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Ángel F. Adames

Abstract

The weak temperature gradient (WTG) approximation is extended to the basic equations on a rotating plane. The circulation is decomposed into a diabatic component that satisfies WTG balance exactly and a deviation from this balance. Scale analysis of the decomposed basic equations reveals a spectrum of motions, including unbalanced inertio-gravity waves and several systems that are in approximate WTG balance. The balanced systems include equatorial moisture modes with features reminiscent of the MJO, off-equatorial moisture modes that resemble tropical depression disturbances, “mixed systems” in which temperature and moisture play comparable roles in their thermodynamics, and moist quasigeostrophic motions. In the balanced systems the deviation from WTG balance is quasi nondivergent, in nonlinear balance, and evolves in accordance to the vorticity equation. The evolution of the strictly balanced WTG circulation is in turn described by the divergence equation. WTG balance restricts the flow to evolve in the horizontal plane by making the isobars impermeable to vorticity and divergence, even in the presence of diabatically driven vertical motions. The vorticity and divergence equations form a closed system of equations when the irrotational circulation is in WTG balance and the nondivergent circulation is in nonlinear balance. The resulting “WTG equations” may elucidate how interactions between diabatic processes and the horizontal circulation shape slowly evolving tropical motions.

Significance Statement

Many gaps in our understanding of tropical weather systems still exist and there are still many opportunities to improve their forecasting. We seek to further our understanding of the tropics by extending a framework known as the “weak temperature gradient approximation” to all of the equations for atmospheric flow. Doing this reveals a variety of motions whose scales are similar to observed tropical weather systems. We also show that two equations describe the evolution of slow systems: one that describes tropical thunderstorms and one for the rotating horizontal winds. The two equations may help us understand the dynamics of slowly evolving tropical systems.

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Hing Ong and Da Yang

Abstract

The compressional beta effect (CBE) arises in a compressible atmosphere with the nontraditional Coriolis terms (NCTs), the Coriolis force from the locally horizontal part of the planetary rotation. Previous studies proposed that the CBE speeds up the eastward propagation and slows down the westward propagation of zonal vertical circulations in a dry atmosphere. Here, we examine how the CBE affects the propagation of convectively coupled tropical waves. We perform 2D (x, z), large-domain cloud-resolving simulations with and without NCTs. This model setup mimics the atmosphere along Earth’s equator, and differences between the simulations highlight the role of the CBE. We analyze precipitation, precipitable water, and surface and upper-level winds from our simulations. Gravity wave signals emerge in all fields. In the no-NCT simulation, eastward and westward gravity waves propagate at the same speed. With NCTs, eastward gravity waves propagate faster than westward gravity waves. To quantify the strength of the CBE, we then measure the difference in gravity wave speed and find that it linearly increases with the system rotation rate. This result is consistent with our theoretical prediction and suggests that the CBE can induce zonal asymmetry in propagation behaviors of convectively coupled waves.

Significance Statement

The rotation of Earth turns eastward motion upward and upward motion westward, and vice versa. This effect is called the nontraditional Coriolis effect and is omitted in most of the current atmospheric models for predicting weather and climate. Using an idealized model with cloud physics, this study suggests that the inclusion of the nontraditional Coriolis effect speeds up eastward-moving rainy systems and slows down westward-moving ones. The speed change agrees with a theory without cloud physics. This study encourages restoring the nontraditional Coriolis effect to the atmospheric models since it increases the accuracy of tropical large-scale weather prediction while the cost is low.

