Limiting spurious evaporation in cloud simulations: Magnussen and Hjertager (1976)'s EDC model, revisited

``It is assumed that an intermittent eddy structure is present in the flow... Thus the rate of evaporation is limited by the rate of heat and mass transfer between these eddies.'' Magnussen and Hjertager (1979)

Various cloud schemes are available to our community that predict the net evaporation rate of a subgrid mixture of clear and cloudy air. But in choosing between two broad cloud modeling strategies: (i) models that resolve supersaturation (S) and ignore subgrid correlations, and (ii) PDF schemes that specify subgrid distributions and assume instantaneous evaporation, we are faced with a dilemma. The resolved-S approach predicts a grid-cell e-folding time, Tefold, of relative humidity that depends on the microphysical reaction time, Treact, and is independent of the mixing time, Tmix. In contrast, the PDF approach predicts a Tefold that is proportional to Tmix independent of Treact. This is the evaporation time-scale dilemma: a choice between two common subgrid cloud modeling strategies that are, in some sense, archetypal, inherently inconsistent, and thus, unsatisfactory.

In this talk we show that the resolution of this dilemma can be found in the combustion literature---the pioneering work of Magnussen and Hjertager (1976) who formulated the Eddy Dissipation Concept (EDC) model. The EDC model postulates that Tefold is proportional to max(Tmix,Treact) and therefore encapsulates both resolved-S and PDF schemes as different limits. Further, a constant droplet radius assumption implies a simple dependence of [Treact,Tmix] on the droplet size spectrum. We validate EDC using 1D eddy-diffusivity simulations and a new PDF approach to cloud mixing and evolution in which evaporation is explicitly resolved and the shape of the PDF is not specified a priori. In addition, the EDC model is shown to exactly solve the non-turbulent problem of spurious production of cloud-edge supersaturations described by Stevens et al. (1996), and produce good results in the more general turbulent case.