DIVISION S-6—SOIL AND WATERMANAGEMENT AND CONSERVATION

Effects of Bicarbonate on Sodium Hazard of Irrigation Water: Alternative Formulation1

S. MlYAMOTO2

ABSTRACTThe conventional equation using the saturation index does

not satisfactorily account for the effect of bicarbonate on sodi-city. We, therefore, examined the existing method and present-ed an alternative formulation. The alternative formulationwas based on direct numerical solutions of well-known carbonateequilibrium reactions, and consisted of the solution of the sec-ond- or the third-order polynomial approximation. The analyti-cal results were then compared with published laboratory, lysi-meter, and field data. The comparison indicates that the con-ventional equation using the saturation index overestimates thesodicity of irrigation water having a high ratio of Ca to HCO3and underestimates otherwise. The method also generally over-estimates the sodicity of drainage water. The proposed third-power polynomial approximation yields a satisfactory predictionof the sodicity of irrigation water, of drainage water, and ofsurface soils. The second-order approximation can also beused for predicting the sodicity of drainage water if the pH ofthe drainage water is known. The proposed methods aresomewhat more complex than the conventional method, butcan be conveniently utilized with a programmable calculatoror a mini-computer.

Additional Index Words: water quality, calcium precipita-tion.

Miyamoto, S. 1980. Effects of bicarbonate on sodium hazard ofirrigation water; alternative formulation. Soil Sci. Soc. Am. 1.44:1079-1084.

WHEN IRRIGATION WATER contains appreciableamounts of carbonates, Ca and, to a lesser ex-

tent Mg may precipitate as CaCO3 or MgCOs- Sincesodium ions generally remain soluble, the precipita-tion of divalent cations increases the sodium adsorp-tion ratio (SAR) and potential sodium hazard. Thisconcept has been recognized and accepted for manyyears, yet the method of quantifying bicarbonate ef-fects has undergone several modifications. This paperexamines existing methods of evaluating bicarbonateeffects on sodium hazard, and proposes an alternativeformulation.

The method of correcting bicarbonate effects onsodicity developed by Bower and his associates (1965)is probably most widely recognized (e.g., Rhoades,1972; Ayers and Westcot, 1977). This method utilizesthe saturation index of Langelier (1936) for predict-ing bicarbonate effects on sodicity. (For the conve-nience of presentation, the sodicity prediction usingthe saturation index will be referred to as the con-ventional method in this paper). For predicting thesodicity of irrigation water and of surface soils, theirequation is

1 Texas Agr. Expt. Sta. J. no. 16014. Received 13 Feb. 1980.Approved 2 May 1980.

2 Assistant Professor, Texas A&M University Research Center,El Paso, 1380 A&M .Circle, El Paso, TX.

1080 SOIL SCI. SOC. AM. J., VOL. 44, 1980

SAR = SAR0 [1 + (8.4 - [1]wherepHc1 = (pK2 - p#cacoa) + p(Ca + Mg) + pAlk [2]

and SARo is the sodium adsorption ratio of irrigationwater computed from water analysis, SAR the ratiothat will be obtained after Ca and Mg precipitation,pHc1 the computed pH, K2 the second dissociation con-stant of carbonic acid, KCacoa the solubility productof CaCO3, both corrected for ionic strength, Ca andMg the molar concentrations of Ca2+ and Mgz+, Alkthe equivalent concentration of HCO3~ and COs2~,and p denotes the negative logarithm. Note that inEq. [2] two modifications were applied to the originalpHc value of Langelier (1936); one being the use of8.4 for the actual pH and the other is the inclusion ofMg for computing pHc. In order to differentiate thetwo, the modified pHc is suffixed. The difference be-tween the actual pH and the computed pH is, ofcourse, referred to as the saturation index. In thesubsequent studies, Bower et al., (1968) extended Eq.[1] for predicting SAR of drainage waters, SAR,jw,to

SARdw = SAR0 [1 + (8.4 - [3]where LF is the leaching fraction.

