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Nedjeljka Žagar
,
Valentino Neduhal
,
Sergiy Vasylkevych
,
Žiga Zaplotnik
, and
Hiroshi L. Tanaka

Abstract

The spectrum of kinetic energy of vertical motions (VKE) is less well understood compared to the kinetic energy spectrum of horizontal motions (HKE). One challenge that has limited progress in describing the VKE spectrum is a lack of a unified approach to the decomposition of vertical velocities associated with the Rossby motions and inertia–gravity (IG) wave flows. This paper presents such a unified approach using a linear Rossby–IG vertical velocity normal-mode decomposition appropriate for a spherical, hydrostatic atmosphere. New theoretical developments show that for every zonal wavenumber k, the limit VKE is proportional to the total mechanical energy and to the square of the frequency of the normal mode. The theory predicts a VKE ∝ k −5 and a VKE ∝ k 1/3 power law for the Rossby and IG waves, assuming a k −3 and a k −5/3 power law for the Rossby and IG HKE spectra, respectively. The Kelvin and mixed Rossby–gravity wave VKE spectra are predicted to follow k −1 and k −5 power laws, respectively. The VKE spectra for ERA5 data from August 2018 show that the Rossby VKE spectra approximately follow the predicted a k −5 power law. The expected k 1/3 power law for the gravity wave VKE spectrum is found only in the SH midlatitude stratosphere for k ≈ 10–60. The inertial range IG VKE spectra in the tropical and midlatitude troposphere reflect a mixture of ageostrophic and convection-coupled dynamics and have slopes between −1 and −1/3, likely associated with too steep IG HKE spectra. The forcing by quasigeostrophic ageostrophic motions is seen as an IG VKE peak at synoptic scales in the SH upper troposphere, which gradually moves to planetary scales in the stratosphere.

Significance Statement

The spectrum of kinetic energy of vertical motions (VKE) is less well understood compared to the kinetic energy spectrum of horizontal motions. One challenge is a lack of a unified approach to the decomposition of vertical velocities associated with the Rossby motions and inertia–gravity (IG) wave flows. This paper presents such a unified approach using a linear Rossby–IG vertical velocity normal-mode decomposition appropriate for a spherical, hydrostatic atmosphere. It is shown that for every zonal wavenumber, the limit VKE is proportional to the total mechanical energy and to the square of the frequency of the normal mode. The theory is successfully applied to the ERA5 data. It leads the way for a more accurate computation of momentum fluxes.

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Andrew Janiszeski
,
Robert M. Rauber
,
Brian F. Jewett
,
Greg M. McFarquhar
,
Troy J. Zaremba
, and
John E. Yorks

Abstract

This paper explores whether particles within uniformly spaced generating cells falling at terminal velocity within observed 2D wind fields and idealized deformation flow beneath cloud top can be reorganized consistent with the presence of single and multibanded structures present on WSR-88D radars. In the first experiment, two-dimensional wind fields, calculated along cross sections normal to the long axis of snowbands observed during three northeast U.S. winter storms, were taken from the initialization of the High-Resolution Rapid Refresh model. This experiment demonstrated that the greater the residence time of the particles in each of the three storms, the greater particle reorganization occurred. For experiments with longer residence times, increases in particle concentrations were nearly or directly collocated with reflectivity bands. For experiments with shorter residence times, particle reorganization still conformed to the band features but with less concentration enhancement. This experiment demonstrates that the combination of long particle residence time and net convergent cross-sectional flow through the cloud depth is sufficient to reorganize particles into locations consistent with precipitation bands. Increased concentrations of ice particles can then contribute, along with any dynamic forcing, to the low-level reflectivity bands seen on WSR-88D radars. In a second experiment, the impact of flow deformation on the reorganization of falling ice particles was investigated using an idealized kinematic model with stretching deformation flow of different depths and magnitudes. These experiments showed that deformation flow provides for little particle reorganization given typical deformation layer depths and magnitudes within the comma head of such storms.

