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Chia Rui Ong, Hiroaki Miura, and Makoto Koike

Abstract

The terminal velocity of cloud drops and raindrops used in numerical model calculations can significantly affect weather predictions. Current formulations rely on laboratory experiments made in the 1940s and 1960s. Because these experiments were performed only at typical environmental conditions of 20°C and 1013 hPa, parameterizations have been introduced to deduce the terminal velocity aloft without rigorous evaluation. In this study, an incompressible two-phase flow direct numerical simulation model is used to calculate the free-falling motion of axisymmetric drops with diameters between 0.025 and 0.5 mm to study the terminal fall velocity. Simulated terminal fall velocities of free-falling drops at 20°C and 1013 hPa agree within 3.2% with the previous empirical parameterization (Beard formula), and 4.5% with existing laboratory data in the diameter range between 0.3 and 0.5 mm. The velocities converge to the analytic Hadamard–Rybczynski solution within 2% for small Reynolds numbers, demonstrating the robustness of our simulations. Simulations under various atmospheric conditions show that existing empirical parameterizations that account for the air density dependence of the terminal velocity have errors up to 11.8% under the conditions examined in this study. We propose a new empirical formula that describes the air density dependence of the terminal velocity. It is also shown that the falling speed of a small drop is not sensitive to shape oscillation, and the terminal velocity decreases by only less than 1.3% when the axis ratio increases by 12% with reduced surface tension. Internal circulation within falling drops is also presented and compared with previous studies.

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Gergely Bölöni, Young-Ha Kim, Sebastian Borchert, and Ulrich Achatz

Abstract

Current gravity wave (GW) parameterization (GWP) schemes are using the steady-state assumption, in which an instantaneous balance between GWs and mean flow is postulated, thereby neglecting transient, nondissipative interactions between the GW field and the resolved flow. These schemes rely exclusively on wave dissipation, by GW breaking or near critical layers, as a mechanism leading to forcing of the mean flow. In a transient GWP, without the steady-state assumption, nondissipative wave–mean-flow interactions are enabled as an additional mechanism. Idealized studies have shown that this is potentially important, and therefore the transient GWP Multiscale Gravity Wave Model (MS-GWaM) has been implemented into a state-of-the-art weather and climate model. In this implementation, MS-GWaM leads to a zonal-mean circulation that agrees well with observations and increases GW momentum-flux intermittency as compared with steady-state GWPs, bringing it into better agreement with superpressure balloon observations. Transient effects taken into account by MS-GWaM are shown to make a difference even on monthly time scales: in comparison with steady-state GWPs momentum fluxes in the lower stratosphere are increased and the amount of missing drag at Southern Hemispheric high latitudes is decreased to a modest but nonnegligible extent. An analysis of the contribution of different wavelengths to the GW signal in MS-GWaM suggests that small-scale GWs play an important role down to horizontal and vertical wavelengths of 50 km (or even smaller) and 200 m, respectively.

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Young-Ha Kim, Gergely Bölöni, Sebastian Borchert, Hye-Yeong Chun, and Ulrich Achatz

Abstract

In a companion paper, the Multiscale Gravity Wave Model (MS-GWaM) has been introduced and its application to a global model as a transient subgrid-scale parameterization has been described. This paper focuses on the examination of intermittency of gravity waves (GWs) modeled by MS-GWaM. To introduce the variability and intermittency in wave sources, convective GW sources are formulated, using diabatic heating diagnosed by the convection parameterization, and they are coupled to MS-GWaM in addition to a flow-independent source in the extratropics accounting for GWs due neither to convection nor to orography. The probability density function (PDF) and Gini index for GW pseudomomentum fluxes are assessed to investigate the intermittency. Both are similar to those from observations in the lower stratosphere. The intermittency of GWs over tropical convection is quite high and is found not to change much in the vertical direction. In the extratropics, where nonconvective GWs dominate, the intermittency is lower than that in the tropics in the stratosphere and comparable to that in the mesosphere, exhibiting a gradual increase with altitude. The PDFs in these latitudes seem to be close to the lognormal distributions. Effects of transient GW–mean-flow interactions on the simulated GW intermittency are assessed by performing additional simulations using the steady-state assumption in the GW parameterization. The intermittency of parameterized GWs over tropical convection is found to be overestimated by the assumption, whereas in the extratropics it is largely underrepresented. Explanation and discussion of these effects are included.