Experimental data obtained thereafter, however, didnot always agree with the projection. The data byBower et al. (1968) and Pratt and Bair (1968), forinstance, indicate that Eq. [3] generally overestimatesSARdw Gumaa et al. (1975) also cited that Eq. [1]generally overestimates the SAR of irrigation water,and that the inclusion of Mg in computing pHc ac-centuates this error. Rhoades (1968) subsequently in-troduced an empirical factor to account for lysimeterdata, using a concept of mineral weathering. Themodified empirical equation well described their lysi-meter data and the greenhouse data by O'Connor(1971), but not necessarily the field data obtained byBingham et al. (1979). It is thus evident that theexisting method using pH,.1 works in some cases butdoes not in other cases.

As a subject of fundamental water chemistry, Ca pre-cipitation in aqueous carbonate systems has beenstudied by many. Tanji and Doneen (1966), for in-stance, studied the following reactions in quantifyingCa precipitation:

HCO3- ^± H2C03 5* CO2 + H20 [4]H+

HC03- ^±+ + C032~ CaCOs (J,).

[5][6]

They have introduced a successive approximation tech-nique to evaluate Ca precipitation, and many othersalso used a similar numerical technique to solve waterquality problems. Unfortunately, however, these nu-merical methods are cumbersome and unsuited forcommon use. The following is an attempt to simplifythe estimate of Ca precipitation, and to incorporateit into the prediction of bicarbonate effects on sodicity.

ANALYSIS AND FORMULATIONThe system in question is irrigation water or surface soils

exposed to the atmosphere. Such a system can be treated as anopen system with various COa partial pressures. From Eq. [4]

through [6], the overall chemical reaction is

Ca"+ + 2HC03- •£ CaCO3 (J) + CO2

with an appropriate equilibrium constant

[C02] KK = [HC03-]2

H2O [7]

[8]

where[HC03-] [HC03-]

[HZC03] ^coy co:= 4.16 X 10-'

[CO,-][HCO.-]

] [CO32-] = 6.00 X ID'8

= 4.82 X 10-"(aragonite)(calcite)

#c.co =

and Ccoj is the CO2 molar concentration at STP, which is 3.38X 10-a, Pco!! is the partial pressure of CO2 in atm in the sur-rounding gas phase (ordinarily 3.3 X 10'4 atm for the atmos-phere), and the brackets denote the activity. All numerical val-sues are for 25°C and obtained from Latimer (1952), Frear and^Johnson (1929), and Sillen and Martell (1964). The substitutionof numerical values into Eq. [8] yields K = 2.413 X 10* forcalcite and 1.95 X 10* for aragonite systems exposed to theatmosphere at 25 °C.

Rewriting Eq. [8] in terms o£ the precipitation amount x,and of ion concentrations, we obtained

K =i« y2 (Ca - x) (HCCy-2x)2 [9]

where YI and y2 are the mono and divalent activity coefficients,and the parenthesis indicate the concentration of respective ions.The rearrangement of Eq. [9] for x yields

x3 + <z2x2 + a^x + a0 = 0 [10]

where

<z2 = -(Ca + HC03)

UT. = (Ca) (HC03) + (HCO3)!!/4

a0 = -(Ca) (HCO,)»/4 + C«M Pco2/(4(The procedure to derive a polynominal equation from anequilibrium relation such as Eq. [8] is widely used, and onemay refer to, for example, Dutt et al. (1972) for details).

The activity coefficients can be estimated by the Debye-Huckel equation

logic Y« =-AZ*

[11]

where A is a temperature dependent constant (0.509 at 25 °C),Z the valence of ions in question, and p the ionic strength. Weused the regression equation developed by Bower et al. (1965)for computing /i as

Table 1—Ionic activity coefficients estimated by the Debye-Hiickel equation with an empirical relation of Bower et al.

(1965) for estimating the ionic strength.

Total salt concentration

meq/liter12468

1015202530405070

100150

mmho/cm

0.10.20.40.60.81.01.52.02.53.04.05.07.0

10.015.0

Ti

0.9520.9390.9190.9050.8980.8830.8620.8460.8320.8210.8000.7800.7590.7300.695

Activity coefficient

y>0.8230.7770.7150.6710.6370.6080.5540.5130.4810.4540.4110.3790.3310.2840.233

T.7.0.780.730.660.610.570.540.480.430.400.370.330.300.250.210.16

7i!7>

0.740.680.600.550.510.470.410.360.330.300.260.230.190.150.11

MIYAMOTO: EFFECTS OF BICARBONATE ON SODIUM HAZARD OF IRRIGATION WATER 1081

It = 0.001 (1.35C + 0.535) [12]where C is the total cation concentration in meq/liter. Thisequation makes it possible to compute p without knowing anioncompositions.

