Water Resources Management

, Volume 27, Issue 13, pp 4579–4590

Evaluating Infiltration Mechanisms Using Breakthrough Curve and Mean Residence Time

Authors

    • State Key Laboratory of Hydrology-Water Resources and Hydraulic EngineeringHohai University
    • College of Water Resources and HydrologyHohai University
  • Wang Tao
    • HydroChina Chengdu Engineering Corporation
  • Bao Weimin
    • State Key Laboratory of Hydrology-Water Resources and Hydraulic EngineeringHohai University
    • College of Water Resources and HydrologyHohai University
  • Shi Peng
    • State Key Laboratory of Hydrology-Water Resources and Hydraulic EngineeringHohai University
    • Department of GeoscienceUniversity of Nevada Las Vegas
  • Zhou Minmin
    • State Key Laboratory of Hydrology-Water Resources and Hydraulic EngineeringHohai University
    • College of Water Resources and HydrologyHohai University
  • Yu Zhongbo
    • State Key Laboratory of Hydrology-Water Resources and Hydraulic EngineeringHohai University
    • Department of GeoscienceUniversity of Nevada Las Vegas
Article

DOI: 10.1007/s11269-013-0427-8

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

Abstract

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.

Keywords

Transfer function modelMean residence timeInfiltration typeBreakthrough curve

1 Introduction

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.

2 Methods

Two infiltration experiments with different isotopic compositions of rainfall were designed in this study. The experimental soil column was made of transparent synthetic glass with 0.5 cm walled thickness, 1 m in height and 15 cm in diameter (Fig. 1). A perforated plate was placed at the bottom of column, which is underlain by geotechnical drape. A cylindrical container made of synthetic glass with a height of 8 cm, a diameter of 15 cm was used to collect water sample under the perforate plate. A 6.4-L Mariotte siphon was used to supply water. A rainfall simulator consists of a sprinkler made of hypodermic needles (Liu et al. 2008) was put above the soil surface. The rainfall intensity could be adjusted through Mariotte siphon and rainfall simulator in the experiment.
https://static-content.springer.com/image/art%3A10.1007%2Fs11269-013-0427-8/MediaObjects/11269_2013_427_Fig1_HTML.gif
Fig. 1

Schematic representation of soil column infiltration equipment

The soil used for this study was cohesive soil (Wu et al. 2003). It was obtained from topsoil of hillside in Tangshan town, Nanjing, Jiangsu province, China. The soil was air-dried, crushed in natural conditions and screened out large particles using electric soil sieves. The soil was preserved sealed for 24 h to keep the soil moisture uniform. The initial weighted water content of the soil was 5.3 % measured by using the oven-drying method and isotopic composition of oxygen and hydrogen were −3.5‰ and −27‰ analyzed by using the vacuum distillation method, respectively (Table 1). The soil column was filled with soil particles in layers with every layer of 8 cm in height and the total height of soil was 84 cm. The average density of soil was 1.2 g/cm3. When filling, the soil was not compacted to prevent the dry cohesive soil clogging the infiltration way after water absorption to swell.
Table 1

Rainfall and soil properties in infiltration experiments

Number of soil column

No.1

No.2

Mass of soil particle (g)

18116.9

18117.6

Mass of rainfall (g)

16319.7

16313.2

Initial soil moisture (%)

5.3

5.3

Duration of rainfall simulation (h)

59.4

40

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

Transfer function model (TFM) was proposed by Jury (Jury 1982; Jury et al. 1982) to simulate the transport of solute bromide (Br). Mathematically, the transport of solute through a soil column can be expressed by using the convolution integral (Ye 1990; Barnes and Bonell 1996; Kirchner et al. 2000; Ren et al. 2000), which states that the composition of output solute at any time, Cout(t), consists of input solute, Cin(t-τ) that enters uniformly into the soil column in the past t-τ, which becomes lagged according to its transfer function, g(τ):
$$ {C}_{out}(t)={\displaystyle \underset{0}{\overset{t}{\int }}g\left(\uptau \right)}{C}_{in}\left(t-\uptau \right) d\uptau =g(t)\ast {C}_{in}(t) $$
(1)
where τ is the lag time between input and output solute composition, g(τ) is the transfer function, and the asterisk represents the short-hand of the convolution operation. Equation (2) is valid for time-independent system and is similar to the linear system approach used in catchment unit hydrograph models (Overton 1970; McCuen 2005). A soil column’s transfer function could have various shapes depending on the exact nature of its flow distribution and flow system. Theoretically, the transfer function can be determined to solve mass conservation and solute transport equations. However, it is not practical to obtain the analytical solution. Usually, we assume the transfer function to compute the output, then through the comparison with observed data to test if the assumed transfer function is appropriate. The most widely used distributions are piston flow model (PFM, Maloszewski and Zuber 1982), exponential model (EM, Maloszewski and Zuber 1982), exponential-piston flow model (EPM, Maloszewski and Zuber 1982; Weiler et al. 2003), Gamma distribution model (GM, Kirchner et al. 2000), polynomial model (PM, White et al. 1986; Ye 1990) and lognormal distribution model (LM, Jury 1982). Transfer function models that were evaluated in this study are shown in Table 2. T is mean residence time of solute in the system, and η is the parameter which equals the total volume of water divided by the exponential flow volume.
Table 2

