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Kaplan, Michael L.

Publications and source records attributed to Kaplan, Michael L..

At least 19 records

Urban Impacts on Convective Squall Lines over Chicago in the Warm Season—Part I: Observations of Multi-Scale Convective Evolution

In this study, our aim is to diagnose how two quasi-linear convective systems (QLCS) are organized so one can determine the possible role of the city of Chicago, IL, USA, in modifying convective precipitation systems. In this Part I of a two-part study, we employ large-scale analyses, radiosonde soundings, surface observations, and Doppler radar data to diagnose the precursor atmospheric circulations that organize the evolution of two mesoscale convective systems and compare those circulations to radar and precipitation. Several multi-scale processes are found that organize and modify convection over the Chicago metroplex. Two sequential quasi-linear convective systems (QLCS #1 and #2) were organized that propagated over Chicago, IL, USA, during an eight-hour period on 5–6 July 2018. The first squall line (QLCS #1) built from the southwest to the northeast while strengthening as it propagated over the city, and the second (QLCS #2) propagated southeastwards and weakened as it passed over the city in association with a polar cold front. The weak upper-level divergence associated with a diffluent flow poleward of an expansive ridge built over and strengthened a low-level trough and confluence zone, triggering QLCS #1. Convective downdrafts from QLCS #1 produced a cold pool that interacted with multiple confluent low-level jets surrounding and focused on the metroplex urban heat island, thus advecting the convection poleward over the metroplex. The heaviest precipitation occurred just south-southeast of Midway Airport, Chicago. Subsequently, a polar cold front propagated into the metroplex, which triggered QLCS #2. However, the descending air above it under the polar jet and residual cold pool from QLCS #1 rapidly dissipated the cold frontal convection. This represents a case study where very active convection built over the metroplex and was likely modified by it, as evidenced in numerical simulations to be described in Part II.

Kaplan, Michael L.

Continued Research into Characterizing the Preturbulence Environment for Sensor Development, New Hazard Algorithms and Experimental Flight Planning

The purpose of the research was to develop and test improved hazard algorithms that could result in the development of sensors that are better able to anticipate potentially severe atmospheric turbulence, which affects aircraft safety. The research focused on employing numerical simulation models to develop improved algorithms for the prediction of aviation turbulence. This involved producing both research simulations and real-time simulations of environments predisposed to moderate and severe aviation turbulence. The research resulted in the following fundamental advancements toward the aforementioned goal: 1) very high resolution simulations of turbulent environments indicated how predictive hazard indices could be improved resulting in a candidate hazard index that indicated the potential for improvement over existing operational indices, 2) a real-time turbulence hazard numerical modeling system was improved by correcting deficiencies in its simulation of moist convection and 3) the same real-time predictive system was tested by running the code twice daily and the hazard prediction indices updated and improved. Additionally, a simple validation study was undertaken to determine how well a real time hazard predictive index performed when compared to commercial pilot observations of aviation turbulence. Simple statistical analyses were performed in this validation study indicating potential skill in employing the hazard prediction index to predict regions of varying intensities of aviation turbulence. Data sets from a research numerical model where provided to NASA for use in a large eddy simulation numerical model. A NASA contractor report and several refereed journal articles where prepared and submitted for publication during the course of this research.

Kaplan, Michael L.

Simulating Virtual Terminal Area Weather Data Bases for Use in the Wake Vortex Avoidance System (Wake VAS) Prediction Algorithm

During the research project, sounding datasets were generated for the region surrounding 9 major airports, including Dallas, TX, Boston, MA, New York, NY, Chicago, IL, St. Louis, MO, Atlanta, GA, Miami, FL, San Francico, CA, and Los Angeles, CA. The numerical simulation of winter and summer environments during which no instrument flight rule impact was occurring at these 9 terminals was performed using the most contemporary version of the Terminal Area PBL Prediction System (TAPPS) model nested from 36 km to 6 km to 1 km horizontal resolution and very detailed vertical resolution in the planetary boundary layer. The soundings from the 1 km model were archived at 30 minute time intervals for a 24 hour period and the vertical dependent variables as well as derived quantities, i.e., 3-dimensional wind components, temperatures, pressures, mixing ratios, turbulence kinetic energy and eddy dissipation rates were then interpolated to 5 m vertical resolution up to 1000 m elevation above ground level. After partial validation against field experiment datasets for Dallas as well as larger scale and much coarser resolution observations at the other 8 airports, these sounding datasets were sent to NASA for use in the Virtual Air Space and Modeling program. The application of these datasets being to determine representative airport weather environments to diagnose the response of simulated wake vortices to realistic atmospheric environments. These virtual datasets are based on large scale observed atmospheric initial conditions that are dynamically interpolated in space and time. The 1 km nested-grid simulated datasets providing a very coarse and highly smoothed representation of airport environment meteorological conditions. Details concerning the airport surface forcing are virtually absent from these simulated datasets although the observed background atmospheric processes have been compared to the simulated fields and the fields were found to accurately replicate the flows surrounding the airport where coarse verification data were available as well as where airport scale datasets were available.

