# Hydraulic Parameters for Sediment Transport and Prediction of Suspended Sediment for Kali Gandaki River Basin, Himalaya, Nepal

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

_{b}), specific stream power (ω), and flow velocity (v) associated with the maximum boulder size transport, were determined throughout the years, 2003 to 2011, by using a derived lower boundary equation. Clockwise hysteresis loops of the average hysteresis index of +1.59 were developed and an average of 40.904 ± 12.453 Megatons (Mt) suspended sediment have been transported annually from the higher Himalayas to the hydropower reservoir. Artificial neural networks (ANNs) were used to predict the daily suspended sediment rate and annual sediment load as 35.190 ± 7.018 Mt, which was satisfactory compared to the multiple linear regression, nonlinear multiple regression, general power model, and log transform models, including the sediment rating curve. Performance indicators were used to compare these models and satisfactory fittings were observed in ANNs. The root mean square error (RMSE) of 1982 kg s

^{−1}, percent bias (PBIAS) of +14.26, RMSE-observations standard deviation ratio (RSR) of 0.55, coefficient of determination (R

^{2}) of 0.71, and Nash–Sutcliffe efficiency (NSE) of +0.70 revealed that the ANNs’ model performed satisfactorily among all the proposed models.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Site Description

^{2}area, comprised of elevations of 529~2000 m MSL covering 1317 km

^{2}(19% coverage); 2000~4700 m MSL covering 3388 km

^{2}(48% coverage); 4700~5200 m MSL covering 731 km

^{2}(10% coverage); and elevations greater than 5200 m MSL covering 1624 km

^{2}(23% coverage). Figure 1a shows the different altitude areas’ coverage map showing river networks, with the locations of meteorological stations, created in ArcGIS 10.3.1 (ERSI Inc., Berkeley, CA, USA) software. The elevations of Kali Gandaki River decrease from 5039 m MSL in the higher Himalayas to 529 m MSL at Setibeni, 5 km upstream of the hydropower dam (Figure 1b). This encompasses a wide variation in mean rainfall, ranging from less than 500 mm year

^{−1}in the Tibetan Plateau to about 2000 mm year

^{−1}in the monsoon-dominated Himalayas [8].

#### 2.2. Data Collection and Acquisition

#### 2.3. Analysis of Shear Stress, Specific Power, and Flow Velocity

^{−1}and is given by:

_{b}is the bed shear stress (N·m

^{−2}), ρ is the density of water (1000 kg·m

^{−3}), g is the acceleration due to gravity (9.81 m·s

^{−2}), R is the hydraulic radius (m), i is the slope of the river bed (m·m

^{−1}), ω is the mean available specific stream power per unit area (w·m

^{−2}), Q is the observed discharge (m

^{3}·s

^{−1}), v is the flow velocity (m·s

^{−1}), and n is Manning’s constant. Manning’s constant, n, in a steep natural channel is calculated by the equation proposed by Jarrett [31]:

#### 2.4. Development of Different Models for Suspended Sediment Predictions

#### 2.4.1. Multiple Linear Regression

#### 2.4.2. Nonlinear Multiple Regression

#### 2.4.3. Sediment Rating Curve

^{−1}), ${Q}_{{w}_{t}}$ is the daily average discharge of river, and a and b are coefficients that depend on the characteristics of a river.

#### 2.4.4. Artificial Neural Networks

#### 2.5. Model Performance

^{2}), and Nash–Sutcliffe efficiency (NSE) [32,35,36]:

^{2}is 1.0; the higher the value of R

^{2}, the better the model’s performance:

## 3. Results and Discussion

^{3}·s

^{−1}with a minimum discharge of 40.73 m

^{3}·s

^{−1}during winter in 2009 and a maximum discharge 2824.50 of m

^{3}·s

^{−1}during summer in 2009. The maximum discharge showed a decreasing trend from 2003 to 2006 whereas an increasing trend from 2007 onwards was observed, as shown in Figure 2a. The yearly transported sediment load increased nearby upstream river bed level elevations of the reservoir (Figure 2b) and sediment deposited into the reservoir decreased the reservoir’s capacity. The effects of climate change in the higher Himalayas appeared in the form of uneven patterns of increasing rainfall, glacial rate erosion, and permafrost degradation, resulting in an increase in landslides and debris flows [2], which also reflects the temporal and spatial variation of the water balance components in the Kali Gandaki basin [37]. The amount and intensity of rainfall around its catchment affected the discharge rating curve [27].

