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Lloyd J. Shapiro

Abstract

Hurricane records for 1899 through 1978 are used to determine the numbers of hurricanes during the period August through October of each year that were present in the Atlantic. The Atlantic basin is subdivided into four geographic regions: the Central Atlantic, East Coast, Gulf of Mexico and Caribbean. An empirical orthogonal function (EOF) analysis is made of the time series of hurricane occurrence in each region to derive the dominant uncorrelated modes of interannual variability of seasonal hurricane incidence. The first EOF mode, accounting for 68% of the variance, represents the overall activity of the hurricane season. The second mode, accounting for 16% of the variance, represents the shift of hurricane incidence between the Gulf plus Caribbean, and the East Coast regions.

A coherency spectrum between the time variations of the first and second modes indicates a significant coherence at periods of about 2.5 and 4.5 years. The coherence at 2.5 years corresponds to the quasi-biennial oscillation (QBO). The results are related to the QBO in monthly hurricane numbers and in the strength and position of the North Atlantic subtropical high found by Angell et al. (1969). It is found that the maximum in East Coast hurricane incidence occurs at the phase of the QBO when the subtropical high is at its farthest northeastern displacement. The relation of the coherence at 4.5 years to the QBO is discussed.

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Lloyd J. Shapiro

Abstract

Correlations are computed between interannual fluctuations of hurricane incidence in the Atlantic basin and large-scale patterns of seasonally-averaged sea-level pressure (SLP; 1899–1978), sea-surface temperature (SST; 1899–1967), and 500 mb heights (Z500; 1946–1978). Dominant modes of interannual variability in average August–September–October (ASO) hurricane incidence are used as measures of overall activity and shifts in activity from region to region. These uncorrelated modes are derived using an empirical orthogonal function (EOF) analysis, as described in Shapiro (1982). The hurricane modes are related to dominant modes of variability in seasonal SLP, SST and Z500, also derived using an EOF analysis. Correlations between the amplitudes of the EOF modes are tested for significance using a measure of artificial skill.

May–June–July (MJJ) large-scale SLP anomalies have predictive skill for ASO hurricane activity, significant at the 1.0% level. The correlation predicts about 17% of the variance in activity. Lower SLP precedes more active seasons.

Other significant correlations are found: High SST just west of Africa precedes more active seasons, but adds little predictive skill to that of SLP. Relationships between Z500 and hurricane track are consistent with steering concepts, and the results of previous investigators. Weaker westerlies are concurrent with more active seasons.

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Lloyd J. Shapiro

Abstract

Composite fields of large-scale variables derived from synoptic-scale wave disturbances observed during Phase III of the GARP Atlantic Tropical Experiment over Africa and the eastern Atlantic are used to determine the vorticity budget of the composite African wave. The velocity, vorticity and divergence fields used are “combined region” composites of the wave disturbances derived by Norquist et al. (1977).

The vorticity budget is made for all eight categories (phases) of the wave at the reference latitude (∼11°N) as well as the latitudes 4° to the north and south of the reference latitude. The large-scale fields are decomposed into a zonal mean and deviations from the zonal mean to separate contributions from the wave and the basic flow in which it is embedded. Cumulus mass fluxes (derived by R. Johnson) are determined from a thermodynamic budget and a spectral cloud model. The average vorticity in the clouds is determined from a simple one-dimensional single-cloud model using the given cumulus man fluxes. Since cumulus mass fluxes and vorticities are determined independently of the large-scale vorticity budget, the parameterized vorticity source due to cumulus is not forced to equal the apparent vorticity source derived from the large-scale balance.

It is found that the large-scale vorticity balance for the wave is linear, with the nonlinear horizontal advective terms approximately cancelling due to the presence of a quasi-nondivergent, single-propagating wave component. The linear waves are approximately advected by the horizontal wind at all levels above 850 mb, even to the south of the easterly jet where the mean zonal wind is small. The curvature term contributes significantly to the balance. The parameterized form of the vertical advection of vorticity due to cumulus accounts well for most features of the apparent vorticity source obtained from the law-scale budget when the vertical cumulus mass flux is specified only for deep clouds. The large apparent source ahead of the trough in the middle troposphere at 11°N is reflected in the parameterized form. Cumulus-scale twisting effects are not needed to explain the major part of the large-scale apparent vorticity source, except possibly near the tropopause.

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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.

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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.

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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.

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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.

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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.

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Lloyd J. Shapiro
and
James L. Franklin

Abstract

A set of nine synoptic-flow cases, incorporating Omega dropwindsonde observations for six tropical storms and hurricanes, is used to deduce the three-dimensional distribution of potential vorticity (PV) that contributed to the deep-layer mean (DLM) wind that steered the cyclones. A piecewise inversion technique, the same as that previously applied by Shapiro to Hurricane Gloria of 1985, is used to derive the DLM wind induced by pieces of anomalous PV restricted to cylinders of different radii centered on each cyclone. The cylinder of PV that induces a DLM wind that best matches the observed DLM wind near the center of each cyclone is evaluated.

It is found that the results can be loosely placed into two categories describing the spatial scale of the PV anomalies that influenced the cyclone’s motion. Four of the cases, including Hurricane Gloria, had “local” control, with a good match (to within ∼40%) between the observed DLM wind near the cyclone center and the DLM wind attributable to a cylinder of PV with a given radius ⩽1500 km. Further decomposition of the PV anomaly into upper (400 mb and above) and lower levels (500 mb and below) indicates the dominance of upper-level features in steering two of the cyclones (Hurricanes Gloria of 1985 and Andrew of 1992), while Hurricane Debby of 1982 was steered by more barotropic features. These results supplement those found in other studies.

Five of the cases, by contrast, had “large-scale” control, with no cylinder of radius ⩽2000 km having a good match between the induced and observed DLM wind. Hurricanes Emily of 1987 and 1993 fell into this category, as did Hurricane Josephine of 1984. Implications of the results for guiding in situ wind measurements to improve hurricane track forecasts are discussed.

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Lloyd J. Shapiro
and
James L. Franklin

Abstract

Potential vorticity (PV) analysts for Hurricane Gloria of 1985 are derived from nested objective wind analyses of Omega dropwindsonde and airborne Doppler radar data. The analyses resolve eyewall-scale features in the inner vortex core and embed analyses of these features within the larger-scale environment. Since three-dimensional geopotential height fields required for evaluation of PV are not available in the core, they are derived using the balance equation. In the process of deriving the heights, the degree of gradient balance is evaluated. The 500-mb tangential winds in the core, averaged azimuthally on the four cardinal points, are close to gradient balance outside the radius of maximum wind.

The resulting depiction of PV is the first presented for a real hurricane. Due to data deficiencies immediately outside the Doppler region, as well as inside the eye, smoothing of the wind data using a filter with a minimum 25-km spatial scale is required to derive a balanced geopotential height distribution consistent with a statically stable vortex. The large-scale PV distribution evidences asymmetries in the middle and upper troposphere that appear to be associated with Gloria's translation to the northwest. Eyewall-scale PV in the core and PY of the azimuthally averaged vortex are also presented.

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