Comparison of Finite Difference Method, Philips Method and GreenAmpt Model in Infiltration Simulatio

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Agron 677 Term Project
Comparison of Finite Difference Method, Philips
Method and Green-Ampt Model in Infiltration
Simulation Zhiming Qi Department of Ag
Engineering
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Outline

• Introduction
• Materials and Methods
• Results and Discussion
• Conclusion
• Suggestion

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Introduction

• Infiltration is a key component to hydrological
  process.
• Mathematical Methods have been developed for
  computing and simulating infiltration
• Green-Ampt Model (1911)
• Philips method for Richards equation
  (1957)
• Finite difference method for Richards
  equation
• Boundary Conditions
• First class boundary constant WC
  upper boundary WC c
• Second class boundary constant
  water influx q c
• 2nd boundary in most
  natural infiltration process
• Third class boundary constant
  change of water influx dq/dt c
• Computer Models have been developed to simulate
  the infiltration procedure.
• DRAINMON (Green-Ampt)
• MIKE-SHE and HYDRUS (Richards,
  Finite difference method)

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Introduction

• Mathematical Methods for infiltration Modeling
• 1. Green-Ampt Model (1911)

Green-Ampt model calculates cumulative
infiltration by assuming water flow into a
vertical soil profile like a piston flow (first
boundary condition)
by Chow et al. (1988)
Parameters required
K
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Introduction

• Mathematical Methods for infiltration Modeling
• 2. Finite difference method for Richards
  equation
• Explicit scheme
• Implicit scheme
• Crank-Nicolson scheme
• (any boundary conditions)

http//hydram.epfl.chf
Parameters required
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Introduction

• Mathematical Methods for infiltration Modeling
• Philips method for Richards equation
  (1957)
• (only for first boundary
  condition)

Parameters required
.
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Materials and Methods
from Haverkamp et al. (1977).

• Soil

• Boundary Condition (2nd)

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Materials and Methods

• Parameters for Green-Ampt Model

K
Parameters required
Initial estimation
0.287-0.10 0.187 cm3/cm3
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Materials and Methods

• Mathematical Method for Green-Ampt Model

Newtons Iteration for the equation after ponding
http//www.krellinst.org/
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Materials and Methods

• Parameters for Implicit Finite Difference
  (Richards)

Parameters required
are known

• Parameters for Philip Method (Richards)

Parameters required
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Materials and Methods

• Evaluation Criteria

Cumulative Infiltration (Mass Balance)
Percentage Error
Model Efficiency
Program running time
Wetting Front
Wetting front plotting
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Results and Discussion

• Implicit Finite Method

PE 0.964 Running Time 8 min
Figure 1. Wetting front by finite difference
method for Richards equation.
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Results and Discussion

• Philips Method

0.287
PE 160 Running Time lt 2 sec.
Figure 2. Wetting front of Philips method using
different WC for the upper boundary condition
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Results and Discussion

• Philips Method

0.287
PE 160 Running Time lt 2 sec.
Figure 2. Wetting front of Philips method using
different WC for the upper boundary condition
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Results and Discussion

• Philips Method

0.287
0.265
PE 14.5 Running Time lt 2 sec.
PE 160 Running Time lt 2 sec.
Figure 2. Wetting front of Philips method using
different WC for the upper boundary condition
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Results and Discussion

• Philips Method

0.287
0.265
PE 14.5 Running Time lt 2 sec.
PE 160 Running Time lt 2 sec.
Figure 2. Wetting front of Philips method using
different WC for the upper boundary condition
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Results and Discussion

• Philips Method

0.287
0.265
0.260
PE 14.5 Running Time lt 2 sec.
PE -0.57 Running Time lt 2 sec.
PE 160 Running Time lt 2 sec.
Figure 2. Wetting front of Philips method using
different WC for the upper boundary condition
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Results and Discussion

• Philip Method Parameters

Figure 3. Parameters of Philip method
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Results and Discussion

• Green-Ampt Method

0.287
0.265
PE 0.20 Running Time lt 2 sec.
PE 0.19 Running Time lt 2 sec.
Figure 4. Wetting front from Green-Ampt model
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Results and Discussion

• Comparison

0.1 Hour
Figure 6. Wetting fronts from finite difference,
Philip methods and Green-Ampt model
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Results and Discussion

• Comparison

0.4 Hour
0.1 Hour
Figure 6. Wetting fronts from finite difference,
Philip methods and Green-Ampt model
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Results and Discussion

• Comparison

0.7 Hour
0.4 Hour
0.1 Hour
Figure 6. Wetting fronts from finite difference,
Philip methods and Green-Ampt model
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Results and Discussion

• Comparison

Table 1. Models strength and drawback
for infiltration
simulation under the 2nd class boundary condition

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Conclusion

• All the models could show high accuracies in
  simulating cumulative infiltration.
• Finite difference method
• best wetting front prediction
• treat the second class boundary best among
  the 3 models
• but sometimes numerically unstable
• Green-Ampt model
• required least parameters and the simplest
  programming
• but the wetting front is not precise
• Philips method
• solve Richards equation much quicker than
  finite difference method
• high numerical stability
• but care should be taken under 2nd boundary
  condition
• programming is much complicated

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Suggestion

• Finite difference method is the best approach for
  cumulative infiltration and wetting front
  prediction
• Philips method is a good alternative for finite
  difference method if there is a problem in
  numerical stability for finite difference method
  or a good computer is not accessible.
• Green-Ampt model is a simple and good method if
  only the cumulative infiltration is concerned.

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