## Abstract

The discharge at Datong station may be not entirely representative of net discharge into the East China Sea due to water abstraction and precipitation along the lower Yangtze River. Therefore, Xuliujing station, which is much nearer to the river mouth, is chosen to accurately estimate the net discharge in this paper. The Multi-Profile Method that considers the cross-sectional variability of flow is applied at Xuliujing station to estimate the tidal discharge. Then, the low-pass filter is used to remove the effects of the tide and the net discharge is obtained. Lastly, the net discharge in Datong and that in Xuliujing are compared. The results show that the net discharge of Xuliujing is obviously larger than that of Datong in the rainy season due to precipitation, but the net discharge of Xuliujing is slightly smaller than that of Datong in the dry season due to persistent abstraction and less precipitation. Therefore, in some degree, the net discharge of Xuliujing is more representative than that of Datong regarding the discharge into the East China Sea.

## NOMENCLATURE

*A*cross-sectional area

- ADCP
Acoustic Doppler Current Profiler

*a*_{0},*a*_{1},*a*_{2}*u-U*model coefficients*b*constant in

*u-U*model*c*_{0},*c*_{1},*c*_{2}polynomial coefficients in

*G-A*relationship model- FPADCP
Fixed-Profile ADCP

*G*water level

*H*depth of water

- IVM
Index Velocity Method

- MPM
Multi-Profile Method

*Q*_{data}discharge measured by VMADCP

*Q*_{fit}estimated discharge

*RMSE*Root Mean Square Error

*RSD*Relative Standard Deviation

*U*mean channel velocity

*U*_{data}*Q*_{data}/*A**U*_{fit}estimated mean channel velocity

*u*index velocity

*u*_{i}index velocity in profile C

_{i}- VMADCP
Vessel-Mounted ADCP

*WN*number of depth bins

*λ*_{i}coefficient of

*u*in_{i}*u-U*model

## INTRODUCTION

Net discharge of estuaries is a key parameter in providing a reliable basis for water resources protection and planning (Kawanisi *et al.* 2009). The Yangtze Estuary, the largest estuary in China, is world-famous for its great abundance and development intensity of soil and water, water transport and fishery resources. With an annual average discharge rate of 3.0 × 10^{4} m^{3}/s, this river accounts for 90% of the total freshwater discharge into the East China Sea (Beardsley *et al.* 1985; Chen *et al.* 2001b). Datong is the last permanent hydrometric station with long discharge records on the main Yangtze River, located at the tidal limit of the Yangtze Estuary (Figure 1(a)). Downstream from this point, there is no large tributary, and the discharge is difficult to observe owing to the tidal influence. Thus, the discharge in Datong is commonly regarded as the net discharge into the East China Sea.

However, Datong is situated over 500 km away from the estuary (Figure 1(a)). On the one hand, the region along the lower Yangtze River is one of the most developed areas in China, containing nine cities and 13 countries. Thus, water abstraction and drainage could reduce the discharge into the estuary substantially during a dry year or a dry period (Chen *et al.* 2002; Zhang *et al.* 2012). In addition, agricultural irrigation and water transfer projects have become most important for seasonal changes in water discharge to the sea (Yang *et al.* 2015). On the other hand, the tributaries of the lower Yangtze River may transfer a considerable amount of runoff discharge to the main stream during the rainy season. In a word, cultivated fields accelerate the speed of runoff from agricultural fields into the Yangtze River during the flood season, while during droughts they take up a tremendous amount of water to the agricultural fields and decrease the water discharge into the estuary (Chen *et al.* 2001a). Therefore, the discharge measured in Datong may not be regarded as the net discharge into the East China Sea (Liu 2016).

The combined effects of water abstraction, agricultural irrigation and precipitation along the lower Yangtze River are likely to decrease, increase or not change the discharge into the sea, the key reference being the net discharge measured in the Yangtze Estuary. Xuliujing is about 110 km from the river mouth (Figure 1(a)) with a cross-sectional width of nearly 6 km (Figure 1(b)), and it is the demarcation point of the South and North tributaries and the starting point of multi-level branching in the Yangtze Estuary. Therefore, Xuliujing is an ideal section for determining the net discharge of the Yangtze River into the East China Sea.

