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
 (h, t )  
 h 
  K (h)  1  S
t
z 
 z 
(1)
 (h)   r
e 
 (1  | h | n ) m
 s r
(2)
1
K ( )  K s e [1  (1   e m ) m ]2
l
(3)
INTEC SITE
Research Site at INEEL
IDAHO
INEEL
#
#
A RC O
#
ID A H O
F A LLS
Lo
s
tR
ive
r
BOISE
B ig
INEEL
N
W
INTEC
E
S
/(20
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
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:
R R

R 
R
t
b
b
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.
Outline
Qr
Qs
a
n
0.045
0.0338
0.0563
0.43
0.145 2.68
Ks
I
0.495
0.323
0.538
0.366
0.495
0.10875
0.18125
2.01
3.35
0.37125
0.61875
0.42075
0.56925
Changes
0.5 BaseLine
QrQr+
QsQs+
Qs-0.85
Qs+1.15
aa+
nn+
KsKs+
KsKs+
0.375 l0.625 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. Results
Sensitive Changes CVBot(cm)Min Change% Time(min) cvBotMax
sand BaseLine
-79.7
0
512
0.639
Qr-74.6
-6.399
512
0.66
Qr+
-84.8 6.398996
512
0.62
X
Qs-128 60.60226
512
0.46
X
Qs+
-31.2 -60.8532
512
0.81
X
Qs-0.85
-109 36.76286
512
0.531
X
Qs+1.15
-50.6 -36.5119
512
0.746
a-81.8 2.634881
512
0.627
a+
-78.5 -1.50565
512
0.643
n-88.9 11.54329
512
0.681
n+
-78.6 -1.38018
512
0.586
X
Ks-16.3 -79.5483
512
0.638
X
Ks+
-143 79.42284
512
0.639
X
Ks-41.7 -47.6788
512
0.639
X
Ks+
-118 48.05521
512
0.642
l-79.7
0
512
0.635
l+
-79.7
0
512
0.651
Change% Time(min) Change%
0 348.738
0
3.286385 358.817 2.890135
-2.9734
338.57 -2.91566
-28.0125 251.431 -27.9026
26.76056 445.834 27.8421
-16.9014 290.176 -16.7925
16.74491 407.193 16.76187
-1.87793 344.424 -1.23703
0.625978 351.328 0.742678
6.57277 330.533 -5.22025
-8.29421 350.601 0.534212
-0.15649 464.774 33.27312
0 279.032 -19.9881
0 410.261 17.64161
0.469484 303.147 -13.0731
-0.62598 348.548 -0.05448
1.877934 348.778 0.01147
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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)
Change in CVBot Flux (%)
80
y = 3.1825x + 0.0627
60
2
R =1
40
20
0
-30
-20
-10
-20
0
10
20
-40
-60
y = -2.4327x - 2E-15
2
R =1
-80
Change in θs (%)
θs
Ks
Linear (Ks)
Linear (θs)
30
Sensitivity in Flux (maximum)
Change in CVBot Flux (%)
30
y = 1.1024x - 0.3521
R2 = 0.9997
20
10
0
-30
-20
-10
-10
0
10
-20
-30
-40
Change in θs (%)
θs
Linear (θs)
20
30
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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 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
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 314, 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.