# Development of an equation to relate electrical conductivity to soil and water salinity in a Mediterranean agricultural environment.

IntroductionThe measurement of the electrical conductivity (EC) in soil saturation extracts has been widely used for years as a fast and reliable evaluation of soil salinity. The empirical linear relationship that arises between EC and the total ionic concentration or salt content explains this extensive use.

Although the chemical physics of the charge transport in ionic solutions has been intensively studied by several authors (Barthel et al. 1998), the behaviour of multicomponent systems such as soil solutions and natural waters is not yet completely understood, and the use of empirical equations is still necessary in these cases. Among the 3 types of empirical equations that are used in the research on complex electrolyte solutions (Barthel et al. 1998), the most widely cited in the soil literature is the relationship between the total ionic concentration and EC (dS/m). Total ionic concentration is a parameter that has been evaluated in several ways. The most reported of them are described as follows (see Table 1 for a full description of symbols used).

Campbell et al. (1948) proposed the following equation (U.S. Salinity Laboratory Staff 1954):

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where [k.sub.1] is the regression coefficient, [a.sub.1] is an empirical constant, and [[summation of].sub.i][N.sub.i] is the total ionic concentration (meq/L). The following equation has also been widely used in soil salinity research (U.S. Salinity Laboratory Staff 1954):

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where TDS is total dissolved salts (mg/L), [k.sub.2] is the regression coefficient, and [a.sub.2] is an empirical constant. The values of both constants [a.sub.1] and [a.sub.2] are usually found between 1.0 and 1.1. For simplicity [a.sub.1] and [a.sub.2] can be considered equal to 1 (Fireman and Reeve 1948) and a linear relationship between the total ionic concentration (TDS and [summation of][N.sub.i]) and EC can be suggested:

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

(4) TDS = [k.sub.2] EC

Ponnamperuma et al. (1966) and Griffin and Jurinak (1973) proposed another equation in which EC was related to an ionic concentration function known as ionic strength:

(5) I = [k.sub.3] EC

where I is the ionic strength (mmol/L) defined as:

(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where [C.sub.i] represents the molar concentration (mmol/L) of the ion i, and [z.sub.i] represents its electric charge. Marion and Babcock (1976) found a better fit to the ionic strength when the logarithms of these parameters were considered:

(7) logI = a + b logEC

Equation 7 can be written as:

(8) I = [10.sup.a] E[C.sup.b]

where a is a regression constant and b is the regression coefficient. The value of the constant b was found by Marion and Babcock (1976) to be between 1.009 and 1.055 depending on the composition of the aqueous system. This value was assumed equal to 1 for simplicity (b = 1), so Eqn 8 becomes equivalent to Eqn 5 with [k.sub.3] = [10.sup.a].

We observe at least 3 different equations (Eqns 3, 4, and 5) to relate EC to total ionic concentration in order to evaluate the salt concentration of aqueous systems. Furthermore, the values of the regression coefficients depend on the specific composition of the solution in agreement with several authors such as Chang et al. (1983) and Tanji and Biggar (1972). For example, Marion and Babcock (1976) found a value for [k.sub.3] in Eqn 5 of 8.55 mol/dS.[m.sup.2] in a pure solution of NaCl and a value of 16.41 mol/dS.[m.sup.2] in a pure solution of MgS[O.sub.4]. Therefore, it is necessary to develop an equation from theory to unify all of the empirical equations cited.

The objectives of this work were (i) to develop an equation from the theory of EC in aqueous solutions to relate EC to total ionic concentration, (ii) to compare the new equation with the empirical Eqns 3, 4, and 5, and (iii) to validate the theoretical equation proposed on the basis of the Faraday constant with observed data and data from literature.

