# Comparison of Seasonal Flow Rate Change Indices Downstream of Three Types of Dams in Southern Quebec (Canada)

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Watersheds and Data Sources

- -
- Type of dam management method or type of regulated hydrological regime. Three management methods were selected for this study: inversion, natural and diversion. The homogenization management method was not analyzed due to the absence of data measured in a natural river and downstream of a dam.
- -
- The existence of continuous flow measurements in natural rivers and downstream of a dam over a longer period of time (at least 10 years).

^{2}) located in the Saint Lawrence Lowlands. In the L’Assomption watershed, two dams were built on its main tributary, the Ouareau River (Figure 1). For this study, we selected the first dam (Rawdon dam or generating station), whose primary purpose is to support low flows from the Ouareau and L’Assomption rivers for recreational and tourism activities and to supply homes with hydroelectric power. This concrete dam was built in 1913. Its height and total holding capacity are 14.6 m and 5,976,417 m

^{3}, respectively. It drains a total surface area of 1259 km

^{2}. This dam created a natural-type regulated hydrological regime. This type of regime is characterized by the occurrence of maximum monthly mean flow in spring during snowmelt and minimum monthly mean flow in winter. This annual hydrological cycle is comparable to that observed in natural rivers. The second watershed is the Matawin River watershed, adjacent to the first (Figure 1). It lies entirely in the Canadian Shield. The Matawin River is the main tributary of the Saint-Maurice River. In 1930, a reservoir dam was built primarily to supply water to hydroelectric power plants on the Saint-Maurice River in winter, at a time when river flow is lowest due to the storage of precipitation as snow on slopes. It does not have a hydroelectric power plant. It is a large concrete dam with a height of 25 m and a total holding capacity of 946,000,000 m

^{3}. It drains a surface area of 4070 km

^{2}. It created an inversion-type regulated hydrological regime. This regime is characterized by the occurrence of maximum monthly mean flow in winter and minimum monthly mean flow in spring during snowmelt. Flow under natural conditions is measured continuously at the Saint-Michel-Des-Saints station (1390 km

^{2}) located upstream of the Matawin dam. It does not influence the flow measured at this station ([24]). Lastly, the last watershed selected is the Manouane River watershed (Figure 1). In 2003, a dam (Manouane dam) was built that diverts water from this river to the Betsiamites River in order to increase the capacity of the Pipmuacan reservoir, which supplies the Bersimis-1 and Bersimis-2 hydroelectric power plants. The Manouane dam created a diversion-type regulated hydrological regime characterized by the occurrence of maximum monthly mean flow in spring and minimum monthly mean flow in winter. The dam’s height and total holding capacity are 9.5 m and 70,000,000 m

^{3}, respectively. It drains a 4600 km

^{2}watershed. Continuous flow measurements have been available since 1979, that is, before and after the dam’s construction.

#### 2.2. Definition of Hydroclimatic Variables

- -
- The series of mean daily maximum temperatures (Tmax);
- -
- The series of mean daily minimum temperatures (Tmin);
- -
- The series of daily mean temperatures (Tme);
- -
- The series of total snowfall (TSF);
- -
- The series of total rainfall (TRF);
- -
- The series of total precipitation (rain and snow, TP).

#### 2.3. Statistical Data Analysis

- -
- In the first step, we compared the means of two CV and CI indices calculated in natural rivers and downstream of dams in the three watersheds using the Kruskal-Wallis non-parametric and parametric variance analysis (ANOVA) tests. The purpose of this step is to identify the influence of dam management methods on flow rate change index values.

- -
- The second step consisted in analyzing the temporal variability of these two indices (CI and CV) to compare their stationarity on the basis of dam management methods. We applied the Lombard test to analyze this stationarity [25,26]. The rationale for selecting this test is that it can detect abrupt or gradual breaks in means, in contrast with all other statistical tests used in hydrology. Such as with the other tests, it also helps determine the dates of such breaks. The test has already been widely described in our previous work (e.g., [27]). Given a series of independent observations ${X}_{1},\dots ,{X}_{n},$ where Xi is the observation taken at time $T=i.$ It is important to assess whether the mean of this series has changed at some unknown time. To this end, one considers as a possible pattern for the mean of these observations the smooth-change model introduced by [25], where the mean of X
_{i}is defined by:$${{\displaystyle \mu}}_{i}=\{\begin{array}{c}{}_{{{\displaystyle \theta}}_{1}}\\ {}_{{{\displaystyle \theta}}_{1}}\\ {}_{{{\displaystyle \theta}}_{2}}\end{array}+\frac{{(i-{{\displaystyle T}}_{1})}^{}({{\displaystyle \theta}}_{2}-{{\displaystyle \theta}}_{1})}{{{\displaystyle T}}_{2}-{{\displaystyle T}}_{1}}\begin{array}{c}i{f}^{}1\le i\le {T}_{1}\\ i{f}^{}{T}_{1}<i\le {T}_{2}\\ i{f}^{}{T}_{2}<i\le {n}^{}\end{array}$$

