Hydraulic residence time (HRT) distribution intuitively reflects flow pattern of constructed wetlands. HRT is able to reflect the merits of flow state clearly. Short-circuiting and mixing are the most important factors on HRT, exerting a significant effect on the flow pattern of wetlands. These two conditions must be avoided in wetlands construction and management. Therefore, it is necessary to select the best indicators measuring short-circuiting and mixing for understanding the flow pattern and the hydraulic performance of wetlands. This paper analyzes numerous indicators reflecting the degree of short-circuiting and mixing, displaying that *t*_{10} and Morril index *t*_{90}/*t*_{10} are optimal indicators measuring short-circuiting and mixing, respectively, according to truncation and stability analysis based on tracer data. Data analysis showed that when water depth dropped, *t*_{10} increased and *t*_{90}/*t*_{10} reduced gradually, indicating the improvement of short-circuiting and mixing. These results were fully consistent with the analysis results of hydraulic parameters, such as effective volume ratio *e* and the number of serial mixing tanks *N*. The excellent indicators of short-circuiting and mixing provide theoretical basis for reasonable design and evaluation of constructed wetlands, contributing to promote the hydraulic performance and purification effect.

## NOMENCLATURE

*A*_{effective}effective area (L

^{2})*A*_{total}total area (L

^{2})*C(t)*concentration (ML

^{−3})*C’(Φ)*normalized concentration (-)

*e*effective volume ratio (-)

*f(t)*distribution function (T

^{−1})- HRT
hydraulic residence time (T)

*h*water depth(cm)

*λ*_{e}hydraulic efficiency based on effective volume ratio (-)

*λ*_{p}hydraulic efficiency based on peak time (-)

*M*injected mass of tracer (M)

*M*_{out}recycled mass of tracer (M)

*Mo*Morril index t

_{90}/t_{10}(-)*N*number of serial mixing tanks (-)

*Q*flow (L

^{3}T^{−1})- RTD
residence time distribution

*Φ*normalized time (-)

*T*test period (T)

*t*time (T)

*t*_{0}initial integration time (T)

*t’*integration variable (T)

*t*_{i}initial arrival time (-)

*t*_{a}time at which a% of the tracer passed through outlet (-)

*t*_{p}^{’}dimensionless peak time(-)

*t*_{n}nominal residence time (T)

*t*_{mean}mean residence time (T)

*t*_{p}peak time (T)

*σ*^{2}variance (T

^{2})*V*volume (L

^{3})*V*_{effective}effective volume (L

^{3})*V*_{total}total volume (L

^{3})*η*recovery ratio (%)

## INTRODUCTION

Constructed wetlands have been utilized as a cost-effective treatment in agricultural nonpoint source pollution, because of their physical, chemical and biological properties and excellent performance in purifying agricultural drainage (Wahl *et al.* 2010; Bodin & Persson 2012). With the extensive application of constructed wetlands, how to optimize the designation and improve purification efficiency becomes a topic of concern. Studies have shown that treatment efficiency is closely related to hydraulic performance. For example, the purification of pollutant is directly related to hydraulic residence time (HRT) of wetlands (Persson & Wittgren 2003; Wahl *et al.* 2010). It is a challenge to find a convenient way to measure the hydraulic performance during the process of constructed wetlands design. Currently, hydraulic performance under different conditions is commonly assessed by hydraulic indicators based on HRT distribution curves, which are obtained through tracer tests.

There are two ideal hydraulic regimes of wetlands flow, plug flow and completely mixed flow (Persson *et al.* 1999; Teixeira & Renote 2008). In plug flow regime, inflow is distributed uniformly in cross section and flows along the forward direction, there is no longitudinal dispersion and mixing, residence time distribution curve is presented in the form of pulse. In the case of completely mixed flow regime, inflow water is quickly mixed with existing wetland water body, internal concentration remains the same all the time, and HRT distribution curve displays exponential decay form under this condition. However, actual flow condition is often a regime between the two kinds of ideal condition. There are different volume sizes of hydraulic dead space and recirculation zones in wetlands, forming a preferential flow path and reducing the hydraulic performance of wetlands (Werner & Kadlec 1996; Persson 2000; Persson & Wittgren 2003).

