Rice Yield Modeling under Salinity and Water Stress Conditions using an Appropriate Macroscopic Root Water Uptake Equation

MATERIALS AND METHODS

Theory: Richards (1931) described the water flow in unsaturated soils including the root extraction term S, as follows:

(1)

where, θ is the volumetric water content (L³ L^-3), t the time (T), C the differential soil water capacity (L^-1) which is equal to the slope dθ/dh of the soil water retention curve, h is the soil water pressure head (L), Z is the gravitational head, as well as the vertical coordinate (L) taken positive upward, K is the soil hydraulic conductivity (L T^-1) and S is the soil water extraction rate by plant roots (L³/L/³/T) that determine:

(2)

where, S_max is the maximum water uptake rate and α(h,h₀) is a dimensionless function of pressure and osmotic head. The macroscopic water uptake reduction functions for the combined stresses are divided into two categories: additive, multiplicative. The additive reduction function (Van Genochten, 1987) is as follows:

(3)

where, h₅₀ is the soil water pressure head at which α(h) is reduced by 0.50, a₁ and a₂ is coefficients that not yet defined either physically and the value is unit and p is an empirical parameter, the value of p was found to be about 3 when, the S-shaped function was applied to salinity stress data. The multiplicative water uptake reduction function suggested by Van Genochten (1987), Dirksen et al. (1993) and Homaee and Feddes (1999). The multiplicative reduction function (Van Genochten, 1987) is as follows:

(4)

where, h_o50 is the soil salinity at which water uptake is reduced by 0.50. Homaee and Feddes (1999) proposed the following equation for the combined stresses:

(5)

where, h_max and h_0max (the second threshold value) is the soil water pressure head and soil osmotic head beyond which the changes of h or h₀ no longer influence the relative transpiration significantly, α₀₁ and α₀₂ is the relative transpiration at h_max and h_0max and p₁ and p₂ are defined as follows:

(6)

(7)

Dirksen et al. (1993) described the multiplicative water uptake reduction function as follows:

(8)

Furthermore, Maas and Hoffman (1977) described the water uptake reduction function as follows:

(9)

Homaee and Feddes (1999) proposed the other equations that is a combination of linear and non-linear functions and differs conceptually from additive and multiplicative theories. Further assumption is that each dS m^-1 salinity beyond the threshold value (EC*) shifts the wilting point 360 cm to the left per unit increase in salinity, therefore, reduction function of water uptake, α, is as follows:

(10)

where, h₃ is the soil water pressure head threshold value and h₄ is the soil water pressure head at wilting. This equation is valid for h_o = h_o* and (h₄-h_o) = h = h₃, respectively.

Stewart et al. (1977) proposed the equation to obtain yield in water stress as follows:

(11)

where, Y_a is the actual crop yield (t ha^-1), Y_m is the maximum expected crop yield (t ha^-1), Ky is the relative yield response factor as water stress and vary over the growing season, i is the consecutive growing stage, n is the number of growing stage, ET_p is the crop

evapotranspiration for standard condition (no water stress) mm d^-1 and ET_c-adj is the adjusted crop evapotranspiration mm d^-1 that proposed:

(12)

where, K_s is the transpiration reduction factor and dependent on available soil water that is vary between 0-1 and under salinity and water stress condition was proposed by Allen et al. (1998) as follows:

(13)

where, D_r is the root zone depletion (mm), TAW is the total available soil water in the root zone (mm), RAW is the readily available water (mm), p is the fraction of TAW that a crop can extract from the root zone without suffering water stress. Therefore, relative yield under water and salinity stress can be estimated by the following equations:

(14)

(15)

(16)

Application of Eq. 16 should usually be restricted to EC_e<EC_e-threshold+50/b and it predicts Y_a = 0 at K_s = 0. In addition, the K_y values are given for only 23 crops by Doorenbos and Kassam (1979) and where K_y is unknown it is suggested to use K_y = 1 or may select the K_y for a crop that has similar behavior.

When K_s in Eq. 12 is replaced by α(h, h₀), Eq. 15 is obtained that is a different method for calculation of ET_c-adj. Then, Eq. 15 is used to estimate relative yield and with knowing the maximum yield, Y_m, the value of actual yield, Y_a, is estimated.

Method: This study was carried out in a greenhouse at College of Agriculture, Shiraz University in years 2005 and 2006. The soil from top 20 cm layer of a rice planting area (Kooshkak, Fars province) with a silty clay texture was used. Some of the physico-chemical properties of this soil are shown in Table 1. The crushed air-dried soil was passed through a 2 mm sieve. An amount of 8.25 kg of this sieved soil was filled in plastic pots with 23.5 cm of height and 23 cm of diameter.

