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 represent model inadequacy better and to 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 long-standing climate biases and is relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups that show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface, and cryosphere of comprehensive weather and climate models 1) gives rise to more reliable probabilistic forecasts of weather and climate and 2) 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 is demonstrated; and future research directions are outlined.

Weather and climate variations on subseasonal to decadal time scales can have enormous social, economic, and environmental impacts, making skillful predictions on these time scales a valuable tool for decision-makers. As such, there is a growing interest in the scientific, operational, and applications communities in developing forecasts to improve our foreknowledge of extreme events. On subseasonal to seasonal (S2S) time scales, these include high-impact meteorological events such as tropical cyclones, extratropical storms, floods, droughts, and heat and cold waves. On seasonal to decadal (S2D) time scales, while the focus broadly remains similar (e.g., on precipitation, surface and upper-ocean temperatures, and their effects on the probabilities of high-impact meteorological events), understanding the roles of internal variability and externally forced variability such as anthropogenic warming in forecasts also becomes important. The S2S and S2D communities share common scientific and technical challenges. These include forecast initialization and ensemble generation; initialization shock and drift; understanding the onset of model systematic errors; bias correction, calibration, and forecast quality assessment; model resolution; atmosphere–ocean coupling; sources and expectations for predictability; and linking research, operational forecasting, and end-user needs. In September 2018 a coordinated pair of international conferences, framed by the above challenges, was organized jointly by the World Climate Research Programme (WCRP) and the World Weather Research Programme (WWRP). These conferences surveyed the state of S2S and S2D prediction, ongoing research, and future needs, providing an ideal basis for synthesizing current and emerging developments in these areas that promise to enhance future operational services. This article provides such a synthesis.