In general, hydraulic performance indicators of constructed wetlands can be divided into two categories, namely short-circuiting indicators and mixing indicators (Teixeira & Renote 2008). Owing to the limitation of actual test conditions, tracer test is often terminated by man-made, causing the loss of tracer data and the truncation of tracer curve. It would lead to the inaccuracy of hydraulic parameters calculation and hydraulic performance evaluation, and produce certain error in data analysis if the test was artificially terminated. Therefore, it is a basic need to assess the influence of truncation, choose the appropriate truncation level and hydraulic parameters. This paper analyzes various relevant indicators according to tracer test curves and data truncation under different levels, analyzing their variability and stability and comparing qualitative with quantitative analysis. This study aims to obtain the best indicator to measure the level of short-circuiting and mixing in wetlands flow (Bodin *et al.* 2013).

## MATERIALS AND METHODS

### Test zone

Field experiments were conducted at Jiangxi Province Center Station of Irrigation Experiment in July 2013. The Jiangxi Province Center Station of Irrigation Experiment is located in Jiangxi plain irrigation area of Poyang lake basin. The geographical coordinate is 115 °49′E ∼ 116 °46′E for longitude, 28 °24′N ∼ 29 °46′N for latitude, belonging to the typical subtropical humid monsoon climate, with mild climate and abundant rainfall. Annual average temperature is 18.1 °C, the lowest average temperature is 4.7 °C in January. Annual average rainfall is 1,685.2 mm.

The designing depth of experimented constructed wetland is 60 cm and its surface area is 490 m^{2} under design depth, slope ratio of both sides is 2:1 (shown in Figure 1). Nelumbo nucifera grew well during test period, with straight stem and an average density of 31.1 plants per square meter, water surface was covered with leaf. Inlet and outlet are installed with inflow and outflow device, controlling flow rate by adjusting valve.

### Data collection

Rhodamine WT was selected as the tracer of this experiment, YSI-600 OMS multiparameter water quality sonde was utilized to monitor tracer concentration. The instrument is produced by American YSI Company, it can be suited with a variety of probe, we chose YSI-6130 probe according to experimental purpose. This kind of probe can be set at a specific time step to record tracer concentration, conductivity and temperature automatically, operating easily and saving time and labor.

Before the study, inlet and outlet must be determined firstly. Flow rate was 2.45L/s, i.e. 8.82 m^{3}/h measured by container and cylinder, water depth was initially set at 0.6 m for the first test. Tracer concentration of verification solution was set to 0, 100 and 200 μg/L with deionized water to check YSI probe with 5 min time step. Instruments were placed at the middle and the outlet of tested constructed wetland.

After water depth was stable, a predetermined mass of tracer was injected into inflow instantaneously. According to the depth and volume, 60 g tracer labeled with 106053 FWT 50 was released into water; mass concentration of this kind of tracer is 5%. During the trial, water depth was stable by adjusting the valve opening. Repeat the same experimental process when water depth was set to 40 cm and 20 cm, respectively, with injected mass of 20 g. Tests were carried out from high to low water depth, leaving certain time interval between each test to rule out the residual effect of previous tracer test on the subsequent one. Test period under different depths was shown in Table 1.

Depth h
. | Start time . | End time . | Test period T
. | Time ratio T/t
. _{n} | Tracer recovery ratio η
. |
---|---|---|---|---|---|

60 | 7–12 6:40 | 7–13 18:40 | 36 | 1.11 | 73.10 |

40 | 7–17 8:50 | 7–18 20:00 | 35 | 1.65 | 58.83 |

20 | 7–19 8:25 | 7–20 17:35 | 33 | 3.16 | 66.31 |

Depth h
. | Start time . | End time . | Test period T
. | Time ratio T/t
. _{n} | Tracer recovery ratio η
. |
---|---|---|---|---|---|

60 | 7–12 6:40 | 7–13 18:40 | 36 | 1.11 | 73.10 |

40 | 7–17 8:50 | 7–18 20:00 | 35 | 1.65 | 58.83 |

20 | 7–19 8:25 | 7–20 17:35 | 33 | 3.16 | 66.31 |

When tracer test was finished, data were exported by EcoWatch software and hydraulic residence time distribution (RTD) curve was plotted to analyze hydraulic performance of tested constructed wetlands.

