# An Innovative Approach to Minimizing Uncertainty in Sediment Load Boundary Conditions for Modelling Sedimentation in Reservoirs

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}) = 0.969 and Nash–Sutcliffe Efficiency (NSE) = 0.966 also facilitated good calibration in morphodynamic calculations with R

^{2}= 0.97 and NSE = 0.96. The model was validated for the sediment deposits in the reservoir with R

^{2}= 0.96 and NSE = 0.95. Due to desynchronization between the glacier melts and monsoon rain caused by warmer climate and subsequent decrease of 17% in sediment supply to the Tarbela dam, our modelling results showed a slight decrease in the sediment delta for the near future (until 2030). Based on the results, we conclude that our overall state-of-the-art modelling offers a significant improvement in computational time and accuracy, and could be used to estimate hydrodynamic and morphodynamic parameters more precisely for different events and poorly gauged rivers elsewhere in the world. The modelling concept could also be used for predicting sedimentation in the reservoirs under sediment load variability scenarios.

## 1. Introduction

^{3}(BCM) and SL of 209.6 million tons (Mt) was among the highest peak flow/SL years from 1969–2008, whereas 1985 had a lower flow/SL than corresponding averages. Similarly, the validation period of five years (1986–1990) also covers both dry and wet periods [11]. The computational time for hydrodynamic calibration was reduced using an automatic calibration method, which updated roughness for each mesh node using backward error propagation. The boundary condition of the morphodynamic model (in cascade modelling) was modified based on [9] studies where (due to the strong hysteresis phenomena) daily SL series was more precisely reconstructed from non-continuous suspended sediment (SSC) samples using WA-ANN. The overall performance of the modelling results was assessed using statistical performance parameters. To confine the length of this paper, detail of daily SL series reconstruction is not repeated here.

## 2. Methods

#### 2.1. Study Area

^{3}(BCM) with reservoir length extending approximately 80 km. The outlet works consist of four tunnels cut through the right abutment of the main dam plus a fifth tunnel between the main dam and the spillways on the left bank. The total installed capacity of the dam is currently 4888 MW, 83% more than was originally envisaged in the initial design, with several turbines installed on tunnels 1–4 (Figure 2). This also includes a recently installed scheme on tunnels 4 under Tarbela IV extension project, which has a power generation capacity of 1410 MW [27].

^{2}(Figure 1), of which over 90% lies between the great Karakoram and the Himalaya ranges. The snowmelt waters from this region contribute a major part of the annual flows regrulated by the reservoir. The remainder of the Basin lying immediately upstream of the dam (Figure 1) is subject to the monsoon rainfall primarily during the months of July to September. The peak flow due to snowmelt can be as high as 5660 m

^{3}/s to 11,300 m

^{3}/s with an additional rainfall contribution typically reaching a maximum of 5660 m

^{3}/s. The average annual inflow to the Tarbela Reservoir is 81 BCM [28].

#### 2.2. Data Description

^{2}. Approximately 3500–4000 measurements of the bed level changes, water depths, and water surface elevations along these range lines are available, which were mostly collected during each survey conducted from September to November. The distance between the cross sections (range lines) and the (measured) data points along these cross sections is not uniform. An average distance between each cross section along the river thalweg is approximately 1.16 km. However, compared to the upstream (upper periphery of the reservoir), the distances between the cross sections are smaller near the dam. The distance between the measured data points along the cross sections (lateral distance in y direction) also varies with a mean of 39 m. The mean cross sectional width near the dam axis is approximately 4–5 km, which reduces to only 300–500 m at the upper periphery. Therefore, the major ponding area is near the dam axis and contains huge sediment deposits (Figure 2).

^{3}. However, observations show that there is no clear boundary of sizes between cohesive and non-cohesive sediments, the definition of cohesive sediment is usually site specific. Normally, cohesion plays a significant role for sediment sizes smaller than 2 m in reservoirs (including the Tarbela). We, therefore, used cohesionless modelling [31,32,33]). Most of the transport processes occur in the summer months; 84% of the total annual discharge and 99% of the SSL transport occur from May to September (Table 3, Figure 3).

