Directory UMM :Data Elmu:jurnal:A:Agricultural Water Management:Vol46. Issue1.Nov2000:

Agricultural Water Management 46 (2000) 43±53

Solute transport in cinnamon soil: measurement
and simulation using stochastic models
Jianbo Cui*, Jiping Zhuang
Institute of Applied Ecology, Chinese Academy of Sciences, Shenyang, 110015, PR China
Accepted 3 December 1999

Abstract
Solute concentration and water content pro®les were measured from an area of 3 m6 m to a
depth of 1.8 m in cinnamon soil. Spatial variability of soil water content and concentration were
simulated using a stochastic model. The results showed that the effect of soil variability on soil
water distributions was relatively small, but the concentration distribution exhibited a profound
variability in the ®eld, especially within the zones with peak values in the vertical pro®les. The
stochastic convection model and the stochastic convection-dispersion model were used to study
mean concentration and concentration variance. Comparison of the simulation results with the ®eld
experimental data showed that the stochastic convection±dispersion model, with lower error
statistics values (ARE, ME, SEE, and CV), described the mean concentration reasonably well. It
also appeared that due to deep leaching, less nutrients will be available for crops in the case of ¯ood
irrigation. # 2000 Elsevier Science B.V. All rights reserved.
Keywords: Solute transport; Field experiment; Stochastic model

1. Introduction
Agricultural systems in semi-arid regions are becoming increasingly dependent on
irrigation and fertilizers. For sustainable agricultural production in these systems we need
to understand the role of irrigation in the transport of soluble chemicals in soil. Increased
public awareness and concern has led to an expanded regulatory effort aimed at providing
accurate assessments of the environmental fate of soluble chemicals (e.g. NO3ÿ) under a

*
Corresponding author. Present address: Laboratoire d0 eÂtude des Transferts en Hydrologie et Environement
Bp 53, 38041, Grenoble, France. Tel.: ‡33-476-825-284; fax: ‡33-476-825-286.
E-mail address: cui@hmg.inpg.fr (J. Cui).

0378-3774/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 3 7 7 4 ( 0 0 ) 0 0 0 7 5 - 5

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J. Cui, J. Zhuang / Agricultural Water Management 46 (2000) 43±53

wide variety of water management and climatic conditions. To this end, numerous
environmental fate and transport models have been developed.
The main feature of field soils is their high spatial heterogeneity and variability, which
affect physical and chemical processes in the soil. Characterization of solute transport in
the natural environment has proven to be a difficult task because of temporal and spatial
variability of soil transport properties. Field experiments are costly because of spatial
heterogeneity. Stochastic models assume that soil properties vary spatially, and as a
consequence solute and water movement vary. These models have evolved with the
recognition of the problems caused by variability for deterministic models. Field studies
and numerical simulations of solute transport through heterogeneous porous media
suggest that stochastic models may be able to simulate solute transport in the field
situation (Russo, 1991, 1993; Yang et al., 1993). Many papers of this type have appeared
in the literature over the past several years, both in terms of mathematical analyses and
the application of stochastic and deterministic models to field data (e.g. Toride and Leij,
1996; Vanderborght et al., 1997; Butters and Jury, 1989; Heuvelman and McInnis, 1999,
etc).
Because of the soil heterogeneity, the distribution of soil water velocity in the field is
chaotic. Biggar and Nielsen (1976) monitored solute movement in an agricultural field
and reported that the apparent velocity of the solute peak was distributed log-normally.
Van de Pol et al. (1977) conducted a field experiment of water and solute transport under

unsaturated steady-state conditions. It was found that the pore scale velocity V and the
apparent dispersion coefficient had lognormal distributions, and the mean value, standard
deviation, and coefficient of variation of ln(V) were 1.203, 0.504 and 43%, respectively. It
is widely recognized that solute distribution in the field is determined by the random
distribution of soil water velocity.
The objectives of this study were to: (1) conduct field experiments to compare the Brÿ
and NO3ÿ transport in cinnamon soil; (2) analyze soil spatial variability and its effects on
soil water movement and solute transport; and (3) perform model discrimination to
examine the transport process operative within a field plot. This study will contribute to
our understanding of agricultural water management in semi-arid regions.

