# An Alternative Statistical Model for Predicting Salinity Variations in Estuaries

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data Source

#### 2.1. Study Area

^{2}, with a total length of more than 1600 km and a coastline extending over 450 km from east to west [32]. There are eight outlets of the Pearl River delta. The North River and the East River mainly flow into the Lingding Bay through four east outlets (Humen, Jiaomen, Hongqimen and Hengmen), while the West River mainly runs into the South China Sea and Huangmao Bay through four west outlets (Modaomen, Jitimen, Hutiaomen and Yamen). Such vast river networks lead to rather complicated hydrodynamics and salinity variations of the PRE.

#### 2.2. Data Source

## 3. Model Development

#### 3.1. Relationship between Salinity and River Discharge

_{t−i}is the daily average river discharge of the previous day t − i and $\tilde{{Q}_{t}}$ is the weighed daily average river discharge.

^{2}) for the three stations, indicating that it is insufficient to simply consider the memory effects of river discharge on salinity. Moreover, when the station is closer to the estuary, the effect of river discharge becomes weaker, as manifested by R

^{2}being reduced from 0.3586 to 0.2684 (Figure 3).

#### 3.2. Relationship between Salinity and Tidal Range

#### 3.3. Model Formulation

_{t}is the salinity on day t and S

_{t−i}is the salinity of the previous day t − i.

_{t}is the predicted salinity on day t and A, B and C are the correction coefficients.

## 4. Model Calibration, Application and Further Tests

#### 4.1. Model Calibration

^{2}), an indicator of the percent of variation of the measured salinity explained by the predicted salinity; (2) the root-mean-square error (RMSE), a measure of the deviation of the predicted salinity from the measured salinity; and (3) the Nash–Sutcliffe efficiency coefficient (NSE), which indicates how well the plot of observed versus predicted data fits the 1:1 linear regression line. The NSE may range between −∞ and 1, with 1 being the optimal value [30]. Mathematical equations of R

^{2}, RMSE and NSE are givenas follows:

_{i}is the measured salinity, $\overline{M}$ is the mean of the measured salinity, P

_{i}is the predicted salinity and $\overline{P}$ is the mean of the predicted salinity.

^{2}, RMSE and NSE show the improved prediction accuracy of the model. For example, R

^{2}gradually increases to 0.9208 from downstream to upstream, and the RMSE ranges from 0.4201 at Pinggang pumping station to 1.2363 at Guangchang pumping station. Tidal dynamics mainly affect the salinity of the upstream river and barely exert influence on that of the downstream river. Therefore, the hysteresis effect on the salinity of the upstream river is stronger than that on the salinity of the downstream river.

#### 4.2. Model Application

^{2}, RMSE and NSE. For the three stations, the values of R

^{2}all reach 0.85, indicating a good match between the measured and predicted salinities. The agreement is further demonstrated by the comparison of salinity measurements and predictions in Figure 7. These results of real-world model application prove that the statistical model considering the memory effects of river discharge and salinity is more accurate.

#### 4.3. Further Tests

#### 4.3.1. Sensitivity Analysis of River Discharge

_{Q}is the predicted salinity contributed by river discharge.

_{Q}changes considerably, whereas S

_{t}varies slightly. In contrast, with a 50% reduction in river discharge, both S

_{Q}and S

_{t}increase notably. The comparison indicates that, when river discharge is small, salinity variation at estuaries is more sensitive to the changes. While under conditions of large river discharge, salinity variation becomes less sensitive.

#### 4.3.2. Cross-Validation

^{2}, RMSE and NSE) of model calibration and application (Table 2) show that the prediction results are satisfactory, further demonstrating the improved model performance.

#### 4.3.3. Analysis of Weekly Prediction

^{3}/s (small), 2000 m

^{3}/s (medium) and 9000 m

^{3}/s (large). Figure 11 shows that salinity prediction for the next 7days in all three cases is relatively accurate. In particular, when river discharge is large enough (e.g., 9000 m

^{3}/s in Figure 11c), it almost completely prevents SI, and the salinity for the next 7 days is close to 0‰, which can be replicated by the statistical model.

#### 4.3.4. Analysis of Short-Term Time-Series

## 5. Conclusions

^{2}, RMSE and NSE.

_{Q}and S

_{t}are significantly higher than the decreasesin S

_{Q}and S

_{t}in the case of a 50% increase in river discharge. Salinity variation is more sensitive to smaller river discharge. In addition, the reliability of salinity prediction for the next 7days was examined using river discharge of three levels: small (1400 m

^{3}/s), medium (2000 m

^{3}/s) and large (9000 m

^{3}/s). In all three cases, the model accurately predicted the salinity variation.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Dataof (

**a**) daily average river discharge measured at Wuzhou station and Shijiao station and (

**b**) daily average salinity measured at Pinggang, Lianshiwan and Guangchang pumping stations collected from October 2007 to February 2008.

**Figure 3.**Regression between weighed daily average river discharge and daily average salinity at (

**a**) Pinggang, (

**b**) Lianshiwan and (

**c**) Guangchang. Lines are the best-fit regression lines.

**Figure 4.**Time series of daily maximum tidal range measured at Sanzao and daily average salinity measured at Pinggang, Lianshiwan and Guangchang from October 2007 to February 2008.