#### 2.3. Model System

#### 2.3.1. TELEMAC-2D for Hydrodynamics

^{2}); ${Z}_{s}$ = free surface elevation (m); t = time (s); x, y = horizontal Cartesian coordinates (m); $\rho $ = density of water (kg/m

^{3}); ${\tau}_{xx}$ and ${\tau}_{yy}$ = depth-averaged turbulent stresses. The bed shear stress is represented as a quadratic function of velocity:

#### 2.3.2. SISYPHE for Morphodynamics

^{3}/m

^{3}); ${q}_{t,x}$ = total sediment transport in x-direction (m

^{2}/s); ${q}_{t,y}$ = total sediment transport in y-direction (m

^{2}/s); $\eta {\prime}_{e}$, $\eta {\prime}_{d}$ are erosion and deposition rates, respectively (m/s).

#### 2.4. Model Setup

#### 2.4.1. Grid Mesh

^{2}. In selecting cell resolution, we tried to achieve a reasonable compromise between accuracy and computational time.

^{2}= 0.99, and a relative difference between the measured and the computed volume = 1%. Furthermore, the longitudinal profile of the mean measured and calculated river bed is also shown in Figure 6. The results confirmed a correct representation of the grid mesh used in the numerical model.

#### 2.4.2. Initial and Boundary Conditions

#### 2.5. Model Performance

^{2}), which is an index of the degree of relationship between the observed and simulated data, ranging from 0 to 1, as follows:

#### 2.6. Model Parameters and Automatic Calibration

- volume of sediments deposited each year after the flood season (between October–November),
- 72 longitudinal profiles along the reservoir over the period 1983 to the present,
- composition of the sediment deposits in some areas,
- flow velocities measured with an ADCP at several cross sections,
- outflow discharge and sediment concentration.

^{2}), ${D}_{*}$ is dimensionless grain diameter, ${Z}_{ref}$ is reference elevation which can be calculated after [43] using $max(\frac{{k}_{s}}{2};0.01m)$, while ${k}_{s}$ is total bed roughness (m) and is obtained from hydrodynamic calculations (Equation (16): friction coefficients from hydrodynamic results) and type of bed-forms (flat, smooth or ripples bed). The ${\tau}^{\prime}$ is total shear stress (N/m

^{2}) includes skin friction which can be calculated using Equation (12):

- linear,
- nearest point,
- natural, and
- cubic

## 3. Results

^{2}), observed standard deviation ratio (RSR), and Nash–Sutcliffe Efficiency (NSE). The results are discussed in detail below.

#### 3.1. Model Calibration

^{2}, RSR, and NSE. The hydro-morphodynamic results of the study are described below.

- linear,
- nearest point,
- natural, and
- cubic.

^{2}, initially, we obtained a statistical mix (S) = 0.933, R

^{2}= 0.90, and NSE = 0.898 (Figure 11). The performance of the model increased to a statistical mix = 0.978, R

^{2}= 0.969, and NSE = 0.966 by iterating n for each node point as per Equation (16) and the process stated in Figure 7. The approximated computational time in each simulation was 12–15 h using a server with 20 physical cores (dual Intel XEON E5-2687W v3 @ 3.1 GHz) and 128 GB of RAM. Due to the large standard deviation (33.9 m) and small RMSE (0.0988) in the water depths, the observation standard deviation ratio (Equation (7)) remained in the range of 10

^{$-3$}in all five simulations.

^{$-5$}m/s at some nodes on high river banks. We solved this issue by specifying no SL transport at equal or less than 1 cm water depth. Our final simulated results from May 1984 to October 1985 showed R

^{2}= 0.97, RSR = 0.36%, and NSE = 0.96 (Figure 12). There was only 0.76% difference between the simulated and measured deposits in the reservoir. However, the mean differences between the simulated and observed river bed was in the range of −5 to 7 m.

