 0.6 3.9 13.5 Calculated 0.7 5.1 42.8 Classical validation parameters Maximum error 1.4 8.5 281.2 Root mean square error 55.0 51.8 479.9 Standardised difference (%) Mean -8.6 -19.0 -31.0 Standard deviation 0.222 0.27 0.195 Standard errorto.os 6 4.7 3.4 [t.sub.calc] 2.9 8.0 18.3 P-value 0.005 <0.003 <0.003 [Alk.sub.SE] [EC.sub.SE] [pH.sub.SP] No. of comparisons 133 133 133 Mean Observed 1.6 4.4 7.9 Calculated 19.8 8.0 8.8 Classical validation parameters Maximum error 55.9 16.5 1.7 Root mean square error 1275 114.8 12.5 Standardised difference (%) Mean -83.8 -27.6 -5.8 Standard deviation 0.056 0.123 0.01 Standard errorto.os 1.0 2.1 0.2 [t.sub.calc] 171.9 25.9 66.2 P-value <0.003 <0.003 <0.003 Table 3. Matrix of product-moment correlation coefficients among the standardised differences (SD) of observations and predictions caused by the preliminary model of dilution factor Correlation coefficients >0.75 are in bold face [SD.sub.Na] [SD.sub.NH4] [SD.sub.K] [MATHEMATICAL EXPRESSION 0.685 NOT REPRODUCIBLE IN ASCII] [SD.sub.K] 0.585 0.24 [SD.sub.Mg] 0.465 0.122 0.621 [SD.sub.Ca] 0.166 -0.125 0.444 [SD.sub.Cl] -0.024 -0.439 0.224 [MATHEMATICAL EXPRESSION -0.012 -0.631 -0.088 NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION 0.090 0.629 -0.098 NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION -0.247 -0.329 0.143 NOT REPRODUCIBLE IN ASCII] [SD.sub.Alk] 0.177 0.108 0.333 [SD.sub.EC] 0.296 -0.037 0.511 [SD.sub.pH] 0.183 0.115 0.392 [SD.sub.Mg] [SD.sub.Ca] [SD.sub.Cl] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.K] [SD.sub.Mg] [SD.sub.Ca] 0.919 [SD.sub.Cl] 0.410 0.466 [MATHEMATICAL EXPRESSION -0.007 0.006 0.068 NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION -0.090 -0.057 -0.042 NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION 0.595 0.804 0.558 NOT REPRODUCIBLE IN ASCII] [SD.sub.Alk] 0.015 -0.046 -0.179 [SD.sub.EC] 0.911 0.938 0.554 [SD.sub.pH] 0.036 -0.028 0.120 [SD.sub.N02] [SD.sub.N03] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.K] [SD.sub.Mg] [SD.sub.Ca] [SD.sub.Cl] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION -0.203 NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION 0.104 -0.048 NOT REPRODUCIBLE IN ASCII] [SD.sub.Alk] 0.098 -0.398 [SD.sub.EC] 0.053 0.022 [SD.sub.pH] 0.037 -0.328 [SD.sub.S04] [SD.sub.Alk] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.K] [SD.sub.Mg] [SD.sub.Ca] [SD.sub.Cl] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.Alk] -0.187 [SD.sub.EC] 0.77 -0.121 [SD.sub.pH] -0.045 0.589 [SD.sub.EC] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.K] [SD.sub.Mg] [SD.sub.Ca] [SD.sub.Cl] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.Alk] [SD.sub.EC] [SD.sub.pH] 0.020 Table 4. Comparison of observations and predictions for the saturated paste extract freely allowed to equilibrate with calcite and gypsum at the C[0.sub.2] partial pressure of the saturated paste SE, Saturated paste extract; SP, saturated paste [Na.sub.SE] [NH.sub4.SE] [K.sub.SE] No. of comparisons 133 6 133 Mean Observed 25.0 0.4 1.2 Calculated 40.7 0.7 4.1 Classical validation parameters Maximum error 55.2 0.8 15.4 Root mean square error 73.0 104.7 325.0 Standardised difference (%) Mean -26.7 -43.9 -55.6 Standard deviation 0.056 0.078 0.089 Standard errorto.os 1.0 8.2 1.5 [t.sub.calc] 54.6 13.8 72.1 P-value <0.003 <0.003 <0.003 [Mg.sub.SE] [Ca.sub.SE] [Cl.sub.SE] No. of comparisons 133 133 133 Mean Observed 6.2 8.4 22.2 Calculated 11.5 5.8 24.7 Classical validation parameters Maximum error 