Comparison of stochastic collection equation solution methods for use in forward simulation of cloud radar Doppler spectra

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Description

Despite advances in the observation and modeling of stratocumulus, the primary processes driving droplet spectral broadening associated with drizzle formation are still debated. Profiling cloud radar measurements of Doppler velocity spectra provides a rich source of information about hydrometeor size distributions that can be used side-by-side with detailed simulations to investigate broadening hypotheses. A size-resolved bin microphysics scheme is most suitable for the simulations since it does not use any predefined functional form to describe drop size distributions (DSDs) as a bulk microphysics model does, thereby allowing detailed evolution of DSDs suitable for forward simulation of Doppler spectra. However, bin microphysics scheme results are sensitive to so-called numerical diffusion, which refers to artificial broadening at the tails of DSDs. Specifically, numerical diffusion that occurs while solving the stochastic collection equation (SCE) causes a well-known overestimation of large drizzle drops—a problem that is heightened when handling reflectivity-weighted size distributions for comparison with radar measurements. Our previous large-eddy simulation (LES) study suggested that the method we adopted before (proposed by Jacobson et al. 1994, hereafter J94) yields a significant spectrum broadening compared with observations. To choose a new scheme, three SCE solution methods are implemented in a box model where only collision of drops is considered. Results show that all three methods agree on a converged DSD at sufficiently fine temporal and size grid resolution, but the convergence rate differs. The J94 method does not converge until extremely fine size grid resolution, whereas the other two methods converge well even at a relatively coarse size grid resolution. Considering temporal convergence and computational efficiency together, we conclude that the method proposed by Bott (2000, hereafter B00) is superior, in contrast to another recent study. With the B00 method newly implemented in our LES model, numerical diffusion is substantially reduced compared with the J94 method. The simulated DSDs and Doppler spectral skewness are also closer to observations, but there remain discrepancies between simulated and observed mean Doppler velocity versus reflectivity, which indicate further in-depth investigation is necessary. We also present preliminary tests of sedimentation, activation, and diffusional growth schemes.