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Xiping Zeng
and
Xiaowen Li

Abstract

A bin (or spectral) model is developed to investigate the sensitivity of warm rain initiation to cloud condensation nuclei (CCN). It explicitly represents CCN with a formula whose parameters come from the Twomey relationship (or CCN measurements). By seamlessly integrating CCN activation and drop collection with thousands of bins, the model can replicate the effect of CCN on rain initiation, providing a benchmark to test the process parameterizations in rain initiation. The model is used to simulate two extreme cases with CCN parameters of maritime and continental clouds, respectively, where other actual cases usually lie between these two extreme cases. Its simulations show that rain can initiate within half an hour or less as observed in cumulus clouds. The fast rain initiation modeled is attributed mainly to a new process: the condensational conversion of cloud drops to raindrops via collision–coalescence initiators (or drops with radius between 28 and 100 μm). Since the new process is more important in rain initiation than the autoconversion of cloud drops to raindrops when large CCN exist, it is suggested that the process be parameterized into the weather and climate models to better represent CCN and subsequently remove the common bias of “too dense clouds.”

Significance Statement

The current weather and climate models represent aerosols via implicit parameterizations and have a bias of “too dense clouds.” Their implicit parameterizations of aerosols usually overlook (or misrepresent) some cloud processes. In this paper and its preceding part (Zeng and Li 2020) we proposed a new framework to explicitly parameterize one subset of aerosols: cloud condensation nuclei (CCN). To embody an explicit parameterization of CCN, we still need quantitative information to connect CCN activation and rain initiation, which motivates this study. In the study we developed an accurate microphysical model to simulate the growth of small CCN to large raindrops, providing information on the sensitivity of rain initiation to CCN. We performed many sensitivity simulations and found the condensational conversion of cloud drops to raindrops via collision–coalescence initiators is a vital process in warm rain initiation. Since the process has been overlooked by all the weather and climate models, the study suggests that the process be introduced in the weather and climate models to properly represent the fast warm rain initiation observed and subsequently remove the bias of “too dense clouds.”

Open access
Xiping Zeng
and
Xiaowen Li

Abstract

To improve the modeling of warm rain initiation, a two-moment bulk parameterization of the drop collection growth in warm clouds is developed by two steps: (i) its prototype is first derived based on the analytic solution of the stochastic collection equation (SCE) with the Golovin kernel, and (ii) the prototype is then revamped empirically to fit the numerical solution of SCE with the real hydrodynamic collection kernel, reaching the final version of the parameterization. Since the final version represents the self-collection of cloud drops explicitly, it replicates warm rain initiation well even when liquid water content (cloud-drop number concentration) is very low (high). It also replicates the autoconversion threshold and time delay of rain initiation via a small autoconversion rate.

Open access
Xiping Zeng
and
Yansen Wang

Abstract

A k–ε turbulence model for the stable atmosphere is extended for the convective atmosphere. The new model represents the buoyancy-induced increase in the kinetic energy and scale of eddies, and is consistent with the Monin–Obukhov similarity theory for convective atmospheric boundary layers (ABLs). After being incorporated into an ABL model with the Coriolis force, the model is tested by comparing the ABL model results with the Businger–Dyer (BD) relationship. ABL model simulations are carried out to reveal the sensitivity of the vertical wind profile to model parameters (e.g., the Obukhov length, friction velocity, and geostrophic wind). When the friction velocity is consistent with geostrophic wind speed (or the turbulence in the inner regime is in equilibrium with that in the outer regime), the modeled wind profile is close to the BD relationship near the ground surface. Otherwise, the modeled wind profile deviates from the BD relationship, resembling the hockey stick transition model.

Open access
Xiping Zeng
,
Wei-Kuo Tao
, and
Joanne Simpson

Abstract

This paper addresses an equation for moist entropy in the framework of cloud-resolving models. After rewriting the energy equation with moist entropy in the place of temperature, an equation for moist entropy is obtained. The equation expresses the internal and external sources of moist entropy explicitly, providing a basis for the use of moist entropy as a prognostic variable in long-term cloud-resolving modeling. In addition, a precise formula for the surface flux of moist entropy from the underlying surface into the air above is derived.

The equation for moist entropy is used to express the Neelin–Held model for the diagnosis of large-scale vertical velocity. After applying the model to a tropical oceanic atmosphere with mean annual soundings, the paper shows the sensitivity of large-scale vertical circulations to the radiative cooling rate and the surface flux of moist entropy, which demonstrates the necessity for a precise equation for moist entropy in the analysis and modeling of large-scale tropical circulations.

