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This study applies a new method and technology to measure the discharge in a lined canal in Taiwan. An Acoustic Digital Current Meter mounted on a measurement platform is used to measure the velocities over the full cross-section for establishing the measurement method. The proposed method primarily employs Chiu’s Equation which is based on entropy to establish a constant ratio the relation between the maximum and mean velocities in an irrigation canal, and compute the maximum velocity by the observed velocity profile. In consequence, the mean velocity of the lined canal can be rapidly determined by the maximum velocity and the constant ratio. The cross-sectional area of the artificial irrigation canal can be calculated for the water stage. Finally, the discharge in the lined canal can be efficiently determined by the estimated mean velocity and the cross-sectional area. Using the data of discharges and stages collected in the Wan-Dan Canal, the correlation of stage and discharge is also developed for remote real-time monitoring and estimating discharge from the pumping station. Overall, Chiu’s Equation is demonstrated to reliably and accurately measure discharge in a lined canal, and can serve as reference for future calibration for a stage-discharge rating curve.

The increasing deficiency of water resources has gradually attracted worldwide attention. It is also the focus of issues in the related governmental units in Taiwan. Due to the increase in world population and advances brought about by industrialization, there is a heavy demand for water in various uses. Agricultural water is the top demand among the various water uses in Taiwan. Therefore, whenever a water deficit occurs, agricultural water is often diverted to supply the water requirements for other uses. The water deficit problem is getting more and more serious in Taiwan every year. Allocating agricultural water for supporting people’s livelihood and other industries often leads to fallow agricultural fields and disputes over the distribution of water resources among different governmental units. Water resources play a crucial role in the economic development and survival in Taiwan. How to effectively use and allocate existing water resources is an inevitable issue. Under the condition that water resources increase in importance, having possession of water rights has become relatively vital and studies regarding water rights and the water market have been carried out [

Irrigation Associations in Taiwan possess partial and important water resources. In order to effectively control the input and output of water, to reasonably allocate water for supplying water demands, and to reduce the probability of water deficit, the Irrigation Associations have to have rapid and accurate access to the water yield data of their irrigation canals. While discharge measurements were always ignored in the past, it has now been taken seriously by the Irrigation Associations due to the need to control water yields in irrigation areas and reasonably allocate the amount of water required. In consideration of sustainable water use in Taiwan, discharge gauging systems have to be installed to effectively monitor and control discharge in irrigation canals. The Wan-Dan First Pumping Station of the Irrigation Association of Pingtung did not have a system for monitoring and measuring discharge for its irrigation canals, hence this study, by carrying out a comprehensive estimate and calibration task, aimed to provide accurate discharge measurements in the irrigation canal of the Wan-Dan First Pumping Station.

In general, empirical equations are often applied to estimate the mean velocity and discharge in streams and canals. The Manning Equation is the most popular one among the empirical equations. However, the Manning Equation is based on the concept of uniform flow, and the roughness coefficient in the equation is not constant, and can be influenced by the factors such as velocity, hydraulic radius [

It is time-consuming and therefore difficult to obtain the required data on the velocity and discharge with the conventional discharge measurement methods. Many methods have been applied for estimation of discharge in irrigation canals. The instruments and facilities to estimate discharge through measuring water stage or head include weirs and flumes [

Recently information entropy has been applied in hydraulics [

The rest of the paper is organized as follows: the computation algorithm is described in the section entitled “Discharge Computation in a Lined Canal” followed by a discussion of the method of data processing in the section “Measurements and Data Processing”. Finally, the data analysis of the Wan-Dan Canal is covered in “Results and Discussion”.

