Correction of residence time distributions and hydraulic indexes affected by tracer release duration in surface flow constructed wetlands

Abstract

In tracer experiments of surface flow constructed wetlands, residence time distributions (RTDs) are generally originated from the normalized concentration data of recovered tracers based on ideal instantaneous tracer release mode. However, this tracer release mode is commonly approximated by finite-continuous tracer release over a relatively short duration. As a result, the accuracy of RTDs and hydraulic indexes cannot be guaranteed if the RTD data and index values were still calculated based on the instantaneous release. To solve this problem, a method for correcting the original RTD data and the index values affected by tracer release duration was proposed. The correction of hydraulic indexes can be performed using analytical formulas, whereas the correction of the RTDs requires an RTD model (such as the gamma distribution and one-dimensional advection-dispersion model) or a smoothing algorithm (such as the simple moving average algorithm) to avoid the increasing effect of random measurement errors caused by the direct use of the RTD correction formulas. The correction method was successfully verified by a specially designed tracer test, and its practical application effect was exemplified. A Monte Carlo test also proved that the RTD correction owed certain robustness to tracer release instability, while the correction of some hydraulic indexes that reflect flow dispersion and comprehensive hydraulic efficiency had inferior robustness. Aside from this, the influence of tracer release duration on RTDs and hydraulic indexes without any correction was analyzed. It was found that the release duration caused the shape of the original RTDs to be more skewed in the positive direction of the x-axis and changed from “thin and high” to “fat and short”, while the duration of the release caused the positive relative errors of most indexes, which became more serious with an increase in the duration or worsening hydraulic performance. Based on these influence rules, 0.01 was defined as the threshold of the normalized release duration which needs to correct RTDs and hydraulic indexes, considering that the relative errors between the uncorrected and corrected indexes were less than 5% when the normalized duration was less than this threshold.