A PROBABILISTIC TWO-REGIME GOVERNING MODEL FOR PREDICTING INFLOW SUSPENDED SEDIMENT CONCENTRATION IN DAM RESERVOIRS

Abstract

Accurate prediction of inflow suspended sediment concentration is a critical prerequisite for the effective management of sedimentation in dam reservoirs. However, most existing approaches rely on classical formulations that are not predictive by construction and suffer from fundamental conceptual and numerical limitations. In particular, widely used log-scale models introduce an arbitrary offset parameter to circumvent the indetermination of the logarithm at zero concentration, implicitly merge zero-transport and active-transport conditions into a single regime, and induce bias when back-transforming predictions to the physical concentration scale. Likewise, traditional sediment rating curves of the form C = aQ^b lack dimensional homogeneity, provide no probabilistic interpretation, and are unable to represent the intermittent, event-driven nature of sediment transport.

This study develops a new probabilistic two-regime governing model for predicting inflow suspended sediment concentration that explicitly addresses these shortcomings. The proposed framework is derived from first principles by recognizing that sediment time series exhibit two physically distinct regimes: (1) a zero or negligible transport regime, and (2) an active transport regime characterized by strictly positive concentrations. The occurrence of zero sediment is modeled probabilistically through a Bernoulli process, whose probability is linked to hydrometeorological predictors via a logistic formulation. Conditional on active transport, sediment magnitude is modeled using a positive-regime formulation based on an inverse hyperbolic sine transformation, which behaves linearly at low concentrations and logarithmically at high concentrations while remaining well-defined at zero without introducing any arbitrary correction parameter.

The resulting predictive model combines the probability of occurrence and the conditional sediment magnitude into a single closed-form forecast expressed as a probability-weighted expectation. All model components are derived explicitly, parameters are estimated through well-defined likelihood-based or least-squares procedures, and the scale parameter governing the transformation is shown to have a clear physical interpretation. A fully worked numerical example demonstrates the transparency, internal consistency, and practical implementation of the proposed approach.

Compared to classical log-scale and rating-curve methods, the new two-regime model offers several decisive advantages: it removes the need for ad hoc numerical fixes, preserves dimensional consistency, separates occurrence and intensity mechanisms, provides a probabilistic interpretation of predictions, and directly targets future sediment concentration at a specified lead time. The proposed framework therefore constitutes a robust and physically consistent alternative for predictive sediment modeling and reservoir sediment management.