_{1}, …, X

_{n}and define the rank score of X

_{i}by:

_{n}is greater than 0.0403 derived for a series of observations. This value of 0.0403 corresponds to the asymptotic theoretical (critical) value as obtained by Lombard [25]. The absence of autocorrelation is necessary for the validity Lombard’s test (see [25,26]).

- -
- Finally, the last step statistical analysis consisted of analyzing the correlation between the flow rate change indices and the six climatic variables in pristine (stations) rivers and downstream from dams.

## 3. Results

#### 3.1. Comparison of the Mean Values of Flow Rate Change Indices in Pristine Rivers and Downstream from Dams

#### 3.2. Analysis of the Temporal Variability of Flow Rate Change Indices

#### 3.3. Analysis of the Influence of Dam Management Modes on the Relationship between Flow Rate Indices and Climate Variables

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Comparison of the interannual variability of values of winter coefficients of variation from 1930 to 2010. Vertical bars indicate years of breaks in mean.

**Figure 3.**Comparison of the interannual variability of values of winter coefficients of variation upstream and downstream of the Matawin dam during the period from 1930 to 2010.

**Figure 4.**Comparison of the interannual variability of values of spring coefficients of variation at the Joliette station (L’Assomption) and downstream of the Rawdon station (Ouareau) during the period from 1930 to 2010. Vertical bars indicate years of breaks in mean.

**Figure 5.**Comparison of the interannual variability of values of spring coefficients of variation upstream and downstream of the Matawin dam during the period from 1930 to 2010.

**Table 1.**Comparison of means (M1 and M2) of coefficients of immoderation (CI) and variation (CV) before (1980–2002) and after (2004–2014) the construction of the Manouane River diversion dam during the period from 1980 to 2014.

Seasons | Indices | Before | After | p-Value (KW) | p-Value (t) | R (%) |
---|---|---|---|---|---|---|

M1 | M2 | |||||

Fall | CI | 7.88 (4.13) | 5.21 (1.83) | 0.027 | 0.011 | −33.9 |

CV | 55.63 (16.62) | 45.13 (12.51) | 0.041 | 0.036 | −18.9 | |

Winter | CI | 1.82 (0.70) | 2.10 (1.84) | 0.671 | 0.594 | − |

CV | 16.64 (10.53) | 17.06 (20.44) | 0.117 | 0.944 | − | |

Spring | CI | 29.75 (11.29) | 28.19 (14.96) | 0.854 | 0.740 | − |

CV | 82.52 (14.55) | 99.09 (24.24) | 0.039 | 0.032 | +20.1 | |

Summer | CI | 6.04 (2.89) | 7.10 (3.48) | 0.421 | 0.349 | − |

CV | 47.32 (14.14) | 48.86 (11.79) | 0.815 | 0.733 | − |

**Table 2.**Comparison of means (M1, M2) of coefficients of immoderation (CI) and variation (CV) of the L’Assomption River (natural station) and Ouareau River (downstream of the Rawdon dam) during the period from 1930 to 2010.

Seasons | Indices | L’Assomption River | Ouareau River | p-Value (KW) | p-Value (t) | R (%) |
---|---|---|---|---|---|---|

M1 | M2 | |||||

Fall | CI | 9.56 (7.03) | 11.26 (15.88) | 0.291 | 0.354 | − |

CV | 53.79 (21.25) | 53.61 (18.54) | 0.879 | 0.928 | − | |

Winter | CI | 7.35 (8.73) | 9.36 (14.66) | 0.714 | 0.747 | − |

CV | 55.00 (42.89) | 56.42 (47.25) | 0.895 | 0.945 | − | |

Spring | CI | 19.73 (9.32) | 26.00 (14.96) | 0.001 | 0.001 | +31.78 |

CV | 81.84 (17.47) | 85.16 (18.27) | 0.213 | 0.239 | − | |

Summer | CI | 9.45 (6.47) | 15.84 (20.53) | 0.049 | − | +67.62 |

CV | 57.36 (21.94) | 59.64 (25.93) | 0.664 | 0.661 | − |

**Table 3.**Comparison of means (M1 and M2) of coefficients of immoderation (CI) and variation (CV) upstream and downstream of the Matawin River dam during the period from 1930 to 2010.

