Current and Emerging Time-Integration Strategies in Global Numerical Weather and Climate Prediction

[1]  Christopher A. Kennedy,et al.  Diagonally implicit Runge–Kutta methods for stiff ODEs , 2019 .

[2]  Emil M. Constantinescu,et al.  Acceleration of the IMplicit–EXplicit nonhydrostatic unified model of the atmosphere on manycore processors , 2017, Int. J. High Perform. Comput. Appl..

[3]  R. Heikes,et al.  DCMIP2016: A Review of Non-hydrostatic Dynamical Core Design and Intercomparison of Participating Models , 2017 .

[4]  Peter Bauer,et al.  Atlas : A library for numerical weather prediction and climate modelling , 2017, Comput. Phys. Commun..

[5]  Torsten Hoefler,et al.  Near-global climate simulation at 1 km resolution: establishing a performance baseline on 4888 GPUs with COSMO 5.0 , 2017 .

[6]  Andrew Stuart,et al.  Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High‐Resolution Simulations , 2017, 1709.00037.

[7]  Pierre Bénard,et al.  RK‐IMEX HEVI schemes for fully compressible atmospheric models with advection: analyses and numerical testing , 2017 .

[8]  N. Jeevanjee Vertical Velocity in the Gray Zone , 2016 .

[9]  Chao Yang,et al.  10M-Core Scalable Fully-Implicit Solver for Nonhydrostatic Atmospheric Dynamics , 2016, SC16: International Conference for High Performance Computing, Networking, Storage and Analysis.

[10]  Janusz A. Pudykiewicz,et al.  An efficient exponential time integration method for the numerical solution of the shallow water equations on the sphere , 2016, J. Comput. Phys..

[11]  Michail Diamantakis,et al.  Sensitivity of the ECMWF Model to Semi-Lagrangian Departure Point Iterations , 2016 .

[12]  Wojciech W. Grabowski,et al.  Towards Global Large Eddy Simulation: Super-Parameterization Revisited , 2016 .

[13]  Mats Hamrud,et al.  A finite-volume module for simulating global all-scale atmospheric flows , 2016, J. Comput. Phys..

[14]  Nils Wedi,et al.  How does subgrid‐scale parametrization influence nonlinear spectral energy fluxes in global NWP models? , 2016 .

[15]  Sascha M. Schnepp,et al.  Pipelined, Flexible Krylov Subspace Methods , 2015, SIAM J. Sci. Comput..

[16]  Piet Termonia,et al.  Discretization in Numerical Weather Prediction: A Modular Approach to Investigate Spectral and Local SISL Methods , 2016 .

[17]  Constantine Bekas,et al.  An extreme-scale implicit solver for complex PDEs: highly heterogeneous flow in earth's mantle , 2015, SC15: International Conference for High Performance Computing, Networking, Storage and Analysis.

[18]  Giovanni Tumolo,et al.  A semi‐implicit, semi‐Lagrangian discontinuous Galerkin framework for adaptive numerical weather prediction , 2015 .

[19]  Peter Bauer,et al.  The quiet revolution of numerical weather prediction , 2015, Nature.

[20]  Gianmarco Mengaldo,et al.  Discontinuous spectral/hp element methods: development, analysis and applications to compressible flows , 2015 .

[21]  Mats Hamrud,et al.  A Partitioned Global Address Space implementation of the European Centre for Medium Range Weather Forecasts Integrated Forecasting System , 2015, Int. J. High Perform. Comput. Appl..

[22]  Silvia Ferrari,et al.  A constrained integration (CINT) approach to solving partial differential equations using artificial neural networks , 2015, Neurocomputing.

[23]  Robert Klöfkorn,et al.  Horizontally Explicit and Vertically Implicit (HEVI) Time Discretization Scheme for a Discontinuous Galerkin Nonhydrostatic Model , 2015 .

[24]  C. Kühnlein,et al.  The modelling infrastructure of the Integrated Forecasting System : Recent advances and future challenges , 2015 .

[25]  Rolf Rannacher,et al.  Multiple Shooting and Time Domain Decomposition Methods , 2015 .

[26]  Rupert Klein,et al.  A Blended Soundproof-to-Compressible Numerical Model for Small- to Mesoscale Atmospheric Dynamics , 2014 .

[27]  Takemasa Miyoshi,et al.  The Non-hydrostatic Icosahedral Atmospheric Model: description and development , 2014, Progress in Earth and Planetary Science.

