Wayne H. Schubert

Interaction of a Cumulus Cloud Ensemble with the Large-Scale Environment, Part I

Abstract A theory of the interaction of a cumulus cloud ensemble with the large-scale environment is developed. In this theory, the large-scale environment is divided into the subcloud mixed layer and the region above. The time changes of the environment are governed by the heat and moisture budget equations for the subcloud mixed layer and for the region above, and by a prognostic equation for the depth of the mixed layer. In the environment above the mixed layer, the cumulus convection affects the temperature and moisture fields through cumulus-induced subsidence and detrainment of saturated air containing liquid water which evaporates in the environment. In the subcloud mixed layer, the cumulus convection does not act directly on the temperature and moisture fields, but it affects the depth of the mixed layer through cumulus-induced subsidence. Under these conditions the problem of parameterization of cumulus convection reduces to the determination of the vertical distributions of the total vertical ma...

Trimodal characteristics of tropical convection

It has long been known that trade wind cumulus and deep cumulonimbus represent primary components of the broad spectrum of cumulus clouds in the Tropics, which has led to the concept of a bimodal distribution of tropical clouds. However, recent analyses of shipboard radar data from Tropical Ocean Global Atmosphere Coupled Ocean‐Atmosphere Response Experiment (COARE) provide evidence of abundant populations of a third cloud type, cumulus congestus. Congestus clouds constitute over half the precipitating convective clouds in COARE and contribute over one-quarter of the total convective rainfall. Global Atmospheric Research Program Atlantic Tropical Experiment studies reveal a similar midlevel peak in the distribution of radar-echo tops. These findings lead to the conclusion that shallow cumulus, congestus,and cumulonimbus are all prominent tropical cumulus cloud types. They are associated with trimodal distributions of divergence, cloud detrainment, and fractional cloudiness in the Tropics. The peaks in the distributions of radar-echo tops for these three cloud types are in close proximity to prominent stable layers that exist over the Pacific warm pool and the tropical eastern Atlantic: near 2 km (the trade stable layer), ;5 km (near 08C), and ;15‐16 km (the tropopause). These stable layers are inferred to inhibit cloud growth and promote cloud detrainment. The 08C stable layer can produce detrainment from cumulonimbi (attendant shelf clouds) and help retard the growth of precipitation-laden and strongly entraining congestus clouds. Moreover, restriction of growth of congestus clouds to just above the 08C level limits further enhancement of cloud buoyancy through glaciation. The three cloud types are found to vary significantly during COARE on the timescale of the 30‐60-day intraseasonal oscillation. The specific roles of clouds of the congestus variety in the general circulation are not yet clear, but some (the shallower ones) contribute to moistening and preconditioning the atmosphere for deep convection; others (the deeper ones) contribute an important fraction of the total tropical rainfall, and both likely produce many midlevel clouds, thereby modulating the radiative heating of the tropical atmosphere.

Polygonal Eyewalls, Asymmetric Eye Contraction, and Potential Vorticity Mixing in Hurricanes

Hurricane eyewalls are often observed to be nearly circular structures, but they are occasionally observed to take on distinctly polygonal shapes. The shapes range from triangles to hexagons and, while they are often incomplete, straight line segments can be identified. Other observations implicate the existence of intense mesovortices within or near the eye region. Is there a relation between polygonal eyewalls and hurricane mesovortices? Are these phenomena just curiosities of the hurricane’s inner-core circulation, or are they snapshots of an intrinsic mixing process within or near the eye that serves to determine the circulation and thermal structure of the eye? As a first step toward understanding the asymmetric vorticity dynamics of the hurricane’s eye and eyewall region, these issues are examined within the framework of an unforced barotropic nondivergent model. Polygonal eyewalls are shown to form as a result of barotropic instability near the radius of maximum winds. After reviewing linear theory, simulations with a high-resolution pseudospectral numerical model are presented to follow the instabilities into their nonlinear regime. When the instabilities grow to finite amplitude, the vorticity of the eyewall region pools into discrete areas, creating the appearance of polygonal eyewalls. The circulations associated with these pools of vorticity suggest a connection to hurricane mesovortices. At later times the vorticity is ultimately rearranged into a nearly monopolar circular vortex. While the evolution of the finescale vorticity field is sensitive to the initial condition, the macroscopic end-states are found to be similar. In fact, the gross characteristics of the numerically simulated end-states are predicted analytically using a generalization of the minimum enstrophy hypothesis. In an effort to remove some of the weaknesses of the minimum enstrophy approach, a maximum entropy argument developed previously for rectilinear shear flows is extended to the vortex problem, and end-state solutions in the limiting case of tertiary mixing are obtained. Implications of these ideas for real hurricanes are discussed.

