Long-term salt equilibrium equation
Long-term water balance of the rootzone and leaching fraction
The basis for understanding the impact of irrigation and drainage management on the salt balance is the water balance of the rootzone. The water balance of the rootzone can be described with the following equation:
I_{i} + P_{e} + G - R - ET = DW_{rz} (1)
where:
I_{i} = irrigation water infiltrated which is the total applied irrigation water minus the evaporation losses and surface runoff (mm);
P_{e} = effective precipitation (mm);
G = capillary rise (mm);
R = deep percolation (mm);
ET = evapotranspiration (mm); and
DW_{rz} = change in moisture content in the rootzone (mm).
On a long-term basis, it can be assumed that the change in soil moisture storage is zero. The water balance then reads:
I_{i} + P_{e} - R* - ET = 0 (2)
where:
R* = net deep percolation, R-G (mm).
Therefore, the depth of water percolating below the rootzone is the amount of water infiltrated minus the water extracted by the plant roots to meet its evaporation demands. The fraction of water percolating from the rootzone is called the leaching fraction (LF).
(3)
Salt equilibrium equation of the rootzone with complete mixing
With each irrigation, salts are added to the rootzone and evapoconcentrated by crop ET. A fraction of the salts is leached below the rootzone with the net deep percolation water. After a certain period, salt accumulation in the soil will approach an equilibrium or steady-state concentration based on the salinity of the applied water and the LF (FAO, 1985b).
The calculation of rootzone salinity makes the following assumptions:
the irrigation water mixes completely with the soil water;
the exchange processes and chemical reactions which take place in the soil are not taken into consideration;
the amount of salts supplied by rainfall and fertilizers and exported by crops are negligible; and
a zone of shallow groundwater is created with the same average salinity concentration as the percolation water.
Under these assumptions, the salinity of the soil water is equivalent to the salinity of the water percolating below the rootzone. The salinity of the water percolating below the rootzone can be estimated from the salt balance:
IW C_{IW} = R* C_{R*} (4)
where:
IW = infiltrated water (Ii + Pe) (mm);
C_{IW} = salt concentration of the infiltrated water (mg/litre); and
C_{R*} = salt concentration of the net percolation water (mg/litre).
The salt concentration of the infiltrated water can be calculated as:
(5)
where:
C_{I} = salt concentration of the irrigation water (mg/litre).
The salinity of the percolation water can also be calculated with the following formula:
(6)
A strong relation exists between the salt concentration C of a solution expressed in milligrams per litre and the electrical conductivity (EC) of a solution in decisiemens per metre (1 dS/m corresponds approximately to 640 mg/litre). Therefore, the salinity of the net deep percolation, which is equivalent to the salinity of the soil water, can also be expressed as:
(7)
where:
EC_{SW} = electrical conductivity of the soil water (dS/m);
EC_{R*} = electrical conductivity of the percolation water (dS/m); and
EC_{IW} = electrical conductivity of the infiltrated water (dS/m).
The EC_{SW} is inversely proportional to LF, i.e. a low LF results in a high EC_{SW} and vice versa. Under the same assumptions for EC as a conservative parameter, one could replace EC by concentrations of boron or selenium.
Salt equilibrium equation incorporating the leaching efficiency coefficient
Figure A4.1. Relation between leaching efficiency coefficient of the percolation water (f_{r}) and leaching efficiency coefficient of the incoming irrigation water (f_{i})
Source: after Van Hoorn and Van Alphen, 1994.
Until now the assumption has been that all the infiltrated water mixes completely with the soil solution. In reality, a fraction of the infiltrated irrigation water percolates directly below the rootzone through cracks and macro-pores without mixing with the soil moisture solution. A more realistic estimate of the rootzone salinity can be obtained by incorporating leaching efficiency coefficients for the preferential flow pathways of salt transport. Figure A4.1 shows the relationship between the leaching efficiency coefficient of the percolation water (f_{r}) and the leaching efficiency coefficient related to the incoming irrigation water that mixes with the soil solution (f_{i}). It is assumed that P_{e} mixes completely with the soil solution.
The leaching efficiency coefficient of the incoming irrigation water is an independent variable determined by soil texture, structure and irrigation method, whereas the leaching efficiency coefficient of the percolation water is a dependent variable. f_{r} can be expressed as:
(8)
Integrating the leaching efficiency coefficient into the salt equilibrium equation results in:
(9)
in which EC_{IWi} is the salinity of the infiltrated water that mixes with the soil solution, and EC_{frR*} is the salinity of the percolation water which has been mixed with the soil solution. EC_{IWi} is equivalent to:
(10)
The leaching fraction of the infiltrated water that mixes with the soil solution (LF_{i}) is:
(11)
Salt equilibrium equation in the rootzone considered as a four-layer profile
It is often assumed that the salinity of the net deep percolation water is equivalent to the average soil salinity (as in the previous sections). However, due to irrigation and rootwater extraction patterns, the salinity in the upper portions of the rootzone is lower than the average due to a higher LF (zone of salt leaching), and the salinity in the bottom portions is higher because of a smaller LF (zone of salt accumulation). Under normal irrigation and rooting pattern, the typical extraction pattern for the rootzone is 40-30-20-10 percent water uptake from the upper to the lower quarter of the rootzone. Where irrigation is applied more frequently, crops tend to extract more water from the upper rootzone and less from the lower rootzone. Under these conditions, the rootzone is generally shallower and the extraction pattern might be 60-30-7-3 (FAO, 1985b).
Figure A4.2. Calculation of rootzone salinity of five successive depths
As shown in Figure A4.2, Equation 9 can also be used to calculate the rootzone salinity of five successive depths under this water uptake pattern to obtain finally the average salinity in the rootzone (EC_{SW}). In most soils, the salinity of the soil water at field capacity is about twice the salinity of the soil water measured on the saturated paste (EC_{e}).
