Management of supplemental irrigation of winter wheat for maximum profit

X. Zhang and D. Pei, Institute of Agricultural Modernization,
Shijiazhuang, The People's Republic of China
Z. Li and J.Li, Dryland Farming Institute, Hengshui, The People's Republic of China
Y. Wang, Hebei Institute of Hydrology, Shijiazhuang, The People's Republic of China

Summary

Irrigation scheduling to manage supplemental water for maximum net profit of winter wheat (Triticum aestivum L.) in the North China Plain was investigated under variable water applications at two sites from 1992 to 2000. The effects of number and timing of irrigation applications on yields were examined. Based on determinations of sensitivity indices to water stress at various growth stages, a dynamic model was used to calculate the net profits of the irrigation treatments. The results indicate that one, two and three irrigations of 60 mm in wet, normal and dry years, respectively, achieve relatively high yields and maximum net profits. Therefore, the four irrigations generally applied to winter wheat may be reduced to three, two or one, with concomitant water savings.

The North China Plain (NCP) is one of the most important grain producing areas in the People's Republic of China, especially for winter wheat. Its output accounts for more than 19 percent of national wheat production. Due to serious water shortages in the NCP, available irrigation is decreasing rapidly. Where groundwater is used, the amounts pumped in recent years have caused serious depletion. At the sites of the experiment the water table is declining at a rate of 1-1.5 m/year. For winter wheat, average rainfall during the growing season from October to May ranges from approximately 60-200 mm. Supplemental irrigation is required because the water consumption is about 450-500 mm. Farmers generally irrigate winter wheat three to five times, with 180-300 mm of the total water application for each season, from wells, rivers or reservoirs.

Despite these serious shortages, wastage of irrigation water is common in the NCP because of inefficient methods and poor scheduling, resulting in decreased water use efficiency (WUE) and profits. The purpose of this research was to determine rational irrigation scheduling for winter wheat with limited availability of water to obtain optimum yields and maximize profits.

The relationships between crop yields and water use are complicated. Yield may depend on when water is applied or on the amount. Information on optimal scheduling of limited amounts of water to maximize yields of high quality crops is essential if irrigation water is to be used most efficiently (Al-Kaisi et al., 1997). The various crop development stages possess different sensitivities to moisture stress (FAO, 1979; English and Nakamura, 1989; Ghahraman and Sepaskhah, 1997). Timing, duration and the degree of water stress all affect yield.

This paper describes field experiments in which winter wheat yields and profits were examined under various irrigation scheduling regimes. Crop yield/water relations were determined. Water sensitivity indices were analysed at various growth stages. Based on the results, optimum irrigation schedules for maximum net profit for winter wheat were established using a dynamic mathematical model.

Materials and methods

Sites and experiments

Irrigation scheduling experiments were carried out with winter wheat at Luancheng Eco-Agro-System Experimental Station (in a high-production region) and at Hengshui Dryland Farming Institute (relatively low- production region) from 1991 to 1993, 1994 to 1995, and 1997 to 2000, i.e. six growing seasons. The stations are located in the central part of the NCP. At Luancheng, there is loamy soil of high organic content; field capacity of 35.5 percent and wilting point of 11.3 percent by volume, for the surface to 100-cm soil layer. At Hengshui, the sandy loamy soil is of relatively low fertility; field capacity is at 30.4 percent and wilting point at 11.0 percent by volume for the same soil layer. Table 1 lists rainfall at the two sites during the experiments. Seasonal rainfall is far less than the water requirement (WR) of winter wheat calculated by the Penman-Monteith equation.

Table 1
Rainfall and water requirements during winter wheat growth at the two experimental sites

The experiments had a randomized design with various combinations of number and timing of irrigations (Table 2), with four replications of each treatment. Surface irrigation was used with plastic tubes, and irrigation water was recorded. Meteorological stations at the experimental sites recorded temperature, rainfall, wind velocity, evaporatio, and solar radiation. Plots were 5x8 m, 2 m apart.

Table 2
Number and scheduling of irrigations applied to winter wheat

Crops and management

The experiments used common varieties. Planting is generally in early October with a row spacing of 16 cm and a seeding density of 300/m². Harvest is in early June. The straw is returned to the soil. Chemical N, P, and K were applied as base fertilizer, and N was re-applied at the jointing stage. Plots were hand-harvested individually, with a thresher used to separate the grain.

Soil water measurements

Soil water contents were monitored using a neutron probe (IH-II, the United Kingdom) at intervals of 7 days for each 20-cm layer; aluminium access tubes were installed to a depth of 200 cm for each plot. Evapotranspiration (ET) was calculated by the following equation:

ET = DS + P + I - D - R     (1)

Where: DS= the change in soil water storage (mm)
P= rainfall (mm)
I= irrigation (mm)
D = drainage from the bottom of root zone (mm)
R= runoff (mm).