The discharge measurement method applied in this study can be used in any kind of flow conditions. It has been verified that the purposed method can be applied to measure discharge during floods [

in which _{est}_{est}_{est}

Chiu’s Equation [

where _{max}_{max} occurs on the water surface, in open channel flows, when _{max} occurs below the water surface [_{max}_{max}

in which _{max}_{max}_{max}

in which

The information entropy [

Mathematically

in which

in which Φ is the constant ratio of _{obs}_{max}_{obs}

in which _{obs}_{obs}

It is obvious that _{max}

In accordance with the method described above, this study first conducts discharge measurements by using the ADC, estimates the maximum velocity on the

Because most of irrigation canals in Taiwan are rectangular in shape and built with reinforced concrete, the cross-sectional area can be estimated as:

in which _{est}_{max}WD

After all of the velocity and water depth measurements are made, the observed discharge can be calculated by the mean-section method. By applying mean-section method, segment discharges are computed between successive verticals. The velocities and depths for successive verticals are each averaged as the mean velocity and depth of the segment. Therefore the discharge of segment is:

in which _{i}_{i}_{i}_{i}_{i}

The determination of mean velocity at a vertical will affect the accuracy of the discharge measurement. The vertical velocity curve method [

Ideally, a rating curve for an artificial irrigation canal can describe a unique functional relationship between water stage and discharge. Therefore the discharge can be estimated by using the stage–discharge rating curve, if the rating curve exists. After sufficient measurements of discharge and water stage suitably distributed throughout the range of water depth are made, a stage–discharge rating curve can be developed for monitoring the discharge in real-time and continuously. Usually the simple stage–discharge curve can be used in an irrigation canal:

in which _{r}

There are five pumps at the Wan-Dan Fist Pumping Station; four of them supply water from the Ga-Ping River to the Wan-Dan Canal, as shown in

A gauge system is installed in the Wan-Dan Canal, approximately 150 m away from the weir. The course of the canal is straight for more than 100 m upstream and downstream from the gauge site. Owing to the concrete lined irrigation canal, the channel bed is stable and free of growth and decay of aquatic matter. Flow is steady and fairly uniformly established across the entire width of canal at the gauge site; it is an ideal location for measuring discharge.

The instrument employed in the study is an ADC, which is a highly accurate measurement instrument and is primarily used to measure velocity in open channels, such as rivers and streams. The ADC measures the velocity of water using a physical principle called the Doppler effect [

In order to remotely monitor the discharge of the canal, a float-type gauge and a staff gauge are installed at the gauge site. The float-type gauge is equipped with an LCD indicating water depth and battery status. For safety, the gauge with default resolution in mm is protected in a 12.7 cm pipe for continuously and uninterruptedly measuring the water stage. Not only is the data stored

Furthermore, in order to measure velocities over the full cross-section of the canal, we design a measurement platform, on which operators can carry out the task and the facilities can be installed, such as the velocity instrument. The platform, which can be easily and quickly assembled and dismantled, is applicable to be used in irrigation canals. Also, after the platform is assembled, it can be lifted and moved easily to the gauge site by two men or a crane. A sounding rod with a gauge is connected with the ADC, and they are installed upon the sliding rail of the platform. By moving up and down or to the left and the right on the sliding rail, the ADC can be easily moved to the velocity measuring positions.

The Wan-Dan Canal is a 3 m wide rectangular channel built with reinforced concrete. To develop a reliable and accurate discharge measurement method for the Wan-Dan Canal, a large amount of data on velocities over the full cross-section is collected. It is conventional to make the nine verticals equidistant for measuring the velocity profiles. Both of the verticals 1 and 2 are 0.2 m away from the vertical sides, and the remaining verticals are 0.325 m apart. Velocity observations in the vertical depend on the water depth. Ten velocity measurements are made equidistantly from the water surface to the channel bottom at each vertical when the water depth is higher than 0.5 m, but otherwise five velocity measurements are measured equidistantly.

While this study is carried out, flow is controlled by the pumps in order to maintain the stability of discharge and stage at the gauge site. After the first discharge measurement is completed, flow in the canal is adjusted for the next measurement. The task is conducted repeatedly till the data of discharge and stage is adequate to develop a stable stage–discharge relationship. Aiming to develop a reliable rating curve, 14 runs of discharge measurement were carried out over the range of water stage variation from 14 March to 16 March 2011, as shown in

^{1.77}. The correlation coefficient which is a measure of relationship between two random variables is up to 0.996. The rating curve throughout the entire range of water stage is the basis for remotely real-time monitoring discharge from the Wan-Dan First Pumping Station.

