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Mark DeMaria

Abstract

A barotropic spectral model (BSM) is developed to investigate the possibility of forecasting tropical cyclone tracks with global, general circulation models. The model is governed by a barotropic vorticity equation in spherical coordinates which is solved wing a spectral method with spherical harmonic basis functions. The model was run with a triangular truncation of 128 on half of the northern hemisphere (180°W–0°W), and was initialized using horizontal winds from the NMC analyses vertically averaged from 1000 to 100 mb. The storm circulation is represented by a specified axisymmetric vortex and the model was tested by making 30 track forecasts of Atlantic tropical cyclones (13 storms) which occurred from 1979 to 1984.

The skill of the model was assessed by comparing the track forecasts to forecasts from a model based on climatology and persistence (CLIPER). The BSM has statistically significant skill for 24 and 36 h track forecasts and longer range of skill for forecasts of low-latitude storms. For low-latitude storms, the BSM had than the operational SANBAR and moveable fine mesh (MFM) models.

The sensitivity of the model to the horizontal resolution is tested. These results suggest that track forecasts could be made with a global spectral model with a triangular truncation of about 96. It might then be feasible to make track forecasts with a global spectral model similar to the operational model at the European Centre for Medium Range Weather Forecasts which uses a triangular truncation of 106.

The sensitivity of the model to the domain sin and to the specification of the initial vortex is also investigated. These results show that when simple lateral boundary conditions are used, the track forecast errors rapidly increase when the model domain is made smaller than half of a hemisphere. These results also show that the track errors are very insensitive to the size of the vortex, provided that the vortex is not unrealistically large. When the shape of the vortex profile is changed to include an anticylonic circulation at large radii, the track errors are smallest when the total angular momentum of the vortex is close to zero. The errors rapidly increase as the total angular momentum becomes negative.

The effect of modifying the initial analyses so that the deep-layer mean wind in the storm region is consistent with the previous storm motion is also studied. The track errors show the most reduction when the analyses within a radius of about 1000 km of the norm am modified.

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Mark DeMaria

Abstract

The hydrostatic form of the primitive equations described by Ooyama is evaluated by comparing nonhydrostatic and hydrostatic integrations of a dry axisymmetric model with a specified entropy (heat) source. In this formulation, pressure is a diagnostic variable, so that the hydrostatic approximation can be included simply by replacing the vertical momentum equation with a diagnostic vertical velocity equation. his diagnostic equation is a one-dimensional (height) second-order elliptic equation that can be solved using a direct method. Results show that hydrostatic solutions are very sensitive to the accuracy of the method used to solve the diagnostic vertical velocity equation. However, this sensitivity can be eliminated by adding an extra term to the diagnostic equation that ensures that the solution does not drift away from hydrostatic balance due to numerical approximation. When the extra term is added, this formulation of the primitive equations allows for the design of a numerical model in height coordinates that can be used in hydrostatic and nonhydrostatic regimes.

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Mark DeMaria

Abstract

Tropical cyclone motion is investigated in the context of a nondivergent barotropic model. For this purpose, the nondivergent barotropic vorticity equation is solved on a doubly-periodic midlatitude, β-plane using a spectral method with Fourier basis functions. The results from previous studies are summarized and illustrated in idealized model simulations. It is shown that the absolute vorticity gradient of the steering current (∇ζ a ) causes an axisymmetric vortex to drift relative to the steering current with a component in the direction of the gradient and a component 90° to the left of the gradient. The implications of the basic principles of vortex motion for operational track prediction models are discussed. By consideration of the horizontal variation of ∇ζ a , it is shown that a vortex track will be more sensitive to initial position errors in regions where ∇2ζ a > 0 than in regions where ∇ζ a < 0. It is also shown that the vortex track is much more sensitive to changes in the outer regions (size changes) than to changes in the inner regions (intensity changes) of the vortex, and that the vortex track is more sensitive to size changes in regions where | ∇ζ a | is large.

The effect of numerical approximation on the vortex track is studied by comparing the spectral model to a second-order finite difference version of the model. These results suggest that the resolution used in some operational tropical cyclone track prediction models is inadequate.