Inertial Stability and Tropical Cyclone Development

Abstract We consider the frictionless, axisymmetric, balanced flow occurring in a thermally forced vortex on an f-plane. Following Eliassen (1952) we derive the diagnostic equation for the forced secondary circulation. This equation contains the spatially varying coefficients A (static stability), B (baroclinity), C (inertial stability), and the thermal forcing Q. Assuming that A is a constant, B = 0, and that C and Q are piecewise constant functions of radius, we obtain analytical solutions for the forced secondary circulation. The solutions illustrate the following points. 1) For a given Q an increase in inertial stability leads to a decrease in the forced secondary circulation and a change in the radial distribution of local temperature change, with enhanced ∂θ/∂t; in the region of high inertial stability. 2) Lower tropospheric tangential wind accelerations are larger inside the radius of maximum wind, which leads to a collapse of the radius of maximum wind. 3) The fraction of Q which ends up as ∂θ/∂t;...

Hurricane Spiral Bands

Abstract The spiral bands that occur in tropical cyclones can be conveniently divided into two classes—outer bands and inner bands. Evidence is presented here that the outer bands form as the result of nonlinear effects during the breakdown of the intertropical convergence zone (ITCZ) through barotropic instability. In this process a zonal strip of high potential vorticity (the ITCZ shear zone or monsoon trough) begins to distort in a varicose fashion, with the potential vorticity (PV) becoming pooled in local regions that are connected by filaments of high PV. As the pooled regions become more axisymmetric, the filaments become thinner and begin to wrap around the PV centers. It is argued that inner bands form in a different manner. As a tropical cyclone intensifies due to latent heat release, the PV field becomes nearly circular with the highest values of PV in the cyclone center. The radial gradient of PV provides a state on which PV waves (the generalization of Rossby waves) can propagate. The nonline...

Mesovortices, Polygonal Flow Patterns, and Rapid Pressure Falls in Hurricane-Like Vortices

Abstract The present work considers the two-dimensional barotropic evolution of thin annular rings of enhanced vorticity embedded in nearly irrotational flow. Such initial conditions imitate the observed flows in intensifying hurricanes. Using a pseudospectral numerical model, it is found that these highly unstable annuli rapidly break down into a number of mesovortices. The mesovortices undergo merger processes with their neighbors and, depending on initial conditions, they can relax to a monopole or an asymmetric quasi-steady state. In the latter case, the mesovortices form a lattice rotating approximately as a solid body. The flows associated with such vorticity configurations consist of straight line segments that form a variety of persistent polygonal shapes. Associated with each mesovortex is a local pressure perturbation, or mesolow. The magnitudes of the pressure perturbations can be large when the magnitude of the vorticity in the initial annulus is large. In cases where the mesovortices merge to...

