Search Results

You are looking at 11 - 20 of 31 items for

  • Author or Editor: Lloyd J. Shapiro x
  • Refine by Access: All Content x
Clear All Modify Search
Lloyd J. Shapiro

Abstract

A triggering mechanism is presented for the transformation of a wave in the easterlies to an intensifying tropical depression. Thermodynamic processes appear to be of secondary importance at this early stage of tropical storm formation. A development criterion is presented that measures the importance of nonlinear vorticity advection for the dynamics of the wave disturbance. If the contributions of the nonlinearities become significant then formation of an intensifying depression is hypothesized. The hypothesis allows one to predict the tune and place of tropical.storm development. Both climatology and the 1975 hurricane season are analyzed in order to test the theory for Atlantic easterly waves. The development criterion is found to have predictive ability in anticipating tropical storms during August and September 1975, several days prior to development.

Full access
Lloyd J. Shapiro

Abstract

Multilevel, multinested analyses of Hurricane Gloria of 1985 are the most comprehensive kinematic dataset yet developed for a single hurricane. A piecewise inversion technique is used with these analyses and the nonlinear balance equation to deduce the three-dimensional distribution of potential vorticity (PV) that contributed to the deep-layer mean (DLM) flow that steered Gloria toward the northwest. The background state is taken to be the azimuthally averaged winds in balance with a geopotential distribution on an f plane. Advantage is taken of the near-linearity of the weak asymmetries near the hurricane's core and of PV in the environment. Thus, ad hoc aspects of the linearization required by other investigators are effectively eliminated. Removal of the hurricane vortex and the use of a climatological mean background state are avoided as well. The insensitivity of the results to the imposed lateral boundary conditions is also demonstrated.

Wind anomalies attributable to pieces of anomalous PV restricted to cylinders of different radii centered on the hurricane are evaluated. The DLM wind that steered Gloria to the northwest is primarily attributable to PV anomalies confined within a cylinder of radius 1000 km and levels 500 mb and above, including positive anomalies associated with a cold low over Cuba. The vector difference between the hurricane's observed motion and the DLM wind at Gloria's center attributable to these PV anomalies is 1.0 m s−1, explaining more than five-sixths of the hurricane's 6.2 m s−1 motion. Implications for measurements required to establish short-term changes of the environmental steering flow are considered. Difficulties in the interpretation of results are discussed for PV anomalies that are confined to noncircular regions; the implication for other studies is considered as well.

Full access
Lloyd J. Shapiro

Abstract

The role of potential vorticity (PV) asymmetries in the evolution of a tropical cyclone is investigated using a three-layer model that includes boundary layer friction, surface moisture fluxes, and a convergence-based convective parameterization. In a benchmark experiment, a symmetric vortex is first spun up on an f plane for 24 h. The symmetric vortex has a realistic structure, including a local PV maximum inside its radius of maximum wind (RMW). A weak azimuthal-wavenumber 2 PV asymmetry confined to the lower two layers of the model is then added to the vortex near the RMW. After an additional 2 h (for a total 26-h simulation), the asymmetric PV anomaly produces changes in the symmetric vortex that have significant differences from those in dry experiments with the present model or previous barotropic studies. A diagnosis of the contributions to changes in the symmetric wind tendency due to the asymmetry confirm the dominance of horizontal eddy fluxes at early times. The barotropic eddy kick provided by the anomaly lasts ∼2 h, which is the damping timescale for the disturbance.

Additional experiments with an imposed isolated double-PV anomaly are made. Contrary to expectation from the dry experiments or barotropic studies, based on arguments involving “wave activity,” moving the anomaly closer to the center of the vortex or farther out does not change the overall evolution of the symmetric vortex. The physical mechanism responsible for the differences between the barotropic studies and those including moist physics as well as for the robustness of the response is established using a budget for the asymmetric vorticity. It is shown that the interactions between the asymmetries and the symmetric hurricane vortex at early times depend on realistic features of the model hurricane and not on interactions between the asymmetries and the boundary layer, which possibly depend on the convective parameterization. In particular, the changes in the symmetric wind tendency due to the asymmetry can be most simply explained by a combination of horizontal advection and damping of wave activity. In conjunction with horizontal advection and damping, the reversal of the radial vorticity gradient associated with the local PV maximum constrains the asymmetries to reduce the symmetric vorticity near the RMW. The location of the PV maximum controls the response to the extent that moving the PV anomaly radially inward or outward has no qualitative effect on the results. The longer-term evolution of the vortex is more problematic and may depend on the convective parameterization used.