25.0 7.6 15.4 Root mean square error 120.1 39.5 17.5 Standardised difference (%) Mean -29.4 39.2 -5.6 Standard deviation 0.144 0.363 0.040 Standard errorto.os 2.5 6.2 0.7 [t.sub.calc] 23.5 12.4 16.4 P-value <0.003 <0.003 <0.003 [NO.sub.2SE] [NO.sub.3SE] [SO.sub.4SE] No. of comparisons 55 129 133 Mean Observed 0.6 3.9 13.5 Calculated 0.7 5.1 24.3 Classical validation parameters Maximum error 1.4 8.5 48.2 Root mean square error 55.0 51.8 114.6 Standardised difference (%) Mean -8.6 -19.0 -25.2 Standard deviation 0.222 0.270 0.095 Standard errorto.os 6.0 4.7 1.6 [t.sub.calc] 2.9 8.0 30.5 P-value 0.005 <0.003 <0.003 [Alk.sub.SE] [EC.sub.SE] [pH.sub.SP] No. of comparisons 133 133 133 Mean Observed 1.6 4.4 7.9 Calculated 5.0 6.1 8.2 Classical validation parameters Maximum error 27.0 6.2 1.4 Root mean square error 382.2 47.3 5.3 Standardised difference (%) Mean -34.9 -16.5 -2.0 Standard deviation 0.242 0.060 0.016 Standard errorto.os 4.2 1.0 0.3 [t.sub.calc] 16.6 31.7 13.8 P-value <0.003 <0.003 <0.003 Table 5. Matrix of product-moment correlation coefficients among the standardised differences of observations and predictions caused by the second model approach Correlation coefficients >0.75 are in bold face [SD.sub.Na] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 0.685 [SD.sub.K] 0.585 [SD.sub.Mg] 0.465 [SD.sub.Ca] -0.561 [SD.sub.Cl] -0.024 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] -0.012 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 0.090 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] -0.129 [SD.sub.Alk] 0.527 [SD.sub.EC] 0.389 [SD.sub.pH] 0.541 [SD.sub.NH4] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.K] 0.240 [SD.sub.Mg] 0.122 [SD.sub.Ca] -0.480 [SD.sub.Cl] -0.439 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] -0.631 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 0.629 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] -0.307 [SD.sub.Alk] 0.335 [SD.sub.EC] -0.169 [SD.sub.pH] 0.495 [SD.sub.K] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.K] [SD.sub.Mg] 0.621 [SD.sub.Ca] -0.274 [SD.sub.Cl] 0.224 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] -0.088 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] -0.098 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 0.286 [SD.sub.Alk] 0.327 [SD.sub.EC] 0.490 [SD.sub.pH] 0.416 [SD.sub.Mg] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.K] [SD.sub.Mg] [SD.sub.Ca] -0.095 [SD.sub.Cl] 0.410 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] -0.007 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] -0.090 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 0.567 [SD.sub.Alk] 0.284 [SD.sub.EC] 0.858 [SD.sub.pH] 0.291 [SD.sub.Ca] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.K] [SD.sub.Mg] [SD.sub.Ca] [SD.sub.Cl] 0.198 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 0.004 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] -0.129 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 0.524 [SD.sub.Alk] -0.886 [SD.sub.EC] 0.058 [SD.sub.pH] -0.858 [SD.sub.Cl] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.K] [SD.sub.Mg] [SD.sub.Ca] [SD.sub.Cl] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 0.068 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] -0.042 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 0.518 [SD.sub.Alk] -0.130 [SD.sub.EC] 0.507 [SD.sub.pH] 0.009 [SD.sub.N02] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.K] [SD.sub.Mg] [SD.sub.Ca] [SD.sub.Cl] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] -0.203 