Judith Berner, Ulrich Achatz, Lauriane Batté, Lisa Bengtsson, Alvaro De La Cámara, Hannah M. Christensen, Matteo Colangeli, Danielle R. B. Coleman, Daan Crommelin, Stamen I. Dolaptchiev, Christian L.E. Franzke, Petra Friederichs, Peter Imkeller, Heikki Järvinen, Stephan Juricke, Vassili Kitsios, François Lott, Valerio Lucarini, Salil Mahajan, Timothy N. Palmer, Cécile Penland, Mirjana Sakradzija, Jin-Song Von Storch, Antje Weisheimer, Michael Weniger, Paul D. Williams, Jun-Ichi Yano, *Stochastic Parameterization: Towards a new view of weather and climate models*, **Bulletin of the American Meteorological Society**, published online July 2016,

**Abstract**

Stochastic parameterizations — empirically derived, or based on rigorous mathematical and statistical concepts — have great potential to increase the predictive capability of next generation weather and climate models.

The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy and improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing longstanding climate biases and relevant for determining the climate response to external forcing.

This article highlights recent developments from different research groups which show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface and cryosphere of comprehensive weather and climate models (a) gives rise to more reliable probabilistic forecasts of weather and climate and (b) reduces systematic model bias.

We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics and turbulence is reviewed, its relevance for the climate problem demonstrated, and future research directions outlined.

And five related papers, from another field:

- Charles T. Perrettia, Stephan B. Munch, and George Sugihara,
*Model-free forecasting outperforms the correct mechanistic model for simulated and experimental data*,**Proceedings of the National Academy of Sciences**(PNAS), March 2013, 110(13). - Hao Ye, Richard J. Beamish, Sarah M. Glaser, Sue C. H. Grant, Chih-hao Hsieh, Laura J. Richards, Jon T. Schnute, and George Sugihara,
*Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling*,**Proceedings of the National Academy of Sciences**(PNAS), March 31 2015, 112(13). A movie related to this paper. - Donald L. DeAngelisa, Simeon Yurek,
*Equation-free modeling unravels the behavior of complex ecological systems*(commentary),**Proceedings of the National Academy of Sciences**(PNAS), March 2015, 112(13). - Ethan R. Deyle, Robert M. May, Stephan B. Munch, George Sugihara,
*Tracking and forecasting ecosystem interactions in real time*,*Proc. R. Soc. B***283**: 20152258, December 2015. - Steven L. Bruntona, Joshua L. Proctor, J. Nathan Kutz,
*Discovering governing equations from data by sparse identification of nonlinear dynamical systems*,**Proceedings of the National Academy of Sciences**(PNAS), April 2016, 113(15).

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