Modelling Na + within the profile

Based on the consistent differences observed between treatments, as well as seasons, it was decided to develop models to estimate soil Na+ _{from simple input parameters which} could be easily measured. The models were developed to predict soil Na+ _{levels after} wastewater application (Table 4.5), as well as at bud break after the winter rainfall (Table 4.6). With regard to the prediction models for soil Na+ _{after wastewater application, the} amounts of Na+ _{applied via the diluted winery wastewater was an important input} parameters. However, in contrast to the estimation of soil Bray II-K where DMP of the pearl millet interception crop emerged as a strong input parameter, DMP of pearl millet was generally an insignificant parameter when estimating soil Na+_.

Based on the foregoing it would be possible to estimate the soil Na+ _{in the 0-30 cm layer} after wastewater application by means of the following simple, linear regression model: Soil Na+ _{= sqrt(0.00648338 + 9.33858E-7 × Na}

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where Naappl is the amount of Na+ applied via the diluted winery wastewater (kg/ha). For the 30-60 cm layer, the simple linear regression model is:

Soil Na+ _{= sqrt(0.00740477 + 4.26821E-7 × Na}

appl2) (Eq. 4.17) where Naappl is the amount of Na+ applied via the diluted winery wastewater (kg/ha).

For the 60-90 cm layer, the simple multiple linear regression model is: Soil Na+ _{= 0.114418 + 0.000616649 × Na}

appl - 0.00813162 DMPPm (Eq. 4.18) where Naappl is the amount of Na+ applied via the diluted winery wastewater (kg/ha) and DMPPm is the dry matter production of the pearl millet interception crop (t/ha).

For the 90-120 cm layer, the simple linear regression model is: Soil Na+ _{= sqrt(0.00796653 - 0.000432853 × sqrt(Na}

appl) (Eq. 4.19) where Naappl is the amount of Na+ applied via the diluted winery wastewater (kg/ha).

There was a good relationship between estimated and actual soil Na+ _{of three selected} treatments, namely river water, winery wastewater diluted to 1000 mg/L and 3000 mg/L COD, respectively (data not shown). Under the prevailing conditions, Na+ _{application via} diluted winery wastewater in excess of 400 kg/ha would increase the soil Na+ _{to levels higher} than the threshold of 0.4 cmol(+)_{/kg recommended for this particular soil (W.J. Conradie,} personal communication) (Fig. 4.14).

Figure 4.14. The estimated effect of sodium (Na+_{) applied via diluted winery}

wastewater on the soil Na+ _{contents in the soil profile after wastewater application}

where 50 kg, 100 kg, 300 kg, 400 kg and 500 kg Na+ _{per ha is applied to a vineyard in a}

sandy soil where a pearl millet interception crop of 5 t/ha dry matter production (DMP) is produced. Dashed vertical line indicates the critical Na+ _{threshold for this particular}

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Table 4.5. The two independent variables, namely amount of sodium (Na+_{) applied via diluted winery wastewater and the dry matter}

production (DMP) of a pearl millet interception crop, used in the estimation of soil Na+ _{after wastewater application in a sandy soil.}

Dependent variable

Independent variables

Applied Na+ _{(kg/ha) Pearl millet DMP (t/ha) Model}

Coefficient p Coefficient p N R2 _{s.e p}

Soil Na+ _{0-30 cm 9.34E-7 0.0009 15 0.58 0.003 0.0009}

Soil Na+ _{30-60 cm 4.27E-7 0.0828 15 0.21 0.003 0.0828}

Soil Na+ _{60-90 cm 0.0006 0.0125 -0.008 0.0035 15 0.53 0.016 0.0102}

Soil Na+ _{90-120 cm 0.0004 0.2436 15 0.10 0.002 0.2436}

Table 4.6. The three independent variables, namely soil sodium (Na+_{) in the 30-60 cm and 60-90 cm soil layer after wastewater}

application and rainfall from February to August (mm) used in the estimation of soil Na+ _{at bud break after the winter rainfall in a sandy}

soil. Dependent variable Independent variables Soil Na+ _{(30-60 cm)} (cmol(+)_/kg) Soil Na+ _{(60-90 cm)} (cmol(+)_/kg)

Rainfall (February - August) (mm)

