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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

A three-layer multinested numerical model is used to evaluate the asymmetric evolution of a hurricane and its interaction with the large-scale environment. The model uses a compressible fluid in isentropic coordinates. In 72 h the hurricane vortex on a beta plane moves northwest at an average speed of 2.4 m s−1. In the presence of a westerly zonal wind in the upper model layer, the hurricane on an f plane moves to the southeast at an average speed of 0.9 m s−1.A series of experiments establishes that the southeastward drift in the presence of westerly shear is primarily due to the southward isentropic gradient of background potential vorticity (PV) in the middle model layer that is associated with the background temperature field. The cyclonic circulation advects low PV air southward on the west side of the vortex, inducing a negative isentropic PV anomaly to the southwest. This anomaly is associated with a wind field that advects the vortex to the southeast, just as the northward isentropic gradient of PV due to the beta effect advects the hurricane to the northwest. The northward gradient of background PV in the upper layer has little effect on the motion. The westerly wind advects upper-layer low PV outside the vortex core to the east, inducing an anticyclonic anomaly that tends to advect the middle-layer vortex to the north; this tendency is secondary to the motion. The role of vertical transports of momentum due to cumulus convection on the hurricane motion is also evaluated.

Results are presented that generalize the homogenization of asymmetric absolute vorticity and oscillation in relative angular momentum (RAM) found on the beta plane in a previous study with a barotropic model. Outside the vortex core and within ∼350 km of the center, the asymmetries reach a near-steady state. The middle-layer asymmetry is associated with a PV gradient that neutralizes the background gradient due to planetary vorticity or environmental temperature, thereby insulating the symmetric vortex from distortion. Horizontal fluxes in the presence of the planetary vorticity gradient tend to counteract the development of strong anticyclonic total RAM within a large circle about the vortex center.

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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

The nonlinear evolution of a barotropic Rossby wave in a nonuniform basic state is studied numerically. The simulations are designed to isolate and clarify the role of advective nonlinearities in the development process. The model is barotropic, nondivergent and inviscid, on a beta-plane. The steady basic flow is zonally and meridionally nonuniform, and is maintained by a specified steady vorticity source. The wave propagates through an isolated inhomogeneity and interacts with the basic flow. Nonlinear effects are isolated by suppressing the nonlinear terms in the equations.

Two sets of experiments have been carried out. In the first the basic state is an isolated steady vortex embedded in a uniform easterly flow. A single plane wave propagates through the isolated vortex inhomogeneity. In the second the basic state is a zonally varying unstable easterly jet. The inhomogeneity is an isolated region of enhanced instability of the jet. The linearly most unstable wave mode is allowed to evolve to finite amplitude in a uniform region of the jet. The wave then propagates through the isolated region of enhanced instability.

It is found that advective nonlinearities enhance the development of the waves evolving in a nonuniform environment by allowing more effective use of sources of vorticity associated with the inhomogeneity. The nonlinearities allow fluid parcels to move more slowly and/or more directly through the vorticity source. The results are compared with both the observed development of tropical storms and previous theoretical results.

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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

An investigation is made of the role of the translation of a hurricane in determining the distribution of boundary layer winds and in the organization of convection. A slab boundary layer model of constant depth is used to analyze the steady flow under a specified translating symmetric vortex in gradient balance. A truncated spectral formulation is used, including asymmetries through wavenumber 2. The role of linear and nonlinear asymmetric effects in the determination of the boundary layer response is diagnosed. These effects am relevant to relatively slowly and rapidly translating hurricanes, respectively.

The analysis is compared to observations of Hurricanes Frederic of 1979 and Allen of 1980, as well as to other observational and theoretical cures. Allen's translation speed was approximately twice that of Frederic. It is found that the simple boundary layer formulation simulates the qualitative features of the wind field observed in Frederic. The distribution of convection in Frederic and Allen compares favorably with boundary layer convergence diagnosed from the model.

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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

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.

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