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Simulation of water and nitrogen dynamics as affected by drip fertigation strategies
Journal of Integrative Agriculture 2015, 14(12): 2434–2445 Available online at www.sciencedirect.com
ScienceDirect
RESEARCH ARTICLE
Simulation of water and nitrogen dynamics as affected by drip fertigation strategies ZHANG Jian-jun1, LI Jiu-sheng2, ZHAO Bing-qiang1, LI Yan-ting1 1 2
Institute of Agricultural Resource and Regional Planning, Chinese Academy of Agricultural Sciences, Beijing 10081, P.R.China State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, P.R.China
Abstract The aim of drip fertigation is synchronising the application of water and nutrients with crop requirements, and maintaining the proper concentration and distribution of nutrient and water in the soil. The wetting patterns and nutrient distributions under drip fertigation have been proved to be closely related to the fertigation strategies. In order to find out the critical factors that affect the nutrient distribution under different drip fertigaiton strategies, a computer simulation model HYDRUS2D/3D was used to simulate the water and nitrate distribution for various fertigation strategies from a surface point source. Simulation results were compared with the observed ones from our previous studies. A 15° wedge-shaped plexiglass container was used in our experiment to represent one-twenty-fourth of the complete cylinder. The height of container is 40 cm, and the radius is 41 cm. The ammonium nitrate solution was added through a no. 7 needle connected to a Mariotte tube with a flexible hose. The soil water content, nitrate and ammonium concentrations were measured. The comparison of simulated and observed data demonstrated that the model performed reliably. The numerical analysis for various fertigation strategies from a surface point source showed that: (1) The total amount of irrigation water, the concentration of the fertilizer solution and the amount of pure water used to flush the pipeline after fertilizer solution application are the three critical factors influencing the distribution of water and fertilizer nitrogen in the soil. (2) The fresh water irrigation duration prior to fertigation has no obvious effect on nitrate distribution. The longer flushing time period after fertigation resulted in nitrate accumulation closer to the wetting front. From the point of avoiding the possibility of nitrate loss from the root zone, we recommended that the flushing time period should be as shorter as possible. (3) For a given amount of fertilizer, higher concentration of the fertilizer applied solution reduces the potential of nitrate leaching in drip irrigation system. While, lower concentration of the fertilizer solution resulted in an uniform distribution of nitrate band closer to the wetted front. Keywords: fertigation, strategy, drip irrigation, modelling, nitrate transport
Received 21 August, 2015 Accepted 17 November, 2015 ZHANG Jian-jun, Mobile: +86-15801181005, Tel: +86-1082108664, E-mail: [email protected]; Correspondence LI Jiu-sheng, Tel: +86-10-68786545, E-mail: [email protected]; ZHAO Bing-qiang, Tel: +86-10-82108664, E-mail: zhaobingqiang @caas.cn © 2015, CAAS. All rights reserved. Published by Elsevier Ltd. doi: 10.1016/S2095-3119(15)61231-X
1. Introduction Nitrogen (N) is an essential nutrient for plant and therefore a main component of fertigation. Nitrate is one of the main forms of nitrogen found in soil which is highly mobile and leachable. Delivery of N fertilizer through fertigation reduces N losses in the soil-plant system by ammonia volatilization
ZHANG Jian-jun et al. Journal of Integrative Agriculture 2015, 14(12): 2434–2445
and nitrate leaching (Alva et al. 2008). Drip irrigation has become an optimal means for providing water and nutrients directly to the roots of crops because of its potential of precisely applying water and chemicals with a high water and fertilizer use efficiency. The aim of drip fertigation is synchronising the application of water and nutrient with crop requirements and maintaining the proper concentration and distribution of nutrient and water (Assouline 2002). It is a common practice that fresh water is applied prior to and after fertigation to ensure fertilizer application uniformity and flushing the drip lines. It has been proved that the distributions of water and nitrate under drip fertigation were closely related to the fertigation strategies (Li et al. 2004; Gärdensäs et al. 2005; Khalil et al. 2007). Improper irrigation management can lead to leakage loss of water and nutrient from the root zone which could create the pollution of shallow groundwater. Therefore, optimal irrigation scheduling is important to improve the crop uptake efficiencies of water and nutrient (Alva et al. 2005). Hence a clear understanding of water and nitrate dynamics in root zone under varying fertigation strategies is important for appropriate design and management of drip fertigation system (Li et al. 2003; Khalil Ajdary 2007). The shape of wetted soil volume and spatial distribution of soil nitrate concentrations under drip fertigation are influenced by many factors, including the irrigation quantity, the time period of using fresh water prior to and after fertigation, and the concentration of the fertilizer solution. Bristow et al. (2000) simulated water and solute distribution in the soil under two fertigation strategies, involving application of solute at the end of and at the beginning of an irrigation cycle from a buried point source. They reported that larger amount of nutrients maintained near to and above the source when solute applied at the beginning of an irrigation cycle. Cote et al. (2003) presented that fertigation at the beginning of the irrigation cycle might reduce nitrate leaching for highly permeable coarse-textured soils. Li et al. (2003, 2004) conducted experiments to study the effects of fertigation strategies on wetting patterns and nitrogen distribution in the soil from a surface point source of nitrate ammonium (NH4NO3). The strategy of 1/4W-1/2N-1/4W (first applying water for one-fourth of the total irrigation time, then applying fertilizer solution for one-half of the total irrigation time, followed by applying water for the remaining one-fourth of the total irrigation time) left the most nitrate close to the source and was therefore recommended. Gärdensäs et al. (2005) found that seasonal leaching was high for coarse-textured soils, and concluded that fertigation at the beginning of the irrigation cycle tends to increase seasonal nitrate leaching. In contrast, fertigation events at the end of the irrigation cycle reduced the potential of nitrate leaching. Li et al. (2007) conducted field experiments in a solar-heated greenhouse
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with drip-irrigated tomato to investigate the effects of drip fertigation strategy and frequency on nitrate dynamics, spatial distribution of nitrate, apparent recovery of nitrogen and fertilizer use efficiency. The results showed that the strategy of applying nutrient at the beginning resulted in a uniform distribution of nitrate in different layers and the nitrate in upper layers increased as the fertilization time was transferred towards the end of an irrigation cycle. As the fertilization time was transferred towards the beginning of an irrigation cycle, potential of nitrate moving towards the boundary of wetted volume was more obvious. The optimal fertilization strategy of 1/4W-1/2N-1/4W was suggested. Phogat et al. (2013) used the HYDRUS 2D/3D model to develop various modelling scenarios to assess the fate of nitrate for different irrigation and fertigation schemes. The results imply that fertigation in a short pulse towards the end of the irrigation event or low concentration fertigation could increase the efficiency of nitrogen fertigation as compared to other options. When reviewing the literature, it becomes clear that useful and reliable information can be derived about rhizosphere processes with computer modelling techniques. Numerical simulations of water flow and nitrate transport can help in understanding of the dynamic processes in the vadose zone. And the management of fertigaiton system can affect the nutrient and water distribution in the root zone. The performance of these systems need to be evaluated, because considerable localized leaching can occur near the driplines and the loss of nutrients, particularly nitrate can pose a serious threat to receiving water bodies (Van et al. 2010). However, the numerical simulation and experimental data of water and nitrate dynamics under different fertigation strategies are still lacking. We could not come across any literature about which are the critical factors that affect the nutrient distribution under different drip fertigaiton strategies. The objective of the present study was to simulate the water and nitrate distribution under various fertigation strategies and various solution concentrations from a surface point source through simulations to investigate the critical factors that affect the nutrient distribution under different drip fertigaiton strategies.
2. Results 2.1. Calibration and validation of the model Simulation results were compared with the observed data obtained from our previous studies (Zhang 2002; Li et al. 2003, 2004) for model evaluation. Table 1 shows the root mean square error (RMSE) and the index of agreement (d) values for the calibration and validation. Fig. 1 shows the soil water profiles as 7.9 L of water were applied at a rate of
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2.0 L h–1, and compares these values with the results of the
source and as a function of the radial distance at depths (z)
HYDRUS 2D/3D simulations. Fig. 2 compares the simulated
of 2.5 and 12.5 cm below the surface are illustrated in Fig. 1.
and the observed distributions of the NO3-N concentrations
For the calibration dataset, RMSE values for soil water
–1
in the soil as 7.9 L of NH4NO3 solutions with 300 mg L
content ranged from 0.017–0.049 cm3 cm–3 with d varying
concentrations was applied at a rate of 2.0 L h–1. Soil water
from 0.852–0.996 (Table 1), indicating an excellent agree-
content as a function of the vertical distance from the surface
ment between the simulated and observed soil water con-
at radial distances (r) of 2.5 and 12.5 cm from the point
tents. Fig. 2 indicates that the model captured the distribution
Table 1 The root mean square error (RMSE) and the index of agreement (d) of the soil water content and nitrate concentration Test no.
