The mysteries of mammatus clouds: Observations and formation mechanisms

Mammatus clouds are an intriguing enigma of atmospheric fluid dynamics and cloud physics. Most commonly observed on the underside of cumulonimbus anvils, mammatus also occur on the underside of cirrus, cirrocumulus, altocumulus, altostratus, and stratocumulus, as well as in contrails from jet aircraft and pyrocumulus ash clouds from volcanic eruptions. Despite their aesthetic appearance, mammatus have been the subject of few quantitative research studies. Observations of mammatus have been obtained largely through serendipitous opportunities with a single observing system (e.g., aircraft penetrations, visual observations, lidar, radar) or tangential observations from field programs with other objectives. Theories describing mammatus remain untested, as adequate measurements for validation do not exist because of the small distance scales and short time scales of mammatus. Modeling studies of mammatus are virtually nonexistent. As a result, relatively little is known about the environment, formation mechanisms, properties, microphysics, and dynamics of mammatus. This paper presents a review of mammatus clouds that addresses these mysteries. Previous observations of mammatus and proposed formation mechanisms are discussed. These hypothesized mechanisms are anvil subsidence, subcloud evaporation/sublimation, melting, hydrometeor fallout, cloud-base detrainment instability, radiative effects, gravity waves, Kelvin-Helmholtz instability, Rayleigh-Taylor instability, and Rayleigh-Bénard-like convection. Other issues addressed in this paper include whether mammatus are composed of ice or liquid water hydrometeors, why mammatus are smooth, what controls the temporal and spatial scales and organization of individual mammatus lobes, and what are the properties of volcanic ash clouds that produce mammatus? The similarities and differences between mammatus, virga, stalactites, and reticular clouds are also discussed. Finally, because much still remains to be learned, research opportunities are described for using mammatus as a window into the microphysical, turbulent, and dynamical processes occurring on the underside of clouds. © 2006 American Meteorological Society

Numerical simulation of mammatus

Mammatus are hanging lobes on the underside of clouds. Although many different mechanisms have been proposed for their formation, none have been rigorously tested. In this study, three-dimensional numerical simulations of mammatus on a portion of a cumulonimbus cirruslike anvil are performed to explore some of the dynamic and microphysical factors that affect mammatus formation and evolution. Initial conditions for the simulations are derived from observed thermodynamic soundings. Five observed soundings are chosen—four were associated with visually observed mammatus and one was not. Initial microphysical conditions in the simulations are consistent with in situ observations of cumulonimbus anvil and mammatus. Mammatus form in the four model simulations initialized with the soundings for which mammatus were observed, whereas mammatus do not form in the model simulation initialized with the no-mammatus sounding. Characteristics of the modeled mammatus compare favorably to previously pub-lished mammatus observations. Three hypothesized formation mechanisms for mammatus are tested: cloud-base detrainment instability, fallout of hydrometeors from cloud base, and sublimation of ice hydrometeors below cloud base. For the parameters considered, cloud-base detrainment instability is a necessary, but not sufficient, condition for mammatus formation. Mammatus can form without fallout, but not without sublimation. All the observed soundings for which mammatus were observed feature a dry-adiabatic subcloud layer of varying depth with low relative humidity, which supports the importance of sublimation to mammatus formation. 1

The performance of filtered leapfrog schemes in benchmark simulations

The stabilisation of the leapfrog time-stepping scheme provided by the Robert–Asselin filter has enabled decades of atmospheric and oceanic research and weather and climate predictions. The unfortunate concomitant reduction from second-order accuracy to first-order accuracy inflicted by the filter has recently ushered in a new generation of leapfrog time filters that preserve the second-order accuracy, including the Robert–Asselin–Williams (RAW) filter and its variants. These modern filtered leapfrog schemes have previously been shown to improve numerical simulations made using both simple conceptual models and comprehensive general circulation models. However, their performance in standard benchmark experiments has not previously been assessed. Here we evaluate these filtered leapfrog schemes in four classic benchmark experiments: linear scalar advection; a nonlinear density current in the quasi-compressible equations; a nonlinear rising warm bubble in the fully compressible equations; and the linked behaviour of nonlinear twin tropical cyclones in the rotating shallow-water equations. For a given time-step size, the filtered leapfrog schemes are found to compare favourably with the third-order Runge–Kutta (RK3) scheme. They are also less computationally expensive than RK3, at roughly one-third to one-half the cost per time step. For a given computational expenditure, the filtered leapfrog schemes are found to produce smaller errors with respect to the analytical solution (where available) than RK3. Furthermore, the filtered leapfrog schemes are found to be numerically stable, even when the discretisation method splits the slow advection and diffusion modes from the fast acoustic and gravity-wave modes. Given that implementing filter upgrades requires only minimally invasive changes to an existing computer code, our results provide support for the continued use of filtered leapfrog schemes in atmosphere and ocean models

