A Tool for Water Balance Analysis of Bioretention Cells

Bioretention has become one of the most popular urban stormwater best management practices. An easy-to-use analytical tool is developed here to investigate the water balance dynamics of bioretention cells. A stochastic differential equation describing the dynamic water balance of bioretention cells is established first. The probability distribution of the water content inside a bioretention cell is then analytically solved from that stochastic differential equation. Based on this probability distribution, analytical equations are derived for estimating the average stormwater capture efficiency provided by a cell, the fraction of time when a cell is processing water, the average amount of water stored inside a cell, and the required storage capacity of a cell to achieve a specified stormwater capture efficiency. The accuracy of this analytical approach is verified and the performance characteristics of different bioretention systems are also investigated.