Theory

Development from ion-transport theory of an equation relating EC to ionic concentration

The specific conductivity of an ion in an aqueous solution ([[sigma].sub.1], dS/m) is defined as (Bockris and Reddy 1998):

(9) [[sigma].sub.i] = [10.sup.-6] [absolute value of [z.sub.i]]F[C.sub.i][u.sub.i]

where F is Faraday's constant and [u.sub.i] is the limiting equivalent ionic mobility (mS.[cm.sup.2].mol/eq.C); the multiplier [10.sup.-6] is needed to maintain the dimensional consistence of the equation. Assuming that EC of the whole ionic solution is equal to the summation of the specific conductivity of each ion we have:

(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Substituting [[sigma].sub.i] in Eqn 10 by its value given in Eqn 9 we obtain:

(11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Using the relationship between the molar concentration and the concentration in equivalents ([N.sub.i] = [absolute value of [z.sub.i]][C.sub.i]) we get:

(12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Now, it is possible to demonstrate the existence of a linear equation between EC and [N.sub.i]. We multiply both sides of Eqn 12 by the following factor, [[summation of].sub.i][N.sub.i]/[[summation of].sub.i][N.sub.i], and rearrange it to obtain:

(13) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

The term in parentheses can be defined as the concentration-weighted mean equivalent mobility:

(14) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

similar to the concentration-weighted mean equivalent conductivity defined by Kramer et al. (1996). So we finally suggest the following equation which relates the sum of ionic species to the EC of an aqueous system:

(15) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

As a first result, we have that Eqn 15 is equal to the empirical Eqn 3 with [k.sub.1] = [10.sup.6]/[bar.u] F.

Aqueous systems with the same relative ionic composition have the same value for the concentration-weighted mean equivalent ionic mobility ([bar.u]), and hence the same value for the regression coefficient in Eqn 3 ([k.sub.1]). Therefore--and unlike it is usually done in order to obtain an empirical equation such as Eqn 3--it would be advisable to split the aqueous systems regarding their relative ionic composition. This result will extend also to Eqns 4 and 5 in the following lines. Once the value of the regression coefficient has been determined, EC can be used to monitor the salinity in a dynamic aqueous system such as a river or a soil using Eqn 3 (Tanji and Biggar 1972).

Comparison of the proposed Eqn 15 with empirical equations

Some of the equations found in the literature can be reduced to Eqn 15 if the adequate rearrangements are performed. In Eqn 4 we can express the total dissolved salts as:

(16) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where [W.sub.i] is the equivalent weight or equivalent-gram of the species i. Then Eqn 4 is:

(17) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

If both sides of Eqn 17 are multiplied by the factor [[summation of].sub.i][N.sub.i]/[[summation of].sub.i][N.sub.i] we get, after rearrangement, to:

(18) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

The term in parentheses can be defined as the concentration-weighted mean equivalent weight ([bar.W]). This substitution leads to:

(19) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Equation 19 is equivalent to Eqn 15, which suggests that the ideas underlying both are the same. We can obtain the value of the regression coefficient k) by direct comparison of both Eqns 19 and 15:

(20) [k.sub.2] = [10.sup.6]([bar.W]/[bar.u] F)

Substituting the values of both [bar.W] and [bar.u] we have:

(21) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Similarly, if Eqn 6 is substituted in Eqn 5 we have:

(22) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Substituting [C.sub.i] by [N.sub.i] / [absolute value of [z.sub.i]] as we did in Eqn 11 we get to:

(23) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

If both sides of Eqn 23 are multiplied by the factor [[summation of].sub.i][N.sub.i]/[[summation of].sub.i][N.sub.i], after rearrangement, we obtain:

(24) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

The term in parentheses can be defined as the concentration-weighted mean charge ([absolute value of [bar.z]]). Then Eqn 24 can be rewritten as:

(25) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Comparison of Eqn 25 with Eqn 15 allows us to obtain a theoretical expression for the regression coefficient [k.sub.3]:

(26) [k.sub.3] = 5 x [10.sup.5]([absolute value of [bar.z]]/[bar.u] F)

Substituting the values of [absolute value of [bar.z]] and [bar.u] we finally have:

(27) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

It has been demonstrated that every equation can be reduced to a linear relationship between [[summation of].sub.i][N.sub.i] and EC and the regression coefficients can be expressed as functions of physicochemical parameters. All this information is summarised in Table 2. Note that for an aqueous system where the regression analysis of TDS against EC and I against EC has not been performed, the regression coefficients can be calculated with the expressions summarised in Table 2 if the chemical analysis is known.

Materials and methods

In all, 179 soil samples and 72 samples of irrigation water were taken along the Valencian Community, eastern Spain, western Mediterranean basin. Every soil and water sample was taken in agricultural lands with a high risk of salinisation and/or sodification. Climate in this region is chararacterised by dry summers and winters, with rainfall in a range of 250-900 mm/year concentrated in a few events in spring and autumn, and evapotranspiration in a range of 800-1300 mm/year. These conditions, in addition to the use of high to medium salt-content irrigation water and/or bad drainage, lead to an increased risk of salinisation and/or sodification in agricultural areas.

