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Lloyd J. Shapiro
and
Dudley B. Chelton

Abstract

In a recent paper, Lanzante reviewed methods for estimating the skill and significance of screening regression models through the use of Monte Carlo simulations. The strategies reviewed have several limitations that were not specified by the author. Due to the influence of true model skill, the Monte Carlo method provides an upper bound on the expected artificial skill, not the expected artificial skill itself as assumed. Lanzante emphasizes the advantages of the use of independent (uncorrelated) predictors. However, the disadvantages of their use and the advantages of dependent predictors in a screening regression were not considered.

The review of the effects of serial correlation on estimates of skill is misleading. The assertion that the formulations developed by Davis and Chelton are erroneous is incorrect. Moreover, contrary to the implication of the review, the use of effective sample size in tests of model significance has practical utility in applications including the Monte Carlo method.

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Lloyd J. Shapiro
and
Stanley B. Goldenberg

Abstract

It has long been accepted that interannual fluctuations in sea surface temperature (SST) in the Atlantic are associated with fluctuations in seasonal Atlantic basin tropical cyclone frequency. To isolate the physical mechanism responsible for this relationship, a singular value decomposition (SVD) is used to establish the dominant covarying modes of tropospheric wind shear and SST as well as horizontal SST gradients. The dominant SVD mode of covarying vertical shear and SST gradients, which comprises equatorially confined near-zonal vertical wind shear fluctuations across the Atlantic basin, is highly correlated with both equatorial eastern Pacific SST anomalies (associated with El Niño) and West African Sahel rainfall. While this mode is strongly related to tropical storm, hurricanes, and major hurricane frequency in the Atlantic, it is not associated with any appreciable Atlantic SST signal.

By contrast, the second SVD mode of covarying vertical shear and horizontal SST gradient variability, which is effectively uncorrelated with the dominant mode, is associated with SST fluctuations concentrated in the main tropical cyclone development region between 10° and 20°N. This mode is significantly correlated with tropical storm and hurricane frequency but not with major hurricane frequency. Statistical tests confirm the robustness of the mode, and lag correlations and physical reasoning demonstrate that the SST anomalies are not due to the developing tropical cyclones themselves. Anomalies of SST and vertical shear during years where the mode has substantial amplitude confirm the resemblance of the individual fields to the modal structure, as well as the association of hurricane development with the warmer SSTs. Although SSTs are of secondary importance to vertical shear in modulating hurricane formation, explaining only ∼10% of the interannual variability in hurricane frequency over the ∼50% explained by vertical shear, the results support the conclusion that warmer SSTs directly enhance development. The lack of correlation with major hurricanes implies that the underlying SSTs are not a significant factor in the development of these stronger systems.

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Lloyd J. Shapiro
and
Katsuyuki V. Ooyama

Abstract

A barotropic, primitive equation (shallow water) model is used on the beta plane to investigate the influence of divergence, total relative angular momentum (RAM) and advective nonlinearities on the evolution of a hurricane-like vortex. The multinested numerical model is based on the spectral application of a finite element representation. The undisturbed fluid depth is taken to be 1 km. Scaling of the vorticity equation, in conjunction with a Bessel function spectral decomposition, indicates that divergence should have a very small effect on the hurricane motion. Simulations with an initially symmetric cyclonic vortex in a resting environment confirm this analysis, and contradict previous published studies on the effect of divergence in a barotropic model.

During a 120 h simulation the cyclonic vortex develops asymmetries that have an influence far from the initial circulation. The total RAM within a large circle centered on the vortex decreases with time, and then oscillates about zero. For circles with radii ≲ 1000 km, the total RAM approaches, but does not reach, zero. An angular momentum budget indicates that the horizontal angular momentum flux tends to counteract the net Coriolis torque on the vortex. If the total RAM of the initial symmetric vortex is zero, the weak far-field asymmetries are essentially eliminated. The motion of the vortex is not, however, related to the RAM in any simple way.

Within a few days the near-vortex asymmetries reach a near-steady state. The Asymmetric Absolute vorticity (AAV) is nearly uniform within ∼350 km of the vortex center. The homogenization of AAV, which occurs within the closed vortex gyre, is likely due to shearing by the symmetric wind, combined with removal of energy at the smallest scales. The homogenization effectively neutralizes the planetary beta effect, as well as the vorticity associated with an environmental wind.

