Email: skamaroc@ucar.edu
Phone: 303-497-8161
Postal Address: P.O. Box 3000, Boulder, CO, 80307-3000
Shipping Address: 3450 Mitchell Lane, Boulder, CO, 80307-3000

Research Interests

I am currently involved in research in a number of areas:

(1) nonhydrostatic atmospheric model development (particularily numerical methods used to solve the compressible Euler equations),
(2) dynamics of convection (convective system initiation and evolution),
(3) the development of ensemble Kalman filter data assimilation techniques,
(4) the modeling of chemistry in clouds, and tracer and chemical species transport,
(5) geophysical fluid dynamics.

skamarock research

Current Research and Associated Publications


Global Modeling and Global Model Development


In the development of MPAS (Model for Prediction Across Scales) and in concert with other collaborations with global weather and climate modeling groups, I am involved in efforts to develop and improve the dynamical cores used in global models. We are currently focussing our efforts on global icosahedral grids (specifically Spherical Centriodal Voronoi Tessellations - SCVTs). A paper describing the MPAS nonhydrostatic atmospheric core that provides for both uniform and variable resolution meshes on the sphere, on limited areas of the sphere, and on Cartesian planes, has been accepted for publication:

A Multi-scale Nonhydrostatic Atmospheric Model Using Centroidal Voronoi Tesselations and C-Grid Staggering. William C. Skamarock, Joseph B. Klemp, Michael G. Duda, Laura Fowler, Sang-Hun Park, and Todd D. Ringler. 2012 Monthly Weather Review, 240, 3090-3105, doi:10.1175/MWR-D-11-00215.1 PDF available

Two papers describing some of the some numerical formulations for the Voronoi mesh used in MPAS:

Numerical Representation of Geostrophic Modes on Arbitrarily Structured C-Grids.
J. Thuburn, T. Ringler, W. Skamarock and J. Klemp. 2009,
Journal of Computational Physics, 228, 8321-8335, doi:10.1016/j.jcp.2009.08.006. PDF available

A Unified Approach to Energy Conservation and Potential Vorticity Dynamics on Arbitrarily-Structured C-Grids
Ringler, Thuburn, Klemp, and Skamarock, 2010
Journal of Computational Physics, 229, 3065-3090, doi:10.1016/j.jcp.2009.12.007 PDF available

I am involved in ongoing work examining the accuracy of solutions on variable-resolution SCVTs. The first paper deals with solutions of the 2D shallow water equations on the sphere:

Exploring a Multiresolution Modeling Approach within the Shallow-Water Equation
T. Ringler, D. Jacobson, M. Gunsburger, L. Ju, M. Duda, and W. Skamarock,
Monthly Weather Review, 139, 3348-3368, doi:10.1175/MWR-D-10-05049.1 PDF available

The second paper deals with solutions of the 3D hydrostatic primative equations for aquaplanet simulations (APE):

Exploring a Global Multi-Resolution Modeling Approach Using Aquaplanet Simulations
S. Rauscher, T. Ringler, W. Skamarock, and A. Mirin
in press, Monthly Weather Review, 2012. PDF available

A third paper deals with solutions of the 3D hydrostatic and nonhydrostatic equations for idealized baroclinic waves using the Jablonowski and Williamson (QJRMS 2006) unstable jet:

Evaluation of global atmospheric solvers using extensions of the Jablonowski and Williamson baroclinic wave test case
S.-H. Park, W. Skamarock, J. Klemp, L. Fowler, and M. Duda
submitted for publication in Monthly Weather Review, 29 March 2012. PDF available

I have also been working on transport schemes for the SCVT grids and I have been exploring a few different approaches. The first approach involves examining an extension to a second-order forward-in-time approach:

Conservative Transport Schemes for Spherical Geodesic Grids: High-Order Reconstructions for Forward-In-Time Schemes.
W. Skamarock and M. Menchaca, 2010,
Monthly Weather Review, Vol. 138, pp. 4497-4508, doi:10.1175/2010MWR3390.1 PDF available

The second approach examines extensions to the spatial discretizations of flux divergence operators for use on SCVT meshes:

Conservative Transport Schemes for Spherical Geodesic Grids: High-Order Flux Operators for ODE-Based Time Integration
W. Skamarock and A. Gassmann, 2011,
Monthly Weather Review, Vol. 139, pp. 2962-2975, doi:10.1175/MWR-D-10-05056.1 PDF available

