Derivation of Sediment Transport Models for Sand Bed Rivers from Data-Driven Techniques

Abstract

Hydraulic engineers and geologists have studied sediment transport in natural streams and rivers for centuries due to its importance in understanding river hydraulics. Erosion and deposition of sediment alters the hydraulic geometry of the channel and may cause increase of flood frequency as well as navigation problems from excessive deposition. Moreover, discharge of industrial and agricultural residuals sets the sediment particles to be the primary transporters of toxic substances that contaminate aquatic systems. High sediment discharge peaks may be destructive for fish habitats and ecosystems, and long-term sediment yield affects the design and function of constructions such as dams and reservoirs, as well as the coastal erosion at the basin outlet. Sediment transport in sand bed rivers and natural streams is a complex process. For its quantification, numerous sediment transport functions have been introduced in the past years based on different concepts. There are four basic approaches used in the derivation of sediment transport formulae (Yang, 1977): 1) The deterministic approach, which obeys the laws of physics and usually is based on an independent variable like slope, shear stress, stream power, unit stream power etc. 2) The regression approach, which has emerged from the thought that sediment transport is such a complex phenomenon that cannot be described by a single dominant variable. 3) The pioneering probabilistic approach of Einstein (1942), which highlighted the complexity and the stochastic nature of the sediment transport in a rather laborious way for common usage in engineering, and 4) The regime approach, which was developed as a result of long-term measurements in equilibrium conditions. The emerging results from all these concepts usually differ drastically from each other and from the measured data. Consequently, none of the published sediment transport equations has gained universal acceptance in confidently predicting sediment transport rates, especially in rivers. An alternative approach may be the usage of data-driven modeling, which is especially attractive for modeling processes, in which knowledge of the physics of the problem is inadequate. The scope of this chapter is the utilization of some widely used data-driven techniques, namely artificial neural networks (ANNs) and symbolic regression based on genetic programming (GP) in order to determine the dominant dimensionless variables that can be used as inputs in such schemes and generate sediment transport models for natural streams and rivers that are based solely on the data without presuming anything about their structure and their degree of nonlinearity. For the proper training of a data-driven scheme, data of good quality are needed. Since field measurements accommodate the peculiarities of the considered streams and the inclusion of noise in the measurement process is inevitable, the training data comprise solely laboratory flume measurements. The testing data, however, comprise exclusively field measurements in order to implement the models in actual applications. Based on this concept, the approach of the basic trend of the function is feasible and the derived model will be applicable to the data range for which it will be trained. Regarding the efficiency of scaling in the sediment transport context, model-prototype comparisons have shown that correspondence of behavior is often well beyond expectations, as has been attested by the successful operation of many structures designed from model tests (Pugh, 2008). This study exhibits the potential of machine learning in capturing functions with physical meaning since the training and testing sets have significant differences in their statistical distributions. The determination of the input variables that best define the problem is accomplished by the assessment of some common independent dimensionless variables based on their correlation with the sediment concentration and the aid of ANNs on the basis of a tentative trial-and-error procedure. Subsequently, ANNs and symbolic regression are utilized in order to derive equations from the selected input combinations.