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 d0eÂtude 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).
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 velocityVand 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 NO3ÿtransport 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
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 Brÿconcentration 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 one-dimensional 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
@t ÿV
@C
@z (1)
whereCis the solution concentration,tis time,zis distance, andVis the solute transport velocity. The boundary and initial conditions for the experiment are:
C z;0 C1 0<z<L
C2; L<z C 0;t C2 t>0
(2)
whereC1andC2are the initial concentrations andLis the depth of the high concentration
water. If the random solute transport velocity is expressed as a lognormal distribution, the probability density function ofVis:
P V 1
wheremandsare 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 C2ÿC1 F1ÿF2 (4)
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 :
The boundary and initial conditions for the experiment are:
C z;0 C1 0<z<L
whereC0is the concentration of irrigation water.
The solution of Model B was given by Van Genuchten and Alves, 1982 as
The mean and variance of the concentration are evaluated by :
A numerical method was used for the integration (Bresler and Dagan, 1983), in which the velocity was divided into n-segments (Viÿ1,Vi) (i1,2,. . ., n) based on the following was taken as a representation of the velocity. By substitutingV iÿ1=2 into model B we
have:
Numerical results calculated withn50, 100, and 200 for the solute velocity probability densityP(V)showed that the accuracy requirement could be met with n50.
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):
AREXPiÿMi
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 fort7 and 35 days, respectively. Distributions of water content were quite similar from 7 to 35 days. To
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 observedVvalues 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 t35 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 NO3ÿcannot be
attributed to deep leaching below the depth of sampling, because NO3ÿdistribution 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 NO3ÿleached. For example, the topsoil of the
denitrification and mineralization. These effects, however, were not investigated in the present study.
To evaluate deep NO3ÿtransport in our study, we compared the mass of Brÿand NO3ÿ
that leached below 90 cm. The fraction of NO3ÿmass that leached below 90 cm was
always greater than the mass of Brÿ. This suggests that the transport processes of Brÿand NO3ÿare different. NO3ÿin 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.
Fig. 2. NO3ÿconcentration pro®le att35 days. (a): the 95% con®dence interval and the average concentration.
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 cmÿ3cmÿ3, 0.06 cmÿ3cmÿ3, and 13.6%, respectively, for the Brÿ predictions (Table 1); while those for the NO3ÿ predictions were 16.6%,
15.5 cmÿ3cmÿ3, 11.2 cmÿ3cmÿ3, 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 cmÿ3cmÿ3, 0.02 cmÿ3cmÿ3, and 6.3%, respectively (Table 1); and 13.0%, 10.0 cmÿ3cmÿ3, 7.8 cmÿ3cmÿ3, and 9.5%, respectively for the NO3ÿpredictions (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, 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 Brÿand NO
3ÿ
Day ARE(%) ME (cmÿ3cmÿ3) SEE (cmÿ3cmÿ3) CV (%)
Model A Model B Model A Model B Model A Model B Model A Model B
(a) Brÿconcentration
ÿ6.90 ÿ3.20 ÿ0.10 ÿ0.02 0.05 0.02 11.40 3.70 14 ÿ7.70 ÿ3.30 ÿ0.08 ÿ0.03 0.05 0.02 13.60 5.30 21 ÿ7.70 1.80 ±0.09 0.02 0.04 0.01 9.30 2.30 28 ÿ8.70 2.00 ±0.04 0.01 0.05 0.02 11.90 4.00 35 ÿ9.30 3.10 ±0.15 ÿ0.02 0.06 0.02 12.90 6.30 (b) NO3ÿconcentration
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%.
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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