This document summarizes research on modeling nutrient distribution under drip fertigation. It discusses how the HYDRUS-2D model was used to simulate water and nutrient movement in soil under different fertigation strategies. The results showed that applying nutrients in the second half of irrigation with a 2 day interval led to more uniform distribution of water and nutrients in the root zone compared to other fertigation strategies or longer irrigation intervals. The model is useful for optimizing drip fertigation system design and management.

1. MODELING NUTRIENT DISTRIBUTION UNDER DRIP
FERTIGATION
DR SANJAY SATPUTE
SCIENTIST,
SOIL AND WATER ENGINEERING
PAU, LUDHIANA

2.  Drip Fertigation is effective for row crops
 Simple, Flexible and Cost Effective
 Capable of delivering water and nutrients to the soil in
small quantities at any time
 Reduces leaching and improves the water distribution
uniformity
INTRODUCTION

3. 1. Determination of N, P and K distribution in soil and
nutrient uptake
2. Simulation of nutrient (N, P and K) distribution using
HYDRUS-2D model
3. Development of guideline

4. Parameters Methodology/ Instruments References
Soil texture Hydrometer Bouyoucos, 1927
pH pH meter (1:2, soil: water) Jackson, 1973
Electrical conductivity Conductivity bridge Jackson, 1973
Bulk density Gravimetric (core) Jackson, 1973
Hydraulic conductivity Constant head permeameter Jackson, 1973
Field capacity Pressure plate apparatus (1/3 bar) Richards and Weaver, 1964
Permanent wilting
point
Pressure plate apparatus (15 bar) Richards and Weaver, 1964
Aggregate size analysis Wet sieving Yoder, 1936
Organic carbon Wet digestion and titration Walkley and Black, 1934
Nitrogen KEL PLUS semi auto analyzer Kjeldahl, 1883
Phosphorus Olsen’s method and Colorimeter Olsen et al. 1954
Potassium Flame Photometer Hanway and Heidal, 1952
Sulfur Turbidimetric method and Colorimeter Chesnin and Yien, 1950
Methodology for Soil analysis

5. PHYSICAL PROPERTIES OF SOIL OF THE EXPERIMENTAL
FIELD
Depth cm Mineral Content % Textural
Class
Bulk
Density
FC
(Vol. %)
PWP
(Vol. %)
Hyd.
Cond.
cm/h
Clay Silt Sand
0-15
16 12 72
Sandy
loam
1.57 17.91 6.25 1.29
15-30
21 10 69
Sandy
clay loam
1.60 26.86 6.22 1.32
30-45
24 20 56
Sandy
clay loam
1.56 26.33 9.86 0.83
45-60
22 26 52
Sandy
clay loam
1.59 28.33 9.94 1.15
60-90
19 26 55
Sandy
clay loam
1.58 25.77 9.61 1.13
90-120
17 26 57
Sandy
clay loam
1.60 28.09 10.54 1.08

6. 5
10
15
20
25
30
35
40
45
0 2 4 6 8 10 12 14
Pressure, bar
0-15
15-30
30-45
45-60
60-75
75-90
90-120
VMC,%
SOIL MOISTURE CHARACTERISTICS CURVE AT THE
EXPERIMENTAL FIELD

7. GRAPHICAL REPRESENTATIONS OF FERTILIZER APPLICATION
STRATEGIES
F1 (fertigation in first half of the irrigation)
F2 (fertigation through out the irrigation)
F3 (fertigation in second half of irrigation)
F4 (fertigation in middle half of the irrigation)

8. Description of HYDRUS-2D
HYDRUS-2D is a finite element model, which solves the
Richard’s equations for variably saturated water flow and
convection-dispersion type equation for heat and solute
transport
HYDRUS-2D was selected because it can simulate the effect of
the following:
• Soil hydraulic properties on water and nutrient movement
• Discharge rate on the water and nutrient distribution
• Time dependent flux boundary on water and nutrient
distribution Timing of water and nutrient application on the
resultant distribution of water and nutrient distribution
within the root zone

9. Model parameters Name of the parameters Value/type/unit
Main Processes Simulation processes Water Flow
Solute Transport
Root Water Uptake
Geometry Information Length units cm
Type of flow Axisymmetrical vertical
flow
Geometry Type Rectangular
Soil profile Number of materials 4
Number of layers 4
Time information Time units hour
Time Discretization
Initial Time
Final Time
Initial time step
Minimum Time Step
Maximum time step
0
3360
0.024
0.00278
4
Input parameters

