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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

Monthly averaged 30 and 50 mb zonal winds at Balboa are used to determine objectively the relationship of the quasi-biennial oscillation (QBO) to seasonal (August through October) Atlantic tropical storm activity during the years 1952–86. The largest correlations between storm activity and the 30 mb wind are found in June, which is 3 months before the center of the season. Extrapolation and direct calculation confirm a near in-phase relationship between tropical storm activity and the zonal wind at about 50 mb.

Zonal winds filtered to remove periods 1 yr are used to establish correlations between the QBO and tropical storm activity for 1955–83 that are essentially independent of the month considered. A correlation at 30 mb is established with a conservative estimate of true skill, from both in-phase and out-of-phase information, that explains 30% of the variance in storm activity. The skill is much greater than that estimated from seasonal classifications of the QBO. The statistics are resilient to removal of the effects of the El Niño cycle. When El Niño years am explicitly excluded, the true skill explains an estimated 32% of the variance. Low-latitude storms are even more strongly related to the QBO.

Physical mechanisms possibly responsible for the observed associations are discussed in light of these results. A mechanism for the observed correlations is suggested that emphasizes the difference between lower-tropospheric steering and the lower-stratospheric zonal wind. The relationships of the results, and suggested physical mechanism, to those of Gray are considered.

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Lloyd J. Shapiro

Abstract

Twice-daily analyses of low-level and 200-mb winds over the tropical Atlantic region, archived by the National Hurricane Center, are used to diagnose the structure of synoptic-scale disturbances in the 3–5 day period band. The large-scale disturbances, extracted by a complex empirical orthogonal function technique, are found to have a preferred shift at 200 mb relative to the low-level troughs of somewhat less than one-quarter cycle. The presentation concentrates on July 1975, during which a repeated series of strong disturbances propagated through the region. The relationship between these disturbances and systems in the eastern Pacific is discussed. An analysis of the vorticity propagation characteristics for the disturbances during the month indicates a very different balance from level to level. At the lower level, advection by the mean wind plays a major rate; at 200 mb, the meridional advection of mean vorticity is more inportant.

Rawinsonde data from several island stations are used to resolve the vertical structure of the disturbances. After adjustment for lower density aloft, the kinetic energy at the lower and upper levels is found to be almost equal. The systems propagate westward faster than the mean zonal wind at any level, with a zonal phase speed that is relatively constant with height. It is inferred that the disturbances most likely propagate as a coherent system due to vertical coupling by convection. Evidence is found that the influence of low-level waves on the evolution of 200-mb systems may be stronger than has been previously described.

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Lloyd J. Shapiro

Abstract

Monthly mean winds have been derived from 200 mb and Analysis of the Tropical Oceanic Lower Layer (ATOLL) winds over the southern North Atlantic, Caribbean, Gulf of Mexico and eastern Pacific during the hurricane seasons (June-November) of 1975 through 1985. After removal of the seasonal cycle, the winds are expressed in terms of empirical orthogonal functions. The dominant mode of variability for the combined 200 mb/ATOLL circulation strongly resembles part of a Walker cell confined near the equator. This mode is strongly correlated with El Niñ index (Weare, 1986), and is associated with the.El Niñ/Southern Oscillation. A positive (El Niñ-like) index tends to be associated with more anticyclonic vorticity at the ATOLL level in the tropics and increases in the vertical shear between about 10° and 30°N. This circulation is unfavorable for tropical storm formation.

Correlations are derived between the monthly mean winds and monthly tropical storm frequency in the Atlantic basin. Contemporaneous correlations in August, September and October, the three most active mouths, as well as correlations between winds and tropical storm formation 1 and 2 months later, are computed. Predictability of monthly tropical storm frequency at the 2-month lead is statistically significant, with true skill approximately 45% of the variance. Only one-sixth of this skill is associated with the El Niñ/Southern Oscillation A favorable environment for storm formation is apparently established atleast 2 months before the given month of formation. The results extend and complement predictions of seasonal tropical storm activity and previous hypotheses concerning the influence of El Niñ on stern formation.

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Lloyd J. Shapiro

Abstract

Statistical model significance, sampling and forecast errors are compared between linear regression models developed from preselected and ordered Empirical Orthogonal Function (ROF) predictors and those selected by a forward stepwise screening technique. As a particular application, grid-point height prodictors are used to forecast tropical storm displacements in a storm-heading oriented coordinate system.

Critical correlations for model significance and upper bounds on expected sampling errors are derived from a Monte Carlo method. It is found that dependence among predictors selected by screening reduces expected sampling errors below those for the same number of independent screened predictors. For the given application, expected forecast errors for screened predictors are only slightly greater than those for EOFs.

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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

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.

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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 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 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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