Full access
Lloyd J. Shapiro and Charles J. Neumann

Abstract

Statistical models for the prediction of tropical cyclone motion traditionally have been formulated in a coordinate system oriented with respect to zonal and meridional directions. An investigation is made here into the forecast error reducing potential of a grid system reoriented with respect to initial storm heading. The developmental data comprise Atlantic forecast situations from 1965 through 1980 on all storms initially north of about 25°N. Reorientation of the coordinate system reduces the total variance in 24 h storm motion by 40%, projects most of the motion onto one (along-track) component of displacement, and makes the components nearly independent of each other. For 48 and 72 h displacements, however, these advantageous effects are substantially diminished or eliminated.

Synoptic predictors derived from current deep-layer mean heights on a grid of 1700 km radius are used to forecast storm displacements. For the developmental data, grid reorientation lowers the 24 h forecast error by 13%, and reduces the slow speed bias by a factor of 2/4. For 24 h forecasts the skill in the prediction of cross-track motion is small. Empirical Orthogonal Function and Principal Estimator Patterns provide insight into the role of reorientation in the reduction of forecast error, and the position of grid-point height predictors selected by a screening technique.

Full access
Lloyd J. Shapiro and J. Dominique Möller

Abstract

Hurricanes Bertha of 1996 and Erin of 2001 both intensified rapidly during part of their time over the North Atlantic. A piecewise potential vorticity (PV) inversion is applied to model output from GFDL hurricane model forecasts to determine the contributions of atmospheric features in the hurricanes’ environment to their intensification. The diagnosis indicates that Hurricane Bertha’s rapid intensification was directly augmented by an upper-level trough to the north. The significant positive impact of the trough provides quantitative confirmation of the inference of other authors. By contrast environmental interactions associated with troughs to the east and west of Hurricane Erin did not contribute directly to its rapid intensification. The implication of this result is that factors other than the troughs, including sea surface temperature, were sufficient to effect Hurricane Erin’s strengthening. Enhanced upper-level outflow concentrated northeast of the hurricane’s center that was associated with upper-level PV features to the north of Erin, including those ahead of the long-wave trough to its west, could have had some indirect contribution to its intensification. The present authors’ previous piecewise inversion applied to a model forecast of Hurricane Opal of 1995 indicated that an approaching upper-level trough did not significantly contribute to the hurricane’s lower-tropospheric intensification. The conclusions of this paper demonstrate that this result is neither an exception nor the rule.

Full access
J. Dominique Möller and Lloyd J. Shapiro

Abstract

Stationary and propagating asymmetric features of atmospheric or oceanic origin near a hurricane are known to have an impact on its evolution. Although theoretical and observational studies have investigated the influence of such features on hurricane intensification, the degree to which either environmental or near-core region asymmetries of heating, friction, or potential vorticity (PV), in contrast to symmetric processes, weaken or intensify a hurricane has not been established. The present study uses the symmetric balanced model formulation of Eliassen and its extension to asymmetric balance (AB) to evaluate the impact of heating and friction, as well as eddy fluxes, on the intensification of Hurricane Opal of 1995 in a Geophysical Fluid Dynamics Laboratory (GFDL) model forecast. The diagnostics are made in cylindrical coordinates, with the symmetric vortex as the basic state and asymmetries as the environment. The application of AB, which explicitly includes the effects of asymmetric heating and friction, uses PV inversion to isolate the balanced asymmetric wind and height fields associated with the asymmetric PV anomaly.

Work by Molinari and coworkers has evaluated the contributions of eddy heat and momentum fluxes associated with environmental features to the intensification of tropical storms. Their studies give some insights into the asymmetric influences on the symmetric secondary circulation and thus the evolution of the symmetric cyclone. Due to data limitations, however, they were not able to evaluate the contributions due to potentially important convective forcing. The GFDL model output includes convective heating and so allows the explicit evaluation of its effects. Persing et al. evaluated symmetric and asymmetric contributions to the intensification of Hurricane Opal of 1995 in a GFDL forecast. Their study diagnosed the various mean and eddy forcings in the tangential momentum budget, and (following the present study) calculated the balanced (Eliassen) response to model-derived eddy vorticity fluxes. The present study diagnoses the same GFDL model forecast as used by Persing et al. to evaluate the contribution of eddy fluxes of heat and momentum, and asymmetric as well as symmetric heating and friction to the symmetric secondary circulation. The evaluation of the balanced contributions to Opal's evolution requires a modification of the symmetric vortex structure. The modification is accomplished by stabilizing the vortex in as local a region as possible.

