Predicting Unsteady Pollutant Removal in Green Stormwater Infrastructure
with Transit Time Distribution Theory
Abstract
In this paper, we explore the use of unsteady transit time distribution
(TTD) theory to model pollutant removal in biofilters, a popular form of
nature-based or “green” stormwater infrastructure (GSI). TTD theory
elegantly addresses many unresolved challenges associated with
predicting pollutant fate and transport in these systems, including
unsteadiness in the water balance (time-varying inflows, outflows, and
storage), unsteadiness in pollutant loading, time-dependent reactions
and scale-up to GSI networks and urban catchments. From a solution to
the unsteady age conservation equation under uniform sampling, we derive
an explicit expression for solute breakthrough with or without
first-order decay. The solution is calibrated and validated with
breakthrough data from 17 simulated storm events (+/- bromide as a
conservative tracer) at a field-scale biofilter test facility in
Southern California. TTD theory closely reproduces bromide breakthrough
concentrations, provided that lateral exchange with the surrounding soil
is accounted for. At any given time, according to theory, more than half
of water in storage is from the most recent storm, while the rest is a
mixture of penultimate and earlier storms. Thus, key management
endpoints, such as the treatment credit attributable to GSI, are
inexorably linked to the age distribution of water stored and released
by these systems.