2. Materials and methods
2.1. Field experiment
In this study, we analyse the experimental data on transport of two inorganic tracers.
The experimental site was located in Kazhuo Agricultural Experiment station in West
Liaoning, China. The experiments lasted 35 days and were conducted on Cinnamon soil
plots (the texture is loam) that have not been tilled for at least 3 years to allow macropore
development. Saturated hydraulic conductivity was measured to a depth of 90 cm using a
double ring method at several locations around the experimental site; the measured values
ranged from 1.1 to 1.44 m per day. A 1.8 m deep trench was dug around a 3 m6 m

experimental plot. After lining the inside wall of the trench with plastic sheets, the trench
was firmly refilled with soil to prevent side seepage. Outside the trench there was a

J. Cui, J. Zhuang / Agricultural Water Management 46 (2000) 43±53

45

protective area with a width of 1.5 m. The experimental plot was divided into eight
1.5 m1.5 m subplots. A border was located between subplots in order to maintain
relatively uniform infiltration. Each subplot was further split into six equal blocks, and
soil samples were taken in the blocks. Prior to solute applications, soil cores were taken
adjacent to the plot for determining background solute concentrations.
After pretreating the experimental site by spraying it with two inorganic tracers, NO3ÿ,
[Ca(NO3)2], and Brÿ [KBr] were applied consecutively by sprayer. Applied solute
concentrations 276.5 gmÿ2 NO3ÿ, and 314.2 gmÿ2 Brÿ were at least three orders of
magnitude higher than the measured background concentrations. The site was left open to
evaporation for 2 days. Before starting the leaching experiment, initial water content and
soil water concentration profiles were measured. Groundwater was used as irrigation
water and sprayed on the experiment plot to maintain an average daily leaching rate of
0.4 cm per day. To prevent evaporation from the soil surface, the experimental area was

covered after spraying. Soil core samples were collected at time intervals of 7 days
starting of the time of application of the tracers. At each sampling site, six different points
were sampled. The vertical sampling locations were at depths of 20, 40, 60, 80, 100, 120,
140, 160, and 180 cm. All core samples were sealed in plastic bags and stored at 48C until
sectioning and extraction. To minimize soil disturbance and compaction at all times, all
holes were backfilled immediately following sampling.
Soil solution was esctracted using a 1:5 soil±water mixture and Brÿ concentration was
determined by colorimetric methods. Nitrate was determined using a colorimetric
procedure on both automated segmented and continuous-flow analysis instruments. The
neutron probe access tube and tensiometer method determined soil volumetric water
content.
2.2. Model description
Two models were used to calculate the solute concentration profile in our study. It is
assumed that solute velocity is homogeneous in the vertical direction and randomly
distributed in the horizontal direction. Therefore, solute transport may be considered onedimensional vertical movement in soil columns with horizontal randomly distributed
solute velocities if the lateral solute transport between the soil columns is neglected. By
neglecting the pore scale dispersion, solute transport in a homogeneous profile can be
expressed as follows (Model A):
@C
@C

ˆ ÿV
@t
@z

(1)

where C is the solution concentration, t is time, z is distance, and V is the solute transport
velocity. The boundary and initial conditions for the experiment are:
C…z; 0† ˆ C1 0 < z < L
ˆ C2; L < z
C…0; t† ˆ C2 t > 0

(2)

where C1 and C2 are the initial concentrations and L is the depth of the high concentration
region near the soil surface. Note C2 is the same as the concentration in the irrigation

