DOI: 10.5061/dryad.fj6q573zw
title: Data from: Barotropic instability during eyewall replacement

description: Prior to landfall in Puerto Rico, Hurricane Maria (2017) underwent an
 eyewall replacement cycle. The National Oceanic and Atmospheric
 Administration (NOAA) San Juan (TJUA) radar captured a robust outer
 convective ring with an inner ring first distorted into an ellipse and
 then disintegrated. To understand the dynamical processes during eyewall
 replacement, this work interprets the eyewall replacement event using the
 non-divergent barotopic model with a linear stability analysis and
 non-linear numerical simulations. For the linear stability analysis, the
 model’s axisymmetric basic state vorticity distribution is piece-wise
 uniform in five regions: eye, inner eyewall, moat, outer eyewall, and far
 field. The stability of such structures is investigated by solving a
 simple eigenvalue/eigenvector problem. For the non-linear model, the
 evolution into a more stable structure is simulated using the non-linear
 barotropic model. Three types of instability and vorticity rearrangement
 are identified: (1) instability across the outer ring of enhanced
 vorticity, (2) instability across the low vorticity moat, and (3)
 instability across the inner ring of enhanced vorticity. This dataset
 includes (1) a loop of the NOAA TJUA radar during the landfall of
 Hurricane Maria (2017) in GIF format to show the convective evolution, (2)
 the output from the five-region linear stability analysis in NetCDF
 format, and (3) the output from the non-divergent barotropic model in
 NetCDF format and GIF format to show the vortex evolution. These data are
 provided without restrictions for further exploration into understanding
 barotropic instability during eyewall replacement.
description: <strong>Five-region linear stability
 analysis</strong> Nondivergent barotropic model
 linear stability analysis results for a two-dimensional family of
 vortices, each having an axisymmetric basic state vorticity with a
 five-region piecewise uniform distribution. These results are for
 understanding which azimuthal wavenumber(s) will become unstable for each
 vortex in the family. <strong>Nondivergent
 barotropic model</strong> Output from a finite
 difference nondivergent barotropic model for tropical cyclones that uses
 high-order accurate discretization and MUDPACK. These results are for
 three specific vortices in which instability develops in the inner-eyewall
 region (Vortex B), in the outer-eyewall region (Vortex C), or across the
 moat between the two eyewalls (Vortex A).
 <strong>NOAA NEXRAD TJUA radar</strong>
 A loop from the NOAA NEXRAD TJUA radar centered on the position
 of Hurricane Maria (2017). The radar reflectivity (dBz) imagery includes
 every base scan starting at 05:42:01 UTC and ending at 09:50:00 UTC on 20
 September 2017.
description: # Data for: Barotropic Instability During Eyewall Replacement *** The
 following dataset includes results and animations from the manuscript
 "Barotropic Instability During Eyewall Replacement" by C.
 Slocum, R. K. Taft, J. P. Kossin, and W. H. Schubert submitted to MDPI
 Meteorology, https://doi.org/10.3390/meteorology2178224. The work is
 motivated by the elliptically-distorted inner eyewall of Hurricane Maria
 (2017) that was visible in the San Juan, Puerto Rico radar during a period
 of concentric eyewalls. The work presents a simple interpretation of this
 event in terms of the nondivergent barotropic model using both a linear
 stability analysis and numerical simulations. There are three components
 to this dataset: 1. Loop of the NOAA NEXRAD TJUA radar during the landfall
 of Hurricane Maria (2017) 2. Output from the five-region linear stability
 analysis 3. Output from the nondivergent barotropic model ### NOAA NEXRAD
 TJUA radar A loop from the NOAA NEXRAD TJUA radar centered on the position
 of Hurricane Maria (2017). The radar reflectivity (dBz) imagery includes
 every base scan starting at 05:42:01 UTC and ending at 09:50:00 UTC on 20
 September 2017. ### Five-region linear stability analysis Nondivergent
 barotropic model linear stability analysis results for a two-dimensional
 family of vortices, each having an axisymmetric basic state vorticity with
 a five-region piecewise uniform distribution. These results are for
 understanding which azimuthal wavenumber(s) will become unstable for each
 vortex in the family. ### Nondivergent barotropic model Output from a
 finite difference nondivergent barotropic model for tropical cyclones that
 uses high-order accurate discretization and MUDPACK. These results are for
 three specific vortices in which instability develops in the inner-eyewall
 region (Vortex B), in the outer-eyewall region (Vortex C), or across the
 moat between the two eyewalls (Vortex A). ## Description of the data and