In solving Eq. [10] for x, the activity coefficient needs to bespecified. (Note that the coefficient is used for computing aa).Since C is dependent on x, y^ is also dependent on x by Eq. [12].In order to solve Eq. [10] precisely, we then have to solve Eq.[10] and [11] simultaneously. Most irrigation waters in westernstates are, however, relatively salty, thus masking out to a largeextent, the decrease in the total salt content following Ca pre-cipitation. For instance, Ca precipitation in typical irrigationwaters in the southwest (containing 10 to 20 meq/liter totalcations) ranges from 1 to 2 meq/liter. This will cause an errorof the coefficient estimate by about 0.01 to 0.02 units, which isinsignificant for the present purpose. Therefore, we approxi-mated y, by using the initial total cation concentration. Forthe convenience of readers, the computed activity coefficient isgiven in Table 1 as a function of the total cation concentration.By substituting y, in fl0, Eq. [10] can then be solved directlyfor x, for instance, by using a programmable calculator.

When the system in question is the closed one, e.g., watersin pipelines or in a deep soil profile, the reaction given byEq. [4] can be ignored. The overall chemical reaction forthe closed system is then

Ca2+ + HC03- -*. CaC03 (|) + H+ [13]with an appropriate equilibrium constant K

After evaluating Ca precipitation x, the SAR of water canbe estimated by definition.

SAR =Na

V(Ca - x) + Mg[17]

K = [14]

This is the equilibrium equation originally considered by Lan-gelier (1936). He rewrote Eq. [14] for [H+] and used its log-arithmic expression for the purpose of predicting the directionof reaction, but not for quantifying the precipitation amount.If Eq. [14] is to be used for a quantitative evaluation, weshould rewrite Eq. [14] in terms of ion concentrations and Caprecipitation, x, as

K = [H+]Vi 72 (Ca - x)(HCOa - x) [15]

*" - (Ca + HC03)x -1- (Ca).(HCO.) - [H+]/(y1y2K) = 0. [16]

where the cation concentrations are in mmol/liter. The follow-ing calculations were made for evaluating the suitability of theconventional equation using the saturation index and the alter-native methods discussed above.

CALCULATIONS AND DISCUSSIONIrrigation Water

Table 2 summarized the data used for calculation,the calculated Ca precipitation, and the SAR of irri-gation water. The initial quality of water is givenin columns (2) through (7), and the measured Caprecipitation and the experimentally determined SARare given, respectively, in columns (8) and (9). Wa-ter samples numbered 1 through 12 were studied byBower et al. (1965) in conjunction with the verifica-tion of pHc as an index of the tendency of Ca precipi-tation. The water samples were prepared in a labora-tory and placed in flasks containing pure precipitatedCaCO3. The samples were exposed to the atmosphereand the dissolved Ca content was measured after equi-librium and filtration. Water samples 13 through 19,representing some of the irrigation waters used inArizona and Texas, were examined by Miyamoto etal. (1975). The experimental procedures were similarto those used by Bower et al. (1965). All the experi-ments were reportedly performed at room tempera-tures 23.5 to 25°C.

In accordance with the conventional method, wefirst computed pHc

J by Eq. [2] and SAR by Eq. [1].The results are given in columns (10) and (11). Ifthe conventional equation is suitable for predictingthe changes in SAR following calcium precipitation,

Table 2—The initial quality of test waters, and the precipitation of Ca and subsequent changes in Na adsorption ratio computedby various methods. The measured values are shown in columns (8) and (9).

Initial qualityNo.