Model

Coefficient p Coefficient p Coefficient p N R2 _{s.e p}

Soil Na+ _{0-30 cm 0.00004 0.0001 20 0.59 2.38 0.0001}

Soil Na+ _{30-60 cm 0.628 0.0002 -0.00016 0.0005 20 0.73 0.01 0.0000}

Soil Na+ _{60-90 cm 0.495 0.0011 -0.00023 0.0001 20 0.68 0.01 0.0001}

Soil Na+ _{90-120 cm -0.00449 0.0000 20 0.65 0.23 0.0000}

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Should the additional Na+ _{applied via the diluted winery wastewater increase to 500 kg/ha,} there would also be a substantial increase in soil Na+ _{in the sub-soil after wastewater} application. It is expected that Na+ _{accumulation would occur to a greater extent in soils with} heavier textures than the sandy, alluvial soil containing c. 3.3% clay which was used in the current study.

In order to prevent the accumulation of soil Na+_{, a halophytic interception crop such as} fodder beet (Beta vulgaris L. Brigadier) could be used to absorb excess Na+ _{as it has been} reported that it can absorb up to 178 kg Na+ _{per ha (Myburgh & Howell, 2014).}

It would be possible to estimate the soil Na+ _{in the 0-30 cm layer at bud break by means of} the following simple, linear regression model:

Soil Na+ _{= 1/(4.81792 + 0.0000423129 × Rainfall}

FA2) (Eq. 4.20) where RainfallFA is the rainfall from February to August (mm).

For the 30-60 cm layer, the simple multiple linear regression model is: Soil Na+ _{= 0.100904+0.627604 × Soil Na}

AWA30-60 - 0.000164219 × RainfallFA (Eq. 4.21) where Soil NaAWA30-60 is soil Na+ in the 30-60 cm layer after wastewater application and RainfallFA is the rainfall from February to August (mm).

For the 60-90 cm layer, the simple multiple linear regression model is: Soil Na+ _{= 0.138816 +0.495405 × Soil Na}

AWA60-90 - 0.000232851 × RainfallFA (Eq. 4.22) where Soil NaAWA60-90 is soil Na+ in the 60-90 cm layer after wastewater application and RainfallFA is the rainfall from February to August (mm).

For the 90-120 cm layer, the simple linear regression model is: Soil Na+ _{= exp(-0.776641 - 0.00448983 × Rainfall}

FA (Eq. 4.23) where RainfallFA is the rainfall from February to August (mm).

Using the models given in Eqs. 4.20 to 4.23 to estimate soil Na+ _{at bud break, with the} exception of two data points, there was a good relationship between estimated and actual soil Na+ _{contents of three selected treatments, namely river water, winery wastewater diluted} to 1000 mg/L and 3000 mg/L COD (data not shown). Regardless of the amount of Na+ applied via diluted winery wastewater and magnitude of rainfall, levels of soil Na+ _{were still} below 0.4 cmol(+)/kg (Fig. 4.15). However, should substantially more Na+ _{be applied via the} wastewater, there is a more pronounced accumulation and redistribution in the deeper soil layers (Fig. 4.15C). Therefore, in the case of heavier textured soil it seems likely that the accumulation and redistribution of Na+ _{would occur to an even greater extent. Results} confirm that using diluted winery wastewater for vineyard irrigation of a deep, sandy soil with excessive drainage could lead to pollution of natural water sources.

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Figure 4.15. The estimated effect of rainfall on the distribution of sodium (Na+₎

contents in the soil profile at bud break after the winter rain where (A) 44 kg, (B) 93 kg and (C) 500 kg per ha Na+ _{is applied via diluted winery wastewater to a vineyard in a}

sandy soil where a pearl millet interception crop of 5 t/ha dry matter production (DMP) was produced. Dashed vertical line indicates the critical Na+ _{threshold for this}

particular soil (Conradie, personal communication).

In general, the ExSP did not exceed the critical threshold of 15% for sustainable agricultural use (Laker, 2004; Seilsepour et al., 2009). The models developed to estimate ExSP after wastewater application in the respective soil layers were insignificant, with low R2_.

It would be possible to estimate the soil ExSP in the 0-30 cm layer at bud break means of the following simple, linear regression model, where R2 _{was 42%:}

Soil ExSP = 1/(0.216304 + 0.00000138595423129 × RainfallFA2) (Eq. 4.24) where RainfallFA is the rainfall from February to August (mm).

For the 30-60 cm layer, the simple multiple linear regression model could explain 36%of the variation in ExSP:

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where Soil ExSPAWA30-60 is soil extractable sodium percentage in the 30-60 cm layer after wastewater application and RainfallJA is the rainfall from June to August (mm).