HYDRUS_1D Sensitivity Analysis

Limin Yang

Department of Biological Engineering Sciences

Washington State University

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.

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).

Governing Equations

)1(1)(),(

Sz

hhK

zt

th

(2)

mn

rs

re h

h

)||1()(

)3(])1(1[)( 21 mme

ls eKK

INTEC SITE

# # #IDAHO FALLS

ARCOBOISE

IDAHO

INEEL

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EW

S

Research Site at INEEL

Big

Los

t Riv

er

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Soil distributions at INTEC

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. α is between 0.0001 and 1.9868. n is between 1.1024 and 4.2289. θr is between 0 and 0.0764. θs is between 0.2247 and 0.6049.

Methods

b

bt

R

RRR

1. 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, ΔR 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

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;

Basic settings (cont’d)

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).

Table 1. OutlineQr Qs a n Ks I Changes

0.045 0.43 0.145 2.68 0.495 0.5 BaseLine0.0338 Qr-0.0563 Qr+

0.323 Qs-0.538 Qs+0.366 Qs-0.850.495 Qs+1.15

0.10875 a-0.18125 a+

2.01 n-3.35 n+

0.37125 Ks-0.61875 Ks+0.42075 Ks-0.56925 Ks+

0.375 l-0.625 l+

NUMERICAL RESULTS α

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 α 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 α changes 25%.

Table 2. ResultsSensitive Changes CVBot(cm)Min Change% Time(min)cvBotMax Change% Time(min) Change%

sand BaseLine -79.7 0 512 0.639 0 348.738 0Qr- -74.6 -6.399 512 0.66 3.286385 358.817 2.890135Qr+ -84.8 6.398996 512 0.62 -2.9734 338.57 -2.91566

X Qs- -128 60.60226 512 0.46 -28.0125 251.431 -27.9026X Qs+ -31.2 -60.8532 512 0.81 26.76056 445.834 27.8421X Qs-0.85 -109 36.76286 512 0.531 -16.9014 290.176 -16.7925X Qs+1.15 -50.6 -36.5119 512 0.746 16.74491 407.193 16.76187

a- -81.8 2.634881 512 0.627 -1.87793 344.424 -1.23703a+ -78.5 -1.50565 512 0.643 0.625978 351.328 0.742678n- -88.9 11.54329 512 0.681 6.57277 330.533 -5.22025n+ -78.6 -1.38018 512 0.586 -8.29421 350.601 0.534212

X Ks- -16.3 -79.5483 512 0.638 -0.15649 464.774 33.27312X Ks+ -143 79.42284 512 0.639 0 279.032 -19.9881X Ks- -41.7 -47.6788 512 0.639 0 410.261 17.64161X Ks+ -118 48.05521 512 0.642 0.469484 303.147 -13.0731

l- -79.7 0 512 0.635 -0.62598 348.548 -0.05448l+ -79.7 0 512 0.651 1.877934 348.778 0.01147

Residual water content θr

It is not strange that θr has only very limited influence on the cumulative bottom flux, since θr is too small comparing to θs. The cumulative bottom flux changes less than 3.5% while θr changes 25%.

Saturated water content θs θs determines θe, 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 θs and the bottom flux. This can also be explained because that it occurs in the formula of θe as a denominator.

Sensitivity in flux (minimum)

y = 3.1825x + 0.0627

R2 = 1

y = -2.4327x - 2E-15

R2 = 1-80

-60

-40

-20

0

20

40

60

80

-30 -20 -10 0 10 20 30

Change in θs (%)

Ch

an

ge

in

CV

Bo

t F

lux

(%

)

θs Ks Linear (Ks) Linear (θs)

Sensitivity in Flux (maximum)

y = 1.1024x - 0.3521

R2 = 0.9997

-40

-30

-20

-10

0

10

20

30

-30 -20 -10 0 10 20 30

Change in θs (%)

Ch

an

ge

in

CV

Bo

t F

lux

(%

)

θs Linear (θs)

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 α and θr. 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.

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 θs are very sensitive

parameters to the vadose zone flow. In reality, Ks and θs 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.

Thank You

ReferencesSimunek, 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/Feasibility Study. INEEL.

  Hull, L.C. et al, 2002, Phase I Monitoring Well and Tracer Study Report

for 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.