The soil samples were air-dried and sieved to 2 mm with subsequent preparation of the saturation extract for each one (U.S. Salinity Laboratory Staff 1954). EC and pH of the saturation extracts were measured with a Crison microCM 2201 conductivimeter with a standard conductivity cell (constant 1.11 [cm.sup.-1]) and with a Crison micropH 2002 pH meter, respectively. Carbonates and bicarbonates were titrated with [H.sub.2]S[O.sub.4], having phenolphthalein and methyl orange as indicators. Nitrates were determined with a selective electrode, chlorides were titrated with AgN[O.sub.3] with potassium chromate as indicator, and sulfates were determined turbidimetrically with Ba[Cl.sub.2] and starch as precipitate stabilising agent. Sodium, potassium, calcium, and magnesium were determined by atomic absorption spectroscopy. The same analytical methods were applied to the water samples.

In addition to these data, data from 15 soil extracts analysed by Griffin and Jurinak (1973) were used to validate Eqn 12.

The charge balance (CB) of every soil extract and irrigation water was assessed with the following equation:

(28) CB = 100 ([absolute value of [summation of][N.sub.+] - [summation of][N.sub.-]])/ [summation of][N.sub.+] - [summation of][N.sub.-]

Those soil extracts and irrigation waters with a charge balance exceeding 10% were rejected, leaving 177 soil saturation extracts and 72 irrigation waters to include in the regression analysis. The database is available from the authors upon request.

The treatment of the data was performed at 3 levels. (a) The linear regression analysis of [[summation of].sub.i][N.sub.i][u.sub.i] against EC, where [u.sub.i] is the limiting equivalent ionic mobility for each ion obtained from the limiting equivalent ionic conductance ([[lambda].sub.i]) (Dean 1985) by application of the following equation: [u.sub.i] = [[lambda].sub.i]/F (Table 3). (b) The linear regression analysis of [[summation of].sub.i]a[u.sub.i]v. EC, where [u.sub.i] stands for the activity in equivalents per L of the ion i. The activity values were obtained from the chemical equilibria modelling computer program SOILSOLN (Wolt 1987). (c) Finally, the presence of ion pairs and their ability to transport charge was considered. The values of ion pair concentrations were obtained from the computer program SOILSOLN and were transformed to activities using the ionic strength calculated with the same program. The limiting equivalent ionic mobilities of the ion pairs were assessed with 2 different formulas, one proposed by Davies (1962) (Eqn 29) and another proposed by Anderko and Lencka (1997) (Eqn 30). The results are shown in Table 3.

(29) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

(30) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where [u.sub.IP] and [absolute value of [z.sub.IP] are, respectively, the limiting equivalent ionic mobility and the charge of the ion pair.

Results and discussion

The EC values found in the irrigation waters analysed were in the range 0.4-45.2 dS/m and those found in the soil saturation extracts were within 0.3-76.0 dS/m. It has been reported that the relationship between the EC and electrolyte concentration for pure salts is not linear over the whole range of solubility of the salt (Anderko and Lencka 1997). In fact, EC reaches a maximum depending on the identity of the salt (Barthel et al. 1998). In order to find the range over which linearity can be assumed for the soil solutions and waters, the identities of the main ions responsible for the charge transport were determined. Correlation analysis matrices for the concentrations of ions and EC were built (Tables 4 and 5). We observed a high correlation among EC, sodium, chloride, magnesium, sulfate, and potassium. Thus, the salinity of soils and waters has a common origin related to the composition of the seawater, where sodium, chloride and magnesium are the dominant ions. Due to this observation, the curve that describes the relationship between EC and concentration of sodium chloride was plotted in the laboratory to determine its shape over a wide range of concentrations. A second-order polynomial fitted the data better than a log-log function (Fig. 1). In contrast, several authors have found the log-log fitting as the most suitable (U.S. Salinity Laboratory Staff 1954; Marion and Babcock 1976). For our data it is possible to consider the relationship between EC and the total ionic concentration to be linear in the range from 0 to 55 dS/m. This led us to restrict the range of applicability of this study to soil extracts and waters of <55 dS/m. This fact only slightly restricts the applicability of this work because higher values of EC correspond to extreme salinity situations that are not usual in agriculture.

