An analytical model for crosswind integrated concentrations released from a continuous source in a finite atmospheric boundary layer

An analytical model for the crosswind integrated concentrations released from a continuous source in a finite atmospheric boundary layer is formulated by considering the wind speed as a power law profile of vertical height above the ground and eddy diffusivity as an explicit function of downwind distance from the source and vertical height. A closed form analytical solution of the resulting advection–diffusion equation for these profiles of wind speed and eddy diffusivity with the physically relevant boundary conditions is derived using the separation of variables technique that leads to a Sturm–Liouville eigen value problem. Various particular cases of the model are deduced.The model is evaluated with the observations obtained from Prairie Grass experiment in various stability classes varying from very unstable to neutral and stable conditions and Hanford diffusion experiment in stable conditions. The agreement is found to be good between the computed and observed concentrations in both the diffusion experiments. For Prairie Grass experiment, the model is predicting 78% cases with in a factor of two and gives a value of NMSE as 0.075. On the other hand, for Hanford observations in stable conditions, it predicts 70% cases with in factor of two. An extensive analysis of statistical measures with the downwind distances from the source reveals that the model is performing well close to the source.