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Megan Bickle, John H. Marsham, Stephen D. Griffiths, Andrew N. Ross, and Julia Crook

Abstract

The West African monsoon has a clear diurnal cycle in boundary layer properties, synoptic flow, and moist convection. A nocturnal low-level jet (LLJ) brings cool, moist air into the continent and we hypothesize that it may support storms by providing vertical wind shear and a source of moisture. We use idealized simulations to investigate how the mean diurnal cycle in temperature and humidity compared with that of the wind shear impacts on mature squall lines. Thermodynamic diurnal changes dominate those of the winds, although when isolated the LLJ wind is favorable for more intense systems. Bulk characteristics of the storms, including in-cloud upward mass flux and—if precipitation evaporation is accounted for—total surface rain rates, correlate well with the system-relative inflow of convectively unstable air and moisture into the storms. Mean updraft speeds and mean rainfall rates over the storms do not correlate as well with system-relative inflows due to variations in storm morphology such as cold pool intensity. We note that storms tend to move near the speed of the African easterly jet and so maximize the inflow of convectively unstable air. Our results explain the observed diurnal cycle in organized moist convection, with the hours from 1800 to 0000 UTC being the most favorable. Storms are more likely to die after this, despite the LLJ supporting them, with the environment becoming more favorable again by midday.

Significance Statement

Large organized storms dominate rainfall in the West African Sahel, but models struggle to predict them at the correct time of day and the underlying mechanisms that control their timings are not well understood. Using idealized simulations, we show that the temperature and humidity of the late evening are favorable for such storms whereas inflow from the low-level jet supports storms overnight. Storm inflows of available energy and moisture predict upward mass transport and total rainfall rates, whereas the strength of the storm’s cold pool is important for storm structure and intensity. Our results demonstrate how the environmental wind profile (which varies throughout the day) interacts with internal storm dynamics, posing a major challenge to parameterized models.

Open access
Yi Lin, Chenggang Wang, Jiade Yan, Ju Li, and Songwei He

Abstract

In this study, we focused on the impacts of the planetary boundary layer (PBL) low-level jet (LLJ) on the horizontal distribution, vertical development, and 3D structure of urban heat island (UHI). Observational datasets were collected from 224 automatic weather stations (AWSs), and an intensive sounding experiment was conducted in Beijing from 28 August to 2 September 2016. Three-dimensional simulations were operated by the Weather Research and Forecasting (WRF) Model. The results show the following: Ri was smaller than 0.25 at both urban and suburban stations near the surface when the LLJ was present. Through turbulent mixing, the LLJ extended the horizontal distribution of the canopy UHI downwind and increased the total UHI area by approximately 1 × 103 km2. The temperature lapse rate in the urban area was 0.7°C (100 m)−1 with the LLJ, twice that in the absence of an LLJ. The jet enhanced the vertical mixing above the urban area, accompanied by a near-surface TKE up to 0.52 m2 s−2, elevating the vertical UHI development height to 200 m. The LLJ is capable of increasing the temperature of the downwind urban area by a maximum of 8.5°C h−1 through warm advection. The temperature advection in the upper air caused by the LLJ also tilted the 3D UHI structure as a plume. Results reproduced the process by which the LLJ affect the 3D UHI structure through turbulence and advection, and could also provide ideas regarding the influence of the LLJ in other PBL processes.

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Ian P. White, Chaim I. Garfinkel, and Peter Hitchcock

Abstract

An idealized model is used to examine the tropospheric response to sudden stratospheric warmings (SSWs), by imposing transient stratospheric momentum torques tailored to mimic the wave-forcing impulse associated with spontaneously occurring SSWs. Such an approach enables us to examine both the ∼2–3-week forcing stage of an SSW during which there is anomalous stratospheric wave-activity convergence, as well as the recovery stage during which the wave forcing abates and the stratosphere radiatively recovers over 2–3 months. It is argued that applying a torque is better suited than a heating perturbation for examining the response to SSWs, due to the meridional circulation that is induced to maintain thermal-wind balance (i.e., the “Eliassen adjustment”); an easterly torque yields downwelling at high latitudes and equatorward flow below, similar to the wave-induced circulation that occurs during spontaneously occurring SSWs, whereas a heating perturbation yields qualitatively opposite behavior and thus cannot capture the initial SSW evolution. During the forcing stage, the meridional circulation in response to an impulse comparable to the model’s internal variability is able to penetrate down to the surface and drive easterly-wind anomalies via Coriolis torques acting on the anomalous equatorward flow. During the recovery stage, after which the tropospheric flow has already responded, the meridional circulation associated with the stratosphere’s radiative recovery appears to provide the persistent stratospheric forcing that drives the high-latitude easterly anomalies, whereas planetary waves are found to play a smaller role. This is then augmented by synoptic-wave feedbacks that drive and amplify the annular-mode response.