[FIGURE 1 OMITTED]

The regression coefficients obtained by fitting the Eqn 12 to the data for soil extracts and irrigation waters can be observed in the first column of Table 6.

The value of Faraday's constant (96485 C/mol) is underestimated in the regression of [[summation of].sub.i][N.sub.i][u.sub.i] against EC. This can be explained considering 2 different points of view: (a) the concentration of species able to transport charge is smaller than that analytically determined, or (b) the ability of those species to transport charge is smaller than that considered based on the limiting equivalent ionic mobility.

Traditionally, the second explanation is considered and the effort is focused on finding out how the equivalent ionic mobilities of the ions are related to the ionic strength of the solution (Bockris and Reddy 1998). This approach involves the derivation of complex mathematical expressions to correct the limiting equivalent ionic mobility of each ion for different ionic strengths (Marion and Babcock 1976). Because the first explanation is simpler than the second one, the first is followed in this work. Thus, the concentration of every ion was corrected for the ionic strength. This was performed by substituting the concentration of each ion by its activity, which is widely recognised as its effective concentration. When the activities were considered instead of the concentrations (second column of Table 6), the regression coefficients became closer to the theoretical value of Faraday's constant (96485 C/mol), especially for the saturation soil extracts from Griffin and Jurinak (1973). However, for our irrigation waters and saturation soil extracts, the value of Faraday's constant was overestimated. This observation may be explained by the fact that there are more ionic species in solution than those considered for the regression analysis, for example ion pairs or soluble organic matter.

When EC due to ion pairs was included in the evaluation, the regression coefficients, shown in the third and fourth columns in Table 6, hardly changed. The use of the Davies' formula (third column) or the Anderko and Lencka formula (fourth column) to assess the limiting ionic mobilities for the ion pairs did not make any significant difference. This result suggests that, in the water systems studied, ion-pair formation was not important. The overestimation of the Faraday's constant was consistent with the use of the Debye-Huckel equation and Davies' equation to predict the activity coefficients of the ions by the speciation program SOILSOLN. The activity coefficients calculated in this way are usually smaller than the experimental activity coefficients measured for ionic strengths up from 0.1 mol/L in the case of the Debye-Huckel equation--0.02 mol/L for sodium chloride--(Bockris and Reddy 1998), and ionic strengths, up from 0.5 mol/L in the case of the Davies' equation (Birkett et al. 1988). The difference between experimental and calculated activity coefficients rises when the ionic strength or total ionic concentration of the aqueous system increases. Thus, the regression analyses were repeated with saturation extracts and waters of EC up to 14, 8, and 4 dS/m (Tables 7 and 8). It can be observed that the value of the regression coefficient gets closer to the theoretical value of the Faraday's constant as aqueous systems of lower EC are considered. This observation is in accordance with the approximation to the ideal behaviour of solutes in more dilute solutions.

Conclusions

A linear equation to relate EC to total ionic concentration in complex systems such as soil solutions and natural waters has been derived from ion-transport theory. Furthermore, some of the most cited empirical equations in the literature used to evaluate the salinity of aqueous systems can be reduced to that theoretical one. The physicochemical significance of the regression coefficients in the empirical equations was found, and it was shown that they depend on the relative solute composition of the aqueous system. Because of this, it is not convenient to study aqueous systems from different relative solute compositions in just one regression analysis of the type of Eqns 3, 4, and 5. In such cases, it would be better to make one regression analysis for each type of aqueous system. The theoretical equation proposed (Eqn 12) was validated in terms of Faraday's constant for aqueous systems over a range of EC where the linearity could be assumed. As a result we observe how the use of activities instead of concentrations could explain the non-ideal effects that lead to a minor ability to transport charge of an aqueous solution. Therefore, being an easier approach, it is worth correcting the concentration of the ions, in order to account for the non-ideal effects, than correcting the value of their limiting equivalent ionic mobility. Finally, although many authors refer to the ion-pair formation as an important issue for the understanding of aqueous solution charge transport, in the aqueous systems studied, the influence of the ion-pair formation on the conductivity was not observed. Thus, the equation proposed should be tested in aqueous systems with a larger proportion of ion-pair formation such as those dominated by magnesium, calcium, and sulfate.

