HYDRUS_1D Sensitivity Analysis

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HYDRUS_1D Sensitivity Analysis

• Limin Yang
• Department of Biological Engineering Sciences
• Washington State University

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INTRODUCTION

• 1. To find the parameters of greatest importance
  in water flow simulation in vadose zone.
• 2. To allow users to budget resources so that the
  most important parameters can be determined with
  the greatest accuracy.

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HYDRUS-1D

• HYDRUS-1D is a commercial software package based
  on finite element model, for simulating the
  one-dimensional movement of water and solute in
  variably saturated media. This program was
  developed by U.S. Salinity Laboratory, U.S.
  Department of Agriculture, Agriculture Research
  Service (Simunek and van Genuchten, 1998).

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Governing Equations
(2)
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INTEC SITE
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Soil distributions at INTEC
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Soil Properties

• There are two major types of soil, sediment and
  basalt, at INTEC. The average surficial alluvium
  samples saturated hydraulic conductivity Ks is
  4.1x10-2 cm/sec. The average interbeds Ks is
  1.221x10-4 cm/sec. a is between 0.0001 and
  1.9868. n is between 1.1024 and 4.2289. ?r is
  between 0 and 0.0764. ?s is between 0.2247 and
  0.6049.

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Methods

• The sensitivity of model results to any given
  parameter can be described by the partial
  derivative of an output variable with respect to
  that parameter.
• 2. The change in cumulative bottom flux was
  calculated as

Where, ?R is percent change in the result value
of the testing function
Rt is result value for using the test parameter
value Rb is result value for using the base
parameter value
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Basic settings

• Only consider water flow
• Only one type soil will be considered with a
  depth of 500 cm, and there is no incline from
  vertical axis
• Totally 512 min with each time step 1e-5, and the
  maximum time step is 25 min
• The maximum number of iteration is 50, with all
  other iteration criteria default

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Basic settings (contd)

• Hydraulic model is van Genuchten without
  air-entry value and no hysteresis
• Soil properties based on sand
• Upper boundary condition is constant pressure
  head Lower boundary condition is free drainage
  Initial condition is in the pressure head (10 cm
  water head on the top, -100 cm water head for
  other part of soil).

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Table 1. Outline
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NUMERICAL RESULTS

• a
• This experimental parameter was introduced for
  expressing the relationship of soil water content
  and the pressure head. It will influence the
  shape of the retention curve. In most case, since
  a is a small number and with a power of n, which
  is bigger than 1, it should not be a sensitive
  factor. Experiments results proved this true as
  shown in Table 2. The cumulative bottom flux
  changes less than 3 while a changes 25.

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Table 2. Results
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• Residual water content ?r
• It is not strange that ?r has only very limited
  influence on the cumulative bottom flux, since ?r
  is too small comparing to ?s. The cumulative
  bottom flux changes less than 3.5 while ?r
  changes 25.
• Saturated water content ?s
• ?s determines ?e, the effective water content,
  which is a critical factor for solving governing
  equation. It is sensitive parameter to the bottom
  flux causing about 60 change in flux while
  itself changes only 25. Notably, there is a
  negative linear relationship between ?s and the
  bottom flux. This can also be explained because
  that it occurs in the formula of ?e as a
  denominator.

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• n
• Empirical parameter n occurs in formula (2, 3) as
  a power of h. It is also less sensitive to the
  flux although its influence to the bottom flux is
  bigger than those of a and ?r. It causes at most
  12 changes in flux while itself changes 25.
• Saturated hydraulic conductivity Ks
• Ks is of most sensitivity in all the parameters,
  as a key factor of equation (1). It also has a
  linear relationship with the cumulative bottom
  flux with a slope of about 3.2, which means that
  one unit change in Ks will cause 3.2 unit changes
  in flux.
• l 
• Empirical factor l is almost fixed as 0.5
  according Simunek, J., M. Sejna, and M. Th. van
  Genuchten. (1998). In this study, it is the least
  important factor to the flux.

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Discussion and conclusions

• Hysteresis is an important phenomenon in soil
  physics and will have influence on the ground
  water flow. But comparisons of the runs of
  HYDRUS_1D indicate it has no significant effect
  on the cumulative flow flux (in most cases no
  effect).
•  
• From the results, Ks and ?s are very sensitive
  parameters to the vadose zone flow. In reality,
  Ks and ?s are localized and cannot easily get
  with respect to the limitations of field methods.
  These will greatly hamper the solution of vadose
  zone flow and in turn influence of solute
  transport.

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Thank You
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References

• Simunek, J., M. Sejna, and M. Th. van Genuchten.
  1998. The HYDRUS_1D Software Package for
  Simulating the One-Dimensional Movement of Water,
  Heat, and Multiple Solutes in Variably-Saturated
  Media. Version 2.0. US Salinity Laboratory,
  ARS/USDA. Riverside, California.
•  
• Hull, L.C. et al, 1999, Draft Work Plan for the
  Waste Area Group 3, Operable Unit 3-14, Tank Farm
  Soil and Groundwater, Remedial Investigation/Feasi
  bility Study. INEEL.
•  
• Hull, L.C. et al, 2002, Phase I Monitoring Well
  and Tracer Study Reportfor Operable Unit 3-13,
  Group 4, Perched Water. DOE.
•  
• Jacomino, V.M.F., Fields, D.E. A critical
  approach to the calibration of a watershed
  model. 1997. American Water Resources
  Association. 33 (1), 143-154
•  
• van Genuchten, M. Th. 1980. A Closed-Form
  Equation for Predicting the Hydraulic
  Conductivity of Unsaturated Soils. Soil Science
  Society American Journal. Vol. 44, pp 892-898.