46

J. Cui, J. Zhuang / Agricultural Water Management 46 (2000) 43±53

water. If the random solute transport velocity is expressed as a lognormal distribution, the
probability density function of V is:
"
#
1
ÿ…ln…V† ÿ m†2
(3)
P…V† ˆ p exp
2s2
2psV

where m and s are the mean and standard deviation of ln(V), respectively. Because only
convection is considered, the concentration front should move downward as piston ¯ow.
The mean concentration and concentration variance are determined as:
C ˆ …C2 ÿ C1 †…F1 ÿ F2 †

(4)

s2c ˆ …C2 ÿ C1 †2 …F1 ÿ F2 †…1 ÿ F1 ‡ F2 †





ln…z=t† ÿ m
ln……z ÿ L†=t† ÿ m
; F2 ˆ F
;
F1 ˆ F
s
s
 2
Z 1
1
ÿZ
p exp
dZ
F…z† ˆ
2
2p

z

Model B used in our study is the stochastic convection-dispersion model. When we
consider pore scale dispersion, the one dimensional convection-dispersion equation is
written as :
@C
@2C
@C
ˆD 2 ÿV
@t
@z
@z
The boundary and initial conditions for the experiment are:

C1 0 < z < L
C…z; 0† ˆ
C2 L < z
8
< C0 0 < t < t0
@C

C…0; t† ˆ
ˆ0
: 0 t0 < t
@z z!1

(5)

(6)

where C0 is the concentration of irrigation water.
The solution of Model B was given by Van Genuchten and Alves, 1982 as

C2 ‡ …C1 ÿ C2 †A…z; t† ‡ …C0 ÿ C1 †B…z; t†; 0  t  t0
C…z; t; V† ˆ
C2 ‡ …C1 ÿ C2 †A…z; t† ‡ …C0 ÿ C1 †B…z; t† ÿ C0 B…z; t ÿ t0 †; t0  t

(7)

where





 
1
z ÿ L ÿ Vt
1
Vz
z ‡ L ‡ Vt
p
p
‡ exp
;
erfc
A…z; t† ˆ erfc
2
2
D
2 Dt
2 Dt


 


1
z ÿ Vt
1
Vz
z ‡ Vt
erfc p
B…z; t† ˆ erfc p ‡ exp
2
2
D
2 Dt
2 Dt

J. Cui, J. Zhuang / Agricultural Water Management 46 (2000) 43±53

The mean and variance of the concentration are evaluated by :
Z 1
Z 1

2
C…z; t; V† ÿ C…z; t† P…V† dv
C…z; t; V†P…V† dV; s2c ˆ
C…z; t† ˆ
0

47

(8)

0

A numerical method was used for the integration (Bresler and Dagan, 1983), in which the
velocity was divided into n-segments (Viÿ1 , Vi) (iˆ1,2,. . ., n) based on the following
condition:
Z vi
1
(9)
P…V† dv ˆ ; i ˆ 1; 2; . . . n
n
viÿ1
where V0ˆ0, Vn!1. The middle point V…iÿ1†=2 ˆ(Viÿ1 ‡Vi)/2 in each segment (Viÿ1 , Vi)
was taken as a representation of the velocity. By substituting V…iÿ1†=2 into model B we
have:
n
ÿ


1X
C z; t; V…iÿ1†=2 ;
n iˆ1
n  ÿ


2
1X
C z; t; V…iÿ1†=2 ÿ C…z; t†
s2c …z; t† ˆ
n iˆ1

C…z; t† ˆ

(10)

Numerical results calculated with nˆ50, 100, and 200 for the solute velocity probability
density P(V) showed that the accuracy requirement could be met with nˆ50.
2.3. Error analysis of model predictions
The ability of models to predict measured water and solute concentration profiles in
our study was characterized using (Ambrose and Roesch, 1982):
X Pi ÿ M i
ARE ˆ
nM
ME ˆ max…Pi ÿ Mi †
"
#0:5
X
2
…Pi ÿ Mi †
SEE ˆ
nÿ1

CV ˆ

SEE
M

where, for our application, ARE is average relative error between the measured and
predicted water and solute concentration pro®les, ME is the maximum error between
measurement and prediction within a pro®le, SEE is the standard error of estimate and
CV is the coef®cient of variation. The magnitudes of the ARE and ME parameters
indicate the average extent (ARE) and maximum extent (ME) to which the model
predictions deviate from the measurements; and their sign indicates whether the model
tends to overestimate the measured values (positive ARE and ME), or underestimate the
measured values (negative ARE and ME). The SEE and CV quantify the amount of
`random scatter' of the predicted and measured values about the 1:1 line (Gold, 1977).