 file structure The `LSA5Region` and `NDBMoutput` contain output from the
 manuscript in UCAR Unidata
 [netCDF](https://www.unidata.ucar.edu/software/netcdf/) format with the
 `.nc` extension. For each netCDF file, there is a corresponding ASCII text
 file with the `.txt` extension that contains output from the UCAR Unidata
 [ncdump
 utility](https://docs.unidata.ucar.edu/nug/current/netcdf_utilities_guide.html) with definitions of all variables, abbreviations, missing data codes, and units. Animations from the NEXRAD and model simulations are in animated GIF format, which has been generated using the ImageMagick convert utility. ### Summary Metrics * File count: 13 * Total file size: 47 GB * File formats: .gif, .nc, .txt, .md ``` . LSA5Region LSA5Region_v01r00_r1_07p5-r2_12p5-dr34_10p0-gamma_0p20-alpha_0p50-vref_20p00-rref_0100.nc LSA5Region_v01r00_r1_07p5-r2_12p5-dr34_10p0-gamma_0p20-alpha_0p50-vref_20p00-rref_0100.txt NDBMoutput NDBM_v02r00_barotropic_model_vortexA.gif NDBM_v02r00_barotropic_model_vortexA.nc NDBM_v02r00_barotropic_model_vortexA.txt NDBM_v02r00_barotropic_model_vortexB.gif NDBM_v02r00_barotropic_model_vortexB.nc NDBM_v02r00_barotropic_model_vortexB.txt NDBM_v02r00_barotropic_model_vortexC.gif NDBM_v02r00_barotropic_model_vortexC.nc NDBM_v02r00_barotropic_model_vortexC.txt NEXRAD NEXRAD_TJUA_s20170920050402_e20170920095000.gif README.md ``` ### Details for: Five-region linear stability analysis The file structure and description for the five-region model analysis is generated from the [ncdump utility](https://docs.unidata.ucar.edu/nug/current/netcdf_utilities_guide.html) and is also provided in `LSA5Region_v01r00_r1_07p5-r2_12p5-dr34_10p0-gamma_0p20-alpha_0p50-vref_20p00-rref_0100.txt`. ``` dimensions: azimuthal_wavenumbers = 11 ; v2 = 1001 ; dr23 = 1001 ; variables: byte azimuthal_wavenumbers(azimuthal_wavenumbers) ; azimuthal_wavenumbers:long_name = "azimuthal wavenumbers" ; azimuthal_wavenumbers:valid_range = 2b, 12b ; azimuthal_wavenumbers:coverage_content_type = "coordinate" ; float v2(v2) ; v2:long_name = "basic state tangential wind v2 at radius r2" ; v2:units = "m s-1" ; v2:valid_range = 15.f, 75.f ; v2:ancillary_variables = "r2" ; v2:coverage_content_type = "coordinate" ; float dr23(dr23) ; dr23:long_name = "width of the moat region as defined by the radial difference r3 - r2" ; dr23:units = "m" ; dr23:valid_range = 5000.f, 75000.f ; dr23:coverage_content_type = "coordinate" ; string case_name ; case_name:long_name = "case name for a specific set of parameters" ; case_name:coverage_content_type = "auxiliaryInformation" ; float rref ; rref:long_name = "reference radius" ; rref:units = "m" ; rref:valid_range = 0.f, 100000.f ; rref:coverage_content_type = "referenceInformation" ; rref:missing_value = -999999.f ; rref:_FillValue = -999999.f ; float vref ; vref:long_name = "basic state tangential wind vref at the reference radius rref" ; vref:units = "m s-1" ; vref:valid_range = 15.f, 75.f ; vref:coverage_content_type = "referenceInformation" ; vref:missing_value = -999999.f ; vref:_FillValue = -999999.f ; float r1 ; r1:long_name = "radius r1; the outer edge of the core region" ; r1:units = "m" ; r1:valid_range = 0.f, 100000.f ; r1:coverage_content_type = "referenceInformation" ; r1:missing_value = -999999.f ; r1:_FillValue = -999999.f ; float r2 ; r2:long_name = "radius r2; the outer edge of the inner ring region" ; r2:units = "m" ; r2:valid_range = 0.f, 100000.f ; r2:coverage_content_type = "referenceInformation" ; r2:missing_value = -999999.f ; r2:_FillValue = -999999.f ; float dr34 ; dr34:long_name = "width of the outer ring as defined by the radial difference r4 - r3" ; dr34:units = "m" ; dr34:valid_range = 0.f, 100000.f ; dr34:coverage_content_type = "referenceInformation" ; dr34:missing_value = -999999.f ; dr34:_FillValue = -999999.f ; float alpha ; alpha:long_name = "vorticity in the core (r=0 to r1) as a fraction of the inner-ring region (r1 to r2) vorticity" ; alpha:units = "1" ; alpha:valid_range = 0.f, 1.f ; alpha:coverage_content_type = "referenceInformation" ; alpha:missing_value = -999999.f ; alpha:_FillValue = -999999.f ; float gamma ; gamma:long_name = "vorticity in the moat (r2 to r3) as a fraction of the outer-ring region (r3 to r4) vorticity" ; gamma:units = "1" ; gamma:valid_range = 0.f, 1.f ; gamma:coverage_content_type = "referenceInformation" ; gamma:missing_value = -999999.f ; gamma:_FillValue = -999999.f ; float growth_rate(azimuthal_wavenumbers, v2, dr23) ; growth_rate:long_name = "growth rate for each azimuthal wavenumber and each vortex in the two-dimensional family of vortices" ; growth_rate:units = "s-1" ; growth_rate:coverage_content_type = "modelResult" ; growth_rate:missing_value = -999999.f ; growth_rate:_FillValue = -999999.f ; // global attributes: :title = "Five region model linear stability analysis" ; :summary = "Results for a two-dimensional