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Reliability of functional forms for calculation of longitudinal dispersion coefficient in rivers.

Roohollah Noori1, Ali Mirchi2, Farhad Hooshyaripor3

  • 1Water, Energy and Environmental Engineering Research Unit, Faculty of Technology, University of Oulu, 90014 Oulu, Finland.

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Summary

This study introduces the bandwidths similarity factor (bws-factor) to assess the reliability of functional forms (FFs) for calculating the longitudinal dispersion coefficient (Kx). Results show poor reliability, impacting water quality model accuracy.

Keywords:
Model reliabilityModified bootstrap methodPollutant dispersionRiver

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Area of Science:

  • Environmental fluid dynamics
  • Hydrology
  • Water quality modeling

Background:

  • Dimensional analysis provides theoretical functional forms (FFs) for the longitudinal dispersion coefficient (Kx).
  • The reliability and parameter sensitivity of these FFs for Kx estimation remain unquantified.
  • Accurate Kx is crucial for one-dimensional water quality models.

Purpose of the Study:

  • To introduce a novel index, the bandwidths similarity factor (bws-factor), for quantifying Kx functional form reliability.
  • To evaluate the sensitivity of Kx estimation to variations in FF parameters.
  • To analyze the implications of unreliable Kx estimation on water quality simulations.

Main Methods:

  • Modified bootstrap approach for resampling calibration datasets from a global tracer study database.
  • Tuning of 200 FFs using the generalized reduced gradient algorithm.
  • Calculation of dimensionless Kx values and correlation coefficients.
  • Quantification of FF reliability using the bws-factor.

Main Results:

  • Correlation coefficients for tuned FFs ranged from 0.60 to 0.98.
  • The bws-factor varied from 0.11 to 1.00, indicating poor reliability of FFs for Kx calculation.
  • Exponents for river aspect ratio and friction terms showed wide variations (-0.76 to 1.50 and -0.56 to 0.87, respectively).

Conclusions:

  • Existing functional forms exhibit poor reliability for estimating the longitudinal dispersion coefficient (Kx).
  • Errors in Kx estimation can stem from various sources within the calculation process.
  • Unreliable Kx values can lead to inaccurate water quality predictions in riverine systems.