#### 3.2. Model Validation

^{2}= 0.96, RSR = 0.37%, and NSE = 0.95, whereas the difference between the measured and simulated deposits was only 0.54%. Similar to the morphodynamic calibration, the mean differences between the simulated and observed river bed were in the range of −5 to 7 m (Figure 14).

#### 3.3. Model Application

^{3}[11]. However, the mean SL from 2000–2008 was decreased to 146 Mt/year with a mean discharge of 75 billion m

^{3}/year. Near future projections from 2010–2030 also suggest a further decrease to 120 Mt/year with a mean discharge of 75 billion m

^{3}/year. These disproportional spatio-temporal trends between SL and discharges are primarily caused by intra-annual shifts in flow discharges from summer to the winter under the influence of warmer climates [11,48]. Our modelling results also showed a stability in sediment delta development due to an average 17% decrease in sediment supply in the near future (Figure 17). However, the overall water availability is expected to slightly decrease in the future, and the significant decrease in sediment load can help to store more water for multi-purpose use (irrigation, hydropower, etc.) and was likely to increase the life span of the reservoirs.

## 4. Discussion

^{2}= 0.90 and NSE = 0.898 to R

^{2}= 0.969, and NSE = 0.966 (Figure 11). In addition, more precise sediment load (SL) boundary conditions obtained using the wavelet artificial neural network (WA-ANN) calibrated the model with R

^{2}= 0.97 and NSE = 0.96 (Figure 12). The model validated the results by predicting the reservoir bed for five years (1986–1990) with R

^{2}= 0.96 and NSE = 0.95 (Figure 14). Although the overall statistical performance of the model was good, it also over-predicted the river bed (0.76%) in the calibration process, particularly upstream of the ponding area (Figure 12). However, the over-predictions were reduced to an average 0.54% in the validation process (Figure 14). The calculations for bed level changes in the ponding area, particularly for the sediment delta, were close to the measurements in both the calibration and validation processes (Figure 13 and Figure 15). In addition, our modelling also shows a stability in the sediment delta development due to significant decrease (17%) in near future sediment load entering the reservoir (Figure 16 and Figure 17).

- inflow of both discharges and SLs,
- particle size distribution of sediments,
- specific weight of sediment deposits,
- geometry of the reservoir, and
- reservoir operation rules [51].

## 5. Conclusions

- More accurate WA-ANN estimated sediment load boundary conditions which better represent the hysteresis phenomenon and hydrological variations for the Indus River enabled the successive morphodynamic model to accurately predict the bed level changes in the Tarbela dam.
- Automatically calibrating hydrodynamics improved the overall statistical performance and reduced the calculation time for long-term simulations. In addition, specifying the bed roughness for each mesh node using the back propagation error method subsequently enhanced the performance of morphodynamic calculations by providing better hydrodynamic variables and total bed roughness for the calculation of sediment erosion, transport and deposit in the flow area.
- The desynchronization between glacier melt and monsoon rainfall due to warmer climate will also cause a significant decrease in future sediment loads and subsequent delta development. Therefore, past hydro-meteorological data (showing higher sediment loads) cannot be used without modification when making future predictions, particularly for the hydropower projects planned at the Indus River/Basin.

- The presented modelling concept can be used to improve/design sediment management strategies for the existing and planned hydraulic structures in other non-gauged or poorly-gauged rivers.
- Although the effect of the bed roughness on the water depths in large dams is not always dominant, the concept of an automatic hydrodynamic calibration can also be used for other water bodies where roughness has a significant influence on water depths.
- In order to reduce computational time for long-term morphodynamic predictions, coupling of the TELEMAC 2D model with a 1D model/ANN is recommended.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ADCP | Acoustic Doppler Current Profiler |

BCM | billion cubic meter |

${c}_{b}$ | sediment concentration in bed load layer |

${C}_{e}q$ | equilibrium near-bed concentration |

${C}_{f}$ | roughness coefficient |

${C}_{f}^{{\phantom{\rule{-2.84544pt}{0ex}}}^{\prime}}$ | combined friction of both drag forms and skin friction |