Descriptions of transfer functions models

Model

Transfer function

Parameters

Exponential (EM)

g(τ) = T− 1 exp(−τ/T)

T

Exponential-piston flow (EPM)

g(τ) = (T/η)− 1 exp(−ητ/T + η − 1) for τ ≥ T(1-η−1)

T, η

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

The outflow occurred after 14.8 h and stopped after 83.4 h of rainfall which lasted for 59.4 h in Column No. 1. The oxygen isotope values of samples collected from outlet of Column No. 1 ranged from −7.7‰ to −3.7‰ with arithmetic average of −6.6‰ (Fig. 2). The δ18O values of outflow in the early time were similar to the values for initial soil water (the difference of δ18O values between them was −0.2‰) due to the impact of rainfall pushing initial soil water out through mixing and dilution. Within 6 h after outflow could be observed at the outlet, the isotopic composition of outflow exhibited greater variation. After 40 h of rainfall, most of the initial soil water was pushed out of the soil and the isotopic composition of outflow was stable and close to the isotopic values of rainfall. The results proved that with constant and continuous rainfall input, the isotopic composition of soil water will approach the isotopic values of rainfall through mixing and exchange processes in the soil.
https://static-content.springer.com/image/art%3A10.1007%2Fs11269-013-0427-8/MediaObjects/11269_2013_427_Fig2_HTML.gif
Fig. 2

Change in the isotopic composition of oxygen of outflow over time in No.1 soil column

In Column No. 2, the outflow started after 11 h and ended after 62 h of rainfall which lasted for 40 h. The δ18O values of samples collected from outlet of Column No. 2 ranged from −0.6‰ to 1.2‰ with arithmetic average of 0.38‰ (Fig. 3). Unlike Column No. 1, δ18O values of the early time outflow varied differently from those of initial soil moisture (the difference is 3.4‰ and the difference of column 1 is −0.2‰). As time went, the δ18O of outflow enriched in heavy isotope slowly and was close to the isotopic composition of rainfall. Additionally, the oxygen isotope composition of outflow in Column No. 2 presented substantial fluctuations in the whole infiltration process.
https://static-content.springer.com/image/art%3A10.1007%2Fs11269-013-0427-8/MediaObjects/11269_2013_427_Fig3_HTML.gif
Fig. 3

Change in the isotopic composition of oxygen of outflow over time in No.2 soil column

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.

Using rainfall δ18O as input, simulations were carried out for δ18O data from outflow of Column No. 1. The transfer function models which provided the best fits are shown in Table 3. The comparison of simulated and measured data is included in Fig. 4.
Table 3

Results of 18O simulation in No.1 soil column

Model

Isotope

Transfer function g(τ)

Fitting formula of Cout(t)(‰)

RMSE(‰)

EM

18O

0.0763exp(−0.0763τ)

−7.2(1-exp(−0.0763 t))

0.393

EPM

18O

0.1349exp(−0.1349τ + 1.049)

−7.2(1-exp(−0.1349 t + 1.049))

0.308

PM

18O

−2.4767 × 10−7τ3 + 0.4513 × 10−4τ2

4.458 × 10−7t4−1.083 × 10−4t3

0.333

−0.285 × 10−2τ + 0.062

+1.027 × 10−2t2−0.4464 t

https://static-content.springer.com/image/art%3A10.1007%2Fs11269-013-0427-8/MediaObjects/11269_2013_427_Fig4_HTML.gif
Fig. 4

Comparison of δ18O concentration with model simulations in No.1 soil column

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.

