Evaluating Infiltration Mechanisms Using Breakthrough Curve and Mean Residence Time
- First Online:
- Cite this article as:
- Simin, Q., Tao, W., Weimin, B. et al. Water Resour Manage (2013) 27: 4579. doi:10.1007/s11269-013-0427-8
- 266 Views
Determination of infiltration mechanism is crucial for the calculation of infiltration flux in the soil which would influence the water balance computation. Two infiltration experiments with different isotopic compositions of rainfall were conducted to analyze the infiltration type by measuring isotopic concentrations (deuterium and oxygen 18) of collected outflow water samples. Models with three transfer functions were used to simulate the isotopic variation of outflows in a soil column. The model performance was evaluated with the comparison of computed and observed isotopic values of outflow. Breakthrough curve based on the isotopic composition of rainfall, initial soil water and outflow, and mean residence time estimated on the best fitting transfer function model were applied to identify the infiltration type in the soil. The results show that infiltration type determination using the comparison between estimated and observed mean residence time and breakthrough curve are similar. Furthermore, we found that soil structure and isotope measurement error affected the determination of mean residence time. Results from this study may provide a framework for describing the infiltration processes in the soil column.
KeywordsTransfer function modelMean residence timeInfiltration typeBreakthrough curve
Determination of infiltration mechanism is very important to the calculation of infiltration flux which will influence the water balance computation in the soil (Kale and Sahoo 2011; Kargas and Kerkides 2011; Morbidelli et al. 2012; Zhao et al. 2010). Usually, representative elementary volume can be used to average processes at the microscopic pore scale and to derive the continuum description of water. Compared with usual micropore, marcopore flow pathways are of a much larger scale. Dual-flow pathways (e.g., by-pass flow, marcopore flow, preferential flow), arising from structures and discontinuities imbedded within the soil, are the routes of water flow (Black and Kipp 1983). A critical feature of dual-flow pathways is that they allow water to by-pass the matrix of the soil with little or no interaction. Dual-flow pathways can be identified visually by directly applying tracers that mark the flow path (White et al. 1986). The presence of non-piston flow processes can be inferred from breakthrough curve and discrepancy between travel times estimated from transient and steady-state tracer techniques, for instance, stable isotopes of water, deuterium (D) and oxygen-18 (18O).
Mean residence time of water flow is a watershed variable that has proven useful to describe the dynamics of catchment hydrology, such as water storage, flow pathways, sources, and mixing patterns (Burns et al. 1998). Transit time is a fundamental watershed descriptor that integrates flow path heterogeneity, and is directly related to internal processes in catchments (McGuire et al. 2005; McGuire and McDonnell 2006; Huang et al. 2011). For example, longer residence time provides more time for biogeochemical reactions to occur as rainfall inputs are transported through catchments toward the outlet of catchments. Despite the importance of the distribution of residence time, it is difficult to measure at the field scale except for highly instrumented catchments. Consequently, lumped parameter models are used to describe the distribution of residence time (Plummer et al. 2001; McGuire and McDonnell 2006). Most studies of mean residence time have used a convolution integral approach that relates rainfall isotopic input to system transfer function to calculate the isotopic values of the output (Barnes and Bonell 1996; Kirchner et al. 2000). The transfer function can be adjusted to fit computed and observed isotopic compositions of outflows. Common model types used in the estimation of distribution of residence time include: piston flow (Maloszewski and Zuber 1982), exponential flow (Maloszewski and Zuber 1982), exponential-piston flow (Maloszewski and Zuber 1982), Gamma distribution (Kirchner et al. 2000), and two parallel linear reservoirs (Weiler et al. 2003).
Various studies on residence time show that the mean residence time varied between shorter than 1 to 5 years, depending on hydrogeological characteristics of the catchment, available data and the goodness-of-fitting data (Stewart and McDonnell 1991; Vitvar et al. 2002). Studies in Maimai catchment (Weiler et al. 2003) indicate that the two parallel linear reservoirs model is more suitable not only because of the better model performance, but also in terms of capturing the runoff generation processes in the catchment through the performance evaluation of different transfer functions using two model estimation indexes: Nash and Sutcliffe coefficient (Nash and Sutcliffe 1970) and the root mean square error-RMSE (Legates and McCabe 1999).
The objectives of this paper are to use the stable isotopes of waters to: 1) estimate the mean residence time of soil water; 2) analyze the breakthrough curve of stable isotope transport; 3) identify infiltration process by using breakthrough curve and comparison between observed and estimated mean residence time. Two soil column experiments with different isotopic compositions of input water were designed and the isotopic values of simulated rainfall, soil water and outflow were analyzed in this study. Three different models were implemented to calculate the mean residence time by fitting the observed outflow points.