#### 3.1. Relationship of Shear Stress, Specific Stream Power, and Flow Velocity with Discharge

#### 3.2. Relationship of Particle Sizes and Fluvial Discharge

^{3}s

^{−1}. This high discharge was responsible for the movement of a maximum boulder size of 4300 mm [6]. The higher shear stress, specific stream power, and flow velocity observed due to a higher fluvial discharge after the breaching of landslide dam were responsible for the transportation of larger sized boulders (Figure 5, Figure 6 and Figure 7).

#### 3.3. Estimation of the Return Period by Gumbel’s Distribution

^{3}·s

^{−1}. According to the Gumbel frequency of flood distribution, the highest flood will occur after a 40 year return period, as shown in Figure 8a, and the observed extreme discharge, as shown in Figure 8b.

#### 3.4. Boulder Movement Mechanisms in the Himalayas

_{w}Gorkha earthquake, Nepal on 25 April 2015 and its aftershocks on 23 May 2015 created cracks in the weathered rocks and weakened the mountain slopes of this catchment, which brought rocks, debris, and mud down into the river [41,42]. The river was blocked about 56 km upstream from the hydropower dam by a landslide on 24 May 2015 for 15 h [41] (Figure 9a,b). The downstream fluvial discharge after the blockage was almost zero and a flash flood occurred after an outburst of the natural landslide dam (Figure 9c,d). Extreme flooding during the monsoon period due to high rainfall and a flash flood (Figure 9b), generated by the overtopping of landslide dams [42], was responsible for the noticeable transport of large boulders in the river bed of Kali Gandaki River.

#### 3.5. Quantification and Prediction of the Suspended Sediment

#### 3.5.1. Hysteresis Curve and Hysteresis Index (HI_{mid}) Analysis

^{−1}for a fluvial discharge of 1053 m

^{3}·s

^{−1}on August 2009. The suspended sediment load decreased on the falling limb of hysteresis from July/September to November. Overall, these six years were characterized by distinct clockwise hysteresis patterns (Figure 10a).

_{mid}is a numerical indicator of hysteresis, which effectively shows the dynamic response of suspended sediment concentrations to flow changes during storm events [47].

#### 3.5.2. Yearly Suspended Sediment Yield and Prediction by Different Models

^{−1}, ${Q}_{w}{}_{i}$ is the fluvial discharge in m

^{3}·s

^{−1}, $dt$ is the time interval, ${t}_{i}$ and ${t}_{i+1}$ are the preceding and succeeding time in seconds, respectively.

_{mid}≈ 0 indicated a weak hysteresis loop whereas HI

_{mid}> 0 indicated a clockwise hysteresis loop, and HI

_{mid}< 0 an anticlockwise hysteresis loop. Moreover, the maximum HI

_{mid}developed was +2.64 in 2006, depicting the higher sediment transport rate in the rising limb but lower sediment transport rate in the falling limb (Figure 10a). The minimum HI

_{mid}developed was +0.53 in 2008, depicting the nearly same paths of the rising and falling limb and indicating a weak hysteresis loop (Figure 10a and Figure 11b).

^{2}, and NSE values of the general power model, log transform models, and ANNs are shown in Table 4, Table 5 and Table 6. In general, the model simulation can be judged as “satisfactory” if NSE > 0.50, and RSR ≤ 0.70, and if the PBIAS value is ±25% for the stream flow and the PBIAS value is ±55% for the sediment [35]. In this study, the predicted values from ANNs (4−10−1−1) showed an RMSE value of 1982 kg·s

^{−1}, PBIAS value of +14.26, RSR value of 0.55, R

^{2}value of 0.71, and an NSE value of +0.70, which indicates that the ANNs model’s performance was satisfactory. Figure 12a–d show the comparison between the model’s predicted transport rates of the suspended sediment discharge in kg·s

^{−1}of the SRC, log transform power model, log transform linear models, and ANNs and the observed suspended sediment values respectively.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Map of Kali Gandaki River catchment area; (

**b**) longitudinal profile of Kali Gandaki River.

**Figure 4.**Relationship of the fluvial discharge, (

**a**) flow velocity, and (

**b**) particle size (boulder).

**Figure 5.**Relationship of shear stress and particle size (boulder) and a comparison with different researchers.

**Figure 6.**Relationship of the specific power and particle size (boulder) and a comparison with different researchers.

**Figure 7.**Relationship of the flow velocity and particle size (boulder) and comparison with different researchers.

**Figure 9.**(

**a**) Natural landslide dam formation on 24 May 2015 (~56 km upstream of dam), (

**b**) lake formation after the blockage of the river, (

**c**) downstream fluvial discharge after the blockage of the river, and (

**d**) extreme fluvial discharge after breaching of the landslide dam on 25 May 2015 (Source: http://kathmandupost.ekantipur.com/news/2015-05-24/blocked-kali-gandaki-river-flows-again-with-photos.html).