Application rate Volume applied (L h–1) (L)
Calibration 1 2 3 4 5 6 7 Validation 8 9 10 11 12 13 14
RMSE Water content (cm3 cm–3)
NH4NO3 concentration (mg L–1)
d NO3-N (mg kg–1)
Water content
NO3-N
0.6 0.9 0.9 1.4 2.0 4.9 4.9
8.0 8.0 8.0 8.3 7.9 14.0 13.2
300 100 300 300 300 300 500
0.0380 0.0336 0.0170 0.0162 0.0225 0.0303 0.0493
18.70 15.36 20.25 14.49 18.08 11.51 12.79
0.8518 0.9803 0.9851 0.9964 0.9915 0.9529 0.9416
0.6176 0.8819 0.6158 0.8778 0.8368 0.8540 0.7819
0.9 1.0 1.0 1.1 2.0 4.8 4.9
6.0 8.1 8.1 10.0 13.1 10.1 15.0
300 500 700 300 300 300 300
0.0275 0.0305 0.0302 0.0335 0.0395 0.0317 0.0443
12.47 13.00 11.97 13.36 19.23 18.56 12.68
0.9947 0.9516 0.9720 0.8817 0.9243 0.9938 0.9353
0.9326 0.7038 0.8149 0.7744 0.6536 0.8770 0.8342
Observed
z=2.5 cm
0.4 0.3 0.2 0.1 0.0
0 5 10 15 20 25 30 35 40 45
0
0
10 20 30 40 Radial distance (cm) Soil water content (cm3 cm–3) 0.1 0.2 0.3 0.4
50
Soil water content (cm3 cm–3)
0.5
0.5
z=12.5 cm
0.4 0.3 0.2 0.1 0.0
0.5
r=2.5 cm Depth (cm)
Depth (cm)
Soil water content (cm3 cm–3)
Simulated
0 5 10 15 20 25 30 35 40 45
0
0
10 20 30 40 Radial distance (cm) Soil water content (cm3 cm–3) 0.1 0.2 0.3 0.4
50
0.5
r=12.5 cm
Fig. 1 Comparisons of the simulated and the observed soil water content profiles as 7.9 L of water were applied at a rate of 2.0 L h–1.
ZHANG Jian-jun et al. Journal of Integrative Agriculture 2015, 14(12): 2434–2445
2.2. Applications of the model
trend of nitrate in the soil well. The RMSE of 11.51–20.25 mg kg–1 and d values of 0.62–0.88 for nitrate concentration (Table 1) indicated good performance of the model. For the validation dataset, RMSE values for soil water content ranged from 0.028–0.044 cm3 cm–3 with d varying from 0.882–0.995 (Table 1). The RMSE values for nitrate concentration ranged from 11.97–19.23 mg kg–1 and d of 0.65–0.93 (Table 1) indicated good performance of the model.
All fertigation scenarios reported are hypothetical. The duration of irrigation cycle is considered 4 h and a fixed fertigation duration of 2 h during the irrigation cycle is used for all drip fertigation events. The time intervals of the additional fresh water irrigation after fertigation varied from 12 to 108 min for different fertigation strategies (Table 2).
350 300 250 200 150 100 50 0
0
0
0
10 20 30 40 Radial distance (cm)
400 300 250 200 150 100
50
50 0
0
r=2.5 cm
5
10
10
15
15
20 25 30
z=12.5 cm
350
Nitrate concentration (mg L–1) 100 200 300 400
5 Depth (cm)
Nitrate concentration (mg L–1)
z=2.5 cm
Observed
Depth (cm)
Nitrate concentration (mg L–1)
Simulated 400
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0
0
20 40 Radial distance (cm)
60
Nitrate concentration (mg L–1) 100 200 300 400 r=12.5 cm
20 25 30
35
35
40
40
45
45
Fig. 2 Comparisons of the simulated and the observed distributions of the NO3-N concentrations in the soil as 7.9 L of NH4NO3 solutions with 300 mg L–1 concentrations was applied at a rate of 2.0 L h–1.
Table 2 Irrigation and fertigation duration and nitrate concentrations in fertilizer solutions applied for different fertigation scenarios Fertigation strategy1) 1W10F9W 2W10F8W 3W10F7W 4W10F6W 5W10F5W 6W10F4W 7W10F3W 8W10F2W 9W10F1W (FT120) FT60 FT180 1)
Total duration (min) 240 240 240 240 240 240 240 240 240 240 240
Concentration of nitrate Time interval of fresh water prior Fertigaiton duration Flush duration (mg kg–1) to fertigation (min) (min) (min) 300 12 120 108 300 24 120 96 300 36 120 84 300 48 120 72 300 60 120 60 300 72 120 48 300 84 120 36 300 96 120 24 300 108 120 12 600 168 60 12 200 48 180 12
1W10F9W means applying water for 1/20 of the total irrigation time, followed by applying fertilizer solution for the 10/20 of the total irrigation time, then applying water for the rest 9/20 of the total irrigation time. FT60, FT120 and FT 180 represent the fertigation strategies with fertigation duration of 60, 120 and 180 min. The same as below.
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2.3. Water and nitrate distribution when fertilizer application ceased The contour plots in Fig. 3 show the simulated soil water content for the nine fertigation strategies when fertilizer application completed. It is clear that a longer time period for fresh water application before fertigation allows water to move faster from the emitter. For example, the surface wetted radii were 26 and 31.5 cm for fertigation strategy of 1W10F9W (1W10F9W means applying water for 1/20 of the total irrigation time, followed by applying fertilizer solution for the 10/20 of the total irrigation time, then applying water for
0
0
5
Radial distance (cm) 10 15 20 25 30 35 40
0
0
5
the rest 9/20 of the total irrigation time. The same as below.) and 9W10F1W, respectively. The vertical wetted depths were 25 and 31.5 cm for fertigation strategy of 1W10F9W and 9W10F1W, respectively. The soil nitrate distributions when fertigation completed for the nine fertigation strategies are presented in Fig. 4. The highest nitrate concentration that was close to the concentration of solutions applied occurred near the emitter. All of the nitrate injected was distributed within the wetted soil profile to a depth of 25–26 cm and a radial distance of 27–28 cm. We note that the total N-added is the same for all fertigation strategies, but the strategies vary between
Radial distance (cm) 10 15 20 25 30 35 40
0
10
10
10
15 20 25
15 20 25
35
35
1W10F9W
40 0
5
0
20 25
0
5
Radial distance (cm) 10 15 20 25 30 35 40
0
10
10
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15
15
25
25
35
35
4W10F6W
0
5
Radial distance (cm) 10 15 20 25 30 35 40
0
25
0
5
Radial distance (cm) 10 15 20 25 30 35 40
0
10
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15
15
35 40
Depth (cm)
10 Depth (cm)
10 Depth (cm)
5
30
20 25 30
7W10F3W
35 40
6W10F4W
40
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25
Radial distance (cm) 10 15 20 25 30 35 40
20
5
20
5
35
5W10F5W
40
40
0
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30
30
0
Depth (cm)
10 Depth (cm)
5
Depth (cm)
5
20
3W10F7W
40
5
20
Radial distance (cm) 10 15 20 25 30 35 40
15
35
2W10F8W
40
Radial distance (cm) 10 15 20 25 30 35 40
5
30
30
30
0
Depth (cm)
5
Depth (cm)
5
Depth (cm)
5
0
0
5
Radial distance (cm) 10 15 20 25 30 35 40
20 25 30
8W10F2W
35 40
9W10F1W
Fig. 3 Spatial distributions of soil water content (cm3 cm–3) when fertigation completed for the nine fertigation strategies simulated.
1W10F9W means applying water for 1/20 of the total irrigation time, followed by applying fertilizer solution for the 10/20 of the total irrigation time, then applying water for the rest 9/20 of the total irrigation time. The same as below.
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the duration of fresh water irrigation prior to fertigation. The ratios of NO3-N mass within a given range from the source to the total amount of nitrogen within the simulation region were determined for each fertigation strategy (Table 3). The mass balance was conducted for four zones, which are 0– 10 cm (zone 1), 10–20 cm (zone 2), 20–30 cm (zone 3), and >30 cm (zone 4) from the source when fertigation completed. As expected, the total amount of NO3-N in the four zones followed the trend: zone 2>zone 1>zone 3>zone 4. The ratios of nitrate mass in the four zones have no significant difference among the nine fertigation strategies when ferti-
0
5
Radial distance (cm) 10 15 20 25 30 35 40
5
Radial distance (cm) 10 15 20 25 30 35 40
0
10
10
10
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15
20 25
20 25
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1W10F9W
5
Radial distance (cm) 10 15 20 25 30 35 40
0
25
0
5
Radial distance (cm) 10 15 20 25 30 35 40
0
10
15
15
15
20 25 30
35
5
Radial distance (cm) 10 15 20 25 30 35 40
0
25
0
5
Radial distance (cm) 10 15 20 25 30 35 40
0
10
10
40
15 20 25 30
30 35
Depth (cm)
10 Depth (cm)
5
25
7W10F3W
35 40
6W10F4W
40
5
20
Radial distance (cm) 10 15 20 25 30 35 40
20
5
15
5
35
5W10F5W
40 0
0
30
35
4W10F6W
40
0
Depth (cm)
10 Depth (cm)
5
10
30
3W10F7W
40
5
25
Radial distance (cm) 10 15 20 25 30 35 40
20
5
20
5
35
2W10F8W
40 0
0
30
30
40
0
Depth (cm)
5
35
Depth (cm)
0
The simulated soil water content when the irrigation cycle completed shows no differences between the nine fertigation strategies with the same amount of application water. The surface wetted radius and the vertical wetted depth were 32.5 and 32.0 cm, respectively, for the nine fertigation strategies.
5
30
Depth (cm)
0
2.4. Water and nitrate distribution when the irrigation cycle completed
5
Depth (cm)
Depth (cm)
0
gation ceased, suggesting the fresh water application prior to fertigation has no obvious effect on nitrate distribution.
0
5
Radial distance (cm) 10 15 20 25 30 35 40
15 20 25 30
8W10F2W
35
9W10F1W
40
Fig. 4 Spatial distributions of nitrate concentration (mg L–1) in soil solution when fertigation completed for the nine fertigation strategies simulated.
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Table 3 Summary of the ratios of the amount of nitrate nitrogen within a given range of distance from the source to the total amount of nitrate nitrogen within the simulation region for the nine fertigation strategies simulated1) Fertigation ceased 1W10F9W 2W10F9W 3W10F9W 4W10F6W 5W10F5W 6W10F4W 7W10F3W 8W10F2W 9W10F1W Irrigation cycle compeleted 1W10F9W 2W10F9W 3W10F9W 4W10F6W 5W10F5W 6W10F4W 7W10F3W 8W10F2W 9W10F1W (FT120) FT60 FT180 1)
Zone 1 (%)
Zone 2 (%)
Zone 3 (%)
Zone 4 (%)
20.9 20.9 20.9 20.9 20.9 20.9 20.9 21.0 21.0
74.5 74.3 74.3 74.2 74.2 74.2 74.3 74.3 74.3
4.6 4.8 4.9 4.9 4.9 4.8 4.8 4.8 4.7
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.1 0.2 0.4 0.9 2.2 5.3 10.6 21.2 7.2
47.3 54.0 60.7 67.4 73.6 79.0 82.8 84.2 81.3 78.5 70.0
52.5 45.9 39.1 32.4 26.0 20.1 14.9 10.5 8.1 0.3 22.8
0.1 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Zones 1, 2, 3, and 4 means the range of 0–10, 10–20, 20-30, and >30 cm from the source. The duration of irrigation cycle is considered 4 h and a fixed fertigation duration of 2 h during the irrigation cycle is used for all drip fertigation events.