Rainfall and soil properties in infiltration experiments
Number of soil column
Mass of soil particle (g)
Mass of rainfall (g)
Initial soil moisture (%)
Duration of rainfall simulation (h)
Isotopic composition of rainfall (‰)
δD = −50 δ18O = −7.2
δ18O = 0.9
Isotopic composition of initial soil water (‰)
δD = −27 δ18O = −3.5
δD = −27 δ18O = −3.5
2.1 Infiltration Experiment with Rainfall Enriched in the Light Isotope
The soil column for infiltration experiment with rainfall enriched in the light isotope was labeled as soil column No. 1. The experiment was performed from 8:00am May 20 to 8:00am May 24, 2008. The temperature ranged from 21.3 °C to 25.9 °C with the average temperature of about 23.1 °C and the relative humidity varied from 48 % to 79 % with the average relative humidity of about 58 % over the experimental period.
Water with isotopic composition of −50‰ in δD and −7.2‰ in δ18O was used to simulate the artificial rainfall for infiltration (Table 1). To ensure the constant isotopic composition of rainfall, water for rainfall simulation was stored in a container with 65 cm in length and 50 cm in width before the experiment. A polymethgl methacrylate lid was designed with a hole in the center plugged to Mariotte siphon attached to the input of soil column closely to avoid evaporation. The infiltration experiment was started at 8:00 am May 20, with initial rainfall intensity of 80 mm/h and ponded water observed after 20 min. Rainfall intensity was adjusted to maintain 3-cm ponding depth at the soil surface. The rainfall resulted in outflow from the soil column starting at 14.8 h. The rainfall was ended at 19:20 May 22 and soil column began recession which ended at 9:00 May 24. After the experiment, soil samples were collected from 0–14 cm, 28–42 cm to 70–84 cm deep to extract soil water for isotopic analysis. Simultaneously, the time to fill up the 30-ml bottle was recorded to compute the outflow rate.
In the early 6 h, water samples were collected densely, for example, every 30-ml volume of water and in the following period water samples were collected with equal time interval, like 1 h, 2 h or 4 h in 30-ml plastic bottles that were subsequently sealed with wax to protect from evaporation.
2.2 Infiltration Experiment with Rainfall Enriched in the Heavy Isotope
The soil column for infiltration experiment with rainfall enriched in the heavy isotope was labeled as soil column No. 2. The experiment was performed in the same place from 8:00am May 25 to 10:30am May 28, 2008. Water was used to simulate the artificial rainfall for infiltration which had been evaporated for over seven months in the open container with isotopic composition of 0.9‰ in δ18O (Table 1). Soils, filling method and experiment equipment were the same as No. 1. The temperature ranged from 23.5 °C to 26.2 °C with the average temperature of about 24.8 °C and the relative humidity varied from 65 % to 89 % with the average relative humidity of about 78 % over the experimental period.
Infiltration experiment for No. 2 was started at 8:00am May 25 and the rainfall resulted in outflow from the soil column starting at 11.03 h. The rainfall was ended at 00:00 May 27 and soil column began recession which ended at 10:30 May 28. In the early 3 h, water samples were collected densely, for example, every 30-ml volume of water and after 3 h of outflow water samples were collected with equal time interval, like 1 h, 2 h or 4 h. Other processes were the same as No. 1.
The collected water samples were analyzed for the isotope composition of oxygen and hydrogen by using MAT-253 mass spectrometry at Isotope Laboratory, Ministry of Land and Resources in Beijing. Water was prepared for oxygen isotope analysis by the equilibration with carbon dioxide and for hydrogen isotope analysis by using the zinc method. The isotopic values are reported using the standard δ notion relative to the IAEA reference materials V-SMOW. The analytical precision was ±0.2‰ and ±2‰ for δ18O and δD, respectively.
2.3 Residence Time Modeling Theory and Approach
Descriptions of transfer functions models
g(τ) = T− 1 exp(−τ/T)
Exponential-piston flow (EPM)
g(τ) = (T/η)− 1 exp(−ητ/T + η − 1) for τ ≥ T(1-η−1)
g(τ) = 0 for τ < T(1-η−1)
Polynominal model (PM)
g(τ) = aτ3 + bτ2 + cτ + d
a, b, c, d
The Exponential Function (EM), Exponential-Piston flow Function (EPM), and the Polynomial Function (PM) were used in this study to fit the time series of δD & δ18O of the outflow from the soil column separately. As recommended by Legates and McCabe (1999), model error was evaluated using the root mean square error (RMSE). On the basis of infiltration experimental data, the isotopic variation of outflow was studied to calculate mean residence time using the transfer function model.