48

J. Cui, J. Zhuang / Agricultural Water Management 46 (2000) 43±53

3. Results and discussion
3.1. Distributions of water content
The soil profile volumetric water content measured with the neutron probe at 7 and 35
days is showed in Fig. 1. The neutron probe measurements showed that the decreasing
flux did not significantly decrease the average volumetric water content during the study.
The hydraulic head measurements also did not reflect significant changes. The volumetric
water content profiles at the six subplots are presented in Fig. 1a and b for tˆ7 and 35
days, respectively. Distributions of water content were quite similar from 7 to 35 days. To

Fig. 1. The volumetric water content pro®les (the 95% con®dence interval and the mean) at the six subplots. a:
for tˆ7, and b: for tˆ35 days, respectively.

J. Cui, J. Zhuang / Agricultural Water Management 46 (2000) 43±53

49

quantify the variability of the volumetric water content y, its mean and coefficient of
variation were calculated at different depths and sampling times. Most CV values are less
than 10%. The average CV of all measurements was 5.6%. Therefore, water movement in
the vertical direction could be approximated as a steady-state flow.
The infiltration variability measured at the end of the leaching experiment was used to
characterize the variability throughout the leaching experiment even though the
infiltration distribution may have changed during this period (especially between the
first and second irrigation). For this field the change in infiltration distribution was
probably minimal, however, since there was no crop and the precipitation events were
light and infrequent with little effect on the soil surface. In the experiment, the infiltration
rate was controlled accurately and its relative error was less than 5%. The coefficient of
variation is larger in the shallow soil than in the deep soil because of the heterogeneity,
resulting in the three-dimensional movement of water. Basic statistical analyses showed
that the observed V values were better described by a log-normal distribution than by a
normal distribution. The mean value and standard deviation of ln (V ) were 0.94 and 0.16,
respectively, and the coefficient of variation was 17%.
3.2. Distribution of solute concentration
The initial profile of solute concentration was a T-shaped distribution. Under the
effects of solute dispersion and water leaching, the solute at the surface layer moved
downward, and the resulting concentration distributions differed greatly in different
subplots as shown in Fig. 2. Depths of the NO3ÿ concentration fronts for tˆ35 days
ranged from 70 to 120 cm. The 90% confidence interval and the average NO3ÿ
concentration shown in Fig. 2a indicated that the variation of concentration was very
large, especially near the concentration front of the average concentration profile.
Averaged solute concentration distributions, calculated from the six replicates at different
sampling times, represent approximately the average solute transport process at the local
scale.
The CV values of the solute concentration were much larger than those of the water
content, especially within the moving-front zone. The CV values ranged from 5.7 to
49.2% for solute concentration and from 2.0 to 12.0% for water content. The larger CV
concentration values were generally located in the zones with peak values.
An examination of the changes in measured solute concentration with depth in the 6
cores sampled showed two types of solute distribution. In the Type I distribution, there
was a gradual decrease in solute concentration with depth, but in the Type II distribution,
solute concentration decreased sharply below about 10 cm. These changes were not
associated with difference in irrigation intensity, and we assume that they are a result of
differences in soil structure and potential preferential flow.
It should be noted, in these experiments, that the apparent loss of NO3ÿ cannot be
attributed to deep leaching below the depth of sampling, because NO3ÿ distribution was
confined to the top 1.2 m, which is less than the sampling depth. Less than full recovery
can be due to several factors, such as local heterogeneity within the plot. However, other
factors may have influenced the amount of NO3ÿ leached. For example, the topsoil of the
cinnamon soil is rich in organic matter which strongly affects the rate of decomposition,

