Deficit irrigation is an optimizing strategy under which crops are deliberately allowed to sustain some degree of water deficit and yield reduction. The fundamental goal of deficit irrigation is to increase Water Use Efficiency (WUE) or Water Productivity (WP), either by reducing irrigation adequacy or by eliminating the least productive irrigation. It is widely recognized that when water supplies are limited or water costs are high, the economic optimum level of irrigation will be something less than would be required for maximum yield. Where there are constraints on capital, energy, labor or other essential resources, or when costs of any of these resources are particularly high, deficit irrigation can be used as a strategy to increase profits. This approach can also be used to maximize profits or stabilise regional crop production (Tavakoli and Oweis, 2004). Deficit irrigation is not without controversy, but if the objective is to maximise profits or stabilise food production it is a valid and useful strategy (Sepaskhah et al., 2006). This new concept of irrigation scheduling has different names, such as regulated deficit irrigation, pre-planned deficit evapotranspiration and deficit irrigation (English et al., 1990).
Optimal allocation of irrigation water and nitrogen fertilizer is very important for agricultural purpose, especially in arid regions or regions where contaminated water is a prime concern in agriculture (Trimmer, 1990; English and Raja, 1996; Godwin and Jones, 1991; Weinhold et al., 1995; Zand-Parsa and Sepaskhah, 2001).
Nitrogen is currently the most widely used fertilizer nutrient and the demand
for it is likely to grow in future (Godwin and Jones, 1991). Nitrogen is a component
of protein and nucleic acid and when nitrogen amount in soil is not optimal,
growth is reduced (Weinhold et al., 1995). Nitrate-N is highly soluble
in water and hence susceptible to leaching, potentially contributing to environmental
contamination. Also, fertilizer N can be lost via denitrification, especially
from moist soils. Denitrification losses reduced the N fertilizer use efficiency
and are environmental concern for the potential role of N2O that
it may play in stratospheric ozone depletion (Qian et al., 1997).
The different amounts of water and nitrogen application were used for corn (Peng and Letey, 1998) and rice (Pirmoradian et al., 2004a, b). They showed that the larger amount of irrigation water, provided larger amount of deep percolation, which resulted in much nitrogen leaching and less yield.
The amounts of applied water and nitrogen for the maximum yield of corn, the maximum profits at the limiting land and water conditions are determined by Zan-Parsa and Sepaskhah (2001). In this study the optimum applied water and nitrogen application rate in land limiting conditions were 0.99 m and 212 kg N ha-1, respectively. These values in water limiting condition were obtained 0.736 m and 206 kg N ha-1, respectively. The results of similar analysis were reported by Sepaskhah et al. (2006) for winter wheat.
This study was conducted to determine optimal irrigation water use for rice in different nitrogen application rates, flowering stage air temperatures and plant populations.
MATERIALS AND METHODS
Conceptual model: A gross income curve is represented. The level of irrigation that would maximise yield is shown as wm in Fig. 1. The straight line in Fig. 1 represents a cost function relating total production costs to applied water. In this Figure the wm is the amount of water for maximum yield and wl is the optimum water for land limiting condition. At the point of wel the net income per unit of land will just equal the net income from full irrigation. The point of ww is the optimum water for water limiting condition. Under this condition, at the point of wew the net income per unit of land will just equal the net income from full irrigation.
It is possible to derive a set of equations to estimate the values of the aforementioned variables (wm, wl, ww, wel, wew). Such equations would be useful for analysis of optimum water use and irrigation water planning (Sepskhah et al., 2006).
Mathematical formulation: The detail mathematical formulation of deficit irrigation was presented by English et al. (1990) and Sepaskhah et al. (2006) based on the production and cost functions as follows:
|| Revenue and cost functions
where, a1, b1, c1, a2 and b2 are constants. The various levels of water use of interest to the analyst (wl, ww, wm, wel, wew) were derived by English et al. (1990) and Sepaskhah et al. (2006) as follows:
Site description: This research was conducted at Kooshkak Agricultural Research Station, of Shiraz University in Islamic Republic (I.R.) of Iran (Lat. 30°7´ N; Long. 52°34´ E; elevation of 1650 m) during the two consecutive growing seasons of 2000 and 2001. The experimental site was placed in the irrigated area of Doroodzan Irrigation District located at south of I.R. of Iran. But the same spot of the Experiment Station Farm was not used in growing seasons of 2000 and 2001; however, the same experimental layout was used in both years. The soil of experimental site was a fine, Carbonatic, mesic, Aquic Calcixerepts soil with pH of 6.9-7.1 (Table 1). Maximum temperatures during the growing season (July-October) ranged from 23 to 39°C in 2000 and from 28 to 40°C in 2001, while the minimum temperature ranged from 7 to 24°C in 2000 and from 8 to 27°C in 2001, respectively. The mean daily maximum and minimum temperatures during the growing season (July-October) are 32.8 and 13.2 in 2000, respectively. These values are 35.4 and 16.2°C in 2001, respectively. Reference crop potential evapotranspirations (ETo) during the growing period for 2000 and 2001 determined based on FAO-Penman method (Doorenbos and Pruitt, 1977) and were 578 and 650 mm, respectively. These may be converted to potential crop evapotanspiration (ETp) by multiplying with crop coefficient (Kc). To these the water loss by wind and evaporation should be added. There was no rainfall during the growing season in either year.
