Ongoing research project |
2013 - 2018

ECMWF hosts the PantaRhei project, the development of an interdisciplinary forecasting system for simulating multi-scale fluid flows (FP7/2012/ERC Advanced Grant agreement no. 320375).

Together with the principal investigator Dr Piotr Smolarkiewicz, the project explores a hybrid approach for forecasting global weather and climate that combines the strengths of established and efficient (at large hydrostatic scales) structured grid numerical weather prediction (NWP) and climate models with control-volume (small-scale) edge-based codes, originating from other computational fluid dynamics (CFD) disciplines. ECMWF's operational forecast model operates at hydrostatic scales and is not equipped to resolve convective motions where nonhydrostatic effects dominate, thus impairing the fidelity of forecasts. While NWP strives to extend the skill towards finer scales, nonhydrostatic research models endeavour to extend their realm towards the global domain. The two routes of development must cross, but the approach how to merge the diverse expertise is far from obvious.

The proposed work will synthesise the complementary skills of two exceptionally successful modelling systems: ECMWF's Integrated Forecasting System (IFS) and the nonhydrostatic research model EULAG formulated by the principal investigator. The IFS is one of the most comprehensive Earth-system models available in the world, while EULAG offers unprecedented expertise in multi-disciplinary computational fluid dynamics (CFD) ranging from simulations of laboratory flows to magneto-hydrodynamics of solar convection. The essence of the proposal is a pioneering numerical approach, where a nonhydrostatic global model is conditioned by global hydrostatic solutions within a single code framework.

The key technologies are EULAG's numerical procedures expressed in time-dependent generalized curvilinear coordinates, pairing the mathematical apparatus of general relativity with modern CFD, most notably the emerging novel edge-based non-oscillatory control volume integrators for nonhydrostatic atmospheric motions. The new model will prepare ECMWF for predicting with greater fidelity extreme weather events that are critical to the protection of society. Moreover, it is envisaged that the next generation forecasting system will be one of the most advanced computing tools available to the European community for operations, research and education.

Recent Publications:

P.K. Smolarkiewicz, C. Kühnlein, N.P. Wedi, 2018: Perturbation equations for all-scale atmospheric dynamics, J. Comput. Phys.,  submitted.
PDF icon Smolarkiewicz_etal2018-png.pdf

M. Waruszewski, C. Kühnlein, H. Pawlowska, P.K. Smolarkiewicz, 2018: MPDATA: Third-order accuracy for variable flows, J. Comput. Phys., 359, 361-379. doi:10.1016/
PDF icon Waruszewski_etal_JCP18.pdf

M. Leutbecher, S.‐J. Lock, P. Ollinaho, S.T.K. Lang, G. Balsamo, P. Bechtold, M. Bonavita, H.M. Christensen, M. Diamantakis, E. Dutra, S. English, M. Fisher, R.M. Forbes, J. Goddard, T. Haiden, R.J. Hogan, S. Juricke, H. Lawrence, D. MacLeod, L. Magnusson, S. Malardel, S. Massart, I. Sandu, P.K. Smolarkiewicz, A. Subramanian, F. Vitart, N. Wedi, A. Weisheimer, 2017: Stochastic representations of model uncertainties at ECMWF: state of the art and future vision, Q. J. R. Meteorol. Soc., 143, 2315-2339. doi: 10.1002/qj.3094

PDF icon qj3094_accepted.pdf


W. Deconinck, P. Bauer, M. Diamantakis, M. Hamrud, C. Kühnlein, P. Maciel, G. Mengaldo, T. Quintino, B. Raoult, P.K. Smolarkiewicz, N.P. Wedi, 2017: Atlas: A library for numerical weather prediction and climate modelling, Comput. Phys. Commun., 220, 188-204. doi: 10.1016/j.cpc.2017.07.006  [open access]
PDF icon Deconinck_etal2017.pdf


Cossette, J.-F., P. Charbonneau, P.K. Smolarkiewicz, and M. Rast, 2017:
Magnetically-modulated heat transport in a global simulation of solar
magneto-convection, Astrophys. J., 841:65, 17 pp., doi 10.3847/1538-4357/aa6d60

PDF icon apj_R3.pdf


C. Kühnlein, P.K. Smolarkiewicz, An unstructured-mesh finite-volume MPDATA

for compressible atmospheric dynamics, J. Comput. Phys. 334 (2017), 16–30.

doi: 10.1016/
PDF icon kuehnlein+smolarJCP2017.pdf


Smolarkiewicz P.K., C. Kühnlein, W.W. Grabowski: A finite-volume module for

cloud-resolving simulations of global atmospheric flow, J. Comput. Phys., 341 (2017)