Table 1. Symbols used in this paper and their units Symbol Meaning Units EC Electrical conductivity dS/m [z.sub.i] Charge of ion i eq/mol (A) [bar.z] Concentration-weighted eq/mol mean charge W Equivalent weight or g/eq equivalent-gram of ion i [bar.W] Concentration-weighted g/eq mean equivalent weight [N.sub.i] Equivalent concentration meq/L of ion i [C.sub.i] Molar concentration mmol/L [a.sub.i] Activity of ion i meq/L TDS Total dissolved salts mg/L I Ionic strength mmol/L [u.sub.i] Limiting equivalent ionic mS.[cm.sup.2]. mobility of ion i mol/eq. C [bar.u] Concentration-weighted mS.[cm.sup.2]. mean limiting equivalent mol/eq. C ionic mobility [[sigma].sub.i] Specific conductivity dS/m of ion i F Faraday's constant C/mol [k.sub.1] Constant in Eqn 3 eq/dS.[m.sup.2] [k.sub.2] Constant in Eqn 4 g/dS.[m.sup.2] [k.sub.3] Constant in Eqn 5 mol/dS.[m.sup.2] [summation of] Sum of cations meq/L [N.sub.+] [summation of] Sum of anions meq/L [N.sub.-] (A) In ionic strength calculations [z.sub.i] has to be taken dimensionless. Table 2. Physicochemical significance of the regression coefficients in a selection of empirical equations found in the literature EC is electrical conductivity in dS/m, [N.sub.i] is the equivalent concentration of the ion i in meq/L, TDS is total dissolved salts in mg/L, I is the ionic strength in mmol/L, F is Faraday's constant in C/mol, [u.sub.i] is the limiting equivalent ionic mobility of the ion i in mS.[cm.sup.2].mol/eq.C, [W.sub.i] is the equivalent weight or equivalent-gram of the ion i in g/eq, and [z.sub.i] is the charge of the ion i in eq/mol Equation: [MATHEMATICAL TDS = [k.sub.2]EC I = [k.sub.3]EC EXPRESSION NOT REPRODUCIBLE IN ASCII.] Regression [MATHEMATICAL [MATHEMATICAL [MATHEMATICAL coefficient EXPRESSION NOT EXPRESSION NOT EXPRESSION NOT ([k.sub.i]) REPRODUCIBLE REPRODUCIBLE REPRODUCIBLE IN ASCII.] IN ASCII.] IN ASCII.] Table 3. Limiting equivalent ionic mobilities ([u.sub.i]) used in this work The data for the simple ions are from Dean (1985). The limiting ionic mobilities for ion pairs were assessed with Davies' formula (29) and with Anderko and Lencka's formula (30). All values shown are in mS.[cm.sup.2].mol/eq.C Species [u.sub.i] Species [u.sub.i] [Na.sup.+] 0.519 [Cl.sup.-] 0.791 [K.sup.+] 0.762 C[O.sub.3.sup.2-] 0.746 [Mg.sup.2+] 0.550 HC[O.sub.3.sup.-] 0.461 [Ca.sup.2+] 0.617 N[O.sub.3.sup.-] 0.740 S[O.sub.4.sup.2-] 0.829 Species Davies' Anderko [u.sub.i] and Lencka' [u.sub.i] KS[O.sub.4.sup.-] 0.588 0.394 NaS[O.sub.4.sup.-] 0.467 0.361 CaHC[O.sub.3.sup.+] 0.385 0.283 MgHC[O.sub.3.sup.+] 0.368 0.258 NaC[O.sub.3.sup.-] 0.446 0.336 Table 4. Correlation analysis matrix for irrigation waters All values shown are Pearson's correlation coefficients among concentrations of ions and electrical conductivity EC [Na.sup.+] [Mg.sup.2+] [Ca.sup.2+] EC 1.00 [Na.sup.+] 0.98 1.00 [Mg.sup.2+] 0.97 0.96 1.00 [Ca.sup.2+] 0.75 0.63 0.73 1.00 [K.sup.+] 0.93 0.93 0.92 0.64 N[O.sub.3.sup.-] 0.09 0.01 0.10 0.45 [Cl.sup.-] 0.99 1.00 0.95 0.65 S[O.sub.4.sup.2-] 0.93 0.89 0.95 0.79 HC[O.sub.3.sup.-] 0.77 0.71 0.81 0.76 [K.sup.+] N[O.sub.3.sup.-] [Cl.sup.-] EC [Na.sup.+] [Mg.sup.2+] [Ca.sup.2+] [K.sup.+] 1.00 N[O.sub.3.sup.-] 0.00 1.00 [Cl.sup.-] 0.92 0.03 1.00 S[O.sub.4.sup.2-] 0.88 0.06 0.88 HC[O.sub.3.sup.-] 0.74 0.24 0.69 S[O.sub.4.sup.2-] HC[O.sub.3.sup.-] EC [Na.sup.+] [Mg.sup.2+] [Ca.sup.2+] [K.sup.+] N[O.sub.3.sup.-] [Cl.sup.-] S[O.sub.4.sup.2-] 1.00 HC[O.sub.3.sup.-] 0.83 1.00 Table 5. Correlation analysis matrix for soil saturation extracts All values shown are Pearson's correlation coefficients among concentrations of ions and electrical conductivity EC [Na.sup.+] [Mg.sup.2+] [Ca.sup.2+] EC 1.00 [Na.sup.+] 0.98 1.00 [Mg.sup.2+] 0.99 0.96 1.00 [Ca.sup.2+] 0.59 0.46 0.60 1.00 [K.sup.+] 0.86 0.84 0.86 0.49 N[O.sub.3.sup.-] 0.03 -0.03 0.03 0.39 [Cl.sup.-] 0.98 1.00 0.97 0.47 S[O.sub.4.sup.2-] 0.95 0.94 0.95 0.64 HC[O.sub.3.sup.-] 0.18 0.12 0.24 0.21 [K.sup.+] N[O.sub.3.sup.-] [Cl.sup.-] EC [Na.sup.+] [Mg.sup.2+] [Ca.sup.2+] [K.sup.+] 1.00 N[O.sub.3.sup.-] 0.08 1.00 [Cl.sup.-] 0.85 -0.03 1.00 S[O.sub.4.sup.2-] 0.79 -0.03 0.93 HC[O.sub.3.sup.-] 0.14 -0.20 0.12 S[O.sub.4.sup.2-] HC[O.sub.3.sup.-] EC [Na.sup.+] [Mg.sup.2+] [Ca.sup.2+] [K.sup.