50

J. Cui, J. Zhuang / Agricultural Water Management 46 (2000) 43±53

Fig. 2. NO3ÿ concentration pro®le at tˆ35 days. (a): the 95% con®dence interval and the average concentration.
(b): concentrations in six different subplots (P1 to P6).

denitrification and mineralization. These effects, however, were not investigated in the
present study.
To evaluate deep NO3ÿ transport in our study, we compared the mass of Brÿ and NO3ÿ
that leached below 90 cm. The fraction of NO3ÿ mass that leached below 90 cm was
always greater than the mass of Brÿ. This suggests that the transport processes of Brÿ and
NO3ÿ are different. NO3ÿ in the topsoil of cinnamon soil was occasionally transported
through the soil without interacting with the soil matrix to any great extent. The more
intensive watering would have favored this process. Therefore, due to deep leaching, less
nutrients will be available for crops in the case of flood irrigation.

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J. Cui, J. Zhuang / Agricultural Water Management 46 (2000) 43±53

Table 1
Average relative error (ARE), maximum error (ME), standard error of estimate (SEE), and coef®cient of
variation (CV) for comparison of measured and predicted concentration pro®les of Brÿ and NO3ÿ
Day

ARE(%)
Model A

Model B

ME (cmÿ3 cmÿ3)

SEE (cmÿ3 cmÿ3)

CV (%)

Model A

Model B

Model A

Model B

Model A

Model B

ÿ0.10
ÿ0.08
±0.09
±0.04
±0.15

ÿ0.02
ÿ0.03
‡0.02
‡0.01
ÿ0.02

0.05
0.05
0.04
0.05
0.06

0.02
0.02
0.01
0.02
0.02

11.40
13.60
9.30
11.90
12.90

3.70
5.30
2.30
4.00
6.30

ÿ11.50
ÿ15.50
ÿ5.50
ÿ3.00
ÿ13.50

ÿ10.00
ÿ5.50
ÿ4.50
ÿ4.50
ÿ9.80

8.30
10.10
5.90
2.70
11.20

5.00
4.00
2.50
2.40
7.80

15.40
20.60
14.30
7.30
19.30

9.50
8.10
6.20
6.30
6.40

ÿ

(a) Br concentration
ÿ6.90
ÿ3.20
14
ÿ7.70
ÿ3.30
21
ÿ7.70
‡1.80
28
ÿ8.70
‡2.00
35
ÿ9.30
‡3.10
(b) NO3ÿ concentration
ÿ15.80
ÿ4.10
14
ÿ16.50
ÿ13.00
21
ÿ13.50
‡1.60
28
ÿ5.90
‡1.70
35
ÿ15.80
ÿ8.90

3.3. Models predictions
Table 1 compares the experimental mean concentration with results calculated by
Models A and B at different times. The maximum ARE, ME, SEE, and CV values using
Model A were only 9.3%, 0.15 cmÿ3 cmÿ3, 0.06 cmÿ3 cmÿ3, and 13.6%, respectively, for
the Brÿ predictions (Table 1); while those for the NO3ÿ predictions were 16.6%,
15.5 cmÿ3 cmÿ3, 11.2 cmÿ3 cmÿ3, and 20.6%, respectively (Table 1). The error statistics
for model B were even lower, with the maximum (absolute value) ARE, ME, SEE, and
CV values being 3.3%, 0.03 cmÿ3 cmÿ3, 0.02 cmÿ3 cmÿ3, and 6.3%, respectively
(Table 1); and 13.0%, 10.0 cmÿ3 cmÿ3, 7.8 cmÿ3 cmÿ3, and 9.5%, respectively for the
NO3ÿ predictions (Table 1). It consequently appears that Model B described the mean
concentration reasonably well.
Compared with the experimental data, the movement of the solute front predicted by
the models was slower (negative ARE and ME). This was because the actual velocity was
greater near the soil surface than in the deep soil Ð due to the better soil structure and
low water content in the shallow soil Ð and was greater than the mean velocity used in
the models. Because the pore scale dispersion was neglected in Model A, the calculated
standard deviation was much larger than the experimental data. The standard deviation
calculated from Model B increased with the decrease of the chosen pore scale
dispersivity. The calculated results from Model B with a pore scale dispersivity of 0.4 cm
matched the experimental data very well. Generally speaking, the differences of the
calculated mean concentration from the two models were not significant. This suggests
that the spread of solute attributable to field heterogeneity may be much larger than the
spread due to pore scale dispersion. Pore scale dispersivity was an important parameter
for the calculation of concentration variance, though it may be neglected for the mean
concentration calculation. These results were consistent with the theoretical analyses,