As rainfall intensity is low during winter wheat growth, no runoff occurs and the drainage from the rootzone is negligible, in which case ET is the sum of rainfall, irrigation and the change in soil water storage.

Crop sensitivity to water stress

Yield decrease is related to the sensitivity of the crop to water stress at various stages of growth. Jensen (1968) proposed a mathematical relationship between relative yield and the relative amount of evapotranspiration as follows:

    (2)

where:Y= the actual yield under partial irrigation (kg/ha)
Y_m = the yield under non-limiting water use from full irrigation (kg/ha)
n = the number of growth stages
ET_i= the actual amount of water used by the crop at growth-stage i (mm)
ET_im=the non-limiting crop water use or potential water requirement at growth-stage i (mm)
= the relative sensitivity (sensitivity index) to water stress during growth-stage i.

The value of for a given crop changes with growth stage. A more sensitive growth stage has a higher value of .

Results and discussion

Relation of crop yield to water consumption

Tables 3 and 4 show the six years of results at the two sites. Different combinations of irrigation number and timing achieved various yields. The largest number of irrigations did not generate the highest yield. A single irrigation produced the highest yield during the 1997-98 season (relatively more rainfall), and four irrigations in the 1999-2000 season (least rainfall) produced the highest yield at Luancheng. Other studies have reported that the relationship between yield and water consumption, including irrigation, is not linear (Yuan et al., 1992). The results of the present study showed that crop yields initially improved with increased water consumption, but that beyond a certain water use level yields decreased (Figure1) over irrigation reduced winter-wheat production.

Figure 1
Relation of winter wheat yield with water consumption during two seasons at Luancheng

Table 3
Effects of timing and number of irrigations on winter wheat yields at Luancheng

Table 4
Effects of timing and number of irrigations on winter wheat yields at Hengshui

Irrigation water use efficiency

The relation of irrigation to crop yield is called the irrigation-production function. Many researchers (Zhang et al., 1993) have reported that this function can be described with a quadratic relationship:

Y = b₀ + b₁W + b₂W₂    (3)

where:
Y =crop yield (kg/ha)
W =total irrigation during the whole crop-growth period (mm)
b₀, b₁ and b₂ are coefficients (kg/ha, kg/ha/mm, kg/ha/mm², respec-tively).

It is possible to divide yield increases with irrigation into three phases. In the first phase, the value of the increased yield exceeds the increase in cost; in the second phase, the value of the increased yield is equal to the increase in cost; and in the third phase, the increase in yield is of less value that the increase in cost. The following equations express these situations:

First phase:
Second phase:
Third phase:

where:
= yield increase from irrigation (kg/ha)
Py= unit price of the crop (price/kg)
Pw= unit price of the water (price/ha/mm)
= increase in irrigation (mm).

In the first phase, net output value increases with irrigation. In the second phase, the net profit from irrigation is maximum. In the third phrase, the net profit from irrigation decreases. Therefore, the irrigation quantity for maximum profit is that for the second phase. By derivation of Equation (3) and combination of it with xPy = xPw, the following equation yields the irrigation amount to maximize profit:.

W = (Pw/Py-b₁)/2b₂    (4)

Table 5 provides correlations of yield with irrigation at the two sites for the various seasons. The total irrigation amount for maximum profit was lower than the irrigation amount for maximum yield. Therefore, it it possible to change the general practice of irrigation for maximum yield in the NCP for increased profit savings in large volumes of water. With the worsening water-shortage problem, irrigation costs may increase in the future, and then further reductions in water use may actually increase profits.

Table 5
Irrigation production function and economic irrigation quota for winter wheat

Optimizing irrigation scheduling for maximum profit

The effect of water stress on the yield of winter wheat depends on the growth stage during which the stress is imposed. Table 6 shows sensitivity indices to water stress from the Jensen model based on water deficit field experiments at Luancheng (Zhang et al., 1999). In the NCP, rainfall varies greatly during the winter growing season. Taking account of the sensitivity index and rainfall, a dynamic model can be used to programme the irrigation schedule for maximum profit.

Table 6
Sensitivity indices of winter wheat to water stress at ivarious growth stages

Target function

The target function is that which maximizes net profit per unit area, according to the following equation:

max I = I* = max(B-C)     (5)

where:
I= net income per unit area (value/ha)
B= total output value per unit area (value/ha)
C= total input value per unit area (value/ha).