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 0.106 [SD.sub.Alk] 0.019 [SD.sub.EC] 0.115 [SD.sub.pH] 0.009 [SD.sub.N03] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.K] [SD.sub.Mg] [SD.sub.Ca] [SD.sub.Cl] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] -0.126 [SD.sub.Alk] 0.052 [SD.sub.EC] 0.099 [SD.sub.pH] 0.002 [SD.sub.SO4] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.K] [SD.sub.Mg] [SD.sub.Ca] [SD.sub.Cl] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.Alk] -0.351 [SD.sub.EC] 0.607 [SD.sub.pH] -0.248 [SD.sub.Alk] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.K] [SD.sub.Mg] [SD.sub.Ca] [SD.sub.Cl] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.Alk] [SD.sub.EC] 0.185 [SD.sub.pH] 0.850 [SD.sub.EC] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.K] [SD.sub.Mg] [SD.sub.Ca] [SD.sub.Cl] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [SD.sub.Alk] [SD.sub.EC] [SD.sub.pH] 0.181 Table 6. Comparison of observations and predictions for the saturated paste extract and the exchange complex freely allowed to equilibrate with calcite, gypsum, and the exchange complex at the C[O.sub.2] partial pressure of the saturated pastes SE, Saturated paste extract; SP, saturated paste; EXC, exchangeable ion content [Na.sub.SE] [K.sub.SE] [Mg.sub.SE] No. of comparisons 132 132 132 Observed 25.1 1.1 6.3 Predicted 25.6 1.1 7.9 Maximum error 17.3 2.2 10.2 Root mean square error 13.1 35.8 46.5 Mean -2.7 -4.1 -10.5 Standard deviation 0.1 0.2 0.2 Standard error x 1.1 2.8 2.7 [t.sub.0.05] [t.sub.calc] 5.0 2.9 7.8 P-value <0.003 0.004 <0.003 [Ca.sub.SE] [S0.sub.4SE] [Alk.sub.SE] No. of comparisons 132 132 132 Mean Observed 8.4 13.6 1.6 Predicted 11.3 17.4 1.5 Classical validation parameters Maximum error 10.1 13.3 1.9 Root mean square error 46.0 38.0 27.9 Standardised difference (%) Mean -14.1 -16.1 2.9 Standard deviation 0.1 0.1 0.1 Standard error.t0.05 2.0 2.0 2.2 tcalc 13.8 16.1 -2.7 P-value <0.003 <0.003 0.008 [Na.sub.EXC] [K.sub.EXC] [Mg.sub.EXC] No. of comparisons 132 132 132 Observed 7.5 7.1 58.1 Predicted 7.1 7.1 56.8 Maximum error 5.6 0.9 9.1 Root mean square error 19.4 2.5 4.2 Mean 1.7 0.1 0.7 Standard deviation 0.1 0.0 0.0 Standard error x 1.7 0.2 0.8 [t.sub.0.05] [t.sub.calc] 1.9 0.9 1.8 P-value 0.057 0.366 0.081 [Ca.sub.EXC] [EC.sub.SE] [pH.sub.SP] No. of comparisons 132 132 132 Observed 46.3 4.4 7.87 Predicted 48.0 5.0 7.84 Maximum error 11.8 1.8 0.27 Root mean square error 6.7 17.0 1.38 Mean -3.1 -7.3 0.22 Standard deviation 0.1 0.0 0.01 Standard error x 1.0 0.7 0.11 [t.sub.0.05] [t.sub.calc] 6.2 21.5 -3.91 P-value <0.003 <0.003 <0.003 Table 7. An estimated carbon budget for the limestone application required to counter 0.5 pH unit acidification associated with 0.3% soil C sequestration C gain C cost Factor (kg C [ha.sup-1] 10 [cm.sup-1] Soil organic matter 3900 accumulation of 0.3% Reaction of 1 t limestone 120 [ha.sup-1] Mineralisation of the 1 %C 130-650 native to the soil, at 1-5% of 13 t [ha.sup-1] Mining, milling, transport, 435-500 spreading of limestone (100-300 km cartage) Total 3900 685-1270 100% 18-33% Assumed bulk density of 1.3 3 g [cm.sup.-3]

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Author: | Visconti, Fernando; de Paz, Jose Miguel |
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Publication: | Soil Research |

Article Type: | Report |

Date: | Oct 1, 2012 |

Words: | 11903 |

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