Table 1:	Physico-chemical properties of the soil used in the experiment

Table 2:	Chemical analysis of the saline irrigation water used in the experiment

Pots were planted with 25 seeds (local cultivar of Kamphiroozi/Ghasrodashti) in each pot on 18 and 27 April, 2005 and 2006, respectively and tap water was used to irrigate each pot to field capacity. Pots were fertilized with nitrogen and phosphorous uniformly at the rate of 163 mg kg^-1 soil of ammonium nitrate (equivalent to 120 kg ha^-1 N) and 51.6 mg kg^-1 soil of triple superphosphate [Ca(H₂PO₄)₂] (equivalent to 50 kg ha^-1 P), respectively. Seedlings were thinned to 15 and 10 per pot and after 2 and 4 weeks, respectively. After second thinning, the irrigation and salinity treatments initiated. Three irrigation treatments consisted of continuous flooding, intermittent flooding with 1 day interval and intermittent flooding with 2 day interval. A flexible drain tube was connected to the bottom end of pot wall for water drainage for intermittent irrigation treatments. These tubes were closed for continuous flood irrigation treatment. A 3 cm of standing water on the soil surface of the continuous flood irrigation was kept by daily water application. In intermittent irrigation treatments water was applied 1- and 2-day after the standing water disappeared. The amount of applied water in these treatments was the sum of water required to raise the soil water to saturation and a standing water depth of 3 cm.

The salinity levels of the irrigation water were 0.6 (tap water), 1.5, 3.0, 4.5 and 6.0 dS m^-1 in year 2005 and 0.6 (tap water), 1.5, 2.5, 3.5 and 4.5 dS m^-1 in year 2006 obtained by adding NaCl and CaCl₂ to the tap water with equal equivalent proportion. The chemical analysis of saline irrigation water is shown in Table 2. The experimental layout was a 3x5 factorial arrangement with four replications. The maximum and minimum air temperatures were 37±7 and 15±5°C, respectively.

Fig. 1:	Soil moisture curve

Undisturbed samples of soils were used to determine the soil water retention curve by hanging water column and pressure plate apparatus. The soil water retention curve is shown in Fig. 1. Soil water content before each irrigation in pots was measured by weighing the pots. Seven times during the growing season drainage water was collected. Electrical conductivity, chloride, Ca+Mg and Na were determined in the drainage water during the growing season. Osmotic potential of the drainage water as soil solution was estimated by the following equation (Richards, 1954):

where, h_o is the osmotic potential in cm and EC_ss is the soil solution salinity in dS m^-1. Soil water content before each irrigation was converted to soil water matric potential by using the soil water retention curve (Fig. 1). Similar pots were filled with water to a height equal to the planted pots and placed between them to measure the daily free water surface evaporation by adding the evaporated water to the pots.

At harvest, the plants were cut at the soil surface and plant tops were dried in an oven at 65°C for 48-72 h. Grains were separated from straw and weighed. The grain weight was corrected to 14% moisture content. Soil samples were collected from pots for chemical analysis. Electrical conductivity, chloride, Ca+Mg and Na were determined in soil saturation extracts.

RESULTS AND DISCUSSION

Root-water uptake coefficient: The ratio of actual transpiration to potential transpiration is defined as root-water uptake coefficient (α), however, in this study, evapotranspiration (ET) was assumed equivalent to transpiration. Therefore, α was taken as the ratio of actual ET to potential ET. Furthermore, Eq. 3, 4, 8-10 were used to estimate the values of α. In these estimations the corresponding values of soil matric and osmotic potentials were determined by Sepaskhah and Yousofi-Falakdehi (2009) and are presented in Table 3.

Table 3:	Soil matric and osmotic potentials at different points in the range of their variations

Table 4:	Mean water uptake function, α(h,h0), with different Eq. 3, 4, 8-10

The measured and estimated mean values of root-water uptake coefficients by different methods are shown in Table 4.

The estimated values of α by Homaee and Feddes (1999) Eq. 10 are closed to those of measured values. The additive equation for root-water uptake coefficient proposed by Van Genochten (1987) Eq. 3 predicted the values of α very lower than the measured values. Therefore, it is indicated that the additive equation by Van Genochten (1987) is not appropriate for estimation of α for rice.

The estimated values of α by Dirksen et al. (1993) Eq. 8 are closer to the measured values (Table 4) but it is not as good as Eq. 10. The estimated values of α by Maas and Hoffman (1977) Eq. 9 are the closest to those predicted by Homaee and Feddes (1999) Eq. 10. These results are in support of those obtained for saffron as reported by Sepaskhah and Yarami (2010). The relationships between the predicted and measured values of α are determined by linear regression. The statistical results are shown in Table 5. The slope of linear relationship between the estimated α(h,h_o) by additive function (Van Genochten, 1987) and the measured values was statistically close to 1.0 but its intercept was statistically different from zero. The slopes of linear relationships between the estimated α(h, h_o) by multiplicative functions (Maas and Hoffman, 1977; Van Genochten, 1987; Dirksen et al., 1993) and the measured values were statistically different from 1.0 but their intercepts were statistically close to zero.