Kaplan, Michael L.

Characterizing the Severe Turbulence Environments Associated With Commercial Aviation Accidents: A Real-Time Turbulence Model (RTTM) Designed for the Operational Prediction of Hazardous Aviation Turbulence Environments

Real-time prediction of environments predisposed to producing moderate-severe aviation turbulence is studied. We describe the numerical model and its postprocessing system designed for said prediction of environments predisposed to severe aviation turbulence as well as presenting numerous examples of its utility. The numerical model is MASS version 5.13, which is integrated over three different grid matrices in real time on a university work station in support of NASA Langley Research Center s B-757 turbulence research flight missions. The postprocessing system includes several turbulence-related products, including four turbulence forecasting indices, winds, streamlines, turbulence kinetic energy, and Richardson numbers. Additionally, there are convective products including precipitation, cloud height, cloud mass fluxes, lifted index, and K-index. Furthermore, soundings, sounding parameters, and Froude number plots are also provided. The horizontal cross-section plot products are provided from 16 000 to 46 000 ft in 2000-ft intervals. Products are available every 3 hours at the 60- and 30-km grid interval and every 1.5 hours at the 15-km grid interval. The model is initialized from the NWS ETA analyses and integrated two times a day.

Kaplan, Michael L.

Characterizing the Preturbulence Environment for Sensor Development, New Hazard Algorithms and NASA Experimental Flight Planning

During the grant period, several tasks were performed in support of the NASA Turbulence Prediction and Warning Systems (TPAWS) program. The primary focus of the research was on characterizing the preturbulence environment by developing predictive tools and simulating atmospheric conditions that preceded severe turbulence. The goal of the research being to provide both dynamical understanding of conditions that preceded turbulence as well as providing predictive tools in support of operational NASA B-757 turbulence research flights. The advancements in characterizing the preturbulence environment will be applied by NASA to sensor development for predicting turbulence onboard commercial aircraft. Numerical simulations with atmospheric models as well as multi-scale observational analyses provided insights into the environment organizing turbulence in a total of forty-eight specific case studies of severe accident producing turbulence on commercial aircraft. These accidents exclusively affected commercial aircraft. A paradigm was developed which diagnosed specific atmospheric circulation systems from the synoptic scale down to the meso-y scale that preceded turbulence in both clear air and in proximity to convection. The emphasis was primarily on convective turbulence as that is what the TPAWS program is most focused on in terms of developing improved sensors for turbulence warning and avoidance. However, the dynamical paradigm also has applicability to clear air and mountain turbulence. This dynamical sequence of events was then employed to formulate and test new hazard prediction indices that were first tested in research simulation studies and then ultimately were further tested in support of the NASA B-757 turbulence research flights. The new hazard characterization algorithms were utilized in a Real Time Turbulence Model (RTTM) that was operationally employed to support the NASA B-757 turbulence research flights. Improvements in the RTTM were implemented in an effort to increase the accuracy of the operational characterization of the preturbulence environment. Additionally, the initial research necessary to create a statistical evaluation scheme for the characterization indices utilized in the RTTM was undertaken. Results of all components of this research were then published in NASA contractor reports and scientific journal papers.

Kaplan, Michael L.