The nitrate was distributed within the soil wetted volume and a quite similar distribution pattern of soil nitrate concentration was observed for the nine fertigation strategies. The contour plots in Fig. 5 show the simulated concentration of nitrate in the soil when the irrigation cycle ceased. All the fertigation strategies generally resulted in a band of nitrate along the periphery of the wetted soil volume with little or no nitrate near the emitter. From Fig. 5 we found that the zone of relatively low nitrate concentration in the vicinity of the emitter becomes larger when the flushing time interval lasted for a longer time, and the band of nitrate moves closer to the wetting front. It is clear that a longer flushing time allows nitrate to move faster away from the emitter. For example, the nitrate reaches 26 and 21 cm for the 1W10F9W and 9W10F1W fertigation strategy, respectively. Fig. 5 also indicates that nitrate moves with water during infiltration and leaching by fresh water after fertigation. As the time period for flushing increased, the band where nitrate accumulation occurred was closer to the wetting front. The longer time period for flushing the drip line resulted in more nitrate distributed faraway from the emitter, increasing the probability of nitrate leaching.
2.5. Effects of fertigation duration on nitrate distribution We note that the total N-added is the same for the FT60,
FT120 and FT180 fertigation strategies, but the fertigation duration varies from 60 to 180 min. The fushing time period is 12 min for the FT60, FT120 and FT180 fertigation strategies. The concentrations of fertilizer solution for the FT60, FT120 and FT180 fertigation strategies are 600, 300 and 200 mg L–1, respectively. The nitrate front in the radial direction reaches 24.0, 29.0 and 32.0 cm, and in the vertical direction reaches 21.5, 27.0 and 31.0 cm for the fertigation strategy FT60, FT120 and FT180, respectively (Fig. 6). The width of the nitrate distribution band increases when the fertigation duration increases from 60 to 180 min, but the nitrate concentration in soil solution decreases. The nitrate concentration was varied from 2–16, 5–50 and 10–100 mg L–1 for the fertigation strategies FT60, FT120 and FT180, respectively. A shorter fertigation duration resulted in a nonuniform distribution of nitrate within the nitrate distribution band. Similarly, the total amount of NO3-N in the four zones followed the trend: zone 2>zone 1>zone 3>zone 4 for the fertigation strategies FT60 and FT120 (Table 3). However, the total amount of NO3-N in the four zones followed the trend: zone 2>zone 3>zone 1>zone 4 for the fertigation strategy FT180. The ratios of nitrate mass in zone 1 is 21.2, 10.6 and 7.2% for the fertigation strategies FT60, FT120 and F180, respectively. The ratios of nitrate mass in zone 3 is 0.3, 8.1 and 22.8% for the fertigation strategies FT60, FT120 and F180, respectively. The mass balance results
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0
5
Radial distance (cm) 10 15 20 25 30 35 40
Radial distance (cm) 10 15 20 25 30 35 40
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15 20 25 30
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4W10F6W
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Depth (cm)
10 Depth (cm)
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20 25 30
30 7W10F3W
6W10F4W
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40 Radial distance (cm) 10 15 20 25 30 35 40
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1W10F9W
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Depth (cm)
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Depth (cm)
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Depth (cm)
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Depth (cm)
Depth (cm)
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35 40
0
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Radial distance (cm) 10 15 20 25 30 35 40
20 25 30
8W10F2W
35
9W10F1W
40
Fig. 5 Spatial distributions of nitrate concentration (mg L–1) in soil solution at the end of the simulation period for the nine fertigation strategies.
clearly showed that the leaching potential increases as the fertigation duration increases.
3. Discussion Water and nitrate distribution under different fertigation scenarios were investigated using the HYDRUS2D/3D model. The results indicated that the distribution of fertilizer nitrogen in the soil under drip fertigaiton was mainly influenced by the following factors, the total amount of irrigation water, the concentration of the fertilizer solution and the amount of pure water used to flush the pipeline after fertilizer solution application.
Simulation results showed that the total amount of irrigation water determines the distribution range of irrigation water in the soil. At the same time, it also determines the range of the possible distribution of fertilizer nitrogen since nitrate distribution is highly associated with water flow. From our simulation results we find that the radial distance and vertical depth of fertilizer nitrogen distributed were always within wetted area. The fresh water application prior to fertigation has no obvious effect on nitrate distribution. But the movement and distribution of nitrate was closely related to the amount of the pure water used to flush the pipeline after fertilizer solution application. The greater amount of pure water used to flush the pipeline after fertilizer solution
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0
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Radial distance (cm) 10 15 20 25 30 35 40
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Radial distance (cm) 10 15 20 25 30 35 40
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35 40
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30 FT180
35 40
Radial distance (cm) 10 15 20 25 30 35 40
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25
30
5
Depth (cm)
5
Depth (cm)
5
Depth (cm)
5
0
30 FT120 (9W10F1W)
35
FT60
40
Fig. 6 Spatial distributions of nitrate concentration (mg L–1) when irrigation cycle completed with 200, 300 and 600 mg L–1 concentrations of NH4NO3 solutions were applied for the FT180, FT120 and FT60 fertigation strategies.
application, the more closer of the nitrate distributed near the wetting front. For a given amount of fertilizer injected, the nitrate distribution was more uniform and the nitrate front was closer to the wetted front when the ferilizer concentration is low. On the contrary, higher concentration of the fertilizer solution resulted in a nonuniform distribution of nitrate and nitrate front closer to the emitter. The extension of the crop rooting system is different for different crop types and different growing stages. The requirements for irrigation water and nutrient are also different. This means that water and nutrient should be provided to the root zone in desirable amount, concentration and location. According to our simulation results, the total amount of irrigation water, the flushing time period and the concentration of fertilizer solution to be the key considerations in the design and management of drip fertigation system.
4. Conclusion The comparison between the simulated and observed ones from our previous studies demonstrated that the HYDRUS2D/3D model performed well in simulation of water and nitrate distribution under fertigation from a surface point source. Then we used the model to simulate the water and nitrate distribution under nine different fertigation strategies. The following conclusions were supported by this study: (1) The total amount of irrigation water, the concentration of the fertilizer solution and the amount of pure water used to flush the pipelines after fertilizer solution application are the three critical factors influencing the distribution of water and fertilizer nitrogen in the soil. (2) The fresh water irrigation duration prior to fertigation has no obvious effect on nitrate distribution. The longer flushing time period after fertigation resulted in nitrate
accumulation closer to the wetting front. From the point of avoiding the possibility of nitrate loss from the root zone, we recommended that the flushing time period should be as shorter as possible. (3) For a given amount of fertilizer injected, higher concentration of the fertilizer solution reduces the potential of nitrate leaching in drip irrigation system. While, lower concentration of the fertilizer solution resulted in an uniform distribution of nitrate band closer to the wetted front.
5. Materials and methods 5.1. Model description The simulations of water flow and nitrate transport under different drip fertigation scenarios were carried out using a computer simulation model, HYDRUS2D/3D (Šimůnek et al. 2011). This software package can simulate the transient two-dimensional or axi-symmetrical three dimensional movements of water and solutes in soil. In presented applications, we simulated three-dimensional axially symmetric water flow, solute transport in soils as applied by drip fertigation, based on the flow equations with finite-element numerical solutions. Axi-symmetrical water flow in variable saturated rigid, isotropic porous medium and surface drip irrigation is described by the modified form of Richards’ equation. The equation is given by: ∂h ∂K ( h) ∂h ∂ ∂θ ( h) 1 ∂ (1) = [ rK ( h) ] + [K ( h) ] + r ∂r ∂z ∂z ∂r ∂z ∂t Where, θ(h) is the volumetric water content (L3 L–3), r and z are the radial and vertical coordinate, respectively (L) , h is the soil water pressure head (L), t is the time (T), and K(h) is the unsaturated hydraulic conductivity function (L T–1). The unsaturated retention and hydraulic conductivity
ZHANG Jian-jun et al. Journal of Integrative Agriculture 2015, 14(12): 2434–2445
fuctions deccribed by the van Genuchten (1980) model, which is defined as follows: θs−θr θr+ for h<0 m
θ (h)=
(2)
1+|αh|n θ (h)=θs
for h≥0 m
2
K(h)=KsSel 1− 1−S1/m e Se=
(3)
θ−θr
(4)
θs−θr
m=1− 1 ; n>1 (5) n Where, θr and θs denote the residual and saturated water contents (L3 L–3), respectively; α is the inverse of air-entry value; n is the pore size distribution index; l is the pore connectivity parameter which was estimated (Mualem 1976) to be 0.5; Ks is the soil saturated hydraulic conductivity (L T–1). The partial differential equations governing nonequilibrium chemical transport of solutes involved in a sequential first-order decay chain during transient water flow in a variably saturated rigid porous medium are taken as follows: For nitrate: ∂c1 ∂θc1 ∂ ∂c1 ∂c1 1 ∂c1 = θDrr +θDrz + θDrr + θDrz ∂z ∂t ∂r ∂r r ∂z ∂r (6) ∂c1 ∂c1 ∂qrc1 qrc1 ∂qzc1 ∂ + θDzz +θDrz − + + ∂z ∂z r ∂r ∂z ∂r +µ0ρ−µw2θc2
For ammonium: ∂θc2 ∂t
+ρ
∂s2 ∂t
=
∂ ∂r
+
∂ ∂z
θDrr
∂c2 ∂r
θDzz
+ θDrz
∂c2 ∂r
∂c2 ∂z
+ θDrz
∂c2 ∂z
+
1 r −
θDrr
∂c2 ∂r
+θDrz
∂c2 ∂z
qrc2 ∂qzc2 (7) + + ∂r ∂z r
∂qrc2
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15° wedge-shaped plexiglass containers. The height of container is 40 cm, and the radius is 41 cm. This container was used to represent one-twenty-fourth of the complete cylinder. This assumption was verified by Lv (2000) who found that there was no significant differences between the 15° wedgeshaped and a 90° wedge-shaped container. The soil used in our experiment was a loam soil. The air-dry soil passed through a 2-mm sieve was packed in the container with 5 cm increments to obtain a constant bulk density of 1.32 g cm–3. The ammonium nitrate solution was added through a no. 7 needle connected to a Mariotte tube with a flexible hose. The outlet of the needle was located at the corner of the container on the soil surface. The soil was covered with a polyethylene sheet to maintain zero evaporation. After each experiment, the container was opened and immediately samples were taken with a metal tube for determination of water content, nitrate and ammonium concentration.