(1)123456789

101112

13*141516171819

TC

meq/liter(2)55

101011141720202171754.57.48.0

11.011.712.539.1

SAR0

(3)2.24.73.16.72.99.09.24.59.5

14.719.439.85.87.24.12.63.86.38.4

Na

(4)2.503.755.07.55.0

11.013.010.0

15.018.055.069.03.76.05.04.36.38.7

23.5

Ca Mg- meq/liter -

(5)2.501.255.02.56.03.04.0

10.05.03.0

16.06.00.61.02.54.43.92.59.1

(6)0000000000000.20.40.52.31.51.36.5

Measured

HCO, ACaf

(7) (8)2.50 1.302.50 0.713.90 3.774.37 2.245.00 4.038.00 2.915.0 3.27

10.0 8.7310.0 4.9011.0 2.955.0 4.433.0 2.012.3 0.12.8 0.65.0 2.12.7 1.83.3 1.92.7 1.24.9 3.4

SAR

(9)3.27.26.4

20.85.0

51.821.512.567.1113.822.948.86.38.97.52.74.87.79.5

Calculated byConventional Eqs.pHc'

(10)7.718.017.177.477.107.237.336.656.957.136.937.578.257.947.377.217.347.586.85

SAR

(11)3.86.67.0

12.96.7

19.519.012.323.233.448.072.96.7

10.58.35.77.9

11.621.3

Calculated byEq.[16][17]

ACa

(12)1.500.473.931.905.162.663.299.514.662.748.77

2.96-0.00

0.272.012.732.791.416.8

SAR

(13)3.56.06.8

13.77.7

26.721.820.236.449.928.955.95.88.07.12.45.57.9

11.2

Calculated by Eq. [10] [17]

ACa

Calcite

(14)1.310.7323.742.244.002.903.248.644.902.964.341.960.2280.6282.261.802.201.343.52

Aragonite

(15)1.230.6583.642.183.902.883.148.544.882.964.261.850.1690.5582.261.732.101.243.52

SAR

Calcite

(16)3.26.96.1

20.85.0

49.121.012.167.0

127.222.748.56.99.68.22.74.97.89.5

Aragonite

(17)3.17.36.3

18.84.8

44.919.811.761.2

127.222.747.96.59.28.22.74.97.69.5

t ACa: The amount of Ca precipitated in meq/liter.t Water no. 13 (well water at Willcox, Az), 14 (well water at Safford, Az), 15 (Tucson Municipal sewage), 16 (Colorado R. at Yuma, Az), 17 (Rio Grande, at El

Paso, Tx), 18 (Salt R. at Phoenix, Az), 19 (Irrig. Return flow at Yuma, Az).

1082 SOIL SCI. SOC. AM. J., VOL. 44, 1980

the computed SAR in column (11) should agree withthe experimentally determined SAR shown in column(9). The comparison indicates that Eq. [1] under-estimates SAR when the ratio of HCO3~ to Ca2+ ishigh, e.g., Water 4, 6, 9, and 10. When the ratio waslow, e.g., Waters 11, 12, 15, 17, and 19, Eq. [1] sig-nificantly overestimated SAR. When Ca2+ and HCO3~concentrations were about equal, the agreement wasimproved.

Table 2 also includes the results computed by thesecond power polynomial approximation, Eq. [16].For computing Ca precipitation, aragonite solubility(6.00 x 10~9) at 25°C was used. Also, H+ activity wasassumed to be 0.446 x 10~8 or pH = 8.35, the equilib-rium pH of pure aqueous lime systems exposed to theatmosphere. The last term of Eq. [16] was computedto be (0.553/yiy2) X 10~6. Since this equation wasdeveloped for a closed system, an agreement betweenthe measured and the predicted values should not bevery good. (All the data are from open system experi-ments). This equation, however, may yield a projec-tion similar to the conventional method, because Eq.[16] was derived from the same equation as the oneused for developing the pHc measure, Eq. [ 14]. In-deed, the computed SAR values are similar, resultingin overestimation when the ratio of HCO3~ to Ca2+

was low, and underestimation when the ratio was high.The reason for this pattern of deviation is related

to the assumption involved in H concentration or pH.In both the conventional and the closed system equa-tion, we assumed a constant pH (or H+ activity).Under an open system, this assumption is not alwaysvalid, as can be seen from the first dissociation reac-tion of carbonic acid.

