# Estimating the Optimal Velocity Measurement Time in Rivers’ Flow Measurements: An Uncertainty Approach

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

## 3. Methods

^{3}/s for the different measurement times. To determine the variation of the uncertainty bandwidth, the percent difference was calculated every second (Equation (1)) where H

_{i}is the bandwidth value at a given time i.

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Dirección General de Aguas (DGA). Manual Básico para Instrucción de Hidromensores; Ministerio de Obras Públicas: Santiago de, Chile, 1991. [Google Scholar]
- U.S. Bureau of Reclamation (USBR). Water Measurement Manual; U.S. Department of the Interior: Washington, WA, USA, 2001.
- Fernández, G.; Fernández, H.; Meissl, A. Determinación de Incertidumbre de Medición de Caudal Líquido en Cauces; XXVII Congreso Latinoamericano de Hidráulica: Lima, Perú, 2016. [Google Scholar]
- U.S. Geological Survey (USGS). Discharge Measurements at Gaging Stations; USGS: Washington, WA, USA, 2010.
- U.S. Geological Survey (USGS). Measurement and Computation of Streamflow: Measurement of Stage and Discharge; USGS: Washington, WA, USA, 1983.
- McMillan, H.; Krueger, T.; Freer, J. Benchmarking observational uncertainties for hydrology: Rainfall, river discharge and water quality. Hydrol. Process
**2012**, 26, 4078–4111. [Google Scholar] [CrossRef] - Westerberg, I.K.; McMillan, H.K. Uncertainty in hydrological signatures. Hydrol. Earth Syst. Sci.
**2015**, 19, 3951–3968. [Google Scholar] [CrossRef] [Green Version] - United Nations Educational, Scientific and Cultural Organization (UNESCO). Hidrología y Desarrollo de Los Recursos Hídricos en un Medio Ambiente Vulnerable; Programa Hidrológico Internacional: París, Francia, 1996. [Google Scholar]
- Coxon, G.; Freer, J.; Westerberg, I.K.; Wagener, T.; Woods, R.; Smith, P.J. A novel framework for discharge uncertainty quantification applied to 500 UK gauging stations. Water Resour. Res.
**2015**, 51, 5531–5546. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Saldías, L. Automatización de Aforos y Reportes de Terreno en Ingeniería Hidráulica. Civil Engineering Thesis, Universidad Católica de la Santísima Concepción, Concepción, Chile, May 2016. [Google Scholar]
- Helmbrecht, J.; López, J.; Villegas, J. Cálculo de Incertidumbres en la Medida de Caudales en Ríos y Canales: Herramientas y Aplicaciones Prácticas Innovadoras. Ingeniería del Agua. 2004. Available online: http://www.ingenieriadelagua.com/2004/jia/jia2011/pdf/p588.pdf (accessed on 28 July 2018).
- International Organization for Standardization (ISO 748-2007). Hidrometría. In Medida del Caudal de Líquidos en Canales Abiertos Utilizando Medidores de Caudal o Flotadores; AENOR: Madrid, España, 2007. [Google Scholar]
- Beven, K.; Binley, A. The future of distributed models: Model calibration and uncertainty prediction. Hydrol. Process
**1992**, 6, 279–298. [Google Scholar] [CrossRef] - Hornberger, G.M.; Spear, R. An approach to the preliminary analysis of environmental systems. J. Environ. Manag.
**1981**, 12, 7–18. [Google Scholar] - Spear, R.C.; Grieb, T.M.; Shang, N. Parameter uncertainty and interaction in complex environmental models. Water Resour. Res.
**1994**, 30, 3159–3169. [Google Scholar] [CrossRef] - Paredes, P. Sobre el rol de la Incertidumbre Hidrológica en la Modelación de Inundaciones a Gran Escala: Río Usumacinta, Tabasco. Master’s Thesis, Universidad Nacional Autónoma de México, México, 2013. [Google Scholar]
- Camacho, L.; Cantor, M. Calibración y análisis de la capacidad predictiva de modelos de transporte de solutos en un río de montaña colombiano. Avances Recursos Hidráulicos
**2006**, 14, 39–52. [Google Scholar] - Shen, Z.Y.; Chen, L.; Chen, T. Analysis of parameter uncertainty in hydrological and sediment modeling using GLUE method: A case study of SWAT model applied to Three Gorges Reservoir Region, China. Hydrol. Earth Syst. Sci.
**2012**, 16, 121–132. [Google Scholar] [CrossRef] - Vargas-Luna, A.; Monroy, J. Estudio del comportamiento de modelos hidrológicos bajo un análisis de sensibilidad e incertidumbre. Ingeniería de Recursos Naturales y del Ambiente
**2011**, 10, 65–77. [Google Scholar]

**Figure 3.**(

**a**) A streamflow calculation simulation for different measurement times, (

**b**) 50,000 streamflow simulations for different measurement times, (

**c**) uncertainty bands for a flow measurement, discarding the 5% highest and lowest simulations, with the black line representing their average.

**Figure 4.**Comparison of percent change of upper and lower uncertainty bands resulting from the inclusion of an instrumental error.

**Figure 5.**Representation of flow measurement results, (

**a**) uncertainty bands, (

**b**) bandwidths with indicators for the criterion of percent variation less than 5%, (

**c**) upper and low slopes with indicators for the criterion of slopes less than 1%.

**Table 1.**Average velocity at various depths for wading measurements [5].

Number of Measurements | Depth (m) | Points Measured from the Water Surface | Mean Velocity Calculation |
---|---|---|---|

1 | 0.09–0.46 | 0.6 | V0.6 |

2 | over 0.46 | 0.2 and 0.8 | 0.5(V0.2 + V0.8) |

3 | over 0.46 | 0.2, 0.6 and 0.8 | 0.25(V0.2 + 2V0.6 + V0.8) |

Flow Measurement | Change (%) from 17 s | |
---|---|---|

to 34 s | to 70 s | |

1 | −0.79 | −1.24 |

2 | −0.46 | −0.78 |

3 | −0.52 | −0.91 |

4 | −0.60 | −1.03 |

5 | −0.37 | −0.64 |

6 | −1.32 | −2.27 |

7 | −0.67 | −1.15 |

8 | −0.24 | −0.40 |

Mean | −0.61 | −1.05 |

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**MDPI and ACS Style**

Clasing, R.; Muñoz, E.
Estimating the Optimal Velocity Measurement Time in Rivers’ Flow Measurements: An Uncertainty Approach. *Water* **2018**, *10*, 1010.
https://doi.org/10.3390/w10081010

**AMA Style**

Clasing R, Muñoz E.
Estimating the Optimal Velocity Measurement Time in Rivers’ Flow Measurements: An Uncertainty Approach. *Water*. 2018; 10(8):1010.
https://doi.org/10.3390/w10081010

**Chicago/Turabian Style**

Clasing, Robert, and Enrique Muñoz.
2018. "Estimating the Optimal Velocity Measurement Time in Rivers’ Flow Measurements: An Uncertainty Approach" *Water* 10, no. 8: 1010.
https://doi.org/10.3390/w10081010