A Two-Moment Bulk Parameterization of the Drop Collection Growth in Warm Clouds

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.

A Bayesian Approach for Statistical–Physical Bulk Parameterization of Rain Microphysics. Part I: Scheme Description

A new framework is proposed for the bulk parameterization of rain microphysics: the Bayesian Observationally Constrained Statistical–Physical Scheme (BOSS). It is designed to facilitate direct constraint by observations using Bayesian inference. BOSS combines existing process-level microphysical knowledge with flexible process rate formulations and parameters constrained by observations within a Bayesian framework. Using a raindrop size distribution (DSD) normalization method that relates DSD moments to one another via generalized power series, generalized multivariate power expressions are derived for the microphysical process rates as functions of a set of prognostic DSD moments. The scheme is flexible and can utilize any number and combination of prognostic moments and any number of terms in the process rate formulations. This means that both uncertainty in parameter values and structural uncertainty associated with the process rate formulations can be investigated systematically, which is not possible using traditional schemes. In this paper, BOSS is compared to two- and three-moment versions of a traditional bulk rain microphysics scheme (denoted as MORR). It is shown that some process formulations in MORR are analytically equivalent to the generalized power expressions in BOSS using one or two terms, while others are not. BOSS is able to replicate the behavior of MORR in idealized one-dimensional rainshaft tests, but with a much more flexible and systematic design. Part II of this study describes the application of BOSS to derive rain microphysical process rates and posterior parameter distributions in Bayesian experiments using Markov chain Monte Carlo sampling constrained by synthetic observations.

Comparison of Heat Flux Observation at Three Different Locations around Bandung, West Java

We observed heat flux profiles at three different locations around Bandung, West Java. Heat flux values were calculated using the covariance method with the vertical flow and potential air temperature fluctuation parameters. Observations have shown diurnal patterns in the three observation locations. We also compared observed heat flux data with estimate values using the Bulk Parameterization method. We found that the estimated heat flux was not able to produce values in accordance with the observation data. Boundary layer mixing scheme and wind shear factor were thought to influence heat flux poor estimation in Bandung using the Bulk Parameterization method.

Performance of a Triclass Parameterization for the Collision–Coalescence Process in Shallow Clouds

Focusing on the formation of precipitation in marine stratiform clouds, a two-moment bulk parameterization for three liquid water classes (cloud, drizzle, and rain) is proposed to describe the process of collision–coalescence. Based on the stochastic collection equation and making use of partial moments to improve the physical representation of the shape of the drop size distribution, new rate equations for both number and mass densities are derived using the modified gamma distribution and an adapted collection kernel. Based on observations and spectral model results, the free shape parameters of the modified gamma distribution of each class are determined closing the set of equations. Idealized simulations of the new parameterization compare well to other studies and prove that the closure assumptions are appropriate, especially as the rate equations are invariant under time-stretching transformations—a key property of the stochastic collection equation. The framework of the one-dimensional kinematic cloud model is used to compare the new bulk parameterization to existing formulations and a spectral model. These results show a good agreement, especially in the sensitivity to the aerosol background concentration and the general development for updraft velocities relevant for shallow clouds. Furthermore, as drizzle dominates the formed precipitation for stratocumulus it becomes a pure transition class for more convective type clouds. The analysis reveals a different quantitative behavior of the various parameterizations in the drizzle regime, which is of special importance for precipitating stratocumulus clouds.

A bulk parameterization of melting snowflakes with explicit liquid water fraction for the COSMO model version 4.14

