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Yoshio Kurihara and Morris A. Bender

Abstract

A numerical scheme to treat the open lateral boundary of a limited-area primitive equation model was formulated. Although overspecification of the boundary condition is inevitable in the pointwise boundary setting, the scheme was designed to keep the overspecification to a minimum degree. To impose the boundary conditions, a damping technique was used. Special care was taken to deal with the boundary layer winds at the lateral boundary. The above scheme is most suitable when gravity waves do not prevail in the vicinity of the open boundary.

The scheme was tested in the numerical integrations of prognostic equations for a Haurwitz-type wave. Experimental results are presented which indicate the utility of the proposed method.

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Yoshio Kurihara and Morris A. Bender

Abstract

The mesh nesting strategy proposed by Kurihara et al.(1979) was used to construct a movable, nested-mesh, 11-level primitive equation model. The framework of the model is described in detail.

With the use of a triply nested mesh system with 1°,⅓° and ⅙° longitude-latitude resolution, a small intense dry vortex in a zonal flow of 10 m s-1 was successfully advected for 48 h. The shape of the vortex was well preserved during the time integration which involved over 50 movements of the innermost mesh. The noise, which was excited when a mesh moved, was suppressed in ∼4 min after the movement. For comparison. the results from similar experiments performed with reduced inner mesh resolutions are also presented.

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Morris A. Bender and Isaac Ginis

Abstract

In order to investigate the effect of tropical cyclone–ocean interaction on the intensity of observed hurricanes, the GFDL movable triply nested mesh hurricane model was coupled with a high-resolution version of the Princeton Ocean Model. The ocean model had 1/6° uniform resolution, which matched the horizontal resolution of the hurricane model in its innermost grid. Experiments were run with and without inclusion of the coupling for two cases of Hurricane Opal (1995) and one case of Hurricane Gilbert (1988) in the Gulf of Mexico and two cases each of Hurricanes Felix (1995) and Fran (1996) in the western Atlantic. The results confirmed the conclusions suggested by the earlier idealized studies that the cooling of the sea surface induced by the tropical cyclone will have a significant impact on the intensity of observed storms, particularly for slow moving storms where the SST decrease is greater. In each of the seven forecasts, the ocean coupling led to substantial improvements in the prediction of storm intensity measured by the storm’s minimum sea level pressure.

Without the effect of coupling the GFDL model incorrectly forecasted 25-hPa deepening of Gilbert as it moved across the Gulf of Mexico. With the coupling included, the model storm deepened only 10 hPa, which was much closer to the observed amount of 4 hPa. Similarly, during the period that Opal moved very slowly in the southern Gulf of Mexico, the coupled model produced a large SST decrease northwest of the Yucatan and slow deepening consistent with the observations. The uncoupled model using the initial NCEP SSTs predicted rapid deepening of 58 hPa during the same period.

Improved intensity prediction was achieved both for Hurricanes Felix and Fran in the western Atlantic. For the case of Hurricane Fran, the coarse resolution of the NCEP SST analysis could not resolve Hurricane Edouard’s wake, which was produced when Edouard moved in nearly an identical path to Fran four days earlier. As a result, the operational GFDL forecast using the operational SSTs and without coupling incorrectly forecasted 40-hPa deepening while Fran remained at nearly constant intensity as it crossed the wake. When the coupled model was run with Edouard’s cold wake generated by imposing hurricane wind forcing during the ocean initialization, the intensity prediction was significantly improved. The model also correctly predicted the rapid deepening that occurred as Fran began to move away from the cold wake. These results suggest the importance of an accurate initial SST analysis as well as the inclusion of the ocean coupling, for accurate hurricane intensity prediction with a dynamical model.

Recently, the GFDL hurricane–ocean coupled model used in these case studies was run on 163 forecasts during the 1995–98 seasons. Improved intensity forecasts were again achieved with the mean absolute error in the forecast of central pressure reduced by about 26% compared to the operational GFDL model. During the 1998 season, when the system was run in near–real time, the coupled model improved the intensity forecasts for all storms with central pressure higher than 940 hPa although the most significant improvement (∼60%) occurred in the intensity range of 960–970 hPa. These much larger sample sets confirmed the conclusion from the case studies, that the hurricane–ocean interaction is an important physical mechanism in the intensity of observed tropical cyclones.

