[1] Turbulent entrainment-mixing mechanisms are investigated by applying a combined approach to the aircraft measurements of three drizzling and two nondrizzling stratocumulus clouds collected over the U.S. Department of Energy's Atmospheric Radiation Measurement Southern Great Plains site during the March 2000 cloud Intensive Observation Period. Microphysical analysis shows that the inhomogeneous entrainment-mixing process occurs much more frequently than the homogeneous counterpart, and most cases of the inhomogeneous entrainment-mixing process are close to the extreme scenario, having drastically varying cloud droplet concentration but roughly constant volume-mean radius. It is also found that the inhomogeneous entrainment-mixing process can occur both near the cloud top and in the middle level of a cloud, and in both the nondrizzling clouds and nondrizzling legs in the drizzling clouds. A new dimensionless number, the scale number, is introduced as a dynamical measure for different entrainment-mixing processes, with a larger scale number corresponding to a higher degree of homogeneous entrainment mixing. Further empirical analysis shows that the scale number that separates the homogeneous from the inhomogeneous entrainmentmixing process is around 50, and most legs have smaller scale numbers. Thermodynamic analysis shows that sampling average of filament structures finer than the instrumental spatial resolution also contributes to the dominance of inhomogeneous entrainment-mixing mechanism. The combined microphysical-dynamical-thermodynamic analysis sheds new light on developing parameterization of entrainment-mixing processes and their microphysical and radiative effects in large-scale models.

[1] Accurate parameterization of the autoconversion rate of the cloud droplet concentration (number autoconversion rate in cm À3 s À1 ) is critical for evaluating aerosol indirect effects using climate models; however, existing parameterizations are empirical at best. A theoretical expression is presented in this contribution that analytically relates the number autoconversion rate to the liquid water content, droplet concentration and relative dispersion of the cloud droplet size distribution. The analytical expression is theoretically derived by generalizing the analytical formulation previously developed for the autoconversion rate of the cloud liquid water content (mass autoconversion rate in g cm À3 s À1 ). Further examination of the theoretical number and mass autoconversion rates reveals that the former is not linearly proportional to the latter as commonly assumed in existing parameterizations. The formulation forms a solid theoretical basis for developing multi-moment representation of the autoconversion process in atmospheric models in general.

[1] Different turbulent entrainment-mixing processes (e.g., homogeneous and inhomogeneous) occur in clouds; accurate representation of these processes is critical for improving cloud-related parameterizations in large-scale models, but poorly understood and quantified. Using in situ aircraft observations over the U. S. Department of Energy's Atmospheric Radiation Measurement Southern Great Plains site during the March 2000 Cloud Intensive Observation Period and numerical simulations with the Explicit Mixing Parcel Model (EMPM), here we explore the potential of using degree of homogeneous mixing as a measure to quantify these different mechanisms and examine various microphysical measures of homogeneous mixing degree and their relationships to entrainment-mixing dynamics as measured by transition scale numbers. Three different microphysical measures for the homogeneous mixing degree are newly defined and each is coupled with one of two different transition scale numbers. Both observations and simulations show that all the combinations have positive correlated relationships; simulations further show that the tightest relationship is between the measure of homogeneous mixing degree considering adiabatic number concentration and the transition scale number accounting for mixing fraction of dry air. A parameterization of the entrainment-mixing processes is advanced according to the relationships of homogeneous mixing degree measures to transition scale numbers.

Joint size and fall velocity distributions of raindrops were measured with a Particle Size and Velocity (PARSIVEL) precipitation particle disdrometer in a field experiment conducted during July and August 2007 at a semiarid continental site located in Guyuan, Ningxia Province, China (368N, 1068169E). Data from both stratiform and convective clouds are analyzed. Comparison of the observed raindrop size distributions shows that the increase of convective rain rates arises from the increases of both drop concentration and drop diameter while the increase of the rain rate in the stratiform clouds is mainly due to the increase of median and large drop concentration. Another striking contrast between the stratiform and convective rains is that the size distributions from the stratiform (convective) rains tend to narrow (broaden) with increasing rain rates. Statistical analysis of the distribution pattern shows that the observed size distributions from both rain types can be well described by the gamma distribution. Examination of the raindrop fall velocity reveals that the difference in air density leads to a systematic change in the drop fall velocity while organized air motions (updrafts and downdrafts), turbulence, drop breakup, and coalescence likely cause the large spread of drop fall velocity, along with additional systematic deviation from terminal velocity at certain raindrop diameters. Small (large) drops tend to have superterminal (subterminal) velocities statistically, with the positive deviation from the terminal velocity of small drops being much larger than the negative deviation of large drops.

