# Application of Stage-Fall-Discharge Rating Curves to a Reservoir Based on Acoustic Doppler Velocity Meter Measurement Data

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## Abstract

**:**

^{3}/s (3.13 m

^{2}/s, specific discharge). In terms of the hydrograph reconstruction, compared with the conventional simple rating curve, the SFD developed using ADVM data exhibited a higher agreement with the measured data in terms of the pattern. Furthermore, the measured discharge over 1000 m

^{3}/s primarily ranged between 97.5% and 2.5% in the graph comparing the ratio of the median and observed discharge. Based on this experiment, it is confirmed that the SFD rating curve with data to represent the backwater effect, such as ADVM data, can reduce the uncertainties induced by the typical rating curve

## 1. Introduction

## 2. Methods

#### SFD Rating Curves

## 3. Study Area and Data

^{3}/s, 14 data points) and the ADCP (under 1000 m

^{3}/s, 23 data points) at Geum nam Br. from 21 February 2017 to 14 November 2017. The water stage is the average value at the start time and end time of the discharge measurement at each water stage gauging station. These data are referred to as “ADCP data”. The second set of data are ADVM data obtained at 10 min intervals from 1 January 2017 to 14 November 2017. When applying the proposed method based on the Bayesian approach, the use of an excessive amount of data may lead to memory and computational problems. Therefore, the available data points (45,513) are reduced to 356 points by excluding certain data. (1) The data observed in July are only used since the largest flood occurred in July. (2) The data with discharge over 750 m

^{3}/s (3.23 m

^{2}/s, specific discharge) was used without data reduction. (3) Among the data with discharge under 750 m

^{3}/s, the data with water level change of less than 5 cm in time series was removed.

## 4. Results

#### 4.1. SFD Rating Curves

^{2}) are introduced. The calculation results are presented in Table 2.

^{2}are closer to zero and one, respectively, indicating a higher agreement between the calculated and observed values. As shown in Table 2, the MAPE of the rating curve derived using the ADVM data is larger than that of the rating curve derived by the ADCP data because the errors in the ADVM data in the low flow range are relatively large. The maximum percentile errors for each sample in the ADCP and ADVM data are 52.8% and 133.8%, respectively. However, the indicators, namely, MAPE, RMSE, RSR, and R

^{2}, indicate that the rating curve derived from the ADVM data is reasonable.

#### 4.2. Error Distribution of SFD Rating Curves

^{3}/s, likely because of the effect of the opening and closing of the sluice gate.

^{3}/s. The difference between the calculated and observed values in the case of the ADVM data is larger than that for the field data because of the automatic flow rate measurement uncertainty and because a large part of the ADVM data pertains to low flow rate sections. In addition, when automatic flow rate measurement data are used, considerable changes in the flow rate may occur even when the upstream and downstream water levels are the same. Therefore, future research must be focused on calculating the representative flow rate.

