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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

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.

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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

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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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

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

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

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

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

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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