A Fuzzy Transformation of the Classic Stream Sediment Transport Formula of Yang

Konstantinos Kaffas,Mike Spiliotis,Matthaios Saridakis,Vlassios Hrissanthou,Maurizio Righetti

doi:10.3390/w12010257

Konstantinos Kaffas, Mike Spiliotis + Show 3 more

Open Access

https://doi.org/10.3390/w12010257

Copy DOI

Abstract

The objective of this study is to transform the arithmetic coefficients of the total sediment transport rate formula of Yang into fuzzy numbers, and thus create a fuzzy relationship that will provide a fuzzy band of in-stream sediment concentration. A very large set of experimental data, in flumes, was used for the fuzzy regression analysis. In a first stage, the arithmetic coefficients of the original equation were recalculated, by means of multiple regression, in an effort to verify the quality of data, by testing the closeness between the original and the calculated coefficients. Subsequently, the fuzzy relationship was built up, utilizing the fuzzy linear regression model of Tanaka. According to Tanaka’s fuzzy regression model, all the data must be included within the produced fuzzy band and the non-linear regression can be concluded to a linear regression problem when auxiliary variables are used. The results were deemed satisfactory for both the classic and fuzzy regression-derived equations. In addition, the linear dependence between the logarithmized total sediment concentration and the logarithmized subtraction of the critical unit stream power from the exerted unit stream power is presented. Ultimately, a fuzzy counterpart of Yang’s stream sediment transport formula is constructed and made available to the readership.

Highlights

The need for knowledge of the amount of sediment reaching specific points of streams and river segments became evident from the early 20th century [1,2,3]
The present study aims to redefine the coefficients of the stream sediment transport formula of Yang [22] with a fuzzy regression, using the very same experimental data that Yang used for the original equation
The objective of this research is to transform the arithmetic coefficients of the total sediment transport rate formula of Yang, into fuzzy numbers, and create a fuzzy relationship that will provide a fuzzy band of in-stream sediment concentration

Summary

Introduction

The need for knowledge of the amount of sediment reaching specific points of streams and river segments became evident from the early 20th century [1,2,3]. As a consequence of that, the investigation of the sediment transport processes and mechanisms emerged as a high significance research topic for hydrologists, physicists and engineers in the years that followed. Water-quality issues, changes in the wet cross-section, increased flooding risk and obstruction of navigation, as a result of excessive depositions, effects on the aquatic ecosystems, decline of macrophyte growth, clogging of spawning gravel, pressures inflicted on coastal zones, effective diminution of dams’ storage volume, due to excessive sedimentation, and extreme erosion rates in the case of sediment-starved water (usually below storage dams—theory of hungry water) [6,7,8,9,10,11], are some of the effects of sediments, which constitute the driving force behind the investigation of sediment transport processes, as well as modeling and quantification efforts. Knowledge about the interrelated interactions among water-biota-sediment in natural rivers is one of the central issues in today’s sustainable river management [12].

Objectives

Methods

Results

Conclusion