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Lloyd J. Shapiro
and
Huch E. Willoughby

Abstract

Eliassen's (1951) diagnostic technique is used to calculate the secondary circulation induced by point sources of heat and momentum in balanced, hurricane-like vortices. Scale analysis reveals that such responses are independent of the horizontal scale of the vortex. Analytic solutions for the secondary circulation are readily obtained in idealized barotropic vortices, but numerical methods are required for more realistic barotropic and baroclinic vortices. For sources near the radius of maximum wind, the local, two-dimensional, streamfunction dipole response of Eliassen is modified by both the spatial variations of the vortex structure and the influences of boundary conditions.

The secondary flow advects mean-flow buoyancy and angular momentum and thus leads to a slow evolution of the vortex structure. In weak systems (maximum tangential wind <35 m s−1), the restraining influences of structure and boundaries lengthen the time scale of the vortex evolution. In stronger vortices, the horizontal scale of the response is smaller, the restraining influences are less important, and the evolution is faster. When the maximum wind exceeds 35 m s−1, recirculation of air within the vortex core tends to form an eye.

The most rapid temporal changes in tangential wind lie inside the eye, where the horizontal gradients of angular momentum are strongest. In most cases, the tangential wind increases most rapidly just inside the radius of maximum wind and decreases near the central axis of the vortex. This effect leads to contraction of the wind maximum as the vortex intensifies. The present results are compared with observations and other theoretical mutts.

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Lloyd J. Shapiro
and
Michael T. Montgomery

Abstract

A three-dimensional balance formulation for rapidly rotating vortices, such as hurricanes, is presented. The asymmetric balance (AB) theory represents a new mathematical framework for studying the slow evolution of rapidly rotating fluid systems. The AB theory is valid for large Rossby number; it makes no formal restriction on the magnitude of the divergence or vertical advection, which need not be small. The AB is an ordered expansion in the square of the ratio of orbital to inertial frequencies, the square of a local Rossby number. The approximation filters gravity and inertial waves from the system. Advantage is taken of the weak asymmetries near the vortex care as well as the tendency for low azimuthal wavenumber asymmetries to dominate. Linearization about a symmetric balanced vortex allows the three-dimensional asymmetric dynamics to be deduced properly. The AB formulation has a geopotential tendency equation with a three-dimensional elliptic operator. The AB system has a uniformly valid continuation to nonlinear quasigeostrophic theory in the environment. It includes the full inertial dynamics of the vortex core, and reduces to Eliassen's formulation for purely axi-symmetric flow. It has a full set of conservation laws on fluid parcels analogous to those for primitive equations, including conservation of potential temperature, potential vorticity, three-dimensional vorticity, and energy. A weakly nonlinear extension of the formulation in the near-vortex region is presented. Appropriate physical applications for the AB system, as well as its limitations, are discussed.

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Michael T. Montgomery
and
Lloyd J. Shapiro

Abstract

A generalized Charney–Stern theorem for rapidly rotating (large Rossby number) baroclinic vortices, such as hurricanes, is derived based on the asymmetric balance (AB) approximation. In the absence of dissipative processes, a symmetrically stable baroclinic vortex is shown to be exponentially stable to nonaxisymmetric perturbations if a generalized potential vorticity gradient on theta surfaces remains single signed throughout the vortex. The generalized potential vorticity gradient involves the sum of an interior potential vorticity gradient associated with the symmetric vortex and surface contributions associated with the vertical shear of the tangential wind. The AB stability formulation is then shown to yield Fjortoft's theorem as a corollary.

In the modem view of shear instabilities the theorems admit simple interpretation. The Charney–Stern theorem represents a necessary condition for the existence of counterpropagating Rossby waves associated with the radial potential vorticity gradient, while Fjortoft's theorem represents a necessary condition for these waves to phase lock and grow in strength. Potential application of these results as well as limitations of the slow-manifold approach are briefly discussed.

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Stanley B. Goldenberg
and
Lloyd J. Shapiro

Abstract

Physical mechanisms responsible for the contemporaneous association, shown in earlier studies, of North Atlantic basin major hurricane (MH) activity with western Sahelian monsoon rainfall and an equatorial eastern Pacific sea surface temperature index of El Niño are examined, using correlations with 200- and 700-mb level wind data for the period 1968–92. The use of partial correlations isolates some of the relationships associated with the various parameters.