5.2. Modeling domain properties and boundary conditions We assumed that the soil is homogeneous in the domain. The infiltration process of a single emitter can be assumed as an axi-symmetrical flow. In the present study the radius r of the flow domain was taken as 40 cm and depth z as 40 cm (Fig. 7). A saturated ponded area develops in the vicinity of the emitter when irrigation starts. The ultimate radius of the ponded area is an exponential function of the application rate for the loam soil (Zhang 2002; Li et al. 2004, 2007). The ultimate radius of the saturated area is assumed to be the water entry zone in our simulation. A constant flux was Location of emitter
Variable flux boundary
−µw1θc2
Where, c1 is nitrate concentration in the liquid phases (M L–3); ρ is the soil bulk density (M L–3); qr and qz are the radial and vertical component of the volumetric flux density (L T–1); Drr and Dzz are the longitudinal and transverse dispersion coefficient tensor (L2 T–1); µ0 is the mineralization rate constant (M M–1 T–1); µw1 is the first-order nitrification rate constant (T–1); µw2 is the first-order denitrification rate constant (d–1); S2 is the absorbed concentration of ammonium (M M–1) which is described as follows: (8) S2=KDc2 Where, KD is the distribution coefficient of ammonium (L3 M–1). The experimental data used to calibrate and validate the model obtained from our previous studies (Zhang 2002; Li et al. 2003, 2004). The experimental set up consisted of a
Atmospheric flux boundary
40 cm No flow boundary Free drainge boundary
40 cm
Fig. 7 Simulation domain and boundary conditions.
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estimated by dividing emitter discharge rate with the area of the saturated zone when a constant application rate and solute concentration was applied. For the different fertigation scenarios, the solute concentration varies with time, so the time-variable flux boundary option was used to address the flux boundary. Bottom boundary was considered as free drainage boundary. Solute was applied with irrigation water and a first-type boundary condition was used to prescribe the concentration at the top boundary.
5.3. Input parameters A loam soil was used in our simulations. Particle size analysis yield an average value of 48% sand, 41% silt and 11% clay (Zhang 2002; Li et al. 2003, 2004). The van Genuchten (1980) model of soil hydraulic properties was selected in the numerical simulations. The pore connectivity parameter (dimensionless) was estimated by Mualem (1976) to be about 0.5 for many soils and this value was adopted in the present study. The values of soil saturated hydraulic conductivity Ks was determined according to the values reported in the literature (Zhang 2002; Li et al. 2003, 2004). The solute transport parameters including longitudinal dispersivity (DL), transversal dispersivity (DT) and molecular diffusion coefficient (DW) were determined according to the values reported in literature (Zhang 2002; Ma 2004). Ammonium was assumed to absorb to the solid phase using a distribution coefficient Kd which was taken as 0.326 cm3 g–1 obtained from experiment (Zhang 2002). Nitrification and denitrification were simulated using the first-order decay coefficients (μw1, μw2 ), and mineralization was modeled using the zero-order coefficient (μ0). The value ranges of μw1, μw2 and μ0 were determined according to literatures (Myrold and Tiedje 1986; Huang et al. 1996). The parameters θs, θr, a, n, μw1, μw2, and μ0 were adjusted by comparing the simulated and observed values of soil water
content and nitrate distribution obtained from our previous researches (Zhang 2002; Li et al. 2003, 2004). The values of the calibrated parameters were selected from the run when predicted and observed values were close enough. The calibrated parameters and all other parameters were summarized in Table 4.
5.4. Model performance criteria The root mean square error (RMSE) and the index of agreement (d) (Willmott 1982) were computed to evaluate the model performance of predicting soil water content and soil ammonium and nitrate concentration.
∑ (O −C ) n
RMSE=
2
i
i =1
i
d=1−
(9)
n
∑ (O −C ) n
∑
i =1
n i =1
2
i
i
Oi −O + Ci −O
(10)
2
Where, Oi and Ci are the observed and calculated values; O is the mean of the observed values; n is the number of measurements; the RMSE with a better agreement close to 0 has a minimum value of 0; the value of d varies from 0 to 1.0 with a better fit close to 1.0.
5.5. Fertigation strategies Fresh water applied prior to fertigation and flushing after fertilizer application finished is usually needed to prevent the plugging of the emitters by the solute remained in the drip pipelines in drip fertigation system. The initial distribution of soil water content and nitrate distribution were assumed to be uniform. The initial water content and nitrate concentration were taken to be 0.12 cm3 cm–3 and 0 mg L–1. The time intervals of the additional fresh water irrigation after fertigation varied from 12 to 108 min for different fertigation strategies which were summarized in Table 2.
Table 4 Calibrated soil hydraulic parameters and soil solute transport parameters and other parameters Calibrated soil hydraulic parameters1)
Values
θs (cm3 cm–3) θr (cm3 cm–3) a (cm–1) n
0.3935 0.0452 0.0107 1.5234
Calibrated solute transport parameters2) Values μw1 (d–1) μw2 (d–1) μ0 (mg kg–1 d–1)
0.05 0.01 1
Other parameters3)
Values
KS (cm d–1) DL (cm) DT (cm) Dw (cm d–1) ρ (g cm–3)
62.5 0.32 0.0032 57.6 1.32
1)
θs, soil saturated water content (cm3 cm–3); θr, soil residual water content (cm3 cm–3); a and n, parameters of the soil hydraulic fuction. μw1, nitrification rate constant (d–1); μw2 , denitrification rate constant (d–1); μ0, mineralization rate constant (mg kg–1 d–1). 3) KS, soil saturated hydraulic conductivity (cm d–1); DL, longitudinal dispersivity (cm); DT, transversal dispersivity (cm); Dw, molecular diffusion coefficient (cm d–1); ρ, soil bulk density (g cm–3). 2)
Acknowledgements This work was financially supported by the Non-Profit
National Research Institute, Ministry of Finance of China (IARRP-2012-202-3) and the Special Fund for Agro-scientific Research in the Public Interest, China (201203077-04-05).