Nonlinear Response of Atmospheric Vortices to Heating by Organized Cumulus Convection

Abstract Using an axisymmetric primitive tropical cyclone model, we first illustrate the way in which nonlinear processes contribute to the development of an atmospheric vortex. These numerical experiment show that nonlinearities allow a given diabatic beat source to induce larger tangential wind (and kinetic energy) changes as the vortex develops and the inertial stability becomes large. In an attempt to gain a deeper theoretical understanding of this process, we consider the energy cycle in the balanced vortex equations of Eliassen. The temporal behavior of the total potential energy P is governed by dP/dt=H−C where H is the rate of generation of total potential energy by diabatic heating, and C is the rate of conversion to kinetic energy. We define a time-dependent system efficiency parameter as η¯(t)=C/H. Then, using the dynamical simplifications of balanced vortex theory, we express η¯(t) as a weighted average of a dynamic efficiency factor η(r, z, t). The dynamic efficiency factor is a measure of th...

Large-Scale Response of the Tropical Atmosphere to Transient Convection

Abstract We consider the problem of the linear response of a stratified, equatorial, β-plane model atmosphere to specified transient sources of heat and momentum. The method of solution involves transforms in all three spatial coordinates. A finite Sturm-Liouville transform is used in z, a Fourier transform in x, and a generalized Hermite transform in y. The resulting spectral equations can then be solved analytically for a specified forcing. Of particular interest is the case of a Gaussian-shaped heat source centered at latitude yo and with e-folding radius a. The heat source is transient and has time scale 1/α. Using the Parceval relation we compute how the forced energy is partitioned between Kelvin, mixed Rossby-gravity, Rossby and gravity modes as a function of a, yo, α. Model results using a heat source centered at 11°S with an e-folding radius of 750 km and a time scale of about a day indicate that many aspects of the summertime upper tropospheric circulation over South America can be explained by ...

Barotropic Aspects of ITCZ Breakdown

Abstract In satellite images the ITCZ (intertropical convergence zone) is sometimes observed to undulate and break down into a series of tropical disturbances. Tropical cyclones may later develop within these disturbances and move into higher latitudes allowing the ITCZ to reform. It has been proposed that ITCZ breakdown results from a convectively modified form of combined barotropic and baroclinic instability of the mean flow. An unstable mean flow can be produced by ITCZ convection in just a couple of days. In this sense, the ITCZ produces favorable conditions for its own instability and breakdown. In this study, a nonlinear shallow water model on the sphere is used to simulate barotropic aspects of ITCZ breakdown. In the shallow-water model, the ITCZ is simulated by a prescribed zonally elongated mass sink near the equator. The mass sink produces a cyclonic potential vorticity (PV) anomaly that has a reversed meridional PV gradient on its poleward side. According to the Ripa theorem, a flow that has a...

Rapid Development of the Tropical Cyclone Warm Core

This paper presents a simple theoretical argument to isolate the conditions under which a tropical cyclone can rapidly develop a warm-core thermal structure and subsequently approach a steady state. The theoretical argument is based on the balanced vortex model and, in particular, on the associated transverse circulation equation and the geopotential tendency equation. These second-order partial differential equations contain the diabatic forcing and three spatially varying coefficients: the static stability A, the baroclinity B, and the inertial stability C. Thus, the transverse circulation and the temperature tendency in a tropical vortex depend not only on the diabatic forcing but also on the spatial distributions of A, B, and C. Experience shows that the large radial variations of C are typically the most important effect. Under certain simplifying assumptions as to the vertical structure of the diabatic forcing and the spatial variability of A, B, and C, the transverse circulation equation and the geopotential tendency equation can be solved via separation of variables. The resultingradialstructureequationsretainthedynamicallyimportantradialvariationofCandcanbe solvedin terms of Green’s functions. These analytical solutions show that the vortex response to a delta function in the diabatic heating depends critically on whether the heating occurs in the low-inertial-stability region outside the radius of maximum wind or in the high-inertial-stability region inside the radius of maximum wind. This resultsuggeststhatrapidintensification isfavoredforstormsthathaveat leastsome oftheeyewallconvection inside the radius of maximum wind. The development of an eye partially removes diabatic heating from the high-inertial-stability region of the storm center; however, rapid intensification may continue if the eyewall heating continues to become more efficient. As the warm core matures and static stability increases over the inner core, conditions there become less favorable for deep upright convection and the storm tends to approach a steady state.