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Mark DeMaria

Abstract

The effect of nonlinear normal mode initialization (NMI) on tropical cyclone simulations is investigated using a three-layer axisymmetric model. It is shown that the balance condition proposed by Machenhauer, which neglects the time tendencies of the gravity-mode amplitudes, is valid in a tropical cyclone simulation. The boundary layer friction, adiabatic nonlinear and diabatic heating terms are important in the balance. A highly truncated version of the model with linearized physical parameterizations is used to analyze the convergence properties of several iterative schemes developed to solve the initialization equations. When diabatic heating is neglected, the schemes will always converge if the linear friction coefficient α is smaller than the Coriolis parameter f. For small horizontal-scale modes, the iterative schemes will also converge for values of α much larger than f. When diabatic beating is included, the rate of convergence of the small horizontal-scale modes becomes extremely slow. The schemes are also tested in the nonlinear version of the model by first running a 7-day tropical cyclone simulation. The initialization schemes are applied at day 5 after the model has produced an intense tropical cyclone. Results show that the tropical cyclone rapidly weakens relative to the uninitialized run during the 6–12 h after the NMI is applied. This weakening occurs because the small horizontal-scale modes do not converge, making the secondary radial circulation much too weak. A scheme is proposed where the NMI is followed by a short integration with the geostrophic modes held fixed. This procedure compensates for the lack of convergence of the small horizontal-scale gravity modes.

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Mark DeMaria

Abstract

A simplified dynamical system for tropical cyclone intensity prediction based on a logistic growth equation (LGE) is developed. The time tendency of the maximum sustained surface winds is proportional to the sum of two terms: a growth term and a term that limits the maximum wind to an upper bound. The maximum wind evolution over land is determined by an empirical inland wind decay formula. The LGE contains four free parameters, which are the time-dependent growth rate and maximum potential intensity (MPI), and two constants that determine how quickly the intensity relaxes toward the MPI. The MPI is estimated from an empirical formula as a function of sea surface temperature and storm translational speed. The adjoint of the LGE provides a method for finding the other three free parameters to make the predictions as close as possible to the National Hurricane Center best-track intensities. The growth rate is assumed to be a linear function of the vertical shear (S), a convective instability parameter (C) determined from an entraining plume, and their product, where both S and C use global model fields as input. This assumption reduces the parameter estimation problem to the selection of six constants. Results show that the LGE optimized for the full life cycle of individual storms can very accurately simulate the intensity variations out to as long as 15 days. For intensity prediction, single values of the six constants are found by fitting the model to more than 2400 Atlantic forecasts from 2001 to 2006. Results show that the observed intensity variations can be fit more accurately with the LGE than with the linear Statistical Hurricane Intensity Prediction Scheme (SHIPS) formulation, and with a much smaller number of constants. Results also show that LGE model solution (and some properties of real storms) can be explained by the evolution in the two-dimensional S–C phase space. Forecast and other applications of the LGE model are discussed.

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Mark DeMaria

Abstract

The three-dimensional response of the tropical atmosphere to an isolated heat source is investigated using a primitive equation model linearized about a resting basic state on an equatorial β-plane. The model equations are solved by applying vertical and horizontal normal mode transforms. The thermal forcing was chosen to simulate the convection which occurs over tropical South America during the Southern Hemisphere summer. The vertical dependence of the forcing is such that the heating is zero at the top and bottom boundaries with a variable level of maximum beating. The model results with steady forcing are compared with the average circulation over tropical South America for a 19-day period in the Southern Hemisphere summer of 1979, and it is shown that the model reproduces many aspects of the observed circulation. The partition of the energy of the steady state response between the vertical modes is calculated, and it is shown that the internal mode with an equivalent depth of 208 m is dominant for a wide range of levels of maximum beating. The model results with transient forcing are compared with the results from a single equivalent depth version of the model, and it is shown that the horizontal structure is quite similar, but there are significant differences in the vertical structure of the response. The transient response is also compared with the steady state response.

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Mark DeMaria

Abstract

The effect of vertical shear on tropical cyclone intensity change is usually explained in terms of “ventilation” where heat and moisture at upper levels are advected away from the low-level circulation, which inhibits development. A simple two-layer diagnostic balance model is used to provide an alternate explanation of the effect of shear. When the upper-layer wind in the vortex environment differs from that in the lower layer, the potential vorticity (PV) pattern associated with the vortex circulation becomes tilted in the vertical. The balanced mass field associated with the tilted PV pattern requires an increased midlevel temperature perturbation near the vortex center. It is hypothesized that this midlevel warming reduces the convective activity and inhibits the storm development.

Previous studies have shown that diabatic heating near the storm center acts to reduce the vertical tilt of the vortex circulation. These studies have also shown that there is an adiabatic process that acts to reduce the vertical tilt of a vortex. The effectiveness of the adiabatic process depends on the Rossby penetration depth, which increases with latitude, horizontal scale, and vortex amplitude. Large-scale analyses from the 1989–1994 Atlantic hurricane seasons are used to show that high-latitude, large. and intense tropical cyclones tend to be less sensitive to the effect of vertical shear than low-latitude, small, and weak storms.