It is not necessary to divide the rootzone into four equal parts (quadrants). The model can be extended into n-number of layers provided that the rootwater extraction pattern is known, e.g. the rootzone can be divided into 15-cm depth increments for 90-cm rooting depth.
Maintaining a favourable salt balance
A major concern in agricultural drainage water management is the buildup of salts and other trace elements in the rootzone to such an extent that it interferes with optimal crop growth. Applying more water than needed during the growing season for evapotranspiration can leach the salts. In areas with insufficient natural drainage, leaching water will need to be removed through artificial drainage.
Where the crop tolerance to salinity and the salinity of the irrigation water are known, the leaching requirement (LR) can be calculated. Rhoades (1974) and Rhoades and Merrill (1976) developed an empirical equation to calculate the LR:
(12)
EC_{ts} is the threshold salinity for a crop in decisiemens per metre of the extract from the saturated soil paste above which the yield begins to decline (Annex 1). In Equation 12, EC_{ts} represents the average rootzone salinity, and the value 5 was obtained empirically (FAO, 1985b).
If all the infiltrated water mixes completely with the soil moisture, the relation between the depth of applied water (AW) for consumptive use and the LR during a cropping season is:
(13)
However, under normal conditions a fraction of the infiltrated irrigation water, equivalent to (1-f_{i}) I_{i}, will percolate directly below the rootzone through cracks and macro-pores without mixing with the soil moisture solution. This water does not contribute to the leaching of salts from the rootzone. Under these conditions, the LR is:
(14)
The total amount of applied water is then:
(15)
Table A4.1. Concentration factors to predict the average EC_{e} for selected leaching fractions
Leaching fraction LF |
Concentration factor X |
0.05 |
3.2 |
0.10 |
2.1 |
0.15 |
1.6 |
0.20 |
1.3 |
0.25 |
1.2 |
0.30 |
1.0 |
0.40 |
0.9 |
0.50 |
0.8 |
0.60 |
0.7 |
0.70 |
0.6 |
0.80 |
0.6 |
Source: FAO, 1985b.
FAO (1985b) takes a different approach to assessing the LR for non-cracking soils. The average rootzone salinity for the four-layer concept can be calculated according to the procedures presented in Figure A4.2 in which fi is assumed to be 1. The concentration of the salts in the rootzone varies with the LF. Table A4.1 shows the concentration factors for the average predicted rootzone salinity (EC_{e}) for a selected number of LF. The concentration factors can be calculated in principle for any LF.
These concentration factors can be used to calculate the relationship between EC_{e} and EC_{IWi} in Figure A4.3. Where the salinity of the infiltrated water and the crop tolerance to salinity are known, the necessary LF can be estimated from this figure. If the y-axis of the figure were EC_{ts}, then the diagonal lines would give a range of LR. Hence, LF and LR are commonly used interchangeably.
Figure A4.3. Assessment of leaching fraction in relation to the salinity of the infiltrated water
Salt storage equations
In previous sections, long-term steady-state conditions were assumed to prevail. To study the impact of irrigation and drainage measures on crop performance, it is important to know the changes in rootzone salinity during a cropping season over multiple time periods as well. The salt storage equation of Van Hoorn and Van Alphen (1994) can be used for such dynamic changes. If the same assumptions are made as for the steady-state equations, i.e. a zone of shallow groundwater is created with the same salinity as the percolation water, exchange processes and mineral dissolution and precipitation are not taken into consideration and it is further assumed that the amount of salts supplied by rainfall and fertilizers and exported by crops are negligible, and the irrigation water mixes completely with the soil solution, then the salt balance for the rootzone can be described with the following equation:
DS = S_{IW} - S_{R*} (16)
where:
S_{IW} = salts in infiltrated water (ECmm);
S_{R*} = salts in net percolation water from the rootzone (ECmm); and
DS = change in salt storage in the rootzone (Ecmm).
The quantity ECmm requires some explanation. The parameter S is the mass of salts obtained from the product of salt concentration and water volume per area. For the sake of convenience, Van Hoorn and Van Alphen (1994) chose to use EC instead of TDS in grams per litre. The unit millimetre equals litre per square metre. Thus, the parameter S corresponds with the amount of salt in grams per square metre. Equation 16 can also be expressed as:
DS = IW EC_{IW} - R* EC_{SW} (17)
The mass of salts at the start of a period and at the end of a period normally differ and can be expressed as:
DS = S_{end} -S_{start} (18)
where:
S_{start} = quantity of salts in the rootzone at the start of the period (ECmm); and
S_{end} = quantity of salts in the rootzone at the end of the period (ECmm).
The salinity in the rootzone can be expressed as the conductivity of soil water or of the saturated paste. As for most soils the soil moisture content of the saturated paste is twice the soil moisture content at field capacity, the salinity at field capacity and of the saturated paste can be expressed as:
and (19)
where:
S = quantity of salts in rootzone (ECmm); and
W_{fc} = moisture content at field capacity (mm).
The average salinity of the soil water during a calculation period is:
(20)
Substituting Equation 20 for EC_{SW} in Equation 17 yields the salt storage equation:
(21)
Equation 21 can be used to calculate changes in soil salinity within a cropping season. The salt storage equation can also be applied to the four-layer concept. For the calculation of the change in rootzone salinity in the first quarter, the equation becomes:
(22)
In the subsequent rootzone quarters, the change in salt storage can be calculated as:
(23)
where:
1 to 4 = suffixes denoting the four quarters of the rootzone.
Integration of the leaching efficiency coefficients in the salt storage equation results in the following equation:
(24)