Full access
Xiping Zeng
,
Yansen Wang
, and
Benjamin T. MacCall

Abstract

A realizable kε turbulence model of incompressible fluid is extended for the stable atmosphere after taking account of the buoyancy damping of gravity waves. The new model is consistent with the Monin–Obukhov similarity theory on the stable atmospheric boundary layer (ABL) over a horizontally uniform surface. The model is incorporated into an ABL model to simulate mean flow against observations. Its ABL-model output is compared with the Leipzig dataset, showing the turbulence model works well for a stable ABL. Specifically, the ABL model properly replicates 1) the mixing length, turbulent viscosity, and mean wind; 2) a significant decrease of the mixing length with height in the upper ABL and thus a reasonable altitude of the ABL top; and 3) a sensitivity of the mixing length and turbulent viscosity to atmospheric stability.

Open access
Stephen E. Lang
,
Wei-Kuo Tao
,
Xiping Zeng
, and
Yaping Li

Abstract

A well-known bias common to many bulk microphysics schemes currently being used in cloud-resolving models is the tendency to produce excessively large reflectivity values (e.g., 40 dBZ) in the middle and upper troposphere in simulated convective systems. The Rutledge and Hobbs–based bulk microphysics scheme in the Goddard Cumulus Ensemble model is modified to reduce this bias and improve realistic aspects. Modifications include lowering the efficiencies for snow/graupel riming and snow accreting cloud ice; converting less rimed snow to graupel; allowing snow/graupel sublimation; adding rime splintering, immersion freezing, and contact nucleation; replacing the Fletcher formulation for activated ice nuclei with that of Meyers et al.; allowing for ice supersaturation in the saturation adjustment; accounting for ambient RH in the growth of cloud ice to snow; and adding/accounting for cloud ice fall speeds. In addition, size-mapping schemes for snow/graupel were added as functions of temperature and mixing ratio, lowering particle sizes at colder temperatures but allowing larger particles near the melting level and at higher mixing ratios. The modifications were applied to a weakly organized continental case and an oceanic mesoscale convective system (MCS). Strong echoes in the middle and upper troposphere were reduced in both cases. Peak reflectivities agreed well with radar for the weaker land case but, despite improvement, remained too high for the MCS. Reflectivity distributions versus height were much improved versus radar for the less organized land case but not for the MCS despite fewer excessively strong echoes aloft due to a bias toward weaker echoes at storm top.

Full access
Wei-Kuo Tao
,
Stephen Lang
,
Xiping Zeng
,
Shoichi Shige
, and
Yukari Takayabu

Abstract

The relationship among surface rainfall, its intensity, and its associated stratiform amount is established by examining observed precipitation data from the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR). The results show that for moderate–high stratiform fractions, rain probabilities are strongly skewed toward light rain intensities. For convective-type rain, the peak probability of occurrence shifts to higher intensities but is still significantly skewed toward weaker rain rates. The main differences between the distributions for oceanic and continental rain are for heavily convective rain. The peak occurrence, as well as the tail of the distribution containing the extreme events, is shifted to higher intensities for continental rain. For rainy areas sampled at 0.5° horizontal resolution, the occurrence of conditional rain rates over 100 mm day−1 is significantly higher over land. Distributions of rain intensity versus stratiform fraction for simulated precipitation data obtained from cloud-resolving model (CRM) simulations are quite similar to those from the satellite, providing a basis for mapping simulated cloud quantities to the satellite observations.

An improved convective–stratiform heating (CSH) algorithm is developed based on two sources of information: gridded rainfall quantities (i.e., the conditional intensity and the stratiform fraction) observed from the TRMM PR and synthetic cloud process data (i.e., latent heating, eddy heat flux convergence, and radiative heating/cooling) obtained from CRM simulations of convective cloud systems. The new CSH algorithm-derived heating has a noticeably different heating structure over both ocean and land regions compared to the previous CSH algorithm. Major differences between the new and old algorithms include a significant increase in the amount of low- and midlevel heating, a downward emphasis in the level of maximum cloud heating by about 1 km, and a larger variance between land and ocean in the new CSH algorithm.