### Indicators of hydraulic regime

Currently, indicators measuring flow conditions of constructed wetlands are commonly indicated by mass recycled response time (Arthur *et al.* 1932; Thirumurthi 1969; Hart 1979; Stamou & Noutsopoulos 1994; Teixeira & Renote 2008). Indicators representing hydraulic performance include effective volume ratio, number of serial mixing tanks, variance and hydraulic efficiency, short-circuiting indicators can be represented by initial arrival time *t _{i}*, mass through time

*t*,

_{10}*t*and dimensionless peak time

_{50}*t*

_{p}^{’}. Mixing indicators can be represented by variance

*σ*, Morril index (

^{2}*Mo*)

*t*and difference between mass through time

_{90}/t_{10}*t*and

_{90}–t_{10}*t*. Optimal indicators would be obtained by analyzing the change of tracer curves under different truncation levels.

_{75}–t_{25}### Hydraulic parameters

*t*, actual residence time

_{n}*t*and peak time

_{m}*t*, in the analysis of hydraulic characteristics of wetlands (Persson

_{p}*et al.*1999). For surface flow wetlands, nominal HRT is calculated as Equation (1):Actual HRT is the value corresponding to the centroid of RTD curve, just as Equation (2) shown below. Peak time is the time corresponding to peak point of RTD curve, which could be identified easily.And to some extent,

*f(t)*can be regarded as probability density function of HRT. The calculation formula is defined as:HRT is the base to analyze hydraulic characteristics of constructed wetlands. Numerous hydraulic parameters can be derived by HRT directly or indirectly.

*Hydraulic RTD Curve* HRT distribution curve is a basic tool to analyze wetlands hydraulic characteristics. In the ideal condition of plug flow, inflow passes through a cross section uniformly, without mixing and dispersion in flow direction. However, actual flow water is mostly in complex condition due to turbulent diffusion. In this case, contaminant in the water will spread around continually, developing into a contaminated group gradually, motioning and changing continuously under the effect of convection.

*Variance*This parameter of RTD curve reflects the degree of deviation from mean value of tracer concentration. The greater the variance is, the more serious it deviates from ideal plug flow condition (Kadlec 1994; Persson 2000).

*Number of Serial Mixing Tanks*This parameter is an index comparing wetlands flow morphology with completely mixed reactor in sewage treatment in chemistry engineering. It reflects the degree of mixing of wetlands water. The greater

*N*value is, the closer wetlands flow regime tends to plug flow. It means that wetlands flow tends to completely mixed regime when

*N*is equal to 1; and it tends to plug flow regime when

*N*tends to infinity (Persson

*et al.*1999; Persson & Wittgren 2003; Bodin & Persson 2012). The equation to calculate

*N*is defined as below:

*Effective Volume Ratio*Short-circuiting is a common phenomena in actual flow. This kind of flow regime would reduce effective volume of wetlands, declining wetlands sewage treatment capacity. Generally, the volume of wetlands water body working in sewage treatment well is called effective volume, represented by effective volume ratio (Persson & Wittgren 2003). Although the effective volume ratio cannot be measured directly, it could be deduced from RTD curves, just as Equation (6) shows.

*Hydraulic Efficiency*Hydraulic efficiency is an indicator to measure the capacity of distributing inflow to the section uniformly, which reflects the integrated impact of short-circuiting and mixing on sewage treatment performance of constructed wetlands (Persson

*et al.*1999). The hydraulic efficiency is calculated as following equation:

According to above equations, *λ _{p}* is related to peak time only, which can be obtained from RTD curve directly.