3 Results and Discussion
3.1 Isotopic Variation of Outflow in Infiltration
3.2 Isotopic Variation of Outflow Modeling
Three different transfer functions (EM, EPM and PM) were investigated to explore which one can provide better results for the observed data set.
Results of 18O simulation in No.1 soil column
Transfer function g(τ)
Fitting formula of Cout(t)(‰)
0.1349exp(−0.1349τ + 1.049)
−7.2(1-exp(−0.1349 t + 1.049))
−2.4767 × 10−7τ3 + 0.4513 × 10−4τ2
4.458 × 10−7t4−1.083 × 10−4t3
−0.285 × 10−2τ + 0.062
+1.027 × 10−2t2−0.4464 t
All three simulations for outflow of Column No. 1 using input data agree quite well with the measured values from the simple inspection of the plot. The EM has the highest RMSE (Table 3) indicating the poorest fit, while the EPM fits better than the PM. From Table 3 and Fig. 4, it can be seen that the EPM provided the most satisfactory fits to the data.
Results of 18O simulation in No.2 soil column
Transfer function g(τ)
Fitting formula of Cout(t)(‰)
0.1191exp(−0.1191τ + 1.617)
0.9(1-exp(−0.1191 t + 1.617))
6.2489 × 10−6τ3−6.6667 × 10−4τ2
1.406 × 10−6t4−2 × 10−4
+1.907 × 10−2τ−0.0968
t3 + 0.8582 × 10−2t2−0.0871 t
3.3 Determination of Infiltration Type
3.4 Determination of Infiltration Type Based on Mean Residence Time
Results from residence time modeling have implied that there is a correlation between mean residence time and infiltration type. It can be demonstrated through the comparison between observed and estimated mean residence times.
For Column No. 1 experiment, the best performing transfer function is EPM, as shown in Eq. (2). It can be deduced that the mean residence time is 15.2 h which is similar to the observed mean residence time 14.8 h, suggesting that the infiltration mechanism is piston flow and EPM can simulate the isotopic variation of outflow. For Column No. 2 experiment, the best matching transfer function is also EPM, as shown in Eq. (3). However, the estimated mean residence time for transfer function distribution is 21.9 h, which varied differently with the observed mean residence time 11 h, indicating the existence of preferential infiltration passage in the infiltration process.
3.5 Factors Influencing Parameters of Transfer Functions Model
There are many factors influencing the determination of parameters in transfer function models. Two possible factors and why they could be of significance in the parameter determination are briefly discussed here.
The first one is soil structure. The weight and average density of the soil in the two soil column experiments are the same, but the isotopic variation of outflow (Figs. 2 and 3) is different which may result from different soil structures. As shown in breakthrough curve (Figs. 6 and 7) and comparison between estimated and observed mean residence times, the mechanism controlling the infiltration in two columns are not the same, piston flow in Column No.1 and preferential flow in No. 2. Evidently, the variation of infiltration processes is an important factor affecting the parameters in transfer function distribution eventually.
Results of D simulation in No.1 soil column
Transfer function g(τ)
Fitting formula of Cout(t)(‰)
0.1072exp(−0.1072τ + 0.558)
−50 (1-exp(−0.1072 t + 0.558))
−2.167 × 10−7τ3 + 0.4424 × 10−4τ2
2.706 × 10−6t4−7.373 × 10−4t3
−0.291 × 10−2τ + 0.063
+7.285 × 10−2t2−3.142 t
4 Summary and Conclusions
Although residence time has been widely studied for flow pathways and storage, this study has shown that the mean residence time, as determined from the transfer function distribution, can be used to analyze the infiltration mechanism. Of the three transfer function models (EM, EPM and PM) evaluated, the EPM provided a reasonable fit to the isotopic data of outflow. However, if under variant rainfall input which model could provide the best performance is still unknown. Results from this study suggest that comparison between observed and estimated mean residence time might help identify the existence of preferential flow. Without the consideration of isotope measurement error of water sample, the parameters of transfer function of D and 18O are very close regardless of the distribution of transfer function, which indicates that the transfer function of two different stable isotope are the same. That means if the transfer function distribution of one kind isotope (e.g., 18O) is known, it can be used to forecast the isotopic variation of the other kind of isotope D. Furthermore, factors influencing the parameters determination had been analyzed, for example, soil structure and isotope measurement error.
This study is supported by National Natural Science Foundation of China (No. 41371048/40901015/41001011), Major Program of National Natural Science Foundation of China (51190090, 51190091), “the Fundamental Research Funds for the Central Universities (B1020062/B1020072)”, the Ph.D. Programs Foundation of Ministry of Education, China (20090094120008), the Special Fund of State Key Laboratory of China (2009586412, 2009585412) and the 111 Project (B08048).