Probability assessment of water turbidity in rivers based on optimizing the distribution function

Abstract

The method of least squares was used to optimize the theoretical water turbidity distribution function; as a result, the function was derived with all the properties of the distribution function (continuous and monotonically increasing function, values ranging from 0 to 1). It was demonstrated that the optimized polynomials can be used to estimate the probability of any water turbidity-related occurrence, but they cannot be used reliably for all time periods. Thus, the obtained polynomials are ineffective for studying the seasonal nature of changes in the turbidity distribution, which is not entirely convenient for modeling and entails the need to search for other mathematical models.