1] The relationships between fractional entrainment rate and key microphysical quantities (e.g., liquid water content, droplet number concentration, volume mean radius, and standard deviation of cloud droplet size distributions) in shallow cumuli are empirically examined using in situ aircraft observations from the Routine Atmospheric Radiation Measurement Aerial Facility Clouds with Low Optical Water Depths Optical Radiative Observations (RACORO) field campaign over the Atmospheric Radiation Measurement Southern Great Plains site. The results show that the microphysical quantities examined generally exhibit strong relationships with entrainment rate and that the relationships collectively suggest the dominance of homogeneous entrainment mixing, which is unfavorable to the formation of large droplets and the initiation of warm rain in the clouds. The dominance of the homogeneous mixing mechanism is further substantiated by the dependency on entrainment rate of relationships among various microphysical variables and of cloud droplet size distributions. The dominance of this mechanism is also quantitatively confirmed by examining the degree of homogeneous mixing in the clouds. The dominance of homogeneous mixing may be an important reason why none of the cumulus clouds studied was drizzling.Citation: Lu, C., S. Niu, Y. Liu, and A. M. Vogelmann (2013), Empirical relationship between entrainment rate and microphysics in cumulus clouds, Geophys.

[1] Entrainment processes in convective clouds often occur stochastically and entrainment rate estimates depend on the distance from the cloud from which the dry air is entrained. However, no observational studies exist on either the distance dependence or probability density function of entrainment rate, hindering understanding and the parameterization of convection. Here entrainment rate in cloud cores is estimated using a recently developed mixing fraction approach that is applied to in situ aircraft measurements of cumuli from the RACORO field program. The results are used to examine, for the first time, probability density functions of entrainment rate and their dependence on the distance from the edge of the cloud core from which the dry air is entrained. The estimated entrainment rate decreases when the dry air is entrained from increasing distance from the edge of the cloud core; this is because the air farther from the edge of the cloud core is drier than the neighboring air that is within the humid shell around the cumulus cloud core. Probability density functions of entrainment rate vary with the distance and height above the cloud-base, and all are well fitted by lognormal distributions. The implications of the results for convection parameterizations are discussed. Citation: Lu, C., Y. Liu, S. Niu, and A. M.Vogelmann (2012), Lateral entrainment rate in shallow cumuli: Dependence on dry air sources and probability density functions,

[1] The simultaneous measurements of vertical velocity and cloud droplet size distributions in cumuli collected during the RACORO field campaign over the Atmospheric Radiation Measurement Program's Southern Great Plains site near Lamont, Oklahoma, US, are analyzed to determine the effects of vertical velocity on droplet number concentration, relative dispersion (the ratio of standard deviation to mean radius), and their relationship. The results show that with increasing vertical velocity the droplet number concentration increases while the relative dispersion decreases. The data also exhibit a negative correlation between relative dispersion and droplet number concentration. These empirical relationships can be fitted well with power law functions. This observational study confirms the theoretical and numerical expectations of the effects of vertical velocity on cloud microphysics by analyzing the data of vertical velocity directly. The effects of vertical velocity on relative dispersion and its relationship with droplet number concentration are opposite to that associated with aerosol loading, posing a confounding challenge for separating aerosol indirect effects from dynamical effects. Citation: Lu, C., Y. Liu, S. Niu, and A. M. Vogelmann (2012), Observed impacts of vertical velocity on cloud microphysics and implications for aerosol indirect effects,

This work empirically examines the dependence of entrainment-mixing mechanisms on the averaging scale in cumulus clouds using in situ aircraft observations during the Routine Atmospheric Radiation Measurement Aerial Facility Clouds with Low Optical Water Depths Optical Radiative Observations (RACORO) field campaign. A new measure of homogeneous mixing degree is defined that can encompass all types of mixing mechanisms. Analysis of the dependence of the homogenous mixing degree on the averaging scale shows that, on average, the homogenous mixing degree decreases with increasing averaging scales, suggesting that apparent mixing mechanisms gradually approach from homogeneous mixing to extreme inhomogeneous mixing with increasing scales. The scale dependence can be well quantified by an exponential function, providing first attempt at developing a scale-dependent parameterization for the entrainment-mixing mechanism. The influences of three factors on the scale dependence are further examined: droplet-free filament properties (size and fraction), microphysical properties (mean volume radius and liquid water content of cloud droplet size distributions adjacent to droplet-free filaments), and relative humidity of entrained dry air. It is found that the decreasing rate of homogeneous mixing degree with increasing averaging scales becomes larger with larger droplet-free filament size and fraction, larger mean volume radius and liquid water content, or higher relative humidity. The results underscore the necessity and possibility of considering averaging scale in representation of entrainment-mixing processes in atmospheric models.