The following equations yield the values for B and C:

B = (P_Y1+P_Y2xL)Y     (6)
    (7)

where:
Y=grain yield of winter wheat (kg/ha)
L=ratio of straw yield to grain yield
W=total irrigation water (m³/ha)
K=daily labour cost (cost/person)
P_Y1, P_Y2 =grain and straw price (value/kg)
P_W1, P_W2 =water fee and irrigation energy cost (cost/m³ and cost/unit energy)
W/50=days needed for irrigation (50 m³ irrigation per day)
4xY/250= harvesting cost (250 kg grain per four days)
F = seed, sowing, fertilizer and other costs (cost/ha)

The Jensen model calculates the effect of water deficit on crop yields:

    (8)

where:
ET_i=water consumption at growth stage i (m³/ha) sensitivity index to water stress at growth stage i
ET_im=water consumption at growth stage i without water stress (m³/ha)
Y_m=grain yield without water stress (kg/ha).

Combining Equations (6), (7) and (8) into (5) yields:

I*= max(B-C)

= max{(P_Y1+P_Y2xL)Y-[(P_W1+P_W2)W+K()+F_C]}

= max{(P_Y1+P_Y2xL Y_mx -(P_W1+P_W2 )W-F_c}

And letting:
(P_Y1+P_Y2xL ) = M

(P_W1+P_W2 ) = N

W = i = 1, 2,..., n

Then, the following equation yields the target function.

I*= max{MxY_mx -Nx -F_C}     (9)

where:
M, N=target coefficients (price/ha)
W_i=irrigation at stage i (m³/ha)
=the value in Table 6.

The calculation of growth stage water consumption without water stress uses the Penman-Menteith equation recommended by FAO, based on average meteorological parameters for 1960 to 1990. The crop coefficient is from field experiments (Liu et al., 1998). The irrigation scheduling for maximum profit in different rainfall years, dry, normal and wet years are programmed. The type of seasonal rainfall is classified by the meteorological statistical method based on the seasonal rainfall data from 1951 to 1999 in the central part of the NCP, with P = 75, 50 and 25 percent, respectively. The quantity of water for each irrigation is assumed to be 60 mm, which is common in the well-pumping irrigation region of the NCP.

Determining the variables

The equation for calculating water allocation for different growth stages is:

q_i+1 = q_i - W_i    (10)

where:
q_i= water allocated at the beginning of growth stage i
q_i+1=water allocated at the beginning of growth stage i+1

The equation for calculating the soil water that can be used at the beginning of a stage:

S_i+1=S_i+P_oi+W_i+K_i+ET_i+E_i    (11)

where:
S =soil water that can be used by the crop at the beginning of growth stage i (m³/ha)
S_i+1=soil water that can be used at the beginning of growth stage i+1 (m₃/ha)
W_i=irrigation at growth-stage i (m₃/ha)
P_0i=effective rainfall at growth stage i (m₃/ha)
ET_i=evapotranspiration at growth stage i (m₃/ha)
K_i=groundwater replenishment to soil water at growth stage i (m₃/ha)
E_i=percolation from rootzone at growth stage i (m³/ha).

The programming uses the following binding conditions:

0 = W_i =q_ii = 1, 2,..., n      (12)

= W     (13)

ß_w = ß = ß_f     (14)

where:
W=available irrigation water during the whole growth period (m³/ha).
ß_f=field capacity (v/v)
ß_w=low limit of soil water content
ß=soil water content.

In most years, the water content (0-200 cm) at sowing time is about 85 percent of field capacity. This value was used for initial soil water content. At the beginning of the first growth stage, available irrigation water is equal to the planned irrigation water for the whole growth period.

An asymptotic approximation method was used to programme the number of irrigations and their timing. Table 7 lists the simulated scheduling with maximum net profits for different seasonal rainfall conditions. The simulated results were similar to those from the field experiments. The irrigations were timed when winter wheat is most sensitive to water stress.

Table 7
Simulated irrigation scheduling for maximum profit of winter wheat

Conclusions

Crop yields and net profits are important considerations in selecting an irrigation management policy in the water deficient NCP region of China. Winter wheat, has a high water requirement. Supplemental irrigation is essential. Farmers generally irrigate for maximum yield but sometimes over irrigate, reducing the yield. With the increasing shortage of water in the NCP, irrigation water fees may rise, whereas grain prices may decrease because of current overproduction in China. The simulated results showed that a single irrigation in wet years, two irrigations in normal years and three in dry years produced maximum profits. The timing of the irrigations would be: at jointing to booting for the single irrigation, at jointing and heading to milky filling for the two irrigations; and before over wintering, jointing, and heading to milky filling for the three irrigations.

References

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