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Hugh Morrison

Abstract

Hybrid bulk–bin microphysics schemes discretize particle size distributions into bins for calculating microphysical process rates, while retaining a limited number of bulk prognostic quantities and assuming an underlying analytic functional form for the particle size distributions as in traditional bulk microphysics schemes. In this paper, the treatment of sedimentation in two-moment bulk and hybrid schemes is compared using different numerical methods. Using the first-order upwind method for calculating sedimentation in conjunction with a widely used, two-step, time-splitting approach that updates model fields after transport by air motion followed by calculation of sedimentation, it is shown analytically that despite using a spectrum of fall speeds corresponding to different particle sizes, hybrid schemes converge with increasing bin resolution toward bulk schemes that utilize only characteristic moment-weighted particle fall speeds. While not strictly convergent, it is also shown that solutions using bulk and hybrid schemes are often similar for other numerical methods and approaches. Noticeable improvement using the hybrid scheme occurs in a few circumstances: when the Courant number associated with falling precipitation is large (>>1), requiring substepping, semi-implicit, or Lagrangian-type methods for numerical stability; or when a one-step approach is employed that calculates hydrometeor transport in a single step using a velocity that combines both vertical air motion and particle fall speed. Thus, it is concluded that the use of hybrid rather than bulk schemes is justified for some, but not all, applications, and care should be taken to determine the appropriateness of hybrid schemes for specific applications.

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Hugh Morrison

Abstract

This paper compares simple theoretical expressions relating vertical velocity, perturbation pressure, updraft size, and dimensionality for cumulus convection, derived in Part I, with numerical solutions of the anelastic buoyant perturbation pressure Poisson equation and vertical velocity w. A range of thermal buoyancy profiles representing shallow to deep moist convection are tested for both two-dimensional (2D) and three-dimensional (3D) updrafts. The theoretical expressions give similar results for w and perturbation pressure difference from updraft top to base Δp compared to the numerical solutions over a wide range of updraft radius R. The theoretical expressions are also consistent with 2D and 3D fully dynamical updraft simulations initiated by warm bubbles of varying width.

Implications for nonhydrostatic modeling in the “gray zone,” with a horizontal grid spacing Δx of O(1–10) km where convection is generally underresolved, are discussed. The theoretical and numerical solutions give a scaling of updraft velocity with R (~Δx) consistent with fully dynamical 2D and 3D simulations in the gray zone, with a rapid decrease of maximum w at relatively small R and a slower decrease at large R. These results suggest that an incorrect representation of perturbation pressure may be an important contributor to biases in convective strength at these resolutions. The theoretical solutions also provide a concise physical interpretation of the “virtual mass” coefficient in convection parameterizations and can be easily incorporated into these schemes to provide a consistent scaling of perturbation pressure effects with R, updraft height, and the buoyancy profile.

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Hugh Morrison

Abstract

New theoretical analytic expressions are derived for the evolution of a passive scalar, buoyancy, and vertical velocity in growing, entraining moist deep convective updrafts. These expressions are a function of updraft radius, height, convective available potential energy (CAPE), and environmental relative humidity R H. They are quantitatively consistent with idealized three-dimensional moist updraft simulations with varying updraft sizes and in environments with differing R H. In particular, the analytic expressions capture the rapid decrease of buoyancy with height due to entrainment for narrow updrafts in a dry environment despite large CAPE. In contrast to the standard entraining-plume model, the theoretical expressions also describe the effects of engulfment of environmental air between the level of free convection (LFC) and height of maximum buoyancy (HMB) required by mass continuity to balance upward acceleration of updraft air (i.e., dynamic entrainment). This organized inflow sharpens horizontal gradients, thereby enhancing smaller-scale lateral turbulent mixing below the HMB. For narrow updrafts in a dry environment, this enhanced mixing leads to a negatively buoyant region between the LFC and HMB, effectively cutting off the region of positive buoyancy at the HMB from below so that the updraft structure resembles a rising thermal rather than a plume. Thus, it is proposed that a transition from plume-like to thermal-like structure is driven by dynamic entrainment and depends on updraft width (relative to height) and environmental R H. These results help to bridge the entraining-plume and rising-thermal conceptual models of moist convection.