ZHANG Jian-jun et al. Journal of Integrative Agriculture 2015, 14(12): 2434–2445
References Alva A K, Paramasivam S, Fares A, Delgado J D, Mattos Jr D, Sajwan K S. 2005. Nitrogen and irrigation management practices to improve nitrogen uptake efficiency and minimize leaching losses. Journal of Crop Improvement, 15, 369–420. Alva A K, Paramasivam S, Mattos J D, Quaggio J A. 2008. Advances in nitrogen fertigation of citrus. Journal of Crop Improvement, 22, 121–146. Assouline S. 2002. The effects of microdrip and conventional drip irrigation on water distribution and uptake. Soil Science Society of America Journal, 66, 1630–1636. Bristow K L, Cote C M, Thorburn P J, Cook F J. 2000. Soil wetting and solute transport in trickle irrigation systems. In: Proceedings of the 6th International Micro-irrigation Technology for Developing Agriculture Conference. Cape Town, South Africa. pp. 22–27. Cote C M, Bristow K L, Charlesworth P B, Cook F J, Thorburn P J. 2003. Analysis of soil wetting and solute transport in subsurface trickle irrigation. Irrigation Science, 22, 143–156. Gärdensäs A I, Hopmans J W, Hanson B R, Šimůnek J. 2005. Two-dimensional modeling of nitrate leaching for various fertigation scenarios under micro-irrigation. Agricultural Water Management, 74, 219–242. Huang Y F, Li Y Z, Lu J W. 1996. Simulation of soil nitrogen transport under field conditions II. Verification and application. Journal of Hydraulic Engineering, 6, 15–23. (in Chinese) Khalil Ajdary D K, Singh A K, Singh M K. 2007. Modelling of nitrogen leaching from experimental onion field under drip fertigation. Agricultural Water Management, 89, 15–28. Li J, Zhang J J, Rao M J. 2004. Wetting patterns and nitrogen distributions as affected by fertigation strategies from a surface point source. Agricultural Water Management, 67, 89–104. Li J, Zhang J J, Ren L. 2003. Water and nitrogen distribution as affected by fertigation of ammonium nitrate from a point source. Irrigation Science, 2, 19–30. Li J, Ji H Y, Li B, Liu Y C. 2007. Wetting patterns and nitrate distributions in layered-textural soils under drip irrigation. Agricultural Sciences in China, 6, 970–980. Li J, Yoder R E, Odhiambo L O, Zhang J J. 2004. Simulation of nitrate distribution under drip irrigation using artificial neural
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networks. Irrigation Science, 23, 29–37. Li Y F, Li J, Li B. 2007. Nitrogen dynamics in soil as affected by fertigation strategies and frequencies for drip-irrigated tomato. Journal of Hydraulic Engineering, 7, 857–865. (in Chinese) Lv D. 2000. Experimental study and simulation of water and salt movement in the soil. MSc thesis, Xi’an University of Science and Technology, China. (in Chinese) Ma J H. 2004. Development of transfer function model and numerical prcdiction on nitrate nitrogen leaching risk at field scale. Ph D thesis, China Agricultural University. (in Chinese) Mualem Y. 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research, 12, 513–522. Myrold D D, Tiedje J. 1986. Simultaneous estimation of several nitrogen cycle rates using 15N: theory and application. Soil Biology & Biochemistry, 6, 559–568. Phogat V, Skewes M A, Cox J W, Alam J, Grigson G, Šimůnek J. 2013. Evaluation of water movement and nitrate dynamics in a lysimeter planted with an orange tree. Agricultural Water Management, 127, 74–84. Šimůnek J, van Genuchten M T, Šejna M. 2011. The HYDRUS Software Package for Simulating Two- and ThreeDimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Media. Technical Manual, ver. 2.0 PC Progress, Prague, Czech Republic. Van der Laan M, Stirzaker R J, Annandale J G, Bristow K L, du Preez C C. 2010. Monitoring and modelling draining and resident soil water nitrate concentrations to estimate leaching losses. Agricultural Water Management, 97, 1779–1786. van Genuchten M Th. 1980. A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 44, 892–1037. Willmott C J. 1982. Some comments on the evaluation of model performance. Bulletin of the American Meteorological Society, 63, 1309–1313. Zhang J J. 2002. Experimental investigation and simulation on water and nitrogen distributions as affected by fertigation from a point source. MSc thesis, Chinese Academy of Agricultural Sciences. (in Chinese) (Managing editor WANG Ning)
ScienceDirect
RESEARCH ARTICLE
Simulation of water and nitrogen dynamics as affected by drip fertigation strategies ZHANG Jian-jun1, LI Jiu-sheng2, ZHAO Bing-qiang1, LI Yan-ting1 1 2
Institute of Agricultural Resource and Regional Planning, Chinese Academy of Agricultural Sciences, Beijing 10081, P.R.China State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, P.R.China
Abstract The aim of drip fertigation is synchronising the application of water and nutrients with crop requirements, and maintaining the proper concentration and distribution of nutrient and water in the soil. The wetting patterns and nutrient distributions under drip fertigation have been proved to be closely related to the fertigation strategies. In order to find out the critical factors that affect the nutrient distribution under different drip fertigaiton strategies, a computer simulation model HYDRUS2D/3D was used to simulate the water and nitrate distribution for various fertigation strategies from a surface point source. Simulation results were compared with the observed ones from our previous studies. A 15° wedge-shaped plexiglass container was used in our experiment to represent one-twenty-fourth of the complete cylinder. The height of container is 40 cm, and the radius is 41 cm. The ammonium nitrate solution was added through a no. 7 needle connected to a Mariotte tube with a flexible hose. The soil water content, nitrate and ammonium concentrations were measured. The comparison of simulated and observed data demonstrated that the model performed reliably. The numerical analysis for various fertigation strategies from a surface point source showed that: (1) The total amount of irrigation water, the concentration of the fertilizer solution and the amount of pure water used to flush the pipeline after fertilizer solution application are the three critical factors influencing the distribution of water and fertilizer nitrogen in the soil. (2) The fresh water irrigation duration prior to fertigation has no obvious effect on nitrate distribution. The longer flushing time period after fertigation resulted in nitrate accumulation closer to the wetting front. From the point of avoiding the possibility of nitrate loss from the root zone, we recommended that the flushing time period should be as shorter as possible. (3) For a given amount of fertilizer, higher concentration of the fertilizer applied solution reduces the potential of nitrate leaching in drip irrigation system. While, lower concentration of the fertilizer solution resulted in an uniform distribution of nitrate band closer to the wetted front. Keywords: fertigation, strategy, drip irrigation, modelling, nitrate transport
Received 21 August, 2015 Accepted 17 November, 2015 ZHANG Jian-jun, Mobile: +86-15801181005, Tel: +86-1082108664, E-mail: [email protected]; Correspondence LI Jiu-sheng, Tel: +86-10-68786545, E-mail: [email protected]; ZHAO Bing-qiang, Tel: +86-10-82108664, E-mail: zhaobingqiang @caas.cn © 2015, CAAS. All rights reserved. Published by Elsevier Ltd. doi: 10.1016/S2095-3119(15)61231-X
1. Introduction Nitrogen (N) is an essential nutrient for plant and therefore a main component of fertigation. Nitrate is one of the main forms of nitrogen found in soil which is highly mobile and leachable. Delivery of N fertilizer through fertigation reduces N losses in the soil-plant system by ammonia volatilization
ZHANG Jian-jun et al. Journal of Integrative Agriculture 2015, 14(12): 2434–2445
and nitrate leaching (Alva et al. 2008). Drip irrigation has become an optimal means for providing water and nutrients directly to the roots of crops because of its potential of precisely applying water and chemicals with a high water and fertilizer use efficiency. The aim of drip fertigation is synchronising the application of water and nutrient with crop requirements and maintaining the proper concentration and distribution of nutrient and water (Assouline 2002). It is a common practice that fresh water is applied prior to and after fertigation to ensure fertilizer application uniformity and flushing the drip lines. It has been proved that the distributions of water and nitrate under drip fertigation were closely related to the fertigation strategies (Li et al. 2004; Gärdensäs et al. 2005; Khalil et al. 2007). Improper irrigation management can lead to leakage loss of water and nutrient from the root zone which could create the pollution of shallow groundwater. Therefore, optimal irrigation scheduling is important to improve the crop uptake efficiencies of water and nutrient (Alva et al. 2005). Hence a clear understanding of water and nitrate dynamics in root zone under varying fertigation strategies is important for appropriate design and management of drip fertigation system (Li et al. 2003; Khalil Ajdary 2007). The shape of wetted soil volume and spatial distribution of soil nitrate concentrations under drip fertigation are influenced by many factors, including the irrigation quantity, the time period of using fresh water prior to and after fertigation, and the concentration of the fertilizer solution. Bristow et al. (2000) simulated water and solute distribution in the soil under two fertigation strategies, involving application of solute at the end of and at the beginning of an irrigation cycle from a buried point source. They reported that larger amount of nutrients maintained near to and above the source when solute applied at the beginning of an irrigation cycle. Cote et al. (2003) presented that fertigation at the beginning of the irrigation cycle might reduce nitrate leaching for highly permeable coarse-textured soils. Li et al. (2003, 2004) conducted experiments to study the effects of fertigation strategies on wetting patterns and nitrogen distribution in the soil from a surface point source of nitrate ammonium (NH4NO3). The strategy of 1/4W-1/2N-1/4W (first applying water for one-fourth of the total irrigation time, then applying fertilizer solution for one-half of the total irrigation time, followed by applying water for the remaining one-fourth of the total irrigation time) left the most nitrate close to the source and was therefore recommended. Gärdensäs et al. (2005) found that seasonal leaching was high for coarse-textured soils, and concluded that fertigation at the beginning of the irrigation cycle tends to increase seasonal nitrate leaching. In contrast, fertigation events at the end of the irrigation cycle reduced the potential of nitrate leaching. Li et al. (2007) conducted field experiments in a solar-heated greenhouse
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with drip-irrigated tomato to investigate the effects of drip fertigation strategy and frequency on nitrate dynamics, spatial distribution of nitrate, apparent recovery of nitrogen and fertilizer use efficiency. The results showed that the strategy of applying nutrient at the beginning resulted in a uniform distribution of nitrate in different layers and the nitrate in upper layers increased as the fertilization time was transferred towards the end of an irrigation cycle. As the fertilization time was transferred towards the beginning of an irrigation cycle, potential of nitrate moving towards the boundary of wetted volume was more obvious. The optimal fertilization strategy of 1/4W-1/2N-1/4W was suggested. Phogat et al. (2013) used the HYDRUS 2D/3D model to develop various modelling scenarios to assess the fate of nitrate for different irrigation and fertigation schemes. The results imply that fertigation in a short pulse towards the end of the irrigation event or low concentration fertigation could increase the efficiency of nitrogen fertigation as compared to other options. When reviewing the literature, it becomes clear that useful and reliable information can be derived about rhizosphere processes with computer modelling techniques. Numerical simulations of water flow and nitrate transport can help in understanding of the dynamic processes in the vadose zone. And the management of fertigaiton system can affect the nutrient and water distribution in the root zone. The performance of these systems need to be evaluated, because considerable localized leaching can occur near the driplines and the loss of nutrients, particularly nitrate can pose a serious threat to receiving water bodies (Van et al. 2010). However, the numerical simulation and experimental data of water and nitrate dynamics under different fertigation strategies are still lacking. We could not come across any literature about which are the critical factors that affect the nutrient distribution under different drip fertigaiton strategies. The objective of the present study was to simulate the water and nitrate distribution under various fertigation strategies and various solution concentrations from a surface point source through simulations to investigate the critical factors that affect the nutrient distribution under different drip fertigaiton strategies.
2. Results 2.1. Calibration and validation of the model Simulation results were compared with the observed data obtained from our previous studies (Zhang 2002; Li et al. 2003, 2004) for model evaluation. Table 1 shows the root mean square error (RMSE) and the index of agreement (d) values for the calibration and validation. Fig. 1 shows the soil water profiles as 7.9 L of water were applied at a rate of
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ZHANG Jian-jun et al. Journal of Integrative Agriculture 2015, 14(12): 2434–2445
2.0 L h–1, and compares these values with the results of the
source and as a function of the radial distance at depths (z)
HYDRUS 2D/3D simulations. Fig. 2 compares the simulated
of 2.5 and 12.5 cm below the surface are illustrated in Fig. 1.
and the observed distributions of the NO3-N concentrations
For the calibration dataset, RMSE values for soil water
–1
in the soil as 7.9 L of NH4NO3 solutions with 300 mg L
content ranged from 0.017–0.049 cm3 cm–3 with d varying
concentrations was applied at a rate of 2.0 L h–1. Soil water
from 0.852–0.996 (Table 1), indicating an excellent agree-
content as a function of the vertical distance from the surface
ment between the simulated and observed soil water con-
at radial distances (r) of 2.5 and 12.5 cm from the point
tents. Fig. 2 indicates that the model captured the distribution
Table 1 The root mean square error (RMSE) and the index of agreement (d) of the soil water content and nitrate concentration Test no.