### Normalization treatment

*et al.*2004; Wahl

*et al.*2010). Tracer concentration could be normalized by tracer mass injected and water volume, because concentration is a function of these two parameters. Similarly, time axis, i.e. horizontal axis, can be normalized by wetland volume and flow rate, because these two parameters could affect HRT of wetland and change the shape of RTD curves (Werner & Kadlec 1996; Holland

*et al.*2004). The normalization formulas are defined below:To eliminate the effect of tracer loss during experiment caused by interception and adsorption on normalization, total tracer mass was substituted by recycled one (Werner & Kadlec 1996; Holland

*et al.*2004).And mass recovery ratio is expressed by equation of

## RESULTS AND DISCUSSION

### Tracer data

HRT distribution curves of experimented constructed wetland under different water depths were recorded by YSI-600 OMS water quality sonde, as shown in Figure 2. Unit of concentration axis was μg/L and time step was 5 min in the timeline.

Qualitative analysis of normalized RTD curves shown in Figure 2(b) indicated that the centroid of curves gradually approached origin with depth increasing, and the value of initial rise point of RTD curves gradually decreased. These results showed that hydraulic performance reduced with the increase of water depth.

Hydraulic elements and parameters were calculated by Equations (1)–(8). With trapezoidal rule instead of integration operation, we got these values under various depths, just as Table 2 shows:

Depth h
. | Volume V
. | Nominal residence time t
. _{n} | Mean residence time t
. _{m} | Variance σ
. ^{2} | Mixing tanks N
. | Effective Volume ratio e
. | Peak time t
. _{p} | Initial arrival time . | 10% mass arrival time . | 50% mass arrival time . | 90% mass arrival time . |
---|---|---|---|---|---|---|---|---|---|---|---|

20 | 92.47 | 10.48 | 8.85 | 13.38 | 5.85 | 0.844 | 6.33 | 4.50 | 6.25 | 10.00 | – |

40 | 187.58 | 21.27 | 14.45 | 45.41 | 4.60 | 0.679 | 8.67 | 7.67 | 9.00 | 22.50 | – |

60 | 285.37 | 32.35 | 13.61 | 33.26 | 5.57 | 0.421 | 9.08 | 4.83 | 8.67 | 14.25 | – |

Depth h
. | Volume V
. | Nominal residence time t
. _{n} | Mean residence time t
. _{m} | Variance σ
. ^{2} | Mixing tanks N
. | Effective Volume ratio e
. | Peak time t
. _{p} | Initial arrival time . | 10% mass arrival time . | 50% mass arrival time . | 90% mass arrival time . |
---|---|---|---|---|---|---|---|---|---|---|---|

20 | 92.47 | 10.48 | 8.85 | 13.38 | 5.85 | 0.844 | 6.33 | 4.50 | 6.25 | 10.00 | – |

40 | 187.58 | 21.27 | 14.45 | 45.41 | 4.60 | 0.679 | 8.67 | 7.67 | 9.00 | 22.50 | – |

60 | 285.37 | 32.35 | 13.61 | 33.26 | 5.57 | 0.421 | 9.08 | 4.83 | 8.67 | 14.25 | – |

It showed that effective volume ratio *e* decreased with water depth increasing. This result indicated that hydraulic performance was negatively correlated with the depth of water, because the size of effective volume ratio can reflect the hydraulic performance of constructed wetlands.

### Hydraulic indicators under different truncation levels

To study the relationship between wetlands hydraulic performance and water depth under different truncation levels, gaining optimal short-circuiting and mixing indicators, normalized HRT distribution curves were truncated under different levels. Reasonability of these indicators was represented by stability and representativeness analysis, as shown in Table 3.

Depth h . | Truncation level . | Initial arrival time t
. _{i} | Dimensionless peak time t
. _{p}' | Mean residence time t
. _{m} | Mass recovery ratio η
. |
---|---|---|---|---|---|