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Hugh Morrison

Abstract

This study investigates relationships between vertical velocity, perturbation pressure, updraft size, and dimensionality for cumulus convection. Generalized theoretical expressions are derived from approximate analytic solutions of the governing momentum and mass continuity equations for both two-dimensional (2D) and axisymmetric quasi-three-dimensional (3D) steady-state updrafts. These expressions relate perturbation pressure and vertical velocity to updraft radius R, height H, and thermal buoyancy. They suggest that the vertical velocity at the level of neutral buoyancy is reduced from perturbation pressure effects by factors of and in 2D and 3D, respectively, where is a nondimensional length, with somewhat different scalings lower in the updraft (α is a parameter equal to the ratio of vertical velocity horizontally averaged across the updraft to that at the updraft center). They also indicate that updrafts are weaker in 2D than 3D, all else being equal, with a difference of up to a factor of 2 in vertical velocity for as a direct result of differences in mass continuity between 2D and axisymmetric 3D flow. Differences between these expressions and other analytic solutions, including those derived from single normal mode Fourier/Fourier–Bessel expansion of the buoyant perturbation pressure Poisson equation, are discussed. Part II of this study compares the theoretical expressions with numerical solutions of the buoyant perturbation pressure Poisson equation for a wide range of thermal buoyancy profiles representing shallow-to-deep moist convection and also with fully dynamical 2D and 3D updraft simulations.

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Hugh Morrison and Jason Milbrandt

Abstract

Idealized three-dimensional supercell simulations were performed using the two-moment bulk microphysics schemes of Morrison and Milbrandt––Yau in the Weather Research and Forecasting (WRF) model. Despite general similarities in these schemes, the simulations were found to produce distinct differences in storm structure, precipitation, and cold pool strength. In particular, the Morrison scheme produced much higher surface precipitation rates and a stronger cold pool, especially in the early stages of storm development. A series of sensitivity experiments was conducted to identify the primary differences between the two schemes that resulted in the large discrepancies in the simulations.

Different approaches in treating graupel and hail were found to be responsible for many of the key differences between the baseline simulations. The inclusion of hail in the baseline simulation using the Milbrant––Yau scheme with two rimed-ice categories (graupel and hail) had little impact, and therefore resulted in a much different storm than the baseline run with the single-category (hail) Morrison scheme. With graupel as the choice of the single rimed-ice category, the simulated storms had considerably more frozen condensate in the anvil region, a weaker cold pool, and reduced surface precipitation compared to the runs with only hail, whose higher terminal fall velocity inhibited lofting. The cold pool strength was also found to be sensitive to the parameterization of raindrop breakup, particularly for the Morrison scheme, because of the effects on the drop size distributions and the corresponding evaporative cooling rates. The use of a more aggressive implicit treatment of drop breakup in the baseline Morrison scheme, by limiting the mean––mass raindrop diameter to a maximum of 0.9 mm, opposed the tendency of this scheme to otherwise produce large mean drop sizes and a weaker cold pool compared to the hail-only run using the Milbrandt––Yau scheme.

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Hugh Morrison and Andrew Gettelman

Abstract

A new two-moment stratiform cloud microphysics scheme in a general circulation model is described. Prognostic variables include cloud droplet and cloud ice mass mixing ratios and number concentrations. The scheme treats several microphysical processes, including hydrometeor collection, condensation/evaporation, freezing, melting, and sedimentation. The activation of droplets on aerosol is physically based and coupled to a subgrid vertical velocity. Unique aspects of the scheme, relative to existing two-moment schemes developed for general circulation models, are the diagnostic treatment of rain and snow number concentration and mixing ratio and the explicit treatment of subgrid cloud water variability for calculation of the microphysical process rates.

Numerical aspects of the scheme are described in detail using idealized one-dimensional offline tests of the microphysics. Sensitivity of the scheme to time step, vertical resolution, and numerical method for diagnostic precipitation is investigated over a range of conditions. It is found that, in general, two substeps are required for numerical stability and reasonably small time truncation errors using a time step of 20 min; however, substepping is only required for the precipitation microphysical processes rather than the entire scheme. A new numerical approach for the diagnostic rain and snow produces reasonable results compared to a benchmark simulation, especially at low vertical resolution. Part II of this study details results of the scheme in single-column and global simulations, including comparison with observations.

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Wojciech W. Grabowski and Hugh Morrison

Abstract

Cloud-scale models apply two drastically different methods to represent condensation of water vapor to form and grow cloud droplets. Maintenance of water saturation inside liquid clouds is assumed in the computationally efficient saturation adjustment approach used in most bulk microphysics schemes. When super- or subsaturations are allowed, condensation/evaporation can be calculated using the predicted saturation ratio and (either predicted or prescribed) mean droplet radius and concentration. The study investigates differences between simulations of deep unorganized convection applying a saturation adjustment condensation scheme (SADJ) and a scheme with supersaturation prediction (SPRE). A double-moment microphysics scheme with CCN activation parameterized as a function of the local vertical velocity is applied to compare cloud fields simulated applying SPRE and SADJ. Clean CCN conditions are assumed to demonstrate upper limits of the SPRE and SADJ difference. Microphysical piggybacking is used to extract the impacts with confidence. Results show a significant impact on deep convection dynamics, with SADJ featuring more cloud buoyancy and thus stronger updrafts. This leads to around a 3% increase of the surface rain accumulation in SADJ. Upper-tropospheric anvil cloud fractions are much larger in SPRE than in SADJ because of the higher ice concentrations and thus longer residence times of anvil particles in SPRE, as demonstrated by sensitivity tests. Higher ice concentrations in SPRE come from significantly larger ice supersaturations in strong convective updrafts that feature water supersaturations of several percent.