52

J. Cui, J. Zhuang / Agricultural Water Management 46 (2000) 43±53

which showed that the concentration variance was inversely proportional to the pore scale
dispersivity (Kapoor and Gelhar, 1994).
3.4. Illustration
The solute transport process observed in our simulation is the true field-scale variance.
It is well known that the field is heterogeneous and that this heterogeneity exerts a
profound impact on chemicals transport. The impact of simultaneously occurring,
kinetically controlled processes on solute transport in heterogeneous soil has significant
implications regarding the potential efficacy of in situ remediation technologies. Nitrate
transport is very complex process in which chemical, physical and biological components
interact. It is impossible to ascertain whether the variance would increase further if the
size of the sampling domain were increased.
We also emphasize that, firstly, even under steady-state conditions, the organization of
the pore volume into macropores (large, continuous pores) and the ped matrix (fine
intraped pores) produces highly irregular patterns of water movement. Secondly, soil
water may be divided into two types: mobile water in liquid-filled pores and immobile
water in dead-end and intra-aggregate pores. Only the mobile part of soil water
participates in the convective transport process (Gamerdinger et al., 1990) and there is a
considerable amount of immobile soil water, even in a homogenous soil column (Yang
et al., 1993). Sporadic preferential flow and the distribution of stagnant water make it
difficult to predict solute transport using an averaged water velocity. The solute
concentration profiles in this analysis are the results of the interplay of numerous factors
including irrigation, preferential flow, evaporation, hydrodynamic dispersion, diffusion,
and exclusion of anionic solute from negatively charged minerals. Because of
inconsistencies in the mass balance, it was not possible to say which model was the
better by comparing their predictions with the experimental data. Unlike laboratory
experiments, field experiments give rise to difficulties in isolating the influence of a
particular factor on transport. Therefore, one should be cautious before extrapolating the
results of laboratory experiments into the field.

4. Conclusions
A field experiment was conducted to study water flow and solute transport in
Cinnamon soil. Our results demonstrate that relatively little spatial and temporal variation
of the soil water content profile was observed with respect to time and space. Therefore,
soil water movement was treated as a steady-state flow in the soil profile. The
concentration distributions exhibited a much larger variability, especially within the peak
zones in the vertical profiles. Small-scale heterogeneity in soil hydraulic properties had a
considerable effect on the variation of the concentration, which was as high as 50%,
whereas the average CV for water content was less than 10%.
The stochastic convection model and the stochastic convection-dispersion model with
mean solute transport velocity and effective dispersivity were used to study mean
concentration and concentration variance. Generally speaking, the mean concentration

J. Cui, J. Zhuang / Agricultural Water Management 46 (2000) 43±53

53

calculated from the models was in reasonable agreement with the experimental data. In
the depth distributions of the volume-averaged solute concentration Models A and B
predicted similarly shaped distributions. However, the error statistics for model B were
lower, with the maximum (absolute) value of ARE, ME, SEE, and CV lower than for
model A.

Acknowledgements
The authors thank Prof. LIAN Hongzhi and Dr. WANG Shixin for providing
constructive comments on earlier version of this manuscript.

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