60 | 1.11 | 0.15 | 0.28 | 13.614 | 0.730 |

1.00 | 13.249 | 0.718 | |||

0.80 | 12.683 | 0.693 | |||

0.60 | 11.791 | 0.632 | |||

40 | 1.65 | 0.36 | 0.41 | 14.451 | 0.588 |

1.50 | 13.874 | 0.571 | |||

1.40 | 13.560 | 0.562 | |||

1.20 | 12.750 | 0.529 | |||

1.00 | 11.842 | 0.487 | |||

0.80 | 10.948 | 0.433 | |||

20 | 3.16 | 0.43 | 0.60 | 8.846 | 0.663 |

3.00 | 8.560 | 0.655 | |||

2.50 | 8.407 | 0.651 | |||

2.00 | 8.575 | 0.658 | |||

1.50 | 8.410 | 0.646 | |||

1.30 | 8.292 | 0.633 | |||

1.10 | 8.002 | 0.591 | |||

1.00 | 7.703 | 0.537 |

Depth h . | Truncation level . | Initial arrival time t
. _{i} | Dimensionless peak time t
. _{p}' | Mean residence time t
. _{m} | Mass recovery ratio η
. |
---|---|---|---|---|---|

60 | 1.11 | 0.15 | 0.28 | 13.614 | 0.730 |

1.00 | 13.249 | 0.718 | |||

0.80 | 12.683 | 0.693 | |||

0.60 | 11.791 | 0.632 | |||

40 | 1.65 | 0.36 | 0.41 | 14.451 | 0.588 |

1.50 | 13.874 | 0.571 | |||

1.40 | 13.560 | 0.562 | |||

1.20 | 12.750 | 0.529 | |||

1.00 | 11.842 | 0.487 | |||

0.80 | 10.948 | 0.433 | |||

20 | 3.16 | 0.43 | 0.60 | 8.846 | 0.663 |

3.00 | 8.560 | 0.655 | |||

2.50 | 8.407 | 0.651 | |||

2.00 | 8.575 | 0.658 | |||

1.50 | 8.410 | 0.646 | |||

1.30 | 8.292 | 0.633 | |||

1.10 | 8.002 | 0.591 | |||

1.00 | 7.703 | 0.537 |

### Hydraulic parameters

Effective volume ratio, number of serial mixing tanks and hydraulic efficiency were selected to reflect hydraulic performance under different depths and compare hydraulic parameter values changing with truncation level under same depth. The results are shown in Figure 3.

Figure 3(a) showed that effective volume ratio decreased with truncation levels lowering when the depth was fixed; effective volume ratio decreased with water depth going up under the same truncation level. Figure 3(b) showed that number of serial mixing tanks tended to increase exponentially in general when truncation levels dropped, indicating that the degree of mixing gradually reduced. That is to say, numerical results reflected that wetland flow tended to plug flow regime gradually with truncation level decreasing. Reason of such a huge difference in mixing tanks number *N* is caused by data truncation, or truncation error. If truncated time is lower, tracer data will be highly concentrated together. The data collected are distributed around nominal residence time, displaying an illusion similar to ideal plug flow. In fact, large numbers of tail data would be lost when the truncated time is too short, these data play an important role in ensuring recovery and validity of tracer test. Tail data could also expand the dispersion of tracer curves, aggravating the degree of flow mixing. Meanwhile, when truncation level was fixed, Figure 3(b) showed that number of mixing tanks decreased with depth rising, indicating that wetland flow tended to completely mixed flow condition. Figure 3(c) displayed that it was unapparent of the impact of truncation level on hydraulic efficiency, while it gradually decreased with depth increasing. All these analysis results obviously indicated that hydraulic performance tended to be positive with water depth decreasing, which was consistent with the results obtained from qualitative analysis of Figure 2(b).

### Short-circuiting indicators

Mass recovery time *t _{10}* and

*t*were described here to compare their variability under different truncation levels to select the best short-circuiting indicators of constructed wetlands. Initial arrival time

_{50}*t*and dimensionless peak time

_{i}*t*are immune to truncation.

_{p}’For short-circuiting indicators, such as *t _{i}*,

*t*and

_{10}*t*, the smaller the value is, the more serious the short-circuiting of wetlands flow is, and the lower the hydraulic performance is. As shown in Figure 4, under same truncation level, as for short-circuiting, such as

_{50}*t*and

_{10}*t*, data analysis indicated that the extent of short-circuiting gradually reduced when the water depth decreased, displaying that hydraulic performance of tested constructed wetland was gradually improved with water depth decreasing. What revealed from Table 4 was that the numerical stability of

_{50}*t*was much better than

_{10}*t*, the impact of truncation on

_{50}*t*was almost negligible. Interpretation of this kind of numerical stability of

_{10}*t*is that the value is calculated by the ratio between area surrounded by curve divided by 10% mass recovery time and area covered by whole raw curve, the denominator is much large than numerator. Thus it is tiny of the influence of truncation on

_{10}*t*compared with the influence on overall area enclosed by RTD curve.