According to the previous study, the flow in Xuliujing is complex and a non-synchronized current exists in the whole section (Zhao *et al.* 2016). Due to the intertidal variations of flow between thalweg and shallow water areas, the Multi-Profile Method (MPM) proposed by Zhao *et al.* (2016) is used for estimating the tidal discharge firstly in this paper. Then, the estimated instantaneous discharge in Xuliujing is low-pass filtered to remove the effects of the tide and the net discharge in Xuliujing can be obtained. Lastly, the net discharge in Datong and that in Xuliujing are compared and the difference between them is also discussed.

## DATA AND METHODS

### Data collection

To obtain the instantaneous discharge, a discharge monitoring system was designed and operated at the Xuliujing section by Zhao *et al.* (2016). Three upward-looking ADCPs with 300 kHz were mounted on the river bed of locations C1, C2 and C3 (Figure 1(b)), named the Fixed-Profile ADCP (FPADCP). The length of depth cell and sampling interval were set as 1.0 m and 0.5 hours in the FPADCP measurement. The tidally averaged depths of the three fixed profiles are 14.9 m, 51.5 m and 9.7 m, respectively. Three groups of FPADCP data in 2011 were extracted for calibrating mean channel velocity models (Table 1). Another three groups of data were also extracted in 2012 for validating the models (Table 2). In addition, a stage station was laid in the south end of the section to estimate the cross-sectional area (Figure 1(b)).

Time of data collection . | N
. | G_{max} (m)
. | G_{min} (m)
. | A_{max} (10^{4} m^{2})
. | A_{min} (10^{4} m^{2})
. | Q_{max}_{,}_{ebb} (10^{4} m^{3}/s)
. | Q_{max}_{,}_{flood} (10^{4} m^{3}/s)
. |
---|---|---|---|---|---|---|---|

Mar. 17 08:00, 2011 to Mar. 18 14:30, 2011 | 62 | 3.65 | 1.10 | 8.39 | 7.28 | 5.72 | −8.48 |

July 02 11:00, 2011 to July 03 16:00, 2011 (spring tide) | 59 | 4.78 | 1.82 | 9.27 | 7.82 | 10.80 | −9.71 |

Oct. 14 11:00, 2011 to Oct. 15 16:30, 2011 | 60 | 4.27 | 1.42 | 8.94 | 7.59 | 8.06 | −10.80 |

Time of data collection . | N
. | G_{max} (m)
. | G_{min} (m)
. | A_{max} (10^{4} m^{2})
. | A_{min} (10^{4} m^{2})
. | Q_{max}_{,}_{ebb} (10^{4} m^{3}/s)
. | Q_{max}_{,}_{flood} (10^{4} m^{3}/s)
. |
---|---|---|---|---|---|---|---|

Mar. 17 08:00, 2011 to Mar. 18 14:30, 2011 | 62 | 3.65 | 1.10 | 8.39 | 7.28 | 5.72 | −8.48 |

July 02 11:00, 2011 to July 03 16:00, 2011 (spring tide) | 59 | 4.78 | 1.82 | 9.27 | 7.82 | 10.80 | −9.71 |

Oct. 14 11:00, 2011 to Oct. 15 16:30, 2011 | 60 | 4.27 | 1.42 | 8.94 | 7.59 | 8.06 | −10.80 |

*N* means the number of records, *G*_{max}, *G*_{min}, *A*_{max}, *A*_{min}, *Q*_{max,ebb} and *Q*_{max,flood} means maximum water level, minimum water level, maximum cross-sectional area, minimum cross-sectional area, maximum discharge of ebb tide and maximum discharge of flood tide during the data collection, respectively.

Time of data collection . | N
. | G_{max} (m)
. | G_{min} (m)
. | A_{max} (10^{4} m^{2})
. | A_{min} (10^{4} m^{2})
. | Q_{max}_{,}_{ebb} (10^{4} m^{3}/s)
. | Q_{max}_{,}_{flood} (10^{4} m^{3}/s)
. |
---|---|---|---|---|---|---|---|

Mar. 10 12:00, 2012 to Mar. 11 17:00, 2012 | 59 | 4.28 | 1.46 | 8.82 | 7.48 | 8.74 | −9.68 |

July 04 12:00, 2012 to July 05 16:00, 2012 (spring tide) | 57 | 5.12 | 1.98 | 9.16 | 7.71 | 11.20 | −9.65 |

Oct. 16 11:00, 2012 to Oct. 17 16:00, 2012 (spring tide) | 59 | 5.38 | 1.37 | 9.39 | 7.48 | 9.61 | −13.80 |