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John Kaplan
and
Mark DeMaria

Abstract

The National Hurricane Center (NHC) and Statistical Hurricane Intensity Prediction Scheme (SHIPS) databases are employed to examine the large-scale characteristics of rapidly intensifying Atlantic basin tropical cyclones. In this study, rapid intensification (RI) is defined as approximately the 95th percentile of over-water 24-h intensity changes of Atlantic basin tropical cyclones that developed from 1989 to 2000. This equates to a maximum sustained surface wind speed increase of 15.4 m s−1 (30 kt) over a 24-h period. It is shown that 31% of all tropical cyclones, 60% of all hurricanes, 83% of all major hurricanes, and all category 4 and 5 hurricanes underwent RI at least once during their lifetimes.

The mean initial (t = 0 h) conditions of cases that undergo RI are compared to those of the non-RI cases. These comparisons show that the RI cases form farther south and west and have a more westward component of motion than the non-RI cases. In addition, the RI cases are typically intensifying at a faster rate during the previous 12 h than the non-RI cases. The statistical analysis also shows that the RI cases are further from their maximum potential intensity and form in regions with warmer SSTs and higher lower-tropospheric relative humidity than the non-RI cases. The RI cases are also embedded in regions where the upper-level flow is more easterly and the vertical shear and upper-level forcing from troughs or cold lows is weaker than is observed for the non-RI cases. Finally, the RI cases tend to move with the flow within a higher layer of the atmosphere than the non-RI cases.

A simple technique for estimating the probability of RI is described. Estimates of the probability of RI are determined using the predictors for which statistically significant differences are found between the RI and non-RI cases. Estimates of the probability of RI are also determined by combining the five predictors that had the highest individual probabilities of RI. The probability of RI increases from 1% to 41% when the total number of thresholds satisfied increases from zero to five. This simple technique was used in real time for the first time during the 2001 Atlantic hurricane season as part of the Joint Hurricane Testbed (JHT).

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Mark Demaria
and
John Kaplan

Abstract

An empirical relationship between climatological sea surface temperature (SST) and the maximum intensity of tropical cyclones in the North Atlantic basin is developed from a 31-year sample (1962–1992). This relationship is compared with the theoretical results described by Emanuel. The theoretical results are in agreement with the observations over a wide range of SST, provided that the tropopause temperature is assumed to be a function of SST. Each storm is examined to determine how close the observed intensity comes to the maximum possible intensity (MPI). Results show that only about 20% of Atlantic tropical cyclones reach 80% or more of their MPI at the time when they are the most intense. On average, storms reach about 55% of their MPI. Storms that are farther west and farther north tend to reach a larger fraction of their MPI. Storms are also more likely to reach a larger fraction of their MPI in August–November than in June–July. There is considerable interannual variability in the yearly average of the ratio of the observed maximum intensity to the MPI.

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John Kaplan
and
Mark DeMaria

Abstract

An empirical model for predicting the maximum wind of landfalling tropical cyclones is developed. The model is based upon the observation that the wind speed decay rate after landfall is proportional to the wind speed. Observations also indicate that the wind speed decays to a small, but nonzero, background wind speed. With these assumptions, the wind speed is determined from a simple two-parameter exponential decay model, which is a function of the wind speed at landfall and the time since landfall. A correction can also be added that accounts for differences between storms that move inland slowly and storms that move inland rapidly. The model parameters are determined from the National Hurricane Center best track intensities of all U.S. landfalling tropical cyclones south of 37°N for the period 1967–93. Three storms that made landfall in Florida prior to 1967 were also included in the sample. Results show that the two-parameter model explains 91% of the variance of the best track intensity changes. When the correction that accounts for variations in the distance inland is added, the model explains 93% of the variance.

This modal can be used for operational forecasting of the maximum winds of landfalling tropical cyclones. It can also be used to estimate the maximum inland penetration of hurricane force winds (or any wind speed threshold) for a given initial storm intensity. The maximum winds at an inland point will occur for a storm that moves inland perpendicular to the coastline. Under this assumption, the maximum wind at a fixed point becomes a function of the wind speed at landfall and the translational speed of motion. For planning purposes, maps of the maximum inland wind speed can be prepared for various initial storm intensities and speeds of motion. The model can also be applied to the entire wind field of an individual storm to provide a two-dimensional field of the maximum wind during a given storm. Examples of each of these applications are presented.

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