Application rate Volume applied (L h–1) (L)
Calibration 1 2 3 4 5 6 7 Validation 8 9 10 11 12 13 14
RMSE Water content (cm3 cm–3)
NH4NO3 concentration (mg L–1)
d NO3-N (mg kg–1)
Water content
NO3-N
0.6 0.9 0.9 1.4 2.0 4.9 4.9
8.0 8.0 8.0 8.3 7.9 14.0 13.2
300 100 300 300 300 300 500
0.0380 0.0336 0.0170 0.0162 0.0225 0.0303 0.0493
18.70 15.36 20.25 14.49 18.08 11.51 12.79
0.8518 0.9803 0.9851 0.9964 0.9915 0.9529 0.9416
0.6176 0.8819 0.6158 0.8778 0.8368 0.8540 0.7819
0.9 1.0 1.0 1.1 2.0 4.8 4.9
6.0 8.1 8.1 10.0 13.1 10.1 15.0
300 500 700 300 300 300 300
0.0275 0.0305 0.0302 0.0335 0.0395 0.0317 0.0443
12.47 13.00 11.97 13.36 19.23 18.56 12.68
0.9947 0.9516 0.9720 0.8817 0.9243 0.9938 0.9353
0.9326 0.7038 0.8149 0.7744 0.6536 0.8770 0.8342
Observed
z=2.5 cm
0.4 0.3 0.2 0.1 0.0
0 5 10 15 20 25 30 35 40 45
0
0
10 20 30 40 Radial distance (cm) Soil water content (cm3 cm–3) 0.1 0.2 0.3 0.4
50
Soil water content (cm3 cm–3)
0.5
0.5
z=12.5 cm
0.4 0.3 0.2 0.1 0.0
0.5
r=2.5 cm Depth (cm)
Depth (cm)
Soil water content (cm3 cm–3)
Simulated
0 5 10 15 20 25 30 35 40 45
0
0
10 20 30 40 Radial distance (cm) Soil water content (cm3 cm–3) 0.1 0.2 0.3 0.4
50
0.5
r=12.5 cm
Fig. 1 Comparisons of the simulated and the observed soil water content profiles as 7.9 L of water were applied at a rate of 2.0 L h–1.
ZHANG Jian-jun et al. Journal of Integrative Agriculture 2015, 14(12): 2434–2445
2.2. Applications of the model
trend of nitrate in the soil well. The RMSE of 11.51–20.25 mg kg–1 and d values of 0.62–0.88 for nitrate concentration (Table 1) indicated good performance of the model. For the validation dataset, RMSE values for soil water content ranged from 0.028–0.044 cm3 cm–3 with d varying from 0.882–0.995 (Table 1). The RMSE values for nitrate concentration ranged from 11.97–19.23 mg kg–1 and d of 0.65–0.93 (Table 1) indicated good performance of the model.
All fertigation scenarios reported are hypothetical. The duration of irrigation cycle is considered 4 h and a fixed fertigation duration of 2 h during the irrigation cycle is used for all drip fertigation events. The time intervals of the additional fresh water irrigation after fertigation varied from 12 to 108 min for different fertigation strategies (Table 2).
350 300 250 200 150 100 50 0
0
0
0
10 20 30 40 Radial distance (cm)
400 300 250 200 150 100
50
50 0
0
r=2.5 cm
5
10
10
15
15
20 25 30
z=12.5 cm
350
Nitrate concentration (mg L–1) 100 200 300 400
5 Depth (cm)
Nitrate concentration (mg L–1)
z=2.5 cm
Observed
Depth (cm)
Nitrate concentration (mg L–1)
Simulated 400
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0
0
20 40 Radial distance (cm)
60
Nitrate concentration (mg L–1) 100 200 300 400 r=12.5 cm
20 25 30
35
35
40
40
45
45
Fig. 2 Comparisons of the simulated and the observed distributions of the NO3-N concentrations in the soil as 7.9 L of NH4NO3 solutions with 300 mg L–1 concentrations was applied at a rate of 2.0 L h–1.
Table 2 Irrigation and fertigation duration and nitrate concentrations in fertilizer solutions applied for different fertigation scenarios Fertigation strategy1) 1W10F9W 2W10F8W 3W10F7W 4W10F6W 5W10F5W 6W10F4W 7W10F3W 8W10F2W 9W10F1W (FT120) FT60 FT180 1)
Total duration (min) 240 240 240 240 240 240 240 240 240 240 240
Concentration of nitrate Time interval of fresh water prior Fertigaiton duration Flush duration (mg kg–1) to fertigation (min) (min) (min) 300 12 120 108 300 24 120 96 300 36 120 84 300 48 120 72 300 60 120 60 300 72 120 48 300 84 120 36 300 96 120 24 300 108 120 12 600 168 60 12 200 48 180 12
1W10F9W means applying water for 1/20 of the total irrigation time, followed by applying fertilizer solution for the 10/20 of the total irrigation time, then applying water for the rest 9/20 of the total irrigation time. FT60, FT120 and FT 180 represent the fertigation strategies with fertigation duration of 60, 120 and 180 min. The same as below.
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2.3. Water and nitrate distribution when fertilizer application ceased The contour plots in Fig. 3 show the simulated soil water content for the nine fertigation strategies when fertilizer application completed. It is clear that a longer time period for fresh water application before fertigation allows water to move faster from the emitter. For example, the surface wetted radii were 26 and 31.5 cm for fertigation strategy of 1W10F9W (1W10F9W means applying water for 1/20 of the total irrigation time, followed by applying fertilizer solution for the 10/20 of the total irrigation time, then applying water for
0
0
5
Radial distance (cm) 10 15 20 25 30 35 40
0
0
5
the rest 9/20 of the total irrigation time. The same as below.) and 9W10F1W, respectively. The vertical wetted depths were 25 and 31.5 cm for fertigation strategy of 1W10F9W and 9W10F1W, respectively. The soil nitrate distributions when fertigation completed for the nine fertigation strategies are presented in Fig. 4. The highest nitrate concentration that was close to the concentration of solutions applied occurred near the emitter. All of the nitrate injected was distributed within the wetted soil profile to a depth of 25–26 cm and a radial distance of 27–28 cm. We note that the total N-added is the same for all fertigation strategies, but the strategies vary between
Radial distance (cm) 10 15 20 25 30 35 40
0
10
10
10
15 20 25
15 20 25
35
35
1W10F9W
40 0
5
0
20 25
0
5
Radial distance (cm) 10 15 20 25 30 35 40
0
10
10
15
15
15
25
25
35
35
4W10F6W
0
5
Radial distance (cm) 10 15 20 25 30 35 40
0
25
0
5
Radial distance (cm) 10 15 20 25 30 35 40
0
10
15
15
15
35 40
Depth (cm)
10 Depth (cm)
10 Depth (cm)
5
30
20 25 30
7W10F3W
35 40
6W10F4W
40
5
25
Radial distance (cm) 10 15 20 25 30 35 40
20
5
20
5
35
5W10F5W
40
40
0
30
30
30
0
Depth (cm)
10 Depth (cm)
5
Depth (cm)
5
20
3W10F7W
40
5
20
Radial distance (cm) 10 15 20 25 30 35 40
15
35
2W10F8W
40
Radial distance (cm) 10 15 20 25 30 35 40
5
30
30
30
0
Depth (cm)
5
Depth (cm)
5
Depth (cm)
5
0
0
5
Radial distance (cm) 10 15 20 25 30 35 40
20 25 30
8W10F2W
35 40
9W10F1W
Fig. 3 Spatial distributions of soil water content (cm3 cm–3) when fertigation completed for the nine fertigation strategies simulated.
1W10F9W means applying water for 1/20 of the total irrigation time, followed by applying fertilizer solution for the 10/20 of the total irrigation time, then applying water for the rest 9/20 of the total irrigation time. The same as below.
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ZHANG Jian-jun et al. Journal of Integrative Agriculture 2015, 14(12): 2434–2445
the duration of fresh water irrigation prior to fertigation. The ratios of NO3-N mass within a given range from the source to the total amount of nitrogen within the simulation region were determined for each fertigation strategy (Table 3). The mass balance was conducted for four zones, which are 0– 10 cm (zone 1), 10–20 cm (zone 2), 20–30 cm (zone 3), and >30 cm (zone 4) from the source when fertigation completed. As expected, the total amount of NO3-N in the four zones followed the trend: zone 2>zone 1>zone 3>zone 4. The ratios of nitrate mass in the four zones have no significant difference among the nine fertigation strategies when ferti-
0
5
Radial distance (cm) 10 15 20 25 30 35 40
5
Radial distance (cm) 10 15 20 25 30 35 40
0
10
10
10
15
15
15
20 25
20 25
35
1W10F9W
5
Radial distance (cm) 10 15 20 25 30 35 40
0
25
0
5
Radial distance (cm) 10 15 20 25 30 35 40
0
10
15
15
15
20 25 30
35
5
Radial distance (cm) 10 15 20 25 30 35 40
0
25
0
5
Radial distance (cm) 10 15 20 25 30 35 40
0
10
10
40
15 20 25 30
30 35
Depth (cm)
10 Depth (cm)
5
25
7W10F3W
35 40
6W10F4W
40
5
20
Radial distance (cm) 10 15 20 25 30 35 40
20
5
15
5
35
5W10F5W
40 0
0
30
35
4W10F6W
40
0
Depth (cm)
10 Depth (cm)
5
10
30
3W10F7W
40
5
25
Radial distance (cm) 10 15 20 25 30 35 40
20
5
20
5
35
2W10F8W
40 0
0
30
30
40
0
Depth (cm)
5
35
Depth (cm)
0
The simulated soil water content when the irrigation cycle completed shows no differences between the nine fertigation strategies with the same amount of application water. The surface wetted radius and the vertical wetted depth were 32.5 and 32.0 cm, respectively, for the nine fertigation strategies.