Time of data collection . | N
. | G_{max} (m)
. | G_{min} (m)
. | A_{max} (10^{4} m^{2})
. | A_{min} (10^{4} m^{2})
. | Q_{max}_{,}_{ebb} (10^{4} m^{3}/s)
. | Q_{max}_{,}_{flood} (10^{4} m^{3}/s)
. |
---|---|---|---|---|---|---|---|

Mar. 10 12:00, 2012 to Mar. 11 17:00, 2012 | 59 | 4.28 | 1.46 | 8.82 | 7.48 | 8.74 | −9.68 |

July 04 12:00, 2012 to July 05 16:00, 2012 (spring tide) | 57 | 5.12 | 1.98 | 9.16 | 7.71 | 11.20 | −9.65 |

Oct. 16 11:00, 2012 to Oct. 17 16:00, 2012 (spring tide) | 59 | 5.38 | 1.37 | 9.39 | 7.48 | 9.61 | −13.80 |

Meaning of the symbols is the same as in Table 1.

Meanwhile, Vessel-Mounted Acoustic Doppler Current Profiler (VMADCP) measurements were also implemented at every 0.5 hour in corresponding periods (Table 1) to obtain the discharge in the measured zone of the cross-section. The discharge of the unmeasured zone at the top and bottom was extrapolated by a best velocity model (Chen *et al.* 2016). Lastly, the discharge defined as *Q*_{data} can be obtained by VMADCP measurements of discharge plus extrapolated discharge of the unmeasured zone. With the calculated cross-sectional area (elaborated in the following section), *Q*_{data} can be used for calibrating and validating mean channel velocity models and evaluating discharge estimation methods.

In order to compare and verify the difference of net discharge between Datong and Xuliujing, the precipitation data in Nanjing and Shanghai cities (Figure 1(a)) on the lower Yangtze are also obtained from the national hydrometric stations. In addition, information about water abstractions and drainages along the river banks are based on documented material from local government agencies and the work of Liu (2016).

### Multi-profile discharge estimation

The following paragraphs will briefly outline the MPM; more details can be found in Zhao *et al.* (2016).

#### Mean channel velocity estimation

*v*at each of the depth bins of a profile. So, the depth-mean velocity

_{i}*u*used as index velocity can be represented as the following: where

*WN*is the number of depth bins. Similarly, index velocity can also be obtained by ultrasonic velocity meters which are set in both sides of the river (Ruhl & Simpson 2005) or Horizontal-ADCP (Simpson & Bland 2000). Then, the relationship between mean channel velocity

*U*and

*u*can be expressed in a linear form (Chen & Chiu 2002) or a polynomial form (Ruhl & Simpson 2005), namely, the

*u-U*model: where

*a*

_{0},

*a*

_{1}and

*a*

_{2}are the model coefficients.

*U*can be solved by VMADCP discharge measurement and bathymetry measurement. Once

*U*and

*u*are acquired, these coefficients can be solved by least squares.

*et al.*2016), so the above Index Velocity Method (IVM) by using a single ADCP profile set at the thalweg cannot get a good estimation of discharge. Then, the relationship between mean channel velocity

*U*with the three index velocities

*u*in Xuliujing can be expressed as the following: where

*u*is the depth-mean velocity of the C

_{i}*profile,*

_{i}*λ*is the coefficient of

_{i}*u*, and

_{i}*b*is a constant. The principle of the multi-profile model depicted in Equation (3) can be understood as being that the mean channel velocity

*U*is the result of the weighted average of all the three depth-mean velocities. The method represents a multiple linear regression with

*u*as independent variables. In theory, the stronger the representativeness of the

_{i}*i*th profile is, the larger

*λ*should be.

_{i}From the above depiction, MPM is an expansion of the traditional IVM by which the mean channel velocity *U* is estimated by the multiple ADCP profiles. The *u-U* model in the IVM is calibrated by only one depth-mean velocity as shown in Equation (2), but the *u-U* model in the MPM is calibrated by two or more depth-mean velocities as shown in Equation (3). In addition, on the one hand, for the IVM, the sole ADCP must be mounted at the thalweg of the section to obtain the velocity of the main stream. However, on the other hand, the multiple ADCPs can be mounted on the thalweg and river banks for the MPM, which can take the flow velocity variation near the bank into account.

