Abstract
The present paper deals with the applicability of the Meyer–Peter and Müller (MPM) bed load transport formula. The performance of the formula is examined on data collected in a particular location of Nestos River in Thrace, Greece, in comparison to a proposed Εnhanced MPM (EMPM) formula and to two typical machine learning methods, namely Random Forests (RF) and Gaussian Processes Regression (GPR). The EMPM contains new adjustment parameters allowing calibration. The EMPM clearly outperforms MPM and, also, it turns out to be quite competitive in comparison to the machine learning schemes. Calibrations are repeated with suitably smoothed measurement data and, in this case, EMPM outperforms MPM, RF and GPR. Data smoothing for the present problem is discussed in view of a special nearest neighbor smoothing process, which is introduced in combination with nonlinear regression.
Highlights
Meyer–Peter, Favre and Einstein [1] published a formula in 1934 related to the transport of uniform sediment on a plane bed, while Meyer–Peter and Müller [2,3] published in 1948 and 1949 the definitive formula related to the transport of sediment mixtures with different values of specific gravity
In view of the fact that the predictive power of the Meyer–Peter and Müller (MPM) formula did not reach high levels, the present paper proposes an Enhanced MPM (EMPM) formula, demonstrating that, under suitable calibration, it shows a much better fitness to field data
The EMPM formula presented in this paper was calibrated with respect to the four parameters kst, α, β and γ, contained in the objective function of Equation (19)
Summary
Meyer–Peter, Favre and Einstein [1] published a formula in 1934 related to the transport of uniform sediment on a plane bed, while Meyer–Peter and Müller [2,3] published in 1948 and 1949 the definitive formula related to the transport of sediment mixtures with different values of specific gravity. The historical development of the MPM formula is described in detail in Hager and Boes [4]. In this formula, the unit submerged sediment discharge is calculated, and the roughness effect of the channel bottom and walls is taken into account. Wong and Parker [5], by using the same databases of Meyer–Peter and Müller, have suggested two substantially revised forms of the MPM (1948) formula, in which no correction for bed forms is made. According to Wong and Parker [5], the form drag correction of the MPM formula is unnecessary in the context of the plane bed transport data. The amended bed load transport relations of Wong and Parker are valid for lower-regime plane bed equilibrium transport of uniform sediment
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