Seasons | Indices | Upstream from Dam | Downstream from Dam | p-Value (KW) | p-Value (t) | R (%) |
---|---|---|---|---|---|---|

M1 | M2 | |||||

Fall | CI | 5.02 (2.31) | 111.72 (71.74) | 0.000 | − | +2125.5 |

CV | 40.50 (12.45) | 90.85 (40.40) | 0.000 | 0.000 | +126.84 | |

Winter | CI | 3.52 (3.10) | 49.93 (66.37) | 0.000 | − | +1318.47 |

CV | 32.37 (24.02) | 46.94 (33.40) | 0.000 | 0.002 | +43.28 | |

Spring | CI | 13.61 (6.40) | 134.56 (100.16) | 0.000 | − | +888.68 |

CV | 69.90 (17.20) | 135.17 (105.88) | 0.000 | 0.000 | +933.38 | |

Summer | CI | 7.22 (3.95) | 93.09 (63.03) | 0.000 | 0.000 | +1189.34 |

CV | 52.93 (17.37) | 94.03 (30.72) | 0.000 | 0.000 | +77.65 |

**Table 4.**Comparison of the temporal variability of two seasonal flow rate indices (CI and CV) from 1930 to 2010.

Seasons | CI | CV | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

L’Assomption River | Ouareau River | L’Assomption River | Ouareau River | |||||||||

S_{n} | T1/T2 | R (%) | S_{n} | T1/T2 | R (%) | S_{n} | T1/T2 | R (%) | S_{n} | T1/T2 | R (%) | |

Fall | 0.0099 | - | − | 0.0024 | − | − | 0.0045 | − | − | 0.0006 | − | − |

Winter | 0.0940 | 1951/52 | −41.46 | 0.0569 | 1973/74 | −2.27 | 0.0594 | 1971/72 | −41.36 | 0.0745 | 1971/72 | −42.01 |

Spring | 0.0688 | 1994/95 | −27.08 | 0.0052 | − | − | 0.0498 | 1973/74 | −13.04 | 0.0244 | − | − |

Summer | 0.0688 | 1994/95 | −70.56 | 0.1410 | 1976/97 | −78.50 | 0.1062 | 1994/95 | −50.08 | 0.1420 | 1982/85 | −52.84 |

**Table 5.**Comparison of the temporal variability of two seasonal flow rate indices (CI and CV) upstream and downstream of the Matawin dam during the period from 1930 to 2010.

Seasons | CI | CV | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Upstream from dam | Downstream from Dam | Upstream from Dam | Downstream from Dam | |||||||||

S_{n} | T1/T2 | R (%) | S_{n} | T1/T2 | R (%) | S_{n} | T1/T2 | R (%) | S_{n} | T1/T2 | R (%) | |

Fall | 0.0770 | 1961/62 | −33.64 | 0.1173 | 1982/83 | +48.30 | 0.0472 | 1986/87 | −27.03 | 0.3150 | 1959/72 | +46.21 |

Winter | 0.0819 | 1970/71 | −52.44 | 0.3079 | 1958/68 | +80.26 | 0.0316 | − | − | 0.3020 | 1960/61 | +59.76 |

Spring | 0.0207 | − | − | 0.0886 | 1981/82 | +37.00 | 0.0699 | 1963/64 | −16.67 | 0.0546 | 1967/68 | 0.32 |

Summer | 0.1009 | 1992/96 | −82.82 | 0.2728 | 1986/87 | +58.94 | 0.0894 | 1993/94 | −31.83 | 0.0144 | − | − |

**Table 6.**Comparison of correlation coefficients calculated between climate variables and the flow rate change indices of the L’Assomption River (upstream) and Ouareau River (downstream of the Rawdon dam) for the period from 1930 to 2010.