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Yoshio Kurihara and Morris A. Bender

Abstract

A scheme is presented for improving the previously proposed method of dynamic initialization of the boundary layer in a primitive equation model (Kurihara and Tuleya, 1978). Performance of the revised scheme is shown for the case of a strong vortex superposed on a zonal flow.

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Yoshio Kurihara, Christopher L. Kerr, and Morris A. Bender

Abstract

A numerical scheme proposed by Kurihara and Bender is modified so as to improve the behavior of open lateral boundaries of a regional model. In the new scheme, both the local values and the gradients of fields from a larger model are used to define the time-dependent reference values toward which the boundary gridpoint values of the regional model prediction are relaxed at each step of the model integration. Use of the gradients in the boundary forcing imposes constraints on the vorticity, divergence and baroclinicity fields for the regional model. The relaxation time of forcing is set to be short for the normal component of wind. For other variables, the relaxation time at a given boundary gridpoint depends on the wind direction at that gridpoint, with a minimum at a point of normal inflow and a maximum at a point of normal outflow. The forcing strength is reduced in the planetary boundary layer so that the boundary layer structure is determined mainly by the surface condition of the regional model. Also, a simple method to control the total mass in the regional model is described. Numerical results from 96-hour integrations with the improved scheme are compared with those from the previous scheme for the cases of the propagations of a wave and a vortex. The behavior of the model at the lateral boundary was noticeably improved with the use of the new scheme, while the solution in the interior domain was little affected by the scheme modification.

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Yoshio Kurihara, Robert E. Tuleya, and Morris A. Bender

Abstract

The Geophysical Fluid Dynamics Laboratory (GFDL) Hurricane Prediction System was adopted by the U.S. National Weather Service as an operational hurricane prediction model in the 1995 hurricane season. The framework of the prediction model is described with emphasis on its unique features. The model uses a multiply nested movable mesh system to depict the interior structure of tropical cyclones. For cumulus parameterization, a soft moist convective adjustment scheme is used. The model initial condition is defined through a method of vortex replacement. It involves generation of a realistic hurricane vortex by a scheme of controlled spinup. Time integration of the model is carried out by a two-step iterative method that has a characteristic of frequency-selective damping.

The outline of the prediction system is presented and the system performance in the 1995 hurricane season is briefly summarized. Both in the Atlantic and the eastern Pacific, the average track forecast errors are substantially reduced by the GFDL model, compared with forecasts by other models, particularly for the forecast periods beyond 36 h. Forecasts of Hurricane Luis and Hurricane Marilyn were especially skillful. A forecast bias is noticed in cases of Hurricane Opal and other storms in the Gulf of Mexico. The importance of accurate initial conditions, in both the environmental flow and the storm structure, is argued.

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Robert E. Tuleya, Morris A. Bender, and Yoshio Kurihara

Abstract

By use of a triply nested, movable mesh model, several ideal simulations OF tropical Cyclone landfall were performed for a strong zonal flow of ∼10 m s-1. The integration domain was a 37 × 45° channel with the innermost mesh having a 22 × 22 point resolution of 1/6°. General characteristics similar to observed landfalling tropical cyclones are obtained in the primary simulation experiment including an abrupt change in the low level (∼68 m) winds at the coastline and a decay of the tropical cyclone at it moves inland. Additional interesting features subject to model and experimental limitations include: little noticeable track change of the model storm when compared to a control experiment with an ocean surface only; a possible temporary displacement or the center of the surface wind circulation from the surface pressure center at landfall; and a distinct decrease in kinetic energy generation and precipitation a few hours after landfall.

The sensitivity to the specified land surface conditions was analyzed by performing additional experiments in which the land surface conditions including surface temperature, moisture, and distribution of surface roughness were changed. It was found that a reasonable change in some of these land conditions can make a considerable difference in behavior for a landfalling tropical cyclone. It was also shown that a small, less intense model storm fills less rapidly. This corresponds well with observations that many landfalling hurricanes decay to approximately the same asymptotic value one day after landfall.