10. Soil hydraulic model Hydraulic model
Hysteresis
Van Genuchten-Mualem
No hysteresis
Water flow parameters Table 3.9
Solute transport Time weighing scheme Crank-Nicholson scheme
Space weighing scheme Galerkin finite elements
Mass units mg
Number of solutes 3
Solute transport
parameters
Soil specific parameters
Bulk density, kg/m3
Longitudinal dispersivity
Transverse dispersivity
1.55
30
3
Solute specific parameters -
Adsorption isotherm coefficient for nutrients Unit: M-1L3
Reaction parameters for
solute
cRoot= 1, all others were kept zero
Root water uptake model Water uptake reduction model
Solute stress model
Feddes
No solute stress
Root water uptake
parameters
Feddes’ parameters Table 3.7

11. Model Validation
• To check the performance of model, generally performance
indicators namely, correlation coefficient (R2), Root mean
square error and mean absolute error and Nash efficiency
is determined
• Sensitivity analysis

12. Nash–Sutcliffe model efficiency coefficient (Ef) is used to
assess the predictive power of hydrological models. It is
defined as:
where and Yi predicted and measured values of the criterion
dependent variable Y, respectively; mean of the measured
values of Y; and n sample size.

13. WATER DISTRIBUTION UNDER DRIP IRRIGATION
Average distribution pattern under drip irrigated treatments
2 days irrigation interval:
24 hrs after irrigation
4 Days Irrigation interval:
24 hrs after irrigation
0
15
30
45
60
0.20 0.22 0.24 0.26 0.28 0.30
Depth,cm
Water content, cm3 cm-3
0
15
22.5
0
15
30
45
60
0.20 0.22 0.24 0.26 0.28 0.30
Depth,cm
Water content, cm3 cm-3
0
15
22.5

14. Spatio-Temporal variations in water content at various
depths and away from emitter
2 Days irrigation interval
15.00
18.00
21.00
24.00
27.00
30.00
0 8 16 24 32 40 48 56 64 72
Watercontent,%
Time, h
0 cm 15 30
45 60
15.00
18.00
21.00
24.00
27.00
30.00
0 8 16 24 32 40 48 56 64 72
Watercontent,%
Time, h
15 cm 15 30
45 60
15.00
18.00
21.00
24.00
27.00
30.00
0 8 16 24 32 40 48 56 64 72
Watercontent,%
Time, h
22.5 cm 15 30
45 60

15. 4 Days irrigation interval
15.00
18.00
21.00
24.00
27.00
30.00
0 24 48 72 96 120
Watercontent,%
Time, h
0 cm 15 30
45 60
15.00
18.00
21.00
24.00
27.00
30.00
0 24 48 72 96 120
Watercontent,%
Time, h
15 cm 15 30
45 60
15.00
18.00
21.00
24.00
27.00
30.00
0 24 48 72 96 120
Watercontent,%
Time, h
22.5 cm 15 30
45 60

16. NUTRIENT DISTRIBUTION UNDER DRIP FERTIGATION
Spatial distribution of nutrient under 2 days and 4 days irrigation interval
second half fertigation
2 days irrigation interval
0
15
30
45
60
0.0200 0.0220 0.0240 0.0260 0.0280 0.0300
Depth,cm
Nutrient concentration, mg/ml
0
15
22.5
4 days irrigation interval
0
15
30
45
60
0.020 0.022 0.024 0.026 0.028 0.030
Depth,cm
Nutrient concentration, mg/ml
0
15
22.5

17. Temporal distribution of nutrient under 2 day’s irrigation interval
and 2nd half fertigation (Best fertigation)
0.010
0.014
0.018
0.022
0.026
0.030
0 8 16 24 32 40 48 56 64 72
Nutrientconcentration,mg/ml
Time, h
0 cm
15 30
45 60
0.010
0.014
0.018
0.022
0.026
0.030
0 8 16 24 32 40 48 56 64 72
Nutrientconcentration,mg/ml
Time, h
15 cm
15 30
45 60
0.010
0.014
0.018
0.022
0.026
0.030
0 8 16 24 32 40 48 56 64 72
Nutrientconcentration,mg/ml
Time, h
22.5 cm 15 30
45 60

18. No Flux
Dripper
position
Solute Transport Boundary conditionWater Flow Boundary conditions
No Flux
Free drainage
Variable
flux
Atmospheric
flux
60 cm
25 cm 5 cm

19. 0.1500.1600.1510.1520.1530.1540.1550.1560.1570.1580.159
Initial conditions: water content
0.01.00.20.40.60.8
Root Distribution

20. 0.008 0.0200.010 0.012 0.014 0.016 0.018
Initial concentration of nutrient in soil

21. 2 day irrigation interval 4 day irrigation interval
Moisture content, one month after transplanting

22. 2 day irrigation interval 4 day irrigation interval
Nutrient distribution two months after fertigation
(Best Fertigation strategy)

23. Various applications of Hydrus
• Depth and placement of laterals
• Spacing between two emitters and lateral
• Application of irrigation and fertigation
• Groundwater recharge estimation
• Plant water uptake
• Many more

24. Thank you.....