There was also recent workshop hosted by NCAR in September 2008: Global Atmospheric Dynamical Core Workshop Report

I have also examined the Finite-Volume core used in the NCAR CCSM and in other global models. The results of this analysis can be found in the following paper:
A Linear Analysis of the NCAR CCSM Finite-Volume Dynamical Core, W. C. Skamarock, 2008, Monthly Weather Review, 136, 2112-2119. PDF available


WRF model - Numerical Methods


The WRF model (Weather Research and Forecast model) is being collaboratively developed by a number of groups, including members of MDG and MPG in NCAR/MMM. The WRF web pages can be found at http://wrf-model.org . A variety of development efforts are associated with WRF model, including

(1) time-integration-scheme development, particularily with respect to time-split schemes and semi-implicit schemes for integrating the fully compressible Euler equations,

(2) the development of solvers based on a number of different equation sets, including

i) flux-form Eulerian solvers based on a geometric height vertical coordinate,

ii) flux-form Eulerian solvers based on a mass (hydrostatic pressure) vertical coordinate.,

(3) and issues associated with the consistent treatment of corrdinate metrics in terrain-following coordinate solvers.

(4) Within the WRF model there are currently two dynamical cores.  The original goal of the WRF model development effort was to produce a single, shared, core.  A proposal for a workshop examining the possibility of consolidating these cores is given in the paper   Why is there more than one dynamical core in WRF?  A technical perspective.  An evaluation of differences in the cores as revealed in the Developmental Test Center's 2005 Winter Forecast Experiment (DWFE) can be found in the AMS August 2005 NWP conference paper titled High-Resolution Winter-Season NWP: Preliminary evaluation of the WRF ARW and NMM models in the DWFE forecast experiment.  W. Skamarock and D. Dempsey

(5) In the summer of 2005, an NCAR technical note was released that provides a complete description of the Advanced Research WRF (ARW) modeling system.  This technical note describes the mass (hydrostatic pressure) vertical coordinate nonhydrostatic model supported by NCAR and available to the community from the WRF web pages.  The technical note is titled A Description of the Advanced Research WRF Version 2.

(6) I have also been working on the evaluation of model dissipation and effective resolution using model forecast spectra. See the spectra white paper and discussion and the Monthly  Weather Review paper Evaluating Mesoscale NWP Models Using Kinetic Energy Spectra.

(7) At the 2003 SRNWP (Short-Range Numerical Weather Prediction) workshop in Bad Orb, Germany, a proposal for A Standard Test Set for Nonhydrostatic Dynamical Cores of NWP Models was presented and strongly endorsed by the workshop participants. At the 2004 AMS NWP-WAF conference (January, Seattle), the proposal was also presented and the wider community was invited to particiapate in the development of the test set. A preliminary web page has been established.   At the most recent SRNWP meeting (November 2005) it was decided to continue adding cases to the web page and consider adding cases to test the moist physics and convection.  Comments on the web page and test cases are welcome, as are contributions.

(8) I have been developing scalar transport schemes for use in the WRF model that include positive-definite and shape-preserving (monotonic) options.  A scheme that is not Courant-number limited is being tested in an experimental version of WRF.  The scheme is described in the paper Positive-Definite and Monotonic Limiters for Unrestricted-Timestep Transport Schemes.


See the papers below for further details concering work in numerical methods related to WRF.

Papers:

A Description of the Advanced Research WRF Version 3
Skamarock, W. C., J. B. Klemp, J. Dudhia, D. O. Gill, D. M. Barker, M. Duda, X.-Y. Huang, W. Wang and J. G. Powers,  NCAR Technical Note, 2008.  PDF available

Evaluation of Scalar Advection Schemes in the Advanced Research WRF Model using Large-Eddy Simulations of Aerosol-Cloud Interaction
H. Wang, W. C. Skamarock and G. Feingold, 2009. Monthly Weather Review, 137, 2547-2558, doi:10.1175/2009MWR2820.1 PDF available

The Impact of Positive-Definite Moisture Transport on NWP Precipitation Forecasts
W. C. Skamarock and M. L. Weisman, 2009, Monthly Weather Review PDF available

A Time-Split Nonhydrostatic Atmospheric Model for Research and NWP Applications.
Skamarock, W. C., J. B. Klemp, 2007, J. Comp. Phys. special issue on environmental modeling.   PDF available