Table 5:	The results of F-test analysis predicted water uptake function with calculated values

Fig. 2:	Variation of water uptake function with osmotic potential in all of treatments

Therefore, the additive and multiplicative functions are not appropriate for estimation of α(h, h_o). Finally, the slope and intercept of the linear relationship between estimated α(h, h_o) by the combination function (Homaee and Feddes, 1999) and the measured values were statistically close to 1.0 and zero, respectively. Therefore, the combination function of Homaee and Feddes (1999) is appropriate for estimation of α(h, h_o).

Variation of root-water uptake coefficient with osmotic potential: As soil osmotic potential (-h_o) is decreased, total soil water potential is reduced and soil water is less available to plant. Figure 2 shows variation of root-water uptake coefficient with osmotic potential for all treatments. Root-water uptake coefficients increased by decrease in the soil osmotic potential from salinity levels of S₀ to S₁ and reach a maximum at salinity level of S₁ and then reduced with further decrease in soil osmotic potential at higher salinity levels. This is in accordance to the finding of Sepaskhah and Yousofi- Falakdehi (2009). They reported that rice dry matter in S₁ treatment was more than S₀. Furthermore, Sepaskhah et al. (2006) showed that root yield of sugar beet increased under soil saturation extract salinity levels up to 1.0 dS m^-1 then decreased with increase in salinity levels.

Fig. 3:	Variation of water uptake function with matric potential in all of treatments

Variation of root-water uptake coefficient with matric potential: The values of α as a function of soil matric potential for different soil water osmotic heads (salinity levels) are shown in Fig. 3. The values of α were decreased by reduction in soil matric potential and soil osmotic potential at salinity levels greater than S₂. The values of α at salinity level of S₁ were higher than those at salinity level of S_o for all soil matric potentials. This is in accordance with those discussed in the earlier.

Yield prediction with root-water uptake coefficient: For prediction of rice grain yield, reported value of K_y by Sepaskhah and Yousofi-Falakdehi (2009) (1.14) was used in Eq. 15 and 16. The relationships between the predicted rice grain yield per pot by Eq. 16 and 15 and the measured values are shown in Fig. 4 and 5, respectively. The calculated values of α by Homaee and Feddes (1999) were used in Eq. 15. Poor estimation of rice grain yield was obtained in FAO method Eq. 16 with coefficient of determination (R²) of 0.44 and 0.63 and slopes of 0.73 and 0.67 for 2005 and 2006, respectively. However, good estimation of rice grain yield was resulted from Homaee and Feddes (1999) method Eq. 15 with R² of 0.93 and 0.94 and slopes of 0.89 and 0.83 for 2005 and 2006, respectively. These results are in accordance to the findings of Sepaskhah and Yarami (2010) for saffron. In FAO method, the calculated values of K_s from Eq. 13 were negative for continuous irrigation with high salinity levels.

Fig. 4:	Comparison of predicted yield from Eq. 14 with 1:1 line (2005)

Fig. 5:	Comparison of predicted yield from Eq. 15 with 1:1 line (2005)

Therefore, poor estimation of the FAO method was obtained.

CONCLUSIONS

Results indicate that the additive function for root-water uptake presented by Van Genochten (1987) Eq. 3 is not suitable for prediction of root-water uptake coefficient to show the interaction effect of salinity and deficit irrigation on yield prediction. Further, the Dirksen et al. (1993) Eq. 8 and multiplicative function proposed by Van Genochten (1987) resulted better estimation of roo-water uptake coefficient than that of additive function of Van Genochten (1987), but still they are not suitable. The Maas and Hoffman (1977) Eq. 9 resulted better estimation of α than those of other additive and multiplicative functions, however, it was not better than those obtained by Homaee and Feddes (1999) equation. This method often predicted α value higher than the measured values. Finally, it is concluded that the best equation for prediction of root-water uptake coefficient is the Homaee and Feddes (1999) Eq. 10. Also, rice yield was predicted by using this equation and FAO method along with production function presented by Stewart et al. (1977). Results indicated that the FAO method did not predict the yield properly especially in continuous flooding and salinity level of more than threshold values, but the Homaee and Feddes (1999) method predicted the grain yield properly with a minimum error.

ACKNOWLEDGMENTS

This research was supported in part by a research project funded by Grant No. 88-GR-AGR-42 of Shiraz University Research Council, Drought National Research Institute and the Center of Excellence for On-Farm Water Management.