P3.25 NOCTURNAL TORNADOES AND LOW-LEVEL STATIC STABILITY

Nocturnal tornadoes, while comprising only about a quarter of verified tornadoes, produce 42.5 percent of tornado fatalities (Ashley 2007). However, very little investigation into the dynamics unique t

Comparison of very high order (O3–18) flux and Crowley flux, and (O3–17) WENO flux schemes with a 2D nonlinear test problem

A two-dimensional, non-linear diffusion-limited colliding plumes simulations were used to demonstrate the improved solution accuracy with very high order O9–18 flux schemes, including upwind-biased and even-centred constant grid flux and Crowley constant grid flux schemes, and odd order weighted essentially non-oscillatory (WENO) flux schemes, along with variations and hybrids of these. All schemes were coupled with comparably high order even-centred Lagrangian interpolations and pressure gradient/divergence approximations, and O18 spatial filtering. Subgrid-scale (SGS) turbulent flux calculations, with a constant eddy-mixing coefficient, were made with O2 spatial approximations (O4–20 accurate SGS turbulent fluxes had little impact). Using a range of resolutions from Δx = Δz = 25–166.66… m for all schemes comparisons against an O17 flux, 25 m resolution reference solution showed solutions made with ≥ O9 fluxes produced (often substantially) improved solutions, both visually and usually objectively, compared to solutions produced with lower order (<O9/10) fluxes, especially at intermediate resolutions (33.33–100 m). Expectedly, odd order solutions were increasingly damped as accuracy was decreased, especially from O9 to O3, especially for WENO solutions, while even order solutions were increasingly contaminated with dispersion and aliasing errors as accuracy was decreased, especially from O10 to O4. Odd order schemes also produced better solutions than even order schemes for <O9/10 fluxes, while the highest order (≥ O13/14) schemes produced the best solutions, for any given resolution. Even order flux and Crowley flux (WENO) solutions were the least (most) computationally expensive, based on either floating-point operations (FPO) or CPU times. Efficient WENO-Sine and proposed hybrid Crowley-WENO(-Sine) schemes required fewer FPOs to produce more accurate solutions than traditional WENO schemes. We are encouraged by the often much improved visual and objective accuracy of very high order (≥ O9) fluxes in simulations of a complex problem, and encourage further testing in numerical weather prediction models

Nonlinear diffusion‐limited 2D colliding plume simulations with very high order numerical approximations

Atmospheric numerical models play a crucial role in operational weather forecasting, as well as improving our understanding of atmospheric dynamics via research studies. Maximising their accuracy is of paramount importance. Use of &gt;O7 flux schemes in atmospheric models is largely undocumented, with no studies considering O3–17 fluxes with formal accuracy‐preserving high order interpolation, pressure gradient / divergence, and subgrid‐scale (SGS) turbulent fluxes. Higher order numerical approximations can reduce truncation, amplitude and phase errors, and potentially improve model accuracy and effective resolution.Here, simulations are presented using very high order O3–17 fluxes, with / without high order O2–18 Lagrangian interpolations, pressure gradient / divergence approximations, and SGS turbulent fluxes for a 2D, highly‐viscous (Re ~ 100) diffusion‐limited, nonlinear colliding plumes problem using 25–200 m spatial resolutions. The highest order flux schemes coupled with higher order interpolations, pressure gradient / divergence and SGS flux approximations produced the best solutions, with higher‐order fluxes and interpolations being most important. Overall solution convergence of ~O1–2 with mode‐split (fast sound / slow advective waves) O3 Runge–Kutta temporal schemes was negatively impacted by ≤O1 temporal convergence with SGS fluxes, divergence damping, and especially spatial filters, compared to ~O3 convergence with these inactivated.While very high order schemes were shown to improve solution accuracy, few cost‐effective higher order highly‐viscous test problem solutions (higher order versus finer resolution) were found using theoretical floating‐point operations (FPO) with CFL‐limited or constant stable Courant number‐based time steps. However, employing CPU time, rather than FPOs, demonstrated there was reduced computational burden using higher order approximations. We conclude that O9–17 flux schemes with or without high‐order ≥O4 interpolations, pressure gradient / divergence approximations, and SGS fluxes can improve atmospheric model solution accuracy, without prohibitive computation costs, compared to O3–7 flux with O2 interpolations, pressure gradient / divergence approximations, and SGS fluxes