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Stephan Rasp, Tobias Selz, and George C. Craig

Abstract

Air parcel ascent in midlatitude cyclones driven by latent heat release has been investigated using convection-permitting simulations together with an online trajectory calculation scheme. Three cyclones were simulated to represent different ascent regimes: one continental summer case, which developed strong convection organized along a cold front; one marine winter case representing a slantwise ascending warm conveyor belt; and one autumn case, which contains both ascent types as well as mesoscale convective systems. Distributions of ascent times differ significantly in mean and shape between the convective summertime case and the synoptic wintertime case, with the mean ascent time being one order of magnitude larger for the latter. For the autumn case the distribution is a superposition of both ascent types, which could be separated spatially and temporally in the simulation. In the slowly ascending airstreams a significant portion of the parcels still experienced short phases of convective ascent. These are linked to line convection in the boundary layer for the wintertime case and an elevated conditionally unstable layer in the autumn case. Potential vorticity (PV) modification during ascent has also been investigated. Despite the different ascent characteristics it was found that net PV change between inflow and outflow levels is very close to zero in all cases. The spread of individual PV values, however, is increased after the ascent. This effect is more pronounced for convective trajectories.

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Brenda G. Cohen and George C. Craig

Abstract

The theoretical predictions derived in Part I of this study for the equilibrium fluctuations of an idealized ensemble of noninteracting, pointlike cumulus clouds are tested against three-dimensional cloud resolving model (CRM) simulations of radiative–convective equilibrium. Simulations with different radiative cooling rates are used to give a range of cloud densities, while imposed vertical wind shear of different strengths is used to produce different degrees of convective organization. The distribution of mass flux of individual clouds is found to be exponential in all simulations, in agreement with the theory. The distribution of total mass flux over a finite region also agrees well (to within around 10%) with the theoretical prediction for all simulations, but only after a correction to the modeled variance to take account of the finite size of clouds has been made. In the absence of imposed vertical wind shear, some spatial clustering of convective cells is observed at lower forcings (−2 and −4 K day−1) on a scale of 10–20 km, while at higher forcings (−8, −12, and −16 K day−1), there is a tendency toward spatial regularity on the same scale. These localized cloud interactions, however, appear to have little effect on the magnitude of the mass flux variability. Surprisingly, the convective organization obtained in the simulations with vertical wind shear has only a small effect on the mass flux statistics, even though it shows clearly in the location of the clouds.

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George C. Craig and Brenda G. Cohen

Abstract

To provide a theoretical basis for stochastic parameterization of cumulus convection, the equilibrium fluctuations of a field of cumulus clouds under homogeneous large-scale forcing are derived statistically, using the Gibbs canonical ensemble from statistical mechanics. In the limit of noninteracting convective cells, the statistics of these convective fluctuations can be written in terms of the large-scale, externally constrained properties of the system. Using this framework, the probability density function of individual cloud mass fluxes is shown to be exponential. An analytical expression for the distribution function of total mass flux over a region of given size is also derived, and the variance of this distribution is found to be inversely related to the mean number of clouds in the ensemble. In a companion paper, these theoretical predictions are tested against cloud resolving model data.

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Adrian M. Tompkins and George C. Craig

Abstract

The response of convection to changing sea surface temperature (SST) in the absence of large-scale flow is examined, using a three-dimensional cloud resolving model. The model includes a five-category bulk microphysical scheme representing snow, ice, graupel, rain, and cloud amounts in addition to an interactive radiation scheme for the shortwave and infrared. Long integrations are made to achieve a radiative–convective equilibrium state for SSTs of 298, 300, and 302 K, for which cloud and convection statistics are analyzed.

The main conclusion of the paper is that, despite significant temperature sensitivities in many of the conversion terms between bulk water categories, convection is very insensitive to changing SST in the absence of large-scale flow. This is a result of the moist adiabatic temperature profile that the tropical atmosphere is constrained to take. A parcel of air rising through a deep convective cloud experiences approximately the same range of temperatures but at higher altitudes as SST increases. Thus the vertical profiles of cloud fraction and other cloud-related statistics are simply shifted in height, but not changed in overall magnitude.

