When the concentration of an aerial pollutant is detected at some observation points in an urban or built environment, immediate source identification allows for application of effective measures to decrease the concentration of the pollutant and its adverse effects. In this case, source identification involves determination of the source position and source strength from measured concentrations.
We propose a novel method for identifying the source of an environmental pollutant continuously released from a point source in a turbulent flow field at a statistically steady state. The method employs the analysis of tracer dispersion released from observation points of the pollutant in a reversed flow field (RFF). The RFF is artificially produced from the forward flow field (FFF) in which the pollutant is transported. The direction of temporal progress and velocity vectors in the RFF are created opposite to those in the FFF.
In a statistically steady turbulent flow and concentration field, the concentration of matter at a position can be expressed as a product of its source strength and expected staying time (EST) per unit volume at the position of a particle of the matter. From the discussion on the probabilistic behavior of a virtual particle in the flow fields, we found that the EST between two related points has an identical value when the release and monitoring points are interchanged in the FFF and RFF. Using the relationship of the EST and the tracer dispersion from the observation points in the RFF, the measured concentration of the pollutant and the EST give the estimated source strength as a function of the position. This property coincides with the duality of the scalar fields analytically derived in the adjoint method.
When they have multiple observation points, each tracer dispersion analysis gives different distributions of the estimated source strength. However, the source strength has to have a unique point value for physical realizability. This condition reduces candidate positions of the pollutant source. When the dispersion of the pollutant occurs in the n-th dimensional space, the number of parameters is n + 1, which contains n space coordinates of the source position and the source strength. Consequently, n + one observation points allow the determination of all parameters in the source identification.
This paper presents the basic idea of the source identification method based on physical consideration of the particle behavior in the RFF. An example of the source identification procedure is also presented for pollutant dispersion in a two-dimensional uniform flow field. However, the solution of source identification obtained with the present method can be very sensitive to the errors that are assumed to occur in the measurement or analysis of flow and concentration fields. For practical applications, an additional method to provide robust solutions against these errors are needed and will be considered in future studies.