The results support previous suggestions that the upper- and lower-level winds over the region in the basin between ∼10° and 20°N where most MHs begin developing are critical determinants of the MH activity in each hurricane season. In particular, interannual fluctuations in the winds that produce changes in the magnitude of vertical shear are one of the most important factors, with reduced shear being associated with increased activity and stronger shear with decreased activity. The results show that most of these critical wind fluctuations are explained by their relationship to the SST and rainfall fluctuations. Results confirm previous findings that positive (warm) eastern Pacific SST and negative (drought) Sahelian rainfall anomalies are associated with suppressed Atlantic basin tropical cyclone activity through an equatorially confined near-zonal circulation with upper-level westerlies and lower-level easterlies that act to increase the climatological westerly vertical shear in the main development region. SST and rainfall anomalies of the opposite sense are related to MH activity through a zonal circulation with upper-level easterly and lower-level westerly wind anomalies that act to cancel out some of the climatological westerly vertical shear. The results also show that changes in vertical shear to the north of the main development region are unrelated to, or possibly even out of phase with, changes in the development region, providing a possible physical explanation for the observations from recent studies of the out-of-phase relationship of interannual fluctuations in MH activity in the region poleward of ∼25°N with fluctuations in activity to the south.

The interannual variability of MH activity explained by Sahel rainfall is almost three times that explained by the eastern Pacific SSTs. It is demonstrated that a likely reason for this result is that the SST-associated vertical shears are more equatorially confined, so that the changes in shear in the main development region have a stronger association with the rainfall than with the SSTs.

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Lloyd J. Shapiro
and
Stanley B. Goldenberg

Abstract

Winds at low (near-surface) and 200-mb levels from National Hurricane Center objective analyses are used to elucidate the structure and dynamics of the tropical and subtropical intraseasonal oscillations for the North Atlantic/northeast Pacific regions, including over the continents, for the years 1980–1989. The intraseasonal oscillations are broken into three bands, with long (50–85 day), intermediate (30–55 day), and short (13–29 day) periods. Winter and summer seasons are analyzed separately. A complex empirical orthogonal function technique is used to derive the dominant modes of intraseasonal variability over the region, including their propagation characteristics. Statistically distinct modes of variability are found only during the winter and only for the long-period and short-period bands.

The dominant mode of coupled 200-mb low-level long-period variability during winter has a dipole structure. It has a substantial equivalent barotropic component in the subtropics, as well as a baroclinic structure consistent with quasigeostrophic midlatitude systems. Negative outgoing longwave radiation anomalies tend to be in phase with a low-level convergence-upper-level divergence couplet, which lies approximately one-quarter wavelength to the east of the cyclonic vorticity centers. The long-period oscillations during 1981–1988 are dominated by three events, with periods between about 60 and 70 days. There is a negative correlation, explaining about 50% of the variance, between the magnitude of the mode and an index of El Niño based on sea surface temperatures in the eastern equatorial Pacific.

The dominant modes of short-period variability during winter appear as zonally oriented wave trains similar to those found by previous investigators of global-scale fluctuations. Rotation of the modes of 200-mb variability effectively separates them into their propagating and standing components. Approximately one-half of the variance in the meridional wind near teleconnection centers of action is found in the eastward propagating component. The dominant mode of coupled 200-mb/iow-level variability propagates to the east, and has a vertical structure similar to that in the long-period band. It has a predominant period near 18 days.

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Lloyd J. Shapiro
and
Duane E. Stevens

Abstract

Dynamic budgets of an average synoptic-scale wave have been made by Stevens (1979) from GARP Atlantic Tropical Experiment Phase III B- and A/B-scale data composited by Thompson et al. (1979). In the present study the apparent sources of momentum and vorticity, computed from the large-scale budgets, are compared with parameterized sources from independently derived cumulus mass fluxes and one-dimensional steady-state cloud models. The cloud models include spectral and bulk, as well as single-cloud models. The cumulus mass fluxes are determined from a thermodynamic budget analysis of Johnson (1 978).

A simple single-cloud model is found to adequately account for the net effect of the cumulus transport and production of vorticity. The one-dimensional cloud models, however, do not account for the apparent momentum source in the upper troposphere. An evaluation is made of the sensitivity of the results to the assumed cloud-base vorticity and radiative heating rate. The limitations of the simple cloud models for the parameterization of convective effects in both the momentum and vorticity budgets are discussed.

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Steven K. Esbensen
,
Lloyd J. Shapiro
, and
Edward I. Tollerud

Abstract

A physical and mathematical framework for the mutually consistent parameterization of the effects of cumulus convection on the large-scale momentum and vorticity fields is proposed. The key to achieving consistency is the understanding that the vorticity dynamics of the clouds below the spatial resolution of a large-scale dynamical model may be neglected in the vorticity budget when the clouds are considered to be independent buoyant elements sharing a common large-scale environment This simplified approach is used to obtain a consistent pair of large-scale momentum and vorticity equations based on Ooyama's theory of cumulus parameterization. The results focus attention on the need to obtain a better understanding of the detrainment process and the pressure interactions between the clouds and their environment.

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