Fall | Winter | Spring | Summer | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

L’Assomption River | Ouareau River | L’Assomption River | Ouareau River | L’Assomption River | Ouareau River | L’Assomption River | Ouareau River | |||||||||

CI | CV | CI | CV | CI | CV | CI | CV | CI | CV | CI | CV | CI | CV | CI | CV | |

Tmax | 0.063 | −0.031 | 0.088 | 0.032 | 0.251 | 0.305 | 0.280 | 0.319 | 0.401 | 0.415 | 0.230 | 0.366 | 0.107 | 0.103 | 0.076 | 0.035 |

Tmin | 0.156 | 0.091 | 0.140 | 0.086 | 0.305 | 0.319 | 0.263 | 0.316 | 0.314 | 0.317 | 0.175 | 0.229 | 0.046 | 0.120 | 0.272 | 0.181 |

Tmoy | 0.129 | 0.040 | 0.135 | 0.071 | 0.308 | 0.340 | 0.292 | 0.333 | 0.383 | 0.402 | 0.209 | 0.324 | 0.109 | 0.013 | 0.366 | 0.172 |

TRF | 0.502 | 0.425 | 0.388 | 0.408 | 0.586 | 0.645 | 0.447 | 0.532 | −0.168 | −0.175 | −0.105 | −0.231 | 0.134 | 0.124 | 0.236 | 0.266 |

TSF | −0.105 | −0.196 | −0.059 | −0.198 | −0.132 | −0.201 | −0.239 | −0.207 | 0.163 | 0.076 | 0.086 | 0.000 | − | − | − | − |

TP | 0.313 | 0.217 | 0.329 | 0.226 | 0.343 | 0.311 | 0.164 | 0.228 | −0.118 | −0.118 | −0.074 | −0.195 | 0.134 | 0.124 | 0.238 | 0.266 |

**Table 7.**Comparison of correlation coefficients calculated between climate variables and the flow rate change indices upstream and downstream of the Matawin River dam for the period from 1930 to 2010.

Fall | Winter | Spring | Summer | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Upstrteam | Downstream | Upstrteam | Downstream | Upstrteam | Downstream | Upstrteam | Downstream | |||||||||

CI | CV | CI | CV | CI | CV | CI | CV | CI | CV | CI | CV | CI | CV | CI | CV | |

Tmax | −0.029 | 0.052 | 0.203 | 0.041 | 0.030 | 0.029 | 0.054 | −0.060 | −0.023 | 0.010 | −0.206 | 0.092 | 0.242 | 0.193 | −0.175 | 0.034 |

Tmin | 0.013 | 0.012 | 0.101 | 0.203 | 0.066 | 0.126 | 0.184 | 0.080 | −0.043 | −0.019 | −0.118 | −0.118 | 0.131 | 0.142 | −0.022 | 0.073 |

Tmoy | −0.012 | 0.030 | 0.177 | 0.118 | 0.035 | 0.073 | 0.129 | 0.022 | −0.031 | 0.003 | −0.150 | −0.001 | 0.223 | 0.190 | −0.109 | 0.056 |

TRF | 0.232 | 0.216 | −0.210 | 0.009 | 0.211 | 0.280 | −0.030 | −0.020 | 0.141 | 0.281 | 0.317 | −0.531 | −0.161 | −0.111 | −0.046 | −0.128 |

TSF | 0.075 | 0.113 | −0.065 | −0.143 | −0.275 | −0.279 | 0.134 | 0.253 | 0.077 | 0.065 | 0.193 | 0.016 | − | − | − | − |

TP | 0.271 | 0.272 | −0.189 | −0.040 | −0.148 | −0.125 | 0.124 | 0.234 | 0.165 | 0.299 | 0.343 | −0.515 | −0.163 | −0.113 | −0.046 | −0.129 |

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**MDPI and ACS Style**

Delisle, F.; Assani, A.A. Comparison of Seasonal Flow Rate Change Indices Downstream of Three Types of Dams in Southern Quebec (Canada). *Water* **2021**, *13*, 2555.
https://doi.org/10.3390/w13182555

**AMA Style**

Delisle F, Assani AA. Comparison of Seasonal Flow Rate Change Indices Downstream of Three Types of Dams in Southern Quebec (Canada). *Water*. 2021; 13(18):2555.
https://doi.org/10.3390/w13182555

**Chicago/Turabian Style**

Delisle, Francis, and Ali Arkamose Assani. 2021. "Comparison of Seasonal Flow Rate Change Indices Downstream of Three Types of Dams in Southern Quebec (Canada)" *Water* 13, no. 18: 2555.
https://doi.org/10.3390/w13182555