### WWRC 88-24

Assessment of Probability Distribution of Dissolved Oxygen Deficit

Abstract

Water quality modeling and prediction in a stream environment is
complicated by the occurance of a number of random processes. Due to the complexity of water quality model, the analytical derivation of the exact probability
distribution of the dissolved oxygen (DO) deficit is difficult. This paper proposes
an approximate but practical method by using first-order analysis of uncertainty in
estimating the statistical moments of the DO deficit. The statistical moments estimated were then used in an appropriate probability distribution for the DO deficit
concentration. Practical issues involved are: (1) Which is the appropriate probability distribution for the DO deficit concentration? and (2) is this appropriate distribution function sensitive to the distribution of water quality parameters? This
paper examines a number of commonly used probability distributions for their appropriateness in describing the random characteristics of the DO deficit concentration under various conditions. Of the distributions considered in the investigation, lognormal distribution proved to be the best model.

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