Formulation of radar reflectivity in two moment cloud parameterizations

1. Formulation of radar reflectivity in two moment cloud parameterizations • Zena N. Kogan and Yefim L. Kogan, • Cooperative Institute for Mesoscale Meteorological Studies, The University of Oklahoma, Norman, OK • Comparison of predicted radar reflectivity (Z) with observations, such as e.g. from the W-band ARM Cloud Radar (WACR), is an essential part of verifying the fidelity of cloud bulk microphysics parameterizations. • The majority of cloud models use two-moment cloud parameterizations which do not predict radar reflectivity directly. The commonly used method to obtain the Z from the Z-R relationship is rather inaccurate. • The radar reflectivity may be precisely calculated from the drop size distributions (DSD); they however are unavailable in bulk models where microphysics is represented only by four moments of the DSD, such as cloud and rain mixing ratios and drop concentrations. • Recently we showed that approximation of DSD by a combination of two Gamma-type functions may rather accurately represent the higher moments of the drop spectra, including radar reflectivity. • The question is how to define the two-mode Gamma type function through the predictive variables available in the bulk model formulation? We simulated several cases of stratocumulus clouds observed during the ASTEX field experiment. The simulations represent cloud layers with different intensities of drizzle in the cloud (Fig. 1) and provided over 19,200 DSDs for each case. Fig 1. Mean and standard deviation of drop spectra parameters for light (LD), moderate (MD) and heavy (HD) drizzling cases. Results Motivation and Objective Reflectivity in 2-momentparameterizations Method The three parameter lognormal fit (L-fit) is: Comparison of analytical fits Most CRM and NWP models use two-moment microphysics parameterizations and, therefore, only two variables are available for definition of a G-fit for. We show that the drizzle drop dispersion, can be approximated as a function of drizzle concentration and mixing ratio (Fig. 4). Assuming a fixed cloud drop dispersion and approximating drizzle drop dispersion as in Fig. 4, we can reduce the number of parameters defining a G-fit to four microphysical variables predicted in the two-moment schemes. Fig. 5 compares the radar reflectivity field Z in a simulation of a drizzling Sc: a) benchmark field defined by the LES predicted DSDs, b) Z parameterized by 3-parameter G-fit; c)Z parameterized by the 2-parameter Gamma fit with approximated drizzle drop dispersion. Panels d-e show fields of total and drizzle liquid water content illustrating the extent of correlation between them and Z. Panel f shows much better, but still inferior relation of Z to the drizzle rate. In the LD case the rain rate is rather well approximated by a unimodal L-fit, although the reflectivity is overestimated. For the HD case (Fig 2) the unimodal fits fail to capture contribution from the tail of the spectrum; thus, rain rate and radar reflectivity are significantly underestimated by either an L-fit (left), or a G-fit (right panels). Fig 3shows that a) bimodal fits result in significantly smaller bias relative to the unimodal fits, and b) the bimodal G-fits have a substantially reduced scatter and a much smaller error envelope (mean ± standard deviation) than L-fits. where rm is the modal radius, N concentration, and s logarithmic drop spectrum width. The three parameter Gamma fit (G-fit) is: where N, a , b. are parameters; G(x) is the gamma function. The 3 parameters defining each fit are expressed through the 0th, 1st and 2nd moments of the LES derived DSDs. The 4th and 6th moments of the fit are then compared with corresponding moments of the DSD from the LES dataset. Note that in Sc these moments represent drizzle flux and reflectivity. Depending on drizzle intensity, drop spectra in Sc may exhibit one or two modes; the 1st mode for cloud and the 2nd for drizzle drops (r>25m). We thus consider two fits. The unimodal fit is defined by 3 parameters expressed through moments of the DSD integrated over the whole drop size range. The bimodal fit is a sum of two fits, each defined by partial moments integrated in the 1st fit over the cloud drop sizes, and in the 2ndover the drizzle drop sizes. Description of Data Fig. 5. The isolines of Sc cloud parameters: a) benchmark reflectivity; b) Z defined by the 3-parameter G-fit; c) Z defined by the 2-parameter G-fitwith parameterized dispersion d) total liquid water content Qt; e) drizzle water content Qr; f) drizzle rate R. L-fit G-fit Fig. 3. As Fig. 2, but using bimodal L-(left) and G-fits (right). heavy drizzle case Conclusions L-fit G-fit • The Gamma-type bimodal fits represent rain rates and radar reflectivities much more accurately than lognormal fits. • Radar reflectivity field can be represented reasonably well in the 2-moment bulk schemes, but most accurately in the 3-moment bulk microphysical parameterizations. Acknowledgments.This research was supported by the Office of Science (BER), U.S. Department of Energy, Grant No. DE-FG02-05ER64062 and by the Office of Naval Research, DOD. Fig. 4. Drizzle drops dispersion s as a function of drizzle drops concentration stratified by the value of Qr Fig. 2. Rain rate and radar reflectivity approximated by a unimodal fit.