Significance Statement

Past research with vertically pointing and scanning radars presents two different perspectives regarding snowfall organization in winter storms. Vertically pointing radars often observe cloud-top generating cells with precipitation fallstreaks descending into a broad stratiform echo at lower altitudes. In contrast, scanning radars often observe snowfall organized in quasi-linear bands. This work attempts to provide a connection between these two perspectives by examining how two-dimensional convergent and deformation flow occurring in winter storms can contribute to the reorganization of snowfall between cloud top and the ground.

Open access
Hugh Morrison
,
Nadir Jeevanjee
,
Daniel Lecoanet
, and
John M. Peters

Abstract

This study uses theory and numerical simulations to analyze the nondimensional spreading rate α (change in radius with height) of buoyant thermals as they rise and entrain surrounding environmental fluid. A focus is on how α varies with initial thermal aspect ratio Ar , defined as height divided by width of the initial buoyancy perturbation. An analytic equation for thermal ascent rate wt that depends on α is derived from the thermal-volume-averaged momentum budget equation. The thermal top height when wt is maximum, defining a critical height zc , is inversely proportional to α. The height zc also corresponds to the thermal top height when buoyant fluid along the thermal’s vertical axis is fully replaced by entrained nonbuoyant environmental fluid rising from below the thermal. The time scale for this process is controlled by the vertical velocity of parcels rising upward through the thermal’s core. This parcel vertical velocity is approximated from Hill’s analytic spherical vortex, yielding an analytic inverse relation between α and Ar . Physically, this αAr relation is connected to changes in circulation as Ar is modified. Numerical simulations of thermals with Ar varied from 0.5 to 2 give α values close to the analytic theoretical relation, with a factor of ∼3 decrease in α as Ar is increased from 0.5 to 2. The theory also explains why α of initially spherical thermals from past laboratory and modeling studies is about 0.15. Overall, this study provides a theoretical underpinning for understanding the entrainment behavior of thermals, relevant to buoyantly driven atmospheric flows.

Significance Statement

Thermals, which are coherent, quasi-spherical regions of upward-moving buoyant fluid, are a key feature of many convective atmospheric flows. The purpose of this study is to characterize how thermals entrain surrounding fluid and spread out as they rise. We use theory and numerical modeling to explain why entrainment rate decreases with an increase in the initial thermal aspect ratio—the ratio of height to width. This work also explains why the nondimensional spreading rate (change in thermal radius with height) of initially spherical thermals from past laboratory and numerical modeling studies is about 0.15. Overall, this work provides a framework for conceptualizing the entrainment behavior of thermals and thus improved understanding of vertical transport in convective atmospheric flows.

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Chongxing Fan
and
Xianglei Huang

Abstract

In the absence of scattering, thermal contrast in the atmosphere is the key to infrared remote sensing. Without the thermal contrast, the amount of absorption will be identical to the amount of emission, making the atmospheric vertical structure undetectable using remote sensing techniques. Here we show that, even in such an isothermal atmosphere, the scattering of clouds can cause a distinguishable change in upwelling radiance at the top of the atmosphere. A two-stream analytical solution, as well as a budget analysis based on Monte Carlo simulations, are used to offer a physical explanation of such influence on an idealized isothermal atmosphere by cloud scattering: it increases the chance of photons being absorbed by the atmosphere before they can reach the boundaries (both top and bottom), which leads to a reduction of TOA upwelling radiance. Actual sounding profiles and cloud properties inferred from satellite observations within 6-h time frames are fed into a more realistic and comprehensive radiative transfer model to show such cloud scattering effect, under nearly isothermal circumstances in the lower troposphere, can lead to ∼1–1.5-K decrease in brightness temperature for the nadir-view MODIS 8.5-μm channel. The study suggests that cloud scattering can provide signals useful for remote sensing applications even for such an isothermal environment.

