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Numerical methods for the next generation weather and climate models

Abstract

Numerical models for atmospheric dynamics, a central piece in weather and climate forecasting, are going through radical changes in order to become adequate for the next generation supercomputers that demand massively parallel processing.This project aims to study two different lines of numerical schemes for this next generation of models: (i) the development and analysis of numerical schemes for quasi-uniform spherical grids, that avoids scalability problems encountered in traditional models; (ii) the exploration of the time dimension as source of parallelism, with methods that radically change the time integration way of thinking of these models.Recently, we have shown that one of the main methodologies used in this new generation of quasi-uniform grid based models lacks consistency (local truncation error fails to converge to zero with increasing resolution). We propose a scheme that circumvents this issue and we aim to add this new scheme to the National Center for Atmospheric Research (NCAR-USA) Model for Prediction Across Scales (MPAS), envisioning to build a numerically and dynamically consistent version of this model. In parallel, we will study other problems arising with this kind of approach, such as numerical instabilities and ways to optimize locally refined quasi-uniform grids. The usage of quasi-uniform grids extends the utility of atmospheric models with respect to its adequacy to modern computer architectures, however, in the long run, their scalability will still be limited by its domain partition communication pattern. We aim in this project to explore the time dimension as a new source of parallelism. Recently, we developed a massively parallel exponential time integrator method, that we intend to couple with a semi-Lagrangian integrator, for nonlinear advection, and with an iterative parallel-in-time scheme, to build a pioneer parallel-in-time method adequate for atmospheric models.This project will be accomplished mainly with the collaboration of researchers from UK universities (Univ. of Exeter and Imperial College), American research centres (Los Alamos Nat. Lab. and NCAR) and the University of Sao Paulo. (AU)