_{10}Depth h . | Indicator . | Statistics . | Mean . | Standard Error of Mean . | Standard deviation . |
---|---|---|---|---|---|

60 | t _{10} | 4 | 0.253 | 0.00122 | 0.00245 |

t _{50} | 4 | 0.374 | 0.00404 | 0.00808 | |

40 | t _{10} | 6 | 0.403 | 0.00123 | 0.00301 |

t _{50} | 6 | 0.525 | 0.00905 | 0.02217 | |

20 | t _{10} | 8 | 0.565 | 0.00181 | 0.00513 |

t _{50} | 8 | 0.763 | 0.00676 | 0.01912 |

Depth h . | Indicator . | Statistics . | Mean . | Standard Error of Mean . | Standard deviation . |
---|---|---|---|---|---|

60 | t _{10} | 4 | 0.253 | 0.00122 | 0.00245 |

t _{50} | 4 | 0.374 | 0.00404 | 0.00808 | |

40 | t _{10} | 6 | 0.403 | 0.00123 | 0.00301 |

t _{50} | 6 | 0.525 | 0.00905 | 0.02217 | |

20 | t _{10} | 8 | 0.565 | 0.00181 | 0.00513 |

t _{50} | 8 | 0.763 | 0.00676 | 0.01912 |

*t _{i}* reflects the interval of tracer diffusion group forward passing through whole wetlands, which is an important short-circuiting indicator to measure flow regime.

*t*represents the interval of the concentration peak reaching outlet, explaining the degree of short-circuiting and actual HRT to a certain extent, and revealing the hydraulic performance of constructed wetlands. However, there is serious volatility in

_{p}’*t*and

_{i}*t*value

_{p}’*,*uncertainty to determine values, for example the effect of wind on

*t*(Thackston

_{p}’*et al.*1987). So

*t*and

_{i}*t*cannot be considered as perfect indicators of short-circuiting.

_{p}’Above all, *t _{10}* was regarded as the best indicator to evaluate short-circuiting of constructed wetlands flow. Lower sensitivity to truncation level, convenient calculation and strong stability were the most significant advantages, reflecting its favorable representation in short-circuiting.

### Mixing indicators

Stability of mixing indicators corresponded to various truncation levels was analyzed to select the best measuring object, and was compared with the results of hydraulic parameters.

Figure 5 showed that all indicators gradually decreased with the reduction of truncated time, reflecting the decline of mixing level. The geometric meaning of each indicator can be seen as the difference of respective area of RTD curve divided by corresponded mass recovery response time. The reason of mixing indicators decreasing with truncation level reduction is that shorter data sequence leads to lower dispersion of data.

Analysis of normalized RTD curves under various depths indicated that effect of truncation on parameter values is negligible if the truncation was made around tail zone of background concentration. For example, when the truncated time was ranged from 1.5 to 3.0, variation of these three mixing indicators was tiny. The closer truncation approached to origin, the greater impact of truncation on data was, and the more obvious reduction of mixing indicators was, which was displayed clearly in Figure 5. Thus, experimental time should not be terminated until the collected data sequences tend to be stable in order to avoid excessive truncation error.

According to the number of serial mixing tanks *N*, the degree of ideal plug flow condition under different depths was sorted from 20 to 40 to 60 cm. The value of *t _{75}–t_{25}* was 40 > 20 > 60 cm,

*t*was 40 > 20 > 60 cm,

_{90}–t_{10}*t*

_{90}/t_{1}_{0}was 60 > 40 > 20 cm, as shown in Figure 5. It was positively correlated between the numerical value of above indicators and the degree of mixing, namely plug flow condition was negatively related with these values. Thus, plug flow regime based on these indicators was 60 cm > 20 cm > 40 cm, 60 cm > 20 cm > 40 cm and 20 cm > 40 cm > 60 cm respectively. Meanwhile, it was unstable of the rank ordering of hydraulic performance based on

*t*and

_{75}–t_{25}*t*under various depths, varying with truncation level. However, the sorting result of

_{90}–t_{10}*t*was not affected by truncation level. According to above analysis,

_{90}/t_{10}*t*, with high stability, was consistent with hydraulic parameter. It displayed great representativeness and superiority on reflecting degree of flow mixing.