[28]  Nils Gustafsson,et al.  Four-dimensional ensemble variational (4D-En-Var) data assimilation for the HIgh Resolution Limited Area Model (HIRLAM) , 2014 .

[29]  Nigel Wood,et al.  Numerical analyses of Runge–Kutta implicit–explicit schemes for horizontally explicit, vertically implicit solutions of atmospheric models , 2014 .

[30]  M. Diamantakis,et al.  An inherently mass‐conserving semi‐implicit semi‐Lagrangian discretization of the deep‐atmosphere global non‐hydrostatic equations , 2014 .

[31]  Christian Kühnlein,et al.  A consistent framework for discrete integrations of soundproof and compressible PDEs of atmospheric dynamics , 2014, J. Comput. Phys..

[32]  Nigel Wood,et al.  Runge-Kutta IMEX schemes for the Horizontally Explicit/Vertically Implicit (HEVI) solution of wave equations , 2013, J. Comput. Phys..

[33]  Emil M. Constantinescu,et al.  Implicit-Explicit Formulations of a Three-Dimensional Nonhydrostatic Unified Model of the Atmosphere (NUMA) , 2013, SIAM J. Sci. Comput..

[34]  Mats Hamrud,et al.  A Fast Spherical Harmonics Transform for Global NWP and Climate Models , 2013 .

[35]  Shian-Jiann Lin,et al.  A Two-Way Nested Global-Regional Dynamical Core on the Cubed-Sphere Grid , 2013 .

[36]  Nigel Wood,et al.  GungHo! A new dynamical core for the Unified Model∗ , 2013 .

[37]  Michael Baldauf,et al.  Consortium for Small-Scale Modelling Technical Report No . 21 A new fast-waves solver for the Runge-Kutta dynamical core by Michael Baldauf April 2013 , 2013 .

[38]  Almut Gassmann,et al.  A global hexagonal C‐grid non‐hydrostatic dynamical core (ICON‐IAP) designed for energetic consistency , 2013 .

[39]  Günther Zängl,et al.  Extending the Numerical Stability Limit of Terrain-Following Coordinate Models over Steep Slopes , 2012 .

[40]  Todd D. Ringler,et al.  A Multiscale Nonhydrostatic Atmospheric Model Using Centroidal Voronoi Tesselations and C-Grid Staggering , 2012 .

[41]  Christiane Jablonowski,et al.  Operator-Split Runge-Kutta-Rosenbrock Methods for Nonhydrostatic Atmospheric Models , 2012 .

[42]  Karim Yessad,et al.  The hydrostatic and nonhydrostatic global model IFS / ARPEGE : deep-layer model formulation and testing , 2012 .

[43]  William M. Putman,et al.  Cloud‐system resolving simulations with the NASA Goddard Earth Observing System global atmospheric model (GEOS‐5) , 2011 .

[44]  Spencer J. Sherwin,et al.  A generic framework for time-stepping partial differential equations (PDEs): general linear methods, object-oriented implementation and application to fluid problems , 2011 .

[45]  Michael Baldauf,et al.  Linear Stability Analysis of Runge–Kutta-Based Partial Time-Splitting Schemes for the Euler Equations , 2010 .

[46]  Francis X. Giraldo,et al.  Semi-Implicit Formulations of the Navier--Stokes Equations: Application to Nonhydrostatic Atmospheric Modeling , 2010, SIAM J. Sci. Comput..

[47]  Markus Clemens,et al.  GPU Accelerated Adams–Bashforth Multirate Discontinuous Galerkin FEM Simulation of High-Frequency Electromagnetic Fields , 2010, IEEE Transactions on Magnetics.

[48]  M. Hochbruck,et al.  Exponential integrators , 2010, Acta Numerica.

[49]  Nigel Wood,et al.  An inherently mass‐conserving iterative semi‐implicit semi‐Lagrangian discretization of the non‐hydrostatic vertical‐slice equations , 2010 .

[50]  Paul A. Ullrich,et al.  A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid , 2010, J. Comput. Phys..

[51]  Pierre Bénard,et al.  Dynamical kernel of the Aladin–NH spectral limited‐area model: Revised formulation and sensitivity experiments , 2010 .

[52]  Louis J. Wicker A Two-Step Adams-Bashforth-Moulton Split-Explicit Integrator for Compressible Atmospheric Models , 2009 .