Characterizing the Severe Turbulence Environments Associated with Commercial Aviation Accidents: Hydrostatic Mesobeta Scale Numerical Simulations of Supergradient Wind Flow and Streamwise Ageostrophic Frontogenesis - Part 2

Simulation experiments reveal key processes that organize a hydrostatic environment conducive to severe turbulence. The paradigm requires juxtaposition of the entrance region of a curved jet stream, which is highly subgeostrophic, with the entrance region of a straight jet stream, which is highly supergeostrophic. The wind and mass fields become misphased as the entrance regions converge resulting in the significant spatial variation of inertial forcing, centripetal forcing, and along- and cross-stream pressure gradient forcing over a mesobeta scale region. This results in frontogenesis and the along-stream divergence of cyclonic and convergence of cyclonic ageostrophic vertical vorticity. The centripetally forced mesoscale front becomes the locus of large gradients of ageostrophic vertical vorticity along an overturning isentrope. This region becomes favorable for streamwise vorticity gradient formation enhancing the environment for organization of horizontal vortex tubes in the presence of buoyant forcing.

Kaplan, Michael L.

Characterizing the Severe Turbulence Environments Associated With Commercial Aviation Accidents: 44 Case Study Synoptic Observational Analyses - Part 1

A 44 case study analysis of the large-scale atmospheric structure associated with development of accident-producing aircraft turbulence is described. Categorization is a function of the accident location, altitude, time of year, time of day, and the turbulence category, which classifies disturbances. National Centers for Environmental Prediction Reanalyses data sets and satellite imagery are employed to diagnose synoptic scale predictor fields associated with the large-scale environment preceding severe turbulence. These analyses indicate a predominance of severe accident-producing turbulence within the entrance region of a jet stream at the synoptic scale. Typically, a flow curvature region is just upstream within the jet entrance region, convection is within 100 km of the accident, vertical motion is upward, absolute vorticity is low, vertical wind shear is increasing, and horizontal cold advection is substantial. The most consistent predictor is upstream flow curvature and nearby convection is the second most frequent predictor.

Kaplan, Michael L.

Numerical Modeling Studies of Wake Vortex Transport and Evolution Within the Planetary Boundary Layer

The fundamental objective of this research is study behavior of aircraft wake vortices within atmospheric boundary layer (ABL) in support of developing the system, Aircraft VOrtex Spacing System (AVOSS), under NASA's Terminal Area Productivity (TAR) program that will control aircraft spacing within the narrow approach corridors of airports. The purpose of the AVOSS system is to increase airport capacity by providing a safe reduction in separation of aircraft compared to the now-existing flight rules. In our first funding period (7 January 19994 - 6 April 1997), we have accomplished extensive model development and validation of ABL simulations. Using the validated model, in our second funding period (7 April 1997 - 6 April 2000) we have investigated the effects of ambient atmospheric turbulence on vortex decay and descent, Crow instability, and wake vortex interaction with the ground. Recognizing the crucial influence of ABL turbulence on wake vortex behavior, we have also developed a software generating vertical profiles of turbulent kinetic energy (TKE) or energy dissipation rate (EDR), which are, in turn, used as input data in the AVOSS prediction algorithms.

Lin, Yuh-Lang

A New Eddy Dissipation Rate Formulation for the Terminal Area PBL Prediction System(TAPPS)

The TAPPS employs the MASS model to produce mesoscale atmospheric simulations in support of the Wake Vortex project at Dallas Fort-Worth International Airport (DFW). A post-processing scheme uses the simulated three-dimensional atmospheric characteristics in the planetary boundary layer (PBL) to calculate the turbulence quantities most important to the dissipation of vortices: turbulent kinetic energy and eddy dissipation rate. TAPPS will ultimately be employed to enhance terminal area productivity by providing weather forecasts for the Aircraft Vortex Spacing System (AVOSS). The post-processing scheme utilizes experimental data and similarity theory to determine the turbulence quantities from the simulated horizontal wind field and stability characteristics of the atmosphere. Characteristic PBL quantities important to these calculations are determined based on formulations from the Blackadar PBL parameterization, which is regularly employed in the MASS model to account for PBL processes in mesoscale simulations. The TAPPS forecasts are verified against high-resolution observations of the horizontal winds at DFW. Statistical assessments of the error in the wind forecasts suggest that TAPPS captures the essential features of the horizontal winds with considerable skill. Additionally, the turbulence quantities produced by the post-processor are shown to compare favorably with corresponding tower observations.

Charney, Joseph J.