With the isovels as shown

The observed data set is randomly split into two independent subsets: the calibration, and validation subsets. The calibration subset with nine sets of data is used for parameter estimation. The validation subset, which consists of four sets of data, is devoted to show the performance of the discharge estimation model. In the calibration phase, a linear relationship passing through origin with a large correlation coefficient (

_{est}_{obs}_{est}

^{2}

The stage-discharge rating curve is then developed; the calibration of rating curve cannot be carried out just once. Several discharge measurements a year may be required to either confirm the consistence of the rating or to detect and follow shifts in the rating curve. With the proposed discharge method as the basis, the discharge of the Wan-Dan Canal can be measured in the gauge site in the future with only a few velocity measurements made on the

Combined with a new method of measurement and new technology, this study develops an efficient and simple method which is applicable to measure the discharge in lined canals. The ADC mounted on the measurement platform employed in the study is able to quickly and precisely measure the velocities over the full cross-section. By collecting a substantial amount of data on velocity observed in the canal for computing mean velocities by Chiu’s Equation, the accuracy of observed discharge can hence be improved for acquiring a precise stage-discharge rating curve.

The proposed method for measuring discharge in an irrigation canal principally applies the correlation of mean and maximum velocities. However it still needs to employ the velocity-area method to derive the observed discharge for computing the observed mean velocity. Then the ratio of observed mean velocity and maximum velocity derived for velocity measurements made by the ADC on the

We are grateful to the Asia Pacific Instrument Corporation for their field coordination and assistance. The financial support was given by the Pingtung Irrigation Association, Taiwan and NSC 100-2625-M-366-001-MY3.

The authors declare no conflict of interest.

All the authors contributed to the manuscript. Chen, Kuo, Yu, Liao and Yang have contributed to the research methods and the results have been discussed among all authors. Authorship credit are based on (1) Chen, Kuo, Yu, Liao and Yang contributed to conception and design, acquisition of data, or analysis and interpretation of data; (2) Chen, Yu, and Yang drafted the article or revised it critically for important intellectual content; and (3) Chen and Yang approved the final version to be published.

Layout of the Wan-Dan First Pumping Station and the gauge site.

Measurement platform mounted with ADC for measuring discharge in the Wan-Dan Canal.

Velocity profiles of Run 1 observed by ADC and calculated by using

The simple stage–discharge relationship of the Wan-Dan Canal.

Isovels and

Stability of the

Relation between observed mean velocity and maximum velocity in the Wan-Dan Canal.

Comparison of the mean velocities measured by ADC and Chiu’s Equation.

Relation between estimates of discharge based on relationship of mean and maximum velocities and those based on cross-sectional ADC measurements.

Discharge and water stage measured in the Wan-Dan Canal.

RUN | Date | G (m) | Q (m^{3}/s) |
---|---|---|---|

1 | 3/14/2011 | 0.92 | 1.84 |

2 | 3/14/2011 | 0.85 | 1.60 |

3 | 3/15/2011 | 1.02 | 2.25 |

4 | 3/15/2011 | 0.95 | 1.94 |

5 | 3/15/2011 | 0.97 | 2.06 |

6 | 3/15/2011 | 0.88 | 1.67 |

7 | 3/16/2011 | 0.78 | 1.40 |

8 | 3/16/2011 | 0.71 | 1.08 |

9 | 3/16/2011 | 0.67 | 0.97 |

10 | 3/16/2011 | 0.63 | 0.84 |

11 | 3/16/2011 | 0.51 | 0.53 |

12 | 3/16/2011 | 0.47 | 0.44 |

13 | 3/16/2011 | 0.42 | 0.32 |

14 | 3/16/2011 | 0.10 | 0.00 |