[53]  Zdzisław Jackiewicz,et al.  General Linear Methods for Ordinary Differential Equations: Jackiewicz/General Linear , 2009 .

[54]  John C. Butcher,et al.  General linear methods for ordinary differential equations , 2009, Math. Comput. Simul..

[55]  Adam A. Scaife,et al.  The role of the stratosphere in the European climate response to El Niño , 2009 .

[56]  A. Arakawa,et al.  Unification of the Anelastic and Quasi-Hydrostatic Systems of Equations , 2009 .

[57]  Nils Wedi,et al.  A framework for testing global non‐hydrostatic models , 2009 .

[58]  Francis X. Giraldo,et al.  A study of spectral element and discontinuous Galerkin methods for the Navier-Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases , 2008, J. Comput. Phys..

[59]  D. Durran A physically motivated approach for filtering acoustic waves from the equations governing compressible stratified flow , 2008, Journal of Fluid Mechanics.

[60]  Piotr K. Smolarkiewicz,et al.  Predicting weather, climate and extreme events , 2008, J. Comput. Phys..

[61]  Masaki Satoh,et al.  Nonhydrostatic icosahedral atmospheric model (NICAM) for global cloud resolving simulations , 2008, J. Comput. Phys..

[62]  Andrew Staniforth,et al.  Aspects of the dynamical core of a nonhydrostatic, deep-atmosphere, unified weather and climate-prediction model , 2008, J. Comput. Phys..

[63]  William C. Skamarock,et al.  A time-split nonhydrostatic atmospheric model for weather research and forecasting applications , 2008, J. Comput. Phys..

[64]  P. Smolarkiewicz Modeling atmospheric circulations with soundproof equations , 2008 .

[65]  Jimy Dudhia,et al.  Conservative Split-Explicit Time Integration Methods for the Compressible Nonhydrostatic Equations , 2007 .

[66]  D. Williamson The Evolution of Dynamical Cores for Global Atmospheric Models(125th Anniversary Issue of the Meteorological Society of Japan) , 2007 .

[67]  Terry Davies,et al.  An iterative time‐stepping scheme for the Met Office's semi‐implicit semi‐Lagrangian non‐hydrostatic model , 2007 .

[68]  Almut Gassmann,et al.  A Consistent Time-Split Numerical Scheme Applied to the Nonhydrostatic Compressible Equations* , 2007 .

[69]  Kazuo Saito,et al.  The Operational JMA Nonhydrostatic Mesoscale Model , 2006 .

[70]  Abraham OCHOCHE,et al.  General Linear Methods , 2006 .

[71]  Hester Bijl,et al.  Fourth-Order Runge–Kutta Schemes for Fluid Mechanics Applications , 2005, J. Sci. Comput..

[72]  A. Staniforth,et al.  A new dynamical core for the Met Office's global and regional modelling of the atmosphere , 2005 .

[73]  Lloyd N. Trefethen,et al.  Fourth-Order Time-Stepping for Stiff PDEs , 2005, SIAM J. Sci. Comput..

[74]  Shian‐Jiann Lin A “Vertically Lagrangian” Finite-Volume Dynamical Core for Global Models , 2004 .

[75]  A. Kværnø,et al.  Norges Teknisk-naturvitenskapelige Universitet Singly Diagonally Implicit Runge-kutta Methods with an Explicit First Stage Singly Diagonally Implicit Runge-kutta Methods with an Explicit First Stage , 2022 .

[76]  D. Keyes,et al.  Jacobian-free Newton-Krylov methods: a survey of approaches and applications , 2004 .

[77]  Pierre Benard,et al.  Stability of Semi-Implicit and Iterative Centered-Implicit Time Discretizations for Various Equation Systems Used in NWP , 2003, physics/0304114.

[78]  Nigel Wood,et al.  SLICE: A Semi‐Lagrangian Inherently Conserving and Efficient scheme for transport problems , 2002 .

[79]  Louis J. Wicker,et al.  Time-Splitting Methods for Elastic Models Using Forward Time Schemes , 2002 .

[80]  Mariano Hortal,et al.  The development and testing of a new two‐time‐level semi‐Lagrangian scheme (SETTLS) in the ECMWF forecast model , 2002 .