#### Cross-sectional area estimation

*G*in the tidal reaches, real-time measurement of cross-sectional area

*A*is impossible. The

*G-A*relationship model provides an available way to solve the problem. The general

*G-A*model can be expressed as a polynomial form (Ruhl & Simpson 2005): where

*c*

_{0},

*c*

_{1}and

*c*

_{2}are polynomial coefficients, and they can also be solved by least squares.

### Calculation of discharge

*U*and the cross-sectional area

*A*, the instantaneous discharge

*Q*

_{fit}can be calculated as

*U*multiplied by

*A*. If the discharge

*Q*

_{data}measured by VMADCP is the true value, the accuracy of the estimated discharge

*Q*

_{fit}can be assessed by the Root Mean Square Error (

*RMSE*) or Relative Standard Deviation (

*RSD*): where

*N*is the number of discharge data. Once the time series of the tidal discharge has been calculated, a low-pass Butterworth filter can be applied to the data to remove the high-frequency tidal signals and then the net discharge can be obtained (Roberts & Roberts 1978). By comparing the net discharge at Xuliujing with that at Datong, the impact of water abstraction and precipitation along the lower Yangtze River on the change of net discharge into the East China Sea can be found.

## RESULTS AND DISCUSSION

### Calculation of tidal discharge

After obtaining the mean channel velocity models and cross-sectional area models which are calibrated by data from 2011, the corresponding three sets of data of cross-sectional area *A* and the mean channel velocities *U* in 2012 can also be calculated. Then, the instantaneous discharges *Q*_{fit} can be estimated. Comparing with the discharge *Q*_{data} measured at the same periods, the *RMSE* and *RSD* can be calculated to assess the accuracy of discharge estimated by the IVM and MPM (Figure 2).

Theoretically, the accuracies of *U*, *A* and *Q* are all influenced by the errors in flow velocity *u* and water level *G*. The influence can be estimated by the law of error propagation. Supposed that the *U* is about 1.0 m/s and the mean *A* is about 78,000 m^{2}, the accuracies of *u* and *G* are less than 0.05 m/s and 0.02 m in our experiment, which will induce about 0.04 m/s of *U* error according to the *u-U* models shown in Equation (3) and 96 m^{2} of *A* error according to Equation (4), and finally will induce 3,141 m^{3}/s of *Q* error and 4.0% of relative estimation error. From this perspective, although the mean channel velocity estimation accuracy of the MPM was only improved by 0.02 m/s relative to that of the IVM (the calculation procedure of mean channel velocity is omitted), the discharge estimation accuracy can be improved by about 1,260 m^{3}/s and 1.3% of relative discharge estimation. However, from Figure 2 we can see, the discharge estimation accuracy of the MPM is improved by 3,750 m^{3}/s and the relative discharge estimation is improved by 5.1% relative to that of the IVM, which are far greater than the theoretical values of 1,260 m^{3}/s and 1.3%, respectively. Therefore, for the Yangtze River with an annual average discharge of 3.0 × 10^{4} m^{3}/s, the improvement in the MPM is necessary and meaningful.

Figure 3 shows the time series of discharges *Q*_{fit} (red line) estimated by the MPM and the measured discharges *Q*_{data} (blue line) in the three periods shown in Table 2. It can be found that both of them have a higher consistency in nearly all the tide cycles except for some peak values. This further proves that the MPM is valid in the tidal discharge estimation of a large estuary.

### Calculation of net discharge

After the data of tidal discharge have been calculated, a low-pass Butterworth filter is applied to the data to remove the high-frequency tidal signals. A stopband period of 30 hours and a passband period of 40 hours are used: signals with periods less than 30 hours are not transmitted to the filtered data; signals with periods greater than 40 hours are transmitted to the filtered data with minimal loss; and signals that fall in the transition between the stopband and the passband are damped, but some fraction of them are transmitted to the filtered data. Filter ringing causes erroneous data at the beginning and end of a continuous data set; therefore, data for 2 days at the beginning and end of the time series and on either side of a data gap are rejected as part of this process.

Figure 4 shows the tidal discharge and filtered (net) discharge in March, July and October of 2011, and Figure 5 shows the monthly precipitation of 2011 at Shanghai and Nanjing, which are located on the lower Yangtze River (Figure 1(a)). It is clear to see that the averaged net discharge in summer (about 42,000 m^{3}/s) is much larger than that in spring (about 10,000 m^{3}/s) and autumn (about 22,000 m^{3}/s). The reason for this is that rainfall along the Yangtze drainage basin directly controls the pattern of annual discharge distribution (Figure 5). The rainy season along the entire Yangtze drainage basin usually occurs from May to September. Precipitation along the lower basin is primarily between March and August, amounting to nearly 73% of the annual total (Chen *et al.* 2001b). In contrast, precipitation in the winter season (December and January) usually represents <1%. In this sense, the calculated net discharge is highly consistent with the precipitation, which indicates its rationality.