Numerical Modeling Studies of Wake Vortex Transport and Evolution Within the Planetary Boundary Layer

In support of the wake vortex effect of the Terminal Area Productivity program, we have put forward four tasks to be accomplished in our proposal. The first task is validation of two-dimensional wake vortex-turbulence interaction. The second task is investigation of three-dimensional interaction between wake vortices and atmospheric boundary layer (ABL) turbulence. The third task is ABL studies. The, fourth task is addition of a Klemp-Durran condition at the top boundary for TASS model. The accomplishment of these tasks will increase our understanding of the dynamics of wake vortex and improve forecasting systems responsible for air safety and efficiency. The first two tasks include following three parts: (a) Determine significant length scale for vortex decay and transport, especially the length scales associated with the onset of Crow instability (Crow, 1970); (b) Study the effects of atmospheric turbulence on the decay of the wake vortices; and (c) Determine the relationships between decay rate, transport properties and atmospheric parameters based on large eddy simulation (LES) results and the observational data. These parameters may include turbulence kinetic energy, dissipation rate, wind shear and atmospheric stratification. The ABL studies cover LES modeling of turbulence structure within planetary boundary layer under transition and stable stratification conditions. Evidences have shown that the turbulence in the stable boundary layer can be highly intermittent and the length scales of eddies are very small compared to those in convective case. We proposed to develop a nesting grid mesh scheme and a modified Klemp-Durran conditions (Klemp and Wilhelmson, 1978) at the top boundary for TASS model to simulate planetary boundary layer under stable stratification conditions. During the past year, our group has made great efforts to carry out the above mentioned four tasks simultaneously. The work accomplished in the last year will be described in the next section.

Lin, Yuh-Lang

An Operational Computational Terminal Area PBL Prediction System

There are two fundamental goals of this research project which are listed here in terms of priority, i.e., a primary and secondary goal. The first and primary goal is to develop a prognostic system which could satisfy the operational weather prediction requirements of the meteorological subsystem within the Aircraft Vortex Spacing System (AVOSS), i.e., an operational computational Terminal Area PBL Prediction System (TAPPS). The second goal is to perform indepth diagnostic analyses of the meteorological conditions during the special wake vortex deployments at Memphis and Dallas during August 95 and September 97, respectively. These two goals are interdependent because a thorough understanding of the atmospheric dynamical processes which produced the unique meteorology during the Memphis and Dallas deployments will help us design a prognostic system for the planetary boundary layer (PBL) which could be utilized to support the meteorological subsystem within AVOSS. Concerning the primary goal, TAPPS Stage 2 was tested on the Memphis data and is about to be tested on the Dallas case studies. Furthermore benchmark tests have been undertaken to select the appropriate platform to run TAPPS in real time in support of the DFW AVOSS system. In addition, a technique to improve the initial data over the region surrounding Dallas was also tested and modified for potential operational use in TAPPS. The secondary goal involved several sensitivity simulations and comparisons to Memphis observational data sets in an effort to diagnose what specific atmospheric phenomena where occurring which may have impacted the dynamics of atmospheric wake vortices.

Lin, Yuh-Lang

An Operational Computational Terminal Area PBL Prediction System

There are two fundamental goals of this research project. The first and primary goal is to develop a prognostic system which could satisfy the operational weather prediction requirements of the meteorological subsystem within the Aircraft Vortex Spacing System (AVOSS). The secondary goal is to perform indepth diagnostic analyses of the meteorological conditions affecting the Memphis field experiment held during August 1995. These two goals are interdependent because a thorough understanding of the atmospheric dynamical processes which produced the unique meteorology during the Memphis deployment will help us design a prognostic system for the planetary boundary layer (PBL) which could be utilized to support the meteorological subsystem within AVOSS. The secondary goal occupied much of the first year of the research project. This involved extensive data acquisition and indepth analyses of a spectrum of atmospheric observational data sets. Concerning the primary goal, the first part of the four-stage prognostic system in support of AVOSS entitled: Terminal Area PBL Prediction System (TAPPS) was also formulated and tested in a research environment during 1996. We describe this system, and the three stages which are planned to follow. This first part of a software system designed to meet the primary goal of this research project is relatively inexpensive to implement and run operationally.

