Optimal applied water and nitrogen for corn

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Abstract

Water and fertilizer applications should be limited due to scarce resources and environmental protection aspects. An analysis of crop yield production and profit maximization was conducted to determine the optimal water and nitrogen allocation. In this analysis based on crop production and cost functions, a series of equations for determination of applied water and nitrogen for three conditions of maximum yield (wm and Nm, respectively), maximum profit under limited land (wl and Nl, respectively) and maximum profit under limited water (ww and Nw, respectively) were derived. The associated crop production function was determined from the results of a corn experiment with four levels of nitrogen fertilization and varying amounts of applied water via a line source of sprinkler irrigation. The previously derived equations were also applied to the experimental field data and finally the optimum amounts of applied water and nitrogen were determined at different conditions (wm, wl, and ww for water and Nm, Nl, and Nw for nitrogen, respectively). At present market value (15.55 Rls/m3 for water and 652 Rls/kg for nitrogen) the amounts of wm, wl, and ww were 1.0, 0.99, and 0.74 m, respectively, and the amounts of Nm, Nl, and Nw were 212, 212, and 206 kg N/ha, respectively. Because of the low price of nitrogen, the optimum amounts of nitrogen at three mentioned conditions were similar. But if the price of nitrogen and water are increased (i.e. 50000 Rls/kg N and 100 Rls/m3 water), then the amounts of applied nitrogen and water at the mentioned three conditions would be 212, 67, and 61 kg N/ha, and 1.00, 0.93, 0.84 m, respectively. When water is limiting, the optimum amount of applied water would not be different by changing the water price, however, it may be increased by a little amount when the nitrogen price is increased.

Introduction

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 (e.g. Tyagi, 1987, Trimmer, 1990, English and Raja, 1996, Godwin and Jones, 1991 Christiansen and Killorn, 1981, Weinhold et al., 1995). The objective of optimal irrigation involves maximizing crop yield or profit but it may also include taking advantage of irrigation water opportunity cost, minimizing deep percolation or leaching and water salinity management (English and Raja, 1996). English (1990) derived equations for optimum application of water based on maximization of crop yield and agricultural net incomes. English and James (1990) and English and Raja (1996) showed the different levels of optimal applied water for different crops.

Nitrogen plays a key role in plant nutrition. It is the mineral element required in the greatest quantity by cereal crop plant and it is the nutrient most often deficient. As a result of its critical roles and low supply, the management of nitrogen resources is an extremely important aspect of crop production (Novoa and Loomis, 1981). 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). Corn is able to utilize both NH4 and NO3 as an N source (Scharader et al., 1972). 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, specially 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).

Pang and Letey (1998) used different amounts of water and nitrogen application for corn field. They showed that larger amount of irrigation depth, provided larger amount of deep percolation, which resulted in much nitrogen leaching and less yield. Also, they showed that any stress by either water or nitrogen, affected corn yield. Liao and Bartholomew (1974) showed that in field conditions where water was not being absorbed by corn plant, NO3 was not absorbed. Therefore, there should be an interaction between nitrogen and water use for corn production.

The objectives of this paper are first to derive equations for determination of water and nitrogen levels leading to maximum crop yield or profit with limited water and land conditions. Then these derived equations are applied to corn experimental field data and the optimal levels of water and nitrogen are determined.

Section snippets

Theory

Crop yield (Y(w,N)) is a function of irrigation water amount and fertilization rate (nitrogen). Cost function (C(w,N) can be determined from the summation of the cost of preparing land for planting, cost of planting, cost of field management, cost of harvesting, etc., and cost of applied water and nitrogen. The net income is dependent on application of water and nitrogen and irrigated area as follows:I=A×i(w,N)where i(w,N) is the net income per unit area, I the total net income and A the

Materials and methods

Corn was planted at 32 rows with spacing of 0.75 m and length of 72 m in Bajgah Agricultural Experiment Station on 20 May 1999. The longitude, latitude and elevation of the station are 29°56′N, 52°02′E and 1850 m above mean sea level, respectively. The field was thinned on 12 June and the population of plants reached 66,666 plants per hectare. The value of rainfall during the crop season was negligible and the average annual pan evaporation was 1941 mm per year. The field was irrigated by a

Results and discussion

After testing different multiple regression models, the production function of corn grain yield was selected asY(w,N)=a0+a1×w+a2×w2+a3×(N+Nr)+a4×(N+Nr)2+a5×w×(N+Nr)+a6×w×(N+Nr)2+a7×w2×(N+Nr)+a8×w2×(N+Nr)2where w is total irrigation depth (m), N and Nr are applied and residual nitrogens in soil (kg N/ha), respectively, and a0, through a8 are constant coefficients. For the corn grain production in our experimental field, the values of a0, through a8 in Eq. (12) were obtained by the multiple

Conclusions

Corn yield production as a function of seasonal applied water and nitrogen can be determined by Eq. (12). When the yield production function is expressed as a function of irrigation water and nitrogen fertilization amounts, then the optimum levels of these parameters could be determined. The amounts of applied water and nitrogen for the maximum yield, the maximum profits at the limiting land and water conditions are determined from pairs of , , , , , , respectively. When land is limiting, farm

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