family of vortices from a nondivergent barotropic model linear stability analysis conducted using the axisymmetric basic state vorticity with a five-region piecewise uniform distribution." ; :product_version = "v01r00" ; :acknowledgment = "This research was funded by the National Science Foundation under grant number AGS-1841326. The scientific results and conclusions, as well as any views or opinions expressed herein, are those of the author(s) and do not necessarily reflect those of NOAA or the Department of Commerce." ; :license = "Creative Commons Zero (CC0)" ; :source = "linear_stability_analysis_five_region" ; :Conventions = "CF-1.10, ACDD-1.3" ; :standard_name_vocabulary = "CF Standard Name Table v79" ; :keywords = "EARTH SCIENCE &gt; ATMOSPHERE &gt; WEATHER EVENTS &gt; TROPICAL CYCLONES" ; :keywords_vocabulary = "GCDM:GCMD Keywords" ; :institution = "DOC/NOAA/NESDIS/STAR/RAMMB &gt; RAMMB, Center for Satellite Applications and Research, NESDIS, NOAA, U.S. Department of Commerce" ; :naming_authority = "gov.noaa.nesdis.star" ; :creator_name = "Chris Slocum" ; :creator_email = "Christopher.Slocum@noaa.gov" ; :creator_url = "https://www.star.nesdis.noaa.gov/star/Slocum_C.php" ; :creator_type = "person" ; :creator_institution = "DOC/NOAA/NESDIS/STAR/RAMMB &gt; RAMMB, Center for Satellite Applications and Research, NESDIS, NOAA, U.S. Department of Commerce" ; :creator_country = "USA" ; :creator_sector = "gov_federal" ; :contributor_name = "Wayne Schubert\n Rick Taft\n COLOSTATE/ATMOS &gt; Dept. of Atmos. Sci., Colorado State University" ; :contributor_role = "collaborator" ; :contributor_url = "http://schubert.atmos.colostate.edu/" ; :project = "Schubert Research Group" ; :cdm_data_type = "Grid" ; :featureType = "grid" ; :processing_level = "Level 4" ; :date_issued = "2021-12-02T21:00:00.000Z" ; :date_metadata_modified = "2022-12-03T16:00:00.000Z" ; :references = "Slocum, C. J., R. K. Taft, J. P. Kossin, and W. H. Schubert, 2023: Barotropic instability during eyewall replacement. Meteorology, 2, Submitted. https://doi.org/10.3390/meteorology2178224." ; :id = "LSA5Region_v01r00_r1_07p5-r2_12p5-dr34_10p0-gamma_0p20-alpha_0p50-vref_20p00-rref_0100.nc" ; :history = "Created 2023-02-06T03:46:20.221Z" ; :date_created = "2023-02-06T03:46:20.221Z" ; :date_modified = "2023-02-06T03:46:20.221Z" ; ``` ### Details for: Nondivergent barotropic model The file structure and description for the nondivergent barotropic model is generated from the [ncdump utility](https://docs.unidata.ucar.edu/nug/current/netcdf_utilities_guide.html) and is also provided in * `NDBM_v02r00_barotropic_model_vortexA.txt` * `NDBM_v02r00_barotropic_model_vortexB.txt` * `NDBM_v02r00_barotropic_model_vortexC.txt` #### Vortex A ``` dimensions: grid_x = 2049 ; grid_y = 2049 ; time = UNLIMITED ; // (289 currently) variables: int maxcy ; maxcy:long_name = "MUDPACK: maximum number of cycles" ; maxcy:ancillary_variables = "method kcycle iprer ipost intpol tolmax" ; maxcy:coverage_content_type = "auxillaryInformation" ; int method ; method:long_name = "MUDPACK: relaxation step method" ; method:ancillary_variables = "maxcy kcycle iprer ipost intpol tolmax" ; method:coverage_content_type = "auxillaryInformation" ; int kcycle ; kcycle:long_name = "MUDPACK: cycle type" ; kcycle:ancillary_variables = "maxcy method iprer ipost intpol tolmax" ; kcycle:coverage_content_type = "auxillaryInformation" ; int iprer ; iprer:long_name = "MUDPACK: number of pre-relaxation sweeps" ; iprer:ancillary_variables = "maxcy method kcycle ipost intpol tolmax" ; iprer:coverage_content_type = "auxillaryInformation" ; int ipost ; ipost:long_name = "MUDPACK: number of post-relaxation sweeps" ; ipost:ancillary_variables = "maxcy method kcycle iprer intpol tolmax" ; ipost:coverage_content_type = "auxillaryInformation" ; int intpol ; intpol:long_name = "MUDPACK: interpolation technique" ; intpol:ancillary_variables = "maxcy method kcycle iprer ipost tolmax" ; intpol:coverage_content_type = "auxillaryInformation" ; float tolmax ; tolmax:long_name = "MUDPACK: tolerance threshold" ; tolmax:ancillary_variables = "maxcy method kcycle iprer ipost intpol" ; tolmax:coverage_content_type = "auxillaryInformation" ; int coarse_factor ; coarse_factor:coverage_content_type = "auxillaryInformation" ; coarse_factor:long_name = "MUDPACK: factor for the coarsest grid" ; coarse_factor:ancillary_variables = "exponential grid_points" ; int exponential ; exponential:coverage_content_type = "auxillaryInformation" ; exponential:long_name = "MUDPACK: power used for determining the number of grid points" ; exponential:ancillary_variables = "coarse_factor grid_points" ; int grid_points ; grid_points:ancillary_variables = "coarse_factor exponential" ; grid_points:coverage_content_type = "auxillaryInformation" ; grid_points:long_name = "MUDPACK: total number of grid points both in x and in y" ; float