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Zachary J. Lebo and Hugh Morrison

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A novel two-moment bulk aerosol parameterization is derived from a state-of-the-art 2D bin microphysics model using power-law relationships and a semi-analytical technique for activation. The activation scheme predicts both number and mass of a lognormal aerosol distribution and permits the evolution of the modal mass with time. The newly developed bulk aerosol scheme is formulated for use in traditional two-moment bulk microphysics models. The new explicit scheme is compared with the 2D bin scheme and a simple scaling aerosol parameterization, in which all the aerosol processes are scaled to the respective cloud process rates, in a kinematic model with a specified flow field. Hybrid simulations in which the explicit activation formulation is coupled to the scaling parameterization are also performed. Model results demonstrate the significance of including a physically realistic representation of aerosols contained in haze, cloud droplets, and rain. It is shown that the explicit aerosol parameterization and scaling method predict similar bulk aerosol quantities and match the results of the 2D bin model only if an explicit treatment of aerosol activation—that is, both aerosol number and mass transfer because of activation—is included in the microphysics model.

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Hugh Morrison and Wojciech W. Grabowski

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This paper describes the development of a new multicomponent detailed bin ice microphysics scheme that predicts the number concentration of ice as well as the rime mass mixing ratio in each mass bin. This allows for local prediction of the rime mass fraction. In this approach, the ice particle mass size, projected area size, and terminal velocity–size relationships vary as a function of particle mass and rimed mass fraction, based on a simple conceptual model of rime accumulation in the crystal interstices that leads to an increase in particle mass, but not in its maximum size, until a complete “filling in” with rime and conversion to graupel occurs. This approach allows a natural representation of the gradual transition from unrimed crystals to rimed crystals and graupel during riming. The new ice scheme is coupled with a detailed bin representation of the liquid hydrometeors and applied in an idealized 2D kinematic flow model representing the evolution of a mixed-phase precipitating cumulus. Results using the bin scheme are compared with simulations using a two-moment bulk scheme employing the same approach (i.e., separate prediction of bulk ice mixing ratio from vapor deposition and riming, allowing for local prediction of bulk rime mass fraction). The bin and bulk schemes produce similar results in terms of ice and liquid water paths and optical depths, as well as the timing of the onset and peak surface precipitation rate. However, the peak domain-average surface precipitation rate produced by the bulk scheme is about 4 times that in the bin simulation. The bin scheme is also compared with simulations that assume the ice particles consist entirely of either unrimed snow or graupel. While overall results are fairly similar, the onset and timing of the peak domain-average surface precipitation rate are substantially delayed in the simulations that treat the ice particles as either unrimed snow or graupel. These results suggest the importance of representing different ice types, including partially rimed crystals, for this case.

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Hugh Morrison and Wojciech W. Grabowski

Abstract

This paper describes further developments of a two-moment warm rain bulk microphysics scheme suitable for addressing the indirect impact of atmospheric aerosols on ice-free clouds in large-eddy simulation (LES) models. The emphasis is on the prediction of supersaturation, activation of cloud droplets, and the representation of microphysical transformations during parameterized turbulent mixing. A comprehensive approach is proposed that is capable of simulating droplet activation at the cloud base, in the cloud interior due to increasing updraft strength, and at the lateral edges due to entrainment. Such an approach requires high spatial resolution to capture maximum supersaturation at cloud base as well as to resolve entraining eddies that lead to additional activation above the cloud base. This approach can be used as a benchmark for developing and testing schemes suitable for lower spatial resolutions.

A novel approach for predicting the supersaturation field is proposed, with an emphasis on its application in an Eulerian framework. This approach produces consistency among the thermodynamic variables and mitigates the problem of spurious cloud-edge supersaturation noted in the past. A new subgrid scheme is also developed to treat microphysical transformations during turbulent entrainment and mixing. This scheme is designed to be as flexible as possible, allowing for the entire range of mixing scenarios from homogeneous to extremely inhomogeneous.

The above developments are applied in 2D simulations of moist convection for an idealized rising thermal, assuming either pristine or polluted aerosol conditions. The mixing scenario has a substantial impact on the cloud microphysical and optical properties. As expected, extremely inhomogeneous mixing results in substantially smaller mean droplet number concentration, larger effective radius, and smaller cloud optical depth compared to the run with homogeneous mixing. The subgrid mixing of cloud condensation nuclei (CCN) and formation of CCN from evaporated droplets during extremely inhomogeneous mixing are relatively less important for this case.

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