Experimental details: The experiment was conducted using 4 replications
in a split plot design with irrigation method as main plots and N levels as
subplots. Main plots consisted of 5 irrigation regimes: (1) sprinkler irrigation
with applied water equal to ETp, (2) sprinkler irrigation with applied
water equal to 1.5ETp, (3) continuous flooding irrigation, (4) intermittent
flooding irrigation with 1 day interval and (5) intermittent flooding irrigation
with 2 days interval. Subplots were composed of three levels of 32, 72 and 112
kg N ha-1 for 2000 and 32, 92 and 152 kg N ha-1 for 2001
applied as urea and ammonium phosphate. The ammonium phosphate at a rate of
200 kg ha-1 was applied before transplanting (32 kg N ha-1).
Subplots were 3x3 m basins enclosed by 50 cm bunds. The land was prepared on
8 to 10 July in 2000 and 28 to 30 June in 2001. The experimental plots were
separated after the plowed land was saturated and puddled by a tiller. A local
cultivar (Champa-Kamphiroozi) of rice seedlings with low tillering ability were
transplanted with 16 and 25 hills per unit area m2 for 2000 and 2001
on 11 and 1 July in 2000 and 2001, respectively. The transplants were about
40 days old. Before transplanting, 200 kg P ha-1 was applied as ammonium
phosphate. For first 10 days, all of the treatments were irrigated with continuous
flooding to establish the seedlings. The applied water in this period was 142
and 166 mm in the years of 2000 and 2001, respectively.
Four sprinklers with a capacity of 0.5 L sec-1 were placed on the
corner of each plot of sprinkler irrigation treatments on a riser with 1.0 m
height. For sprinkler treatments, the applied water for each irrigation was
obtained by the mean of ETp for 3 pervious days plus evaporation
from droplet from the air and wind drift losses of the sprinklers. Evaporation
and wind drift losses were determined by measuring the water collected in 45
cans placed in each replication of the experimental plots during water application
period. The difference between applied water and collected water in cans was
considered as evaporation and wind drift losses. Due to strong wind at daytime
and high day temperature, the mean value of this loss was 28.8% in the growing
season. For flooding treatments, the water depth in plots was maintained at
5 to 10 cm in irrigation period. For surface irrigation treatments, the water
was distributed by pipe to each plot. Therefore, there was no effect of water
flow from canals to the plots of surface irrigation treatments. The weed populations
were higher in the sprinkler and intermittent flood irrigation treatments. The
weeds were removed by hand weeding. In intermittent irrigation treatments, the
standing water depths on the plots disappeared after about 24 h and the plots
irrigated again before their surface were cracked. Volumetric water meters were
used to measure the volume of the delivered water for every main plot in four
Ten days after transplanting, one half of N requirements for different treatments (as urea) i.e., 20 and 40 kg N ha-1 for year of 2000 and 30 and 60 kg N ha-1 for year of 2001 and irrigation treatments were applied. The remaining N was applied at 40 and 50 days after transplanting (before flowering stage) for 2000 and 2001 years, respectively. During the growing season weeds were controlled by hand weeding. The crop was harvested manually on 8 and 13 October in 2000 and 2001, respectively.
At the end of growing season, yield samples were harvested from 1x1 m area
at the middle of plots. Samples were air dried for 5 days before being oven
dried at 70°C for 48 h. Then, grain yield was determined. The grain yield
and applied water were used to derive the water production function. The revenue
per unit area (ha) was calculated by multiplying the produced grain yield (kg
ha-1) by price of unit grain weight (_ kg-1). The fixed
cost [a2 in Eq. 2] was calculated by summing the
land rent, land preparation, fertilizer (except nitrogen), planting, cropping
activities and harvest costs for unit area (ha). The variable cost [b2
in Eq. 2] was calculated by multiplying the amounts of applied
water and nitrogen per unit area (ha) by their unit prices.
