3.5.1. Hysteresis Curve and Hysteresis Index (HImid) Analysis

The relationship between the suspended sediment concentration and fluvial discharge can be studied by the nonlinear relationship between them known as hysteresis [44]. Generally, a clockwise hysteresis loop is formed due to an increasing concentration of sediment that forms more rapidly during rising limb, which suggests a source of sediment close to the monitoring point and sediment depletion in the channel system. Conversely, an anticlockwise hysteresis loop shows a long gap between the discharge and concentration peak, which suggests that the source is located far from the monitoring point or bank collapse [45,46].

Clockwise hysteresis loops were developed, increasing the suspended sediment load on the rising limb of hysteresis from December to July, leading to a maximum value of the suspended sediment load of 10,691 kg·s−<sup>1</sup> for a fluvial discharge of 1053 m3·s−<sup>1</sup> 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).

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

The midpoint discharge was calculated by Lloyd [46] and Lawler [47]:

$$Q\_{\rm mid} = k(Q\_{\rm max} - Q\_{\rm min}) + Q\_{\rm min}.\tag{18}$$

where *k* is 0.5, *Qmax* is the peak discharge, and *Qmin* is the starting discharge of an event.

The hysteresis index value was calculated by Lloyd [46] and Lawler [47]:

$$\text{pH}\_{\text{mid}} = \left(\frac{Q\_{s\text{RL}}}{Q\_{s\text{FL}}}\right) - 1 \text{ for a clockwise loop} \,\text{V} \tag{19}$$

$$\text{pH}\_{\text{mid}} = \left( -1 / \left( \frac{Q\_{sRL}}{Q\_{sFL}} \right) \right) + 1 \text{ for an anticlockwise loop}, \tag{20}$$

where *QsRL* and *QsFL* are the suspended sediment on the rising and falling limb, respectively.

**Figure 10.** (**a**) Seasonal hysteresis loop of the sediment load. (**b**) Suspended sediment–discharge rating curve.

3.5.2. Yearly Suspended Sediment Yield and Prediction by Different Models

A regression equation derived from the observed data (2006 to 2011) of the suspended sediment versus the discharge of the river shown in Figure 10b is given by:

$$Q\_s = 2.858 \times 10^{-7} \times Q\_w^{3.435} \text{( $R^2 = 0.92$ )}.\tag{21}$$

The total suspended sediment yield from the catchment is given by:

$$Y\_s = \int\_{t=0}^{T} \mathbb{C}\_{wi} Q\_{wi} dt = \sum\_{i=1}^{365} \mathbb{C}\_{wi} Q\_{wi} \times 10^{-3} \times (t\_{i+1} - t\_i) \,\tag{22}$$

where *Ys* is the total annual sediment yield from the catchment, *Cwi* is the suspended sediment concentration in mg·L<sup>−</sup>1, *Qwi* is the fluvial discharge in m3·s<sup>−</sup>1, *dt* is the time interval, *ti* and *ti*+<sup>1</sup> are the preceding and succeeding time in seconds, respectively.

This study showed that the median ASSL transported by KaliGandaki River in the hydropower reservoir was 0.003 Mt during winter, increased to 0.026 Mt during spring, was 41.405 Mt during the summer season, and decreased 0.175 Mt during the autumn season (Figure 11a). Compared to the seasonal transport of suspended sediment, more than 96% of the suspended sediment was transported during the summer season. This depicts a wide seasonal variability of the suspended sediment caliber, which was nearly 14,000 times higher than the winter season (Figure 11a). The maximum observed ASSL transported by the river was 58.426 Mt in 2009, and after that it decreased (Figure 11b).

The HImid ≈ 0 indicated a weak hysteresis loop whereas HImid > 0 indicated a clockwise hysteresis loop, and HImid < 0 an anticlockwise hysteresis loop. Moreover, the maximum HImid 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 HImid developed was +0.53 in 2008, depicting the nearly same paths of the rising and falling limb and indicating a weak hysteresis loop (Figures 10a and 11b).

Different types of MLR, NLMR, general power, log transform linear, and ANNs models, including inputs of the fluvial discharge and average rainfall of the catchment, were developed to select the most suitable model and the results are shown in Tables 2–6, respectively. The performance parameters of MLR and NLMR were satisfactory but predicted negative sediment values for low fluvial discharges and low rainfall, thus these models are unacceptable.

**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 (HImid).


**Table 2.** MLR models.


14.02*Rt* + 64.44*Rt*−<sup>1</sup> − 784.15




**Table 5.** Log transform models.


**Table 6.** ANN models.

The RMSE, PBIAS, RSR, R2, and NSE values of the general power model, log transform models, and ANNs are shown in Tables 4–6. 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<sup>−</sup>1, PBIAS value of <sup>+</sup>14.26, RSR value of 0.55, R<sup>2</sup> 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−<sup>1</sup> of the SRC, log transform power model, log transform linear models, and ANNs and the observed suspended sediment values respectively.

Among the SRC, power, log transform, and ANN models, the best median ASSL predicted by the ANN model was 37.611 Mt for the period of 2006 to 2011, whereas the observed median ASSL was 41.678 Mt. The mean ASSL transported by the river to the hydropower reservoir was 40.904 ± 12.453 Mt for 2006 to 2011 and the ANNs' predicted mean value was 35.190 ± 7.018 Mt (Figure 13). Struck [8] reported that the average annual suspended sediment transported by this river was 36.9 ± 10.6 Mt.

**Figure 12.** Observed and predicted sediment (**a**) SRC (Qw and Qs) model, (**b**) power model (Qw), (**c**) log transform linear model (Qw and Rt), 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.

#### **4. Conclusions**

Shear stress, specific stream power, and flow velocity are important key hydraulic parameters to describe sediment transport in river systems. The monsoon fluvial discharge and landslide dam outburst flood (LDOF) were responsible for boulder movements in Kali Gandaki River, Nepal. The lower boundary equation derived from a broad range of observed and calculated data sets estimated that a maximum particle size of 840 mm was transported by the monsoon fluvial discharge from 2003 to 2011. The ASSL transported by KaliGandaki River in the hydropower reservoir increased from winter to pre-monsoon to monsoon, respectively, and decreased in the post-monsoon period. It was estimated that 40.904 ± 12.453 Mt suspended sediment is lost annually from the higher Himalayas. Additionally, the ANN model provided satisfactory results for the prediction of the suspended sediments' transport rate in Kali Gandaki River, where the annual predicted mean ASSL value was 35.190 ± 7.018 Mt. These parameters are important for visualizing sediment loss from the higher Himalayas to the sea and also for monitoring the dead storage volume of reservoirs for hydroelectric power generation.

**Author Contributions:** For the conceptualization and methodology, M.B.B. and T.A.; software, validation, formal analysis, and writing—original draft preparation, M.B.B.; writing—review and editing T.A. and S.M.D.H.J.; supervision T.A.; data curation S.K.C.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors would like to give thanks to Saitama University for managing the research environment. We would also like to thank to Nepal Electricity Authority for providing fluvial and sediment data and Ministry of Energy, Water Resources and Irrigation, Department of Hydrology and Meteorology, Nepal for providing historical fluvial and climate data.

**Conflicts of Interest:** The authors declare no conflict of interest.