L" J ~ yi (HC03-)For a given system, KI, Cco2, Pco2, and yj can be con-sidered fixed constants. Then, the activity of H ionswill fluctuate depending on the equilibrium HCO3~concentrations. For instance, if water containsHCO3~ in an amount greater than Ca2+ in equivalentunits, an excess HCO3~ concentration will result atequilibrium. This will drop H activity below that

assumed, and causes a greater precipitation of Ca thanthe projected. Conversely, if water contains lessHCO3~ than Ca2+, the equilibrium HCO3~ concen-tration would deplete, and the equilibrium H+ con-centration would increase over the assumed, thus yield-ing a smaller precipitation. In essence, we cannot usethe conventional equation or the second power approx-imation for predicting the sodicity of water ex-posed to the atmosphere.

We have also tested the suitability of the third-powerpolynomial approximation, Eq. [10]. For computingCa precipitation the atmospheric CO2 partial pressure(3.3 X 10~4 atm) was assumed. Also, both aragoniteand calcite solubility at 25°C were used just for acomparison. The last term of Eq. [10], CC02 PCOZ/(4yi\2K), was computed to be (0.143 X 10-9)/yi2y2for aragonite and (0.155 X 10~9)/yi2y2 for calcite. Thecalculation based on aragonite solubility yields some-what smaller Ca precipitation than that based oncalcite (columns 16 and 17). The difference prob-ably bears no practical significance, however. Sub-sequently, we determined the correlation coefficient(r2) between the measured and the predicted SAR,assuming aragonite solubility. The analysis has showna good correlation, r2 = 0.986, as compared to theconventional equation yielding r2 = 0.312.

Drainage WaterThe data used for calculation were obtained from

the published article by Rhoades et al. (1973). Theyhave simulated various types of irrigation water andanalyzed the drainage water through extensive lysi-meter tests. They have provided the data for LF =0.1, LF = 0.2, and LF = 0.3. The data for LF = 0.1were not used, because some of them did not appear tobe in equilibrium. We have first computed pH,.1 byEq. [2] and estimated the SAR of irrigation waterby Eq. [ 1 ]. The results are listed in columns (8)and (9) of Table 3. Then, the SAR of drainage waterwas computed by the conventional equation, [3].The results shown in column (12) are much greaterthan the measured SAR shown in column (11). Oneobvious reason for overestimation is related to theuse of 8.4 for pHa, the actual pH. The experimental

Table 3—Irrigation water quality, the leaching fraction, and the measured and the computed Na adsorption ratio of drainage water,SARdw. The measured data are from Rhoades et al. (1972).

Predicted SARIrrigation water quality

No. TC SAR0

meq/liter(1) (2) (3)1 9.0 1.8

2 10.1 6.0

3 14.1 1.5

4 14.3 6.4

5 20.5 4.8

6 31.7 7.3

7 37.5 3.2

Na Ca Mg HCO, PHC' SARLeaching Measuredfraction SAR

Conven-tional

2nd PowerAragonite Soil lime

3rd PowerAragonite

——————— meq/liter ———————(4)3.0

7.1

3.4

9.6

10.6

18.5

11.4

(5)4.1

2.0

6.9

3.2

3.7

7.2

17.0

(6)1.9

0.8

3.6

1.3

6.1

5.9

9.1

(7)3.2

6.3

3.7

3.2

5.2

3.2

3.1

(8)7.3

7.3

7.0

7.5

6.9

7.1

6.8

(9)3.8

12.6

3.6

12.2

12.0

16.8

8.3

(10)0.20.30.20.30.20.30.20.30.20.30.20.30.20.3

(11)4.13.2

15.511.23.92.5

13.39.6

10.48.3

16.014.07.66.0

(12)8.56.9

28.223.18.16.6

27.222.326.922.037.630.718.615.2

(13)4.63.4

16.911.63.93.0

15.711.311.99.0

18.613.67.75.8

(14)4.23.0

14.39.73.72.7

13.89.7

11.28.4

17.612.67.55.3

(15)4.23.2

18.512.63.62.7

14.911.011.89.1

16.713.18.97.2

MIYAMOTO: EFFECTS OF BICARBONATE ON SODIUM HAZARD OF IRRIGATION WATER 1083

data for the present case indicates that pHa of drain-age water ranges from 6.6 to 7.2 with an average valueof 6.8, instead of the assumed value of 8.4. The useof the measured pH value, in place of 8.4, should dropthe saturation index, consequently yielding smallervalues for SARdw, even though Eq. [3] is not in-tended to be used in this fashion. We have also com-puted the SAR of drainage water by using the min-eral weathering factor of Rhoades (1968) in Eq. [3].The use of this factor improved the agreement atLF = 0.3, but accentuated deviation at LF = 0.2.