208-229. doi: 10.1016/

PDF icon SKG2017.pdf


Sanjay Kumar , R. Bhattacharyya , Bhuwan Joshi , P. K. Smolarkiewicz, 2016: On the role of repetitive magnetic reconnections in evolution of magnetic flux ropes in solar corona, Astrophysical Journal, 830:80, 12pp,  doi: 10.3847/0004-637X/830/2/80

PDF icon Kumar_etalAPJ2016.pdf


A. Strugarek , P. Beaudoin , A.S. Brun , P. Charbonneau , S. Mathis , P.K. Smolarkiewicz, 2016: Modeling turbulent stellar convection zones: Sub-grid scales effects, Advances in Space Research, 58, 1538-1553, doi: 10.1016/j.asr.2016.05.043

PDF icon Strugarek_etalASR2016.pdf


G. Guerrero , P. K. Smolarkiewicz , E. M. de Gouveia Dal Pino , A. G. Kosovichev , N. N. Mansour, 2016: Understanding solar torsional oscillations from global dynamo models, Astrophysical Journal Letters, 828:L3, 7pp, doi: 10.3847/2041-8205/828/1/L3
PDF icon Guerrero_etalAPJL2016.pdf


P.K. Smolarkiewicz, J. Szmelter, F. Xiao, 2016: Simulation of all-scale atmospheric dynamics on unstructured meshes, J. Comput. Phys., 322, 267-287, doi: 10.1016/

PDF icon smolar_etalJCP2016o.pdf


W. Deconinck , M. Hamrud, C. Kühnlein, G. Mozdzynski, P. K. Smolarkiewicz, J. Szmelter, N. P. Wedi, 2016: Accelerating Extreme-Scale Numerical Weather Prediction, in Parallel Processing and Applied Mathematics, LNCS 9574, Springer International Publishing, 583-593, doi: 10.1007/978-3-319-32152-3_54
PDF icon Deconinck_etalLNCS2016.pdf


Z. P. Piotrowski , B. Matejczyk , L. Marcinkowski , P. K. Smolarkiewicz, 2016: Parallel ADI Preconditioners for All-Scale Atmospheric Models,,  in Parallel Processing and Applied Mathematics, LNCS 9574, Springer International Publishing, 607-618, doi: 10.1007/978-3-319-32152-3_56

PDF icon Piotrowski_etalLNCS2016.pdf


P. K. Smolarkiewicz, W. Deconinck, M. Hamrud, C. Kuhnlein, G. Mozdzynski, J. Szmelter and N. P. Wedi:

A finite-volume module for simulating global all-scale atmospheric flows, J. Comput. Phys., 314, pp.287-304, doi: 10.1016/

PDF icon finite_PS.pdf


G. Guerrero, P. K. Smolarkiewicz, E. M. de Gouveia Dal Pino, A. G. Kosovichev, N. N. Mansour: On the role of tachoclines in solar and stellar dynamos, Astrophysical Journal, 819, doi: 10.3847/0004-637X/819/2/104

PDF icon tachoclines_PS.pdf


S. Kumar, R. Bhattacharyya, and P. K. Smolarkiewicz, 2015: On the role of topological complexity in spontaneous development of current sheets, Physics of Plasmas, 22, 082903 doi: 10.1063/1.4905643

PDF icon Kumar_Bhattacharyya_Smolarkiewicz_2015.pdf


M. J. Kurowski, W. W. Grabowski, and P. K. Smolarkiewicz, 2015: Anelastic and compressible simulation of moist dynamics at planetary scales, J. Atmos. Sci., 72, 3975-3995, doi: 10.1175/JAS-D-15-0107.1

PDF icon Kurowski_Grabowski_Smolarkiewicz_2015.pdf


J. Szmelter, Z. Zhang, and P.K. Smolarkiewicz, 2015: An unstructured-mesh atmospheric model for nonhydrostatic dynamics: Towards optimal mesh resolution, J. Comput. Phys., 294, 363-381, doi: 10.1016/

PDF icon Szmelter_Zhang_Smolarkiewicz_2015.pdf


D. Jarecka, A. Jaruga, and P.K. Smolarkiewicz, 2015: A spreading drop of shallow water,
J. Comput. Phys., 289, 53-61, doi: 10.1016/

PDF icon Jarecka_Jaruga_Smolarkiewicz_2015.pdf


M. Siena, J.D. Hyman, M. Riva, A. Guadagnini, C.L. Winter, P.K. Smolarkiewicz, P. Gouze, S. Sadhukhan, F. Inzoli, G. Guedon, and E. Colombo, 2015: Direct numerical simulation of fully saturated flow in natural porous media at the pore scale: a comparison of three computational systems, Computat. Geosci., 19, 423-437, doi: 10.1007/s10596-015-9486-7