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Yi Dai, Sharanya J. Majumdar, and David S. Nolan

Abstract

It is widely known that strong vertical wind shear (exceeding 10 m s−1) often weakens tropical cyclones (TCs). However, in some circumstances, a TC is able to resist this strong shear and even restrengthen. To better understand this phenomenon, a series of idealized simulations are conducted, followed by a statistical investigation of 40 years of Northern Hemisphere TCs. In the idealized simulations, a TC is embedded within a time-varying point-downscaling framework, which is used to gradually increase the environmental vertical wind shear to 14 m s−1 and then hold it constant. This controlled framework also allows for the separation of the TC-induced flow from the prescribed environmental flow. The TC-induced outflow is found to withstand the strong upper-tropospheric environmental flow, and this is manifested in the TC-induced shear difference (TCSD) vector. The TCSD vector, together with the environmental shear vector, defines an azimuthal range within which most of the asymmetric convection is located. The statistical analysis confirms the findings from the idealized simulations, and the results are not strongly sensitive to the TC intensity or basin. Moreover, compared with total shear, the inclusion of TCSD information creates a slightly better correlation with TC intensity change. Overall, the TCSD vector serves as a diagnostic to explain the ability of a TC to resist strong environmental shear through its outflow, and it could potentially be used as a parameter to predict future intensity change.

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Takatoshi Sakazaki

Abstract

Using global precipitation datasets (GSMaP, TRMM) and the latest reanalysis data (ERA5), we performed a comprehensive analysis of the tropical rainfall variability that accompanies global-scale, low-frequency normal modes: Rossby, Rossby–gravity, and Kelvin modes. Cross-spectral analysis and lag-regression analysis both showed that coherent rainfall variations accompany not only the wavenumber-1 gravest Rossby mode (“5-day” wave) but other low-frequency modes. The normal mode rainfall variations are enhanced in regions such as the Amazon basin, but also include circumglobally traveling structures with substantial amplitude over the open ocean. These results are remarkably consistent among the three datasets including even ERA5 rainfall data. The circumglobal rainfall signals may be considered primarily as a response to the normal mode dynamical variations. We found that the phase relationship between rainfall and dynamical field variability is strongly dependent on the type of mode and even on the zonal wavenumber. We suggest that this is explained by the difference in relative importance of two underlying processes: 1) moisture-flux convergence and 2) rainfall enhancement associated with adiabatic cooling. Our determined rainfall signals are the response to quasi-monochromatic, periodic waves that have a simple vertical structure and represent one special case of tropospheric wave–rainfall coupling. Implications for the mechanism of 12-h rainfall oscillations believed to be forced by the atmospheric tide are also considered.

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Andrew J. Heymsfield, Aaron Bansemer, Alexander Theis, and Carl Schmitt

Abstract

This study quantifies how far snow can fall into the melting layer (ML) before all snow has melted by examining a combination of in-situ observations from aircraft measurements in Lagrangian spiral descents from above through the ML and descents and ascents into the ML, as well as an extensive database of NOAA surface observer reports during the past 50 years. The airborne data contain information on the particle phase (solid, mixed, or liquid), population size distributions and shapes, along with temperature, relative humidity, and vertical velocity. A wide range of temperatures and ambient relative humidities are used for both the airborne and ground-based data. It is shown that an ice bulb temperature of 0°C, together with the air temperature and pressure (altitude), are good first order predictors of the highest temperature snowflakes can survive in the melting layer before completely melting. Particle size is also important, as is whether the particles are graupel or hail. If the relative humidity is too low, the particles will sublimate completely as they fall into the melting layer. Snow as warm as +7°C is observed from aircraft measurements and surface observations. Snow pellets survive to even warmer temperatures. Relationships are developed to represent the primary findings.

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Bowen Zhou, Yuhuan Li, and Shiguang Miao

Abstract

A scale adaptive model is developed for the representation of dry convective boundary layer (CBL) turbulence in numerical models operating at O(100 m - 1 km) horizontal resolution, also known as the model gray zone of the CBL. The new model is constructed based on a planetary boundary layer (PBL) scheme and a large-eddy simulation (LES) closure that are both turbulence kinetic energy-based parameterizations. Scale adaptivity is achieved by “blending” the PBL scheme with the LES closure through an inverse averaging procedure that naturally accounts for vertical variations of the dominant turbulent length scales, hence the gray zone range. High-resolution wide-domain LES benchmark cases covering a broad range of CBL bulk stability are filtered to gray zone resolutions, and analyzed to determine the averaging coefficients. Stability dependence of the dominant length scales is revealed by the analysis and accounted for in the new model. The turbulence model is implemented into a community atmospheric model, and tested for idealized cases. Compared to two established gray zone models, the new model performs equally well under strongly convective conditions, and is more advantageous for the weakly unstable and near neutral CBL.