The small changes in cloud properties that do occur lead to a small reduction in cloud fraction as SST increases. This appears to be due to an increase in graupel amounts with respect to snow, giving smaller cloud fractions since graupel has a higher fall velocity. The radiative effects of the changes in atmospheric properties are examined and it is found that the model atmosphere exhibits no supergreenhouse effect since atmospheric relative humidity is not altered significantly by the SST changes. The water vapor feedback effect is largely canceled by the change in temperature. Clouds have a negligibly small, but highly nonlinear, feedback in the model climate, in the absence of large-scale flow.

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George C. Craig and Han-Ru Cho

Abstract

The linear stability of two atmospheric flows is examined, with basic-state data taken from environments where comma clouds were observed to form. The basic states each feature a baroclinic zone associated with an upper-level jet, with conditional instability on the north side. The semigeostrophic approximation is used, along with a simple parameterization for cumulus heating, and the eigenvalue problem is solved using a Chebyshev spectral method. The instabilities can be regarded as resulting from the interaction of potential-vorticity anomalies from three sources: advection along isentropic surfaces of the basic-state potential-vorticity (PV) gradient. advection of the surface potential temperature gradient (which is equivalent to a PV gradient in a thin layer at the surface), and potential vorticity generated by release of latent heat.

It is found that for the comma clouds the instability is a baroclinic interaction of upper- and lower-level PV anomalies. However, heating is an important source of potential vorticity in these modes, and substantially influences their structure. This is reflected in a tendency for the surface depression to be confined to the heating region on the cold-air side of the jet, particularly in one of the cases where the surface temperature gradient was very weak. It also results in a shorter wavelength due to a reduced vertical scale as the midtropospheric PV anomaly associated with the upper part of the heating region becomes stronger than the anomaly produced at the PV gradient at the tropopause.

The solutions am also compared with observations of the systems early in their development. For both cases the confined low-level structure associated with heating is found to match the observed cyclogenesis closely in both position and extent. The predicted wavelengths and phase speeds are also consistent with observations, although precise comparison is difficult with the available data.

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George C. Craig and Han-Ru Cho

Abstract

Observational studies show that polar air stream cyclones form preferentially to the north of the polar front in regions of high vorticity and low static stability, although the baroclinicity may be stronger elsewhere. This phenomenon is investigated by considering a semigeostrophic linear stability analysis of a constant potential vorticity zonal jet in the presence of parameterized cumulus heating in the cold air mass. Three types of unstable modes are found for different amounts of heating. With relatively small heating rates, the usual baroclinic instability occurs, with the disturbance centered on the jet axis. With moderate heating, the fastest growing mode is again a mainly baroclinic system, but with significant amplitude only in the region of heating on the cold-air side of the jet. Finally, for sufficiently large heating rates, a small-scale disturbance, which is driven primarily by diabatic processes, forms in the cold air mass. There is a continuous transition between the three types of instability as the heating is varied. The short wavelength and meridionally confined structure of the second type of mode are characteristic of observed comma clouds. Sensitivity tests show that while it is necessary to have the release of latent heat confined to a part of the domain in order to produce a localized instability, confined modes only appear for physically reasonable parameter values in the high-vorticity, low-stability environment of the cyclonic shear region of the jet. It appears that this is due primarily to the effects of the reduced vertical stability in enhancing the feedback between convective heating and low-level convergence.

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Tobias Selz, Lucas Fischer, and George C. Craig

Abstract

The spatial scale dependence of midlatitude water vapor variability in the high-resolution limited-area model COSMO is evaluated using diagnostics of scaling behavior. Past analysis of airborne lidar measurements showed that structure function scaling exponents depend on the corresponding airmass characteristics, and that a classification of the troposphere into convective and nonconvective layers led to significantly different power-law behaviors for each of these two regimes. In particular, scaling properties in the convective air mass were characterized by rough and highly intermittent data series, whereas the nonconvective regime was dominated by smoother structures with weaker small-scale variability. This study finds similar results in a model simulation with an even more pronounced distinction between the two air masses. Quantitative scaling diagnostics agree well with measurements in the nonconvective air mass, whereas in the convective air mass the simulation shows a much higher intermittency. Sensitivity analyses were performed using the model data to assess the impact of limitations of the observational dataset, which indicate that analyses of lidar data most likely underestimated the intermittency in convective air masses due to the small samples from single flight tracks, which led to a bias when data with poor fits were rejected. Though the quantitative estimation of intermittency remains uncertain for convective air masses, the ability of the model to capture the dominant weather regime dependence of water vapor scaling properties is encouraging.