5
30
Depth (cm)
0
2.4. Water and nitrate distribution when the irrigation cycle completed
5
Depth (cm)
Depth (cm)
0
gation ceased, suggesting the fresh water application prior to fertigation has no obvious effect on nitrate distribution.
0
5
Radial distance (cm) 10 15 20 25 30 35 40
15 20 25 30
8W10F2W
35
9W10F1W
40
Fig. 4 Spatial distributions of nitrate concentration (mg L–1) in soil solution when fertigation completed for the nine fertigation strategies simulated.
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Table 3 Summary of the ratios of the amount of nitrate nitrogen within a given range of distance from the source to the total amount of nitrate nitrogen within the simulation region for the nine fertigation strategies simulated1) Fertigation ceased 1W10F9W 2W10F9W 3W10F9W 4W10F6W 5W10F5W 6W10F4W 7W10F3W 8W10F2W 9W10F1W Irrigation cycle compeleted 1W10F9W 2W10F9W 3W10F9W 4W10F6W 5W10F5W 6W10F4W 7W10F3W 8W10F2W 9W10F1W (FT120) FT60 FT180 1)
Zone 1 (%)
Zone 2 (%)
Zone 3 (%)
Zone 4 (%)
20.9 20.9 20.9 20.9 20.9 20.9 20.9 21.0 21.0
74.5 74.3 74.3 74.2 74.2 74.2 74.3 74.3 74.3
4.6 4.8 4.9 4.9 4.9 4.8 4.8 4.8 4.7
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.1 0.2 0.4 0.9 2.2 5.3 10.6 21.2 7.2
47.3 54.0 60.7 67.4 73.6 79.0 82.8 84.2 81.3 78.5 70.0
52.5 45.9 39.1 32.4 26.0 20.1 14.9 10.5 8.1 0.3 22.8
0.1 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Zones 1, 2, 3, and 4 means the range of 0–10, 10–20, 20-30, and >30 cm from the source. The duration of irrigation cycle is considered 4 h and a fixed fertigation duration of 2 h during the irrigation cycle is used for all drip fertigation events.
The nitrate was distributed within the soil wetted volume and a quite similar distribution pattern of soil nitrate concentration was observed for the nine fertigation strategies. The contour plots in Fig. 5 show the simulated concentration of nitrate in the soil when the irrigation cycle ceased. All the fertigation strategies generally resulted in a band of nitrate along the periphery of the wetted soil volume with little or no nitrate near the emitter. From Fig. 5 we found that the zone of relatively low nitrate concentration in the vicinity of the emitter becomes larger when the flushing time interval lasted for a longer time, and the band of nitrate moves closer to the wetting front. It is clear that a longer flushing time allows nitrate to move faster away from the emitter. For example, the nitrate reaches 26 and 21 cm for the 1W10F9W and 9W10F1W fertigation strategy, respectively. Fig. 5 also indicates that nitrate moves with water during infiltration and leaching by fresh water after fertigation. As the time period for flushing increased, the band where nitrate accumulation occurred was closer to the wetting front. The longer time period for flushing the drip line resulted in more nitrate distributed faraway from the emitter, increasing the probability of nitrate leaching.
2.5. Effects of fertigation duration on nitrate distribution We note that the total N-added is the same for the FT60,
FT120 and FT180 fertigation strategies, but the fertigation duration varies from 60 to 180 min. The fushing time period is 12 min for the FT60, FT120 and FT180 fertigation strategies. The concentrations of fertilizer solution for the FT60, FT120 and FT180 fertigation strategies are 600, 300 and 200 mg L–1, respectively. The nitrate front in the radial direction reaches 24.0, 29.0 and 32.0 cm, and in the vertical direction reaches 21.5, 27.0 and 31.0 cm for the fertigation strategy FT60, FT120 and FT180, respectively (Fig. 6). The width of the nitrate distribution band increases when the fertigation duration increases from 60 to 180 min, but the nitrate concentration in soil solution decreases. The nitrate concentration was varied from 2–16, 5–50 and 10–100 mg L–1 for the fertigation strategies FT60, FT120 and FT180, respectively. A shorter fertigation duration resulted in a nonuniform distribution of nitrate within the nitrate distribution band. Similarly, the total amount of NO3-N in the four zones followed the trend: zone 2>zone 1>zone 3>zone 4 for the fertigation strategies FT60 and FT120 (Table 3). However, the total amount of NO3-N in the four zones followed the trend: zone 2>zone 3>zone 1>zone 4 for the fertigation strategy FT180. The ratios of nitrate mass in zone 1 is 21.2, 10.6 and 7.2% for the fertigation strategies FT60, FT120 and F180, respectively. The ratios of nitrate mass in zone 3 is 0.3, 8.1 and 22.8% for the fertigation strategies FT60, FT120 and F180, respectively. The mass balance results
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ZHANG Jian-jun et al. Journal of Integrative Agriculture 2015, 14(12): 2434–2445
0
5
Radial distance (cm) 10 15 20 25 30 35 40
Radial distance (cm) 10 15 20 25 30 35 40
0
10
10
10
15 20 25
15 20 25 30
0
5
0
20 25
0
5
0
10
10
15
15
15
20 25
35
4W10F6W
0
5
Radial distance (cm) 10 15 20 25 30 35 40
0
25
0
5
0
10
10
15
15
15
35 40
Depth (cm)
10 Depth (cm)
5
20 25 30
30 7W10F3W
6W10F4W
40 Radial distance (cm) 10 15 20 25 30 35 40
5
25
Radial distance (cm) 10 15 20 25 30 35 40
20
5
20
5
35
5W10F5W
40
40
0
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30
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0
Depth (cm)
10 Depth (cm)
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30
3W10F7W
40 Radial distance (cm) 10 15 20 25 30 35 40
5
25
Radial distance (cm) 10 15 20 25 30 35 40
15
5
20
5
35
2W10F8W
40 Radial distance (cm) 10 15 20 25 30 35 40
0
30
35
1W10F9W
40 0
Depth (cm)
5
35
Depth (cm)
5
5
30
Depth (cm)
0
0
5
Depth (cm)
Depth (cm)
0
35 40
0
5
Radial distance (cm) 10 15 20 25 30 35 40
20 25 30
8W10F2W
35
9W10F1W
40
Fig. 5 Spatial distributions of nitrate concentration (mg L–1) in soil solution at the end of the simulation period for the nine fertigation strategies.
clearly showed that the leaching potential increases as the fertigation duration increases.
3. Discussion Water and nitrate distribution under different fertigation scenarios were investigated using the HYDRUS2D/3D model. The results indicated that the distribution of fertilizer nitrogen in the soil under drip fertigaiton was mainly influenced by the following factors, the total amount of irrigation water, the concentration of the fertilizer solution and the amount of pure water used to flush the pipeline after fertilizer solution application.
Simulation results showed that the total amount of irrigation water determines the distribution range of irrigation water in the soil. At the same time, it also determines the range of the possible distribution of fertilizer nitrogen since nitrate distribution is highly associated with water flow. From our simulation results we find that the radial distance and vertical depth of fertilizer nitrogen distributed were always within wetted area. The fresh water application prior to fertigation has no obvious effect on nitrate distribution. But the movement and distribution of nitrate was closely related to the amount of the pure water used to flush the pipeline after fertilizer solution application. The greater amount of pure water used to flush the pipeline after fertilizer solution
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ZHANG Jian-jun et al. Journal of Integrative Agriculture 2015, 14(12): 2434–2445
0
0
5
Radial distance (cm) 10 15 20 25 30 35 40
0
0
5
Radial distance (cm) 10 15 20 25 30 35 40
0
10
10
10
15
15
15
20
20
25
35 40
25
30 FT180
35 40
Radial distance (cm) 10 15 20 25 30 35 40
20
25
30
5
Depth (cm)
5
Depth (cm)
5
Depth (cm)
5
0
30 FT120 (9W10F1W)
35
FT60
40
Fig. 6 Spatial distributions of nitrate concentration (mg L–1) when irrigation cycle completed with 200, 300 and 600 mg L–1 concentrations of NH4NO3 solutions were applied for the FT180, FT120 and FT60 fertigation strategies.
application, the more closer of the nitrate distributed near the wetting front. For a given amount of fertilizer injected, the nitrate distribution was more uniform and the nitrate front was closer to the wetted front when the ferilizer concentration is low. On the contrary, higher concentration of the fertilizer solution resulted in a nonuniform distribution of nitrate and nitrate front closer to the emitter. The extension of the crop rooting system is different for different crop types and different growing stages. The requirements for irrigation water and nutrient are also different. This means that water and nutrient should be provided to the root zone in desirable amount, concentration and location. According to our simulation results, the total amount of irrigation water, the flushing time period and the concentration of fertilizer solution to be the key considerations in the design and management of drip fertigation system.
4. Conclusion The comparison between the simulated and observed ones from our previous studies demonstrated that the HYDRUS2D/3D model performed well in simulation of water and nitrate distribution under fertigation from a surface point source. Then we used the model to simulate the water and nitrate distribution under nine different fertigation strategies. The following conclusions were supported by this study: (1) The total amount of irrigation water, the concentration of the fertilizer solution and the amount of pure water used to flush the pipelines after fertilizer solution application are the three critical factors influencing the distribution of water and fertilizer nitrogen in the soil. (2) The fresh water irrigation duration prior to fertigation has no obvious effect on nitrate distribution. The longer flushing time period after fertigation resulted in nitrate
accumulation closer to the wetting front. From the point of avoiding the possibility of nitrate loss from the root zone, we recommended that the flushing time period should be as shorter as possible. (3) For a given amount of fertilizer injected, higher concentration of the fertilizer solution reduces the potential of nitrate leaching in drip irrigation system. While, lower concentration of the fertilizer solution resulted in an uniform distribution of nitrate band closer to the wetted front.