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Michael J. Reeder, Thomas Spengler, and Clemens Spensberger

Abstract

It is thought that the sensible heat fluxes associated with sea surface temperature (SST) fronts can affect the genesis and evolution of atmospheric fronts. An analytic model is developed and used to explore this idea. The model predictions are compared with climatologies of atmospheric fronts over the North Atlantic Ocean identified in reanalyses. The climatologies are divided into times when fronts are detected at a point and times when they are not, and compared with model results with and without fronts in their initial conditions.

In airstreams with fronts, both the climatologies and model show that adiabatic frontogenesis is much more important than diabatic frontogenesis. They also show that there is weak diabatic frontogenesis associated with differential sensible heating over the SST front and frontolysis either side of it. Because of the upstream and downstream frontolysis, the SST front has relatively little net effect on atmospheric fronts in the model. This result holds true as the width and strength of the SST front changes.

In airstreams initially without fronts, a combination of adiabatic and diabatic frontogenesis is important for the local genesis of atmospheric fronts over the SST front. The model shows sustained frontogenesis only when the deformation is sufficiently strong or when the translation speed is low, as advection otherwise weakens the potential temperature gradient. This strong localized diabatic frontogenesis, which is amplified by adiabatic frontogenesis, can result in a front, which is consistent with atmospheric fronts in the region being most frequently located along the SST front.

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Chaim I Garfinkel, Ofer Shamir, Itzhak Fouxon, and Nathan Paldor

Abstract

Variability in the tropical atmosphere is concentrated at wavenumber-frequency combinations where linear theory indicates wave-modes can freely propagate, but with substantial power in between. This study demonstrates that such a power spectrum can arise from small scale convection triggering large scale waves via wave-wave interactions in a moderately turbulent fluid. Two key pieces of evidence are provided for this interpretation of tropical dynamics using a nonlinear rotating shallow water model: a parameter sweep experiment in which the amplitude of an external forcing is gradually ramped up, and also an external forcing in which only symmetric or only anti-symmetric modes are forced. These experiments do not support a commonly accepted mechanism involving the forcing projecting directly onto the wave-modes with a strong response, yet still simulate a power spectrum resembling that observed, though the linear projection mechanism could still complement the mechanism proposed here in observations. Interpreting the observed tropical power spectrum using turbulence offers a simple explanation as to why power should be concentrated at the theoretical wave-modes, and also provides a solid footing for the common assumption that the back-ground spectrum is red, even as it clarifies why there is no expectation for a turbulent cascade with a specific, theoretically derived slope such as -5/3. However it does explain why the cascade should be towards lower wavenumbers, that is an inverse energy cascade, similar to the midlatitudes even as compressible wave-modes are important for tropical dynamics.

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Jerry Y. Harrington, G. Alexander Sokolowsky, and Hugh Morrison

Abstract

Numerical cloud models require estimates of the vapor growth rate for ice crystals. Current bulk and bin microphysical parameterizations generally assume that vapor growth is diffusion limited, though some parameterizations include the influence of surface attachment kinetics through a constant deposition coefficient. A parameterization for variable deposition coefficients is provided herein. The parameterization is an explicit function of the ambient ice supersaturation and temperature, and an implicit function of crystal dimensions and pressure. The parameterization is valid for variable surface types including growth by dislocations and growth by step nucleation. Deposition coefficients are predicted for the two primary growth directions of crystals, allowing for the evolution of the primary habits. Comparisons with benchmark calculations of instantaneous mass growth indicate that the parameterization is accurate to within a relative error of 1%. Parcel model simulations using Lagrangian microphysics as a benchmark indicate that the bulk parameterization captures the evolution of mass mixing ratio and fall speed with typical relative errors of less than 10%, whereas the average axis lengths can have errors of up to 20%. The bin model produces greater accuracy with relative errors often less that 10%. The deposition coefficient parameterization can be used in any bulk and bin scheme, with low error, if an equivalent volume spherical radius is provided.

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