Optimizing water, nitrogen and crop density in canola cultivation using response surface methodology and central composite design

Figures & data

Table 1 Coded and actual levels of independent variables

	Coded level of variables			Actual level of variables
Run	(X1)	(X2)	(X3)	Irrigation (m^3 ha^−1)	N fertilizer (kg ha^−1)	Density (plant m^−2)
1	−1	−1	−1	1500	0	50
2	+1	−1	−1	4000	0	50
3	−1	+1	−1	1500	400	50
4	+1	+1	−1	4000	400	50
5	−1	−1	+1	1500	0	150
6	+1	−1	+1	4000	0	150
7	−1	+1	+1	1500	400	150
8	+1	+1	+1	4000	400	150
9	−1	0	0	1500	200	100
10	+1	0	0	4000	200	100
11	0	−1	0	2750	0	100
12	0	+1	0	2750	400	100
13	0	0	−1	2750	200	50
14	0	0	+1	2750	200	150
15	0	0	0	2750	200	100
16	0	0	0	2750	200	100
17	0	0	0	2750	200	100
18	0	0	0	2750	200	100
19	0	0	0	2750	200	100
20	0	0	0	2750	200	100

Figure 1 Trend of precipitation (mm) and average temperature (°C) for two experimental years in Mashhad, Iran.

Table 2 Physical and chemical properties of the soil

Organic matter (%)	pH	EC (dS m^−1)	Potassium (ppm)	Phosphorus (ppm)	Nitrogen (%)	Texture
1.3	7.47	2.1	117	13.2	0.07	Loamy silt

EC, electrical conductivity.

Table 3 Table of analysis of variance (ANOVA) (Mean Square) for the measured traits of canola (Brassica napus L.)

SOV	df	Yield	N losses	NUE	WUE
Run	19	325035**	40.09**	0.042**	828.2**
Year	1	1362.5 ns	1.79 ns	0.0023 ns	42.70 ns
Error	19	1707.6	0.88	0.0012	18.38

SOV, Sources Of Variation; N, nitrogen; NUE, nitrogen use efficiency; WUE, water use efficiency; ns, non significant; *, significant at 5% level; **, significant at 1% level.

Table 4 Bartlett’s test for equal variance of the measured traits of canola (Brassica napus L.) versus year

	Yield	N losses	NUE	WUE
Chi-square	0.043	0.164	0.053	0.322
p-value*	0.836	0.685	0.818	0.570

N, nitrogen; NUE, nitrogen use efficiency; WUE, water use efficiency; *p-value > 0.05, indicating homogeneity of variance.

Figure 2 Comparison of estimated and observed value of seed yield, nitrogen (N) losses, nitrogen use efficiency (NUE) and water use efficiency (WUE) by 1:1 line.

Table 5 Analysis of variance (ANOVA) (Mean Square) table for the responses and variables

SOV	df	Yield	N losses	NUE	WUE
Regression	9	336114**	871.9**	41.81**	0.044**
Linear	3	174983**	66.06**	9.55**	0.016**
Square	3	382114**	92.50**	6.69**	0.024**
Interaction	3	19635**	218.7**	4.23**	2.44ns
Residual error	10	6281	2.08	0.462	0.0004
Lack-of-fit	5	9139ns	2.92ns	0.791ns	0.0003ns
Pure error	5	3424	1.24	0.133	0.0004
Total	19	–	–	–	–
R^2	–	96.1	99.5	97.6	98.2

N, nitrogen; NUE, nitrogen use efficiency; WUE, water use efficiency; SOV, Sources Of Variation.

Figure 3 The yield response to in dependent variable of nitrogen (N) fertilizer, irrigation water and canola (Brassica napus L.) density.

Table 6 Central composite design (CCD) and response results for the study of three experimental variables in coded units

	Factors			Responses
Run	Irrigation	N fertilizer	Density	Yield (kg ha^−1)	N losses (kg N ha^−1)	NUE (kg seed kg^–1 N)	WUE (kg seed m^–3 water)
1	−1	−1	−1	774.0	8.60	11.38	0.52
2	+1	−1	−1	1099.0	15.28	16.16	0.27
3	−1	+1	−1	1058.2	37.25	4.20	0.71
4	+1	+1	−1	1678.3	83.09	6.66	0.42
5	−1	−1	+1	952.3	6.69	14.00	0.63
6	+1	−1	+1	1497.8	13.37	22.03	0.37
7	−1	+1	+1	1294.4	34.38	5.14	0.86
8	+1	+1	+1	2095.8	73.54	8.32	0.52
9	−1	0	0	1178.8	30.56	7.37	0.79
10	+1	0	0	2027.6	53.48	12.67	0.51
11	0	−1	0	1374.5	10.51	20.21	0.50
12	0	+1	0	1935.2	58.26	7.68	0.70
13	0	0	−1	1477.4	45.84	9.23	0.54
14	0	0	+1	1902.6	38.20	11.89	0.69
15	0	0	0	1852.7	41.07	11.58	0.67
16	0	0	0	1964.0	42.02	12.28	0.71
17	0	0	0	1846.0	40.11	11.54	0.67
18	0	0	0	1843.1	41.07	11.52	0.67
19	0	0	0	1808.1	42.98	11.30	0.66
20	0	0	0	1923.9	40.11	12.02	0.70

N, nitrogen; NUE, nitrogen use efficiency; WUE, water use efficiency.

Figure 4 The nitrogen (N) losses response to in dependent variable of N fertilizer, irrigation water and canola (Brassica napus L.) density.

Figure 5 The nitrogen use efficiency (NUE; kg seed kg⁻¹ N) response to in dependent variable of nitrogen (N) fertilizer, irrigation water and canola (Brassica napus L.) density.

Figure 6 The water use efficiency (WUE; kg seed m⁻³ water) response to in dependent variable of nitrogen (N) fertilizer, irrigation water and canola (Brassica napus L.) density.

Table 7 Optimizing of independent variables and obtained values for response variables

		Scenario
		Economic	Environmental	Eco-environmental
Response variable	Seed yield (kg ha^−1)	2011	1080	1633
	N losses (kg N ha^−1)	44	10	29
	NUE (kg seed kg^−1 N)	14	16	18
	WUE (kg seed m^−3 water)	0.59	0.67	0.76
Independent variable	Irrigation (m^3 ha^−1)	3411	1802	2347
	N (kg ha^−1)	178	11	92
	Densities (Plant m^−2)	119	122	114

N, nitrogen; NUE, nitrogen use efficiency; WUE, water use efficiency.