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Scientific publications (17)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
FARIA, NUNO R.; MELLAN, THOMAS A.; WHITTAKER, CHARLES; CLARO, INGRA M.; CANDIDO, DARLAN DA S.; MISHRA, SWAPNIL; CRISPIM, MYUKI A. E.; SALES, FLAVIA C.; HAWRYLUK, IWONA; MCCRONE, JOHN T.; et al. Genomics and epidemiology of the P.1 SARS-CoV-2 lineage in Manaus, Brazil. Science, v. 372, n. 6544, p. 815+, . (20/04558-0, 19/21568-1, 19/21301-5, 18/14389-0, 17/13981-0, 20/04272-9, 18/25468-9, 16/18445-7, 19/21858-0, 18/17176-8, 19/12000-1, 19/07544-2, 18/12579-7, 19/24251-9)
NONOTA, LUIS GUSTAVO; PEIXOTO, PEDRO; PEREIRA, TIAGO; SAGASTIZABAL, CLAUDIA; SILVA, PAULO J. S.. Robot Dance: A mathematical optimization platform for intervention against COVID-19 in a complex network. EURO JOURNAL ON COMPUTATIONAL OPTIMIZATION, v. 10, p. 13-pg., . (13/07375-0, 16/04190-7, 16/18445-7, 18/24293-0)
FERREIRA, CLEUDIA P.; MARCONDES, DIEGO; MELO, MARIANA P.; OLIVA, SERGIO M.; PEIXOTO, CLEUDIA M.; PEIXOTO, PEDRO S.. A snapshot of a pandemic The interplay between social isolation and COVID-19 dynamics in Brazil. PATTERNS, v. 2, n. 10, . (19/22157-5, 16/18445-7)
PEIXOTO, PEDRO S.; SCHREIBER, MARTIN. SEMI-LAGRANGIAN EXPONENTIAL INTEGRATION WITH APPLICATION TO THE ROTATING SHALLOW WATER EQUATIONS. SIAM JOURNAL ON SCIENTIFIC COMPUTING, v. 41, n. 5, p. B903-B928, . (16/18445-7)
PEIXOTO, PEDRO S.; THUBURN, JOHN; BELL, MICHAEL J.. Numerical instabilities of spherical shallow-water models considering small equivalent depths. QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, v. 144, n. 710, p. 16-pg., . (16/18445-7)
POLICARPO, J. M. P.; RAMOS, A. A. G. F.; DYE, C.; FARIA, N. R.; LEAL, F. E.; MORAES, O. J. S.; PARAG, K. V.; PEIXOTO, P. S.; BUSS, L.; SABINO, E. C.; et al. Scale-free dynamics of COVID-19 in a Brazilian city. Applied Mathematical Modelling, v. 121, p. 19-pg., . (18/14389-0, 16/17612-7, 16/18445-7)
SCHMITT, A.; SCHREIBER, M.; PEIXOTO, P.; SCHAEFER, M.. A numerical study of a semi-Lagrangian Parareal method applied to the viscous Burgers equation. COMPUTING AND VISUALIZATION IN SCIENCE, v. 19, n. 1-2, p. 13-pg., . (16/18445-7)
SCHMITT, A.; SCHREIBER, M.; PEIXOTO, P.; SCHAEFER, M.. A numerical study of a semi-Lagrangian Parareal method applied to the viscous Burgers equation. COMPUTING AND VISUALIZATION IN SCIENCE, v. 19, n. 1-2, SI, p. 45-57, . (16/18445-7)
CANDIDO, DARLAN S.; CLARO, INGRA M.; DE JESUS, JAQUELINE G.; SOUZA, WILLIAM M.; MOREIRA, FILIPE R. R.; DELLICOUR, SIMON; MELLAN, THOMAS A.; DU PLESSIS, LOUIS; PEREIRA, RAFAEL H. M.; SALES, FLAVIA C. S.; et al. Evolution and epidemic spread of SARS-CoV-2 in Brazil. Science, v. 369, n. 6508, SI, p. 1255+, . (20/04558-0, 16/00194-8, 19/21301-5, 18/14389-0, 18/14933-2, 17/13981-0, 20/04836-0, 18/25468-9, 16/18445-7, 18/09383-3, 18/17176-8, 19/12000-1, 19/07544-2, 19/24251-9)
DIAS, FABIO L.; ASSUMPCAO, MARCELO; PEIXOTO, PEDRO S.; BIANCHI, MARCELO B.; COLLACO, BRUNO; CALHAU, JACKSON. Using Seismic Noise Levels to Monitor Social Isolation: An Example From Rio de Janeiro, Brazil. Geophysical Research Letters, v. 47, n. 16, . (16/18445-7, 17/00159-0)
SANTOS, LUAN F.; PEIXOTO, PEDRO S.. Topography-based local spherical Voronoi grid refinement on classical and moist shallow-water finite-volume models. Geoscientific Model Development, v. 14, n. 11, p. 6919-6944, . (16/18445-7, 17/25191-4)
YU, YONGGANG G.; WANG, NING; MIDDLECOFF, JACQUES; PEIXOTO, PEDRO S.; GOVETT, MARK W.. Comparing Numerical Accuracy of Icosahedral A-Grid and C-Grid Schemes in Solving the Shallow-Water Model. MONTHLY WEATHER REVIEW, v. 148, n. 10, p. 4009-4033, . (16/18445-7)
NICOLELIS, MIGUEL A. L.; RAIMUNDO, RAFAEL L. G.; PEIXOTO, PEDRO S.; ANDREAZZI, CECILIA S.. The impact of super-spreader cities, highways, and intensive care availability in the early stages of the COVID-19 epidemic in Brazil. SCIENTIFIC REPORTS, v. 11, n. 1, . (16/18445-7)
PEIXOTO, PEDRO S.; THUBURN, JOHN; BELL, MICHAEL J.. Numerical instabilities of spherical shallow-water models considering small equivalent depths. QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, v. 144, n. 710, A, p. 156-171, . (16/18445-7)
PEIXOTO, PEDRO S.; MARCONDES, DIEGO; PEIXOTO, CLAUDIA; OLIVA, SERGIO M.. Modeling future spread of infections via mobile geolocation data and population dynamics. An application to COVID-19 in Brazil. PLoS One, v. 15, n. 7, . (16/18445-7)
RAPHALDINI, B.; PEIXOTO, P. S.; TERUYA, A. S. W.; RAUPP, C. F. M.; BUSTAMANTE, M. D.. Precession resonance of Rossby wave triads and the generation of low-frequency atmospheric oscillations. Physics of Fluids, v. 34, n. 7, p. 21-pg., . (15/50686-1, 20/14162-6, 16/18445-7, 21/06176-0, 17/23417-5)
POVEDA, LEONARDO A. A.; PEIXOTO, PEDRO. On pointwise error estimates for Voronoi-based finite volume methods for the Poisson equation on the sphere. ADVANCES IN COMPUTATIONAL MATHEMATICS, v. 49, n. 3, p. 37-pg., . (21/06176-0, 16/18445-7)

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