Full access
Xiping Zeng
,
Zbigniew Ulanowski
,
Andrew J. Heymsfield
,
Yansen Wang
, and
Xiaowen Li

Abstract

The stability of ice crystal orientation is studied by modeling the airflow around ice crystals at moderate Reynolds number, where an ice crystal is approximated by a cylinder with three parameters: diameter D, length L, and zenith angle of the axis θ. In this paper, the torque acting on ice crystals is simulated at different θ first, and then a special θ with zero horizontal torque, denoted as θe , is sought as an equilibrium of ice crystal orientation. The equilibrium is classified into two kinds: stable and unstable. Ice crystals rotate to θe of stable equilibriums while deviating from θe of unstable ones once they are released into quiet air. Multiple equilibriums of ice crystal orientation are found via numerical simulations. A cylinder with D/L close to one has three equilibriums, two of which are stable (i.e., θe = 0° and 90°). A cylinder with D/L away from one has only two equilibriums, one of which is stable (i.e., either θe = 0° or 90°). In addition, an asymmetric cylinder has two, three, or five equilibriums, and their θe is sensitive to the distance between its geometrical center and its center of gravity. The sensitivity of θe to crystal asymmetry suggests large symmetric ice crystals tend to become asymmetric (or irregular) and subsequently oriented randomly.

Significance Statement

Ice crystal orientation impacts high-cloud reflectance and satellite-based observations of high clouds significantly. However, its laboratory and field observations look dissimilar: the percentage of horizontally oriented ice crystals (HOICs) observed in the laboratory is quite high, while in the field it is often low and varies greatly in space and time. The motivation for this study is to elucidate what causes the difference between the laboratory and field observations. The torque acting on ice crystals are computed by modeling the airflow around ice crystals, revealing the conditions for nonhorizontal orientations of ice crystals. In quiet air, an ice crystal is oriented either horizontally or vertically when its shape is close to sphere. When its shape is elongated in one direction, its orientation depends on its asymmetry in density and shape. The sensitivity of ice crystal orientation to ice crystal asymmetry explains the low percentage of HOICs in the field, because asymmetric ice crystals are common in clouds. As an application, this sensitivity together with the observed percentage of HOICs can be used to infer the processes of ice crystal growth in clouds, providing clues to better representation of ice crystals in weather and climate models.

Open access
Nick Guy
,
Xiping Zeng
,
Steven A. Rutledge
, and
Wei-Kuo Tao

Abstract

Two mesoscale convective systems (MCSs) observed during the African Monsoon Multidisciplinary Analyses (AMMA) experiment are simulated using the three-dimensional (3D) Goddard Cumulus Ensemble model. This study was undertaken to determine the performance of the cloud-resolving model in representing distinct convective and microphysical differences between the two MCSs over a tropical continental location. Simulations are performed using 1-km horizontal grid spacing, a lower limit on current embedded cloud-resolving models within a global multiscale modeling framework. Simulated system convective structure and microphysics are compared to radar observations using contoured frequency-by-altitude diagrams (CFADs), calculated ice and water mass, and identified hydrometeor variables. Vertical distributions of ice hydrometeors indicate underestimation at the mid- and upper levels, partially due to the inability of the model to produce adequate system heights. The abundance of high-reflectivity values below and near the melting level in the simulation led to a broadening of the CFAD distributions. Observed vertical reflectivity profiles show that high reflectivity is present at greater heights than the simulations produced, thought to be a result of using a single-moment microphysics scheme. Relative trends in the population of simulated hydrometeors are in agreement with observations, though a secondary convective burst is not well represented. Despite these biases, the radar-observed differences between the two cases are noticeable in the simulations as well, suggesting that the model has some skill in capturing observed differences between the two MCSs.

Full access
Toshihisa Matsui
,
Xiping Zeng
,
Wei-Kuo Tao
,
Hirohiko Masunaga
,
William S. Olson
, and
Stephen Lang

Abstract

This paper proposes a methodology known as the Tropical Rainfall Measuring Mission (TRMM) Triple-Sensor Three-Step Evaluation Framework (T3EF) for the systematic evaluation of precipitating cloud types and microphysics in a cloud-resolving model (CRM). T3EF utilizes multisensor satellite simulators and novel statistics of multisensor radiance and backscattering signals observed from the TRMM satellite. Specifically, T3EF compares CRM and satellite observations in the form of combined probability distributions of precipitation radar (PR) reflectivity, polarization-corrected microwave brightness temperature (Tb ), and infrared Tb to evaluate the candidate CRM.

T3EF is used to evaluate the Goddard Cumulus Ensemble (GCE) model for cases involving the South China Sea Monsoon Experiment (SCSMEX) and the Kwajalein Experiment (KWAJEX). This evaluation reveals that the GCE properly captures the satellite-measured frequencies of different precipitating cloud types in the SCSMEX case but overestimates the frequencies of cumulus congestus in the KWAJEX case. Moreover, the GCE tends to simulate excessively large and abundant frozen condensates in deep precipitating clouds as inferred from the overestimated GCE-simulated radar reflectivities and microwave Tb depressions. Unveiling the detailed errors in the GCE’s performance provides the better direction for model improvements.

Full access