On the basis of experimental data from Column No. 1, under constant rainfall input, the function of isotopic values of oxygen of outflow from the soil column can be expressed as (Table 3):
$$ {C}_{\mathrm{out}}(t)=-7.2\left(1- \exp \left(-0.1349t+1.049\right)\right) $$
(2)
For Column No. 2 experiment, the rainfall was enriched in more heavy isotope (0.9‰) than the initial soil water (−3.5‰). Of the models tested, three of the transfer function distributions provided satisfactory model simulations to the observed isotopic data (i.e., RMSE ranged from 0.212 to 0.388) for all distributions (Table 4). However, only the EPM distribution performed consistently well for all measured data set (Fig. 5). The system response functions (or transfer function distributions) obtained for the EM in enriched heavy isotope input case are illustrated in Fig. 5. It can be seen from Fig. 5 that the δ18O value of outflow varied from negative value to positive value, and the EM cannot simulate the variation. In this experiment, EPM produced the best matches to the data:
Table 4

Results of 18O simulation in No.2 soil column

Model

Isotope

Transfer function g(τ)

Fitting formula of Cout(t)(‰)

RMSE(‰)

EM

18O

0.0263exp(−0.0263τ)

0.9(1-exp(−0.0263 t))

0.388

EPM

18O

0.1191exp(−0.1191τ + 1.617)

0.9(1-exp(−0.1191 t + 1.617))

0.212

PM

18O

6.2489 × 10−6τ3−6.6667 × 10−4τ2

1.406 × 10−6t4−2 × 10−4

0.236

+1.907 × 10−2τ−0.0968

t3 + 0.8582 × 10−2t2−0.0871 t

https://static-content.springer.com/image/art%3A10.1007%2Fs11269-013-0427-8/MediaObjects/11269_2013_427_Fig5_HTML.gif
Fig. 5

Comparison of δ18O concentration with model simulations in No.2 soil column

$$ {C}_{\mathrm{out}}(t)=0.9\left(1- \exp \left(-0.1191t+1.617\right)\right) $$
(3)

3.3 Determination of Infiltration Type

Figure 6 demonstrates the breakthrough curve of the observed δ18O values of outflow in Column No. 1. V is the accumulated volume of outflow, V0 is the volume of pores in the soil (equals to the volume of the column multiply by using initial soil moisture), C0 is the isotopic concentration of initial soil water, Cj is the isotopic concentration of outflow, CP is isotopic value of rainfall and (Cj-C0)/(CP-C0) is relative concentration. It can be observed from Fig. 6 that the breakthrough curves of δ18O of outflow show a similar “piston flow” character. Relative concentration varied from nearly zero to 1. When V/V0 is greater than 1.0, the relative concentration (Cj−C0) /(CP−C0) is close to 1.0, indicating that as accumulated outflow volume is greater than the volume of pores, most initial soil water has been pushed out by infiltrated rainfall through mixing and diffusional exchange with stored water held in the soil pores without preferential flow.
https://static-content.springer.com/image/art%3A10.1007%2Fs11269-013-0427-8/MediaObjects/11269_2013_427_Fig6_HTML.gif
Fig. 6

Breakthrough curve of 18O transport in No.1 soil column

Figure 7 presents the measured δ18O values of outflow in Column No. 2. It is noted that the relative concentration did not start at zero but 0.8 which suggests that the isotopic composition of early time outflow deviated from that of initial soil water, which indicates that there are larger proportion of rainfall in the early time outflow. Compared with Column No. 1, the breakthrough curve for Column No. 2 exhibited greater fluctuation. The mass of soil and rainfall are nearly identical for two column experiments (Table 1); however, the times consumed from the beginning of rainfall to outflow are different (14.8 h in Column No. 1 and 11.0 h in No. 2), in other words, they have different outflow velocity which may result from different soil structures. A review on the breakthrough curve, outflow time and outflow velocity may attain the conclusion that there exists preferential infiltration passages in Column No. 2 and the rainfall infiltration type is not piston flow.
https://static-content.springer.com/image/art%3A10.1007%2Fs11269-013-0427-8/MediaObjects/11269_2013_427_Fig7_HTML.gif
Fig. 7

Breakthrough curve of 18O transport in No.2 soil column

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.

The second one is the isotope measurement error of water sample. The isotope of oxygen and hydrogen transports with water together exhibits strong correlation. Theoretically, the parameters determined based on the transfer function distribution of D and 18O should be identical. However, in Column No. 1 experiment, there is minor difference between the parameters of oxygen and hydrogen transfer function models, for EPM, the mean residence time is 14.5 h from hydrogen fitting curve equation (Table 5), however, the mean residence time is 15.2 h from oxygen fitting curve equation (Table 3). Factors causing this difference may result from the isotope measurement error of water samples.
Table 5

Results of D simulation in No.1 soil column

Model

Isotope

Transfer function g(τ)

Fitting formula of Cout(t)(‰)

RMSE(‰)

EM

D

0.0766 exp(−0.0766τ)

−50(1-exp(−0.0766 t))

3.065

EPM

D

0.1072exp(−0.1072τ + 0.558)

−50 (1-exp(−0.1072 t + 0.558))

2.934

PM

D

−2.167 × 10−7τ3 + 0.4424 × 10−4τ2

2.706 × 10−6t4−7.373 × 10−4t3

3.008

−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.

Acknowledgements

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).

Copyright information

© Springer Science+Business Media Dordrecht 2013