*3.1. Model Calibration*

The model was calibrated for a period of nine years (2005–2013). The gradational analysis showed that on average, the Indus River transported silt (56.68%) as compared to sand (33.94%) and clay (9.78%).

Further, an extensive analysis of available particle size data of Besham Qila gauging station for 1983, 1989, 1991, 1994, and from 2002–2012 was conducted to calculate its variations with flow. Firstly, as mentioned in the previous paragraph, the average percentages for sand-, silt-, and clay-sized particles were calculated for all flow conditions. Then, the data were segregated into different sets corresponding to the indicated flow ranges in Table 4, and average percentages for sand-, silt-, and clay-sized particles were calculated for those particular flow ranges/bands. The analysis showed conclusively that the percentages of gradations across the sediment classes changed significantly with changing flow bands and were liable to affect sediment transport behavior as the flows increase/decrease. This analysis was important to study and model the morphodynamics across changing low and high flow bands accurately. The results are shown in Table 4 and entered in the sediment module of HEC-RAS as an adjunct to SRC and WA-ANN load series.


**Table 4.** Gradation percentages vis-à-vis increasing flow bands.

First, only hydrodynamic calibration was carried out up to 2013 by changing the value of Manning's roughness (n) throughout the length of the reservoir and comparing the calculated water levels with the observed water levels at different locations along the 66 available cross-sections. Initially, a uniform hydraulic roughness n = 0.04 from the literature [42,43] was adopted and subsequently adjusted in a plausible range of 0.035–0.04, throughout the 73 R/Lines of the reservoir and by comparing with available observed water levels, achieving an NSE and R<sup>2</sup> of 0.916 and 0.940, respectively. Next, hydro-morphodynamic calibration was attempted by varying both bed roughness and sediment parameters in the model.

Applying SRC sediment load at the inlet, it was noticed that the Ackers–White transport formula with the sorting method of Exner (7) was producing somewhat higher values of NSE and R2. Exner (5) and Exner (7) are common bed sorting methods (sometimes called the mixing or armoring methods), which keep track of the bed gradation used by HEC-RAS to compute grain size-specific capacities and also to simulate armoring processes. Exner (5) uses a three-layer bed model that forms an independent coarse armor layer, which limits the erosion of deeper layers, whereas Exner (7) is an alternate version of Exner (5) designed for sand bed rivers as it forms armor layers more slowly and computes more erosion.

Hence, by keeping the combination of Ackers–White + Exner (7) constant, different fall velocities were tested to better the results. Amongst provisions to input commonly-used fall velocity methods like van Rijn, Ruby, and Tofaletti, HEC-RAS has an option to input the Report 12 fall velocity method, which finds solution iteratively by using the same curves as van Rijn, but using the computed fall velocity to compute the new Reynolds number until the assumed velocity matches with the computed velocity within tolerable limits. Consequently, a third tier calibration effort was attempted by varying scaling factors for transport and mobility functions of the transport formula as allowed by the HEC-RAS model for calibration fine-tuning, the result of which emerged with NSE and R<sup>2</sup> of 0.943 and 0.959, respectively. The default value of scaling factors was one, which was manipulated to achieve the maximum hydrodynamic calibration of NSE and R<sup>2</sup> of 0.996. It is worth mentioning here that for the sediment simulation and management study in Tarbela Reservoir in 1998 [44], the Ackers–White transport formula [45] was selected. The work in [43] also suggested the adoption of the Ackers–White formula, for the total load transport capacity of sand-sized fractions. However, other formulas were also tested in the calibration process as detailed in Table 5. A comparison with observed bed levels of 2013 was made and presented in Figure 7.

**Figure 7.** Comparison of observed and SRC simulated bed levels during calibration for 2013: (**a**) along the Tarbela Reservoir; (**b**) R/Line 66; (**c**) R/Line 41; (**d**) R/Line 25; (**e**) R/Line 2.

**Table 5.** Statistical performance of HEC-RAS with SRC sediment series by the input of different transport formulae and varying parameters.


Further, another extensive calibration exercise was carried out applying WA-ANN-based boundary conditions. Again, the Ackers–White transport formula with the sorting method of Exner (5) showed better results. Next, the above combination (Ackers–White + Exner-5) was evaluated by changing the fall velocity equations. Similar to the SRC case, the Tofaletti technique showed the best results hitherto, prior to application of scaling factors. Consequently, the best combination of input parameters (Ackers–White + Exner-7 + Tofaletti) was subjected to rigorous scaling of transport formula parameters. Hence, the highest NSE of 0.979 was achieved during calibration, and the results of the

exercise tabulated in Table 6 in increasing order of NSE values. A comparison with observed bed levels of 2013 was made and presented in Figure 8.

**Table 6.** Statistical performance of HEC-RAS with WA-ANN sediment series by the input of different transport formulae and varying parameters.


**Figure 8.** Comparison of observed and WA-ANN-simulated bed levels during calibration for 2013: (**a**) along the Tarbela Reservoir; (**b**) R/Line 66; (**c**) R/Line 41; (**d**) R/Line 25; (**e**) R/Line 2.