5. Materials and methods 5.1. Model description The simulations of water flow and nitrate transport under different drip fertigation scenarios were carried out using a computer simulation model, HYDRUS2D/3D (Šimůnek et al. 2011). This software package can simulate the transient two-dimensional or axi-symmetrical three dimensional movements of water and solutes in soil. In presented applications, we simulated three-dimensional axially symmetric water flow, solute transport in soils as applied by drip fertigation, based on the flow equations with finite-element numerical solutions. Axi-symmetrical water flow in variable saturated rigid, isotropic porous medium and surface drip irrigation is described by the modified form of Richards’ equation. The equation is given by: ∂h ∂K ( h) ∂h ∂ ∂θ ( h) 1 ∂ (1) = [ rK ( h) ] + [K ( h) ] + r ∂r ∂z ∂z ∂r ∂z ∂t Where, θ(h) is the volumetric water content (L3 L–3), r and z are the radial and vertical coordinate, respectively (L) , h is the soil water pressure head (L), t is the time (T), and K(h) is the unsaturated hydraulic conductivity function (L T–1). The unsaturated retention and hydraulic conductivity
ZHANG Jian-jun et al. Journal of Integrative Agriculture 2015, 14(12): 2434–2445
fuctions deccribed by the van Genuchten (1980) model, which is defined as follows: θs−θr θr+ for h<0 m
θ (h)=
(2)
1+|αh|n θ (h)=θs
for h≥0 m
2
K(h)=KsSel 1− 1−S1/m e Se=
(3)
θ−θr
(4)
θs−θr
m=1− 1 ; n>1 (5) n Where, θr and θs denote the residual and saturated water contents (L3 L–3), respectively; α is the inverse of air-entry value; n is the pore size distribution index; l is the pore connectivity parameter which was estimated (Mualem 1976) to be 0.5; Ks is the soil saturated hydraulic conductivity (L T–1). The partial differential equations governing nonequilibrium chemical transport of solutes involved in a sequential first-order decay chain during transient water flow in a variably saturated rigid porous medium are taken as follows: For nitrate: ∂c1 ∂θc1 ∂ ∂c1 ∂c1 1 ∂c1 = θDrr +θDrz + θDrr + θDrz ∂z ∂t ∂r ∂r r ∂z ∂r (6) ∂c1 ∂c1 ∂qrc1 qrc1 ∂qzc1 ∂ + θDzz +θDrz − + + ∂z ∂z r ∂r ∂z ∂r +µ0ρ−µw2θc2
For ammonium: ∂θc2 ∂t
+ρ
∂s2 ∂t
=
∂ ∂r
+
∂ ∂z
θDrr
∂c2 ∂r
θDzz
+ θDrz
∂c2 ∂r
∂c2 ∂z
+ θDrz
∂c2 ∂z
+
1 r −
θDrr
∂c2 ∂r
+θDrz
∂c2 ∂z
qrc2 ∂qzc2 (7) + + ∂r ∂z r
∂qrc2
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15° wedge-shaped plexiglass containers. The height of container is 40 cm, and the radius is 41 cm. This container was used to represent one-twenty-fourth of the complete cylinder. This assumption was verified by Lv (2000) who found that there was no significant differences between the 15° wedgeshaped and a 90° wedge-shaped container. The soil used in our experiment was a loam soil. The air-dry soil passed through a 2-mm sieve was packed in the container with 5 cm increments to obtain a constant bulk density of 1.32 g cm–3. The ammonium nitrate solution was added through a no. 7 needle connected to a Mariotte tube with a flexible hose. The outlet of the needle was located at the corner of the container on the soil surface. The soil was covered with a polyethylene sheet to maintain zero evaporation. After each experiment, the container was opened and immediately samples were taken with a metal tube for determination of water content, nitrate and ammonium concentration.
5.2. Modeling domain properties and boundary conditions We assumed that the soil is homogeneous in the domain. The infiltration process of a single emitter can be assumed as an axi-symmetrical flow. In the present study the radius r of the flow domain was taken as 40 cm and depth z as 40 cm (Fig. 7). A saturated ponded area develops in the vicinity of the emitter when irrigation starts. The ultimate radius of the ponded area is an exponential function of the application rate for the loam soil (Zhang 2002; Li et al. 2004, 2007). The ultimate radius of the saturated area is assumed to be the water entry zone in our simulation. A constant flux was Location of emitter
Variable flux boundary
−µw1θc2
Where, c1 is nitrate concentration in the liquid phases (M L–3); ρ is the soil bulk density (M L–3); qr and qz are the radial and vertical component of the volumetric flux density (L T–1); Drr and Dzz are the longitudinal and transverse dispersion coefficient tensor (L2 T–1); µ0 is the mineralization rate constant (M M–1 T–1); µw1 is the first-order nitrification rate constant (T–1); µw2 is the first-order denitrification rate constant (d–1); S2 is the absorbed concentration of ammonium (M M–1) which is described as follows: (8) S2=KDc2 Where, KD is the distribution coefficient of ammonium (L3 M–1). The experimental data used to calibrate and validate the model obtained from our previous studies (Zhang 2002; Li et al. 2003, 2004). The experimental set up consisted of a
Atmospheric flux boundary
40 cm No flow boundary Free drainge boundary
40 cm
Fig. 7 Simulation domain and boundary conditions.
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estimated by dividing emitter discharge rate with the area of the saturated zone when a constant application rate and solute concentration was applied. For the different fertigation scenarios, the solute concentration varies with time, so the time-variable flux boundary option was used to address the flux boundary. Bottom boundary was considered as free drainage boundary. Solute was applied with irrigation water and a first-type boundary condition was used to prescribe the concentration at the top boundary.
5.3. Input parameters A loam soil was used in our simulations. Particle size analysis yield an average value of 48% sand, 41% silt and 11% clay (Zhang 2002; Li et al. 2003, 2004). The van Genuchten (1980) model of soil hydraulic properties was selected in the numerical simulations. The pore connectivity parameter (dimensionless) was estimated by Mualem (1976) to be about 0.5 for many soils and this value was adopted in the present study. The values of soil saturated hydraulic conductivity Ks was determined according to the values reported in the literature (Zhang 2002; Li et al. 2003, 2004). The solute transport parameters including longitudinal dispersivity (DL), transversal dispersivity (DT) and molecular diffusion coefficient (DW) were determined according to the values reported in literature (Zhang 2002; Ma 2004). Ammonium was assumed to absorb to the solid phase using a distribution coefficient Kd which was taken as 0.326 cm3 g–1 obtained from experiment (Zhang 2002). Nitrification and denitrification were simulated using the first-order decay coefficients (μw1, μw2 ), and mineralization was modeled using the zero-order coefficient (μ0). The value ranges of μw1, μw2 and μ0 were determined according to literatures (Myrold and Tiedje 1986; Huang et al. 1996). The parameters θs, θr, a, n, μw1, μw2, and μ0 were adjusted by comparing the simulated and observed values of soil water
content and nitrate distribution obtained from our previous researches (Zhang 2002; Li et al. 2003, 2004). The values of the calibrated parameters were selected from the run when predicted and observed values were close enough. The calibrated parameters and all other parameters were summarized in Table 4.
5.4. Model performance criteria The root mean square error (RMSE) and the index of agreement (d) (Willmott 1982) were computed to evaluate the model performance of predicting soil water content and soil ammonium and nitrate concentration.
∑ (O −C ) n
RMSE=
2
i
i =1
i
d=1−
(9)
n
∑ (O −C ) n
∑
i =1
n i =1
2
i
i
Oi −O + Ci −O
(10)
2
Where, Oi and Ci are the observed and calculated values; O is the mean of the observed values; n is the number of measurements; the RMSE with a better agreement close to 0 has a minimum value of 0; the value of d varies from 0 to 1.0 with a better fit close to 1.0.
5.5. Fertigation strategies Fresh water applied prior to fertigation and flushing after fertilizer application finished is usually needed to prevent the plugging of the emitters by the solute remained in the drip pipelines in drip fertigation system. The initial distribution of soil water content and nitrate distribution were assumed to be uniform. The initial water content and nitrate concentration were taken to be 0.12 cm3 cm–3 and 0 mg L–1. The time intervals of the additional fresh water irrigation after fertigation varied from 12 to 108 min for different fertigation strategies which were summarized in Table 2.
Table 4 Calibrated soil hydraulic parameters and soil solute transport parameters and other parameters Calibrated soil hydraulic parameters1)
Values
θs (cm3 cm–3) θr (cm3 cm–3) a (cm–1) n
0.3935 0.0452 0.0107 1.5234
Calibrated solute transport parameters2) Values μw1 (d–1) μw2 (d–1) μ0 (mg kg–1 d–1)
0.05 0.01 1
Other parameters3)
Values
KS (cm d–1) DL (cm) DT (cm) Dw (cm d–1) ρ (g cm–3)
62.5 0.32 0.0032 57.6 1.32
1)
θs, soil saturated water content (cm3 cm–3); θr, soil residual water content (cm3 cm–3); a and n, parameters of the soil hydraulic fuction. μw1, nitrification rate constant (d–1); μw2 , denitrification rate constant (d–1); μ0, mineralization rate constant (mg kg–1 d–1). 3) KS, soil saturated hydraulic conductivity (cm d–1); DL, longitudinal dispersivity (cm); DT, transversal dispersivity (cm); Dw, molecular diffusion coefficient (cm d–1); ρ, soil bulk density (g cm–3). 2)
Acknowledgements This work was financially supported by the Non-Profit
National Research Institute, Ministry of Finance of China (IARRP-2012-202-3) and the Special Fund for Agro-scientific Research in the Public Interest, China (201203077-04-05).
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