On the transient storage equations for longitudinal solute transport in open channels: temporal moments accounting for the effects of first-order decay

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Abstract
Solute concentrations in streams due to instantaneous slug releases are frequently influenced both by decay and by exchange with dead zones, among others. Based on the transient storage equations with first-order decay terms, explicit relationships are given for the computation of the zeroth to third temporal moments. The equations presented were applied within the framework of moment-based similarity functions which yield approximate temporal distributions of concentration. Results thus obtained were subsequently compared to finite difference solutions of the transient storage equations, in order to investigate the relationship between these approaches. Within the previously established ranges of applicability of the two similarity functions employed the comparisons indicated fairly good agreement.