PDF icon Siena_etal2015.pdf


A. Jaruga, S. Arabas, D. Jarecka, H. Pawlowska, P.K. Smolarkiewicz, and M. Waruszewski, 2015: libmpdata++1.0: a library of parallel MPDATA solvers for systems of generalised transport equations, Geosci. Model Dev., 8, 1005-1032, DOI: 10.5194/gmd-8-1005-2015 [open access]
PDF icon Jaruga_etalGMD2015.pdf


D. Kumar, R. Bhattacharyya, and P. K. Smolarkiewicz, 2015: Repetitive formation and decay of current sheets in magnetic loops: An origin of diverse magnetic structures, Physics of Plasmas, 22, 012902 doi: 10.1063/1.4905643

PDF icon Kumar_etal2015.pdf


S. Kumar, R. Bhattacharyya, and P. K. Smolarkiewicz, 2014: Formation of magnetic discontinuities through viscous relaxation, Physics of Plasmas, 21, 052904 doi: 10.1063/1.4878955

PDF icon Kumar_Bhattacharyya_Smolarkiewicz_2014.pdf


R. Abgrall, P. Smolarkiewicz, F. Xiao, and S. Zaleski, 2014: Editorial, Frontiers in Computational Physics: Modeling the Earth System, 271, 1, doi: 110.1016/

PDF icon Abgrall_Smolarkiewicz_Xiao_Zaleski_2014.pdf


J.-F. Cossette, P. K. Smolarkiewicz, and P. Charbonneau, 2014: The Monge–Ampère trajectory correction for semi-Lagrangian schemes, J. Comput. Phys., doi: 10.1016/ 

PDF icon Cossette_Smolarkiewicz_Charbonneau_2014.pdf


M. J. Kurowski, W. W. Grabowski, and P. K. Smolarkiewicz, 2014: Anelastic and compressible simulation of moist deep convection, J. Atmos. Sci, doi: 10.1175/JAS-D-14-0017.1

PDF icon Kurowski_Grabowski_Smolarkiewicz_2014.pdf


P.K. Smolarkiewicz, C. Kühnlein, and N.P. Wedi, 2014: A consistent framework for discrete integrations of soundproof and compressible PDEs of atmospheric dynamics, J. Comput. Phys., 263, 185-205. doi: /10.1016/

PDF icon Smolarkiewicz_Kühnlein_Wedi_2014.pdf

G. Guerrero, P.K.  Smolarkiewicz, A.G. Kosovichev, et al., 2013: Differential rotation in solar-like stars from global simulations, Astrophys. J., 779, 176.  doi: 10.1088/0004-637X/779/2/176

PDF icon Guerrero_etal2013.pdf

M.J. Kurowski, W.W. Grabowski, and P.K. Smolarkiewicz, 2013: Towards multiscale simulation of moist flows with soundproof equations, J. Atmos. Sci., 70, 3995-4011.
doi: 10.1175/JAS-D-13-024.1

PDF icon Kurowski_Grabowski_Smolarkiewicz_2013.pdf

P.K. Smolarkiewicz, J. Szmelter, and A.A. Wyszogrodzki, 2013: An unstructured-mesh atmospheric model for nonhydrostatic dynamics, J. Comput. Phys., 254,184-199.
doi: 10.1016/

PDF icon Smolarkiewicz_Szmelter_Wyszogrodzki_2013.pdf

J.-F .Cossette, P. Charbonneau, and P.K. Smolarkiewicz, 2013: Cyclic thermal signature in  a global MHD simulation of solar convection, Astrophys. J. Lett., 777, L29.
doi: 10.1088/2041-8205/777/2/L29

PDF icon Cossete_etal2013.pdf


D. Kumar, R. Bhattacharyya, and P.K. Smolarkiewicz, 2013: Formation of magnetic discontinuities through superposition of force-free magnetic fields: Periodic boundaries, Phys. Plasmas, 20,  112903. doi: 10.1063/1.4831743

PDF icon Kumar_etal2013.pdf


P. Charbonneau and P.K. Smolarkiewicz, 2013: Modeling the Solar Dynamo, Science, 340, 42-43. doi: 10.1126/science.1235954
PDF icon CharbonneauSmolarScience2013.pdf


J.D. Hyman, P.K. Smolarkiewicz, and C.L. Winter, 2013: Pedotransfer functions for permeability: A computational study at pore scales, Water Resources Res., 49, 2080-2092.
doi: 10.1002/wrcr.20170  

PDF icon Hyman_Smolarkiewicz_Winter_2013.pdf


P. K. Smolarkiewicz and P. Charbonneau, 2013: EULAG, a computational model for multiscale flows: An MHD extension, J. Comput. Phys., 236, 608-623. doi: 10.1016/


P. Beaudoin, P. Charbonneau, E. Racine and P. K. Smolarkiewicz, 2013: Torsional Oscillations in a Global Solar Dynamo, Solar Physics, 282, 335-360. doi: 10.1007/s11207-012-0150-2

European Research Council