Results of the present study indicate that the symmetric tangential wind acceleration in the inner core of Hurricane Opal due to symmetric heating and friction is much greater than that from asymmetric eddy forcing. At the time of the analysis, during a period of rapid intensification, eddy forcing made a small contribution to Opal's lower-tropospheric near-core spinup. The diagnosis shows that the induced balanced symmetric secondary circulation can make a substantial contribution to the tangential momentum budget and should therefore be included in order to obtain a complete depiction of the factors responsible for the evolution of the vortex. The results imply that an unbalanced secondary circulation in the eyewall region counteracts the symmetric heating, thereby reducing its effective contribution to Opal's intensification by about one-half, and that gradient unbalanced regions of the vortex induce an unbalanced secondary circulation that counteracts effective momentum sinks, thereby intensifying the vortex in those regions. Moreover, asymmetric heating and friction tend to accelerate the inner core of the hurricane, opposing the deceleration induced by the asymmetric PV. The diagnostics also imply that only a fraction of the asymmetric heating and friction contributes effectively to the response. Implications of the results for the influence of an upper-level trough on Opal's intensification are discussed.

Full access
J. Dominique Möller and Lloyd J. Shapiro

Abstract

While previous idealized studies have demonstrated the importance of asymmetric atmospheric features in the intensification of a symmetric tropical cyclone vortex, the role of convectively generated asymmetries in creating changes in the azimuthally averaged cyclone is not well understood. In the present study the full-physics nonhydrostatic fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) is used to evaluate the influence of such asymmetries. Rather than adding winds and temperatures in balance with a specified potential vorticity (PV) asymmetry, or temperature perturbations themselves, to a symmetric vortex as in previous studies, a diabatic heating asymmetry is imposed on a spunup model hurricane. The impact of short-duration eyewall-scale monochromatic azimuthal wavenumber diabatic heating on the short- and long-term evolution of the azimuthally averaged vortex is evaluated, and a tangential wind budget is made to determine the mechanisms responsible for the short-term impact.

It is found that the small eddy kick created by the additional diabatic heating asymmetry leads to a substantially amplified long-term change in the azimuthally averaged vortex, with episodes of strong relative weakening and strengthening following at irregular intervals. This behavior is diabatically controlled. It is also found that the symmetric secondary circulation can be active in creating short-term changes in the vortex, and is not simply a passive response as in previous studies with dry physics. A central conclusion of the study is that the structure of the spunup hurricane vortex, in particular preexisting asymmetric features, can have a substantial influence on the character of the response to an additional diabatic heating asymmetry. The results also imply that a small change in the factors that control convective activity will have a substantial lasting consequence for the intensification of a hurricane.

Full access
Lloyd J. Shapiro and J. Dominique Möller

Abstract

Although Hurricane Opal of 1995 is one of the most intensely studied hurricanes ever, the cause of the hurricane's rapid intensification over the Gulf of Mexico is still a matter of controversy. While some authors have concluded that an approaching upper-level atmospheric trough had a significant impact on intensification, others have inferred only a small impact of the trough on the hurricane's strengthening. A recent study by the present authors diagnosed a Geophysical Fluid Dynamics Laboratory (GFDL) model forecast and found that eddy fluxes made only a small contribution to the lower-tropospheric evolution of the model hurricane vortex near the core. Thus, at face value, this previous study supported the conclusion that the upper-level trough was not important to the intensification of Opal. As noted in that study, however, in order to isolate the contribution of the trough by itself, the technique of piecewise potential vorticity (PV) inversion is required. The present study is the first to use this method in a diagnostic framework to determine the asymmetric features that contribute to tropical cyclone intensification.

The present study uses the same GFDL hurricane model forecast as in the previous study to diagnose the balanced contribution of various pieces of the asymmetric PV anomaly to the intensification of the model Opal vortex. Though the upper-level trough is an outer-environmental feature, its influence is found to extend into Opal's inner-core region. The eddies associated with the trough induce an upper-level inner-core acceleration. An estimate of the impact of convective feedback on the influence of the upper-level trough on Opal's evolution is made. The results elucidate and modify the conclusions of other authors. There is no indication from the present diagnosis that the upper-level trough was a significant contributor to Opal's lower-tropospheric intensification.

Full access
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.

Full access
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.

Full access