${d}_{50}$ | mean diameter |

${D}_{*}$ | dimensionless grain diameter |

${d}^{o}$ | observed water depth |

${d}^{s}$ | simulated water depth |

g | gravitational acceleration |

h | water depth |

HEC-RAS | Hydrologic Engineering Center-River Analysis System |

k | von Karman coefficient |

km | kilometre |

${k}_{s}$ | bed roughness |

${k}_{s}^{{}^{\prime}}$ | roughness height |

masl | mean above sea level |

Mt | million ton |

MW | megawatt |

n | Manning roughness |

NSE | Nash–Sutcliffe Efficiency |

$p\prime $ | bed porosity |

ppm | part per million |

${q}_{t,x}$ and ${q}_{t,y}$ | total sediment transport in x and y direction |

R^{2} | coefficient of determination |

R/line | range lines or cross section |

RESSASS | Reservoir Survey Analysis and Sedimentation Simulation |

RSR | observations standard deviation ratio |

RWL | reservoir water level |

S | statistical mix |

SL | sediment load |

SRC | sediment rating curve |

SSL | suspended sediment load |

SSC | suspended sediment concentration |

SUPG | Streamline-Upwinded Petrov–Galerkin |

t | time |

$u,v$ | depth-averaged flow velocity components in x and y direction |

$\rho $ | density |

${\tau}_{xx}$ and ${\tau}_{yy}$ | depth-averaged turbulent stresses |

${\delta}_{b}$ | bedload layer thickness |

$\eta {\prime}_{e}$ | erosion rate |

$\eta {\prime}_{d}$ | deposition rate |

${X}_{i}^{obs}$ | observed parameter |

${X}_{i}^{sim}$ | simulated parameter |

${\tau}^{{}^{\prime}}$ | shear stress due to skin friction |

${\tau}_{cr}$ | critical shear stress |

${\tau}_{b}$ | total bed shear stress |

$\mu $ | bed form coefficient |

${\alpha}_{ks}$ | calibration coefficient |

UIB | Upper Indus Basin |

${W}_{s}$ | settling velocity |

WA-ANN | wavelet artificial neural network |

WAPDA | Water and Power Development Authority |

yr | year |

${Z}_{b}$ | bed elevation |

${Z}_{ref}$ | reference elevation |

${Z}_{s}$ | free surface elevation |

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**Figure 1.**Location map of the study area, modified from [17].

**Figure 3.**Sediment inflow, reservoir water level and discharges in 1984 (dash line represents outflow from the dam).

**Figure 4.**Measured data points (grey) along cross sections/range lines and TELEMAC simulated water depth at 30 September 1983.

**Figure 7.**Algorithm for model calibration. The algorithm for TELEMAC and SISYPHE works in an uncoupled way where morphodynamic calibration only start after hydrodynamic calibration finished.

**Figure 8.**Interpolated Manning roughness (n). Grey lines represent the measurements along the cross sections/range lines (R/line).

**Figure 10.**Comparison between measured (circles) and simulated water depths at selected cross sections (R/line) for 1983’ event. Measurements starts from the orographically left side of the reservoir.

**Figure 12.**Longitudinal profile of mean measured and computed river bed at the end of the calibration process.

**Figure 13.**Comparison between measured and simulated river bed at four selected cross sections/range lines (R/line) at the end of calibration process. Measurements start orographically from the left side of the reservoir.

**Figure 14.**Longitudinal profile of mean measured and computed river bed at the end of the validation process.

**Figure 15.**Comparison between measured and simulated river bed at four selected cross sections (R/line) at the end of the validation process. Measurements start orographically from left side of the reservoir.

**Figure 17.**Longitudinal profile of predicted river bed using WA-ANN predicted sediment boundary conditions.

**Table 1.**Statistical performance of WA-ANN for reconstructing SSL in study period (only high flows from May to September). Sediment load was calculated in [11].