### Comparison between the net discharge in Datong and Xuliujing

To quantify the difference of net discharge between the upstream and downstream of the Yangtze Estuary, net discharge in Datong (blue solid line), Xuliujing (red solid line) and the difference between them (green solid line) in 2011 are calculated and shown in Figure 6. It can be seen that the net discharge in Datong is basically consistent with that in Xuliujing during the whole year. However, in summer and autumn, especially in June, July, August and September, the net discharge in Xuliujing is obviously larger than that in Datong. In contrast, the net discharge of Xuliujing is slightly smaller than that of Datong in spring.

In order to explain the inconsistency of net discharge in some months of 2011, Figure 7 presents the monthly abstraction (blue bar), drainage (red bar) and the difference between them (green bar) from Datong to Xuliujing in 2011. According to Figure 7, it can be found that there is not much difference in abstraction through the whole year with all of them in the range 15 × 10^{8}–40 × 10^{8} m^{3}. However, the difference in drainage between the 12 months is remarkable due to precipitation and the values range from 5 × 10^{8} m^{3} (dry season) to 95 × 10^{8} m^{3} (rainy season). As a result, the difference of net discharge between Xuliujing and Datong (drainage minus abstraction) is positive in the rainy season and the net discharge is negative in the dry season. In other words, the net discharge of Xuliujing is more than that of Datong in the rainy season due to precipitation, but the net discharge of Xuliujing is slightly smaller than that of Datong in the dry season due to persistent abstraction and less precipitation.

Moreover, it is also worth noting that the discharge peak in Xuliujing is obviously delayed compared to that in Datong. According to a previous study (Zhang *et al.* 2012), 6 days are usually regarded as the time required for water to travel from Datong to the estuary. Therefore, the net discharge in Xuliujing is advanced by 6 days (red dotted line), and the difference between it and the net discharge in Datong is also calculated and shown in Figure 6 (green dotted line). From the figure, we can see that the advanced net discharge curve of Xuliujing is in good agreement with that of Datong, especially at the peak values. However, the conclusion remains unchanged that the net discharge of Xuliujing is larger than that of Datong in the rainy season and less than that of Datong due to the huge abstraction. The most likely explanation is that the deviation can be justified by the fact of flood (or generally hydrograph) routing.

## CONCLUSIONS

- (1)
The discharge estimation accuracy of the MPM is improved by 3,750 m

^{3}/s and relative discharge estimation is improved by 5.1% relative to that of the IVM in our experiments, which are far greater than the theoretical values of 1,260 m^{3}/s and 1.3%, respectively. Therefore, for large rivers like the Yangtze River, Nile River, Mississippi River and Amazon etc., the improvement is necessary and meaningful. - (2)
Rainfall along the Yangtze drainage basin directly controls the pattern of annual discharge distribution so that the averaged net discharge in summer is much larger than that in spring and winter.

- (3)
The net discharge of Xuliujing is more than that of Datong in the rainy season due to precipitation, but the net discharge of Xuliujing may be less than that of Datong in the dry season due to persistent abstraction and less precipitation. Therefore, in some degree, the net discharge of Xuliujing is more representative than that of Datong for regarding discharge into the East China Sea.

## ACKNOWLEDGEMENTS

The authors are grateful to the Yangtze Estuary Hydrology and Water Resources Survey Bureau for their generosity of providing the valuable observation data. This work would also not have been possible without the funding support of NSFC (Natural Science Foundation of China) (coded by 41404026), the Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG (coded by WE2016008), Research Funding of East China University of Technology (coded by DHBK2015312), Research Foundation of Education Bureau of Jiangxi Province (coded by GJJ150559), Natural Science Foundation of Jiangxi Province, China (coded by 20161BAB206163) and Director Foundation of the Second National Oceanic Research Institute of the State Oceanic Administration (coded by JG-1508).

## REFERENCES

*Water Abstraction along the Yangtze River Downstream from Datong to Estuary and Its Impact on Water Discharge into Estuary*

*Master's Thesis*

*.*