_{90}/t_{10}*t*was the best indicator to measure the degree of mixing.

_{90}/t_{10}## CONCLUSIONS

Based on the tracer experiment and truncation curves of constructed wetland under different water depths, the results of data analysis showed that hydraulic performance was improved with water depth decreasing and degraded with truncation level lowering. It was negative and slight of the effect of truncation on effective volume ratio and hydraulic efficiency. Number of serial mixing tanks was affected significantly by truncation level, it is mainly due to the dispersion degree of RTD curves influenced by truncation levels sensitively, causing the obvious change of this mixing indicator which reflecting the extent of dispersion.

*t _{10}* was regarded as the optimal indicator to measure the degree of short-circuiting condition of constructed wetlands. Analysis results of short-circuiting indicators of

*t*and

_{10}*t*was consistent with the results of hydraulic parameters, i.e., the degree of short-circuiting was gradually lessened with water depth decreasing. Hydraulic performance was improved step by step when water depth decreased from 60 to 20 cm, indicating the reasonableness of short-circuiting indicators

_{50}*t*and

_{10}*t*on reflecting hydraulic performance of constructed wetlands. Analysis of truncation error on RTD curves displayed that it was small of the influence of truncation on

_{50}*t*and

_{10}*t*. However,

_{50}*t*showed a better numerical stability than

_{10}*t*, there is a great advantage in representativeness compared with

_{50}*t*and

_{i}*t*as well. After compared with

_{p}*t*and

_{75}–t_{25}*t*, Morril index

_{90}–t_{10}*t*was regarded as the best indicator to measure the degree of mixing. Hydraulic performance deduced from

_{90/}t_{10}*t*was consistent with the analysis result of hydraulic parameter, number of serial mixing tanks. The degree of mixing of constructed wetlands was reduced with depth decreasing, flow regime tended to plug flow when water depth decreased gradually. Effect of truncation level on numerical stability was negligible if RTD curves were truncated around the zone of background concentration. The closer the truncation approached to original point, the more significant the impact on related indicators was.

_{90}/t_{10}To optimize the design and operation management of constructed wetlands, improve its hydraulic performance, and play the best sewage purification capability, we need to carry on a reasonable hydraulic design. Short-circuiting and mixing are the main internal causes that affect hydraulic performance of constructed wetlands, and there are many external factors influencing it. Reasonable designation of aspect ratio and arrangement of inlet and outlet can improve the flow regime significantly, reduce the occurrence of short-circuiting and mixing, and improve the hydraulic performance. In general, it is recommended that the appropriate aspect ratio value ranges from 2:1 to 4:1, inlet and outlet should be set with opposite layout. And water distribution uniformity is the best influent mode which would improve the hydraulic performance greatly. In addition, it is very important to the comprehensive performance of reasonable water depth (0.4–0.6 m) and species and distribution of aquatic plants (with the vertical arrangement in the direction of flow)

## ACKNOWLEDGEMENTS

The authors thank the Chinese Ministry of Water Resources Project NO. 948 (Grant No. 201229) and Agricultural non-point source pollution ecological restoration technology research in Poyang Lake basin by the cooperation between China and the United States (Grant No. 20111017) for financial aid. The authors would like also to acknowledge the Jiangxi Province Center Station of Irrigation Experiment for providing a superior experiment condition, Yaqun Xu master and staff of Hong Shi and Shuo Cai for assistance. Meanwhile, the authors thank Chunguo Liu and Dapeng Feng for their hard work during the experiment. At last, extend my heartfelt thanks to Professor Yuanlai Cui for his detailed guidance.