Evaluation of Water Vapor Diffusion Equation Solving Schemes for Use in Forward Simulation of Cloud Doppler Radar Spectra of Drizzling Stratocumulus

Doppler velocity spectra measured by vertically pointing cloud radars within drizzling stratocumulus provide rich information on the characteristics of cloud drop size distributions (DSDs), which bear signatures of the formation and evolution of drizzle. In the framework of a large-eddy simulation, with the aid of a forward simulator, a size-resolved bin microphysics scheme that represents DSDs without any predefined functional form is able to simulate the evolution of DSDs in a manner that is sufficiently realistic for comparison directly with measured Doppler spectra whereas a bulk microphysics scheme is generally not. However, numerical schemes used to calculate each process included in a bin microphysics scheme are prone to numerical diffusion that leads to artificial broadening at the tails of DSDs, which may be particularly problematic when forward-simulating radar variables.

Here we extend our previous study on numerical solutions of the stochastic collection equation to those of the water vapor diffusion equation. We examine three solution approaches: a method that distributes drops with arbitrary mass into two adjacent bins to conserve the number and mass of drops, a piecewise parabolic method that treats the condensation and evaporation as advection along the mass axis, and a flux method that is also used for the stochastic collection equation. Results using a simple box model reveal that all the methods fail to simulate narrowing DSDs during condensation that is seen in an exact solution and show distinct numerical diffusion at a practical bin width. Large-eddy simulations on weakly drizzling stratocumulus are performed using the aforementioned three methods and Doppler spectra obtained using a forward simulator are compared with observations. A preliminary comparison of numerical diffusion attributable to the imperfect numerics with physical broadening induced by subgrid-scale supersaturation inhomogeneities is also made.