**Figure 10.**(

**a**) Seasonal hysteresis loop of the sediment load. (

**b**) Suspended sediment–discharge rating curve.

**Figure 11.**(

**a**) Seasonal suspended yield from the catchment. Central lines indicate the median, bottom and top edges of the box indicate the 25th and 75th percentiles respectively. The whiskers extend to the most extreme data points not considered outliers, the ‘+’ symbol represents outliers (1.5 fold interquartile range), the circle shows the mean value. (

**b**) Yearly suspended sediment transport and hysteresis index (HI

_{mid}).

**Figure 12.**Observed and predicted sediment (

**a**) SRC (Q

_{w}and Q

_{s}) model, (

**b**) power model (Q

_{w}), (

**c**) log transform linear model (Q

_{w}and R

_{t}), and (

**d**) ANN model.

**Figure 13.**Comparison of different models’ predicted and observed yearly total suspended sediment transport. Central lines indicate the median, and bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, the ‘+’ symbol represents outliers (1.5-fold interquartile range), and the circle shows the mean value.

Parameters | |
---|---|

Catchment area | 7060 km^{2} |

Length of river up to dam | 210 km |

Mean gradient of river | 2.20% |

Extreme discharge | 3280 m^{3} s^{−1} in 1975, 2824.5 m^{3} s^{−1} in 2009 |

Elevation ranges | 529 m MSL–8143 m MSL |

Precipitation | Tibetan plateau <500 mm year^{−1}, monsoon dominated Himalayas~2000 mm year^{−1} |

Model Scenario | RMSE (kg·s^{−1}) | PBIAS | RSR | R^{2} | NSE | Model Equation |
---|---|---|---|---|---|---|

${Q}_{t}$ | 2498 | +0.47 | 0.66 | 0.53 | +0.56 | ${Q}_{s}=7.12{Q}_{t}-920.70$ |

${R}_{t}$ | 2729 | +0.34 | 0.73 | 0.44 | +0.47 | ${Q}_{s}=199.54{R}_{t}-229.07$ |

${Q}_{t}{R}_{t}$ | 2442 | +0.22 | 0.64 | 0.55 | +0.59 | ${Q}_{s}=5.31{Q}_{t}+71.0{R}_{t}-897.03$ |

${Q}_{t}{R}_{t-1}$ | 2494 | +0.35 | 0.66 | 0.53 | +0.56 | ${Q}_{s}=6.68{Q}_{t}+18.12{R}_{t-1}-920.66$ |

${Q}_{t}{Q}_{t-1}{R}_{t}{R}_{t-1}$ | 2339 | +0.29 | 0.59 | 0.59 | +0.65 | ${Q}_{s}=13.47{Q}_{t}-8.02{Q}_{t-1}-14.02{R}_{t}+64.44{R}_{t-1}-784.15$ |

Model Scenario | RMSE (kg·s^{−1}) | PBIAS | RSR | R^{2} | NSE | Model Equation |
---|---|---|---|---|---|---|

${Q}_{t}$ | 2314 | +0.33 | 0.57 | 0.59 | +0.67 | ${Q}_{s}=5.02\times {10}^{-3}{Q}_{t}^{2}+0.71{Q}_{t}-111.61$ |

${R}_{t}$ | 2697 | +0.66 | 0.71 | 0.46 | +0.49 | ${Q}_{s}=1.30{R}_{t}^{2}+138.75{R}_{t}-36.72$ |

${Q}_{t}{R}_{t}$ | 2280 | +0.15 | 0.56 | 0.61 | +0.68 | ${Q}_{s}=4.04\times {10}^{-3}{Q}_{t}^{2}+0.74{Q}_{t}+0.57{R}_{t}^{2}+24.10{R}_{t}-188.70$ |

${Q}_{t}{R}_{t-1}$ | 2303 | +0.32 | 0.57 | 0.59 | +0.67 | ${Q}_{s}=5.14\times {10}^{-3}{Q}_{t}^{2}-0.17{Q}_{t}-0.024{R}_{t-1}^{2}+30.46{R}_{t-1}-93.99$ |