RESULTS AND DISCUSSION
Production function: The production function of rice grain yield was obtained by multiple regression analysis as follow:
||Grain yield in kg ha-1.
||Nitrogen application rate in kg ha-1.
||The seasonal amount of applied irrigation water in mm.
||Air temperature at flowering stage in °C.
||Plant population in number of hills per unit area (m-2).
The values of coefficient of determination (R2), Standard Error (SE) and number of observations were 0.91, 445.6 and 30, respectively. The F-value of this multiple regression equation was significant at p = 4.74x10-12 level of probability. In contradiction to the production function for other crops, i.e., wheat, the nitrogen application does not show a quadratic function (Sepaskhah et al., 2006). This was due to the fact that the highest rate of applied nitrogen was 152 kg ha-1 which was not high enough to cause yield reduction at higher nitrogen application rate. The Eq. 10 is valid for Na up to 152 kg ha-1, air temperature at flowering stage up to 33°C and plant population up to 25 hills per unit area (m-2). The slope of regression line is near to slope of 1:1 line and there is not statistically difference between these lines (Fig. 2).
By comparing Eq. 1 and 10, the coefficients
of production function were obtained as follows:
||Relationship between measured (Ym) and predicted
(Yp) grain yields Eq. 10 for the experimental
|a1, b1 and c1
||The coefficients of production function.
||Nitrogen application rate in kg ha-1
||Air temperature at flowering stage in °C
||Plant population in number of hills per unit area (m-2).
The coefficient of a1 was obtained for different application rates of N (0, 40, 60, 80 and 120 kg ha-1), air temperatures at flowering stage, Tf (23.9 and 28.2°C) and plant population, P (16 and 25 hills m-2) (Table 2). The revenue was obtained by multiplying grain yield (kg ha-1) by unit price of the grain (0.26 _ kg-1).
Production cost function: The coefficients of production cost function a2 and b2 (Eq. 2) were determined as follows:
||Nitrogen application rate in kg ha-1.
The fixed costs (production cost except water and N fertilizer costs) were
obtained as 1029.32 _ ha-1. The unit price of nitrogen fertilizer
was 0.069 _ kg-1. The water price was considered as 0.0055 _ m-3.
The water price was considered for water from a well with 10 m depth that is
used in the study area (Table 2). The production cost function
is similar to that reported for wheat (Sepaskhah et al., 2006), however,
the coefficients are different.
Economic analysis: Using Eq. 3, 4
and 6, the values of wm, wl and wel,
for two different combinations of air temperatures at flowering stage (23.9
and 28.2°C) and plant populations (16 and 25 hills m2) were calculated
as 2138, 2120 and 2102 mm, respectively. These values were not dependent on
the Tf, plant population and N application rates. Similar results
were reported by Sepaskhah et al. (2006). By increasing nitrogen application
rate, the optimum amount of water for different flowering stage air temperature
and plant population conditions was decreased (Fig. 3).
||The intercepts of production function [a1 in Eq.
1] and cost function [a2 in Eq. 2] for
different nitrogen application rated (N), kg ha-1 flowering stage
air temperature (Tf), °C and plant population (P) (hills
The optimum amounts of water (ww) decreased at a higher rate (from
1988 to 1226 mm) by increase in nitrogen application rate (from 0 to 150 kg
N ha-1) at higher flowering stage air temperatures and plant population.
These values were 2692 to 2191 mm of water for 0 to 150 kg N ha-1
for low air temperature at flowering stage and plant population. Under unfavorable
air temperature condition and low plant population, the ww and wew
decreased by 19 and 0%, respectively, at 150 kg N ha-1, compared
with 0 kg N ha-1. However, under favorable air temperature condition
and high plant population, these values were 38 and 62%, respectively. Therefore,
under water limiting conditions in the study area, the higher plant population
and favorable climatological factor can highly reduce the optimum irrigation
water at higher N application rate. However, this result is in contradiction
to those obtained for wheat in which ww increased at higher nitrogen
application rate (Sepaskhah et al., 2006). This might be due to the flooding
nature of rice plantation.