We have subsequently computed SARdw by usingthe second-order polynomial approximation, Eq. [16].In using Eq. [16], we must use ion concentrationsand activity coefficients corrected for LF, and a realis-tic estimate of H+ activity. The correction for LF wasmade by dividing the ionic concentration of irrigationwater by LF. We used pH = 6.8, the average valueobserved in the drainage water as given by Rhoadeset al. (1973), for computing H+ activity. Also, ara-gonite solubility product 6.4 X 10~9 at 20°C was usedto meet the mean soil temperature observed in the ex-periment. The last term of Eq. [16] was computed tobe 21.0 x 10~6/ri72 for this case. The computed Caprecipitation was generally greater than the measured,except in Water 7 which contained 22.4 meq/liter ofSO4 in irrigation water. Obviously, gypsum in addi-tion to CaCO3 have precipitated in this case. In othercases, the overestimation of Ca precipitation was part-ly expected, since we ignored Mg precipitation.

As reported by Oster and Rhoades (1975), the ex-perimental data imply some precipitation of Mg. InWater 5, it is possible that the Mg-Ca exchange wasleft incomplete, since the Mg-to-Ca ratio of this waterwas exceptionally high. The Mg precipitation, and inone case, the incomplete Mg-Ca exchange may havecompensated for the overestimation of Ca precipi-tation, thus yielding a reasonably good estimate ofSARdw The correlation coefficient between the com-puted and the measured SARdW was, for instance, 0.974with the unit slope. This agreement indicates thatEq. [16] in combination with Eq. [17] is usable forpredicting SARdw if a pH of drainage water is pro-vided, but not necessarily for computing the preciseamount of Ca precipitation. Considering the over-estimation in Ca precipitation, we have also used agreater solubility product for CaCO3 (11.3 x 10~9)as suggested by Suarez (1977). He obtained the solu-bility for soil CaCO3 by analyzing well water beneathirrigated fields in Arizona. The use of this solubilityin Eq. [16] somewhat improved the prediction ofCa precipitation, and consequently SARdw (column14).

Considering the fact that the second-power ap-proximation produced extremely inconsistent predic-tions of sodicity of irrigation water, the good predic-

tion obtained with the drainage water sodicity maysound surprising. Even the conventional equationusing pHc1 yielded a high correlation coefficient al-though the regression coefficient (or the slope) wasmuch less than unity. In the case of drainage water,it is reasonable to assume that the lower portion ofthe lysimeters created a condition analogous to aclosed system. The actual pH values (6.6 ̂ 7.2) wereindeed much lower than the equilibrium pH of anopen system, indicating the accumulation of CO2 andcarbonic acid. Both the conventional equation andthe second-power approximation were developed fora closed system, providing a reason that these equa-tions may work. An additional point is that the sodic-ity prediction by these equations depended on theHCO3~ to Ca2

+ ratio in irrigation water, but, as wesee here, not in the case of drainage water. This canbe explained by examining the definition of the firstdissociation reaction for a closed system;

- yi(HC03-)'

Notice that the pH of water under a closed system isgoverned by a ratio of H2CO3 to HCO3~, instead ofHCO<r alone. The reduction in HCO3~ followingCa precipitation is accompanied by an increase inH2CO3. Thus, the pH under a closed system becomesnearly independent of Ca2+/HCO3~ ratios, providinga basis for a consistent prediction of Ca precipitation.