${Q}_{t}{Q}_{t-1}{R}_{t}{R}_{t-1}$ | 2250 | +0.43 | 0.55 | 0.62 | +0.69 | ${Q}_{s}=3.73\times {10}^{-3}{Q}_{t}^{2}-8.10\times {10}^{-4}{Q}_{t-1}^{2}+4.97{Q}_{t}-3.02{Q}_{t-1}+8.18\times {10}^{-2}{R}_{t}^{2}+0.91{R}_{t-1}^{2}+8.27{R}_{t}+0.28{R}_{t-1}-272.04$ |

Model Scenario | RMSE (kg·s^{−1}) | PBIAS | RSR | R^{2} | NSE | Model Equation |
---|---|---|---|---|---|---|

General power model 1 ${Q}_{t}$ | 2039 | +3.81 | 0.56 | 0.67 | +0.68 | ${Q}_{s}=1.027\times {10}^{-3}{Q}_{t}^{2.238}$ |

General power model 2 ${Q}_{t}$ | 2039 | +0.22 | 0.56 | 0.67 | +0.68 | ${Q}_{s}=0.847\times {10}^{-3}{Q}_{t}^{2.263}+71.08$ |

Model Scenario | RMSE (kg·s^{−1}) | PBIAS | RSR | R^{2} | NSE | Model Equation |
---|---|---|---|---|---|---|

Linear model (SRC) $log{Q}_{t}$ | 4451 | −21.65 | 1.23 | 0.59 | −0.51 | $log{Q}_{s}=3.435\mathrm{log}{Q}_{t}-6.544$ ${Q}_{s}=2.858\times {10}^{-7}{Q}_{t}^{3.435}$ |

General power model 2 $log{Q}_{t}$ | 4039 | −17.50 | 1.12 | 0.59 | −0.25 | $log{Q}_{s}=3.915log{Q}_{t}^{0.931}-7.131$ |

Linear model $log{Q}_{t}log{R}_{t}$ | 3715 | −15.47 | 1.03 | 0.61 | −0.05 | $log{Q}_{s}=3.112\mathrm{log}{Q}_{t}+0.10log{R}_{t}-5.714$ |

Model Scenario | RMSE (kg·s^{−1}) | PBIAS | RSR | R^{2} | NSE | Model Equation |
---|---|---|---|---|---|---|

$log{R}_{t}$ $1-10-1-1$ | 2768 | +54.07 | 0.77 | 0.45 | +0.41 | Levenberg-Marguardt |

$log{Q}_{t}$ $1-10-1-1$ | 2070 | +14.91 | 0.57 | 0.67 | +0.66 | Levenberg-Marguardt |

$log{Q}_{t}log{R}_{t}$ $2-10-1-1$ | 2052 | +15.99 | 0.56 | 0.71 | +0.68 | Levenberg-Marguardt |

$log{Q}_{t}log{R}_{t-1}$ $2-10-1-1$ | 2123 | +22.95 | 0.59 | 0.69 | +0.66 | Levenberg-Marguardt |

$log{Q}_{t}log{Q}_{t-1}log{R}_{t}log{R}_{t-1}$ $4-10-1-1$ | 1982 | +14.26 | 0.55 | 0.71 | +0.70 | Levenberg-Marguardt |

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**MDPI and ACS Style**

Baniya, M.B.; Asaeda, T.; K.C., S.; Jayashanka, S.M.D.H. Hydraulic Parameters for Sediment Transport and Prediction of Suspended Sediment for Kali Gandaki River Basin, Himalaya, Nepal. *Water* **2019**, *11*, 1229.
https://doi.org/10.3390/w11061229

**AMA Style**

Baniya MB, Asaeda T, K.C. S, Jayashanka SMDH. Hydraulic Parameters for Sediment Transport and Prediction of Suspended Sediment for Kali Gandaki River Basin, Himalaya, Nepal. *Water*. 2019; 11(6):1229.
https://doi.org/10.3390/w11061229

**Chicago/Turabian Style**

Baniya, Mahendra B., Takashi Asaeda, Shivaram K.C., and Senavirathna M.D.H. Jayashanka. 2019. "Hydraulic Parameters for Sediment Transport and Prediction of Suspended Sediment for Kali Gandaki River Basin, Himalaya, Nepal" *Water* 11, no. 6: 1229.
https://doi.org/10.3390/w11061229