Lin, Yuh-Lang

Meso-beta scale numerical simulation studies of terrain-induced jet streak mass/momentum perturbations

Mesoscale model simulations provide insight into the complex jet streak adjustments on 11-12 July 1981 that preceded the first of two significant gravity wave events to have been generated over the Rocky Mountains in Montana. Simulations employing a variety of terrain treatments indicate that prior to wave formation, geostrophic adjustment processes modified the structure of the mid-upper tropospheric jet streak by creating secondary jetlets to the southeast of the polar jet streak in proximity to the gravity wave generation region. This simulated restructuring of the mid-upper tropospheric jet streak is the result of a four stage process. During stage 1, the wind adjusts to the mass field as the jet streak exit region propagates into the inflection point between the upstream trough and downstream ridge in the height field. Stage 2 is initiated as the mass field is forced to adjust to the new ageostrophic wind field created during stage 1. Stage 3 is defined by a second geostrophic adjustment process occurring in a similar manner but to the south and east of the adjustment which occurs during stage 1. A low-level mesoscale jetlet is formed during stage 4 in response to the low-level pressure falls that are established during stage 3. The perturbation of this jetlet, caused by orographically-induced adiabatic and diabatic physical processes, is the likely mechanism responsible for the generation of the first and second episode of observed gravity waves. The dynamics responsible for this wave episode are discussed as differential surface sensible heating inducing an orographically-forced mountain-plains solenoid, resulting in the formation of additional mesoscale jetlets and internal gravity waves. Also discussed is how convective latent heating modifies the numerically simulated terrain-induced internal gravity waves, especially their amplitude and phase velocities, which provide better agreement with those wave characteristics observed in nature. Finally, the three-dimensional linear response of a zonally uniform barotropic flow in a vertically unbounded, continuously stratified, Boussinesq atmosphere which is perturbed from geostrophic equilibrium is investigated.

Lin, Yuh-Lang

Meso-beta scale numerical simulation studies of terrain-induced jet streak mass/momentum perturbations

An in-depth analysis of observed gravity waves and their relationship to precipitation bands over the Montana mesonetwork during the 1981 CCOPE case study indicates that there were two episodes of coherent internal gravity waves. One of the fundamental unanswered questions from this research, however, concerns the dynamical processes which generated the observed waves, all of which originated from the region encompassing the borders of Montana, Idaho, and Wyoming. While geostrophic adjustment, shearing instability, and terrain where all implicated separately or in concert as possible wave generation mechanisms, the lack of upper-air data within the wave genesis region made it difficult to rigorously define the genesis processes from observations alone. In this report we employ a mesoscale numerical model to help diagnose the intricate early wave generation mechanisms during the first observed wave episode.

Lin, Yuh-Lang

Meso-beta scale numerical simulation studies of terrain-induced jet streak mass and momentum perturbations

An in-depth analysis of observed gravity waves and their relationship to precipitation bands over the Montana mesonetwork during the 11-12 July 1981 CCOPE case study indicated two episodes of coherent waves. While geostrophic adjustment, shearing instability, and terrain were all implicated separately or in combination as possible wave generation mechanisms, the lack of upper-air data within the wave genesis region made it difficult to define the genesis processes from observations alone. The first part of this paper, 3D Numerical Modeling Studies of Terrain-Induced Mass/Momentum Perturbations, employs a mesoscale numerical model to help diagnose the intricate early wave generation mechanisms during the first observed gravity wave episode. The meso-beta scale numerical model is used to study various simulations of the role of multiple geostrophic adjustment processes in focusing a region for gravity wave genesis. The second part of this paper, Linear Theory and Theoretical Modeling, investigates the response of non-resting rotating homogeneous and continuously stratified Boussinesq models of the terrestrial atmosphere to temporally impulsive and uniformly propagating three-dimensional localized zonal momentum sources representative of midlatitude jet streaks. The methods of linear perturbation theory applied to the potential vorticity (PV) and wave field equations are used to study the geostrophic adjustment dynamics. The total zonal and meridional wind perturbations are separated into geostrophic and ageostrophic components in order to define and follow the evolution of both the primary and secondary mesocirculations accompanying midlatitude jetogenesis forced by geostrophic adjustment processes. This problem is addressed to help fill the gap in understanding the dynamics and structure of mesoscale inertia-gravity waves forced by geostrophic adjustment processes in simple two-dimensional quiescent current systems and those produced by mesoscale numerical models simulating the orographic and diabatic perturbation of three-dimensional quasi-geostrophically balanced synoptic scale jet streaks associated with complex baroclinic severe storm producing environments.