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Yoshio Kurihara, Gregory J. Tripoli, and Morris A. Bender

Abstract

A numerical scheme to construct a two-way, movable, nested-mesh primitive equation model is proposed. Dynamical coupling in a two-way nesting system is performed at a dynamical interface which is separated from a mesh interface by two coarse-grid intervals. Dynamical interaction is achieved by a method which conserves mass, momentum and internal energy of the system. During the course 'Of integration, the nested mesh moves so that the central position of the disturbance contained in The fine-mesh area never deviates from the center of the nest by more than one coarse-mesh interval. New grid data near the leading and trailing edges of the moving nest are obtained by an interpolation method which has a conservation property. The proposed methods of dynamical coupling and mesh movement were extensively tested by a one-dimensional shallow water equation model. Numerical results of these experiments are presented.

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Yoshio Kurihara, Morris A. Bender, and Rebecca J. Ross

Abstract

A scheme is presented to improve the representation of a tropical cyclone in the initial condition of a high-resolution hurricane model. In the proposed method, a crudely resolved tropical cyclone in the large-scale analysis is replaced by a vortex that is properly specified for use in the prediction model.

Appropriate filters are used to remove the vortex from the large-scale analysis so that a smooth environmental field remains. The new specified bogus vortex takes the form of a deviation from this environmental held so that it can be easily merged with the latter field at the correct position. The specified vortex consists of both axisymmetric and asymmetric components. The symmetric component is generated by the time integration of an axisymmetric version of the hurricane prediction model. This ensures dynamical and thermodynamical consistency in the vortex structure, including the moisture field, and also compatibility of the vortex with the resolution and physics of the hurricane model. In the course of the integration of the axisymmetric model, the tangential wind component is gradually forced to a target wind profile determined from observational information and empirical knowledge. This makes the symmetric vortex a good approximation to the corresponding real tropical cyclone. The symmetric flow thus produced is used to generate an asymmetric wind field by the time integration of a simplified barotropic vorticity equation, including the beta effect. The asymmetric wind field, which can make a significant contribution to the vortex motion, is then added to the symmetric flow. After merging the specified vortex with the environmental flow, the mass field is diagnosed from the divergence equation with an appropriately controlled time tendency. The wind field remains unchanged at this step of initialization.

Since the vortex specified by the proposed method is well adapted to the hurricane prediction model, problems of initial adjustment and false spinup of the model vortex, a long-standing difficulty in the dynamical prediction of tropical cyclones, are alleviated. It is anticipated that the improvement of the initial conditions can reduce the error in hurricane track forecasting and extend the feasibility of tropical cyclone forecasting to intensity change.

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Morris A. Bender, Robert E. Tuleya, and Yoshio Kurihara

Abstract

A triply-nested, movable mesh model was used to study the effects of a mountain range on a landfalling tropical cyclone embedded in an easterly flow of ∼10 m s−1. The integration domain consisted of a 37° wide and 45° long channel, with an innermost mesh resolution of 1/6°. An idealized mountain range with maximum height of ∼958 meters was placed parallel to the shoreline. The mountain range, which spanned 19° in the north–south direction and 5° in the east–west direction, was centered in the middle of the channel. Results obtained were compared with a previous landfall simulation, performed without the effect of the mountain range included. In particular, comparison was made of the total storm rainfall, maximum wind distribution and storm decay rate. It was found that the storm filled much more rapidly in the simulation run with the mountain included. The mountain range affected the decay rate through reduction in the supply of latent and kinetic energy into the storm circulation during, as well as after, passage of the storm over the mountain. It was found that a low-level, warm and dry region was produced where the storm winds descended the mountain slope.

In order to better isolate the effect of the mountain on the basic easterly flow, a supplemental integration was performed for the flow without the storm. It revealed that the mountain range caused a significant change in the basic flow over the mountain as well as up to several hundred kilometers downstream and extending considerably above the mountain top. A low-level southerly jet was observed to the west of the mountain base.

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