The net income at any condition was obtained from difference between amounts
of revenue and cost. Figure 4 shows that the net income was
increased with increasing nitrogen application rate, flowering stage air temperature
and plant population. Under unfavorable air temperature condition and low plant
population, the net income was negative (Fig. 4a) for all
rates of N application and applied irrigation water. Similarly, for unfavorable
air temperature at flowering stage and high plant population the net income
was negative except for N application of 120 kg ha-1 and applied
irrigation water between 1600 to 2300 mm in which a small positive net income
was obtained (Fig. 4b).
||Variation of Ww and Wew for different
nitrogen application rates and irrigation water in different air temperatures
at flowering stage (Tf) and plant population (P): (a) for Tf
= 23.9°C, P = 16 hills m-2; (b) for Tf = 23.9°C,
P = 25 hills m-2; (c) for Tf = 28.2°C, P = 16
hills m-2; (d) for Tf = 28.2°C, P = 25 hills m-2
||Variation of net income at different amounts of irrigation
water and nitrogen application rates for different air temperatures at flowering
stage (Tf) and plant population (P): (a) for Tf =
23.9°C, P = 16 hills m-2; (b) for Tf = 23.9°C,
P = 25 hills m-2; (c) for Tf = 28.2°C, P = 16
hills m-2; (d) for Tf = 28.2°C, P = 25 hills m-2
However, as air temperature became favorable, the net income was negative for
N application rates of lower than 80 kg ha-1 (Fig.
4c), but by application of 1720 mm of water and 120 kg N ha-1
positive net income was obtained (Fig. 4c). Furthermore, positive
net income was resulted by N application at water application of greater than
1500 mm (Fig. 4d). For a given amount of net income, a lower
irrigation water with higher N application rate can be used, i.e., the net income
obtained by 80 kg N ha-1 and 2300 mm applied irrigation water was
similar to that obtained by 120 kg N ha-1 and 1300 mm applied irrigation
water. Therefore, for a higher net income, one kg ha-1 increase in
N was equivalent to 25 mm decrease in water. Similarly, zero net income was
obtained by 40 kg N ha-1 and 1500 mm applied irrigation water and
60 kg N ha-1 and 1300 mm applied irrigation water or one kg ha-1
of N was equivalent to 10 mm decrease of water (Fig. 4d).
The maximum net income was obtained in Tf = 28.2°C, P = 25 hills m-2, 120 kg ha-1 N application and 2138 mm applied irrigation water (Fig. 4d). The optimum and low critical air temperatures during the flowering stage of rice are reported to be 30-33 and 22°C, respectively (Smith and Hamel, 1999). Therefore, the maximum net income was obtained in near optimum air temperature during the flowering stage. Furthermore, it should be noted that all of the effective factors on yield can be affected by the results of economic analysis. Therefore, some of these uncontrollable factors, particularly climatological factor should be considered in economic analysis.
The results indicated that the optimum irrigation water for maximum yield production
(wm) was 2138 mm. In land limiting conditions, wl and
wel were obtained as 2120 and 2102 mm, respectively. In water limiting
conditions in the study area, the optimum irrigation water was affected by field
management (N application rate and plant population) and climatological factors
such as air temperature at the flowering stage. The optimum amounts of water
(ww) decreased at a higher rate (from 1988 to 1226 mm) by increase
in nitrogen application rate (from 0 to 150 kg N ha-1) at higher
flowering stage air temperatures and plant population. These values were 2692
to 2191 mm of water for 0 to 150 kg N ha-1 for low air temperature
at flowering stage and plant population. Under unfavorable air temperature condition
and low plant population, the ww and wew decreased by
19 and 0%, respectively, at 150 kg N ha-1, compared with 0 kg N ha-1.
However, under favorable air temperature condition and high plant population,
these values were 38 and 62%, respectively. Therefore, under water limiting
conditions in the study area, the higher plant population and favorable climatological
factor can highly reduce the optimum irrigation water at higher N application
Also, N application rate, plant population, air temperature at the flowering stage and applied irrigation water affected the net income. The maximum net income was obtained in Tf = 28.2°C (near optimum air temperature during the flowering stage, 30-33°C), P = 25 hills m-2, 120 kg ha-1 N application and 2138 mm applied irrigation water. The field management factors such as applied irrigation water, nitrogen application rate and plant population can be controlled by field manager and the optimum amounts may be applied. However, the climatological factors are unpredictable, therefore, these factors should be considered in economic analysis of crop yield production and field management.
This research was supported in part by Grant No. 85-GR-AGR 42 of Shiraz University Research Council and Center of Excellence on Farm Water Management.