Phone: 303-497-8161
Office: Foothills Laboratory; FL3-3008
Postal Address: P.O. Box 3000, Boulder, CO, 80307-3000
Shipping Address: 3450 Mitchell Lane, Boulder, CO, 80307-3000


Dr. Skamarock received his PhD in 1987 from Stanford University in Computational Geophysical Fluid Dynamics in a joint degree program from the Department of Computer Science and the Department of Engineering.  He is currently a Senior Scientist at NCAR where he has worked since leaving Stanford.  He is head of the Mesoscale Prediction Group in the Mesoscale and Microscale Meteorology division in the NCAR Earth System Laboratory.

Dr. Skamarock is very active in the development of fluid-flow solvers and atmospheric models, particularly nonhydrostatic solvers suitable for cloud-permitting simulations.   He is one of the principal architects of the Weather Research and Forecast model, and he is currently working on developing global solvers based on unstructured centroidal Voronoi tessellations and is leading NCAR’s effort in the development of the Model for Prediction Across Scales (MPAS).  Dr. Skamarock continues to work on problems in atmospheric dynamics at large scales (baroclinic waves), small scales (deep convection) and interactions between scales.  He collaborates in studies of chemistry and chemical species transport in deep convective clouds.

Dr. Skamarock regularly organizes international workshops on atmospheric model development, including the 2008 Workshop on Global Atmospheric Cores and the 2011 Workshop on Next Generation Weather and Climate Models and Workshop on Transport Schemes on the Sphere.  He is a member of the American Meteorological Society and the American Geophysical Union. He was Co-Chief editor of Monthly Weather Review for five years and has chaired the Publications Strategic Planning Committee of the American Meteorological Society

Current Research and Associated Publications

Global Modeling and Global Model Development

I am involved in the development of the global modeling system MPAS (Model for Prediction Across Scales). The modeling system uses a horizontal discretization based on Spherical Centriodal Voronoi Tessellations (SCVT's) that allow both a quasi-uniform discretization (the classical icosahedral mesh) and variable resolution meshes. Multiple geophysical solvers comprise the MPAS system, including atmosphere, ocean, and ice models. MPAS is being jointly developed by NCAR and DOE's Los Alamos National Labs, with NCAR leading the atmospheric component development, LANL the ocean model development, and the infrastructure being jointly developed. The web site for the MPAS project is

Papers describing the MPAS mesh, components, and preliminary testing are given below:

A description of the nonhydrostatic atmospheric solver:

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/ 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/ 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
accepted for publication in Monthly Weather Review, 2013. 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

A second approach examines extensions to the spatial discretizations of flux divergence operators for use on SCVT meshes, currently used in MPAS:

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

A third approach, based on an extension the forward-in-time scheme of Skamarock and Menchaca (2010):

An Upwind-Biased Transport Scheme Using a Quadratic Reconstruction on Spherical Icosahedral Grids. Hiroaki Miura, William C. Skamarock, 2013, Monthly Weather Review Volume 141, Issue 2 (February 2013) pp. 832-847 doi: PDF available

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) continues to be collaboratively developed by a number of groups, including members of Mesoscale Dynamics Section (MDS) and Mesoscale Prediction Section (MPS) in NCAR/NESL/MMM. The WRF web pages can be found at .

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


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

Test cases for nonhydrostatic models


A decade ago, 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 for NWP models was presented and strongly endorsed by the workshop participants. A web page was established shortly after this meeting; it contains a number of 2D (x,z) test cases.   The page continues to be used even though several of the proposed test cases have not been posted. Nonhydrostatic model development is now largely focussed on global solvers, and a test-case suite has been proposed in the DCMIP (Dynamical Core Model Intercomparison Project). We anticipate filling out the remaining 2D test cases given the large-scale focus of the DCMIP test cases and the cost of simuting nonhydrostatic motions on the sphere.

Atmospheric dynamics, convection and chemistry


I have been involved in a number of studies concerning atmospheric dynamics, convection and chemistry (see the papers in Publications or Dr. Skamarock's CV). With the development of MPAS, I will be working on scale interactions between convection and synoptic/globe circulations.


Bill Skamarock