+] N[O.sub.3.sup.-] [Cl.sup.-] S[O.sub.4.sup.2-] 1.00 HC[O.sub.3.sup.-] 0.22 1.00 Table 6. Progressive approximation of the regression coefficients to the value of Faraday's constant (96485 C/mol) with the level of treatment of the ionic concentration All values shown are regression coefficients and 95% confidence interval in C/mol. EC is electrical conductivity in dS/m, [u.sub.i] is the limiting equivalent ionic mobility of the species i in mS.[cm.sup.2].mol/eq.C, and [N.sub.i] and [a.sub.i] are, respectively, the concentration and the activity of the species i in meq/L. The activities are assessed with the ion speciation program SOILSOLN EC v. [[summation EC v. [[summation of].sub.i][u.sub.i] of].sub.i][u.sub.i] [N.sub.i] [a.sub.i] Level of treatment of Non corrected the ionic for ion pair concentration formation Irrigation waters 56000 [+ or -] 500 109300 [+ or -] 1500 Soil extracts 49000 [+ or -] 700 113000 [+ or -] 3000 Soil extracts (A) 65200 [+ or -] 1400 98000 [+ or -] 2000 EC v. [[summation of]. sub.i][u.sub.i][a.sub.i] Corrected for ion pair formation Level of Ion pair mobility by Ion pair mobility by treatment of Davies' formula (29) Anderko & Lencka's the ionic dormula (30) concentration Irrigation waters 108600 [+ or -] 1400 108800 [+ or -] 1500 Soil extracts 112000 [+ or -] 3000 112000 [+ or -] 3000 Soil extracts (A) 98000 [+ or -] 2000 98000 [+ or -] 2000 (A) Data from Griffin and Jurinak (1973). Table 7. Progressive approximation of the regression coefficient to the value of Faraday's constant (96485 C/mol) with the decreasing maximum electrical conductivity of the irrigation waters considered for the regression analysis Number of samples in parentheses. All values shown are regression coefficients and 95% confidence interval in C/mol. EC is electrical conductivity in dS/m, [u.sub.i] is the limiting equivalent ionic mobility of the species i in mS.[cm.sup.2].mol/eq.C, and [a.sub.1] is the activity of the species i in meq/L. The activities are assessed with the ion speciation program SOILSOLN EC v. [[summation of]. sub.i][u.sub.i][a.sub.i] Corrected for ion pair formation Level of treatment Non corrected for Ion pair mobility by of the ionic ion pair formation Davies' formula (29) concentration EC [less than or 115000 [+ or -] 6000 114000 [+ or -] 5000 equal to] 14 (70) EC [less than or 110000 [+ or -] 6000 109000 [+ or -] 6000 equal to] 8 (69) EC [less than or 103000 [+ or -] 12000 103000 [+ or -] 8000 equal to] 4 (53) EC v. [[summation of].sub.i][u.sub.i] [a.sub.i] Corrected for ion pair formation Level of treatment Ion pair mobility by of the ionic Anderko & Lencka's concentration formula (30) EC [less than or 114000 [+ or -] 5000 equal to] 14 (70) EC [less than or 110000 [+ or -] 6000 equal to] 8 (69) EC [less than or 103000 [+ or -] 8000 equal to] 4 (53) Table 8. Progressive approximation of the regression coefficient to the value of the Faraday's constant (96485 C/mol) with the decreasing maximum electrical conductivity of the soil saturation extracts considered for the regression analysis Number of samples in parentheses. All values shown are regression coefficients and 95% confidence interval in C/mol. EC is electrical conductivity in dS/m, [u.sub.i] is the limiting equivalent ionic mobility of the species i in mS.[cm.sup.2].mol/eq.C, and [a.sub.1] is the activity of the species i in meq/L. The activities are assessed with the ion speciation program SOILSOLN EC v. [[summation of]. sub.i][u.sub.i][a.sub.i] Corrected for ion pair formation Level of treatment Non corrected for Ion pair mobility by of the ionic ion pair formation Davies' formula (29) concentration EC [less than or 119000 [+ or -] 7000 119000 [+ or -] 7000 equal to] 14 (167) EC [less than or 113000 [+ or -] 8000 113000 [+ or -] 8000 equal to] 8 (161) EC [less than or 104000 [+ or -] 12000 104000 [+ or -] 12000 equal to] 4 (138) EC v. [[summation of].sub.i][u.sub.i] [a.sub.i] Corrected for ion pair formation Level of treatment Ion pair mobility by of the ionic Anderko & Lencka's concentration formula (30) EC [less than or 119000 [+ or -] 7000 equal to] 14 (167) EC [less than or 113000 [+ or -] 8000 equal to] 8 (161) EC [less than or 104000 [+ or -] 12000 equal to] 4 (138)