A new snow melting parameterization is presented for the non-hydrostatic limited-area COSMO ("consortium for small-scale modelling") model version 4.14. In contrast to the standard cloud microphysics of the COSMO model, which instantaneously transfers the meltwater from the snow to the rain category, the new scheme explicitly considers the liquid water fraction of the melting snowflakes. These semi-melted hydrometeors have characteristics (e.g., shape and fall speed) that differ from those of dry snow and rain droplets. Where possible, theoretical considerations and results from vertical wind tunnel laboratory experiments of melting snowflakes are used as the basis for characterizing the melting snow as a function of its liquid water fraction. These characteristics include the capacitance, the ventilation coefficient, and the terminal fall speed. For the bulk parameterization, a critical diameter is introduced. It is assumed that particles smaller than this diameter, which increases during the melting process, have completely melted, i.e., they are converted to the rain category. The values of the bulk integrals are calculated with a finite difference method and approximatively represented by polynomial functions, which allows an efficient implementation of the parameterization. Two case studies of (wet) snowfall in Germany are presented to illustrate the potential of the new snow melting parameterization. It is shown that the new scheme (i) produces wet snow instead of rain in some regions with surface temperatures slightly above the freezing point, (ii) simulates realistic atmospheric melting layers with a gradual transition from dry snow to melting snow to rain, and (iii) leads to a slower snow melting process. In the future, it will be important to thoroughly validate the scheme, also with radar data and to further explore its potential for improved surface precipitation forecasts for various meteorological conditions.

A review of the theoretical basis for bulk mass flux convective parameterization

Most parameterizations for precipitating convection in use today are bulk schemes, in which an ensemble of cumulus elements with different properties is modelled as a single, representative entraining-detraining plume. We review the underpinning mathematical model for such parameterizations, in particular by comparing it with spectral models in which elements are not combined into the representative plume. The chief merit of a bulk model is that the representative plume can be described by an equation set with the same structure as that which describes each element in a spectral model. The equivalence relies on an ansatz for detrained condensate introduced by Yanai et al. (1973) and on a simplified microphysics. There are also conceptual differences in the closure of bulk and spectral parameterizations. In particular, we show that the convective quasi-equilibrium closure of Arakawa and Schubert (1974) for spectral parameterizations cannot be carried over to a bulk parameterization in a straightforward way. Quasi-equilibrium of the cloud work function assumes a timescale separation between a slow forcing process and a rapid convective response. But, for the natural bulk analogue to the cloud-work function, the relevant forcing is characterised by a different timescale, and so its quasi-equilibrium entails a different physical constraint. Closures of bulk parameterizations that use a parcel value of CAPE do not suffer from this timescale issue. However, the Yanai et al. (1973) ansatz must be invoked as a necessary ingredient of those closures.

A review of the theoretical basis for bulk mass flux convective parameterization

Most parameterizations for precipitating convection in use today are bulk schemes, in which an ensemble of cumulus elements with different properties is modelled as a single, representative entraining-detraining plume. We review the underpinning mathematical model for such parameterizations, in particular by comparing it with spectral models in which elements are not combined into the representative plume. The chief merit of a bulk model is that the representative plume can be described by an equation set with the same structure as that which describes each element in a spectral model. The equivalence relies on an ansatz for detrained condensate introduced by Yanai et al. (1973) and on a simplified microphysics. There are also conceptual differences in the closure of bulk and spectral parameterizations. In particular, we show that the convective quasi-equilibrium closure of Arakawa and Schubert (1974) for spectral parameterizations cannot be carried over to a bulk parameterization in a straightforward way. Quasi-equilibrium of the cloud work function assumes a timescale separation between a slow forcing process and a rapid convective response. But, for the natural bulk analogue to the cloud-work function (the dilute CAPE), the relevant forcing is characterised by a different timescale, and so its quasi-equilibrium entails a different physical constraint. Closures of bulk parameterization that use the non-entraining parcel value of CAPE do not suffer from this timescale issue. However, the Yanai et al. (1973) ansatz must be invoked as a necessary ingredient of those closures.

A Bulk Parameterization of Giant CCN

A parameterization for giant cloud condensation nuclei (GCCN), suitable for use in bulk microphysical models, has been developed that uses precise representations of the condensational growth of aerosol particles in the subcloud layer. The formulation employs an observationally based GCCN distribution function and directly observable parameters of GCCN, such as concentration and the shape of the aerosol spectra. The parameterization couples naturally to parameterizations of sea salt flux from the ocean surface. The behavior of the GCCN parameterization in a large eddy simulation (LES) framework is consistent with simulations employing explicit, size-resolving microphysical methods. The parameterization properly represents the sensitivity of cloud, drizzle, turbulence, and radiative properties to changes in GCCN concentration for polluted and clean background CCN environments.