M. Tamer AYVAZ Department of Civil Engineering Pamukkale University Denizli, TURKEY

Optimal Estimation of Manning’s Roughness in Open Channel Flows Using a Linked Simulation-Optimization Model M. Tamer AYVAZ Department of Civil Engineering Pamukkale University Denizli, TURKEY E-mail: tayvaz@pau.edu.tr Ömer GENÇ Department of Civil Engineering Pamukkale University Denizli, TURKEY E-mail: omergenc@live.com

Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions Presentation Outline Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ●○ ○ ○○○ ○○○ ○○○○○○○○ ○ Objective Estimation of Manning’s surface roughness is an important step since spatial distribution of this parameter is of primary importance in any study involving open channel flows. In practice, distribution of this parameter is usually determined using trial-and-error procedures. These procedures aim to minimize the error between the measurements and model results which require high computation times especially for the large channel networks. Also, accuracy of this kind of parameter estimation procedures usually depends on the modeller’s experience. Therefore, optimal estimation of roughness distributions becomes a challenging task. Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

The main objective of this study is to propose a linked simulation-optimization model to determine Manning’s roughness values for 1-Dimensional free-surface flows. In the proposed model, hydrodynamic flow simulations have been performed by modeling the channel section on HEC-RAS in the simulation model. This model is then linked to an optimization model where heuristic Harmony Search (HS) Algorithm is used. The main objective of the HS based optimization model is to determine the roughness parameters by minimizing the error value between observed and calculated stage values for selected observation stations. The performance of the proposed model is tested on three open channel flow examples for both error-free and measurement error conditions. Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ○● ○ ○○○ ○○○ ○○○○○○○○ ○ Objective Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

In this study, the hydrodynamic flow process is simulated using HEC-RAS, which is a well known flow model for one-dimensional shallow water flows. HEC-RAS simulates the flow process by solving the Saint Venant equations St. Venant equations: Manning’s Equation Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ○○ ● ○○○ ○○○ ○○○○○○○○ ○ Simulation Model Momentum Equation Continuity Equation Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ○○ ○ ●○○ ○○○ ○○○○○○○○ ○ Harmony Search Optimization Algorithm (HS) • HS is a newly proposed heuristic optimization algorithm and gets its computational basis from the musical processes. • The purpose of the musical processes isto seek a musically pleased harmony through making severalimprovisations • This process is analogous to the optimization process since the main objective of the optimization is to find a solution through several iterations. • Each musician is analogous to a decision variable and the collection of notes in the musicians' memories is analogous to values of the decision variables. • Computational structure of HS is based on three operations: • Harmony memory consideration • Pitch adjusting • Random selection Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ○○ ○ ○●○ ○○○ ○○○○○○○○ ○ Harmony Search Optimization Algorithm (HS) Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ○○ ○ ○○● ○○○ ○○○○○○○○ ○ Harmony Search Optimization Algorithm (HS) • Solution of an optimization problem using HS is performed based on the following scheme: Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ○○ ○ ○○○ ●○○ ○○○○○○○○ ○ Problem Formulation • The problem of roughness estimation can be solved by establishing an optimization model. • Optimization model runs the HEC-RAS model for the each iteration and calculates the objective function value based on the hydrodynamic response for the generated roughness distribution. Objective Function: Subject to Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ○○ ○ ○○○ ○●○ ○○○○○○○○ ○ Problem Formulation • The performance and robustness of the proposed model is also evaluated for measurement error conditions. • With this purpose, all the measurements are usually perturbed with error terms with normal distribution. • The term of α is used to adjust the level of noise. The proposed ranges for α : α< 0.10 low • 0.10 ≤ α ≤ 0.15 moderate • α > 0.15 high and are the set of measured and perturbed stages, is a fraction, and is the error matrix which includes the error terms with zero mean and 1 standard deviation. Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ○○ ○ ○○○ ○○● ○○○○○○○○ ○ Problem Formulation • Since the required measurement data is hypothetically developed for the known roughness distribution, it is possible to evaluate model results with true ones. • With this purpose, identification results have been evaluated using the normalized error (NE), percent average estimation error (PAEE), and standard deviation (SD). Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ○○ ○ ○○○ ○○○ ●○○○○○○○ ○ Numerical Applications • The performance of the proposed simulation-optimization model is evaluated using three hypothetical examples. • For all the examples; • Bed slope is considered as 0.0004, • Channel cross-sections are trapezoidal with a base width of 25 m and side slope of 0.5, • Upstream boundary condition is generated using the following Synthetic hydrograph formula: 1 2500 Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ○○ ○ ○○○ ○○○ ○●○○○○○○ ○ Numerical Applications The related parameters of the syntetic hydrograph and true roughness values: • All the problems have been solved for both error-free and measurement error conditions. • For the solutions with measurement errors, 5 different realizations have been considered. • After getting the results for different realizations, averages of them are used for model evaluation. Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ○○ ○ ○○○ ○○○ ○○●○○○○○ ○ Example 1 • This example deals with the flow in a single channel reach with a length of 12 km. • The measurement data includes hourly collected stage observations. • Using the given HS solution parameters, the model result for error-free measurements can be obtained as: Single n Observation Station Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ○○ ○ ○○○ ○○○ ○○○●○○○○ ○ Example 1 Comparison of stage data for error-free and moderate error conditions: Identification Results for Different Size of Noise Levels: Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

This example also deals with the flow in asingle channel reach with a length of 12 km The key difference of this example is that it includes 3 different roughness values. Model result for error-free measurements: Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ○○ ○ ○○○ ○○○ ○○○○●○○○ ○ Example 2 n1 n2 n3 Observation Stations Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ○○ ○ ○○○ ○○○ ○○○○○●○○ ○ Example 2 Identification Results for Different Size of Noise Levels: Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

This example deals with the flow in a channel network with 3 different reaches. As can be seen, two different input hydrographs are provided from points A and B and effect of these discharges is observed in Point C. There are three observation stations (e.g. points 1, 2, and 3) where stage measurements are recorded hourly. Model result for error-free measurements: Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ○○ ○ ○○○ ○○○ ○○○○○○●○ ○ Example 3 Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ○○ ○ ○○○ ○○○ ○○○○○○○● ○ Example 3 Identification Results for Different Size of Noise Levels: Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

In this study, a linked simulation-optimization model is proposed for solving the roughness estimation problem in open channel flows. The proposed model uses the HEC-RAS model to perform the hydrodynamic flow calculations in the simulation model. This model is then linked to HS based optimization model to determine the roughness distribution. The main advantages of the proposed model are that it is capable of solving the many problems that HEC-RAS can solve and it is independent from the initial value settings since the optimization model used in this study is heuristic based. The performance of the proposed model is tested on three open channel examples for error-free and measurement error conditions. Identification results indicate that the proposed model give acceptable results even if the measurements include moderate or high noise levels. Objective Simulation Model Optimization Model Problem Formulation Numerical Applications Conclusions ○○ ○ ○○○ ○○○ ○○○○○○○○ ● Conclusions Ayvaz & Genç, 30th May 2012, Ohrid, Macedonia

M. Tamer AYVAZ Department of Civil Engineering Pamukkale University Denizli, TURKEY E-mail: tayvaz@pau.edu.tr Thank you for your attention... Ömer GENÇ Department of Civil Engineering Pamukkale University Denizli, TURKEY E-mail: omergenc@live.com This study is supported by The Turkish Academy of Sciences (TUBA) - The Young Scientists Award Programme (GEBIP)

M. Tamer AYVAZ Department of Civil Engineering Pamukkale University Denizli, TURKEY