**Figure 5.**Comparison of salinity calculated by Equations (5), (7) and (8) and measured salinity at (

**a**) Pinggang, (

**b**) Lianshiwan and (

**c**) Guangchang.

**Figure 6.**Plots of measured salinity versus simulated salinity at (

**a**) Pinggang, (

**b**) Lianshiwan (

**c**) Guangchang during the model calibration period. Lines are the best fit 1:1 regression lines.

**Figure 7.**Comparison of measured and predicted salinity at (

**a**) Pinggang, (

**b**) Lianshiwan, (

**c**) Guangchang and (

**d**) Pinggangfrom September 2012 to February 2013.

**Figure 8.**Comparison of S

_{Q}and S

_{t}of different river discharges at Guangchang station. (

**a**) S

_{Q}of different river discharges at Guangchang station (

**b**) S

_{t}of different river discharges at Guangchang station.

**Figure 9.**Comparison of measured and predicted salinity at (

**a**) Pinggang station and (

**b**) Guangchangstation from September 2011 to February 2012.

**Figure 10.**Comparison of measured and predicted salinity at (

**a**) Pinggang, (

**b**) Guangchangand (

**c**) Pinggang stations.

**Figure 11.**Comparison of measured and predicted salinity of the upcoming 7 days under conditions of (

**a**) small, (

**b**) medium and(

**c**) large river discharge at Guangchang station.

**Figure 12.**Comparison of measured and simulated salinity at (

**a**) Pinggang, (

**b**) Guangchang and (

**c**) Pinggang stationsfrom October 2007 to December 2007.

**Figure 13.**Comparison of measured and predicted salinity at (

**a**) Pinggang, (

**b**) Guangchang and (

**c**) Pinggang stations from January 2008 to February 2008.

Location | A | B | C |
---|---|---|---|

Pinggang | 2.4429 | −0.0013 | 0.5711 |

Lianshiwan | 3.1579 | −0.0006 | 0.6701 |

Guangchang | 4.8074 | −0.0005 | 0.6349 |

**Table 2.**Summary statistics of model calibration from 2007 to 2008 and model application from 2011 to 2013.

Location | n | $\overline{\mathit{O}}$ (‰) | O_{min} (‰) | O_{max} (‰) | R^{2} | RMSE (‰) | NSE |
---|---|---|---|---|---|---|---|

Pinggang | |||||||

Calibration (2007–2008) | 130 | 1.0847 | 0.0146 | 5.7379 | 0.9208 | 0.4201 | 0.9207 |

Application (2011–2012) | 176 | 1.1040 | 0.0212 | 5.7767 | 0.9195 | 0.5066 | 0.8750 |

Application (2012–2013) | 154 | 0.1622 | 0.0158 | 2.6646 | 0.8560 | 0.1551 | 0.8377 |

Lianshiwan | |||||||

Calibration (2007–2008) | 130 | 3.1935 | 0.1633 | 8.8179 | 0.8823 | 0.8553 | 0.8822 |

Application (2011–2012) | 142 | 2.8297 | 0.0053 | 9.2096 | 0.8904 | 0.8946 | 0.8882 |

Guangchang | |||||||

Calibration (2007–2008) | 130 | 4.7043 | 0.3429 | 9.2829 | 0.7836 | 1.2363 | 0.7876 |

Application (2011–2012) | 176 | 5.2052 | 0.0173 | 15.9654 | 0.8617 | 1.4963 | 0.8503 |

**Table 3.**Summary statistics of model performance for model calibration from October 2007 to December 2007 and model application from January 2008 to February 2008.

Location | n | $\overline{\mathit{O}}$ (‰) | O_{min} (‰) | O_{max} (‰) | R^{2} | RMSE (‰) | NSE |
---|---|---|---|---|---|---|---|

Pinggang | |||||||

Calibration (23 October 2007 to 31 December 2007) | 70 | 1.1142 | 0.0200 | 5.7379 | 0.9361 | 0.3763 | 0.9361 |

Application (1 January 2008 to 29 February 2008) | 60 | 1.0502 | 0.0146 | 5.0863 | 0.9025 | 0.4702 | 0.9012 |

Lianshiwan | |||||||

Calibration (23 October 2007 to 31 December 2007) | 70 | 3.1534 | 0.2342 | 8.2496 | 0.8694 | 0.8761 | 0.8694 |

Application (1 January 2008 to 29 February 2008) | 60 | 3.2403 | 0.1633 | 8.8179 | 0.8593 | 0.8946 | 0.8339 |

Guangchang | |||||||

Calibration (1 January 2008 to 29 February 2008) | 70 | 5.0674 | 0.8933 | 9.2304 | 0.7235 | 1.3283 | 0.7235 |

Application (1 January 2008 to 29 February 2008) | 60 | 4.2807 | 0.3429 | 9.2829 | 0.8359 | 1.1329 | 0.8294 |

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## Share and Cite

**MDPI and ACS Style**

Ye, R.; Kong, J.; Shen, C.; Zhang, J.; Zhang, W.
An Alternative Statistical Model for Predicting Salinity Variations in Estuaries. *Sustainability* **2020**, *12*, 10677.
https://doi.org/10.3390/su122410677

**AMA Style**

Ye R, Kong J, Shen C, Zhang J, Zhang W.
An Alternative Statistical Model for Predicting Salinity Variations in Estuaries. *Sustainability*. 2020; 12(24):10677.
https://doi.org/10.3390/su122410677

**Chicago/Turabian Style**

Ye, Ronghui, Jun Kong, Chengji Shen, Jinming Zhang, and Weisheng Zhang.
2020. "An Alternative Statistical Model for Predicting Salinity Variations in Estuaries" *Sustainability* 12, no. 24: 10677.
https://doi.org/10.3390/su122410677