Jun-Ichi Yano, Michał Z. Ziemiański, Jeanette Onvlee, M. J. P. Cullen, Alberto Carrassi, Vaughan T. J. Phillips, Martin Kohler, Richard Davy, Silas Michaelides, Víctor Homar, Pedro M. M. Soares, Andrzej A. Wyszogrodzki, Lisa Bengtsson, Suzanne L. Gray, Piet Termonia, S. O. Krichak, Anna Deluca, Centre national de recherches météorologiques (CNRM), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire Midi-Pyrénées (OMP), Institut de Recherche pour le Développement (IRD)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Institut de Recherche pour le Développement (IRD)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Centre National de la Recherche Scientifique (CNRS), United Kingdom Met Office [Exeter], Institut Royal Météorologique de Belgique [Bruxelles] - Royal Meteorological Institute (IRM), Nansen Environmental and Remote Sensing Center [Bergen] (NERSC), University of Reading (UOR), European Centre for Medium-Range Weather Forecasts (ECMWF), Centro de Computação Gráfica (CCG), Météo France-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Institut Royal Météorologique de Belgique [Bruxelles] (IRM), Yano J.-I., Ziemianski M.Z., Cullen M., Termonia P., Onvlee J., Bengtsson L., Carrassi A., Davy R., Deluca A., Gray S.L., Homar V., Kohler M., Krichak S., Michaelides S., Phillips V.T.J., Soares P.M.M., and Wyszogrodzki A.A.
Numerical weather prediction (NWP) models are increasing in resolution and becoming capable of explicitly representing individual convective storms. Is this increase in resolution leading to better forecasts? Unfortunately, we do not have sufficient theoretical understanding about this weather regime to make full use of these NWPs.\ud \ud After extensive efforts over the course of a decade, convective–scale weather forecasts with horizontal grid spacings of 1–5 km are now operational at national weather services around the world, accompanied by ensemble prediction systems (EPSs). However, though already operational, the capacity of forecasts for this scale is still to be fully exploited by overcoming the fundamental difficulty in prediction: the fully three–dimensional and turbulent nature of the atmosphere. The prediction of this scale is totally different from that of the synoptic scale (103 km) with slowly–evolving semi–geostrophic dynamics and relatively long predictability on the order of a few days.\ud \ud Even theoretically, very little is understood about the convective scale compared to our extensive knowledge of the synoptic-scale weather regime as a partial–differential equation system, as well as in terms of the fluid mechanics, predictability, uncertainties, and stochasticity. Furthermore, there is a requirement for a drastic modification of data assimilation methodologies, physics (e.g., microphysics), parameterizations, as well as the numerics for use at the convective scale. We need to focus on more fundamental theoretical issues: the Liouville principle and Bayesian probability for probabilistic forecasts; and more fundamental turbulence research to provide robust numerics for the full variety of turbulent flows.\ud \ud The present essay reviews those basic theoretical challenges as comprehensibly as possible. The breadth of the problems that we face is a challenge in itself: an attempt to reduce these into a single critical agenda should be avoided.