Open access
Richard Rotunno

Abstract

In a previous paper a formula was derived for the maximum potential intensity of the tangential wind in a tropical cyclone called PI+. The formula, PI+2 = EPI2 + αrmwmηm, where EPI is the maximum potential intensity of the gradient wind and αrmwmηm represents the supergradient winds. The latter term is the product of the radius rm, the vertical velocity wm, the azimuthal vorticity ηm at the radius and height of the maximum tangential wind (rm, zm), and the (nearly constant) α. Examination of a series of simulations of idealized tropical cyclones indicate an increasing contribution from the supergradient-wind term to PI+ as the radius of maximum wind increases. In the present paper, the physical content of the supergradient-wind term is developed showing how it is directly related to tropical cyclone boundary layer dynamics. It is found that rmwmηmumin2zm(rm)/lυ(zm)rm, where −u min is the maximum boundary layer radial inflow velocity and lυ(z) is the vertical mixing length.

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Tobias Selz, Michael Riemer, and George C. Craig

Abstract

This study investigates the transition from current practical predictability of midlatitude weather to its intrinsic limit. For this purpose, estimates of the current initial condition uncertainty of 12 real cases are reduced in several steps from 100% to 0.1% and propagated in time with a global numerical weather prediction model (ICON at 40 km resolution) that is extended by a stochastic convection scheme to better represent error growth from unresolved motions. With the provision that the perfect model assumption is sufficiently valid, it is found that the potential forecast improvement that could be obtained by perfecting the initial conditions is 4–5 days. This improvement is essentially achieved with an initial condition uncertainty reduction by 90% relative to current conditions, at which point the dominant error growth mechanism changes: With respect to physical processes, a transition occurs from rotationally driven initial error growth to error growth dominated by latent heat release in convection and due to the divergent component of the flow. With respect to spatial scales, a transition from large-scale up-amplitude error growth to a very rapid initial error growth on small scales is found. Reference experiments with a deterministic convection scheme show a 5%–10% longer predictability, but only if the initial condition uncertainty is small. These results confirm that planetary-scale predictability is intrinsically limited by rapid error growth due to latent heat release in clouds through an upscale-interaction process, while this interaction process is unimportant on average for current levels of initial condition uncertainty.

Significance Statement

Weather predictions provide high socioeconomic value and have been greatly improved over the last decades. However, it is widely believed that there is an intrinsic limit to how far into the future the weather can be predicted. Using numerical simulations with an innovative representation of convection, we are able to confirm the existence of this limit and to demonstrate which physical processes are responsible. We further provide quantitative estimates for the limit and the remaining improvement potential. These results make clear that our current weather prediction capabilities are not yet maxed out and could still be significantly improved with advancements in atmospheric observation and simulation technology in the upcoming decades.

Open access
Kuan-Yu Lu and Daniel R. Chavas

Abstract

Recent work found evidence using aquaplanet experiments that tropical cyclone (TC) size on Earth is limited by the Rhines scale, which depends on the planetary vorticity gradient β. This study aims to examine how the Rhines scale limits the size of an individual TC. The traditional Rhines scale is first reexpressed as a Rhines speed to characterize how the effect of β varies with radius in a vortex whose wind profile is known. The framework is used to define the vortex Rhines scale, which is the transition radius that divides the vortex into a vortex-dominant region at smaller radii, where the axisymmetric circulation is steady, and a wave-dominant region at larger radii, where the circulation stimulates planetary Rossby waves and dissipates. Experiments are performed using a simple barotropic model on a β plane initialized with a TC-like axisymmetric vortex defined using a recently developed theoretical TC wind profile model. The gradient β and initial vortex size are each systematically varied to investigate the detailed responses of the TC-like vortex to β. Results show that the vortex shrinks toward an equilibrium size that closely follows the vortex Rhines scale. A larger initial vortex relative to its vortex Rhines scale will shrink faster. The shrinking time scale is well described by the vortex Rhines time scale, which is defined as the overturning time scale of the circulation at the vortex Rhines scale and is shown to be directly related to the Rossby wave group velocity. The relationship between our idealized results and the real Earth is discussed. Results may generalize to other eddy circulations, such as the extratropical cyclone.