Open access
Jun-Ichi Yano
and
Robert S. Plant

Abstract

The importance of the convective life cycle in tropical large-scale dynamics has long been emphasized, but without explicit analysis. The present work provides it by coupling the convective energy cycle under the framework of Arakawa and Schubert’s convection parameterization with a shallow-water analog atmosphere. A careful derivation of the system is first presented, because it is rather missing in the literature. The squared frequency of linear convectively coupled waves is given by a squared sum of the dry gravity wave and the convective energy cycle frequencies, shortening the period of the convective cycle through the large-scale coupling. In a weakly nonlinear regime, the system follows an equation analogous to the Korteweg–de Vries equation, which exhibits a solitary wave solution, with behavior reminiscent of observed tropical westerly wind bursts.

Significance Statement

The present work suggests that a nonlinear description of a large-scale tropical system with an explicit convective life cycle may provide a simple model of tropical westerly wind bursts. At the same time, an important lesson to learn is that, if the focus of a study is on the global scale of the atmosphere, it is wise not to try to include a convective life cycle explicitly into the model. Such a configuration will simply be dominated by the short convective-scale variabilities, which one would wish to filter out.

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Kerry Emanuel

Abstract

Large values of convective available potential energy (CAPE) are an important ingredient for many severe convective storms, yet there has been comparatively little research on how, physically, such large values arise or why they take on the observed values and climatology. Here we build on recently published observational and theoretical work to construct a simple, one-dimensional coupled soil–atmosphere model of preconvective boundary layer growth, driven by a single diurnal cycle of prescribed net surface radiation. Based on this model and previously published research, we suggest that high CAPE (>∼1000 J kg−1) results when air masses that have been significantly modified by passage over dry, lightly vegetated soils are advected over moist and/or moderately vegetated soils and then exposed to surface solar heating. Several diurnal cycles may be needed to raise the moist static energy of the boundary layer to levels consistent with high CAPE. The production of CAPE and erosion of convective inhibition (CIN) are strongly affected by the potential temperature of the desert-modified air mass, the level of near-surface soil moisture (and root-zone soil moisture if significant vegetation is present), the type of soil, and the characteristics of the vegetation. Consequently, CAPE production and severe convective weather may be significantly affected by regional-scale land-use changes and by climate change.

Significance Statement

The energy available for severe convective storms depends strongly on the properties of the underlying soil and vegetation and the temperature of air masses formed over dry terrain upstream. This implies that the severity of convective storms can be strongly affected by changes in land use and by climate change.

Open access
Marius Levin Thomas
and
Volkmar Wirth

Abstract

Banner clouds are clouds in the lee of steep mountains or sharp ridges on otherwise cloud-free days. Previous studies investigated various aspects of banner cloud formation in numerical simulations, most of which were based on idealized orography and a neutrally stratified ambient atmosphere. The present study extends these simulations in two important directions by 1) examining the impact of various types of orography ranging from an idealized pyramid to the realistic orography of Mount Matterhorn and 2) accounting for an ambient atmosphere that turns from neutral to stably stratified below the mountain summit. Not surprisingly, realistic orography introduces asymmetries in the spanwise direction. At the same time, banner cloud occurrence remains associated with a coherent area of strong uplift, although this region does not have to be located exclusively in the lee of the mountain any longer. In the case of Mount Matterhorn with a westerly ambient flow, a large fraction of air parcels rises along the southern face of the mountain, before they reach the lee and are lifted into the banner cloud. The presence of a shallow boundary layer with its top below the mountain summit introduces more complex behavior compared to a neutrally stratified boundary layer; in particular, it introduces a dependence on wind speed, because strong wind is associated with strong turbulence that is able to raise the boundary layer height and, thus, facilitates the formation of a banner cloud.