Since the second-power polynomial approximationproduced an adequate estimate of SARdw, the use ofthe third-power equation may be merely academic.Just to verify the applicability, we proceeded with theestimate by using the measured average COg partialpressure of 0.13 atm and the solubility of aragonite.(The adjustment of CO2 partial pressure is essentialfor using this equation in drainage water. If the valueis now known, it can be computed from pH and HCOsdata.) The results (column 15) agreed reasonably wellwith the measured SARdw, but not necessarily withthe measured Ca for the reasons mentioned earlier.

Surface Soils

Finally, we have tested the applicability of the con-ventional equation and the proposed equations inpredicting the exchangeable sodium percentage (ESP)of field soils (Table 4). The data were obtained byBingham et al. (1979) through 8 years of monitoringin an orange orchard in California. The measuredvalues listed in Table 4 are the average values for1966 to 1973 and for 1971 to 1973, and the soil sam-ples were collected from the top 0 to 30 cm. Likemany other field data, there are considerable varia-

Table 4—Irrigation water quality, the measured exchangeable sodium percentage (ESP) of surface soils, and the computed sodiumadsorption ratio (SAR). The field data are from Bingham et al. (1979).

Irrigation water quality

No.

1234

TCmeq/liter

5.112.824.613.0

SAR0

1.12.53.72.7

Na

1.55.0

10.05.2

Ca Mg

2.9 0.75.2 2.69.7 4.96.6 0.7

HCO,

2.82.95.62.8

pHc'

7.507.266.777.27

Measured ESP

1966-73

1.82.84.02.5

1971-73

2.13.44.42.7

Computed SAR

Conventional

2.25.49.75.8

2nd power

1.63.45.64.0

3rd power

1.32.64.22.9

1084 SOIL SCI. SOC. AM. J., VOL. 44, 1980

tions in measured ESP, e.g., ranging from 1.4 to 2.8in Water 1.

Since the leaching fraction at the surface soil wasnot known, we simply applied the equations used forestimating SAR of irrigation water to the present case.(The sodicity of surface soils under normal irrigationis often equal to that of irrigation water after exposedto the atmosphere). We also assumed that SAR isapproximately equal to ESP, although this is not al-ways the case. The conventional Eq. [1] generallyoverestimated ESP, and the second-power polynomialequation also overestimated ESP of soils irrigated withWaters 2 through 4. Recall that these equations gen-erally overestimate Ca precipitation and SAR whenirrigation water contains Ca substantially greater thanHCO3. Irrigation Waters 2 through 4 fall into thiscategory, whereas Water 1 contains nearly equalamounts of Ca and HCO3. The third-power poly-nomial approximation provided reasonable estimatesin Waters 2 through 4, and a somewhat lower esti-mate in Water 1.

Results of the above tests are encouraging so far.One may further test the applicability of the proposedequations under given local soil and water conditions.Considering the increasing evidence that water in-filtration and crop growth are related more closelyto the sodicity of irrigation water (or surface soils)than that of drainage water, the bicarbonate effect onsodicity can best be characterized by the proposedcubic equation, and whenever desirable, supplementedwith the quadratic equation. The proposed equationsare not expected to be applicable when certain fertili-zer elements or water conditioners are applied to ir-rigation water. Water-application of NH3, a commoncultural practice in the southwest, for instance, dras-tically increases Ca precipitation and the sodicity ofirrigation water, while acid application may reduceprecipitation. These special cases are considered else-where (Miyamoto and Ryan, 1976). The proposedequation may also fail when water or soils are rich inCa and SO4. Of course, irrigation waters rich in gyp-sum seldom cause sodium hazards.

In summary, the present analysis indicates that theconventional equation based on the saturation indexdoes not always yield a satisfactory prediction of bicar-bonate effects on sodicity. The proposed third-powerpolynomial equation appears to be more reliable forpredicting bicarbonate effect on the sodicity of irri-gation water, of surface soils, and of drainage water.The second-power polynomial approximation can alsobe used for predicting the sodicity of drainage waterif an appropriate pH value of the drainage wateris provided. From a practical point of view, the effectof bicarbonate on sodicity is much smaller than hasbeen claimed. The simplified numerical method dis-cussed here would be useful for a routine evaluationof the bicarbonate effect, providing that no fertilizer

elements or water conditioners are to be applied tothe water.