grid_spacing ; grid_spacing:units = "m" ; grid_spacing:coverage_content_type = "auxillaryInformation" ; grid_spacing:long_name = "spacing between grid points both in x and in y" ; int total_steps ; total_steps:long_name = "total number of time steps" ; total_steps:coverage_content_type = "auxillaryInformation" ; float time_step ; time_step:long_name = "time step" ; time_step:units = "s" ; time_step:coverage_content_type = "auxillaryInformation" ; float diffusion ; diffusion:long_name = "diffusion coefficient; kinematic viscosity" ; diffusion:units = "m2 s-1" ; diffusion:coverage_content_type = "auxillaryInformation" ; float rayleigh ; rayleigh:long_name = "coefficient of Rayleigh friction" ; rayleigh:units = "s-1" ; rayleigh:coverage_content_type = "auxillaryInformation" ; float coriolis ; coriolis:long_name = "constant Coriolis parameter" ; coriolis:standard_name = "coriolis_parameter" ; coriolis:units = "s-1" ; coriolis:coverage_content_type = "auxillaryInformation" ; float density ; density:long_name = "density" ; density:standard_name = "air_density" ; density:units = "kg m-3" ; density:coverage_content_type = "auxillaryInformation" ; float time(time) ; time:long_name = "time since start of the simulation" ; time:standard_name = "time" ; time:units = "s" ; time:axis = "T" ; time:coverage_content_type = "coordinate" ; float grid_y(grid_y) ; grid_y:long_name = "y distance" ; grid_y:standard_name = "projection_y_coordinate" ; grid_y:units = "m" ; grid_y:axis = "Y" ; grid_y:coverage_content_type = "coordinate" ; float grid_x(grid_x) ; grid_x:long_name = "x distance" ; grid_x:standard_name = "projection_x_coordinate" ; grid_x:units = "m" ; grid_x:axis = "X" ; grid_x:coverage_content_type = "coordinate" ; float courant(time) ; courant:long_name = "Courant number for the Courant-Friedrichs-Lewy condition" ; courant:units = "1" ; courant:coverage_content_type = "auxillaryInformation" ; float kinetic_energy(time) ; kinetic_energy:long_name = "area-integrated kinetic energy" ; kinetic_energy:standard_name = "atmosphere_kinetic_energy_content" ; kinetic_energy:units = "J m-2" ; kinetic_energy:coverage_content_type = "auxillaryInformation" ; float enstrophy(time) ; enstrophy:long_name = "domain enstrophy" ; enstrophy:units = "m2 s-2" ; enstrophy:coverage_content_type = "auxillaryInformation" ; float palinstrophy(time) ; palinstrophy:long_name = "domain palinstrophy" ; palinstrophy:units = "s-2" ; palinstrophy:coverage_content_type = "auxillaryInformation" ; float circulation(time) ; circulation:long_name = "domain circulation" ; circulation:units = "m2 s-1" ; circulation:coverage_content_type = "auxillaryInformation" ; float vorticity(time, grid_y, grid_x) ; vorticity:standard_name = "atmosphere_relative_vorticity" ; vorticity:long_name = "vorticity" ; vorticity:units = "s-1" ; vorticity:coverage_content_type = "modelResult" ; float streamfunction(time, grid_y, grid_x) ; streamfunction:standard_name = "atmosphere_horizontal_streamfunction" ; streamfunction:long_name = "stream function" ; streamfunction:units = "m2 s-1" ; streamfunction:coverage_content_type = "modelResult" ; float uwind(time, grid_y, grid_x) ; uwind:standard_name = "eastward_wind" ; uwind:long_name = "u-component of the wind" ; uwind:units = "m s-1" ; uwind:coverage_content_type = "modelResult" ; float vwind(time, grid_y, grid_x) ; vwind:standard_name = "northward_wind" ; vwind:long_name = "v-component of the wind" ; vwind:units = "m s-1" ; vwind:coverage_content_type = "modelResult" ; float pressure(time, grid_y, grid_x) ; pressure:standard_name = "difference_of_air_pressure_from_model_reference" ; pressure:long_name = "Pressure field deviation from the surrounding environment" ; pressure:units = "Pa" ; pressure:coverage_content_type = "modelResult" ; float q_field(time, grid_y, grid_x) ; q_field:units = "s-2" ; q_field:coverage_content_type = "modelResult" ; q_field:long_name = "Q field = psi^2_xy - psi_xx * psi_yy" ; q_field:comment = "Particles regions with Q &lt; 0 (motion is elliptic) will not separate exponentially in time; regions with Q &gt; 0 (motion is hyperbolic) are turbulent and vorticity gradients grow exponentially; Q^-1/2 is defined as the filamentation time." ; // global attributes: :title = "Nondivergent barotropic model output" ; :summary = "Finite difference nondivergent barotropic model for tropical cyclones that uses high-order accurate discretization and MUDPACK." ; :keywords = "EARTH SCIENCE &gt; ATMOSPHERE &gt; WEATHER EVENTS &gt; TROPICAL CYCLONES" ; :keywords_vocabulary = "GCMD:GCMD Keywords" ; :Conventions = "CF-1.10, ACDD-1.3" ; :id = "barotropic_model_vortexA.nc" ; :naming_authority = "gov.noaa.nesdis.star" ; :history = "Created 2023-01-02T21:40:19Z" ; :source = "Output from NDBMv2" ; :processing_level = "Level 4" ; :comment = "" ; :license = "Creative Commons Zero (CC0)" ; :standard_name_vocabulary = "CF Standard Name Table v79" ; :creator_name = "Chris Slocum" ; :creator_email = "Christopher.Slocum@noaa.gov" ; :creator_url = "https://www.star.nesdis.noaa.gov/star/Slocum_C.php" ; :creator_type = "person" ; :creator_institution = "DOC/NOAA/NESDIS/STAR &gt; Center for Satellite Applications and Research, NESDIS, NOAA, U.S. Department of Commerce" ; :creator_country = "USA" ; :creator_sector = "gov_federal" ; :institution = "DOC/NOAA/NESDIS/STAR &gt; Center for Satellite Applications and Research, NESDIS, NOAA, U.S. Department of Commerce" ; :project = "Schubert Research Group" ; :product_version = "2.0.0" ; :cdm_data_type = "Grid" ; :featureType = "grid" ; :date_created = "2023-01-02T21:40:19Z" ; :date_issued = "2023-01-02T21:40:19Z" ; :date_metadata_modified = "2023-01-02T21:40:19Z" ; :experiment_name = "barotropic_model_vortexA" ; :jacobian_discretization = "Fourth-order Arakawa Jacobian" ; :laplacian_discretization = "Nine-point stencil Laplacian" ; :temporal_discretization = "Fourth-order Runge-Kutta method" ; :omp_num_threads = 54 ; :acknowledgment = "Supported by the National Science Foundation under grant AGS-1841326 and the National Oceanic and Atmospheric Administration. The scientific results and conclusions, as well as any views or opinions expressed herein, are those of the author(s) and do not necessarily reflect those of NOAA or the Department of Commerce." ; :MUDPACK_version = "5.0.1" ; :references = "Slocum, C. J., R. K. Taft, J. P. Kossin, and W. H. Schubert, 2023: Barotropic instability during eyewall replacement. Meteorology, 2, Submitted. https://doi.org/10.3390/meteorology2178224." ; ``` #### Vortex B ``` dimensions: grid_x = 2049 ; grid_y = 2049 ; time = UNLIMITED ; // (289 currently) variables: int maxcy ; maxcy:long_name = "MUDPACK: maximum number of cycles" ; maxcy:ancillary_variables = "method kcycle iprer ipost intpol tolmax" ; maxcy:coverage_content_type = "auxillaryInformation" ; int method ; method:long_name = "MUDPACK: relaxation step method" ; method:ancillary_variables = "maxcy kcycle iprer ipost intpol tolmax" ; method:coverage_content_type = "auxillaryInformation" ; int kcycle ; kcycle:long_name = "MUDPACK: cycle type" ; kcycle:ancillary_variables = "maxcy method iprer ipost intpol tolmax" ; kcycle:coverage_content_type = "auxillaryInformation" ; int iprer ; iprer:long_name = "MUDPACK: number of pre-relaxation sweeps" ; iprer:ancillary_variables = "maxcy method kcycle ipost intpol tolmax" ; iprer:coverage_content_type = "auxillaryInformation" ; int ipost ; ipost:long_name = "MUDPACK: number of post-relaxation sweeps" ; ipost:ancillary_variables = "maxcy method kcycle iprer intpol tolmax" ; ipost:coverage_content_type = "auxillaryInformation" ; int intpol ; intpol:long_name = "MUDPACK: interpolation technique" ; intpol:ancillary_variables = "maxcy method kcycle iprer ipost tolmax" ; intpol:coverage_content_type = "auxillaryInformation" ; float tolmax ; tolmax:long_name = "MUDPACK: tolerance threshold" ; tolmax:ancillary_variables = "maxcy method kcycle iprer ipost intpol" ; tolmax:coverage_content_type = "auxillaryInformation" ; int coarse_factor ; coarse_factor:coverage_content_type = "auxillaryInformation" ; coarse_factor:long_name = "MUDPACK: factor for the coarsest grid" ; coarse_factor:ancillary_variables = "exponential grid_points" ; int exponential ; exponential:coverage_content_type = "auxillaryInformation" ; exponential:long_name = "MUDPACK: power used for determining the number of grid points" ; exponential:ancillary_variables = "coarse_factor grid_points" ; int grid_points ; grid_points:ancillary_variables = "coarse_factor exponential" ; grid_points:coverage_content_type = "auxillaryInformation" ; grid_points:long_name = "MUDPACK: total number of grid points both in x and in y" ; float grid_spacing ; grid_spacing:units = "m" ; grid_spacing:coverage_content_type = "auxillaryInformation" ; grid_spacing:long_name = "spacing between grid points both in x and in y" ; int total_steps ; total_steps:long_name = "total number of time steps" ; total_steps:coverage_content_type = "auxillaryInformation" ; float time_step ; time_step:long_name = "time step" ; time_step:units = "s" ; time_step:coverage_content_type = "auxillaryInformation" ; float diffusion ; diffusion:long_name = "diffusion coefficient; kinematic viscosity" ; diffusion:units = "m2 s-1" ; diffusion:coverage_content_type = "auxillaryInformation" ; float rayleigh ; rayleigh:long_name = "coefficient of Rayleigh friction" ; rayleigh:units = "s-1" ; rayleigh:coverage_content_type = "auxillaryInformation" ; float coriolis ; coriolis:long_name = "constant Coriolis parameter" ; coriolis:standard_name = "coriolis_parameter" ; coriolis:units = "s-1" ; coriolis:coverage_content_type = "auxillaryInformation" ; float density ; density:long_name = "density" ; density:standard_name = "air_density" ; density:units = "kg m-3" ; density:coverage_content_type = "auxillaryInformation" ; float time(time) ; time:long_name = "time since start of the simulation" ; time:standard_name = "time" ; time:units = "s" ; time:axis = "T" ; time:coverage_content_type = "coordinate" ; float grid_y(grid_y) ; grid_y:long_name = "y distance" ; grid_y:standard_name = "projection_y_coordinate" ; grid_y:units = "m" ; grid_y:axis = "Y" ; grid_y:coverage_content_type = "coordinate" ; float grid_x(grid_x) ; grid_x:long_name = "x distance" ; grid_x:standard_name = "projection_x_coordinate" ; grid_x:units = "m" ; grid_x:axis = "X" ; grid_x:coverage_content_type = "coordinate" ; float courant(time) ; courant:long_name = "Courant number for the Courant-Friedrichs-Lewy condition" ; courant:units = "1" ; courant:coverage_content_type = "auxillaryInformation" ; float kinetic_energy(time) ; kinetic_energy:long_name = "area-integrated kinetic energy" ; kinetic_energy:standard_name = "atmosphere_kinetic_energy_content" ; kinetic_energy:units = "J m-2" ; kinetic_energy:coverage_content_type = "auxillaryInformation" ; float enstrophy(time) ; enstrophy:long_name = "domain enstrophy" ; enstrophy:units = "m2 s-2" ; enstrophy:coverage_content_type = "auxillaryInformation" ; float palinstrophy(time) ; palinstrophy:long_name = "domain palinstrophy" ; palinstrophy:units = "s-2" ; palinstrophy:coverage_content_type = "auxillaryInformation" ; float circulation(time) ; circulation:long_name = "domain circulation" ; circulation:units = "m2 s-1" ; circulation:coverage_content_type = "auxillaryInformation" ; float vorticity(time, grid_y, grid_x) ; vorticity:standard_name = "atmosphere_relative_vorticity" ; vorticity:long_name = "vorticity" ; vorticity:units = "s-1" ; vorticity:coverage_content_type = "modelResult" ; float streamfunction(time, grid_y, grid_x) ; streamfunction:standard_name = "atmosphere_horizontal_streamfunction" ; streamfunction:long_name = "stream function" ; streamfunction:units = "m2 s-1" ; streamfunction:coverage_content_type = "modelResult" ; float uwind(time, grid_y, grid_x) ; uwind:standard_name = "eastward_wind" ; uwind:long_name = "u-component of the wind" ; uwind:units = "m s-1" ; uwind:coverage_content_type = "modelResult" ; float vwind(time, grid_y, grid_x) ; vwind:standard_name = "northward_wind" ; vwind:long_name = "v-component of the wind" ; vwind:units = "m s-1" ; vwind:coverage_content_type = "modelResult" ; float pressure(time, grid_y, grid_x) ; pressure:standard_name = "difference_of_air_pressure_from_model_reference" ; pressure:long_name = "Pressure field deviation from the surrounding environment" ; pressure:units = "Pa" ; pressure:coverage_content_type = "modelResult" ; float q_field(time, grid_y, grid_x) ; q_field:units = "s-2" ; q_field:coverage_content_type = "modelResult" ; q_field:long_name = "Q field = psi^2_xy - psi_xx * psi_yy" ; q_field:comment = "Particles regions with Q &lt; 0 (motion is elliptic) will not separate exponentially in time; regions with Q &gt; 0 (motion is hyperbolic) are turbulent and vorticity gradients grow exponentially; Q^-1/2 is defined as the filamentation time." ; // global attributes: :title = "Nondivergent barotropic model output" ; :summary = "Finite difference nondivergent barotropic model for tropical cyclones that uses high-order accurate discretization and MUDPACK." ; :keywords = "EARTH SCIENCE &gt; ATMOSPHERE &gt; WEATHER EVENTS &gt; TROPICAL CYCLONES" ; :keywords_vocabulary = "GCMD:GCMD Keywords" ; :Conventions = "CF-1.10, ACDD-1.3" ; :id = "barotropic_model_vortexB.nc" ; :naming_authority = "gov.noaa.nesdis.star" ; :history = "Created 2023-01-02T21:41:52Z" ; :source = "Output from NDBMv2" ; :processing_level = "Level 4" ; :comment = "" ; :license = "Creative Commons Zero (CC0)" ; :standard_name_vocabulary = "CF Standard Name Table v79" ; :creator_name = "Chris Slocum" ; :creator_email = "Christopher.Slocum@noaa.gov" ; :creator_url = "https://www.star.nesdis.noaa.gov/star/Slocum_C.php" ; :creator_type = "person" ; :creator_institution = "DOC/NOAA/NESDIS/STAR &gt; Center for Satellite Applications and Research, NESDIS, NOAA, U.S. Department of Commerce" ; :creator_country = "USA" ; :creator_sector = "gov_federal" ; :institution = "DOC/NOAA/NESDIS/STAR &gt; Center for Satellite Applications and Research, NESDIS, NOAA, U.S. Department of Commerce" ; :project = "Schubert Research Group" ; :product_version = "2.0.0" ; :cdm_data_type = "Grid" ; :featureType = "grid" ; :date_created = "2023-01-02T21:41:52Z" ; :date_issued = "2023-01-02T21:41:52Z" ; :date_metadata_modified = "2023-01-02T21:41:52Z" ; :experiment_name = "barotropic_model_vortexB" ; :jacobian_discretization = "Fourth-order Arakawa Jacobian" ; :laplacian_discretization = "Nine-point stencil Laplacian" ; :temporal_discretization = "Fourth-order Runge-Kutta method" ; :omp_num_threads = 54 ; :acknowledgment = "Supported by the National Science Foundation under grant AGS-1841326 and the National Oceanic and Atmospheric Administration. The scientific results and conclusions, as well as any views or opinions expressed herein, are those of the author(s) and do not necessarily reflect those of NOAA or the Department of Commerce." ; :MUDPACK_version = "5.0.1" ; :references = "Slocum, C. J., R. K. Taft, J. P. Kossin, and W. H. Schubert, 2023: Barotropic instability during eyewall replacement. Meteorology, 2, Submitted. https://doi.org/10.3390/meteorology2178224." ; ``` #### Vortex C ``` dimensions: grid_x = 2049 ; grid_y = 2049 ; time = UNLIMITED ; // (289 currently) variables: int maxcy ; maxcy:long_name = "MUDPACK: maximum number of cycles" ; maxcy:ancillary_variables = "method kcycle iprer ipost intpol tolmax" ; maxcy:coverage_content_type = "auxillaryInformation" ; int method ; method:long_name = "MUDPACK: relaxation step method" ; method:ancillary_variables = "maxcy kcycle iprer ipost intpol tolmax" ; method:coverage_content_type = "auxillaryInformation" ; int kcycle ; kcycle:long_name = "MUDPACK: cycle type" ; kcycle:ancillary_variables = "maxcy method iprer ipost intpol tolmax" ; kcycle:coverage_content_type = "auxillaryInformation" ; int iprer ; iprer:long_name = "MUDPACK: number of pre-relaxation sweeps" ; iprer:ancillary_variables = "maxcy method kcycle ipost intpol tolmax" ; iprer:coverage_content_type = "auxillaryInformation" ; int ipost ; ipost:long_name = "MUDPACK: number of post-relaxation sweeps" ; ipost:ancillary_variables = "maxcy method kcycle iprer intpol tolmax" ; ipost:coverage_content_type = "auxillaryInformation" ; int intpol ; intpol:long_name = "MUDPACK: interpolation technique" ; intpol:ancillary_variables = "maxcy method kcycle iprer ipost tolmax" ; intpol:coverage_content_type = "auxillaryInformation" ; float tolmax ; tolmax:long_name = "MUDPACK: tolerance threshold" ; tolmax:ancillary_variables = "maxcy method kcycle iprer ipost intpol" ; tolmax:coverage_content_type = "auxillaryInformation" ; int coarse_factor ; coarse_factor:coverage_content_type = "auxillaryInformation" ; coarse_factor:long_name = "MUDPACK: factor for the coarsest grid" ; coarse_factor:ancillary_variables = "exponential grid_points" ; int exponential ; exponential:coverage_content_type = "auxillaryInformation" ; exponential:long_name = "MUDPACK: power used for determining the number of grid points" ; exponential:ancillary_variables = "coarse_factor grid_points" ; int grid_points ; grid_points:ancillary_variables = "coarse_factor exponential" ; grid_points:coverage_content_type = "auxillaryInformation" ; grid_points:long_name = "MUDPACK: total number of grid points both in x and in y" ; float grid_spacing ; grid_spacing:units = "m" ; grid_spacing:coverage_content_type = "auxillaryInformation" ; grid_spacing:long_name = "spacing between grid points both in x and in y" ; int total_steps ; total_steps:long_name = "total number of time steps" ; total_steps:coverage_content_type = "auxillaryInformation" ; float time_step ; time_step:long_name = "time step" ; time_step:units = "s" ; time_step:coverage_content_type = "auxillaryInformation" ; float diffusion ; diffusion:long_name = "diffusion coefficient; kinematic viscosity" ; diffusion:units = "m2 s-1" ; diffusion:coverage_content_type = "auxillaryInformation" ; float rayleigh ; rayleigh:long_name = "coefficient of Rayleigh friction" ; rayleigh:units = "s-1" ; rayleigh:coverage_content_type = "auxillaryInformation" ; float coriolis ; coriolis:long_name = "constant Coriolis parameter" ; coriolis:standard_name = "coriolis_parameter" ; coriolis:units = "s-1" ; coriolis:coverage_content_type = "auxillaryInformation" ; float density ; density:long_name = "density" ; density:standard_name = "air_density" ; density:units = "kg m-3" ; density:coverage_content_type = "auxillaryInformation" ; float time(time) ; time:long_name = "time since start of the simulation" ; time:standard_name = "time" ; time:units = "s" ; time:axis = "T" ; time:coverage_content_type = "coordinate" ; float grid_y(grid_y) ; grid_y:long_name = "y distance" ; grid_y:standard_name = "projection_y_coordinate" ; grid_y:units = "m" ; grid_y:axis = "Y" ; grid_y:coverage_content_type = "coordinate" ; float grid_x(grid_x) ; grid_x:long_name = "x distance" ; grid_x:standard_name = "projection_x_coordinate" ; grid_x:units = "m" ; grid_x:axis = "X" ; grid_x:coverage_content_type = "coordinate" ; float courant(time) ; courant:long_name = "Courant number for the Courant-Friedrichs-Lewy condition" ; courant:units = "1" ; courant:coverage_content_type = "auxillaryInformation" ; float kinetic_energy(time) ; kinetic_energy:long_name = "area-integrated kinetic energy" ; kinetic_energy:standard_name = "atmosphere_kinetic_energy_content" ; kinetic_energy:units = "J m-2" ; kinetic_energy:coverage_content_type = "auxillaryInformation" ; float enstrophy(time) ; enstrophy:long_name = "domain enstrophy" ; enstrophy:units = "m2 s-2" ; enstrophy:coverage_content_type = "auxillaryInformation" ; float palinstrophy(time) ; palinstrophy:long_name = "domain palinstrophy" ; palinstrophy:units = "s-2" ; palinstrophy:coverage_content_type = "auxillaryInformation" ; float circulation(time) ; circulation:long_name = "domain circulation" ; circulation:units = "m2 s-1" ; circulation:coverage_content_type = "auxillaryInformation" ; float vorticity(time, grid_y, grid_x) ; vorticity:standard_name = "atmosphere_relative_vorticity" ; vorticity:long_name = "vorticity" ; vorticity:units = "s-1" ; vorticity:coverage_content_type = "modelResult" ; float streamfunction(time, grid_y, grid_x) ; streamfunction:standard_name = "atmosphere_horizontal_streamfunction" ; streamfunction:long_name = "stream function" ; streamfunction:units = "m2 s-1" ; streamfunction:coverage_content_type = "modelResult" ; float uwind(time, grid_y, grid_x) ; uwind:standard_name = "eastward_wind" ; uwind:long_name = "u-component of the wind" ; uwind:units = "m s-1" ; uwind:coverage_content_type = "modelResult" ; float vwind(time, grid_y, grid_x) ; vwind:standard_name = "northward_wind" ; vwind:long_name = "v-component of the wind" ; vwind:units = "m s-1" ; vwind:coverage_content_type = "modelResult" ; float pressure(time, grid_y, grid_x) ; pressure:standard_name = "difference_of_air_pressure_from_model_reference" ; pressure:long_name = "Pressure field deviation from the surrounding environment" ; pressure:units = "Pa" ; pressure:coverage_content_type = "modelResult" ; float q_field(time, grid_y, grid_x) ; q_field:units = "s-2" ; q_field:coverage_content_type = "modelResult" ; q_field:long_name = "Q field = psi^2_xy - psi_xx * psi_yy" ; q_field:comment = "Particles regions with Q &lt; 0 (motion is elliptic) will not separate exponentially in time; regions with Q &gt; 0 (motion is hyperbolic) are turbulent and vorticity gradients grow exponentially; Q^-1/2 is defined as the filamentation time." ; // global attributes: :title = "Nondivergent barotropic model output" ; :summary = "Finite difference nondivergent barotropic model for tropical cyclones that uses high-order accurate discretization and MUDPACK." ; :keywords = "EARTH SCIENCE &gt; ATMOSPHERE &gt; WEATHER EVENTS &gt; TROPICAL CYCLONES" ; :keywords_vocabulary = "GCMD:GCMD Keywords" ; :Conventions = "CF-1.10, ACDD-1.3" ; :id = "barotropic_model_vortexC.nc" ; :naming_authority = "gov.noaa.nesdis.star" ; :history = "Created 2023-01-04T10:06:29Z" ; :source = "Output from NDBMv2" ; :processing_level = "Level 4" ; :comment = "" ; :license = "Creative Commons Zero (CC0)" ; :standard_name_vocabulary = "CF Standard Name Table v79" ; :creator_name = "Chris Slocum" ; :creator_email = "Christopher.Slocum@noaa.gov" ; :creator_url = "https://www.star.nesdis.noaa.gov/star/Slocum_C.php" ; :creator_type = "person" ; :creator_institution = "DOC/NOAA/NESDIS/STAR &gt; Center for Satellite Applications and Research, NESDIS, NOAA, U.S. Department of Commerce" ; :creator_country = "USA" ; :creator_sector = "gov_federal" ; :institution = "DOC/NOAA/NESDIS/STAR &gt; Center for Satellite Applications and Research, NESDIS, NOAA, U.S. Department of Commerce" ; :project = "Schubert Research Group" ; :product_version = "2.0.0" ; :cdm_data_type = "Grid" ; :featureType = "grid" ; :date_created = "2023-01-04T10:06:29Z" ; :date_issued = "2023-01-04T10:06:29Z" ; :date_metadata_modified = "2023-01-04T10:06:29Z" ; :experiment_name = "barotropic_model_vortexC" ; :jacobian_discretization = "Fourth-order Arakawa Jacobian" ; :laplacian_discretization = "Nine-point stencil Laplacian" ; :temporal_discretization = "Fourth-order Runge-Kutta method" ; :omp_num_threads = 54 ; :acknowledgment = "Supported by the National Science Foundation under grant AGS-1841326 and the National Oceanic and Atmospheric Administration. The scientific results and conclusions, as well as any views or opinions expressed herein, are those of the author(s) and do not necessarily reflect those of NOAA or the Department of Commerce." ; :MUDPACK_version = "5.0.1" ; :references = "Slocum, C. J., R. K. Taft, J. P. Kossin, and W. H. Schubert, 2023: Barotropic instability during eyewall replacement. Meteorology, 2, Submitted. https://doi.org/10.3390/meteorology2178224." ; ``` ## Sharing/Access information Links to other publicly accessible locations of the data: * NOAA Next Generation Radar (NEXRAD) Level 2 Base Product data for the WSR-88D in San Juan, Puerto Rico (TJUA) is available from the NOAA National Centers for Environmental Information at \\url{https://doi.org/10.7289/V5W9574V}. Data was derived from the following sources: * Details for the five-region linear stability analysis and nondivergent barotropic model are discussed in \\url{https://doi.org/10.3390/meteorology2178224}.