Open access
C. Todd Rhodes
,
Varavut Limpasuvan
, and
Yvan Orsolini

Abstract

Traveling planetary waves surrounding sudden stratospheric warming events can result from direct propagation from below or in situ generation. They can have significant impacts on the circulation in the mesosphere and lower thermosphere. Our study runs a series of ensembles initialized from the Whole Atmosphere Community Climate Model, version 4, nudged up to 50 km by 6-hourly Modern-Era Retrospective Analysis for Research and Application, version 2, reanalysis to compile a library of sudden stratospheric warming events. To our knowledge, we present the first composite or ensemble study that attempts to link direct propagation and in situ generation by evaluating the wave geometries associated with the overreflection perspective, a framework used to describe how planetary waves interact with critical and turning levels. The present study looks at the evolution of these interactions through the onset of sudden stratospheric warmings with an elevated stratopause (ES-SSWs). Robust and unique features of ES-SSWs are determined by employing an ensemble study that compares ES-SSWs with normal winters. Our study evaluates the production and impacts of westward-propagating, quasi-stationary, and eastward-propagating planetary waves surrounding ES-SSWs. Our results show that eastward-propagating planetary waves are generated within the westward stratospheric wind layer after ES-SSW onset which aids in restoring the eastward stratospheric wind. The interaction of quasi-stationary and westward-propagating waves with the westward stratospheric wind is explored from an overreflection perspective and reaffirms that westward-propagating planetary waves are produced from instabilities at the top of the westward stratospheric wind reversal.

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Daniel J. Lloveras
,
Dale R. Durran
, and
James D. Doyle

Abstract

We use convection-permitting idealized simulations of moist midlatitude cyclones to compare the growth of synoptic-scale perturbations derived from an adjoint model with the growth of equal-energy-norm, monochromatic-wavelength perturbations at the smallest resolved scale. For initial magnitudes comparable to those of initial-condition uncertainties in present-day data assimilation systems, the adjoint perturbations produce a “forecast bust,” significantly changing the intensity and location of the cyclone and its accompanying precipitation. In contrast, the small-scale-wave perturbations project strongly onto the moist convection, but the upscale growth from the random displacement of individual convective cells does not significantly alter the cyclone’s development nor its accompanying precipitation through 2–4-day lead times. Instead, the differences in convection generated at early times become negligible because the development of subsequent convection is driven by the mostly unchanged synoptic-scale flow. Reducing the perturbation magnitudes by factors of 10 and 100 demonstrates that nonlinear dynamics play an important role in the displacement of the cyclone by the full-magnitude adjoint perturbations, and that the upscale growth of small-magnitude, small-scale perturbations is too slow to significantly change the cyclone. These results suggest that a sensitive dependence on the synoptic-scale initial conditions, analogous to that of the Lorenz (1963) system, may be more relevant to 2–4-day midlatitude-cyclone forecast busts than the upscale error growth in the Lorenz (1969) model.

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Stephen T. Garner

Abstract

Three-level and thee-layer models of tropical cyclones (TCs) have provided a more conceptual view of TC dynamics than conventional numerical models. They have been purpose-built, with special treatments of boundary layers and/or convection. We show that a further simplification with minimal parameterization and a seamless connection to higher resolution captures TCs about as well. The framework of radiative–convective equilibrium avoids ambiguities from temporal and spatial boundaries. For the TCs, the minimal grid provides one level for outflow and one level for most of the inflow. A version with 10 levels is used for comparison. For the same average pressure intensity, the wind field is slightly broader around the three-level vortices, with stronger subsidence in the core and 25% more mass and moisture flux. However, thermodynamic efficiency, mechanical efficiency, and TC counts are about the same. Across runs with different surface temperatures and cooling rates, global energy scaling makes reasonable predictions of the maximum velocity allowing for variations in the effective forcing/dissipation area and surface humidity. TC count is inconsistent with theories for size as a function of Coriolis parameter. An overturning circuit is isolated within a composite vortex and analyzed using energy and entropy budgets to mirror analytical models. Effective radiation and dissipation temperatures are less extreme than often assumed in such models, yielding a smaller thermodynamic efficiency near the global value of ∼0.1. The pressure deficit arises mostly from inflow enthalpy increase, as expected, but dissipation reduces the contribution from an outflow pressure increase. The influence of ambient CAPE makes up most of the difference.

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