Conservative Split-Explicit Time Integration Methods for the Compressible Nonhydrostatic Equations.
Klemp, J. B., W. C. Skamarock and J. Dudhia, 2007. Accepted for publication in Monthly Weather Review PDF available

Positive-Definite and Montonic Limiters for Unrestricted-Timestep Transport Schemes.
W. C. Skamarock, 2006, Monthly Weather Review. PDF available

A Description of the Advanced Research WRF Version 2
Skamarock, W. C., J. B. Klemp, J. Dudhia, D. O. Gill, D. M. Barker, W. Wang and J. G. Powers,  NCAR Technical Note, 2005.  PDF available

Evaluating Mesoscale NWP Models Using Kinetic Energy Spectra
W. C. Skamarock, 2004, Monthly Weather Review, 132, 3019-3032.  PDF available

Numerical Consistency of Metric Terms in Terrain Following Coordinates,
Klemp, J. B., W. C. Skamarock and Oliver Fuhrer, 2003, Monthly Weather Review, 131, 1229-1239. PDF available

An Evaluation of Filtering and Effective Resolution in the WRF Mass and NMM dynamical cores,
W. Skamarock and M. Baldwin, research report, November 2003. PDF available

Time Splitting Methods for Elastic Models Using Forward Time Schemes.
Wicker, L. J., and W. C. Skamarock, 2002, Monthly Weather Review, 130, 2088-2097 PDF available

A Time-Splitting Scheme for the Elastic Equations Incorporating Second-Order Runge-Kutta Time Differencing.
Wicker and Skamarock, 1998, Monthly Weather Review, 126, 1992-1999 PDF available


Clouds, Chemistry, and Transport


Three efforts are ongoing in clouds, chemistry and transport with which I am involved.

(1) Post-analysis of the real-time forecast supporting the MILAGRO/MIRAGE field program that took place in March 2006. The real-time forecasts can be found here.

(2) Work associated with the STERAO project (primarily examining NOx production by lightning, and cloud transport and chemistry in the clouds); see the papers below.

(3) WRF-Chem model development (See WRF working group 11 home page - http://wrf-model.org/development/wg11/wg11.php

Papers:

A meteorological overview of the MILAGRO field campaigns.   Fast et al, 2007:  Atmos. Chem. Phys. PDF available

Simulations of the redistribution of formaldehyde, formic acid, and peroxides in the 10 July 1996 Stratospheric-Tropospheric Experiment: Radiation, Aerosols, and Ozone deep convection storm.   M. C. Barth, S.-W. Kim, W. C. Skamarock, A. L. Stuart, K. E. Pickering, L. E. Ott. 2007 :  J. Geophys. Res., doi:10.1029/2006JD008046 doi:10.1016/j.atmosenv.2005.04.027 PDF available

Fully coupled "online" chemistry within the WRF model.  Grell, Peckham, Schmidtz, McKeen, Frost, Skamarock, and Eder, 2005:  Atmospheric Environment, 39, 6957-6975. doi:10.1016/j.atmosenv.2005.04.027 PDF available

Observational and Modeling-Based Budget of Lightning Produced NOx in a Continental Thunderstorm.  Skamarock, Dye, Defer, Barth, Stith, Ridley, and Baumann, Journal of Geophysical Research, 108 (D10), 4305, doi:10.1029/2002JD002163, 2003. PDF available

Numerical Simulations of the 10 July STERAO/Deep Convection Experiment Storm: Redistribution of Soluble Tracers.  Barth, Stuart, and Skamarock, 2001,Journal of Geophysical Research, 106, 12,381-12,400 PDF available

Numerical Simulations of the 10 July STERAO/Deep Convection Experiment Convective System: Kinematics and transport.  Skamarock, Powers, Barth, Dye, Matejka, Bartels,Baumann, Stith, and Parrish, and Hubler, 2000: Journal of Geophysical Research, 105, 10023-10045.
--> Online is the final version of paper before JGR technical editing. PDF available

Coastal Meteorology


Papers:

Catalina Eddies and Coastally Trapped Disturbances
Skamarock, Rotunno and Klemp, 2002:JAS, 59, 2270-2278 PDF available

Models of Coastally Trapped Disturbances
Skamarock, Rotunno and Klemp, 1999: JAS, 56, 3349-3365 PDF available


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