Process | Duration | R^{2} | RSR | NSE |
---|---|---|---|---|

Calibration | 1984–1985 | 0.842 | 0.019 | 0.837 |

Validation | 1986–1990 | 0.888 | 0.019 | 0.871 |

Sand | ||||||
---|---|---|---|---|---|---|

Grain size (mm) | 1.0 | 0.5 | 0.25 | 0.125 | 0.0625 | Pan |

Fraction (%) | 100 | 99.87 | 96.98 | 85.85 | 71.98 | 71.97 |

Silt | ||||||

Grain size (mm) | 0.0442 | 0.0312 | 0.0221 | 0.0156 | 0.011 | 0.0078 |

Fraction (%) | 64.51 | 57.12 | 49.59 | 41.07 | 32.70 | 25.29 |

Clay | ||||||

Grain size (mm) | 0.0055 | 0.0039 | ||||

Fraction (%) | 17.43 | 10.32 |

**Table 3.**Suspended sediment load and flow volume distribution in million tons (Mt) and billion cubic meters (BCM) from 1984–1990. Outflow also includes the minor contribution (0.04% and 0.16%) of the Siran and Brandu tributaries.

Months | Average SSL (Mt) | Average inflow (BCM) | Average outflow (BCM) |
---|---|---|---|

Jan–Apr | 0.98 | 5.67 | 11.85 |

May–Sep | 157.9 | 65.54 | 55.18 |

Oct–Dec | 1.11 | 5.50 | 11.25 |

Parameter | Value/methods |
---|---|

Hydrodynamics | |

Numerical scheme | Centred semi implicit scheme plus SUPG |

Solver for hydrodynamic propagation step | Generalized minimum residual method |

Equations | Saint-Venant finite element |

Hydrodynamic calibration factor (K) | 1.0 |

Manning roughness (n) | 0.035–0.045 |

Mean Manning roughness (n) | 0.0395 |

TELEMAC and SISYPHE model coupling | Internal |

Morphodynamics | |

Bed porosity ($p\prime $) | 0.375 |

Fluids viscosity ($\nu $) | $1\times {10}^{-6}$ |

Suspended sediment transport formula | [43] |

Calibration coefficient (${\alpha}_{ks}$) | 3 |

von Karman coefficient (k) | 0.40 |

Shields parameter | 0.047 |

Friction angle of sediment (${\varphi}_{s}$) | 32 |

Minimum depth required for sediment transport | 1 cm |

Formula for deviation | [46] |

Parameter for deviation ($\beta 2$) [46] | 0.85 |

Stream wise slope effect ($\beta $) | 1.3 |

Solver for suspension | Conjugate gradient |

Critical evolution ratio | 0.5 |

Numerical treatment of the advection term | Edge-based N-scheme |

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**MDPI and ACS Style**

Ateeq-Ur-Rehman, S.; Bui, M.D.; Hasson, S.U.; Rutschmann, P.
An Innovative Approach to Minimizing Uncertainty in Sediment Load Boundary Conditions for Modelling Sedimentation in Reservoirs. *Water* **2018**, *10*, 1411.
https://doi.org/10.3390/w10101411

**AMA Style**

Ateeq-Ur-Rehman S, Bui MD, Hasson SU, Rutschmann P.
An Innovative Approach to Minimizing Uncertainty in Sediment Load Boundary Conditions for Modelling Sedimentation in Reservoirs. *Water*. 2018; 10(10):1411.
https://doi.org/10.3390/w10101411

**Chicago/Turabian Style**

Ateeq-Ur-Rehman, Sardar, Minh Duc Bui, Shabeh Ul Hasson, and Peter Rutschmann.
2018. "An Innovative Approach to Minimizing Uncertainty in Sediment Load Boundary Conditions for Modelling Sedimentation in Reservoirs" *Water* 10, no. 10: 1411.
https://doi.org/10.3390/w10101411