Acknowledgments

We thank the Spanish International Cooperation Agency (AECI), the Universitat dc Valencia EG, and the Spanish Education Ministry for funding the stay of Dr Raul Zapata in the Centro de Investigaciones sobre Desertificacion during 2001 2002. We also thank the Conselleria dc Medi Ambient of the Valencian Community for funding this research in the framework of the Restoration and Protection of Natural Resources Program (14.04.442.40) line T3133000.

References

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Manuscript received 3 November 2003, accepted 16 February 2004

F. Visconti Reluy (A,B), J. M. de Paz Becares (A,D), R. D. Zapata Hernandez (C), and J. Sanchez Diaz (A,B)

(A) Centro de Investigaciones sobre Desertificacion (CSIC-UV-GV), Cami de la Marjal s/n, 46470 Albal, Valencia, Spain.

(B) Departament de Biologia Vegetal, Facultat de Farmacia, Universitat de Valencia EG, Avda Dr. Moliner 50, 46100 Burjassot, Valencia, Spain.

(C) Escuela de Geociencias, Facultad de Ciencias, Universidad Nacional de Colombia Sede Medellin, Autopista Norte Carrera 64, Calle 64, Apartado Aereo 3840 Medellin, Colombia.

(D) Corresponding author email: jose.m.depaz@uv.es