Lin, Yuh-Lang

Numerical modeling studies of wake vortex transport and evolution within the planetary boundary layer

The proposed research involves four tasks. The first of these is to simulate accurately the turbulent processes in the atmospheric boundary layer. TASS was originally developed to study meso-gamma scale phenomena, such as tornadic storms, microbursts and windshear effects in terminal areas. Simulation of wake vortex evolution, however, will rely on appropriate representation of the physical processes in the surface layer and mixed layer. This involves two parts. First, a specified heat flux boundary condition must be implemented at the surface. Using this boundary condition, simulation results will be compared to experimental data and to other model results for validation. At this point, any necessary changes to the model will be implemented. Next, a surface energy budget parameterization will be added to the model. This will enable calculation of the surface fluxes by accounting for the radiative heat transfer to and from the ground and heat loss to the soil rather than simple specification of the fluxes. The second task involves running TASS with prescribed wake vortices in the initial condition. The vortex models will be supplied by NASA Langley Research Center. Sensitivity tests will be performed on different meteorological environments in the atmospheric boundary layer, which include stable, neutral, and unstable stratifications, calm and severe wind conditions, and dry and wet conditions. Vortex strength may be varied as well. Relevant non-dimensional parameters will include the following: Richardson number or Froude number, Bowen ratio, and height to length scale ratios. The model output will be analyzed and visualized to better understand the transport, decay, and growth rates of the wake vortices. The third task involves running simulations using observed data. MIT Lincoln Labs is currently planning field experiments at the Memphis airport to measure both meteorological conditions and wake vortex characteristics. Once this data becomes available, it can be used to validate the model for vortex behavior under different atmospheric conditions. The fourth task will be to simulate the wake in a more realistic environment covering a wider area. This will involve grid nesting, since high resolution will be required in the wake region but a larger total domain will be used. During the first allocation year, most of the first task will be accomplished.

Lin, Yuh-Lang

Meso-Beta scale numerical simulation studies of terrain-induced jet streak mass/momentum perturbations

The Control-B simulation experiment was designed to improve on the Control-A experiment performed with the GMASS model. This experiment addressed several inadequacies with the first smooth terrain numerical simulation by including: (1) increased nested-grid resolution to better define the simulated gravity waves, (2) increased horizontal diffusion to remove outflow boundary condition noise, and (3) the use of reanalyzed rawinsonde data and surface observations in the initial state to increase the definition of the observed jet streak as well as other low-level features. A smoothed-terrain dry simulation with the nested-grid GMASS model has revealed many important aspects of the processes which resulted in the generation of gravity waves in the region and time when and where they were observed. However, the vertical structure, number, and characteristics of the waves are still quite different from observed waves as diagnosed thus necessitating future improved simulations. However, this control simulation has produced substantial insight into processes which occur on many spatial scales over a 30 hour time period thus allowing one to draw promising inferences as to the mechanisms for the complex process which occurred in nature during the CCOPE case study. The theoretical aspects of the project have focus on understanding the nature of the ageostrophic circulations which are produced in idealized models of the atmosphere in which the troposphere is modeled in one of two ways. The first model assumes that the lower atmosphere can be represented as a single layer of homogeneous fluid whose upper surface is free to exhibit vertical displacement. Two-dimensional internal convergence (divergence) occurring during the adjustment to an asymptotic equilibrium state from an ageostrophic initial state whose momentum structure is representative of a midlatitude localized zonal wind anomaly will cause the free upper surface of the homogeneous atmosphere to rise (fall), and therefore the response can be viewed as being physically three-dimensional. The second model assumes that the troposphere can be represented by an unbounded continuously stratified Boussinesq fluid of constant Brunt-Vaisala frequency N, where the vertical gradient of the basic state potential temperature profile allows for the existence of vertically propagating internal inertia-gravity waves.

Lin, Yuh-Lang

Meso-beta scale numerical simulation studies of terrain-induced jet streak mass/momentum perturbations

The first section is on 3-D numerical modeling of terrain-induced circulations and covers the following: (1) additional insights into gravity wave generation mechanisms based on the control simulation; (2) ongoing nested-grid numerical simulations; (3) work to be completed during the remainder of FY-93; and (4) work objectives for FY-94. The second section is on linear theory and theoretical modeling and covers the following: (1) the free response of a uniform barotropic flow to an initially stationary unbalanced (ageostrophic) zonal wind anomaly; and (2) the free response of a uniform barotropic flow to an initially stationary balanced zonal wind anomaly.

Lin, Yuh-Lang