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Prediction of scour pattern around hydraulic structures using geostatistical methods

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Abstract

Simulation of sediment movement, identification of scour pattern, and sediment variations play an important role in river rehabilitation and protection of hydraulic structures considering their stability and safety. In general, different shapes of abutments (circular, vertical, and wing wall) and also spur dikes were employed to protect against scouring. The main purpose of this paper is to investigate spatial variations of local scour depth around these hydraulic structures using deterministic spatial estimator known as InverseDistance Weighed (IDW), and two geostatistical approaches known as Ordinary Kriging (OK) and Bayesian Maximum Entropy (BME). To achieve this goal, experimental tests were conducted to measure scour pattern under three types of abutments and spur dikes. To evaluate the results of scour depth, leave-one-out cross-validation technique has been used. The comparison of the computed versus observed scour depth depicts that geostatistical methods (OK and BME) can estimate the maximum scour depth more reliably and accurately than IDW method. Experimental results show that the trend of scour depth for all abutment types does not significantly differ. Maximum scour depths at the wing wall abutment were lower than vertical abutment.

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Author information

Authors and Affiliations

  1. Department of Civil Engineering, Semnan University, Semnan, Iran

    Hojat Karami, Bardia Bayat & Khosrow Hosseini

  2. School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Mohsen Nasseri

Authors
  1. Hojat Karami
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  2. Bardia Bayat
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  3. Khosrow Hosseini
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  4. Mohsen Nasseri
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Corresponding author

Correspondence to Hojat Karami.

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Responsible Editor: Stefan Grab

Appendix

Appendix

Percent Average Estimation Error (PAEE):

$$ PAEE=\frac{1}{\overline{X}N}\sum \limits_{i=1}^N abs\left\{X\left({\overrightarrow{s}}_i\right)-\hat{X}\left({\overrightarrow{s}}_i\right)\right\}, $$
(A)

where, \( \overline{X} \)is average of the observed values, N is number of observed values, \( X\left({\overrightarrow{s}}_i\right) \)is observed values in location \( \overrightarrow{s}=\left({s}_1,{s}_2\right) \), \( \hat{X}\left({\overrightarrow{s}}_i\right) \)is estimated values in location \( \overrightarrow{s}=\left({s}_1,{s}_2\right) \) and abs is returns absolute value.

Normalized Mean Square Error (NMSE):

$$ NMSE=\frac{1}{S^2N}\sum \limits_{i=1}^N{\left\{X\left({\overrightarrow{s}}_i\right)-\hat{X}\left({\overrightarrow{s}}_i\right)\right\}}^2, $$
(B)

where S2 is the variance of observed values.

Mean Absolute Error (MAE) or Bias:

$$ MAE=\frac{1}{N}\sum \limits_{i=1}^N abs\left\{X\left({\overrightarrow{s}}_i\right)-\hat{X}\left({\overrightarrow{s}}_i\right)\right\}. $$
(C)

Mean Square Error (MSE):

$$ MSE=\frac{1}{N}\sum \limits_{i=1}^N{\left\{X\left({\overrightarrow{s}}_i\right)-\hat{X}\left({\overrightarrow{s}}_i\right)\right\}}^2. $$
(D)

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Karami, H., Bayat, B., Hosseini, K. et al. Prediction of scour pattern around hydraulic structures using geostatistical methods. Arab J Geosci 12, 801 (2019). https://doi.org/10.1007/s12517-019-4992-x

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  • DOI: https://doi.org/10.1007/s12517-019-4992-x

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