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George C. Craig and Suzanne L. Gray

Abstract

Examination of conditional instability of the second kind (CISK) and wind-induced surface heat exchange (WISHE), two proposed mechanisms for tropical cyclone and polar low intensification, suggests that the sensitivity of the intensification rate of these disturbances to surface properties, such as surface friction and moisture supply, will be different for the two mechanisms. These sensitivities were examined by perturbing the surface characteristics in a numerical model with explicit convection. The intensification rate was found to have a strong positive dependence on the heat and moisture transfer coefficients, while remaining largely insensitive to the frictional drag coefficient. CISK does not predict the observed dependence of vortex intensification rate on the heat and moisture transfer coefficients, nor the insensitivity to the frictional drag coefficient since it anticipates that intensification rate is controlled by frictional convergence in the boundary layer. Since neither conditional instability nor boundary moisture content showed any significant sensitivity to the transfer coefficients, this is true of CISK using both the convective closures of Ooyama and of Charney and Eliassen. In comparison, the WISHE intensification mechanism does predict the observed increase in intensification rate with heat and moisture transfer coefficients, while not anticipating a direct influence from surface friction.

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Julia M. Windmiller and George C. Craig

Abstract

Self-aggregation in numerical simulations of tropical convection is described by an upscale growth and intensification of dry and moist regions. Previous work has focused on determining the relevant mechanism that induces moist regions to get moister and dry regions to get drier. Though different mechanisms have been identified, the spatial evolution of self-aggregation is remarkably universal. The first part of this study shows that different mechanisms can lead to a similar evolution of self-aggregation, if self-aggregation is described by a phase separation of moist and dry regions, through a process called coarsening. Though it was previously introduced based on a convection–humidity feedback, coarsening, importantly, is not tied to a specific feedback process but only requires an intensification of local humidity perturbations. Based on different feedback loops, three simple models of the evolution of the humidity field are introduced, all of which lead to coarsening. In each model, diffusive transport of humidity is assumed, which approximates a humidity increase due to convection, within a finite region around convective cores. In the second part, predictions made by coarsening are compared with atmospheric model simulations. Analyzing a set of radiative–convective equilibrium simulations shows that coarsening correctly predicts the upscale growth of the moist and dry regions in the early stages of self-aggregation. In addition, coarsening can explain why self-aggregation is not observed for small domains and why the shape of the final moist region changes with the shape of the domain.

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Tobias Selz, Lotte Bierdel, and George C. Craig

Abstract

Research on the mesoscale kinetic energy spectrum over the past few decades has focused on finding a dynamical mechanism that gives rise to a universal spectral slope. Here we investigate the variability of the spectrum using 3 years of kilometer-resolution analyses from COSMO configured for Germany (COSMO-DE). It is shown that the mesoscale kinetic energy spectrum is highly variable in time but that a minimum in variability is found on scales around 100 km. The high variability found on the small-scale end of the spectrum (around 10 km) is positively correlated with the precipitation rate where convection is a strong source of variance. On the other hand, variability on the large-scale end (around 1000 km) is correlated with the potential vorticity, as expected for geostrophically balanced flows. Accordingly, precipitation at small scales is more highly correlated with divergent kinetic energy, and potential vorticity at large scales is more highly correlated with rotational kinetic energy. The presented findings suggest that the spectral slope and amplitude on the mesoscale range are governed by an ever-changing combination of the upscale and downscale impacts of these large- and small-scale dynamical processes rather than by a universal, intrinsically mesoscale dynamical mechanism.

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