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Joint frequency analysis of river flow rate and suspended sediment load using conditional density of copula functions

  • Research Article - Hydrology
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Abstract

In this study, the river flow rate and suspended sediment load at Deh Molla hydrometric station in Zohreh River in the period of 1983–2018 were used for copula-based joint frequency. The Frank copula was selected as the best copula. The joint frequency analysis of the studied variables was performed based on the conditional density of the copula functions, which leads to the conditional occurrence probability of the variables. The results showed that with increasing river flow rate and suspended sediment load, the joint return period increases. Also, the joint return period for the "and" state is longer than the joint return period for the "or" state. When the river flow rate exceeds the threshold of 100 m3/s and suspended sediment load exceeds the threshold of 2.7 × 104 ton/day, the joint return periods for the "and" state and for the "or" state, are about 11 and 4 years, respectively.

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Abbreviations

ICA:

Imperialist Competitive Algorithm

GWO:

Gray Wolf Optimization Algorithm

EA:

Election Algorithm

RMSE:

Root Mean Square Error

NSE:

Nash–Sutcliffe

R 2 :

Coefficient of Determination

SSC:

Suspended Sediment Concentration

AR:

Autoregressive

NRMSE:

Normalized Root Mean Square Error

IFM:

Inference Functions for Margins

Q w :

River flow rate (m3/s)

Q s :

Suspended sediment load (ton/day)

X m :

Measured data

X p :

Predicted data

\(\overline{X}_{m}\) :

Mean of the measured data

\(\overline{X}_{p}\) :

Mean of the predicted data

\(X_{{m_{\max } }}\) :

Maximum value of the measured data

\(X_{{m_{{{\text{min}}}} }}\) :

Minimum value of the measured data

F X(x):

Distribution of arbitrary margin of x

F Y(y):

Distribution of arbitrary margin of y

C :

Copula

F X,Y(x, y):

Joint distribution function

f Y(y):

Density functions of FY(y)

f X(x):

Density functions of FX(x)

Φ :

Generator function

τ :

Kendall’s tau

Ɵ :

Copula parameter

\(\ln L_{C}\) :

Log likelihood function

JRP:

Joint Return Period

CP:

Conditional Probability

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Acknowledgements

The authors would like to thank Khuzestan Water and Power Authority (KWPA) for providing the data.

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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Authors and Affiliations

  1. Department of Water Engineering, University of Birjand, Birjand, Iran

    Matina Pronoos Sedighi, Yousef Ramezani & Mohammad Nazeri Tahroudi

  2. Khuzestan Water and Power Authority (KWPA), Ahvaz, Iran

    Mehrdad Taghian

Authors
  1. Matina Pronoos Sedighi
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  2. Yousef Ramezani
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  3. Mohammad Nazeri Tahroudi
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  4. Mehrdad Taghian
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Correspondence to Yousef Ramezani.

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Edited by Dr. Ankit Garg (ASSOCIATE EDITOR) / Dr. Michael Nones (CO-EDITOR-IN-CHIEF).

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Pronoos Sedighi, M., Ramezani, Y., Nazeri Tahroudi, M. et al. Joint frequency analysis of river flow rate and suspended sediment load using conditional density of copula functions. Acta Geophys. 71, 489–501 (2023). https://doi.org/10.1007/s11600-022-00894-5

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  • DOI: https://doi.org/10.1007/s11600-022-00894-5

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