[81]  Paul J. Kushner,et al.  Tropospheric response to stratospheric perturbations in a relatively simple general circulation model , 2002 .

[82]  Jean Côté,et al.  The CMC-MRB Global Environmental Multiscale (GEM) Model. Part III: Nonhydrostatic Formulation , 2002 .

[83]  George Em Karniadakis,et al.  A semi-Lagrangian high-order method for Navier-Stokes equations , 2001 .

[84]  J. McGregor,et al.  The CSIRO Conformal-Cubic Atmospheric GCM , 2001 .

[85]  R. Lewis,et al.  Low-storage, Explicit Runge-Kutta Schemes for the Compressible Navier-Stokes Equations , 2000 .

[86]  Francis X. Giraldo,et al.  Lagrange—Galerkin methods on spherical geodesic grids: the shallow water equations , 2000 .

[87]  D. Durran Numerical methods for wave equations in geophysical fluid dynamics , 1999 .

[88]  Francis X. Giraldo,et al.  The Lagrange-Galerkin Spectral Element Method on Unstructured Quadrilateral Grids , 1998 .

[89]  Louis J. Wicker,et al.  A Time-Splitting Scheme for the Elastic Equations Incorporating Second-Order Runge–Kutta Time Differencing , 1998 .

[90]  M. Falcone,et al.  Convergence Analysis for a Class of High-Order Semi-Lagrangian Advection Schemes , 1998 .

[91]  F. Giraldo Lagrange-Galerkin Methods on Spherical Geodesic Grids , 1997 .

[92]  J. Holton,et al.  Stratosphere‐troposphere exchange , 1995 .

[93]  Jeffrey S. Scroggs,et al.  A global nonhydrostatic semi-Lagrangian atmospheric model without orography , 1995 .

[94]  Steven J. Ruuth,et al.  Implicit-explicit methods for time-dependent partial differential equations , 1995 .

[95]  Pierre Bénard,et al.  Integration of the fully elastic equations cast in the hydrostatic pressure terrain-following coordinate in the framework of the ARPEGE/Aladin NWP system , 1995 .

[96]  A. Simmons,et al.  Implementation of the Semi-Lagrangian Method in a High-Resolution Version of the ECMWF Forecast Model , 1995 .

[97]  André Robert,et al.  Spurious Resonant Response of Semi-Lagrangian Discretizations to Orographic Forcing: Diagnosis and Solution , 1994 .

[98]  P. Smolarkiewicz,et al.  A class of semi-Lagrangian approximations for fluids. , 1992 .

[99]  W. Skamarock,et al.  The stability of time-split numerical methods for the hydrostatic and the nonhydrostatic elastic equations , 1992 .

[100]  René Laprise,et al.  The Euler Equations of Motion with Hydrostatic Pressure as an Independent Variable , 1992 .

[101]  A. Staniforth,et al.  Semi-Lagrangian integration schemes for atmospheric models - A review , 1991 .

[102]  W. Schiesser The Numerical Method of Lines: Integration of Partial Differential Equations , 1991 .

[103]  Dale R. Durran,et al.  The Third-Order Adams-Bashforth Method: An Attractive Alternative to Leapfrog Time Differencing , 1991 .

[104]  Clive Temperton,et al.  An Efficient Two‐Time‐Level Semi‐Lagrangian Semi‐Implicit Integration Scheme , 1987 .

[105]  J. Butcher The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods , 1987 .

[106]  Harold Ritchie,et al.  Semi-Lagrangian advection on a Gaussian grid , 1987 .

[107]  Jeff Cash,et al.  The integration of stiff initial value problems in ODEs using modified extended backward differentiation formulae , 1983 .

[108]  A. Jameson,et al.  Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes , 1981 .

[109]  Jeff Cash,et al.  On the integration of stiff systems of O.D.E.s using extended backward differentiation formulae , 1980 .

[110]  J. R. Cash,et al.  Diagonally Implicit Runge-Kutta Formulae with Error Estimates , 1979 .

[111]  J. Klemp,et al.  The Simulation of Three-Dimensional Convective Storm Dynamics , 1978 .

[112]  R. Brayton,et al.  A new efficient algorithm for solving differential-algebraic systems using implicit backward differentiation formulas , 1972 .

[113]  G. Strang On the Construction and Comparison of Difference Schemes , 1968 .

[114]  T. E. Hull,et al.  Numerical solution of initial value problems , 1966 .