Significance Statement

Tropical cyclones vary in size significantly on Earth, but how large a tropical cyclone could potentially be is still not understood. The variation of the Coriolis parameter with latitude is known to limit the size of turbulent circulations, but its effect on tropical cyclones has not been studied. This study derives a new parameter related to this concept called the “vortex Rhines scale” and shows in a simple model how and why storms will tend to shrink toward this size. These results help explain why tropical cyclone size tends to increase slowly with latitude on Earth and can help us understand what sets the size of tropical cyclones on Earth in general.

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Xiang-Yu Li, Bernhard Mehlig, Gunilla Svensson, Axel Brandenburg, and Nils E. L. Haugen

Abstract

It was previously shown that the superdroplet algorithm for modeling the collision–coalescence process can faithfully represent mean droplet growth in turbulent clouds. An open question is how accurately the superdroplet algorithm accounts for fluctuations in the collisional aggregation process. Such fluctuations are particularly important in dilute suspensions. Even in the absence of turbulence, Poisson fluctuations of collision times in dilute suspensions may result in substantial variations in the growth process, resulting in a broad distribution of growth times to reach a certain droplet size. We quantify the accuracy of the superdroplet algorithm in describing the fluctuating growth history of a larger droplet that settles under the effect of gravity in a quiescent fluid and collides with a dilute suspension of smaller droplets that were initially randomly distributed in space (“lucky droplet model”). We assess the effect of fluctuations upon the growth history of the lucky droplet and compute the distribution of cumulative collision times. The latter is shown to be sensitive enough to detect the subtle increase of fluctuations associated with collisions between multiple lucky droplets. The superdroplet algorithm incorporates fluctuations in two distinct ways: through the random spatial distribution of superdroplets and through the Monte Carlo collision algorithm involved. Using specifically designed numerical experiments, we show that both on their own give an accurate representation of fluctuations. We conclude that the superdroplet algorithm can faithfully represent fluctuations in the coagulation of droplets driven by gravity.

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Kamal Kant Chandrakar, Hugh Morrison, Wojciech W. Grabowski, and George H. Bryan

Abstract

Advanced microphysics schemes (such as Eulerian bin and Lagrangian superdroplet) are becoming standard tools for cloud physics research and parameterization development. This study compares a double-moment bin scheme and a Lagrangian superdroplet scheme via large-eddy simulations of nonprecipitating and precipitating cumulus congestus clouds. Cloud water mixing ratio in the bin simulations is reduced compared to the Lagrangian simulations in the upper part of the cloud, likely from numerical diffusion, which is absent in the Lagrangian approach. Greater diffusion in the bin simulations is compensated by more secondary droplet activation (activation above cloud base), leading to similar or somewhat higher droplet number concentrations and smaller mean droplet radius than the Lagrangian simulations for the nonprecipitating case. The bin scheme also produces a significantly larger standard deviation of droplet radius than the superdroplet method, likely due to diffusion associated with the vertical advection of bin variables. However, the spectral width in the bin simulations is insensitive to the grid spacing between 50 and 100 m, suggesting other mechanisms may be compensating for diffusion as the grid spacing is modified. For the precipitating case, larger spectral width in the bin simulations initiates rain earlier and enhances rain development in a positive feedback loop. However, with time, rain formation in the superdroplet simulations catches up to the bin simulations. Offline calculations using the same drop size distributions in both schemes show that the different numerical methods for treating collision–coalescence also contribute to differences in rain formation. The stochastic collision–coalescence in the superdroplet method introduces more variability in drop growth for a given rain mixing ratio.

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