New Plume Rise Parameterization - Incorporating Water Thermodynamic Effects in Modelling Plume Rise from Buoyant Sources

We have developed and evaluated a new algorithm for estimating the final (equilibrium) height of buoyant plumes emitted from high-temperature industrial stacks which incorporates the effects of latent heat release or uptake associated with phase changes of emitted and ambient water within the rising plume. The new algorithm combines empirical parametrizations with cloud parcel microphysics to perform layered (vertical) calculations of buoyancy reduction of a rising plume parcel. Effluents emitted from high temperature stacks usually contain significant amounts of combustion-generated water. Additionally, ambient water (vapour, condensed, ice) can entrain into the parcel as the rising plume expands and mixes with the ambient air. As a result of exit momentum and buoyancy, the emitted effluents rise above the stack top (release height) by tens to hundreds of meters (depending on stack and ambient atmospheric conditions). As the plume parcel rises and cools, condensation of water content (emitted and entrained) can result in latent heat release and prolong parcel buoyancy. Conversely, the (re)evaporation of within-parcel condensed water can result in latent heat absorption (parcel cooling), which in turn limits the plume rise. The addition of condensed water can also increase the net density of the plume parcel, and act as a rise-limiting factor. We note that the thermodynamic effects of within-plume water are not unidirectional and can either boost or limit the plume rise. This process is further complicated in the presence of complex ambient atmospheric conditions (e.g., convection, stratification, presence of cloud and rain droplets), which may vary with height, and which makes parameterizing the plume rise and determining the final equilibrium height challenging. Previous attempts in plume rise parametrization for stack sources, which didn’t account for these latent heat effects, had various degrees of success with large discrepancies (> 50%) between predicted and observed plume heights. In our approach, we perform layer by layer calculations of plume parcel buoyancy while accounting for latent heat exchange effects and keeping track of condensed water content within the parcel. Evaluations against SO₂ plumes observed during a 2018 aircraft campaign over the Canadian Oil Sands show up to 50% improvement in model simulated plume heights using the new approach. We also discuss the potential impact on within plume aqueous phase chemistry due to this additional condensed water. Our new plume rise algorithm is comprised of a 1D model (with user defined resolution/parameters), which uses source information (e.g., exit volume flux, temperature) and ambient air state variables to estimate plume final (equilibrium) height. This algorithm can be used either as a standalone model or embedded within a 3D chemical/transport model to provide online sub-grid scale parametrization for vertical distribution of emitted (pollutant) mass.