#### 4.3. Comparison between SFD and the General-Regression-Based Rating Curve

## 5. Conclusions

^{3}/s is considered to evaluate the influence of the gate operation and flow regime on the variable slope. This aspect is determined using the graph comparing the ratio of the median and observed discharge.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Westphal, J.A.; Thompson, D.B.; Stevens, G.T., Jr.; Strauser, C.N. Stage-Discharge Relations on the Middle Mississippi River. J. Water Resour. Plan. Manag.
**1999**, 125, 48–53. [Google Scholar] [CrossRef] - Gergov, G.; Karagiozova, T. Unique discharge rating curve based on the morphology parameter Z. Int. Assoc. Hydrol. Sci. Publ.
**2003**, 278, 3–8. [Google Scholar] - Reitan, T.; Petersen-Øverleir, A. Dynamic rating curve assessment in unstable rivers using Ornstein-Uhlenbeck processes. Water Resour. Res.
**2011**, 47. [Google Scholar] [CrossRef] - Fenton, J.D.; Keller, R.J. The Calculation of Streamflow from Measurements of Stage; CRC for Catchment Hydrology: Boca Raton, FL, USA, 2001. [Google Scholar]
- Herschy, R.W. Streamflow Measurement; CRC Press: Boca Raton, FL, USA, 2002. [Google Scholar]
- Petersen-Øverleir, A.; Reitan, T. Bayesian analysis of stage-fall-discharge models for gauging stations affected by variable backwater. Hydrol. Process.
**2009**, 23, 3057–3074. [Google Scholar] [CrossRef] - Schmidt, A.R. Analysis of stage-discharge relations for open channel flow and their associated uncertainties. Ph.D. Thesis, University of Illinois at Urbana-Champaign, Champaign, IL, USA, 2002. [Google Scholar]
- Kim, Y.; Tachikawa, Y.; Kim, S.; Shiiba, M.; Yorozu, K.; Noh, S.J. Simultaneous estimation of inflow and channel roughness using 2D hydraulic model and particle filters. J. Flood Risk Manag.
**2013**, 6, 112–123. [Google Scholar] [CrossRef] - Lee, J.J.; Kwon, H.H. A basic study of stage-discharge rating stabilization at the Ssang-chi Gauging station. J. Korean Soc. Civ. Eng.
**2010**, 30, 81–87. [Google Scholar] - Lee, S.H.; Gang, S.U. Stream discharge estimation by hydraulic channel routing and stage measurement. J. Korea Water Resour. Assoc.
**2001**, 34, 543–549. [Google Scholar] - Corbett, D.M. Stream-Gaging Procedure, a Manual Describing Methods and Practices of the Geological Survey; US Government Printing Office: Washington, DC, USA, 1943. [Google Scholar] [CrossRef]
- Mansanarez, V.; Le Coz, J.; Renard, B.; Lang, M.; Pierrefeu, G.; Vauchel, P. Bayesian analysis of stage-fall-discharge rating curves and their uncertainties. Water Resour. Res.
**2016**, 52, 7424–7443. [Google Scholar] [CrossRef][Green Version] - Bayesian Hydraulic Rating Curve Programs. Available online: http://folk.uio.no/trondr/hydrasub/ratingcurve.html (accessed on 30 July 2020).
- Reitan, T.; Petersen-Øverleir, A. Bayesian power-law regression with a location parameter, with applications for construction of discharge rating curves. Stoch. Environ. Res. Risk Assess.
**2008**, 22, 351–365. [Google Scholar] [CrossRef] - Kim, Y.; Kim, J.Y.; An, H.U.; Jung, K.S. Improvement of the method using the coefficient of variation for automatic multi-segmentation method of a rating curve. J. Korea Water Resour. Assoc.
**2015**, 48, 807–816. [Google Scholar] [CrossRef]

**Figure 3.**Water levels at Sejong-ri and Geum nam Br. gauging stations and the differences between the values.

Location | Latitude | Longitude | Gauge Height of Zero Flow | Distance from Outlet (km) |
---|---|---|---|---|

Geum nam Br. | 127-16-15 | 36-28-40 | 10.308 | 102.49 |

Sejong-ri | 127-18-09 | 36-30-20 | 11.336 | 106.99 |

Classification | MAPE | RMSE | RSR | R^{2} |
---|---|---|---|---|

SFD_ADCP | 12.72% | 149.922 | 0.119 | 0.994 |

SFD_ADVM | 11.43% | 114.245 | 0.091 | 0.996 |

Time | W.L. at Geum Nam Br. (EL. m) | W.L. at Sejong-ri (EL. m) | Measured Q |
---|---|---|---|

2017.7.16 21:19 | 15.72 | 17.08 | 3594.04 |

2017.7.16 20:45 | 15.87 | 17.32 | 3498.74 |

2017.7.16 16:15 | 15.64 | 17.65 | 4566.66 |

2017.7.16 17:09 | 15.97 | 17.8 | 4223.44 |

**Table 4.**Estimated RMSE of the hydrograph from July to September, reproduced considering the rating curves with ADCP data and ADVM data measured from July to September.

Classification | ADVM Data | ADCP Data |
---|---|---|

HQ_TP (Typical rating curve) | 68 | 102 |

SFD_ADCP (SFD using ADCP data) | 84 | 136 |

SFD_ADVM (SFD using ADVM data) | 61 | 99 |

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**MDPI and ACS Style**

Kim, Y.; Oh, S.; Lee, S.; Byun, J.; An, H. Application of Stage-Fall-Discharge Rating Curves to a Reservoir Based on Acoustic Doppler Velocity Meter Measurement Data. *Water* **2021**, *13*, 2443.
https://doi.org/10.3390/w13172443

**AMA Style**

Kim Y, Oh S, Lee S, Byun J, An H. Application of Stage-Fall-Discharge Rating Curves to a Reservoir Based on Acoustic Doppler Velocity Meter Measurement Data. *Water*. 2021; 13(17):2443.
https://doi.org/10.3390/w13172443

**Chicago/Turabian Style**

Kim, Yeonsu, Sungryul Oh, Seungsoo Lee, Jisun Byun, and Hyunuk An. 2021. "Application of Stage-Fall-Discharge Rating Curves to a Reservoir Based on Acoustic Doppler Velocity Meter Measurement Data" *Water* 13, no. 17: 2443.
https://doi.org/10.3390/w13172443